A Systematic Framework and Nanoperiodic Concept for Unifying

Review pubs.acs.org/CR

A Systematic Framework and Nanoperiodic Concept for Unifying Nanoscience: Hard/Soft Nanoelements, Superatoms, Meta-Atoms, New Emerging Properties, Periodic Property Patterns, and Predictive Mendeleev-like Nanoperiodic Tables Donald A. Tomalia* Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States Department of Physics, Virginia Commonwealth University, Richmond, Virginia 23284, United States National Dendrimer & Nanotechnology Center, NanoSynthons LLC, 1200 North Fancher Avenue, Mt. Pleasant, Michigan 48858, United States

Shiv N. Khanna* Department of Physics, Virginia Commonwealth University, Richmond, Virginia 23284, United States ABSTRACT: Development of a central paradigm is undoubtedly the single most influential force responsible for advancing Dalton’s 19th century atomic/molecular chemistry concepts to the current maturity enjoyed by traditional chemistry. A similar central dogma for guiding and unifying nanoscience has been missing. This review traces the origins, evolution, and current status of such a critical nanoperiodic concept/ framework for defining and unifying nanoscience. Based on parallel efforts and a mutual consensus now shared by both chemists and physicists, a nanoperiodic/systematic framework concept has emerged. This concept is based on the well-documented existence of discrete, nanoscale collections of traditional inorganic/organic atoms referred to as hard and soft superatoms (i.e., nanoelement categories). These nanometric entities are widely recognized to exhibit nanoscale atom mimicry features reminiscent of traditional picoscale atoms. All unique superatom/nanoelement physicochemical features are derived from quantized structural control defined by six critical nanoscale design parameters (CNDPs), namely, size, shape, surface chemistry, flexibility/rigidity, architecture, and elemental composition. These CNDPs determine all intrinsic superatom properties, their combining behavior to form stoichiometric nanocompounds/assemblies as well as to exhibit nanoperiodic properties leading to new nanoperiodic rules and predictive Mendeleev-like nanoperiodic tables, and they portend possible extension of these principles to larger quantized building blocks including meta-atoms.

CONTENTS 1. Introduction 2. Background 2.1. The Cosmological Origin and Evolution of Hierarchical Matter to Higher Complexity 2.2. Magic Numbers, Hidden Symmetries, and Periodicity Observed in Hierarchical Matter 2.3. Hierarchical Information Transfer: Critical Hierarchical Design Parameters (CHDPs) 2.3.1. Subatomic Information Transfer: Nucleons (CSADPs) → Atoms (CADPs) 2.3.2. Atoms (CADPs) → Molecules (CMDPs) 2.4. Mendeleev’s Periodic Table of the Elements: Elemental Periodic Patterns/Properties Directed by Critical Atomic Design Parameters (CADPs) 2.5. Magic Numbers, Quantized Building Blocks, CHDP-Directed Assembly, and New Emerging Properties beyond the Atom © 2016 American Chemical Society

2.5.1. Magic Numbers Defined by Quantized Building Blocks 2.5.2. Combining Quantized Building Blocks To Produce New Emerging Properties Resulting from Hierarchical Symmetry Breaking 3. Atom Mimicry: Consensus Derived from the Parallel Worlds of Physicists (Hard Superatoms/ Nanoclusters) and Chemists (Soft Superatoms/ Nanoclusters) 3.1. Hard Superatoms: A Historical Perspective 3.1.1. Closed Geometric Atom Shells and Closed Electronic Shells

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Received: June 23, 2015 Published: January 29, 2016 2705

DOI: 10.1021/acs.chemrev.5b00367 Chem. Rev. 2016, 116, 2705−2774

Chemical Reviews 3.1.2. General Hard Superatom Features and Categories 3.2. Dendrimers: A Window to Quantized, Periodic Soft Superatoms at the Nanoscale Level 3.2.1. Dendrimer Shape Changes: Nanoscale Molecular Morphogenesis 3.2.2. Quantized Size Control and Monodispersity 3.3. Soft Superatoms: Dendrimers 3.3.1. Chemical Bond Formation, Valency, and Stoichiometric Binding Ratios with Dendrimers To Form (Dendrimer)n Megamer-Type Nanocompounds/Assemblies 3.4. Dendrimers as Heuristic Soft Superatom Mimics of Traditional Picoscale Atoms 3.4.1. Comparison of Atom Electron Aufbau and Periodic Symmetries with Dendrimers 3.4.2. Remarkable Self-Reactivity Patterns Experimentally Observed for Picoscale Elemental Atoms and Nanoscale Dendrimers Possessing Unsaturated Outer Shells 3.4.3. Heuristically Similar Valency/Symmetry Features Observed in Both Picoscale Atoms and Soft Superatoms Such as Dendrimers 3.4.4. Nanoscale Atom Mimicry: Hard and Soft Superatom Features 3.5. First Evidence for Hard Superatoms 3.6. First Evidence for Soft Superatoms 3.7. Using Soft Superatoms (i.e., Dendrimers) as Host Templates for the Synthesis of Hard Superatoms (i.e., Metal Nanoclusters) 3.8. Brief Overview of Nanoscale Atom Mimicry, Nanoperiodicity, and the Taxonomy of Hard/ Soft Superatoms 4. A Systematic Nanoperiodic Concept and Framework for Unifying and Defining Nanoscience 4.1. A Systematic Nanoperiodic Concept/Framework Roadmap 4.2. Chemical and Supramolecular Combinations of Soft/Hard Nanoelements (i.e., Superatoms) To Create Combinatorial Libraries of Stoichiometric Superatomic Nanocompounds/ Assemblies 4.2.1. Hard−Hard Nanocompounds/Assemblies 4.2.2. Soft−Soft Nanocompounds and Assemblies 4.2.3. Soft−Hard Nanocompounds 5. CNDP Directed Nanoperiodic Property Patterns, Rules, and New Emerging Properties 5.1. Traditional Picoscale, Atomic Element Periodic Patterns Preceding the Emergence of Mendeleev’s Periodic Table 5.2. CNDP Directed, Soft Superatom Nanoperiodic Property Patterns 5.2.1. Intrinsic Dendrimer-Based Periodic Chemical Reactivity/Physical Size Property Patterns

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5.2.2. Size and Surface Chemistry Dependent Nonradiative Energy Transfer between InGaN Quantum Wells (QW) and Poly(amidoamine) (PAMAM) Dendrimers as a Function of Generation 5.3. CNDP Directed Hard Superatom Nanoperiodic Property Patterns 5.3.1. Size-Directed Nanoperiodicity: Systematic Melting Point Variation as a Function of Dimensions (i.e., Metal Nanoclusters [H-1]-Type Hard Superatoms) 5.3.2. CNDP Directed Nanoperiodic Property Patterns (i.e., Stoichiometries and Symmetries) Observed in Superatomic Lattice Structures 5.3.3. Dependency of Nanoperiodic Fluorescent Emission Patterns on Superatom Size. Comparison of Metallic Gold Nanodots with Semiconducting Metal Chalcogenides (i.e., Quantum Dots) 5.3.4. Surface Chemistry and Size Dependency on Magnetic Moments for Metal Chalcogenide: Fullerene Superatomic Lattices; [H-2]:[H-5]-Type Superatomic Lattices 5.3.5. Size Dependent Nanoperiodicity in [H1]n-Type Pt Metal Nanoclusters; Kinetic Limiting Currents and Catalytic Activity; When n = 12, 28 and 60 5.3.6. Size Dependent Cytotoxicity of [H-1] Gold Nanoclusters 5.3.7. Elemental Composition (i.e., Stoichiometry) Influence on Electronic States of Quantum Dots 5.4. CNDP Directed Hard−Soft Superatom Nanoperiodic Property Patterns 5.4.1. Nanoperiodic Size Dependency in Superatomic Lattice Packing 5.5. New Emerging Superatom/Superatomic Molecular Property Behavior 5.5.1. Unique New Band Gap Properties Resulting from Architecture Driven Electronic Communication within Covalent Stoichiometric Hard−Hard Superatomic Nanocompounds; [Metal Oxide:(Metal Oxide)′]; [H-3:(H-3)′]-Type Nanocompounds 5.5.2. Unique Emerging Band Gap Properties by Manipulating Dimensional Architecture (i.e., 0-D, 1-D, 2-D) for Superatomic, Hard−Hard Ionic Lattices 6. Predictive Hard/Soft Superatom and Superatomic Nanocompound/Nanoassembly Based Nanoperiodic Rules and Nanoperiodic Mendeleev-like Tables 6.1. Predictive Nanoperiodic Rules 6.1.1. Valency Rules Defined by Size Dependent Spheroidal Nanosterics 6.1.2. Shape Directed Nanoperiodic Property Patterns Defining Self-Assembly Modes 6.2. First Examples of Mendeleev-like, Predictive Nanoperiodic Tables for Hard/Soft Superatoms and Nanocompounds/Assemblies

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Chemical Reviews 6.2.1. Insights to Synthetic Mimicry of Biological Quasi-Equivalence with [S-1]Type Amphiphilic Dendrons Reported by Percec 6.2.2. Amphiphilic Dendron Self-Assembly Libraries Directed by Critical Nanoscale Design Parameters (CNDPs) 6.2.3. Predicting Amphiphilic Dendron SelfAssembly to Supramolecular Dendrimers Based on the Critical Nanoscale Design Parameters (CNDPs) 6.3. First Examples of Predictive, Mendeleev-like Nanoperiodic Tables 7. New Quantized Nanoscale/Mesoscale Building Blocks: Metamaterials and Meta-Atoms/MetaMolecules 7.1. Brief Overview of Metamaterials 7.2. Superatoms and Meta-Atoms as Quantized Nanoscale/Mesoscale Building Blocks 8. Conclusions Author Information Corresponding Authors Notes Biographies Acknowledgments References

Review

by a “central paradigm,” nanotechnology may very well languish into a substantially empirical activity rather than a true science. This review article will focus on significant progress made by both chemists and physicists in a critical quest for a systematic framework and unifying central paradigm for defining nanoscience. Successful progress in this interdisciplinary effort rests largely on independent and parallel observations of atom mimicry at the nanoscale level. As such, new thinking and mutually compatible perspectives by both chemists and physicists have evolved concerning well-defined nanoscale collections of atoms that behave as traditional atoms, as well as the role they play in transferring information and order beyond the atomic level. These discrete nanoscale entities are referred to as artif icial atoms, superatoms, nanoelements, unif ying atoms, meta-atoms, etc.2 Over the past several decades, this mutual consensus has led to the recent emergence of a proposed new nanoperiodic concept and systematic framework for unifying nanoscience. This unifying framework involves the extension of critical firstprinciples from chemistry/physics, as well as important new thinking concerning quantized, nanoscale building blocks such as hard/sof t superatoms, hard/sof t nanoelement categories, stoichiometric nanocompounds, nanoperiodic relationships, and more recently a new category of nanoscale structures/architectures referred to as meta-atoms/molecules.3 These well-defined nanoscale building blocks will be examined in the context of their many self-similar, atom mimicry features, ability to form stoichiometric nanocompounds/assemblies, manifestation of predictable nanoperiodic properties/patterns, and most importantly the basis for new emerging nanoscale properties based on “hierarchical, symmetry breaking principles” according to the Nobel Laureate Physicist, P. W. Anderson.4 Advancement of these concepts has led to the emergence of recent new predictive Mendeleev-like nanoperiodic tables and unprecedented nanoperiodic rules directed by only six critical nanoscale design parameters (CNDPs): (1) sizes, (2) shapes, (3) surface chemistries, (4) rigidity/flexibilities, (5) architectures, and (6) elemental compositions.6

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1. INTRODUCTION Throughout history, the physical sciences have used the unique periodic features associated with atomic level, elemental property patterns (i.e., the Mendeleev periodic table) as a means for predicting critical physicochemical properties and for understanding specific atomic and molecular relationships. The sciences of chemistry and physics have literally emerged from insights derived from these iconic periodic property patterns. These critical insights have led to first-principles, a taxonomy and systematic framework for these disciplines, all of which have defined a unifying central dogma. These pervasive paradigms have allowed an articulate description of hierarchical matter from the subpicoscale (i.e., nuclear physics/quantum chemistry) to the subnanoscale (i.e., molecular physics/chemistry) and constitute the contemporary definition of traditional chemistry and physics. This central dogma provided a common perspective for communicating important ideas, hypotheses, and concepts which not only consolidated traditional small molecule chemistry/physics, but also provided a critical scientific basis of understanding that nurtured the emergence of important subdisciplines and related activities such as the materials sciences, engineering, cosmology, geology, biology, and medicine. Without question, it was these systematic central dogmas that allowed traditional chemistry and physics to contribute the diverse and immeasurable enhancements to both society and the human condition.1 The rapidly emerging field of nanotechnology has presented a similar dilemma, namely, the urgent need for a “consolidating central dogma”. The very active area of nanotechnology has revealed many new emerging properties, unprecedented phenomena, and discrete nanometric structures/objects derived from both inorganic (i.e., hard) and organic (i.e., soft) matter. That withstanding, in the absence of an equivalent nanoscale Mendeleev-like taxonomy and consolidating framework guided

2. BACKGROUND It is widely recognized that essentially all well-defined, hierarchical matter and complexity, both hard (i.e., inorganic) and soft (i.e., organic), is assembled according to a specific order associated with discrete, sequential multiples (i.e., magic numbers or stoichiometries) of quantized building blocks including subatomic particles, atoms, small molecules, monomers, polymers, etc. That withstanding, several major questions still remain. What is the genesis of this order? What def ines the parameters, principles, rules, and strategies that direct these hierarchical assemblies? Is there a unif ying system or f ramework for understanding this transfer of information and order? Could such insights produce a paradigm for “a priori” prediction of behavior and new emerging properties of matter beyond simple atoms and molecules? In order to answer these questions, one has to briefly consider the cosmological beginning of all things. 2.1. The Cosmological Origin and Evolution of Hierarchical Matter to Higher Complexity

A prevailing model that is believed to best describe the cosmological origin and evolution of the universe is referred to as the “big bang theory.” This theory proposes that the universe originated approximately 14 billion years ago1,5 from a unique singular state. This singular state was characterized as a 2707


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Figure 1. Cosmological “big bang” event occurring ∼14 billion years ago leading to all hierarchical matter in the universe.

play a significant role in the discrete evolutionary assembly of matter at least penultimate to the micron-sized structures/ assemblies required for the beginning of life. Based on the amazing reproducibility/fidelity of these initial CHDP-directed abiotic organizations, hierarchical matter evolved into more complex chemical structures and bioassemblies. These critical precursors set the stage for evolving the early prototypes of life including biological cells, bacteria, plants, animals, and ultimately humanity as shown in Figure 1.

convergent point of ultraextreme energy, density, and temperature in cosmological time. Following a brief expansion phase, this singular state cooled sufficiently to allow formation of critical and basic subatomic particles. It was at this point that these basic particles initiated their intrinsic relationships with each other, thus producing what we now recognize as some of the firstprinciples of chemistry and physics. These early events were soon followed by nucleon particle assembly into the first light primordial atoms,1 thereby setting the stage for evolution into the heavier elements, molecular structure/assemblies, and more complex matter as we recognize it today. This time dependent evolution first led to abiotic matter (i.e., molecules, macromolecules, assemblies, etc.), all of which was derived from traditional first chemistry/physical principles. With time, these initial abiotic substances were found to self-assemble into a wide range of more complex, higher dimensional matter. That withstanding, it is now becoming recognized that much of this more complex matter is very well-defined and may indeed be structurally quantized as a function of only six critical hierarchical design parameters (CHDPs), namely, size, shape, surface chemistry, rigidity/f lexibility, architecture, and elemental composition. It is believed that these CHDPs constitute important intrinsic structural information that may be transferred in nonchaotic assembly events to produce more complex, ordered matter. More specifically, it is proposed that this CHDP information may be transferred via certain key hierarchical building blocks. When this CHDP information is transferred from the atomic/molecular to the nanoscale level, these parameters appear to direct and influence important assembly events that produce well-defined stoichiometries, magic numbers and periodic property patterns beyond simple atoms and molecules. As these features emerge in a variety of large nanoscale structures (>1 nm), they appear to mimic traditional atoms at the picoscale level.6 As such, it is presumed that CHDPs

2.2. Magic Numbers, Hidden Symmetries, and Periodicity Observed in Hierarchical Matter

In systems derived from discrete, quantized components according to well-defined assembly rules, one usually observes interesting geometric or arithmetic patterns. These patterns may involve unique symmetries, repetitive structures, with or without scaling, or regular sequences of numbers describing periodic quantities of the components referred to as magic numbers. These patterns are not only aesthetically pleasing, but more importantly they may be used as predictive tools for understanding these ordered systems. Recent thinking by Boeyens and Levendis7 has proposed that all self-assembly schemes leading to well-defined complex matter (i.e., Figure 1) are rooted in the quantized, intrinsic periodic features found at the subatomic level7 in nucleons (i.e., protons, neutrons, electrons, etc.). They propose that characteristic magic numbers exhibited by these quantized subatomic particles are derived from nucleon relationships based on number theory, as well as certain periodic properties and hidden symmetries.8 It is further believed that these critical subatomic design parameters (CSADPs) are subsequently transferred to atomic structure and become manifested as familiar periodic behavior represented in the Mendeleev periodic table of the elements. The observation of magic numbers and periodic property parameters associated with 2708


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Figure 2. (a) Nucleon configurations associated with nucleon magic numbers. (Reprinted with permission of ref 26. Copyright 1965 National Academy of Sciences USA.) (b) Number of stable isotones as a function of neutron number. (Reproduced with permission from MIT OpenCourseWare: ocw.mit. edu/terms. Image adapted by W. E. Meyerhof.) (c) Straight line periodic relationships and hidden symmetry occurring for optimum nucleon proton/ neutron ratios. (Reprinted with permission from ref 7. Copyright 2008 Springer Science + Business Media B.V.)

Figure 3. Transfer of CSADP information to CADPs by combining nucleons with electrons. (Image adapted in part with permission from ref 30. Copyright 2003 Walker Publishing.)

traditional atoms9 and molecular structures10,11 has been documented extensively throughout most of the 20th century.12,13 However, examination of critical parameters such as magic numbers and periodicity in the realm of nanoscale structures (i.e., dimensions > 1 nm) did not occur until later in the early 1990s. It was at that time that parallel thinking and experimental results from both chemists14−17 and physicists18−23 began to develop a convergent and mutually coherent perspective. This coherent

perspective involved the observation of magic numbers, discrete stoichiometries, and periodic property patterns which were often associated with new emerging properties at the nanoscale level. It was noted that these magic numbers and periodic property patterns were associated with well-defined nanoscale structures and were invariably defined by the six critical nanoscale design parameters (CNDPs) mentioned earlier. Furthermore, it was noted that many of these nanoscale features appeared to phenomenologically mimic the behavior of atoms if properly 2709


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Figure 4. Transfer of CADP information to CMDPs by combining atomic orbitals to form molecular orbitals. (Image adapted in part with permission from ref 30. Copyright 2003 Walker Publishing.)

nucleons associated with magic numbers as shown in Figure 2.26 Nuclei with magic numbers of neutrons/protons are found to be especially stable as may be seen from a comparison of stable isotones as a function of neutron number as shown in Figure 2b.27 It is interesting to note that this nuclear shell model was successfully applied to an analysis of metallic clusters which will be discussed later.28 It is information contained in these well-defined, quantized, nucleon particles that is transferred with high fidelity upon adding electrons to produce completed electronic orbitals as found in atomic structure. Several important features of this transferred nucleon information, termed critical subatomic design parameters (CSADPs), may be visualized by the various three-dimensional sizes, shapes, and elemental surface chemistries that are manifested by the resulting electron orbitals as illustrated in Figure 3. In fact, it has been shown recently that the quantized masses of neutrons and protons, respectively, are so precise and important relative to each other that the big bang nucleosynthesis (BBN) would have led to an entirely different universe.29 2.3.2. Atoms (CADPs) → Molecules (CMDPs). Either the association or linear combinations of these unique electron orbitals, as they are presented at the atomic/molecular level, produces a new ensemble of discrete relationships. These new molecular level relationships are directed by the transfer of elemental structural information referred to as critical atomic design parameters (CADPs). Evidence for these discrete atomic or molecular structural relationships is readily observed in the formation of either three-dimensional (3-D) atomic or 3-D molecular crystal lattices as illustrated in Figure 4. Large multiples of atoms or their compounds tend to assemble into bulk crystals by ordering into long-range periodic patterns that are directed by the unique features of their unit cells. As such, these periodic atom/compound patterns are classified according to one of 14 well-known assembly patterns referred to as Bravais lattices. As one considers these traditional Bravais lattice type relationships found in atoms or molecular/compound relationships and compares them to those observed in nanoscale, size quantized, hard/soft nanoclusters (superatoms), one cannot

controlled. As such, these quantized nanostructures are now referred to as superatoms or nanoelement categories and will be discussed later. 2.3. Hierarchical Information Transfer: Critical Hierarchical Design Parameters (CHDPs)

Natural evolution during the last 4.5 billion years has cleverly produced a system of quantized building blocks,6,18,24,25 each of which exhibits a discrete ensemble of physicochemical properties referred to as critical hierarchical design parameters (CHDPs). These CHDPs are unique to each building block, as well as to their respective hierarchical status. Therefore, each atomic element has its unique collection of critical atomic design parameters (CADPs) and all stoichiometric molecules manifest well-defined CMDPs. Similarly, discrete, structure-controlled nanomaterials would exhibit their own respective quantized CNDPs. These critical hierarchical building blocks and their respective CHDPs are now recognized to systematically control the transfer of important structural and functional information both within and between hierarchical levels.18 This important information transfer universally defines the emergence of all new properties and the currently known hierarchical complexity of all biological and abiotic materials (Figure 1). Beginning with the periodic elements, CHDPs have played a critical role in hierarchical evolution to the complexity associated with the emergence of life and higher complexity. 2.3.1. Subatomic Information Transfer: Nucleons (CSADPs) → Atoms (CADPs). According to Boeyens and Levendis,7 the genesis of all atomic level periodic properties and magic numbers begins at the subatomic, nucleon level. As such, each nucleon relationship provides the unique scaffolding and information that determines specific properties associated with each element. A brief example of such subatomic periodicity, wherein nucleon stabilities are shown to be determined by specific proton/neutron ratios, stoichiometries, or magic numbers (i.e., 2, 8, 28, 50, 82, 126, etc.) that correspond to highly stabilized nucleon shells and hidden symmetries, is illustrated in Figure 2. Considerable evidence suggests that nuclei possess shell-like structures, wherein each nucleus consists of an assembly of 2710


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Figure 5. Major crystal structures and unit cells for certain metallic elements (i.e., bulk state) in the periodic table resulting from transfer of CADP information to CMDP dimensions. (Image adapted in part with permission from ref 30. Copyright 2003 Walker Publishing.)

Figure 6. (A) Magic numbers obtained by mass analyses of discrete closed shell quantized (NaI)nNa+ building blocks. (Reprinted with permission from ref 34. Copyright 1996 Elsevier Ltd.) (B) Growth patterns of (TiN)n. (a) TOF mass spectrum of (TiN)n clusters. Abundance patterns indicate that the clusters have cubic structures resembling pieces of the fcc lattice of solid TiN. (b) Proposed structures of (TiN)n clusters based on magic numbers observed in the mass spectrum. (Reprinted with permission from ref 35. Copyright 1993 American Institute of Physics.)

new insights are revealing compelling similarities in these quantized nanoscale building blocks that are reminiscent of traditional atoms and will be discussed later. Primary structural repeating components (i.e., elemental unit cells) that determine the various Bravais lattice types ultimately determine the extended periodic 3-D crystal lattice structure

always predict their intra- and intercluster (i.e., aggregation) relationships using traditional paradigms. According to Petkov et al.,31 evidence is accumulating that new thinking and rules may have to be applied.32 That withstanding, with these new nanoscale rules many intracluster atom relationships found in hard/soft superatoms are becoming understood. As such, these 2711


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patterns. These extended 3-D Bravais lattices manifest unique periodic relationships between their constituent elemental atoms (i.e., usually metallic/inorganic) based on their CADPs as they interact with each other and grow to higher hierarchical dimensions. It is widely recognized that transfer of this CADP information occurs with high fidelity. As such, these information transfer sequences involve atomic (CADPs) → molecular/ subnanoscale (CMDPs) → nanoscale (CNDPs) → micron-scale (CMicDPs) → macroscale (CMacDPs) as the crystal lattices grow to macroscale dimensions clearly manifesting features of the unit cell type from which they are derived. Essentially all metallic elements found in the periodic table exhibit well-defined CADP-driven relationships as evidenced by their crystallization into one of several major crystal lattice types as illustrated in Figure 5. It is noteworthy that, according to mass spectrometry analyses, certain alkali metal salts (i.e., NaI) are found to exhibit discrete, magic number, quantized multiunit cell entities (i.e., building blocks). These closed shell entities self-assemble to produce higher dimension lattices, ultimately leading to the bulk crystal lattice. This occurs with complete hierarchical transfer of CADP/ CMDP/CNDP/CMicDP/CMacDP information as shown in Figure 6. This demonstrates unequivocal evidence for conservation of these CHDPs throughout the self-assembly process from the atomic to the macroscale state.33 There is no doubt that crystallization patterns are strongly influenced by surface chemistry. A comparison of similarities between picoscale and nanoscale surface chemistry and the influence of surface chemistry on picoscale/nanoscale particle crystallization patterns was reported as early as 2005 by Ozin and Arsenault.36 These investigators noted that surface chemistry parameters such as surface moiety density, particle curvature, and specific corona features directly influenced Bravais-type crystallization patterns for nanoscale metal nanoclusters. These nanoparticle surface chemistry parameters were observed to mimic similar features exhibited by picoscale atoms. For example, comparing metal nanoclusters possessing short chain with long chain alkanethiolate surface groups (i.e., dense vs diffuse outer corona shells) led to Bravais-type crystallization patterns that mimicked similar valence electron features found in atoms as illustrated in Figure 7.

Figure 7. Comparison of periodic surface chemistry parameters and resulting Bravais-type crystallization patterns observed for picoscale atoms and nanoscale modules (i.e., surface modified metal nanoclusters). (Reprinted with permission from ref 36. Copyright 2005 The Royal Society of Chemistry.)

driven by the unique relationships defined by the six specific CADPs associated with each element. These CADP-driven relationships are clearly apparent in both vertical and horizontal periodic trends (Figure 8) and provide invaluable predictive value which is the essence of Mendeleev’s periodic table. Based on these same first-principles, similar “superatom/nanoelement” behavior as well as nanoperiodic property patterns have been observed to emerge at the nanoscale and will be discussed later. Throughout the 19th and early 20th centuries, the properties and periodic behavior of picoscale matter (i.e., atoms) was extensively investigated and confirmed. This activity led to deep insights concerning the predictable periodic behavior of these quantized atomic building blocks, as well as their chemical combinations to produce a myriad of stoichiometric molecular structures exhibiting many new emerging properties. These efforts led to acceptance of the iconic Mendeleev periodic table of the elements in 1867. More contemporary examination of subatomic precursors (i.e., nucleons, etc.) to atoms revealed that similar periodic behavior is also observed at the subatomic level. However, extension of such a similar periodic paradigm to more complex hierarchical building blocks beyond the atom (i.e., nanoscale level) has been proposed and examined only within recent decades.6,18,24,37,38

2.4. Mendeleev’s Periodic Table of the Elements: Elemental Periodic Patterns/Properties Directed by Critical Atomic Design Parameters (CADPs)

Unique subatomic, nucleon information (CSADP) is transferred to the atomic level (Figure 4) to give specific physicochemical features for each element. Therefore, in Mendeleev’s periodic table of the elements, atoms are arranged according to their chemical nature and periodic behavior. These unique elemental arrangements conform to the electronic theory of atoms, and the resulting electron aufbau sequence adheres to a centrosymmetric Coulomb potential. As such, closed electronic shells appear for the noble gases which are chemically inert. The electronic configurations for all other self-reactive elements with atomic number Z can be expressed in terms of the maximum valence Z −nrg*, where nrg* is the shell closing number of the underlying noble gas configuration. These simple notions constitute key assumptions in the central dogma for chemistry. Within this context, it becomes apparent that CSADP → CADP information clearly transfers to produce predictable periodic patterns/properties at the atomic level. More significantly, it should be noted that these periodic features are

2.5. Magic Numbers, Quantized Building Blocks, CHDP-Directed Assembly, and New Emerging Properties beyond the Atom

2.5.1. Magic Numbers Defined by Quantized Building Blocks. It is widely recognized that, within any hierarchical systems assembled with discrete well-defined components according to ordered, systematic rules, certain geometric or numerical patterns are expected to emerge. Hierarchical matter is no exception and these unique number patterns, referred to as magic numbers,12 have now been observed for subatomic, atomic, molecular, and more recently nanoscale building blocks.13−16,39 These magic numbers may involve specific symmetries,8 repetitive structures, with or without scaling, discrete stoichiometries, or regular sequences of numbers that 2712


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Figure 8. Mendeleev’s periodic table illustrating systematic vertical and horizontal correlations of critical atomic design parameters (CADPs) which include structure controlled atomic (a) sizes, (b) shapes, (c) surface chemistry, (d) flexibility/polarizability, (e) architecture, and (f) elemental composition. (Reprinted with permission from ref 37. Copyright 2012 The Royal Society of Chemistry.)

Figure 9. Continuum of critical hierarchical design parameters associated with subatomic building blocks (CSADPs), atomic building blocks (CADPs), molecuar building blocks (CMDPs), nanoscale (CNDPs), and micron-scale (CMiDPs) up to the macroscale level (CMacDPs). Concurrent symmetry breaking throughout this continuum leads to new emerging properties.

not only on their intrinsic periodic properties, but also on their ability to undergo a wide range of stoichiometric hybridizations (i.e., chemical bonding and supramolecular assembly) to produce a plethora of hard/soft nanocompounds/assemblies exhibiting new emerging properties. These issues will be discussed in more detail later. 2.5.2. Combining Quantized Building Blocks To Produce New Emerging Properties Resulting from Hierarchical Symmetry Breaking. According to P. W. Anderson,4 hierarchical symmetry breaking by combining quantized building blocks at any of the hierarchical levels (i.e., subatomic to macroscale) will result in products that are not only greater than the precursor building blocks, but will also exhibit new emerging properties that will be entirely different (Figure 9). A compelling example demonstrating (a) hierarchical quantized building blocks, (b) CHDP-directed assembly processes, (c) resulting magic numbers based on stoichiometries of self-assembly, and (d) new emerging properties is readily apparent in the self-assembly sequence leading to the formation of biological tendons. As shown in Figure 10, an exquisite transfer of CHDP structural information occurs according to welldefined stoichiometric processes involving either covalent bond formation or supramolecular chemistry to produce a sequence of

describe quantities of a hierarchical component required to produce and define a preferred architecture, structure, morphology, lowest energy state, or most stable closed system. These magic numbers are observed at the subatomic level where it is known that magic number directed ratios of neutrons:protons are required to produce most stable isotopes;40 the atomic levelrecognized electron orbital filling patterns leading to well-defined magic numbers of electrons to saturate outer electron shells to produce stable noble gas configurations;9 and at the molecular levelthe magic number directed Hückel theory, wherein 4n + 2 p-electrons are required for aromaticity.41−45 At the nanoscale level, it has now been observed that certain magic numbers of electrons, atoms, or monomers are required to produce closed electronic shells in smaller “jellium-type” metal nanoclusters or filling of discrete atom shells in larger nanoclusters as they produce so-called hard superatoms. Similarly, it has also been shown that in the generational construction of dendrimers, magic numbers of monomers are required to close and saturate the generational monomer shells in these nanostructures14,46 to produce nobel gas type configurations referred to as sof t superatoms. These new hard and soft superatoms are now viewed as quantized, nanoscale building blocks that mimic traditional atoms.6,18,24 This is based 2713


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Figure 10. Hierarchical transfer of structural information involving critical hierarchical design parameters (CHDPs) to produce biological tendons. Beginning sequentially with atoms (CADPs), to molecular structures (CMDPs), to nanoscale structures (CNDPs), to micron-scale structures (CMicDPs) to macroscale structures, biological tendons may be assembled via quantized, structure controlled hierarchical building blocks. These quantized building blocks (QBB) exhibit stoichiometrically driven magic numbers designated by stars (★) throughout this assembly process. (Image adapted with permission from an original illustration courtesy of Prof. Eric Baer, Case Western Reserve University.)

Figure 11. Sequence of quantized hierarchical building blocks (QHBB) as a function of structural complexity (i.e., dimensions, nm). These QHBBs are structure controlled at each level of complexity (i.e., atomic, CADP; molecular, CMDP; or nanoscale, CNDP), respectively, as a function of size, shape, surface chemistry, rigidity/flexibility, architecture, and elemental composition. (Reprinted with permission from ref 48. Copyright 2014 John Wiley & Sons.)

hierarchy appears to be a universal strategy determined by

quantized building blocks defined by magic numbers (★). As this biological self-assembly process proceeds through the various hierarchical symmetry levels, one observes the development of a sequence of new emerging properties ending in the final high complexity of a biological tendon. This multilevel structural

natural selection for developing new emerging properties and function in organisms and higher complexity. Zhang et al.47 have developed quasi-self-similar models that describe how certain 2714


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Figure 12. Shell index (K) plotted against N1/3 for (Na)n. Two types of shells are observed. For small N (i.e., jellium type structures), the observed electronic shell closings are compared with those predicted using pseudoquantum number 3n + t. For large N (i.e., core−shell type structures), the observed shells of atoms are compared with those predicted assuming icosahedral (cuboctahedral) symmetry. (Image adapted in part with permission from ref 34. Copyright 1996 Elsevier Ltd.)

mass selected clusters involving virtually any element in the periodic table. These techniques have been refined to allow examination of cluster properties one atom or one electron at a time. With these techniques, one can now examine new emerging cluster properties that appear as one transitions (a) from discrete quantum conditions that exist in small subnanoscale clusters, (b) to boundary constrained properties exhibited in traditional nanoparticles, and (c) to the bulk phase, wherein properties are insensitive to boundaries. Since the forces that bind atoms are electrostatic, an early fundamental question has been raised. Do the atomic arrangements and stability patterns associated with clusters have any commonality with nuclear physics, wherein protons and neutrons are joined together by large nuclear forces to form nuclei? In the 1980s, Knight and co-workers10 provided first insights into this commonality when they generated size selected Na clusters by using molecular beam techniques. It was astonishing to find that clusters containing 2, 8, 18, 20, 40, ... atoms were distinctly more prominent than any other cluster sizes. These unique cluster sizes were called magic numbers and were considered to be similar to magic numbers observed for atomic nuclei. In fact, the origin of the magic numbers could be readily understood within a model that paralleled the nuclear shell model. Subsequent experiments demonstrated that all electronic properties such as the ionization potential, electron affinity, and even reactivity were directed and distinguished by specific shell effects.10 As such, the ionization potential and polarizability exhibited distinct periodic features, wherein magic clusters exhibited a local maxima in ionization potentials and a minima in electron affinity. Knight and co-workers10 hypothesized that such periodic features can originate from a centrosymmetrical potential and consequently proposed a simple “jellium model”, wherein the positive charge of the ionic cores are spread over the entire sphere dimension defined by the cluster size. As such, the electronic states in such a confined electronic space tend to consolidate into electronic cluster shells designated 1S2, 1P6, 1D10, 2S2, 1F14, ... in much the same way as in nuclei or as in traditional individual atoms. Clusters that corresponded to electronic clouds that saturated these electronic shells exhibited enhanced stability, thus leading to their prominence in the observed mass spectrum. Therefore, in small (Na)n clusters where n = 2−100, one observes characteristic “jellium orbital” type behavior, wherein closed electronic shells consistent with certain magic numbers may be observed by mass spectroscopy and are noted in Figure 12. On the other hand, for large (Na)n

quantized building blocks may interact to produce an optimal hierarchy for producing desired load-bearing biological materials. Similarly, CHDP controlled QBB may be found throughout the abiotic hierarchical stair steps leading to higher structural complexity. These QBBs are generally characterized by several fundamental features, namely, (a) they are highly monodispersed (i.e., >90%) collections of atoms, (b) they occupy well-defined space (i.e., zero- (0), one- (1), two- (2), or three-dimensional (3D) space) based on Pauli exclusion properties of their constituent atoms, and (c) they exhibit well-defined chemical or supramolecular stoichiometric relationships associated with (d) discrete sizes, surface chemistries, shapes, or architectures as illustrated in Figure 11.

3. ATOM MIMICRY: CONSENSUS DERIVED FROM THE PARALLEL WORLDS OF PHYSICISTS (HARD SUPERATOMS/NANOCLUSTERS) AND CHEMISTS (SOFT SUPERATOMS/NANOCLUSTERS) 3.1. Hard Superatoms: A Historical Perspective

In general, atomic clusters are defined as nanoscale collections of atoms joined together by physicochemical interactions that may range from weak van der Waals forces to stronger metallic, covalent, or ionic bonds. Atomic clusters have always been entities of extreme interest, wherein their specific atomic arrangements may exhibit unique, unexpected properties. These new emerging properties not only arise from unique architectures, but they may also be due to their reduced dimensions, as well as specific electronic states, and are generally expected to be completely different from the same atoms in the bulk state. As such, atomic clusters may be engineered as a function of their size, architecture, elemental composition, or charged state. The earliest interest in atomic clusters began nearly 150 years ago when Faraday synthesized and demonstrated the size dependent colors of colloidal gold in the 1850s.49 This work provided early insights into the unique colors associated with the famous Lycurgus cup and glass-coloring processes involving colloidal metals. More contemporary work in atomic clusters began in the 1980s with the development of experimental techniques and use of specialized protocols involving molecular beams, laser vaporization supersonic cluster beams, various spectroscopic techniques, and chemical synthesis methods. These more advanced methodologies have allowed the production of specific 2715


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clusters where n > 54, the sodium atoms self-assemble to form more stabilized clusters by closing shells of sodium atoms to form

Figure 14. Schematic illustration of (a) (M55)55 giant cluster, (b) giant clusters of different magic nuclearities; (Pd 561 )n, with circles corresponding to diameters of the clusters calculated on the basis of the effective volume of an individual nanocrystal; and (c) TEM image of Pd561 nanocrystals forming giant clusters. The numbers correspond to the proposed number of nanocrystal shells, designated by (n). (Reprinted from ref 53. Copyright 2001 American Chemical Society.)

3.1.1. Closed Geometric Atom Shells and Closed Electronic Shells. Some of the most interesting properties of transition elements, either as free atoms or in the metallic bulk state, result from incomplete filling of the d shell in the ground state. In a similar fashion, transition element clusters manifest behavior and properties based on d electron localized behavior unlike simple sp-type metal clusters or bulk solids which exhibit properties derived from delocalized external sp electron dynamics.56 This delocalized character leads to many unique properties of high interest in sp electron derived clusters; for example, the ability to form electronic shells, as well as the possibility to undergo shell closing which appear to mimic free atoms. More specifically, these electronic shell effects are frequently found in Cu, Ag, or Au metal clusters as their d electrons may develop complete d10 shells in these atoms. When cluster sizes reach a certain size, there is substantial evidence that icosahedral arrangements generally occur, providing the underlying scaffolding or fundamental lattice of the bulk crystal structure. Such atom shell closing properties with icosahedral symmetry are routinely observed in rare gas clusters.57 Such icosahedra growth events and the formation of completed atomic shells may be monitored and observed58 by mass spectrometry. In the case of sodium clusters, the critical size is observed to be approximately 1500 atoms;59 therefore, when the cluster sizes approach Nc = 1500−22000, the preferred structures as determined by mass spectrometry are usually icosahedra or fcc cuboctahedra. In the case of alkaline earth metals, these icosahedral clusters may generally be observed at smaller sizes. For example, it occurs with N between 13 and 55 atoms60,61for barium clusters, whereas with magnesium clusters N may exceed 147 atoms62 and yet appear to exhibit icosahedral structures. It was this interesting electronic and geometric shell mimicry behavior that led Khanna and Jena to propose20 combining electronic and geometric parameters to form both stable and reactive clusters that would mimic periodic chemical properties of elemental atoms in the Mendeleev periodic table. As such, these clusters were regarded as superatoms and provided the first compelling evidence that these clusters might be viewed as nanoscale atom mimics and indeed were defining a possible third dimension to the traditional periodic table as noted in Figure 15.21−23 3.1.2. General Hard Superatom Features and Categories. Generally speaking, hard superatoms may be described as discrete collections of atoms ranging from small multiples to dozens of constituents with sizes varying from subnanoscale to

Figure 13. Mass spectra of (Na)n clusters photoionized with 2.99 and 2.93 eV photons. Minima occur at values of n corresponding to the icosahedral shell closings listed at the top. (Reprinted with permission from ref 34. Copyright 1996 Elsevier Ltd.)

core−shell type clusters which generally assume an icosahedral (cuboctahedral) type symmetry (Figure 12). Evidence for these geometrically closed shells of atoms is shown in Figure 13, wherein the minima correspond to the icosahedral (cuboctahedral) core−shell type shell closings. As such, sequential cluster growth forces the atoms to reorganize into completely new structures each time an atom is added to the cluster when it is small. Eventually, a preferred symmetry becomes defined in the cluster (i.e., closed atom shell), wherein subsequent atom growth occurs by adding layers of atoms to this defined core. Each defined atom layer is referred to as a geometric closed shell of atoms.34 It has been demonstrated experimentally that larger clusters possessing complete geometric shells are substantially more stable.50 Related work by Schmid 51,52 and Rao 53 has clearly demonstrated that shells of atoms or core−shell type metal nanoclusters (i.e., Au and Pd etc.) are routinely obtained from closed atom shells containing magic numbers of metal atoms (i.e., 13, 55, 147, 309, 561, and 1415). These core−shell, hard superatom arrangements correspond to closed metal atom shells as cubic (ccp) or hexagonal (hcp) close packed structures containing 10n2 + 2 atoms, wherein the shell number n = 1, 2, 3, 4, 5, and 7 (Figure 14). It is amazing to note, how these selfsimilar, core−shell metal clusters heuristically mimic the traditional electron periods (shells) in elemental atoms, as well as the monomer shells (i.e., generations) as found in soft superatoms such as dendrimers. These issues will be discussed in more detail later. Schmid noted that these clusters are substantially more robust when ligand stabilized.54 However, much like traditional atoms, unfilled outer shells of atoms in naked core−shell type gold nanoclusters were shown to behave much like traditional atoms by exhibiting substantially higher reactivity compared to noble gas like configurations represented by the saturated core−shell nanoclusters possessing completely filled shells of atoms (i.e., (Au)55).55 2716


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Figure 15. Extension of the 2-D Mendeleev periodic table in the context of hard superatom type elements into a Khanna hypothesized 3-D perspective. (Reprinted from ref 63. Copyright 2014 American Chemical Society.)

Figure 16. (a) Simplified structural version of a dendrimer molecule; generation = 2 taken from a series of dendrimer structures reported by Tomalia et al.;69−71 wherein the spacer represents a poly(amidoamine) segment containing four aliphatic carbons and an amide group. (b) Relationship between molecular weight M and radius R for these dendrimer molecules with spacers of P monomers and extended length Pa. (Reprinted with permission from ref 68. Copyright 1983 EDP Sciences (http://dx.doi.org/10.1051/jphyslet:01983004409035100).)

3.2. Dendrimers: A Window to Quantized, Periodic Soft Superatoms at the Nanoscale Level

nanoscale dimensions. Quite amazingly, when these atom multiples are in unique ordered arrangements/combinations, they behave collectively as traditional picoscale elements. These multiple atom collections are usually derived from inorganic/metal based elements with the exception of fullerenes, which are based totally on carbon. Various categories of hard superatoms are beginning to emerge based on the mimicry of traditional element groups in the Mendeleev periodic table. The emergence of these nanoelement categories is based on unique superatom orbitals, electronic shell closing or atom shell closing features, as well as stoichiometric surface chemistry that mimics traditional elements. As such, there are those exhibiting physicochemical atom mimicry, surface chemistry, and magic numbers that mimic noble gases (i.e., by their robust, nonreactive nature), group I metals, alkaline earth metals,23 halogens,64 phosphorus, Hund’s rule, atomic magnetism, etc.63 In fact, there is now evidence that one can form a class of hard superatoms with property analogies to virtually any element in the periodic table.22,65

Beginning in 1983, Prof. P.-G. de Gennes (Collège de France)66 and one of the authors (D.A.T.) initiated a decade-long dialogue focused on the extraordinary structural order and mathematically defined mass and surface group amplifications observed in soft matter such as dendrimers. This scientific dialogue began with Prof. de Gennes at the Winter Polymer Gordon Conference (January 1983, Santa Barbara, CA),70 after the first public dendrimer lecture which he attended. De Gennes became very excited about these soft matter nanoparticles, especially since they were discrete, highly ordered, monodisperse, macromolecules which could be readily synthesized from commercial monomers in a stepwise manner to produce a fourth major architectural class of polymers with unprecedented new properties.67 These dendritic macromolecules differed architecturally from all other traditional polymers, wherein their onionlike, core−shell structures were initiated from a central core around which concentric shells of branched monomers (i.e., generations) were grown and tethered back to the core. 2717


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Figure 17. Mathematical expressions for calculating the theoretical number of surface groups (Z), branch cells (BC), and molecular weights (MW) for [core: cystamine]; (G = 0−7); {dendri-poly(amidoamine)-(NH2)z} (PAMAM) dendrimers as a function of generation. Approximate hydrodynamic diameters (Gen = 0−7) based on gel electrophoretic comparisons with the corresponding ethylene diamine core PAMAM dendrimers. (Reprinted with permission from ref 24. Copyright 2010 The Royal Society of Chemistry.)

Figure 18. New emerging properties are observed as one advances from picoscale to nanoscale complexity (i.e., CADP → CMDP → CNDP). (a) Molecular simulations for [core: NH3]; (G = 0−5); {dendri-poly(amidoamine)-(NH2)n} PAMAM dendrimers and a generational comparison of hydrodynamic diameters. (b) Comparison of molecular shape change, two-dimensional branch cell amplification surface branch cells, surface groups (Z), and molecular weights as a function of generation: G = 0−5. (Adapted with permission from ref 24. Copyright 2010 The Royal Society of Chemistry.)

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molecular shape changes from flat, floppy conformations to robust spheroids as first predicted by Goddard et al.85 Shape change transitions were subsequently confirmed by extensive photophysical measurements pioneered by Turro et al.86−89 and solvatochromic measurements by Hawker et al.90 Depending upon the accumulative core and branch cell multiplicities of the dendrimer family under consideration, these transitions were found to occur between G = 3 and G = 5. Ammonia core, PAMAM dendrimers (Nc = 3, Nb = 2) exhibited a molecular morphogenesis break at G = 4.5, whereas the ethylenediamine (EDA) PAMAM dendrimer family (Nc = 4; Nb = 2) manifested a shape change break around G = 3−485 and the Fréchet-type convergent dendrons (Nb = 2) around G = 4.90 It is readily apparent that increasing the core multiplicity from Nc = 3 to Nc = 4 accelerates congestion and forces a shape change at least one generation earlier. Beyond these generational transitions, one can visualize these dendrimeric shapes as nearly spheroidal or slightly ellipsoidal core−shell type architectures. Just as the CADPs of atomic/elemental unit cells are associated with the transfer of structural information up the hierarchy ladder via their crystallization sequences, so does the dendrimer interior of branch cells communicate important CNDP information from its core to the surface of the dendrimer. These branch cells determine the various covalent interior dendritic lattice types for a specific dendrimer family as a function of the dendrimer core and shell level (i.e., generation). Unique periodic dendritic lattice relationships emerge as a function of the CADP/CMDP information transferred. This information transfer occurs with high fidelity at each generation level according to the following sequence. Beginning with an atomic/molecular core, the sequence (CADPs) → (CMDPs) → (CNDPs) defines new emerging properties and periodic properties/patterns as a function of dendrimer generation and these nanoperiodic property patterns are referred to as dendritic ef fects.37 Dendritic branch cells as they occur in well-defined interior dendrimer lattice structures are reminiscent of traditional unit cells in atomic crystal lattices. In each case, under either controlled crystallization or dendrimer propagation conditions, they produce quantized entities (i.e., building blocks) manifesting new emerging properties and unique periodic patterns/properties as they transfer their respective CHDPs with high fidelity as described in Figure 18. In contrast to flexible dendrimer architectures, Mullen et al.91 have systematically engineered rigid polyphenylene dendrimer (PPD) architectures as a function of their size, shape, architecture, and interior compositions. These modifications clearly demonstrated that PPD architectures represent a distinctly different field of dendrimer chemistry based on their rigidity and shape-persistent structures. As such, they were observed to produce many new emerging properties including unique amphiphilic Janus-type dendrimers that self-assemble into high aspect ratio nanofibers92 as well as libraries of unprecedented weakly coordinating cations (WCC) and complementary weakly coordinating anions (WCA).93 3.2.2. Quantized Size Control and Monodispersity. The bottom-up synthesis of dendrons/dendrimers provides one of the most precise and tunable strategies known for constructing a systematic continuum of quantized, soft matter nanoscale structures. Size and structure control observed for dendron/ dendrimer synthesis rival that expected for proteins and DNA/ RNA. In fact, dendrimers are often referred to as artif icial proteins.94−96 Based on the close mimicry of globular protein size scaling and their monodispersity, they are often used as protein

These unique architectural growth features were completely unprecedented in traditional polymers. This compelled de Gennes to publish an early report that anticipated dendrimer structure growth induced surface congestion68 nearly 2 years before the first dendrimer paper actually appeared in the literature.69 In this seminal paper, de Gennes analyzed the consequence of ideal dendrimer growth as a function of generation. He determined that since the concentric dendrimer generation growth increased in a linear fashion (i.e., ∼1 nm/ generation) and the number of surface monomers/groups increased exponentially as a function of generation (i.e., nG/ generation), there should be a mathematically predictable generation, wherein steric induced defects would begin to occur. De Gennes determined that a limiting generation (m1), radius (R1), or molecular weight (M1) exists beyond which the termini of dendrimer structure becomes too sterically hindered to allow perfect structural growth. As such, de Gennes proposed that the limiting m1 varies as a function of the spacer length (P− Pa) according to m1 = 2.88 ln P + 4.4 + M0, as shown in Figure 16. More recently, sterically induced dendrimer structural defects were experimentally confirmed at higher generation levels by mass spectroscopy25 as well as photophysical labeling72 and appeared to be consistent with de Gennes’ predictions. Regular dialogue and invited visits to the Collège de France with de Gennes (1983−1990s) generally focused on the highly ordered features of dendrimers. These personal interactions provided critical stimulation and inspiration for many of the concepts developed in this article, including the widely recognized designation of sterically induced dendritic congestion as de Gennes dense packing.25 Mathematically, both the core multiplicity (Nc) and branch cell multiplicity (Nb) determine the precise number of terminal groups (Z) and mass amplification as a function of generation (G). The iterative, generational reaction sequences involved in all divergent dendrimer growth may be viewed as quantized polymerization events. The iterative assembly of reactive monomers,16,71 branch cells,16,73,74 or dendrons73,75,76 around atomic/molecular cores to produce dendrimers according to divergent/convergent dendritic branching principles is widely recognized and well demonstrated. The systematic filling of space around cores by the exponential amplification of branch cells as a function of generation (branch cell shells) produces discrete quantized bundles of mass which have been shown to be mathematically predictable (Figure 17).14,77,78 These predicted dendrimer masses have been confirmed by mass spectroscopy79−81 and other analytical methods.16,75,82−84 For example, predicted numbers of branch cells, terminal groups (Z), and molecular weights as a function of generation for a cystamine core (Nc = 4) PAMAM dendrimer are shown in Figure 17. It should be noted that the molecular weights approximately double as one progresses to the next generation. The surface groups (Z) and branch cells (BC) amplify mathematically according to a power function, thus producing discrete, monodispersed structures with precise molecular weights and nanoscale diameter enhancement as described in Figure 17. These predicted values are routinely verified by mass spectroscopy for the earlier generations (i.e., G = 4−5); however, with divergent dendrimers, minor mass defects are often observed for higher generations as congestion-induced de Gennes dense packing begins to take affect (Figure 18). 3.2.1. Dendrimer Shape Changes: Nanoscale Molecular Morphogenesis. As illustrated in Figure 18, flexible dendrimers such as PAMAMs undergo congestion-induced 2719


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eration, with a remarkable uniformity of mass distribution over five generations exhibiting polydispersities ranging from 1.005 to 1.130. 3.3. Soft Superatoms: Dendrimers

The highly ordered structural features of dendrimers distinguish this macromolecular category of soft matter as perhaps some of the most compelling examples of sof t superatoms. Their widely recognized super atomistic features include (a) structure controlled uniform sizes, (b) highly ordered architectural features mimicking atoms (i.e., core, interior, surface chemistry), (c) quantized interior Bohr-like monomer shells, and (d) mathematically defined magic numbers for predicting monomer shell filling aufbau, surface chemistry valency, and dendrimer molar masses. Other atom mimicry features include the ability of these soft nanoclusters to function as individual nanoscale-like atoms as they combine to form a wide variety of stoichiometric nanocompounds and assemblies. Other soft matter superatom categories exhibit certain atom mimicry features, however, not to the degree that is observed with dendrimers. These other soft superatom categories include abiotic synthetic polymers such as monodisperse nanolatexes, living polymers, and copolymeric micelles, as well as biological polymers/assemblies such as proteins, viral capsids, and DNA/RNA. In general, these soft superatom categories are constructed with internal binding features involving covalent, ionic, or supramolecular type bonding. 3.3.1. Chemical Bond Formation, Valency, and Stoichiometric Binding Ratios with Dendrimers To Form (Dendrimer)n Megamer-Type Nanocompounds/Assemblies. Certain quantized, soft superatom features of dendrimers have been investigated recently by van Dongen et al.106 As such, they have defined at least three types of nanoclusters (i.e., nanocompounds) that may arise from their atom-like stoichiometric interactions, namely, (a) extended 1-D, 2-D, or 3-D nanostructures (i.e., fibers, sheets, or lattices); (b) stochastic nanoclusters; and (c) precise nanoclusters (i.e., stoichiometric nanocompounds) as illustrated in Figure 22. Supramolecular examples of all three of these superatom based nanoassemblies were documented with atomic force microscopy (AFM). These studies clearly demonstrated the remarkably rich array of nanoassembly patterns and related stoichiometric binding ratios that were possible by simply spreading dilute solutions of amine terminated, G = 9; poly(amidoamine)

Figure 19. (a−f) Transmission electron micrographs (TEMs) of Gen 5−10 PAMAM dendrimers. Sample (f) contains three molecules of Gen = 10 dendrimer for comparison. Bar length = 50 nm. (Reprinted from ref 99. Copyright 1998 American Chemical Society.)

replacements/substitutes in many nanomedicinal applications.48,94,95,97,98 Dendrimer mass and size uniformity has been exhaustively demonstrated by electron microscopy (TEM),99 (Figure 19), ESI/MALDI-TOF mass spectrometry,79,104 (Figure 20B), gel electrophoresis,82,83,100,101,105 (Figure 21A), size exclusion chromatography (Figure 21B),105 and atomic force microscopy (AFM),102 to mention a few.103 Within a specific dendrimer family, it is possible to produce a systematic, reproducible continuum of nanosizes and precise masses as a function of generations (see Figures 18, 19, and 21). It should be noted that dendrimer mass approximately doubles, generation to gen-

Figure 20. (a) Yamamoto-type [core: p-phenylene]; (G = 4); {dendri-poly(phenylazomethine)} (DPA) dendrimers. (b) MALDI-TOF of the G4; DPA dendrimer. (Reprinted from ref 104. Copyright 2001 American Chemical Society.) 2720


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Figure 21. (A) Gel electrophoresis of PAMAM dendrimers with various generations (G = 0−6) and cores (1,2-diaminoethane, EDA; 1,4diaminobutane, DAB; 1,6-diaminohexane, HEX; 1,12-diaminododecane, DODE; cystamine, CYST). (B) Size exclusion chromatography (SEC) of [core: EDA]; 1 → 2; dendri-poly(amidoamine)-(NH2)x; (G = 0−8) versus a random coil polymer (---). (Reprinted with permission from ref 105. Copyright 2005 Elsevier Ltd.)

Figure 22. Dendrimer based covalent nanocompounds (i.e., megamers) controlled soft, super atom based nanostructures can be classified as (I) extended nanostructures including 1-D, 2-D, or 3-D types (i.e., fibers, sheets, and lattices); (II) stochastic nanoclusters; and (III) precise nanoclusters (i.e., soft, superatomic nanocompounds). (Reprinted with permission from ref 106. Copyright 2013 The Royal Society of Chemistry.)

synthesize a variety of type III (Figure 22), precise covalent nanocompounds (Figure 24B) which were analyzed by ultra performance liquid chromatography (UPLC) and characterized by mass spectrometry.

(PAMAM) dendrimers on a mica surface with a 30° stream of argon.102,107,108 As shown in Figure 23, one can readily observe single isolated G = 9 modules, dimers, trimers and a wide variety of oligomeric assemblies (i.e., megamers) that clearly exhibit well-defined 2-D combining ratios on a mica surface. Knowing the nanoscale dimensions of these G = 9 dendrimer modules, this library of two-dimensional megamer assemblies below (Figure 23) clearly illustrates the heuristic mimicry of traditional small molecules such as methane, ethane, cyclopropane, and pentane, respectively, thus further elaborating the notion of atom mimicry. Covalent examples of all three soft superatom derived nanostructure categories (i.e., megamers) have been reported earlier by Tomalia et al.109−111 and recently by Banaszak Holl et al.106 In more recent work, atom mimicry was demonstrated by engineering the dendrimer surface chemistry to exhibit mono-, di-, tri-, and tetravalent reactivity as illustrated in Figure 24A. These discrete valency defined building blocks were then used to

3.4. Dendrimers as Heuristic Soft Superatom Mimics of Traditional Picoscale Atoms

As early as 1990,14−17 a heuristic112 comparison of dendrimerbased, core−shell nanoscale architectures was made with traditional picoscale atoms. This comparison revealed that many unique similarities existed between aufbau components in atoms (i.e., nucleons and electrons) and dendrimer structures (i.e., cores and branch cell monomers). Remarkable heuristic analogies were also noted between dimensionally different parameters in each case such as (a) picoscale electron shells vs nanoscale monomer shells (generations), (b) mathematically defined aufbau filling patterns for electron shells vs monomer 2721


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Figure 23. Atomic force microscopy (AFM) images (i.e., tapping mode) of [core: EDA]; dendri-poly(amidoamne)-(NH2)2048 (G = 9); PAMAM dendrimer molecules on a mica surface102,107 (a−c). Dendrimer-based superatom molecular mimics reminiscent of traditional methane, ethane, cyclopropane, and n-pentane molecules. (Reprinted with permission from ref 102. Copyright 2001 Wiley-VCH Verlag GmbH & Co. KGaA.)

Figure 24. (A) UPLC chromatograms of mono-, di-, tri-, and tetravalent “click functionalized” PAMAM dendrimers. (B) UPLC chromatograms (210 nm) of covalent (a) dimer-, (b) trimer-, (c) tetramer-, and (d) pentamer-type nanocompounds obtained by combinatorial “click reactions” of these discretely functionalized soft, superatom PAMAM dendrimers. (Reprinted with permission from ref 106. Copyright 2013 The Royal Society of Chemistry.)

shells, (c) saturation levels (i.e., magic numbers) for electron shells vs monomer shells, (d) periodic atomic weights compared to periodic dendrimer molecular weights as a function of shell level and saturation level, and (e) periodic elemental atom reactivity compared dendrimer reactivity as a function of shell saturation levels. These remarkable atom mimicry features appear to exist between picoscale (atomic elements) and nanoscale dendrimers. Furthermore, just as the Pauli exclusion principle assures that electrons occupy well-defined space around their nuclei as a function of elemental periods, so is this excluded space pattern observed within dendrimer generational periods at the nanoscale level. A notable difference, however, is that although non-Newtonian physics is required to define picoscale atoms, there appears to be no evidence that such physics principles are required to describe soft superatoms such as dendrimers. Finally, it is indeed noteworthy to observe an

analogous systematic and periodic size continuum within both the picoscale atomic structures and nanoscale dendrimer structures, respectively, as well as to observe certain mutually exclusive magic numbers associated in each case as illustrated in Figure 25.17,18,24,25 3.4.1. Comparison of Atom Electron Aufbau and Periodic Symmetries with Dendrimers. The precise, quantized core−shell structures of dendrimers demonstrated in the late 1980s15,16 conjured remarkable visions of dendrimerbased atom mimicry. This concept of atom mimicry was based ̈ similarities noted for the internal structures largely on the naive of atoms (i.e., core−electron shells) and dendrimers (i.e., core− monomer shells), respectively.6,14,15,39,78 Subsequent experimental evidence rapidly extended acceptance this mimicry well beyond those early considerations. More specifically, mass spectrometry techniques began to emerge that allowed the 2722


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Figure 25. Comparison of dimensions and physics principles required to define picoscale versus nanoscale structures. Heuristic atom mimicry similarities noted for atom electron and dendrimer monomer aufbau stages for picoscale and nanoscale structures. A systematic and periodic continuum of saturated spheroidal shell dimensions representing rare gas configurations associated with quantized picoscale and nanoscale structures, respectively. (Reprinted with permission from ref 24. Copyright 2010 The Royal Society of Chemistry.)

Figure 26. Simulated, ideal poly(amidoamine) (PAMAM) dendrimers possessing saturated outer monomer shells (i.e., generations; G = 1−5) (right side) are compared as heuristic nanoscale analogues to saturated picoscale atomic outer electron shells associated with filled, noble gas configurations (left side) at the picoscale level. (Reprinted with permission from ref 38. Copyright 2012 Cambridge University Press.)

similar mass determinations obtained earlier by Aston for saturated outer electron shells associated with noble gas elements. More specifically, these quantized mass features were well demonstrated by Aston for atoms and described in his Nobel Lecture (1922). In essence, a quantized “monomer shell filling aufbau process” appeared to be occurring throughout the

precise mass determinations of large, well-defined protein structures79,113,114 in the early 1990s. Applying these protocols to dendrimers showed that79,80,81,104,115 precise relative molecular masses could be determined for each dendrimer generation (G) (i.e., outer saturated monomer shell). These data revealed that the results obtained for dendrimers could be compared to 2723


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Figure 27. Bohr-type elemental periodic table (upper horizonal row) genealogy of electron shells, surface chemistry, and complexity as a function of electron periods: (bottom horizonal row) sizes, atomic orbital shapes, and complexity as a function of electron periods; (vertical columns) reactive surface chemistry penultimate to inert noble gas configurations at the bottom of each horizontal column. (Image adapted in part from ref 96. Copyright 2003 Elsevier Ltd.)

Figure 28. Bohr-type (i.e., Tomalia version) dendrimeric periodic table (upper horizonal row) genealogy of monomer shells (i.e., generations; G = 0− 3), surface chemistry, rigidity/flexibility, and complexity as a function of monomer shells (generations); (bottom horizonal row) sizes, molecular weights, shapes, and complexity as a function of generations; (vertical columns) reactive surface chemistry penultimate to nonautoreactive (i.e., inert noble gas type) closed monomer shell dendrimer configurations at the bottom of each horizontal column. This dendrimeric periodic table illustrates monomer aufbau in a typical PAMAM dendrimer (e.g., [core: NH3]; (3 → 2): dendri-{poly(amidoamine)-(NH2)z}; (G = 0, 1, 2, 3): PAMAM dendrimer. (Image adapted in part with permission from ref 17. Copyright 2005 Elsevier Ltd.)

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Figure 29. (a) Electron filling aufbau steps leading to saturation levels observed at each principle electron shell level (i.e., n = 1−6) to produce inert gas configurations for all atomic elements in the periodic table. (b) Monomer filling aufbau steps leading to heuristic saturation levels observed at each principle monomer shell level (i.e., generations = 1−8) to produce, non-self-reactive ideal, theoretical dendrimers. (Reprinted with permission from ref 38. Copyright 2012 Cambridge University Press.)

divergent growth of a dendrimer family that mimicked the electron aufbau process that occurs with atoms. As such, theoretical, saturated outer monomer shell dendrimer structures may be considered to be heuristic analogues of saturated outer electron shell, noble gas configurations as illustrated in Figure 26. 3.4.1.1. Hidden Symmetries Manifested by Bohr-Type Elemental and Dendrimer Periodic Tables. A comparison of the core−shell hierarchy within a Bohr-type elemental periodic table (Figure 27) and a Bohr-type dendrimeric table (Figure 28)

reveals some amazing symmetries and similarities at the picoscale and nanoscale levels. The electron aufbau ordering within each elemental period leading to closed electron shells is truly reminiscent of the monomer aufbau ordering within each dendrimer generation leading to closed monomer shells. In each case, magic numbers of electrons or monomers, respectively, are required to saturate and close these shells. 3.4.1.2. Similarities between Picoscale Electron and Nanoscale Monomer Aufbau Stages and Reactivity. In each case 2725


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Figure 30. Abbreviated dendrimer periodic table heuristically modified to reflect certain features of the elemental Mendeleev periodic table. As such, the generation levels are intentionally ilustrated to mimic electron periods (i.e., eletron shells), wherein, it is clearly apparent that the monomer shell filling aufbau stages (i.e., G = 0−2) mimic respective electron shell filling aufbau stages that occur in picoscale atoms. Molecular simulations of dendrimer shell saturated generations (i.e., G = 0−4) are illustrated at right adjacent to the core−shell (i.e., shell saturated) stick configurations. Note: The self-reactive combination of the two dendrimer, G = 2, species (20*) heuristically mimics the atomic element chlorine by forming dimeric products due to formation of an interdendrimer amide cross-link involving an outer monomer shell amine moiety (∗) and a penultimate unfilled outer monomer shell ester group (---), as illustrated in species 20 above. (Image adapted in part with permission of ref 25. Copyright 2012 Cambridge University Press.)

gas configurations for He, Ne, and Ar with atomic numbers 2, 10, and 18 in periods 1, 2, and 3 (Figure 29a). As illustrated in Figures 29b and 30, it is apparent that a similar aufbau-like introduction of β-alanine monomer units (∼∼) produces analogous saturation states for the first three dendrimer periods, namely, generations = 0−2. It is shown in Figure 30 that the sequential introduction of three β-alanine monomer units leads to the saturated state for the G = 0 monomer shell associated with dendrimer number 3. Similarly, the sequential introduction of six more monomer units produces the shell unsaturated dendrimer number species 4, 5, 6, 7, and 8 leading ultimately to the saturated state for that the generation = 1 monomer shell associated with a dendrimer number of 9 (i.e., to give a total of a nine monomer unit) attached to six surface amine groups, all of which are tethered to the NH3 core. The final aufbau steps requires a sequential addition of 12-monomer units to produce the corresponding unsaturated monomer shell species with dendrimer numbers 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20, respectively, leading to the saturated outer monomer shell species 21, heuristically analgous to the noble gas element argon (Figure 30). It is now quite apparent that the highlighted dendrimer shell unsaturated species 20 (i.e., containing (20*) monomers in the outer shell) is deficient by one monomer unit and penultimate to the heuristic, saturated nobel gas type, ideal dendrimer species 21. This striking comparison clearly suggests that species 20 may be regarded as heuristically analogous to the atomic element chlorine. Similarly, the saturated outer monomer shell species 21 possesses 21 monomer units and saturates this outer monomer shell to yield a heuristic dendrimer analogue reminiscent of the noble gas atomic element, namely, argon. Quite remarkably, the dendrimer species (20*) has been shown

(Figures 28 and 29), CHDP parameters such as sizes (i.e.,weights/masses), shapes, surface chemistry, period/generation genealogy, and complexity increase horizonally (left to right). Functionally, the surface chemistry features (i.e., selfreactivity) appear to be analogous, wherein self-reactivity is observed penultiumate to shell closing in each case. A closer examination of typical electron shell filling aufbau steps leading to a closed shell (i.e., inert gas configurations) (Figure 29a) defines magic numbers of electrons for shell closure associated with magic number atomic weights for the noble gas configurations. Similarly, monomer shell (generation) filling aufbau steps leading to closed shell dendrimers are associated with magic number molecular weights for ideal dendrimer structures (Figure 29b). The parameters, namely, atomic numbers, number of electrons, and atomic weights for atomic elements, are heuristically compared with the dendrimer number, number of monomer units, and dendrimer molecular weights, respectively (Figure 29). As illustrated in Figure 30, a similar comparison of the first three periods in a Mendeleev-type periodic table of atomic elements (Figures 26 and 27) above with the first three periods (i.e., generations 0, 1, and 2) of an abbreviated dendrimer-based periodic table for a poly(amidoamine) dendrimer family (Figure 28) clearly demonstrates a striking example of atom mimicry for these soft superatoms. More specifically, examination of the first three generations of [core: NH3]; (3 → 2); dendri-{poly(amidoamine)-(NH2)z}; (G = 0, 1, 2) PAMAM dendrimer family may be used to understand this mimicry. The Mendeleevtype, element-based periodic tables (Figures 26 and 27) clearly illustrate the stepwise electron aufbau steps that are required to produce the sequence of elements leading to the saturated noble 2726


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Figure 31. Quantized, closed shell module reactivity patterns at the picoscale and subnanoscale level (i.e., atoms), lower nanoscale level (i.e., dendrimers), and higher nanoscale level (i.e., core−shell tecto (dendrimers)) involving principle outer unsaturated (a) electron shells, (b) monomer shells, or (c) dendrimer valence shells. (Reprinted with permission from ref 6. Copyright 2009 Springer.)

dendrimer reactions with other small or nanoscale molecules.117−120 The initial concept of atom mimicry was based largely on the ̈ heuristic comparison of the highly ordered Bohr-like naive, atomic (i.e., core−electron shells) and dendrimeric (i.e., core− monomer shells) internal structures observed in each case.6,14,15,78 That withstanding, it soon became apparent that this mimicry extended well beyond those initial considerations, as illustrated in Figure 31. The emergence of critical new mass spectrometry techniques appeared for the precise determination of large, well-defined protein structures79,113,114 in the early 1990s that allowed for similar mass determinations of dendrimers.79,80,81,104,115 These new techniques showed that precise, periodic molecular masses accompanied each saturated shell/generation level for dendrimers much as was demonstrated for each saturated level for atomic electron shells at the end of each period for the rare gas elements. These quantized mass properties were seminal features historically demonstrated for elemental atoms/isotopes by F. W. Aston with his invention of mass spectroscopy and was recognized by the Nobel Prize in Chemistry (1922). In essence, it is now apparent that a quantized and periodic “monomer aufbau” process is involved throughout the divergent, dendrimer monomer shell filling sequence that heuristically parallels a similar “electron aufbau” process observed for elemental atoms. Hence, one observes specific required quantized numbers (i.e., magic numbers) of monomers (Z) for

experimentally to be self-reactive by forming a dimeric product much as elemental chlorine. In contrast, the saturated dendrimer species 21 has been shown to be non-self-reactive much as an inert gas configuration for an atomic element such as argon. This remarkable atom mimicry feature is described in more detail; wherein, atoms are compared to dendrimers and core-shell tecto(dendrimers), respectively in Figure 31. Just as known traditional reactive chemistry involves subsaturated atomic elements (i.e., non noble gas configurations), so does one observe a similar behavior with dendrimers. During the course of a divergent synthesis of dendrimers, using a subsaturation quantity of reactive monomer in the shell filling process invariably produces highly, autoreactive (i.e., selfreactive), unsaturated outer shell dendrimer species such as (20*) illustrated in Figures 30 and 31. Clearly, this outer unsaturated shell dendrimer species behaves heuristically much like a chlorine atom possessing an unsaturated outer electron valence shell, by undergoing rapid dimerizations or oligomerizations.14,78,110 Similarly, adding one monomer unit beyond the saturated noble gas configuration for the G = 3 dendrimer (i.e., argon mimic) would be expected to produce a dendrimer species that, relative to G = 3 shell filling, heuristically mimics the corresponding group I alkali metal, namely, potassium. Finally, the well-defined stoichiometries and reproducible mass combining properties that are inextricably associated with atomic elements possessing unsaturated outer electron shells are widely observed in all interdendrimer reactions,116 as well as 2727


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Figure 32. Heuristic similarities observed from the perspective of VSEPR theory applied to valency/symmetry features found in picoscale (a) atoms123 and nanoscale (b) spheroidal nanomodule dendrimers or metal nanoclusters.6,17,25,116,124 (Reprinted with permission from ref 25. Copyright 2012 Cambridge University Press.)

filling the outer shells of each generation. As such, each completed dendrimer generation is associated with a specific quantized,“magic number molecular weight”. These quantized magic number patterns observed for each dendrimer generation at the nanoscale level appear to mimic and parallel quantized numbers of electrons and corresponding atomic weights associated with saturated electron shell species at the end of each atomic element period (Figures 26 and 27). It should be noted that precise magic numbers may be mathematically predicted and are experimentally observed for each saturated monomer shell level within a dendrimer family and are dependent on the dendrimer core multiplicity (Nc), the monomer branch cell multiplicity (Nb), and the generation level as described earlier in Figure 17. 3.4.2. Remarkable Self-Reactivity Patterns Experimentally Observed for Picoscale Elemental Atoms and Nanoscale Dendrimers Possessing Unsaturated Outer Shells. Nineteenth century chemists determined that the reactivity of an atom was associated with the electron occupancy levels residing between the electron shell saturation levels that completed each period. These features were determined experimentally without the benefit of quantum mechanics or electronic theory.1,121,122 Furthermore, these atomic elements were observed to combine with precise valences and stoichiometries to give traditional molecular compounds with predictable mass combining ratios. In a similar manner, dendrimers possessing unfilled outer monomer shells were observed to be highly self-reactive. Experimentally, these dendrimers were observed to readily form intermolecular “allotropic-like” nanocompounds or intramolecular macrocycle structures via self-reactive pathways. Alternatively, ideal dendrimers possessing saturated outer monomer shells with specific,

magic number masses as defined mathematically in Figure 17 were observed to exhibit no self-reactivity and remained shell stable for years when properly stored. This robust dendimer feature is heuristically reminiscent of known behavior for noble gas type, inert atomic elements. It is noteworthy that similar selfreactive, allotropic-like behavior was also observed for the next higher level of core−shell complexity, namely, outer dendrimer shell, unsaturated core−shell tecto(dendrimers).110 whereas outer, dendrimer shell saturated analogues were robust and did not exhibit any self-reactive properties.116 It is noteworthy that specific magic numbers and robust, non-self-reactive properties have been observed to be associated with all closed shell, core− shell type structural entities ranging from picoscale atoms to nanoscale single dendrimers and beyond to more complex nanoscale core−shell tecto(dendrimers) as illustrated in Figure 31. These mutually common nanoscale reactivity patterns shared with traditional picoscale atoms provide compelling examples for the soft superatom features of dendrimers. In a similar fashion, noble gas magic number features were also observed for ligand protected, hard superatoms such as gold nanoclusters. Various spherical gold nanoclusters (Au)n, in all cases, attained filled outer electronic shells by ligand association to produce superatom assemblies exhibiting extraordinary stability.46 It is also noteworthy that Schmid et al.55 observed dramatically enhanced reactivity for naked, nonligated, core− shell gold nanoclusters possessing unfilled outer gold atom shells versus those containing filled shells, thus validating and corroborating these reactivity patterns in both hard and soft superatoms. 3.4.3. Heuristically Similar Valency/Symmetry Features Observed in Both Picoscale Atoms and Soft Superatoms Such as Dendrimers. A widely recognized 2728


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r1/r2 = 0.155−1.20). Striking experimental evidence for the dimensional scalability of these spheroid relationships is readily apparent when r1/r2 = 1, as would be the case for homogeneous metal nanoclusters. As shown in Figure 32b, one obtains a valency of 12 and an icosahedral (Ih) symmetry as predicted for the first geometrically closed metal shell for all homogeneous metal nanoclusters. This predicted valency is definitely consistent with that reported for hard superatoms such as core−shell type metal nanoclusters (i.e., gold nanoclusters) as reported by Schmid et al.51,52,125 (Figure 34). Extension of these principles to soft superatoms will be discussed later where it was possible to demonstrate and confirm these principles using spheroidal, nanoscale dendrimers to produce discrete, soft dendrimer clusters referred to as core−shell (tecto dendrimers).6,24,116 Experimentally, these soft superatom (dendrimer) clusters were found to manifest very well-defined covalent core valencies by merely adjusting core spheroid/shell spheroid radii as described later (Figure 52). 3.4.4. Nanoscale Atom Mimicry: Hard and Soft Superatom Features. The term superatoms, first coined by Khanna/Castleman et al.,22,23 is now widely attributed to discrete nanoscale collections or clusters of atoms that behave as a single unit or quantized building block (QBB). These nanoscale atom clusters are distinguished by exhibiting unique electron, atom, or monomer shell aufbau shell filling features, as well as QBB combining behavior that is stoichiometric and reminiscent of individual atoms.63 Such collective multiple atom behavior has been exhibited by both hard (i.e., inorganic) and soft (i.e., organic) superatoms and documented by both physicists and chemists. Just as traditional elemental atoms such as carbon and hydrogen may be combined to produce simple traditional

theoretical model for predicting the geometric arrangement of traditional terminal atoms or groups of atoms surrounding a central atom in a covalent compound or charged ion is known as the valence shell electron pair repulsion (VSEPR) theory. This concept is based largely on the repulsion dynamics of electron pairs present in the valence shell of the central atom. This VSEPR premise assumes that all valence electron pairs surrounding a central atom will electrostatically repel each other and as a consequence adopt an energy minimized arrangement. In essence, these charge repulsion dynamics define space occupied by the valence electrons and ultimately determine specific shapes and molecular geometries exhibited by the bonded structure. The number of bonding and nonbonding electron pairs surrounding an atom is often referred to as its steric number and may influence important spacial relationships around a central atom. Therefore, the VSEPR theory may be used to predict specific arrangements of electron pairs surrounding one or more central molecular atoms which ultimately determines the overall geometry, architecture, and shape of molecular structures.123 As such, these VSEPR-type electrostatic core−shell relationships are frequently used to explain a wide range of valency, symmetry, and geometry features observed for traditional atoms in molecular structures (see Figure 32a, left column). It is presumed that essentially all of these CADP directed charge repulsion geometries are manifestations of subatomic (CSADP) core−shell (i.e., nucleon−electron) relationships. Therefore, it is from these reproducible CADP directed geometries (i.e., atomic shapessee Figure 3) that VSEPR principles conserve and transfer shape defining features to the molecular level, thus producing CMDPs. These considerations should now be applied to a similar core− shell space analysis that assesses the implications of Pauliexclusion-like space filling and steric feature issues manifested by the relationship between various sized nanoscale core and shell spheroids (Figure 32b, right column). More specifically, these core−shell saturation relationships have been analyzed as a function of the ratio of core spheroid (r1) to shell spheroid (r2) radii,124 wherein the core spheroid size is systematically increased relative to the shell spheroids. It is striking to find that this VSEPR assessment produces a systematic sequence of welldefined boundaries for core saturation valencies, symmetries, and geometries that closely mimic those observed for traditional atoms at the picoscale level. For example, an r1/r2 value of 0.155 produces a core valence of 3 for these shell spheroids with a trigonal geometry (D3h). At boundary values for r1/r2 = 0.255− 0.414, a core valency of 4 is observed accompanied by tetrahedral (Th) symmetry, whereas, at r1/r2 = 0.255 one observes a core valency of 8 for the shell spheroids with octahedral (Oh) symmetry (see Figure 32b, right column). Clearly, these assessed valencies, symmetries, and geometries appear to produce space saturation values (i.e., core valencies) derived from core−shell spheroid interactions (i.e., defined by r1/r2 values) that mimic picoscale atoms and appear to be valid at any dimensional level. As such, it is apparent that these core spheroid, space saturation values may be engineered by simply tuning the relative radii (i.e., r1/r2) values of the core and shell, respectively, to produce valency values that may scale at any dimension. This provides a powerful and useful strategy for defining spheroid contact valency for virtually any surface reactive spheroid including nanoobjects/structures. It may be seen that combining a small core reagent with a large shell reagent allows attachment of a very limited number of shell-type reagents surrounding the core (i.e.,

Figure 33. (A) Comparison of traditional carbon and hydrogen atoms and (B) gold cluster superatoms as precursors to traditional atom-based molecular structures and superatom-based superatomic molecular structures, respectively. (Reprinted with permission from ref 126. Copyright 2014 John Wiley & Sons.)

molecules (Figure 33A), so can superatoms be combined to yield superatom molecules as illustrated in Figure 33B.126 3.5. First Evidence for Hard Superatoms

First evidence for core−shell type hard superatoms exhibiting magic numbers associated with concentric shells of atoms heuristically analogous to picoscale electron shells in Bohr-type atoms evolved from early atom cluster work in the 1970−1980s. Pioneering work by Echt, Sattler, and Recknagel57 demonstrated by mass spectrometry that discrete xenon clusters dominated and 2729


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Figure 34. Comparison of filled (i.e., closed) electron shell, atomic picoscale particles (i.e., noble gases), filled metal shell (i.e., geometrically closed), hard nanocluster/superatoms (gold nanoclusters), and filled monomer shell (i.e., closed) soft nanoclusters/superatoms (dendrimers). (Reprinted with permission from ref 6. Copyright 2009 Springer.) Center image: hard nanomatter. (Reprinted with permission from ref 54. Copyright 1990 Elsevier Ltd.)

counterparts as described earlier and illustrated in Figures 30 and 31. Extensive studies by Rao et al.53,131 and Schmid et al.132,133 have shown that elemental gold and palladium atoms selfassemble into a systematic hierarchy of discrete, well-defined, self-similar, closed core−shell aggregates. The first core−shell aggregate is a metal cluster consisting of a single metal atom surrounded by a shell of 12-metal atoms (Figure 34). This basic 13-atom metal cluster (i.e., Au13), as well as higher clusters (i.e., Au55) with shell numbers (n) of 2−5 appear to behave as robust nanoscale building blocks.51 They are reported to self-assemble into discrete, stoichiometric aggregates that that are readily characterized by TEM and illustrated later in section 4.2.2.2 (Figure 54). Recent evidence for the behavior of these core−shell type, metal clusters as hard superatoms has also been reported by Roduner et al.134 It was found that the closed atom shell structure for the Pt13 nanocluster (Figure 35A) exhibited enhanced diamagnetism due to the delocalized superatom valence orbitals as illustrated by Figure 35B. Analogous to traditional atomic theory, another facet of the superatom electronic theory predicts metal cluster/nanoparticle stability and reactivity based on their ability to delocalize electrons throughout the entire cluster to form so-called superatomic orbitals. As such, an appropriate aufbau rule has emerged for metal clusters, wherein these delocalized superatomic orbitals are defined as 1S2|1P6|1D10|2S2 1F14|2P6 1G18|2D10 3S2 1H22|..., wherein S−P−D−F−G−H− denotes the angular momentum characters.135 Pioneering experimental mass spectrometry work by Castleman et al.19 led to a second type of hard superatoms. This investigation reported unexpected stability properties for certain

exhibited certain magic numbers associated with specific robust atom multiples (i.e., N = 13, 55, 147, 309, 561, 923) that corresponded to concentric, geometrically closed atom shells (i.e., n = 1−6). These magic numbers were consistent with the systematic packing of spheres into a family of closed icosahedral arrangements named after MacKay.127 Observed cluster sizes appeared to arise from discrete van der Waals stabilized assemblies associated with noble gases (i.e., Xe) and noble metals (i.e., Au), as well as certain main group and transition metal clusters. Related work pioneered by Wade,128 Mingos,129 and others focused on certain magic numbers and predictive periodic rules associated with borane, carboborane, and metallocene clusters. A heuristic comparison of magic numbers, electronic shell filling, atom shell filling, and monomer shell filling for atoms, metal clusters, and dendrimers, respectively, is made as illustrated in Figure 34. It should be noticed that well-defined magic numbers of electrons, metal atoms, or monomers are required to fill the outer shells of specific atoms, metal clusters, or dendrimers, respectively, as a function of atomic electron period, cluster atom shell level, or dendrimer monomer shell level (i.e., generation). As a consequence of complete outer shell filling, robust, non-selfreactive, noble gas like configurations are formed in each case which possesses precise atomic or molecular weights at each of these hierarchical levels. Reminiscent of traditional atom reactivity, it is interesting to note that metal nanoclusters possessing unfilled outer atom shells exhibit unusually high chemical reactivity compared to their geometrically closed shell counterparts.130 Similarly, soft superatoms such as dendrimers that possess unfilled outer monomer shells exhibit dramatically higher self-reactivity behavior compared to their filled outer monomer shell 2730


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cluster science, wherein “one atom makes a difference”, has been led primarily by physicists and is now undergoing explosive growth. Much of this current activity can be attributed to extensive theoretical insights led by Khanna, Jena, and others at Virginia Commonwealth University137−144 in collaboration with critical experimental effort pioneered by Castleman and others at Pennsylvania State University.63 Based on early experimental mass spectroscopy investigations by Castleman et al.,19 the unprecedented robustness and reaction behavior of Al13 clusters as a hard superatom is reminiscent of the behavior of traditional atoms. This may be rationalized and understood by a comparison of electron shell filling features of the Al13 and Al13− clusters with the traditional chlorine atom and chloride ion as shown in Figure 36. Discrete magic number, gold nanoclusters stabilized by various ligands constitute another category of hard superatoms currently under active investigation.344 Similar to atom−ligand complexes, superatoms may be electronically stabilized by association with ligands. Pioneering work by Hakkinen et al.145 has defined a unified view for all ligand-protected superatom complexes. Generally speaking, this ligand stabilization is attributable to a compact, symmetrical core and complete steric protection to produce superatoms possessing completely filled outer electron shells accompanied by major energy gaps to unoccupied states. For example, Kornberg et al.146 have reported the crystallization and X-ray structure for a discrete gold nanocluster derived from 102 gold atoms and 44 p-mercaptobenzoic acids (p-MBA). This discrete structure appears to consist of a central Au79 core surrounded by a Au23(p-MBA) shell.147 The discrete nature and superatom properties observed for this ligand stabilized nanocluster appear to be due to the closing of a 58-electron shell to give a hard superatom structure corresponding to a noble gas electronic configuration.46 This Au102 superatom was discrete and robust enough to be used as a synthetic building block and a label for site specific targeting of viral capsid surfaces as described later (Figure 56, section 4.2.3.2).148

Figure 35. Mechanism of diamagnetism is ascribed to magnetic-fieldinduced ring currents which are localized on the atoms and lead to a small magnetic moment that scales with the square of the radius and is antiparallel to the external magnetic field (A) (left). Owing to the superatom nature of clusters, the ring current operates in the delocalized valence orbitals (B) (right). The strongly enhanced diamagnetism is due to the cluster radius and the larger number of electrons involved. (Reprinted with permission from ref 134. Copyright 2014 John Wiley & Sons.)

aluminum metal cluster sizes, wherein they exhibited inertness against reactivity with oxygen. This property was later rationalized by Khanna et al.20 to be due to closed electronic shells that mimicked the behavior of noble gas elements. These unique nanoscale aluminum clusters were initially referred to as unif ied atoms.22 This work was soon followed by critical theoretical insights pioneered as early as 1992 by Khanna et al.,20,136 who noted the effect of geometry and electronic features on the stability of clusters and introduced the conceptual basis of superatoms as stable clusters that have compact geometry as well as quantized electronic shells. The introduction of superatoms provided a unified framework that could also account for the periodicity in electronic properties (ionization potential, electron affinity, and polarizability) observed in alkali and other clusters. As such, the physical and chemical properties of these subnanoscale and nanoscale cluster systems are often found to differ from those exhibited by bulk samples and display a unique dependence on CNDPs such as size, geometry, and composition. Indeed, most interesting are those systems exhibiting properties that vary discontinuously with the number of atoms and composition, rather than scale linearly with size. This realm of

3.6. First Evidence for Soft Superatoms

Extensive experimental work performed on dendrimers throughout the decade following their discovery (i.e., 1979) provided

Figure 36. Electronic levels in a Cl atom and a Cl− ion, compared with those in Al13 and Al13− clusters.20 2731


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Figure 37. Schematic representation of layer-by-layer stepwise accumulation of metal chloride in phenylazomethine dendrimer (DPAG4). (Reprinted from ref 150. Copyright 2014 American Chemical Society.)

substantial evidence for their atom mimicry properties at the nanoscale level. These atom mimicry features were first reported in the early 1990s.14,16,78 Observation of these atom mimicry features in soft nanostructures (i.e., dendrimers) was largely due to the demonstrated structural control and associated new emerging properties that accompanied their stepwise construction from the atomic to the nanoscale level. This continuum of structural control (i.e., atomic → molecular → nanoscale) included all six of the critical hierarchical design parameters (CHDPs), namely, size, shape, surface chemistry, rigidity/ flexibility, architecture, and elemental composition. The emerging properties included the usual traditional properties expected at the atomic/molecular level followed by new unprecedented, periodic nanoscale properties that emerged as a function of generational level in the dendrimers. These generationally dependent, periodic dendrimer properties have been referred to collectively as dendritic ef fects.37,149 As described earlier in sections 3.2−3.4, first published reports citing dendrimer-based nanoscale atom mimicry and their soft superatom behavior appeared in the early 1990s.14,16,78 These reports compared at least three features found in each system,16 namely, (a) hidden infrastructure symmetries observed in both dendrimer monomer shells and atom electron shells, (b) aufbau of dendrimer monomer shell filling (i.e., generations) compared to the aufbau of atom electron shell filling (i.e., periods), and (c) certain surface chemistry reactivity/inertness associated with partially/completely filled outer generational or electronic shells in dendrimers and atoms, respectively. Finally, it is indeed remarkable that the very highly ordered, atom-like features present in dendrimers have recently been shown to serve as versatile ligation templates for “atom by atom assembly” of metals to produce hard superatoms as described below (see Figures 37−39) and reviewed elsewhere.345

etry as illustrated in Figure 37 and later in section 4.2.3.6 (Figure 61). Subsequent metal reduction within these dendrimer templates produced a variety of precise “hard superatom nanoclusters” which could be controlled “atom by atom.” Hence the “soft

3.7. Using Soft Superatoms (i.e., Dendrimers) as Host Templates for the Synthesis of Hard Superatoms (i.e., Metal Nanoclusters)

Figure 38. Dendrimer-based “superatom synthesizer” that allows programmed “atom by atom” ligation of metals involving interior metal salt ligation followed by reduction to zerovalent metal nanoclusters (metal superatoms). (Reprinted from ref 150. Copyright 2014 American Chemical Society.)

Pioneering work by Yamamoto et al.150 has now shown that soft superatom dendrimers (i.e., phenylazomethane dendrimers) may be used as template hosts for the precise atom by atom interior placement of guest metal atoms to form discrete metal nanoclusters. These metal encapsulation events occur stoichiometrically as part of a very well-defined sequence beginning at the dendrimer core and proceeding outwardly as a function of generation. These generation specific ligation events are mathematically predictable to produce well-defined stoichiom-

superatom dendrimer templates” have been referred to as hard superatom synthesizers as shown in Figure 38. As early as 1997, work by Tomalia et al.151,152 demonstrated that commercially accessible poly(amidoamine) (PAMAM) dendrimers (NanoSynthons LLC, Polysciences, Inc.) could also be used to encapsulate a wide variety of metal salts including 2732


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Figure 39. Schematic process involving (a) templated metal complexation in the dendrimer interior and (b) reduction of dendrimer interior complexed metal salts to zero valence metal clusters. This provides a precision “atom by atom” synthesis strategy for producing hard superatoms (i.e., metal nanoclusters). (Reprinted from ref 151. Copyright 1998 American Chemical Society.)

Figure 40. (a) Measured and predicted ion mobility cross sections for gold cluster cations. (b) Calculated low-energy isomers of gold cluster cations. (Reprinted with permission from ref 154. Copyright 2002 American Institute of Physics.)

Figure 41. (a) Excitation (dashed) and emission (solid) spectra of different gold nanoclusters. Emission from the longest wavelength sample was limited by the detector response. Excitation and emission maxima shift to longer wavelength with increasing initial Au concentrations, suggesting that increasing nanocluster size leads to lower energy emission. (Reprinted with permission from ref 163. Copyright 2004 American Physical Society.) (b) Gold nanocluster (core) within the PAMAM dendrimer (shell) (i.e., AuNC@PAMAM).

templates for systematically assembling precise gold clusters (Au)n with metal multiplicities (n) of 3−38. They utilized tertiary amine moieties in the soft, superatom-type, poly(amidoamine) (PAMAM) dendrimer interior as ligating templates much as described above by Yamamoto. By carefully controlling the amount of gold reagent added to the dendrimer, followed by reduction, one could sequentially produce, a systematic series of jellium-type, gold clusters; n = 3−12, as shown in Figure 40.

gold, silver, copper, cadmium, lead, nickel iron, cobalt, etc. which when allowed to react with hydrogen sulfide produced watersoluble metal sulfides in their encapsulated forms. Dendrimer encapsulated metal salts such as gold, silver, and copper were readily reduced to produce zerovalent metal nanoclusters151,152 as described in Figure 39. Subsequent work by Zheng, Dickson et al.153 showed that these PAMAM dendrimers could be used as unique host 2733


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Continued addition of gold readily led to the first saturated atom shell species, namely, n = 13. Quite surprisingly, these “jelliumtype gold superatoms” exhibited an unprecedented new emerging property, namely, size dependent fluorescent emission properties much as observed for traditional cadmium chalcogenide, semiconducting quantum dots. Analogous to semiconducting quantum dots, small jellium-type gold nanoclusters (i.e., 800 nm) as shown in Figure 41a. Both excitation and emission maxima shift to lower energy emission as a function of gold concentration. This suggests that larger gold clusters are produced to give a size tunable gold cluster fluorophore which may be engineered to emit as desired from the UV to the infrared region. 3.8. Brief Overview of Nanoscale Atom Mimicry, Nanoperiodicity, and the Taxonomy of Hard/Soft Superatoms

It is notable that core−shell type architectural patterns are observed for essentially all hard/soft superatom types exhibiting nanoscale atom mimicry. As illustrated in Figure 42a, core−shell patterns with discrete multiple shell levels are noted for all the major hard 0-D nanoparticle types, whereas within the soft 0-D nanoparticle types (Figure 42b) only dendrimers and perhaps viral capsids display such discrete core−shell features. In all cases, the outer corona of surface chemistry exhibited by these discrete hard/soft nanoparticles plays some role in defining certain nanoscale atom mimicry features. This is especially true if they display well-defined outer shell valency properties as they interact to form stoichiometric nanocompounds or assemblies. The “jellium model” is a critical guiding principle for evaluating new superatom candidates.10,65 In this system, all the charges of the nuclei and core electrons in the cluster are uniformly distributed throughout the cluster spheroid. As such, the energy levels for electrons interacting with such a charge distribution correspond to 1S2, 1P6, 1D10, 2S2, 1F14, 2P6, etc. As opposed to traditional atomic energy levels, the first valence shell of a superatom contains s, p, d, and f orbitals. Therefore, a filled superatom electron shell is defined by a “magic number” which coincides with an exceptionally stable filled electronic state. Just as traditional atomic elements exhibit characteristic properties that associate it with a particular group in the periodic table, so does this occur for the various superatom categories. Currently superatom reactivities have been shown to mimic rare gases,19 alkaline earth elements,23 alkali metals,165 multivalent elements,166 and magnetic atoms.167 Similarly recent work by Nakajima168 et al. has shown that superatom mimicry may be attained by changing the central atom of M@Si16, where M = Ti, Zr, or Hf.

Table 1. Photophysical Properties of PAMAM-Encapsulated Gold Nanoclusters in Water163 gold cluster

excitation (fwhm) (eV)

emission (fwhm) (eV)

quantum yield (%)

lifetime (ns)

intrinsic decay rate (×109 GHz)

Au5 Au8 Au13 Au23 Au31

3.76 (0.42) 3.22 (0.54) 2.86 (0.38) 1.85 (0.21) 1.62 (0.20)

3.22 (0.45) 2.72 (0.55) 2.43 (0.41) 1.65 (0.26) 1.41 (0.10)

70 42 25 15 10

3.5 7.5 5.2 3.6 −

0.2 0.056 0.048 0.042 −

Figure 42. (a) Taxonomy of core−shell architectures possessing multiple shells associated with major hard superatom type nanoparticles. (b) Taxonomy of core−shell architectures associated with major soft superatom nanoparticles. Note: Dendrimers constitute the only soft superatom category possessing a core with multiple concentric shells. (Reprinted with permission from ref 6. Copyright 2009 Springer.) 2734


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Figure 43. (A) Taxonomy of hard superatom categories and their electron filling properties relative to traditional elements and a heuristic comparison of hard superatom categories to traditional atomic element types based on outer shell electron count. (B) Taxonomy of soft superatom categories (i.e., dendrimers) and their monomer filling properties relative to traditional elements in the periodic table (see Figure 30 for a comparison with chlorine). A heuristic comparison of soft superatom categories to traditional atomic element types based on outer shell monomer count (see section 3.4.1.2 and Figures 29−31).

heuristic atom mimics,6,17,24,172,173 artificial atoms or colloidal atoms.18,346 Historically, the physics perspective has focused primarily on nanoscale atom mimicry associated with inorganic, hard superatoms, as well as their electron orbital behavior, electron shell closure, and geometrical atom shell closure. Defined as any collection of atoms that exhibits certain characteristic properties of elemental atoms, an early example of a hard superatom was the observed clustering of sodium atoms from the vapor state into magic numbers of atom clusters (i.e., 2, 8, 20, 40, 58, etc.). The first two magic numbers in this series (i.e., 2, 8) are recognized as the number of electrons required to fill the first and second electronic shells, respectively. As such, this superatom mimicry is related to new cluster orbitals defined by free electrons associated collectively with the atoms in the cluster rather than each individual atom. Chemically speaking, superatoms appear to behave analogously to traditional atoms in a way that allows them to attain closed shells of electrons in this new cluster electron orbital counting scheme. Pioneering physicists including Khanna, Castleman, Jena et al.,23,64 Hakkinen,145 and others174 have demonstrated examples of hard superatoms, many of which involved metal atom clusters. On the other hand, chemists have focused largely on nanoscale atom mimicry6,24,39,175,346 associated with well-defined nanovalency, nanosterics, nanostoichiometries, monomer aufbau, and shell closings observed in soft superatoms as described in section 3.4. Dendrimers which are soft, organic heteroatomic nanoclusters provided the window to these special features and properties which were first noted in the early 1990s.14,78 For example, it was observed that dendrimers possessing unfilled outer monomer shells exhibited a propensity to be highly selfreactive, leading to the formation of dimers or oligomers. On the other hand, ideal outer monomer shell saturated dendrimers did not exhibit this self-reactivity, which is reminiscent of the noble gas atomic elements. Other discrete soft nanoparticles, such as proteins, viral capsids, DNA/RNA, nanolatexes, polymeric micelles, and monodispersed synthetic polymers have exhibited

From this perspective, a general classification of various hard superatoms has evolved based on valence electron count and their mimicry of certain traditional element types. As such, at least four major categories are beginning to emerge for hard superatoms, namely, (1) superatom noble type gases (i.e., with a closed shell), (2) superhalogens (i.e., one electron less than a closed shell), (3) superalkalis (i.e., one electron more than a closed shell), and (4) superatomic alkaline earth metals as illustrated in Figure 43A. Similarly, this same heuristic comparison to traditional element types can be made with soft superatoms such as dendrimers. By invoking a monomer count in the dendrimer outer shell or generation (see earlier discussion section 3.4.1.2 and Figures 29−31), emergence of these same four superatom categories as described above becomes apparent and is as indicated in Figure 43B. A recent consensus has evolved between chemists and physicists beginning in 2012169 (an invited lecture to the American Physics Society)18 concerning the general concepts of nanoscale atom mimicry, nanoscale superatoms, nanoelements, and nanoperiodicity.2 Although the two disciplines had been working in parallel worlds on these same concepts/issues for nearly two decades, this interdisciplinary consensus has now grown to recognize nanoperiodicity, atom mimicry and stoichiometric, nanoelements/compounds. Most importantly, there is mutual agreement on the existence of hard/soft superatoms that consist of discrete nanoscale atom collections (i.e., 103 larger than atoms) that actually manifest many physicochemical and building block features reminiscent of individual picoscale atoms.64,170 These chemically bonded or supramolecularly assembled collections of atoms are generally structure controlled entities that exhibit well-defined CNDPs such as sizes (i.e., masses), shapes, surface chemistries (i.e., valency), flexibilities/rigidities, atomic compositions, and architecture. In fact, this consensus has grown to include an expanded range of terminology which includes nanoscale superatoms,23,64,166,170 atom equivalents,171 nanoelements,6 2735


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Figure 44. Overview of a “systematic nanoperiodic concept and framework.” Based on first-principles defining the “central dogma” for traditional chemistry, several new emerging criteria developed for critical nanoscale design parameters (CNDPs), nanoscale atom mimicry, superatoms, nanoelement categories, nanoscale stoichiometric reactions/assemblies, nanocompounds/assemblies, and nanoperiodic property behavior were applied to well-defined hard (inorganic) and soft (organic) nanoparticles. This treatment produced at least 12 nanoelement (i.e., superatom) types which were classified into six hard particle and six soft particle nanoelement (i.e., superatom) categories. Chemically bonding or supramolecular assembly of these hard and soft nanoelements leads to hard:hard, soft:hard or soft:soft type nanocompound/nanoassembly categories. Many examples of these hard/soft superatoms and superatom derived nanocompounds/assemblies have been reported in the literature. Discrete, CNDP quantized features associated with these nanoelements, superatoms, and their nanocompounds/assemblies inextricably influence the manifestation of well-defined nanoperiodic property patterns, many of which are reported in the literature. (Reprinted with permission from ref 6. Copyright 2009 Springer.)

and defining nanoscience has been proposed. Just as 19th century first-principles led to a central paradigm and a periodic system for traditional atom/small molecule chemistry, it is now proposed that a similar nanoperiodic system might be defined for discrete, well-defined nanomodules as described in section 4.

explicit nanoscale atom mimicry and have been referred to as soft nanoelements/superatoms. More specifically, many of these heteroatomic, soft, organic nanoclusters exhibit chemical and supramolecular combining patterns to produce well-defined stoichiometric nanocompounds and closed shell-type behavior normally associated with traditional elemental atoms. Based on a plethora of literature based experimental data, these hard/soft superatoms or nanoscale atom mimics appear to fulfill a pivotal functional role as quantized nanoscale building blocks reminiscent of elemental atoms at the pico/subnanoscale level. From this perspective, these poly(atomic) structures/entities have been classified and referred to as hard and sof t nanoelement categories.6,24 As such, nanoscale atom mimics have been shown to form stoichiometric nanocompounds/assemblies that exhibit well-defined intrinsic nanoperiodic property patterns much as atomic elements and their compounds. As a consequence of these “nanoscale atom mimicry” features, many hard/soft superatoms clearly manifest predictable nanoproperty patterns. It is becoming recognized that these experimentally documented nanoperiodic property patterns constitute primary evidence for a broad paradigm upon which a new nanoperiodic system for unifying nanoscience has been proposed.6 More specifically, this nanoperiodic paradigm based on the dependency/influence of six critical hierarchical design parameters (CHDPs) provides a sound scientific foundation of first-principles for understanding why these well-defined nanoscale building blocks (i.e., both soft/hard nanoelements) combine in well-defined stoichiometries and exhibit nanoperiodic property patterns reminiscent of traditional atomic elements. In the context of this perspective and using “traditional chemistry first-principles” initiated by Lavoisier, Dalton, Mendeleev, and others, a new systematic framework for unifying

4. A SYSTEMATIC NANOPERIODIC CONCEPT AND FRAMEWORK FOR UNIFYING AND DEFINING NANOSCIENCE There is general agreement that one of the greatest challenges facing today’s interdisciplinary field of nanoscience is the absence of a central paradigm, as well as a nanomaterials classification/ taxonomy roadmap for organizing and defining the growing number of discrete, stoichiometric nanostructures and assemblies that are appearing in the literature.175 4.1. A Systematic Nanoperiodic Concept/Framework Roadmap

Many of the technical issues described above were examined as the focus of a National Science Foundation (NSF) Workshop (2007) entitled, “Periodic Patterns, Relationships and Categories of Well-Defined Nanoscale Building Blocks”.176 A consensus of optimism and possibilities for a systematic nanoperiodic concept and framework did emerge from this NSF Workshop. It was based on many anecdotal observations described by the participants, as well as a plethora of unorganized literature documentation. Foremost, in a partial list of critical issues/topics was the following: (1) the need for developing a taxonomy/ classification for well-defined nanoparticle types, (2) examples and the implications of nanoscale atom mimicry, (3) observed nanoscale combining stochiometries reminiscent of traditional atom/molecular chemistry, (4) defining critical design parameters influencing nanoparticle relationships, etc. Subsequent 2736


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Figure 45. Six soft superatom types, namely, (1) dendrons/dendrimers, (2) nanolatexes, (3) polymeric micelles, (4) proteins, (5) viral capsids, and (6) DNA/RNA, respectively, designated by shorthand notations: [S-n], where n = 1−6. Six hard superatom types, namely, (1) metal nanoclusters, (2) metal chalcogenide nanoclusters, (3) metal oxide nanoclusters, (4) silica nanoparticles, (5) fullerenes, and (6) carbon nanotubes, respectively, designated by shorthand notations: [H-n], where n = 1−6. Three combinatorial libraries of possible hard−hard, hard−soft, and soft−soft superatom based binary nanocompounds/assemblies, respectively. Those combinations designated by “×” are reported in the literature and described elsewhere.6,24,25,37 A limited number of nanocompounds/assemblies derived from binary soft/hard superatom combinations designated by “∗” are described in section 4.2.

nanoperiodic property patterns usually associated with traditional atoms. These nanoperiodic property patterns may be arbitrarily classified as either intrinsic physicochemical or functional/application types. Examples of these nanoperiodic property patterns are abundantly documented and pervasive throughout the literature.6,24,25,37 It is now recognized, that these unique nanoperiodic property patterns are inextricably directed by their six structure-controlled critical nanoscale design parameters (CNDPs). Recent evidence has confirmed that these CNDP directed patterns/trends define many important nanoperiodic rules and Mendeleev-like nanoperiodic tables much as observed for traditional elemental atoms and their CADPs in the 19th century as was illustrated earlier in Figure 8.

extensions of this effort evolved into an embryonic conceptual framework consisting of (a) a nanomaterials classification roadmap, (b) a table of well-defined nanomodule (element) categories (i.e., superatoms), (c) combinatorial libraries of nanocompounds/assemblies, and (d) many observed examples of nanoperiodic property patterns in the literature. Much of this early stage thinking was described as part of an NSF report in 2008176 and subsequently expanded into a peer reviewed journal article in (2009)6 with the addition of appropriate post workshop results and enhancements.6,18,24,25 This expanded perspective focused primarily on well-defined, monodisperse (0-D/1-D) nanoscale materials and the division of these well-defined materials into hard and soft nanoparticle categories. These two categories reflected critical features associated with traditional inorganic and organic materials such as rigidity/flexibility, architectural criteria, and elemental compositions (Figure 44). There is now substantial evidence showing that important CADP and CMDP information may be strictly conserved and effectively transferred from the atomic/ molecular level to these hard/soft nanoelement categories/ superatoms by using appropriate synthesis and assembly protocols.6,16,63,150 These nanoscale construction protocols are based on specific assembly principles that ensure strict structural control of their CNDPs. By controlling these CNDP features, it was found that these structure controlled nanoconstructs exhibited certain intrinsic features that mimicked traditional properties/behavior of atoms (i.e., atom mimicry) and are now referred to as hard/soft nanoelement categories or hard/soft superatoms.2 A consequence of these superatom features/properties, is their intrinsic ability to react or self-assemble into combinatorial libraries of stoichiometric, hard−hard, hard−soft, or soft−soft nanocompounds or nanoassemblies (see Figures 44−46). Furthermore, these hard/soft nanoelements/superatoms and their nanocompounds/assemblies were found to exhibit many

4.2. Chemical and Supramolecular Combinations of Soft/Hard Nanoelements (i.e., Superatoms) To Create Combinatorial Libraries of Stoichiometric Superatomic Nanocompounds/Assemblies

The first table of well-defined, quantized soft matter (organic) and hard matter (inorganic) nanoelement categories, referred to as soft and hard superatoms, have now been defined and reported as described in (Figure 44). This first choice of superatom/ nanoelement categories, based on selection criteria and assumptions described elsewhere,6,18,24,25,39 is reminiscent of Dalton’s first table of 20 atomic elements published in 1808 which rapidly expanded throughout the 19th and 20th centuries to a current list of over 115 elements. It is expected that this first abbreviated list of soft/hard nanoelement categories/superatoms will undoubtedly be expanded and further refined in the future. These first 12 soft and hard nanoelement (superatom) categories have been designated [S-n] and [H-n], respectively. Many examples of these first 12 hard/soft superatoms and their stoichiometric nanocompounds and assemblies are reported in the literature. These hard/soft nanoelements (superatoms) and their nanocompounds are widely recognized to exhibit many unique new emerging properties. Quite 2737


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Figure 46. Schematic illustrations of (a) a self-similar, giant nanocluster obtained from the self-assembly of 55 smaller nanoclusters, each consisting of 55 metal atoms resulting from two (n = 2), geometrically closed metal shells. This giant nanocluster is designated as (M55)55. (b) Series of self-similar, giant Pd nanoclusters possessing various magic number nuclearities (i.e., 13, 55, 147, 309, 541, and 1415 metal atoms). The illustrated series of circles corresponds to the respective diameters of the various magic number clusters varying from Pd13 to Pd1415. (c) TEM image of Pd561 nanocrystals forming giant clusters. The numbers correspond to the proposed number of nanocrystal shells designated by n. (Reprinted from ref 53. Copyright 2001 American Chemical Society.)

4.2.1.2. (Gold)25 Superatom-Ligated Nanocompounds [(H1)13(H-1)12:(Thiolate)18] = [(Gold)25:(Thiolate)18] Nanocompound. Jin et al.177 report the synthesis and X-ray structure for an unusually stable (Au)25-type nanocompound which results from the combination of an Au13 superatom with 12 gold atoms

remarkably, they are also observed to manifest unprecedented CNDP directed nanoperiodic property patterns6,24,25 reminiscent of those exhibited by traditional atoms and their molecular compounds. Within the three combinatorial libraries of possible nanocompounds (Figure 45), there are many well-documented examples reported in the literature. Some of these literature examples are designated by “×” (see Figure 45 and are extensively reviewed elsewhere.6,20,22−25,32,64,106 Due to the overwhelming number of such examples in the literature, in this account we will focus on only a limited number of these hard/soft superatom nanocompound and assemblies which are designated by “∗” (see Figure 45). 4.2.1. Hard−Hard Nanocompounds/Assemblies. 4.2.1.1. Metal (Au, Pd) Superatom Nanoassemblies; (Metals)n; [H-1]13, [H-1]55, [H-1]147, etc.; Assembly into Self-Similar, Spherical (Icosahedral) Aggregates. Extensive studies by Rao et al.53,131 and Schmid et al.132,133 have shown that elemental gold and palladium atoms self-assemble into discrete, well-defined, closed core−shell, self-similar, spherical aggregates. The first core−shell aggregate is a metal cluster consisting of a single metal atom surrounded by a shell of 12 metal atoms. It is notable that this stoichiometry is predicted and consistent with the Mansfield−Tomalia−Rakesh equation as described in Figure 79.124 These core−shell aggregation structures are systematically formed by sequential, concentric self-assembly of metal atom shells (n) to produce well-defined, discrete aggregation numbers for each metal shell level (i.e., metal atom shell, magic saturation numbers). This self-assembly process is illustrated for (Pd)n, showing a distribution of well-defined core−shell Pd nanoclusters derived from discrete, stoichiometrically defined numbers of metal atoms as shown in Figure 46. These are stoichiometric hard superatom nanoassemblies derived from systematic atom shell filling as described earlier by Knight et al.10 for sodium atom nanoclusters and are larger than their “jelliumtype” precursors. It is indeed noteworthy that the oxidation behavior of various sized gold nanoparticles demonstrated that saturated atom shell, [H-1]-type, hard superatom, namely, n = 2; Au55 exhibited the greatest resistance to oxidation. This nonreactive surface chemistry property observed for this closed-atomic magic cluster Au55 is reminiscent of traditional noble gas behavior.55

Figure 47. Crystal structures of various (Au)n cluster precursors leading to a Au25(SR)18 cluster architecture (where R is phenylethyl group): (A) icosahedral Au13 core; (B) Au13 core plus the 12 exterior Au atoms; (C) the whole Au25 cluster protected by 18 thiolate ligands (for clarity, only S was shown; magenta, Au; yellow), S). (Reprinted from ref 177. Copyright 2008 American Chemical Society.)

stabilized by 18 thiolate groups as illustrated in Figure 47. It is speculated that the Au13 is formed first followed by the “atom by atom” growth of the outer Au12 shell which is stabilized by ligation with the thiolate groups. 4.2.1.3. Aluminum Superatom Nanocompounds [H-1]13I; Aluminum Cluster (i.e., Super Halogens) Exhibiting Combining Properties Reminiscent of Traditional Elemental Halogens. An inspection of the electronic aufbau and electron levels in traditional chlorine atom/ion and the corresponding hard superatom Al13 and Al13 − clusters (Figure 48a) clearly illustrates the nanoscale mimicry and the predicted behavior of the Al nanocluster as a hard superatom. As such, Castleman, Khanna, et al.64 demonstrated the expected super halogen combining behavior by observing the formation of Al13I− in the mass spectrometer (Figure 48c) and determining that the electronic charge density resided primarily around the Al13 cluster as shown in Figure 48b. 4.2.1.4. Self-Reaction of a Superatom (i.e., Al13−) To Produce the Superatom-Based Al23− Nanocompound. Example of a Hard Superatom Derived, [H-1]23− Type Nanocompound. Based on mass spectrometry stability studies, 2738


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Figure 48. Electronic levels in a Cl atom and a Cl− ion compared with those in Al13 and Al13− clusters. (a) Lowest energy structure for Al13I−. (b) Charge density map of the HOMO for Al13I−. Color code: blue, aluminum; red, iodine. (c) Mass spectra showing the reaction of aluminum clusters with HI: growth of Al13I− peak in the presence of oxygen demonstrates the cluster’s stability. (Reprinted from ref 63. Copyright 2014 American Chemical Society.)

Figure 49. (a) Reaction of 2Al13− to form the superatomic molecule Al23−. (b) Reaction of two Au13 clusters to form various superatomic molecules (i.e., Au23, Au25). (Reprinted with permission from ref 178. Copyright 2014 The Royal Society of Chemistry.)

Figure 50. Examples of cyclical cluster-assembled materials consisting of Al13 superatoms and K3O ligands with a class of repeating or multidecker sandwich structures. (a) Calculated binding energies and ionization potentials for discrete molecules created from ultrahalogenic Al13 clusters and KnO and NanO units. (b) Larger molecular assemblies with ultra-alkali K3O and Na3O motifs. (Image adapted from ref 165. Copyright 2007 American Chemical Society.)

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Figure 51. Combining a C70 acceptor with an Et-group functionalized donor ligand produces a face centered cubic nanolattice, whereas reaction of a C60 acceptor with a Me-group functionalized donor ligand produces a rhombohedral nanolattice. (Reprinted with permission from ref 32. Copyright 2013 American Association for the Advancement of Science.)

Figure 52. TEM micrographs and dimensions (nm) of [core: EDA]; dendri-{poly(amidoamine)-(NH 2)n}; (G = 5−10) (PAMAM) dendrimers. Combining a limited amount of amine terminated PAMAM, G = 7 (i.e., soft superatom (core reagent; [S-1]G=7), with an excess of carboxylic acid terminated PAMAM, G = 5 (i.e., soft superatom (shell reagent [S-1]G=5)), to produce a covalent [S-1(G):(S-1(G))n] core−shell type nanocompound with 1:13 stoichiometry, wherein all surface dendrimers are carboxylic acid terminated.116

Tsukada and Koyasu178 hypothesized that two Al13− superatoms may react to form the stable superatomic molecule Al23− as described in Figure 49a. That withstanding, there may also be evidence that a similar reaction occurs between two Au13 superatoms as illustrated in Figure 49b. 4.2.1.5. Oligomerization of Superatom Al13 with Ligands To Form Cyclic Al13 Superatomic Molecular Oligomers. Calculated binding energies (Figure 50a) suggest the use of ultrahalogenic Al13 clusters as a building block reactant with ultra-alkali K3O ligands to form superatomic molecular oligomers as shown in Figure 50b.165

Other related strategies utilizing hard, superatom-type, metal nanoclusters in polymerization schemes have also been reported.179−181 4.2.1.6. Fullerene: Metal Chalcogenide Superatom Nanoassemblies; [H-5:H-3]-Type Nanolattices. It has been shown by Roy et al.32 that superatom nickel tellurides [H-3] function as donor reactants when combined with superatom fullerene [H-5] acceptors to produce superatom based nanolattices as illustrated in Figure 51. By merely changing the size of the fullerene acceptor (i.e., C60 → C70) and the donor ligation surface chemistry from a Me to an Et group on the [H-3] superatom reactant, one could readily change the crystal structure of the resulting nanolattice from rhombohedral to face centered cubic. 2740


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These superatomic lattices exhibited very interesting size and surface chemistry dependent nanoperiodic magnetic properties which will be described later (section 5.3.4; Figure 71). 4.2.2. Soft−Soft Nanocompounds and Assemblies. A wide variety of [soft−soft] type nanocompounds/assemblies (Figure 45) derived from amphiphilic dendrons have been reported in the literature as noted in Figure 53. For example, Percec et al.182 have produced vast libraries of stoichiometric spherical/cylindrical supramolecular dendrimers [S-1]n by the self-assembly of certain amphiphilic [S-1]-type amphiphilic dendrons as described in Figure 53. These constructs may be viewed as superatomic nanocompounds/assemblies derived from [S-1]-type superatoms, much as oligomeric S8 is viewed to be an allotropic type, molecular compound derived from the atomic element sulfur. Merely combining soft superatoms such as dendrimers with other dendrimers has produced soft superatom based nanocompounds possessing well-defined stoichiometries116 which are referred to as core−shell tecto(dendrimers) or [S-1:(S-1)′n]-type core−shell nanocompounds. Similarly, the covalent grafting of linear-PEGs poly(ethylene glycols) to dendrimers is reported to produce discrete, stoichiometric [S-1:(S-3)n]-type core−shell compounds.120 4.2.2.1. Soft Superatom Based [Dendrimer(G)−(Dendrimer(G))n]; [(S-1(G)):(S-1′(G))n] Core−Shell Type Nanocompounds. Soft superatom based nanocompounds (Figure 52) are routinely synthesized using a two-step approach. The first step of this approach involves the charge neutralized, selfassembly of excess carboxylic acid terminated dendrimers [S-1G] (i.e., shell reagent) around a limited amount of a core reagent such as an amine terminated dendrimer [S-1′G] (i.e., core reagent) in the presence of LiCl. This self-assembly step is then followed by the use of a carbodiimide reagent107,116,183 to produce robust covalent amide bond formation between the core and dendrimer shell reagents referred to as core−shell tecto(dendrimers). These soft, superatom based stoichiometric nanocompounds possess saturated outer shells and are prime examples of stoichiometrically precise, covalent polydendrimer clusters. The number of outer shell reagent dendrimers that may be attached to the core defines the valency of the core and may be mathematically predicted by the Mansfield−Tomalia−Rakesh equation (Figures 32 and 79).17,124 These structures have been verified unequivocally by experimental mass spectrometry, gel electrophoresis, and atomic force field microscopy (AFM).17,107,110,111,116,183 4.2.2.2. Self-Assembly of [Dendrons]n; [S-1]n into Supramolecular Spherical/Cylindrical Dendrimer-Type Nanocompounds/Assemblies. Some of the best examples of stoichiometric, supramolecularly assembled [dendrons]n; [S-1]n-type nanoassemblies (i.e., supramolecular megamers) are contained in the enormous libraries of spherical/cylindrical supramolecular dendrimers reported by Percec et al.182,184,185 Using a variety of simple amphiphilic dendrons, Percec et al. demonstrated some of the most compelling examples of heuristic atom mimicry and nanoperiodic property patterns reminiscent of atomic building blocks. Most notable was the ability to use primary dendron CNDP features such as size, shape, and surface chemistry to predict periodic property patterns leading to new emerging properties, specific architectures/morphologies, and stoichiometric mass combining ratios. Just as atomic elements such as phosphorus and sulfur self-assemble into discrete P4 and S8 clusters, respectively,186 so do appropriately functionalized Percec dendrons (Figure 53). It is widely recognized that earlier Zimmerman-type dendron self-assemblies187,188 have generally

Figure 53. Supramolecular self-assembly of Percec-type amphiphilic dendrons (i.e., [S-1]-type nanoelements) into spherical supramolecular dendrimers (i.e., [S-1]n, where n = discrete, stoichiometric aggregation numbers ranging from 72 to 155. The interior morphologies in this series follow a periodic continuum (i.e., small solid to large hollow interiors) for these various [S-1]n-type stoichiometric nanocompounds/ nanoassemblies) that is directed by specific CNDP features present in the primary structure of the amphiphilic dendron precursors. (Image adapted in part from ref 185. Copyright 2008 American Chemical Society.)

involved only small, single-digit aggregation numbers; however, Percec’s amphiphilic dendrons have generally required large double digit aggregation numbers of dendrons to self-assemble into supramolecular dendrimers. For example, spherical supramolecular dendrimers exhibiting new emerging properties such as interior hollowness have involved aggregation numbers of 72− 155.185 Recently, such a remarkably large supramolecular dendrimer has been reported which required the self-assembly of 770 dendrons (i.e., 1.73 × 106 g/mol).184 This hollow, spherical giant supramolecular dendrimer completes a periodic continuum of dendrimer morphologies (i.e., solid to hollow interiors) that has been defined between small filled and large hollow dendrimers. This periodic, interior morphology continuum (i.e., small solid to large hollow interiors) defines a unique sequence of emerging properties for this series of supramolecular dendrimers. These new emerging properties appear to be directed solely by the well-defined CNDP features contained in the primary structure of the precursor dendrons. As such, this provides compelling evidence for the ability to design predictable new emerging nanoscale properties into these selfassembling dendrons by systematically engineering the CNDPs present in the primary structure of the amphiphilic dendron precursor. 4.2.2.3. (Dendrimers)n; [S-1]n; Formation of Self-Similar, Spherical Aggregates (i.e., Supramolecular Megamers) by Supramolecular Self-Assembly. It is noteworthy, that Tomaliatype, soft superatom PAMAM dendrimers (i.e., [core: NH3]; (3 → 2); dendri-{poly(amidoamine)-(CO2Na)48}; (G4.5)) selfassemble into [S-1]n based supramolecular, core−shell type aggregates as shown in Figure 54a. Such self-assemblies are reminiscent of those observed for hard superatom (Pd)n; [H-1]ntype nanoclusters (Figure 46). These self-similar aggregation patterns were also noted by Amis et al.,99 who described corroborating TEM studies that confirm similar aggregation properties for high generation (i.e., G = 10) amine terminated PAMAM dendrimers. It is believed that these spheroidal dendrimers are self-assembling much like metal nanoclusters to give closed atom-like shells/aggregates such as [S-1]13, [S-1]55, [S-1]147, etc. (Figure 54a) which then aggregate into larger assemblies as shown in Figure 54b. However, a systematic 2741


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covalent attachment of fullerenes to produced precise [S-1:(H4)n]-type core−shell structures (Figure 55). On the other hand, combining dendrimers with hard superatom, metal nanoclusters has produced a variety of unique (i.e., [(H-1)n:S-1] and [(S-1): (H-1)n] core−shell type nanocompounds.96,280,281 Dendrimers have also been used as templates to produce precisely sized [H-1] (core): [S-1] (shell) type nanoassemblies as described earlier (Figures 37−39), as well as [H-3]-type, metal oxide nanocrystals which have exhibited interesting quantum size effects as described elsewhere.24,150,345 4.2.3.1. [Dendrimer−(Fullerene)n]; [S-1:(H-5)n] Core−Shell Type Nanocompounds. Allowing a [core:1,2-diaminoethane]; {dendri-poly(amidoamine)-(NH2)64}; (G = 4), PAMAM dendrimer to react with an excess of buckminsterfullerene (C60)119 readily produced high yields of covalent, soft−hard, [dendrimer (core): fullerene (shell)] nanocompounds. Using an excess of (C60), it was determined that only 30 (C60) moieties bonded to the dendrimer surface to produce a well-defined, stoichiometric [dendrimer (core):fullerene (shell)] nanocompound] (i.e., [S-1: (H-5)30] core−shell type) as shown in Figure 55. These structures were extensively characterized by MALDI-TOF, TGA, UV−vis, and FTIR. New emerging properties such as fullerene-like solubility and fullerene-type surface chemistry were observed. More specifically, unique singlet (1O2) type photoproperties were noted which could now be readily generated in either aqueous/organic solvents, whereas other hybridized features included larger sizes and nanocontainer type metal encapsulation properties that would normally be associated only with the dendrimer core interior. 4.2.3.2. Viral Capsid−(Gold Nanocluster)n Type Nanocompounds; [(S-5):(H-1)102]. Hakkinen et al.148 site specifically conjugated multiples of maleimide functionalized [H-1]-type gold nanocluster superatoms to several enteroviruses (i.e., echovirus 1 and coxsackie virus B3). This was accomplished by utilizing the selective reaction of the maleimide function with region-specific presentations of cysteine sites on the viral surface to produce [S-5]:[H-1]n type nanocompounds. These nanocompounds exhibited very well-defined cysteine site patterns on the viral capsid surface which could be observed by TEM as shown in Figure 56. 4.2.3.3. Gold Nanocluster:Viral Capsid; [(H-1)1−2 core:(S-5) shell] Type Nanocompounds. The first example of a hard superatom (i.e., [H-1]; gold nanocluster) encapsulation into the interior of a soft superatom (i.e., [S-5; viral capsid]) was reported by Dragnea et al.191 This investigation reported the successful

Figure 54. (a) Proposed closed shell, soft superatom dendrimer clusters by analogy to closed shell, hard superatom metal nanoclusters. (Reprinted with permission from ref 54. Copyright 1990 Elsevier Ltd.) (b) TEM of soft nanoparticle, [core: NH3]; (3 → 2); dendri{poly(amidoamine)-(CO2Na)48}; (G = 4.5) based [S-1]n aggregation structures which appear reminiscent of hard nanoparticle, gold and palladium based; [H-1]n type nanoclusters (Figure 46). (Reprinted from ref 189. Copyright 1998 American Chemical Society.)

determination of precise aggregation numbers for these selfassembly processes has yet to be reported. It should be noted that AFM studies reported by Astruc et al.190 clearly demonstrate that his ferrocenyl functionalized metallodendrimers exhibit similar discrete, aggregation behavior on a mica surface much as metal atoms behave in monodisperse metal nanoclusters. As described by Astruc, his metallodendrimers behaved like atoms by forming relatively monodispersed nanoaggregates for all generations below G = 7. 4.2.3. Soft−Hard Nanocompounds. Various combinations of soft and hard superatoms to produce well-defined covalent, ionic, or supramolecularly derived soft−hard nanocompounds appear to be largely dependent on the presence of suitable superatom surface chemistry in each case. In many cases, interesting new emerging properties are observed to arise from these combinations. For example, it is interesting to note that combining a hard superatom such as fullerene with a soft superatom such as dendrimers, possessing suitable surface chemistry, can lead to

Figure 55. Soft−hard superatom based, core−shell structures confirmed for the PAMAM core:fullerene shell; [S-1:(H-5)30] core−shell type nanocompounds, where Z = terminal −NH2 or −NH− groups on the soft superatom PAMAM dendrimer core component of the core−shell nanocompound.119 (Reprinted with permission from ref 24. Copyright 2010 The Royal Society of Chemistry.) 2742


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Figure 56. Site-specific targeting of enterovirus capsid by functionalized monodisperse gold nanoclusters. (Reprinted with permission from ref 148. Copyright 2014 National Academy of Sciences USA.)

Figure 57. (a) Transmission electron micrographs (TEMs) of dissociated and reassociated BMV virions enclosing Au nanoparticles (dark spots) with diameters between 2.5 and 4.5 nm. (b) Rayleigh resonance spectra from two different selected BMVs containing pairs of gold nanoclusters. A double peaked spectrum is explained through close association particle coupling, while a single peak spectrum is assigned to particles which are too far apart to couple. (Reprinted from ref 191. Copyright 2003 American Chemical Society.)

Figure 58. (a) Transmission electron micrograph (TEM) of negatively stained virus-like particles (VLPs) obtained by encapsulating functionalized gold clusters (black centers, 12 nm) with BMV capsid proteins. (b) Comparison of encapsulation yields for citrate, TEG functionalized Au cluster, and native RNA. TEMs of (c) empty BMV capsid, (d) citrate-coated VLP, and (c) TEG functionalized VLP. (Reprinted from ref 193. Copyright 2006 American Chemical Society.)

spectrum (Figure 57b) while a single-peak spectrum is assigned to separated particles too far apart to couple. Similarly, it was shown that CdSe/ZnS quantum dots could be encapsulated into BMV capsids to give [(H-2)2−3 core:(S-5) shell] type nanocompounds.192 4.2.3.4. Gold Nanocluster (core)−Viral Capsid (shell): [(H-1) core:(S-5) shell] or [(H-1) core:(S-4)180 shell]. Dragnea et al.193 have utilized functionalized gold nanoclusters (16 ± 2 nm) as

encapsulation of gold nanoclusters (i.e., 2.5−4.5 nm) into a single brome mosaic virus (BMV) capsid. The icosahedral BMV capsid is composed of 180 protein subunits and has a diameter of 28 nm (Figure 57a). Although the encapsulation efficiency was low (i.e., ∼ 2%), the Rayleigh resonance spectra revealed that those viral capsids containing two tightly associated gold nanoclusters (i.e., coupled particles) exhibited a double peaked 2743


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templates around which they were able to self-assemble protein subunits derived from BMV to produce new virus-like particles (VLPs). These templated self-assemblies were possible by designing the gold nanocluster sizes and electrostatic surface chemistry to match the inner BMV capsid diameter and to mimic nucleic acid components involved in the formation of native viruses. These symmetrical VLP structures were shown to have an encapsulation efficiency of greater than 95% and possessed protein/Au cluster stoichiometry of ∼180 protein/Au cluster. They exhibited icosahedral packing behavior with a diameter = 26 ± 2 nm and were similar to the native virus as shown in Figure 58. These hard core−soft shell structures are designated as [(H1) core:(S-4)180 shell] type core−shell nanocompounds. 4.2.3.5. Protein−Gold Nanocluster; [S-4:H-1] Nanocompounds. A glutathione ligated gold nanocluster (Au71) was

Figure 60. Generation selective, layer-by-layer, precise templating of four different metal salts within a dendrimer to produce a stoichiometric, hetero-four-component metal core−shell superatomic nanocompound, namely, [(H-1Fe)2:(H-1Ga)4:(H-1Au)8:(H-1Sn)16]@[S-1] core−shell type nanocompound. (Reprinted from ref 150. Copyright 2014 American Chemical Society.)

shape, surface chemistry, and elemental composition in the synthesis of DNA programmable superatom-derived lattices.These hard−soft superatom lattices exhibit atom equivalency which is consistent with the CNDP-driven nanoperiodic concept. This seminal work has shown that soft superatoms such as [S-6] (i.e., DNA) may be combined with a variety of hard superatoms such as [H-1], [H-2], and [H-3] using suitable superatom surface chemistry (i.e., click chemistry) to produce hard−soft superatomic nanocrystal lattices that exhibit remarkable atomlike features (Figure 62).

5. CNDP DIRECTED NANOPERIODIC PROPERTY PATTERNS, RULES, AND NEW EMERGING PROPERTIES

Figure 59. Separation of Au71 MPC−scFv conjugate from unreacted scFv on Mono Q. An SDS gel stained for protein (Coomassie blue) and for gold is shown. The scFv eluted at 130 mM NaCl (lane 1) while the conjugate eluted at 190 mM NaCl (lane 2). (Reprinted from ref 194. Copyright 2006 American Chemical Society.)

5.1. Traditional Picoscale, Atomic Element Periodic Patterns Preceding the Emergence of Mendeleev’s Periodic Table

Similar to the development of axioms for geometry, Newtonian physics, or Darwinian biology, traditional chemistry developed a central idea (dogma) during the 19th century based on Mendeleev’s periodic table. This periodic table provided a systematic, CADP based framework of elemental features/ properties upon which this discipline could be defined, unified, and grown. Historically, it is interesting to note that many minor elemental periodic property patterns were documented and accumulated before final consolidation occurred to the framework of Mendeleev’s periodic table.9 A small sampling of these well-known minor periodic element property patterns is as described below: • elemental chemical and physical properties repeated in a series of periodic intervals as a function of atomic number both horizontally and vertically123 • valency in the early elements appeared to increase as a function of atomic number • Newland’s “law of octaves”121,123 • Dobereiner’s “law of triads”121,123 • De Chancourtois’s “telluric screw” which demonstrated periodic property patterns that appeared to repeat or become similar after every sixteen atomic weight units9 Nearly all of these picoscale, atomic level periodic relationships are now recognized to be dependent upon CADPs. Similarly, analogous nanoperiodic property patterns are currently accumulating for nanoscale hard and soft supertoms. Many CNDP dependent nanoperiodic property patterns have been docu-

conjugated to a single chain Fv antibody fragment (scFv) which had been raised against influenza neuramidase proteins.194 These [H-1:S-4] supermolecular conjugates were proposed to function as gold labeling reagents for the characterization of viruses. Successful synthesis of this superatomic molecular conjugate was confirmed by polyacrylamide gel electrophoresis (PAGE) as illustrated in Figure 59. These gold cluster−antibody fragment conjugates were shown to be very effective labeling agents that formed stoichiometric adducts with targeted proteins residing on the viral capsid surface.194 4.2.3.6. [(Iron)2; (Gallium)4; (Gold)8; (Tin)16] (Core):Dendrimer (Shell); [(H-1Fe)2; (H-1Ga)4; (H-1Au)8; (H-1Sn)16]:[S-1] Core−Shell Type Nanoassemblies. Based on the specific binding constants exhibited by various metals for the interior ligation sites located within Yamamoto-type dendrimers, it was possible to produce precise, four component, stoichiometric heterometal core−shell nanoassemblies as illustrated in Figure 60.150 Yamamoto et al.150 described a wide range of soft superatom dendrimer templates based on the number of dendrons in the dendrimer, that exhibited discrete metal ligation stoichiometries varying from 1 to 61 as shown in Figure 61. 4.2.3.7. Atom Equivalency Demonstrated by Formation of Predictable Superatomic Lattices. Mirkin et al.171 have validated the importance of controlled CNDPs such as size, 2744


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Figure 61. Various Yamamoto-type [core:p-phenylene]; (G = 4); {dendri-poly(phenylazomethine)} (DPA) dendrimers containing from one to four dendrons. These dendrimer templates possess a wide range a wide variety of quantized, regiospecifically located metal ligation sites (i.e., stoichiometries 1−61 as indicated above) suitable for synthesizing, stoichiometric metal nanoclusters. (Reprinted from ref 150. Copyright 2014 American Chemical Society.)

5.2.1. Intrinsic Dendrimer-Based Periodic Chemical Reactivity/Physical Size Property Patterns. Dendron/ dendrimer based, [S-1]-type soft superatom nanoelements exhibit completely different physicochemical properties (i.e., nanoperiodic property patterns) compared to compositionally isomeric traditional polymers. These property differences are largely due to the core tethered dendritic architecture that induces congestion properties (see section 3.2.1). These unprecedented nanoperiodic property patterns are uniquely characteristic of dendrons and dendrimers and emerge as a function of generational growth (Figures 17 and 18). For example, at least four intrinsic features such as intrinsic viscosity [η], density (d), surface area per Z group (Az) and refractive index for a Tomalia-type PAMAM dendrimer series (Figure 63) exhibit systematic, nanoperiodic patterns as a function of generation. These data clearly show intrinsic viscosity [η] maxima or minima at generations 3−5 and are corroborated by computer-assisted molecular-simulation predictions,16,195 as well as extensive photochemical probe experiments reported by Turro et al.73,86−89,196

mented in the literature and are expected to provide compelling evidence for nanoperiodicity. There is no doubt that collectively these nanoperiodic property patterns will eventually evolve into a grand, encompassing framework which should be expected to define an ultimate version of a Mendeleev-like nanoperiodic system. A small sampling of such examples is presented in section 5.2. 5.2. CNDP Directed, Soft Superatom Nanoperiodic Property Patterns

As one examines the literature from the CNDP driven nanoperiodic perspective described earlier, it soon becomes apparent that there is an abundance of reported examples. We have arbitrarily categorized these property patterns into two categories, namely, intrinsic and functional/application types. As such, the sheer number does not allow an exhaustive overview and we present only a few specific cases followed by a sampling of examples for soft superatoms, hard superatoms, and their combinatory libraries of superatomic nanocompounds as described in Tables 2 and 3, respectively. 2745


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Figure 62. Synthesis scheme for nanoparticle-based PAEs. (a) Hydrophobic-ligand-capped nanoparticles were first functionalized with an amphiphilic polymer containing both hydrophobic alkyl chains (which intercalated with the hydrophobic capping ligands on the nanoparticle, shown as gray brushes) and hydrophilic carboxylates and azide (green) modified ethylene glycol groups and solubilized the particles in aqueous solvent. These particles were then functionalized with DNA using dibenzocyclooctyl (purple) terminated DNA strands and azide−alkyne click chemistry to produce a dense DNA shell around the nanoparticle. Multiple different inorganic particle cores, labeled with different colors, QD (blue), Fe3O4 (red), Au (dark yellow) and Pt (dark brown) were used each capped with different hydrophobic ligands. (b) Gel electrophoresis analysis of QD-PAEs, imaged both under white light (left) and under ultraviolet light (right). (c) DLS analysis of hydrophobic-ligand-capped QDs, N3-PMAO-coated QDs and QD-PAEs. (Reprinted with permission from ref 171. Copyright 2013 Nature Publishing Group.)

where Az is the surface area per terminal group Z, AD is the dendrimer surface area, and Nz is the number of surface groups Z per generation. This relationship predicts the surface area per Z group at higher generations (G) and becomes increasingly smaller as it finally approaches the cross-sectional area or van der Waals dimension of the surface groups Z at higher generations. Dendritic congestion resulting at higher generations (G) due to tethering to a common core is referred to as de Gennes densepacking.16 Ideal dendritic growth without branch defects is possible only for those generations preceding this dense-packed state. This critical dendrimer property gives rise to self-limiting dendrimer dimensions, which are a function of the branch cell segment length (l), the core multiplicity Nc, the branch cell juncture multiplicity Nb, and the steric dimensions of the terminal group Z. The dendrimer radius (r) in the above expression is largely dependent on the branch cell segment lengths l. Larger l values would be expected to delay congestion. On the other hand, larger Nc and Nb values and larger Z dimensions dramatically enhance congestion. These congestion properties are unique for each dendrimer family and are determined by specific values for l, Nc, and Nb. These three parameters determine the lowest generation level within a dendrimer family that will exhibit nanoencapsulation properties. Higher Nc and Nb values are expected to produce enhanced surface congestion properties, thus causing guest encapsulation features to occur at lower generation levels as shown in Figure 65. These congestion issues are observed as intrinsic nanoperiodic patterns and are characteristic for all dendrimer families, including so-called giant redox active metallodendrimers recently reported by Astruc et al.190 5.2.2. Size and Surface Chemistry Dependent Nonradiative Energy Transfer between InGaN Quantum

Dendrimer-based intrinsic viscosities [η] initially increase in a classical fashion as a function of molar mass (generation), but dramatically decline beyond a critical generation due to a congestion induced shape change. A dendrimer shape change occurs from an extended, compressible, floppy configuration in the early generations (i.e., G = 0−3) to more rigid globular shapes in the later generations (i.e., G = 4−10) (see Figure 18). In effect, Tomalia-type PAMAM dendrimers within this series act more like an Einstein spheroid at critical generations (i.e., G = 3− 4 and higher). In another instance, Yamamoto et al.196 clearly demonstrated precise internal stoichiometries for chelating a wide range of metals with phenylazamethine dendrimers. The intrinsic, mathematically defined, valency properties exhibited by this dendrimer family served as periodic templates for synthesizing a variety of precise [H-1]n type hard superatoms.150 Similarly, Betley et al.183 clearly demonstrated with atomic force microscopy studies that dendrimers exhibit well-defined, monodispersed molecular volumes as a function of generation and pH as shown in Figure 64. Intrinsic viscosity is a physical property expressed in deciliters per gram, which in essence is the ratio of volume to mass. As the generation number increases and transition occurs to a spherical shape, the volume of the spherical dendrimer increases in cubic fashion while its mass increases exponentially; hence, the value of [η] must decrease once a certain generation is reached. This prediction has now been widely confirmed for many different dendrimer families.16,198,199 Dendrimer surface congestion may be appraised mathematically as a function of generation according to the following simple relationship: Az =

AD r2 ∝ Nz NcN bG 2746


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Table 2. Nanoperiodic Property Patterns Observed for Soft Superatoms

Nanoelement (Intrinsic Physicochemical) Periodic Properties encapsulation: [S-1],16,85,150−153,201 [S-4],202,203 [S-5]202,203 melting points/glass transition temperatures: [S-1]204−206 reactivity/sterics: [S-1],16,94,207 [S-2],208 [S-4]94 refractive indices: [S-1]16 self-similar aggregation: [S-1]69,99,209 valency/directionality: [S-1],16,94,210 [S-2],208 [S-4],94,210 [S-6]211,212 viscosity: [S-1]16,213 surface chemistries: [S-1],25,37,214 [S-4]215 super atomic lattice formation: [S-1],182,216 [S-4],203 [S-5],203 [S-6]217 shape control: [S-1]96,218 shape directed self-assembly: [S-1],182,184,219 [S-3],219 [S-4],219 [S-5]219 size directed self-assembly: [S-1]182,184 architectural forms: [S-6]220 Nanoelement (Functional/Application) Periodic Properties catalysis: [S-1],202,221 [S-4],202 [S-5]202 electronic: [S-1]172,222 imaging: [S-1]223−225 magnetic: [S-1]226 nanotoxicity: [S-1]227 photonics: [S-1]228,229 nanomedicine: [S-1],98,224,227,230,231 [S-3],231 [S-4]231

behavior232 as a function of nanoparticle dimensions (Figure 67). Such a size dependent periodic property does not exist in bulk materials of the same elemental composition. The magic numbers associated with these closed shell saturation levels have been widely documented by mass spectrometry.233 These closed shell, metal nanoclusters not only exhibit systematic periodic melting point phenomena (Figure 67), but also represent a very important intrinsic nanoperiodic property pattern for all hard superatom nanoclusters.234 Many other CNDP directed, nanoperiodic property patterns observed for hard superatoms (i.e., nanoelements) are as described in Table 3. 5.3.2. CNDP Directed Nanoperiodic Property Patterns (i.e., Stoichiometries and Symmetries) Observed in Superatomic Lattice Structures. Bottom-up self-assembly of quantized building blocks such as atoms, molecules, and welldefined nanoparticles (i.e., hard/soft superatoms/nanoelements) is a fundamental theme found in chemistry, biology, and materials science. Recent seminal work focused on binary nanoparticle superlattices (BNSLs)267 has clearly demonstrated the pivotal role and dramatic influence that CNDPs impose on the stoichiometry, periodicity. and architecture of a wide range of (BNSLs) (Figure 68). Just as atom radius ratios play a significant role in determining binary atomic crystal structure at the picoscale level, so does one observe similar atom mimicry behavior with hard superatoms at

Wells (QW) and Poly(amidoamine) (PAMAM) Dendrimers as a Function of Generation. Recent work200 has shown that PAMAM dendrimers perform very efficient nonradiative energy transfers between semiconducting InGaN quantum wells (QWs) and the dendrimers as a function of dendrimer generation. An exponential increase in energy transfer efficiency from the QWs to the PAMAM dendrimer is observed as a function of generation (Figure 66). The authors propose a new dendrimer based FRET system, wherein the energy from the InGaN QWs is transferred to the PAMAM dendrimers via optical wave guiding. 5.3. CNDP Directed Hard Superatom Nanoperiodic Property Patterns

5.3.1. Size-Directed Nanoperiodicity: Systematic Melting Point Variation as a Function of Dimensions (i.e., Metal Nanoclusters [H-1]-Type Hard Superatoms). At the nanoscale level, CNDPs involving specific sizes are known to dramatically influence both electronic and physical properties including melting points. For example, as one systematically reduces dimensions as occurs in a series of magic number closed shell metal nanoparticles (Figure 67), one can expect an enhancement in the percentage of surface atoms. However, if the coordination number of the surface atoms becomes smaller than 9, then these surface atoms become more prone to rearrange than those in the interior, thereby leading to earlier flow and observed melting point events. It is believed that these nanoparticle size factors directly influence the systematic decreases in melting points and associated melting point 2747


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Table 3. Nanoperiodic Property Patterns Observed for Hard Superatoms

Nanoelement (Intrinsic Physicochemical) Periodic Properties superatomic, electronic shell filling: (a) superatomic noble gases: [H-1]10,19,63 (b) superatomic halogens (VIIA group): [H-1]23,63,64 (c) superatomic alkalis (1A group): [H-1],63 [H-3]165 (d) superatomic alkaline earth metals (IIA group): [H-1]63,166 (e) Magnetic super atoms (VIIB/VIIB group): [H-1]167,235 superatomic, atom shell filling: [H-1],33,51,236 [H-5]33 encapsulation: [H-5]33 melting points: [H-1]33,232,234 fluorescence: [H-1],162,237,238[H-2]239 unfilled versus filled atom shell reactivity: [H-1]130 self-similar aggregation: [H-1]51,53 valency/directionality reactivity → polymers: [H-1]180,240179 conductivity: [H-1]241 cluster size (jellium) versus nanoparticle size (plasmonic): [H-1]238,242 superlattice formation: [H-1]217,239 shape control: [H-1],243,244[H-2]245 band gap control: [H-1]246 Nanoelement (Functional/Application) Periodic Properties catalysis: [H-1],150,247 [H-3]247 electronic: [H-1],241 [H-2]239 imaging: [H-3]248,249 magnetic: [H-3],250 [H-1]134,238 nanotoxicity: [H-4],251,252 [H-5],253,254[H-6],249,255,256 photonics: [H-1],171,238,257,258 [H-2]259,260 photodynamic therapy: [H-1],261 [H-2],261 [H-3]261−264 nanomedicine: [H-1],265 [H-3],231[H-4],231 [H-6],249,266

Figure 64. Soft superatom, PAMAM dendrimer molecular volumes (nm3) as a function of generation and pH. Dendrimer samples deposited on mica from solutions of pH 1 (blue diamonds) and pH 6 (red triangles). The green squares depict the theoretical volumes for generations 5−9 based on known molecular weights and estimated densities. (Reprinted from ref 183. Copyright 2002 American Chemical Society.)

Figure 63. Comparison of intrinsic dendrimer properties such as viscosity (η), density (d), refractive index, and surface area/headgroup (Z) and as a function of generation: G = 1−9.16,197 (Reprinted with permission from ref 73. Copyright 2001 Wiley VCH Verlag GmbH & Co. KGaA.)

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Figure 65. Congestion induced dendrimer shape changes (I, II, III) with development of nanocontainer properties for a family of [core: 1,2diaminoethane]; (4 → 2); dendri-{poly(amidoamine)-(NH2)z}; (G = 0−10) PAMAM dendrimers: Nc = 4; Nb = 2, where Z−Z = distance between surface groups as a function of generation. (Reprinted with permission from ref 24. Copyright 2010 The Royal Society of Chemistry.)

illustrated in Figure 68B. A wide range of semiconducting, metallic, magnetic, and plasmonic superatom building blocks have been utilized in this strategy.269 Many other similar examples have been overviewed elsewhere.65 It has been shown by O’Brien et al.267 that important CNDPs such as size, shape, surface chemistry (i.e., surface wetting), and elemental composition can dramatically influence the packing symmetry, stoichiometries, and new emerging properties of the resulting super nanolattices as shown in Figure 69. 5.3.3. Dependency of Nanoperiodic Fluorescent Emission Patterns on Superatom Size. Comparison of Metallic Gold Nanodots with Semiconducting Metal Chalcogenides (i.e., Quantum Dots). Very interesting size dependent nanoperiodic property patterns have been observed for quantum confined metal nanoclusters (i.e., [H-1]-type (Au)n and [H-2]-type (CdS)n quantum dots). For example, one observes size dependent fluorescence emissions for [H-1]-type, hard superatoms such as gold nanoclusters. For the smallest gold nanocluster sizes of Au3−Au13 (i.e., jellium type), the cluster emission energies fit very well with the energy scaling law EFermi/ N1/3, wherein N is the number of atoms in each cluster. This suggests that electronic structure transitions of these small Au particles are best described by a spherical harmonic potential well (see Figure 70a). Increasing N (i.e., Au23 → Au33 and above) gradually distorts the potential energy well to a Woods−Saxon type potential and eventually a square well potential characteristic of larger metal nanocluster sizes.163 It is interesting to note that size dependent fluorescence emission properties are observed for both gold nanoclusters and semiconducting quantum dots (i.e., emission energies (eV) and decrease as a function of N). That withstanding, the scaling law for semiconducting quantum dots differs from that for metal nanoclusters by adhering to the one electron, artificial atom Bohr-type model, namely, N−2/3 as illustrated in Figure 70b. 5.3.4. Surface Chemistry and Size Dependency on Magnetic Moments for Metal Chalcogenide: Fullerene Superatomic Lattices; [H-2]:[H-5]-Type Superatomic Lattices. It has been shown by Lee et al.270 that hard superatom nanocompounds (lattices) derived from donor-type nickel telluride clusters [H-2] and acceptor fullerenes [H-4] (i.e., C60 or C70) may be readily modified to manipulate their magnetic properties in a very predictable fashion. These investigators were able to generate predictable nanoperiodic magnetic property

Figure 66. Size dependence of the measured energy transfer efficiency as a function of PAMAM dendrimer generation. (Reprinted from ref 200. Copyright 2015 American Chemical Society.)

Figure 67. Nanoperiodic property pattern involving the relationship between superatom gold nanocluster size, total number of atoms in the metal cluster filled outer shells, and their melting points. (Reprinted with permission from ref 234. Copyright 1990 American Physical Society.)

the nanoscale level. O’Brien et al.268 have shown that nanoscale binary superlattices may be predictably manipulated to produce a wide variety stoichiometries and nanoperiodic patterns in binary superatomic lattices according to nanoscale radius ratio rules as 2749


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Figure 68. (A) The superlattices are assembled from (a) 13.4 nm of γ-Fe2O3 and 5.0 nm of Au, (b) 7.6 nm of PbSe and 5.0 nm of Au, (c) 6.2 nm of PbSe and 3.0 nm of Pd, (d) 6.7 nm of PbS and 3.0 nm of Pd, (e) 6.2 nm of PbSe and 3.0 nm of Pd, (f) 5.8 nm of PbSe and 3.0 nm of Pd, (g) 7.2 nm of PbSe and 4.2 nm of Ag, (h) 6.2 nm of PbSe and 3.0 nm of Pd, (i) 7.2 nm of PbSe and 5.0 nm of Au, (j) 5.8 nm of PbSe and 3.0 nm of Pd, (k) 7.2 nm of PbSe and 4.2 nm of Ag, and (l) 6.2 nm of PbSe and 3.0 nm of Pd nanoparticles. Scale bars: (a−c, e, f, i−l) 20 nm; (d, g, h) 10 nm. The lattice projection is labeled in each panel above the scale bar. (B) Binary superlattices can be assembled in a number of stoichiometries by merely varying the relative size ratios of the super atom building blocks in a manner analogous to the “radius ratio rules” that are used to predict assembly patterns and stoichiometries in binary atomic crystals. (Reprinted from ref 268. Copyright 2008 American Chemical Society.)

(Pt)12) exhibited higher current densities and catalytic activity compared to the larger (Pt)28−60 nanoclusters. 5.3.6. Size Dependent Cytotoxicity of [H-1] Gold Nanoclusters. Schmid et al.271 report dramatic size directed, nanoperiodic cytotoxicity properties for [H-1]-type gold nanoclusters. Cellular exposure to 1.4 nm (i.e., Au55) nanoclusters lead to rapid cell death by necrosis within 12 h, whereas closely related 1.2 nm particles lead to predominately programmed cell death by apoptosis. In contrast, larger gold nanoparticles (i.e., 15 nm diameter particles) exhibit substantially less toxicity and require 60−100-fold higher concentrations for similar effects. Based on in vitro studies, it appears that 1.4 nm (Au)55 nanoclusters bind to the major groove in natural B-DNA with high selectivity and stability. 5.3.7. Elemental Composition (i.e., Stoichiometry) Influence on Electronic States of Quantum Dots. It is well-known that quantum dot (QD) sizes and shapes dramatically influence their optoelectric properties; however, little was known about the impact of QD elemental stoichiometry on their electronic structure. Understanding this issue is of high importance for optimizing the use of QDs in many optoelectronic applications. Grossman et al.272 have recently reported that QD stoichiometry can significantly alter their structures and electronic properties. This investigation has revealed that (i) stoichiometric PbS QDs are generally free from midgap states even without ligand passivation and independent of shape; however, (ii) off stoichiometry in PbS QDs introduces new lattice structures and gap states that are highly localized on certain surface atoms, and (iii) further deviations in stoichiometry lead to QDs with “metallic” behavior with a dense number of energy states near the Fermi level. The effect of PbS-QD stoichiometry on lattice structure and electronic states is as illustrated in Figure 73.

Figure 69. In the panels above, wedges of LaF3 have been coassembled with spheres of either Ag or Au. The arrangements of the particles in the panels from left to right in the series are dictated by the energetic interaction with the surface on which the nanocrystals have been assembled. (a) On a hydrophobic amorphous surface, all particles “wet” the surface. (b) A silicon nitride membrane support provides a less hydrophobic surface, causing LaF3 wedges to orient to reduce the contact of their organic stabilizers with the surface. (c) A SiO2 substrate presents a hydrophilic surface; particles arrange to reduce the contact of the organic stabilizers further. Thus, shape and surface interactions can both be employed along with control of particle size and composition to engineer the superlattice structure. (Image adapted in part with permission from ref 267. Copyright 2006 Nature Publishing Group.)

patterns for these hard superatom nanocompounds by merely modifying certain CNDPs (i.e., fullerene size (C60 or C70) and metal chalcogenide surface chemistry components) of the [H-2]: [H-4] superatom nanolattices as shown in Figure 71. 5.3.5. Size Dependent Nanoperiodicity in [H-1]n-Type Pt Metal Nanoclusters; Kinetic Limiting Currents and Catalytic Activity; When n = 12, 28 and 60. Yamamoto et al.150 have shown that both the kinetic limiting currents and catalytic activity of platinum nanoclusters may be systematically enhanced by decreasing the Pt atom count [i.e., (N) = Pt60 → Pt28 → Pt12] of these hard superatom particles as described in Figure 72. As shown, the smaller jellium-type nanoclusters (i.e., 2750


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Figure 70. (a) Sequence of size dependent surface potentials for gold clusters at difference size scales. The small “jellium-type” clusters (i.e., Au3−Au13) fits the EFermi/N1/3 relationship. A distortion of the surface potential to a Woods−Saxon type well is observed for larger gold nanoclusters (i.e., Au23 → Au38). Sizes beyond Au38 lead to increased electron screening and the potential bounding each electron flattens, thus increasing anharmonicity to give a square well type surface potential. (b) Correlation of the number of atoms, N, per nanocluster with emission energy. Emission energy decreases with increasing number of atoms. For the spherical jellium model, N quantitatively fits EFermi/N1/3 between the spherical harmonic potential and the Woods− Saxon potential. For the one electron artificial atom (Bohr model), such as semiconductor quantum dots, N quantitatively fits EFermi/N2/3. (Reprinted with permission from ref 163. Copyright 2004 American Physical Society.)

5.4. CNDP Directed Hard−Soft Superatom Nanoperiodic Property Patterns

5.4.1. Nanoperiodic Size Dependency in Superatomic Lattice Packing. Hard superatom type, gold nanoclusters [H1] functionalized with complementary, [S-6]-type, single strand DNA building block connectors are readily self-assembled into 3D superatomic lattices as demonstrated in seminal work by Mirkin et al.273 These hard−soft superatomic lattices were reported to mimic a wide variety of 3-D Bravais-type lattices usually observed for traditional inorganic salts. This investigation not only demonstrated compelling atom mimicry and superatom features/properties, but also clearly described first examples of predictable CNDP directed nanoscale rules and mathematical relationships for these superatomic lattices. A profound CNDP dependency based on hard superatom size274 and soft superatom, DNA connector sizes was especially notable. These nanoperiodic lattice patterns and nanoscale rules were recently extended to a wide variety of hard superatoms/nanoelement categories including [H-1]-type metal nanoclusters, [H-2]-type metal chalcogenides (quantum dots), and [H-3]-type metal oxide nanoparticles as described in Figure 74. Clearly Mirkin et al. recognized the superatom/atom mimicry features they had validated by referring to these nanoclusters as atom equivalents.171 Other strategies for size controlling soft superatoms (i.e., dendrimer-linear polymer based clusters) have involved supramolecular assembly of functionalized dendrimers and linear PEI.275

Figure 71. Dependency of magnetic moments for [H-2]:[H-4]-type superatom nanolattices as a function of fullerene size and [H-2] donor surface chemistry. (Reprinted from ref 270. Copyright 2014 American Chemical Society.)

5.5. New Emerging Superatom/Superatomic Molecular Property Behavior

5.5.1. Unique New Band Gap Properties Resulting from Architecture Driven Electronic Communication within Covalent Stoichiometric Hard−Hard Superatomic Nanocompounds; [Metal Oxide:(Metal Oxide)′]; [H-3:(H-3)′]Type Nanocompounds. Hard [H-3]-type metal oxide superatoms such as TiO2 and WO3 are widely recognized to play pivotal roles in many renewable energy applications such as dye-sensitized solar cells and photocatalysts. Seminal investigations reported by Hamers et al.276 have shown that stoichiometric hard−hard superatomic nanocompounds; [metal oxide:(metal oxide)′] can be readily formed using “click-type” chemistry. This covalent click chemistry produces triazole-type heterojunction architecture between the two differentiated hard superatoms [H-3] and [(H-3)′] to form the

Figure 72. (A) Comparison of kinetic limiting currents and (B) catalytic performances normalized by the weight of platinum for different sized, hard superatom nanoparticles. (Reprinted from ref 150. Copyright 2014 American Chemical Society.)

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Figure 73. Influence of elemental composition (i.e., Pb/S stoichiometry) on electronic states of PbS quantum dots. (Reprinted with permission from ref 272. Copyright 2013 American Physical Society.)

Figure 74. Various binary superatomic lattices assembled from arbitrary combinations of hard superatoms such as QD-, DAu-, and Fe3O4-PAEs. Hard superatoms derived from these above compositions and various sizes were used to CNDP engineer and synthesize the described superlattices. These superatomic lattices were CNDP engineered as a function of hard superatom size and elemental superatom compositions, as well as soft superatom DNA connectors, wherein antiparticle distance and crystal symmetry that could be independently controlled. (a−f) SAXS data for 7 nm QD, 3 nm QD CsCl lattices (a); 7 nm QD, 4.5 nm DAu CsCl lattices (b); 8 nm Fe3O4, 4.5 nm DAu CsCl lattices (c); 8 nm Fe3O4, 7 nm QD CsCl lattices (d); 10 nm Fe3O4, 4.5 nm DAu AlB2-type lattices (e); and 20 nm Fe3O4, 7 nm QD Cs6C60-type lattices (f). Experimental data are shown in black, and predicted scattering patterns are shown in red. (g−i) STEM images of 7 nm QD, 4.5 nm D Au CsCl lattices (g); 8 nm Fe3O4, 4.5 nm DAuCsCl lattices (h); and 10 nm Fe3O4, 4.5 nm DAu AlB2-type lattices (i). The insets at the right corner are higher-magnification images with labels denoting nanoparticle composition. (Reprinted with permission from ref 171. Copyright 2013 Nature Publishing Group.)

superatomic molecular structure [H-1:H-1′] as illustrated in Figure 75. Quite remarkably, these covalent triazole heterojunctions were found to manifest very facile electronic communication between the two hard superatom components of this hard−hard superatomic nanocompound. Evidence supporting this contention was obtained by illumination of these [metal oxide: (metal oxide)′]; [H-3:(H-3)′]-type nanocompounds. Irradiation

showed that the covalent triazole heterojunction connecting the WO3/TiO2 superatom components induced charge separation. This charge separation facilitated electrochemical oxidation at the TiO2 nanoparticle surface accompanied by a corresponding reduction reaction at the WO3 particle surface leading to enhanced photocatalytic activity. This unprecedented electronic communication between the dyadic superatom components presumably involves a separated electron−hole pair type 2752


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Figure 75. Covalent assembly of an alkyne modified hard TiO2 superatom with an azide functionalized hard WO3 superatom to produce a triazole heterojunction linked hard−hard [H-1:H-1′] type superatomic nanocompound using traditional click chemistry. (Reprinted from ref 276. Copyright 2012 American Chemical Society.)

Figure 77. Experimental and theoretical band gap energies for 23 cluster assembled materials. The bar graph and symbols indicate the experimental and theoretical band gap energies. The symbol indicates the class of arsenic-based cluster used in the assembly. Red corresponds to As7, green corresponds to Pd-linked As7, yellow is gold-linked As7, gray is Zn- or Cd-linked As7, and blue is M(CO)3As7; M = Cr, Mo, W. The control of the dimensionality through choice of linkers is shown with the synthesis of 0-D Au2(As7)24 assembly, a 1-D Au2(As7)24 assembly linked by K, a 2-D Au2(As7)24 linked by Cs, and a 3-D assembly of Zn(As7)24 linked by Cs. (Reprinted from ref 277. Copyright 2013 American Chemical Society.)

Figure 76. Proposed sequential stages in photoinitiated charge transfer between hard superatom WO3 and hard superatom TiO2 components linked with a triazole heterojunction. These sequential stages involve absorption (left), followed by hole migration (center), with the resulting separated electron−hole pair (right). (Reprinted from ref 276. Copyright 2012 American Chemical Society.)

mechanism as shown in Figure 76. This work provided critical evidence for electronic communication through an extended triazole heterojunction linking the two hard superatom components that heuristically mimicked traditional molecular bonds between picoscale atoms. This work clearly indicates that covalent chemistry using “click chemistry” triazole architecture may be an important alternate strategy to the usual linear combination of superatomic orbitals to produce useful superatomic molecular structures. 5.5.2. Unique Emerging Band Gap Properties by Manipulating Dimensional Architecture (i.e., 0-D, 1-D, 2-D) for Superatomic, Hard−Hard Ionic Lattices. Engineering superatomic nanoassemblies also offers the ability to control band gap energies by merely changing the superatomic assembly dimensionality. In a synergistic effort by Khanna and co-workers, this potential was demonstrated by synthesizing and characterizing at least 23 cluster assemblies based on Zintl polyvalent ions. In these assemblies, anionic As73− was combined with countercations including alkali metals and cryptated K+ ions as well as building motifs that included Zintl ions covalently linked with Hg, Zn, Cd, Pd, etc. These synthesized assemblies possessed dimensionalities ranging from 0-D to 3-D, with atomic structures and observed band gap energies as shown in Figure 77. It is apparent that band gap energies may be controlled as a function of dimensionality as illustrated by the patterns shown in Figure 77. The studies revealed that the band gap energy can be varied from 1.09 to 2.21 eV. First-principles electronic structure studies identified the differing physical mechanisms that enable a control of the band gap edges. For assemblies with alkali counters, the top of the valence band is localized on the arsenic cluster, while the conduction band edge is located on the alkali metal counterions. Changing the counterion changes the position of the conduction band edge, enabling control of the band gap

energy. The architecture of the ionic solid may also be varied by incorporating cryptated counterions, which provide charge but are separated from the clusters by bulky ligands. They also found that covalently linking arsenic clusters into composite building blocks also yielded control of the band gap energy and a theoretical description based on cluster orbital theory showed how the mixing between orbitals leads to such a control.277

Figure 78. (a) [Au2(As7)2]4− and (K-crypt)+ in 1 viewed along the b axis. (b) [Au2(As7)2]4−, two arsenic clusters A and B linked through a gold dimer in 1. (c) One-dimensional arrangement of 2 as viewed along the b axis. (d) Two different naked K+ cations with [Au2(As)]4− in 2. (e) Two-dimensional distorted honeycomb-like layers of [Au2(As7)2]4− linked by Cs+ in 4 as viewed along the a axis. (f) Cs+ cations with [Au2(As7)2]4− in 4. As is red, Cs is purple, K is blue, and Au is gold; the crypt is not shown. (Reprinted with permission from ref 246. Copyright 2010 American Chemical Society.) 2753


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Table 4. Combinatorial Libraries of Soft−Soft, Soft−Hard, and Hard−Hard Nanocompounds Exhibiting Nanoperiodic Property Patterns

Nanocompound (Intrinsic Physicochemical) Periodic Properties (A, B, C) (D) (E) (E, C, F) (E) (H, I, A) (E, J, K) (L) (K) (M) (N) (O, P, E) (E, M, Q, R)

encapsulation: [S-5:H-1],193 [S-5:H-3],278 [S-1:H-2],280,281 reactivity/sterics: [H-1:H-6]279 self-similar aggregation: [S-1:H-1]51 valency/directionality: [S-1:H-1],280−283 [S-1:H-2],280,281 [S-6:H-1]211,212,279,284 atomic ordering: [S-1:H-1]31 superatomic lattice formation: [H-3]:@[S-4],203 [S-1:S-5],285 [H-1]:@[S-5]203 Nanocompound (Functional/Application) Periodic Properties catalysis: [S-1:H-1],286 [S-4:H-1],287 [H-1:H-1]288 electronic: [S-1:S-1]222 imaging: [H-1:H-1]289 magnetic: [S-1:H-3]290 nanotoxicity: [S-1:H-5]254 photonics: [H-1:H-4],265 [H-2:H-2],291 [S-1:H-1]292 nanomedicine: [S-1:H-1],293 [S-1:H-3],294 [S-4:H-2],295 [S-4:H-6]296

Figure 79. (a) Symmetry boundary properties and valencies (Nmax) for various core−shell tecto(dendrimer) structures, when r1/r2 < 1.20. (b) Sterically induced stoichiometry (SIS) defined shell capacities (Nmax), based on the respective core and shell radii, when r1/r2 < 1.20. (c) Mansfield−Tomalia− Rakesh equation for calculating the maximum shell filling value (capacity) (Nmax), when r1/r2 > 1.20.17,24,124 It should be noted that this analysis correctly predicts 12-shell atoms for hard superatoms [H-1]-type nanoelement category such as gold nanoclusters; where r1/r2 = 1.6 (Image adapted with permission from ref 17. Copyright 2005 Elsevier Ltd.)

In another study, ionic lattice architectures (i.e., 0-D, 1-D, 2D) derived from superatom clusters (i.e., [As7−Au2−As7]4−)

were synthesized with the expectation that higher connectivities (i.e., 0-D → 1-D, 2-D) would lead to decreased band gap energies 2754


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through band broadening. However, it was found that moving from zero- to two-dimensional architecture produced an increase in band gap energy (Figure 78). This work demonstrated that proximity of counterions played a pivotal role in these superatomic molecular structures by stabilizing local electronic states to give higher band gap eneregies.246 Other documented nanoperiodic property patterns (i.e., intrinsic physicochemical and functional/application types) for combinatorial libraries of superatomic nanocompounds may be found in Table 4.

6. PREDICTIVE HARD/SOFT SUPERATOM AND SUPERATOMIC NANOCOMPOUND/NANOASSEMBLY BASED NANOPERIODIC RULES AND NANOPERIODIC MENDELEEV-LIKE TABLES 6.1. Predictive Nanoperiodic Rules

Figure 80. Polyhedra are separated into four categories of organization as indicated by liquid crystals, plastic crystals, crystals, and disordered (glassy) phases. Subcategories (classes) are indicated by shades. The assembly category of liquid crystals contains the classes discotic columnar, smectic, and nematic. Plastic crystal classes are FCC (dark), BCC (medium), and TCP (light). In the case of crystals, we distinguish Bravais lattices (right side) and non-Bravais lattices (left side). “RT” stands for random tiling. For the glasses, no assembly is observed, and we distinguish those that strongly order locally with preferential face-toface alignment (light orange) from those with only weak local order (dark orange). The pie chart in the center compares the relative frequency of the 10 observed classes. In each of the classes, polyhedra are listed in decreasing order of the isoperimetric quotient. A polyhedron is included multiple times if it was found to assemble into more than one ordered structure. (Reprinted with permission from ref 219. Copyright 2012 American Association for the Advancement of Science.)

6.1.1. Valency Rules Defined by Size Dependent Spheroidal Nanosterics. The fundamental properties described earlier for dendrimers (section 5.2.1, Figures 63−66) clearly illustrate the unique and intrinsic nanoperiodic property patterns manifested by this soft superatom [S-1]-type nanoelement category. That withstanding, other nanoperiodic property patterns have been documented for the behavior, assembly, and reactions of dendrimers with other dendrimers, as well as with other well-defined soft/hard superatom categories. For example, work on this soft superatom [S-1]-type nanoelement category17,107,124 has demonstrated that mathematically defined, periodic size properties of spheroidal dendrimers can determine chemical reactivity patterns with other dendrimers. These reactivity patterns, based on the relative sizes of targeted dendrimer cores and dendrimer shell components, strongly influence the assembly stoichiometries exhibited by precise dendrimer clusters referred to as core−shell (tecto)dendrimers. Mathematical relationships (i.e., the Mansfield−Tomalia− Rakesh equation) predict dendrimer cluster saturation levels (i.e., magic numbers for dendrimer shells) as a function of the core dendrimer size relative to the size of the shell dendrimers that are being used to construct the dendrimer cluster (Figure 79).25,39,124 Quite remarkably, these periodic property patterns and magic shell relationships are reminiscent of those observed for the self-assembly of hard superatom [H-1]-type metal nanocrystals. For example, the predicted number of touching elemental metal spheroids for the first shell surrounding a central core metal atom is 12 as shown above, wherein r1/r2 = 1.00. This is a well-known value (i.e., 12 atoms) for the first shell of all core− shell, metal nanoclusters51,53,131 (Figure 79) to produce a metal cluster magic number of 13. However, when r1/r2 ≥ 1.20, enhanced space surrounding the core allows the attachment of more spheroidal shell reagents up to discrete saturation values (Nmax). This saturation value (Nmax) is discrete and can be determined from the general expression described by the Mansfield−Tomalia−Rakesh equation.124 6.1.2. Shape Directed Nanoperiodic Property Patterns Defining Self-Assembly Modes. Glotzer et al.219 have recently reported shape directed nanoperiodic property patterns for predicting the self-assembly of hard/soft superatoms. This work demonstrated that anisotropic shapes played a pivotal role and could be used to predict the self-assembly patterns for over 145 convex hard/soft superatoms including nanoparticles such as proteins or viruses. This remarkable CNDP directed influence and superatom anisotropic shape dependency subsequentially

led to a unique nanoperiodic table based on superatom polyhedral types for predicting self-assembly categories/modes as illustrated in Figure 80. The fundamental role of CNDP based shape dependency associated with these self-assembly patterns further validated and supported the proposed CNDP based nanoperiodic concept. Substantial progress has been made in controlling this CNDP feature in both hard superatoms and soft superatoms. For example, facet development during platinum nanotube growth provides a critical strategy for controlling superatom shapes.297 Many other shape controlling strategies have been reviewed elsewhere.218,243,298,299 In the case of soft superatom shape control (i.e., dendrimers), it was shown that the use of cleavable cyst amine cores96 or other shape engineered cores in combination with site selective blocking of certain core surface chemistry sites to prevent dendritic growth have become demonstrated strategies for designing shape, as well as sizes and ultimate surface chemistry of dendrimers.96,218 6.2. First Examples of Mendeleev-like, Predictive Nanoperiodic Tables for Hard/Soft Superatoms and Nanocompounds/Assemblies

6.2.1. Insights to Synthetic Mimicry of Biological Quasi-Equivalence with [S-1]-Type Amphiphilic Dendrons Reported by Percec. Klug et al.300−302 were the first to report important stoichiometric, self-assembly relationships between the genomic and the protein subunit based viral capsid components in the formation of tobacco mosaic viruses more than three decades ago. A well-defined stoichiometric relationship between the viral core and the viral capsid was observed and 2755


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Figure 81. Tobacco mosaic virus (TMV). An example of a well-defined nanocompound [S-6:(S-4)2130] consisting of an ss-RNA (core):protein subunits (shell) which has nanodimensions of diameter 18 nm and length 300 nm, and helical symmetry.302,303 (Image adapted with permission from ref 302. Copyright 1978 Scientific American.)

Figure 82. Controlling CNDPs such as size, shape, surface chemistry, and flexibility/rigidity of amphiphilic dendrons allows predictable structural engineering for self-assembling amphiphilic dendrons into cylinders or spheroids. (Image adapted from ref 313. Copyright 2007 American Chemical Society.)

are possible by the self-assembly of [S-4], [S-5], and [S-6] type soft superatoms is described elsewhere.304 More importantly, these historical observations related to the self-assembly of protein subunits to produce the discrete and exquisite TMV300,301 structures subsequently inspired Percec305 to examine analogous abiotic systems involving dendrons and dendrimers. The quasi-equivalent similarity of assembling abiotic amphiphilic dendrons into nanocylinders with the supramolecular assembly of protein subunits to produce cylindrical TMV was compared by Percec et al.306 as early as 1992. As such, abiotic dendrons were shown to produce a rich variety of cylindrical and spherical supramolecular dendrimers that exhibited quasiequivalency much as is noted in many viral capsids. Based on

carefully documented by X-ray studies. This work rigorously demonstrated that exactly 2130 protein subunits assembled to form a viral capsid shell around an ss-RNA core to produce tobacco mosaic virus (TMV) with diameter = 18 nm, length = 300 nm, and helical symmetry. Elucidation of this self-assembly process together with the unprecedented characterization of this viral assembly by X-ray analysis garnered the Nobel Prize for A. Klug in 1982. In the context of the present systematic, nanoperiodic perspective,6 this viral construct was viewed as a well-documented example of a stoichiometric, supramolecular, soft−soft superatom, core:shell [S-6:(S-4)2130]-type, superatomic nanoassembly as described in Figure 81. A recent critical review of the wide range of the sizes, shapes, compositions, and genome:protein capsid stoichiometries that 2756


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Figure 83. Typical retrostructural analysis of supramolecular dendrimers [S-1]μ derived from the self-assembly library of AB2; 3,4-disubstituted-(PBp)type amphiphilic dendrons; [S-1]. (Image adapted from refs 182 and 184. Copyright 2009 American Chemical Society.)

molecular solid angle (α′), as well as a typical transition from lamellar to columnar and spherical assemblies. Increasing the generation number does not necessarily increase the diameter of the supramolecular dendrimer (D); it tends to reduce the aggregation number (i.e., μ) or number of dendrons required to form a supramolecular sphere or cross section of a supramolecular column. Deviations from these typical patterns usually indicate the formation of hollow core supramolecular dendrimers or other novel self-assembly mechanism. Generally AB3; 3,4,5trisubstitued libraries exhibit more spherical structures when compared to AB2; 3,4-disubstituted dendron libraries. Furthermore, it was shown by Percec et al.182,184 that, simply knowing four CNDPs, namely, (a) size, (b) shape, (c) surface chemistry, and (d) flexibility of the primary dendron structure, one can predict self-assembly patterns leading to tertiary and quaternary structures with greater than 85−93% accuracy as shown in nanoperiodic tables I−III (Figures 84−87). 6.2.3. Predicting Amphiphilic Dendron Self-Assembly to Supramolecular Dendrimers Based on the Critical Nanoscale Design Parameters (CNDPs). It is widely recognized that the primary structures of proteins ultimately determine their tertiary structure. Similarly, Percec examined these same features in his amphiphilic dendrons as he compared dozens of his AB2 and AB3 derived dendron libraries in an effort to determine trends or nanoperiodic self-assembly patterns as proposed by others.6 Percec’s seminal comparison produced the first three Mendeleev-like, predictive nanoperiodic tables I−III for the self-assembly of aryl ether dendrons as illustrated in Figures 84−86. Both tertiary and quaternary structures that are formed for similar primary dendron structures are summarized in these Mendeleev-like nanoperiodic tables. These predictive nanoperiodic tables describe general trends in the sequence− structure relationship (i.e., primary → secondary → tertiary →

his engineering of dendron CNDPs such as size, shape, surface chemistry, and flexibility, Percec et al.307−310 were able to unequivocally demonstrate the quasi-equivalent mimicry of viral capsids310 as outlined in Figure 82. This remarkable comparison corroborates and documents many dendron libraries and other examples of dendron/dendrimer-based protein mimicry.96,311,312 6.2.2. Amphiphilic Dendron Self-Assembly Libraries Directed by Critical Nanoscale Design Parameters (CNDPs). The Percec group synthesized and analyzed innumerable libraries of self-assembling amphiphilic dendrons.182 Inspired by Klug’s work on TMV, the dendron primary structures were compared systematically to the tertiary structures of the self-assembled supramolecular dendrimers, as well as the final quaternary structure of the crystal lattices for each library. A sampling of these libraries reveals primary dendron structures derived from AB2; 3,4-, AB2; 3,5-, and AB3; 3,4,5-substituted dendrons, to mention a few.184 A typical library for an AB2; 3,4disubstituted biphenyl (Bp) dendron family was examined according to its respective dendron CNDPs such as generation (size), surface/apex chemistry, as well as shape and flexibility as shown in Figure 82. These analyses clearly reveal important dendron parameters such as the (a) molecular solid angle (α′) of the dendron (Figure 82), (b) morphology (shape) of the supramolecular dendrimer, and (c) aggregation number (μ) (i.e., supramolecular dendrimer stoichiometry) varied in a predictive manner to produce important self-assembly patterns as a function of dendron generation. It should be noted that very precise reproducible stoichiometries were observed for all of these dendron self-assemblies as evidenced by their discrete aggregation numbers, namely, [S-1]n (Figure 83). These library analyses also showed other interesting patterns such as increasing the generation number causes a change in 2757


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Figure 84. Nanoperiodic table I. Primary soft superatom dendron structures; [S-1] compared to three-dimensional supramolecular dendrimer structures [S-1]μ for libraries of AB3 supramolecular dendrimers. Bn, benzyl ether; Pr, phenylpropyl ether; Bp, biphenyl-4-methyl ether; BpPr, biphenylpropyl ether. (Image adapted from ref 184. Copyright 2009 American Chemical Society.)

to form lamellar structures than the other two nanotables. The columnar structures formed from G = 2 dendrons in the 3,5-table exhibit mostly hollow core type (Øh) lattices. Unlike the 3,4- and 3,4,5-tables, very few spherical structures are observed for G = 2 in the 3,5-table. The propensity for columnar self-organization in the 3,5-table is observed into G = 3−4. Unlike the 3,4- and 3,4,5tables, which form only spherical structures at the G = 3, the 3,5table, G = 3 dendrons exhibit a nearly even distribution of columnar, spherical, and lamellar structures. The high degree of architectural polymorphism observed in table III is undoubtedly due to the greater flexibility of the 3,5-branching system caused by diminished steric effects. This decreased steric crowding also contributes to the formation of columnar and lamellar structures that likely result from the highly wedge-like conformation of the dendron. This greater flexibility may also contribute to the tendency to pack into noncubic lattices of spherical supramolecular dendrimers at higher generations. In all three nanoperiodic tables (I−III), it is notable that, for a given primary dendron structure, changes in the apex chemistry (i.e., functionality) rarely perturb the type of tertiary structure or corresponding quaternary lattice structure that is formed. However, it should be noted that changing the apex group from a non-hydrogen bonding ester to a hydrogen bonding alcohol or carboxylic acid will result in decreased dendrimer size, increased phase transition temperatures, and partial or total elimination of interior pores. It is important to note that Percec’s work is solidly supported by the extensive use of X-ray

quaternary structures). Furthermore, they identify clustered regions where specific structures may be expected to be found. The various supramolecular dendrimer structures formed may be classified into lamellar, columnar, or spherical morphologies by analogy to β-sheets, helical structures of fibrillar proteins, and the pseudospherical structure of globular proteins. In the case of the AB3; 3,4,5-trisubstituted dendron based nanoperiodic table I, most self-assemblies lead to predominately spherical structures at G = 3 and entirely spherical forms from G = 3−5. The spherical supramolecular dendrimers generally pack to form Cub-type crystal lattices. At G = 1, the columnar structures form various Ø lattices. At G = 2, columnar structure pack almost exclusively into the Øh lattice. In the case of the AB2; 3,4-disubstituted dendron based nanoperiodic table II (Figure 85), the G = 1 dendrons are the same as table I. At G = 2, the 3,4-disubstituted table is similar to the 3,4,5-trisubstituted table, forming mostly spherical and hollow spherical structures. At G = 2, the 3,4-table differs, containing lamella, unknown, and more hollow columnar structures clustered around the (4-(3,4,5))2; 12G = 2 primary structure. At G = 3−4, only spherical structures are observed. As is the case with the 3,4,5-trisubstituted nanotable, most of the spherical supramolecular dendrimers form Cub-type lattices. The AB2; 3,5-disubstituted dendron based nanoperiodic table III (Figure 86) exhibits a much greater degree of architectural polymorphism than the 3,4- and 3,4,5-tables. For example, G = 2 dendrons in the 3,5-nanotables have a much greater propensity 2758


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Figure 85. Nanoperiodic table II. Primary dendron structures; [S-1] vs 3-D supramolecular dendrimer structure; [S-1]μ relationships for all 3,4disubstituted libraries of AB2 supramolecular dendrimers. Bn, benzyl ether; Pr, phenylpropyl ether; Bp, biphenyl-4-methyl ether; BpPr, biphenylpropyl ether. (Image adapted in part from ref 184. Copyright 2009 American Chemical Society.)

somes,315 is extending these predictable, CNDP directed nanoperiodic principles to even higher dimensions (i.e., 80− 330 nm) and complexity. They now report the self-assembly of “single−single” amphiphilic Janus dendrimers into uniform, multilayer onion-like dendrimersomes316 (Figure 88A) with predictable sizes as high as 330 nm by simple injection of their solutions into water or buffer. Whereas the original dendrimersomes exhibited a single bilayer membrane around a core, these new entities exhibit true atom-like mimicry, wherein a desired number of bilayer membrane shells may be designed and engineered into the final onion-like nanostructure. Architecturally, this amazing structural control of soft core−(shell)n type matter allows heuristic mimicry of electron shells as found in picoscale atoms (10−12 m) and generation layers in traditional nanoscale dendrimers (10−9 m). Interestingly, they observed that the number of bilayer shells formed in these onion-like dendrimersomes can be predictably engineered by controlling the final Janus dendrimer precursor concentration used in the self-assembly process. At very low concentrations, two- and fourbilayer shells are formed as shown in Figure 88B. Increasing the Janus dendrimer concentration systematically produced more bilayer membrane shells. The number of bilayers is proportional to their radii and can be calculated from the equation N = R/α, where N and R, refer, respectively, to the number of bilayers and radius of the individual onion-like vesicle. whereas α is the average spacing between vesicle layers (Figure 88C). In conclusion, many examples of hard and soft quantized superatom behavior such as nanoscale atom mimicry,

methodologies to confirm his tertiary and quaternary supramolecular dendrimer lattice structures, much as Klug used for confirmation of his analogous TMV.302,314 6.3. First Examples of Predictive, Mendeleev-like Nanoperiodic Tables

Extensive work by Percec/Rosen et al.182 has clearly demonstrated by retrostructural analyses of tertiary and quaternary supramolecular assemblies illustrated in Figures 83−87 that CNDP directed, nanoperiodic patterns derived from the primary structures of these [S-1]-type dendron structures could be used to predict X-ray confirmed tertiary and quaternary structures as described in Figure 87. These predictions were made with an accuracy of 85−93%. By simply knowing only four CNDPs for the primary [S-1]-type amphiphilic dendrons, namely, (a) size, (b) shape, (c) apex/surface chemistry, and (d) flexibility,6,24,25 and applying these nanoperiodic patterns/rules to the combinatorial libraries of these [S-1]-type soft superatoms, it was possible to produce the first examples of predictive, Mendeleev-like, superatom-based nanoperiodic tables. In summary, the Mendeleev-like, Percec/Rosen nanoperiodic tables describing the self-assembly properties of amphiphilic, Janus-type dendrons represent some of the first examples of predictable, well-defined nanoperiodic property patterns that appear to confirm the concept of nanoperiodic property patterns and their dependency on CNDPs.6 More recent work from the Percec group, involving the selfassembly of Janus-type dendrimers to produce dendrimer2759


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Figure 86. Nanoperiodic table III. Primary dendron structures; [S-1] vs 3-D supramolecular dendrimer structures; [S-1]μ for all 3,5-disubstituted libraries of AB2 supramolecular dendrimers. Bn, benzyl ether; Pr, phenylpropyl ether; Bp, biphenyl-4-methyl ether; BpPr, biphenylpropyl ether. (Image adapted from ref 184. Copyright 2009 American Chemical Society.)

Figure 87. CNDP based dependency of self-assembly patterns leading to tertiary and quaternary dendron assemblies derived from primary structure controlled dendron CNDPs such as size, shape, surface/apex chemistry, and flexibility. (Image adapted from ref 184. Copyright 2009 American Chemical Society.)

on traditional chemistry/physics first-principles. The CNDP dependent rules/patterns and the predictive features of the new emerging Mendeleev-like nanoperiodic tables should provide invaluable tools for engineering optimal nanostructure/application properties especially in the field of nanomedicine.48 Perhaps most notably is the fact that these CNDP directed predictive nanoscale rules/tables may be initiating a predictive central

stoichiometry, new emerging properties, and new nanoperiodic property patterns/rules have appeared in extensive work reported by V. Percec, C. Mirkin, S. Glotzer, M. Banaszak Holl, P. Jena, A. W. Castleman, Jr., and P. Weiss, as well as a recent periodic table of protein complexes.347 These results appear to both fulfill and validate this present CNDP directed nanoperiodic system for defining and unifying nanoscience based 2760


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traditional picometer-sized atoms. Therefore, uniquely designed spacial arrangements and combinations of meta-atoms will yield meta-molecules and associated behavior reminiscent of traditional atoms and molecules. One of the most compelling examples of heuristic meta-atom mimicry reminiscent of traditional atoms is their chiral behavior.

Figure 89. Examples of (a) 3-D and (b) 2-D enantiomeric meta-atoms. (c) Illustration of the difference in light transmission for in-plane chiral split ring versus a straightened split ring (rod dimer) type meta-atom. (Reprinted with permission from ref 320. Copyright 2011 Optical Society of America.)

Figure 88. (A) Cross-sectional views of traditional and onion-like dendrimersome architectures. (B) Cross-sectional views of multiple bilayer membrane shells formed as a function of Janus dendrimer concentration. (C) Correlation of number of bilayers formed as a function of dendrimersome diameter according to N = R/α, where N and R, refer, respectively, to the number of bilayers and radius of the individual onion-like vesicle, whereas α is the average spacing between vesicle layers.316,317 (Reprinted with permission from ref 316. Copyright 2014 National Academy of Sciences USA.)

For example, meta-atom interactions with light are indeed similar to asymmetric properties widely recognized for traditional atoms/molecules. Examples of enantiomeric 3-D and 2-D meta-atoms are illustrated in Figure 89a,b, whereas Figure 89c shows how simple in-plane arrangements of split rings or “straightened split ring” rod dimer type structures can also interact with light to manifest profound chiral properties.320 These metamaterials are finding applications in a wide variety of advanced technology applications including negative index, invisibility cloaking,321,322 super lens,323,324 and the alteration of magnetic properties,325 to mention a few. There is currently enormous interest in engineering CNDPs−CMicDPs to produce metamaterials at a fine scale (i.e., nanosubmicron scale) such that their interactive properties with electromagnetic radiation and magnetism may be exploited in a wide range of advanced technology applications. Historically, while researching the interaction of matter with the magnetic component of light (1967), Prof. Victor Veselago (Applied Physics, Moscow Institute of Physics and Technology) proposed the possibility of light refraction with a negative sign. Up to this point, refractive index was traditionally regarded as exhibiting only positive values. As one reflects on Maxwell’s equations, a refractive index with a negative sign is the result of permittivity ε < 0 and magnetic permeability μ < 0.321,326 Veselago’s first seminal report on this topic was entitled, “The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ.”327 In this paper, he was able to show that a refractive index may also be negative. He hypothesized that negative refraction may occur when both the (electric) permittivity (ε < 0) and the magnetic permeability (μ < 0) of a material are negative. This prediction was confirmed 33 years later when his concept was validated/accepted by mainstream science largely due to a paper entitled, “Controlling Electromagnetic Fields” published by Prof. J. Pendry (Imperial College, U.K.) in 2006.328 In this work, Pendry et al. demonstrated the possibility of negative index, light cloaking devices by manipulating light as described by the Maxwell equation through the two key parameters, namely, electric permittivity (ε) and

paradigm that may be used with confidence for defining important risk/benefit/performance boundaries in the nanoscience field.

7. NEW QUANTIZED NANOSCALE/MESOSCALE BUILDING BLOCKS: METAMATERIALS AND META-ATOMS/META-MOLECULES 7.1. Brief Overview of Metamaterials

The general term metamaterials describes a new emerging class of materials not found in nature that derive their unique properties from their specifically engineered sizes, shapes, architectures, and relationships to each other. Although they are made from traditional atoms and molecules, it is their engineered CNDP/ CMicDPs, as well as their relationships to each other, that determine their specific metamaterial properties. Unlike traditional materials, their most important properties (i.e., their interaction with electromagnetic radiation and magnetism) are not due to their elemental compositions. Appropriately engineered metamaterials may be used to dramatically influence electromagnetic radiation, magnetism, or sound in a manner not possible with traditional nonengineered atomic, molecular, nanoscale, or bulk materials.3 Metamaterials usually function as periodic multiples/collections of specifically engineered units referred to as meta-atoms. Meta-atoms are nanosubmicron scale cells (i.e., material entities) with sizes smaller than the wavelength of the electromagnetic radiation they are designed to influence. In traditional materials, their unique interactions with electric and magnetic fields, as well as with photons, are determined by their specific elemental compositions.318,319 However, in metamaterials, so-called meta-cells take the role of atoms in a material that is homogeneous at scales larger than the cells. Thus, in metamaterials the meta-cell acts as a meta-atom (i.e., a larger scale magnetic dipole) and functions analogously to 2761


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Figure 90. (A) Diagram of electric permittivity (ε) and magnetic permeability (μ) and associated materials exhibiting these properties.3,330 (Image adapted in part with permission from ref 3. Copyright 2011 The Royal Society of Chemistry.) (B) Photograph of the actual metamaterial lattice used to demonstrate negative refraction. The array of square split-ring resonators gives the material a negative magnetic permeability (μ), whereas the array of straight wires gives it a negative permittivity (ε). (Reprinted with permission from ref 329. Copyright 2003 American Physical Society.)

Figure 91. (A) Systematic AFM assisted assembly of gold nanocluster based meta-atoms to produce meta-molecules (i.e., dimers, trimers, tetramers, etc.). (B) Numerically simulated and experimentally measured dark-field scattering spectra of the assembled meta-molecules including (a) monomer, (b) dimer, (c) trimer, and (d) asymmetric tetramer. The insets of (c) and (d) represent magnetic near-field distribution at 768 nm (c) and at 761 nm (d). (e) Electric near-field distribution of trimer at 768 nm (i.e., resonance wavelength of magnetic dipole). (f) Electric near-field distribution of asymmetric tetramer at 761 nm (i.e., resonance wavelength of magnetic dipole). In both trimer and asymmetric tetramer, the circulating electric fields were clearly verified at the resonance wavelength of magnetic dipole. (Reprinted with permission from ref 335. Copyright 2015 Optical Society of America.)

manner as illustrated in Figure 91. Thus, it is clearly apparent that nanoscale, hard/soft superatoms may indeed be precursors to many other as yet undiscovered meta-atoms and meta-molecules. Presumably, many recently discovered large gold nanoclusters (i.e., [H-1]-type hard superatoms) as reported by Negishi, Hakkinen, et al.242 and illustrated in Figure 92 could serve as critical nanoscale building block precursors for assembling new meta-atoms/meta-molecules according to AFM protocols described above. Thus, it is clearly apparent that nanoscale, hard/soft superatoms may indeed be precursors to many other as yet undiscovered meta-atoms and meta-molecules.

magnetic permeability (μ), which are illustrated in Figure 90.3,329,330 Within months after the Pendry submission describing possible invisibility cloaking theories and negative index materials, a practical “proof of concept” device was built and demonstrated by Smith, Schurig et al.331−334 which was shown to be effective with microwave radiation. Until recently, the development of metamaterials has relied on conventional lithographic techniques such as e-beam lithography, focused ion beam lithography, and photolithography.3 Recently very facile techniques involving the manipulation of highly spheroidal gold nanoclusters using AFM manipulations has demonstrated that certain large gold nanoclusters (i.e., ∼100 nm) may behave as meta-atoms. For example, these (Au)n metaatoms were systematically assembled into meta-molecules (i.e., monomers, dimers, trimers, tetramers, etc.) as illustrated in Figure 91A, much as shown earlier for soft superatoms such as dendrimers (see section 3.3.1, Figures 22 and 23). Quite remarkably, these gold nanocluster based meta-molecules were subsequently shown to exhibit characteristic metamaterial type electric/magnetic resonance properties in a highly reproducible

7.2. Superatoms and Meta-Atoms as Quantized Nanoscale/Mesoscale Building Blocks

The explosive evolution of nanomaterials into new emerging areas of metamaterials (i.e., especially photonic metamaterials) has been overviewed recently.336 Just as traditional atom/molecules have served as critical QBB precursors to nanoscale superatoms/molecules, it is apparent that current nanoscale building blocks (i.e., hard/soft supera2762


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Figure 92. Molecular-like gold nanoclusters (Au)n (where n = 25−144) at the interface with bulk-like (plasmonic) gold clusters (Au)n (where n = 187−520). (Reprinted from ref 242. Copyright 2015 American Chemical Society.) Figure 94. Computer generated enlargement of a boundary site in a Mandelbrot set (generated in a Graphiklabor “Dynamische Systeme” by Heinz-Otto Peitgen, P. H. Rickter, and D. Saupe, Universität Bremen). (Reprinted with permission from ref 16. Copyright 1990 John Wiley & Sons.)

toms, nanoelements) will be expected to fill that role for the evolution of new classes of large nanosubmicron building blocks, namely, meta-atoms/-molecules (Figure 93).

8. CONCLUSIONS In the natural hierarchy of matter, there is growing evidence that self-similar, quantized building blocks may behave as closepacked platonic objects (i.e., polygons in 2-D and polyhedral in 3-D)338 in concert with their CHDPs to provide a scaled assembly continuum leading to higher complexity. Widely recognized magic numbers related to hierarchical stoichiometries and atomic periodic properties (i.e., closed shell robustness/ stability or reactivity properties) appear to extend to the nanoscale level. These periodic features are indeed observed and pervasive from the picoscale to the nanoscale level and perhaps beyond. In all cases, these magic numbers are unique to the specific hierarchical level and appear to be dependent upon the six CHDPs associated with a specific level of complexity. This suggests that these scalable hierarchical QBBs may function as “self-similar,” entity sequences (i.e., nesting spheres) that provide a common thread from picoscale to macroscale complexity. These self-similar QBB sequences may be visualized in the context of a Mandelbrot-type, self-similar fractal as illustrated in Figure 94. In many cases, these scaled platonic QBB objects exhibit unique mathematically defined stoichiometric relationships, wherein this order driven complexity may involve electron counting at the CADP level, atom counting at the CMDP level, or superatom counting at the CNDP nanoscale level. Soft superatoms such as dendrimers may be analyzed from this perspective as illustrated in Figure 95.

As such, the emergence of new properties due to symmetry breaking according to Anderson4 may be observed at each discrete hierarchical level. These new emerging properties undoubtedly involve the integration of CHDP driven spacial relationships, as well as both hard and soft QBBs to produce certain quasi-self-similar hierarchical materials found in nature, including tendons, bone, and shells as described by Zhang et al.47 and Lakes339 as illustrated in Figure 96. It is indeed interesting to note that the organizational patterns observed in atomic nuclei and atomic clusters may indeed prevail well into macroscale dimensions as observed by the Nobel Laureate D. Shechtman for quasicrystals.340 The striking formation of these periodic, quasi-ordered macroscale solids strongly suggests that atomic structure may be analyzed as a quasi-self-similar periodic arrangement of clusters. For example, it is known in one class that the elementary building blocks are icosahedrons that combine to create a systematic sequence of inflated self-similar icosahedrons as illustrated in Figure 97.341,342 The stability of these icosahedra relates to the magic numbers observed in elemental atom clusters thus offering a “self-similartype” unified paradigm that may indeed link nanoscale hierarchy with macroscale quasi-periodic ordered behavior. A contemporary evolutionary biologist, Prof. A. Lima-de-Faria, has recently proposed that both symmetry and periodicity information at the atomic level is conserved and transferred through the continuum of hierarchical levels to highest

Figure 93. (A) Traditional atomic/molecular building blocks (i.e., pico-subnanoscale). (B) Superatoms/molecules (nanoscale; 1−100 nm),6,18,24,38. (C) Meta-atoms each showing charge (colors) and current (arrows) distributions for one of their modes. (a) Canon spiral, (b) V-antenna, (c) split-ring resonator, (d) sphere, (e) horseshoe, and (f) twisted crosses. (Reprinted with permission from ref 337. Copyright 2014 American Physical Society.) 2763


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Figure 95. Aufbau-type roadmap directed by mathematically defined, bottom-up critical hierarchical design parameters (CHDPs) for constructing and transferring CADP → CMDP information to produce the CNDP conserved nanoscale, soft superatom [S-1]-type nanoelement complexity. (Reprinted with permission from ref 39. Copyright 2005 Elsevier Ltd.)

Figure 97. Planar cross section of the (AlPdMn) quasicrystal structure. The self-similar rings consisting of 10 atoms are the primary building blocks. (Reprinted with permission from ref 341. Copyright 1996 American Physical Society.)

Figure 96. Quasi-self-similar hierarchical material. Every structure level consists of slender hard matter inclusions (blue) aligned in a parallel staggered pattern in the soft matrix (gray). The aspect ratios may vary from level to level. The inclusions of the (n + 1)th level are made of the staggered microstructure at the nth length. (Adapted with permission from ref 47. Copyright 2011 The Royal Society.)

These QNBBs exhibit varying degrees of atom mimicry. This mimicry is related to certain reactivity patterns driven by electronic or geometric shell closings, the formation of stoichiometric soft/hard superatom-based nanocompounds/ assemblies, as well as new emerging properties. By analogy to elemental atom behavior which is directed by critical atomic design parameters (CADPs) and organized horizonally/ vertically in the Mendeleev periodic table, so are these more complex QNBB relationships directed accordingly by their analogous critical nanoscale design parameters (CNDPs), namely, (1) sizes, (2) shapes, (3) surface chemistries, (4) rigidity/flexibility, (5) architecture, and (6) elemental compositions. Continued examination and validation of these “CNDP driven nanoperiodic concept” principles is expected to strengthen and

complexity levels including humanity.343 Lima-de-Faria presents compelling evidence which advocates that critical structural information including left/right handed symmetry properties, as well as periodicity features, are conserved and transferred through all the hierarchical levels to the macroscale level with concurrent new emerging properties as illustrated in (Figure 98). In summary, this review has traced the origin and emergence of a new “unifying nanoperiodic concept” based on first-principles which is now accepted by both phyicists and chemists.2,18 This concept has led to first examples of predictive nanoperiodic property patterns, tables, and rules based on discrete quantized nanoscale building blocks (QNBBs), referred to as hard/sof t superatoms, hard/sof t nanoelements, and meta-atoms (Figure 99). 2764


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Figure 98. (A) Occurrence of left-handed and right-handed structures from molecules to humans: (1) DNA (Z configuration) in its left (methylated) and right (methylated) forms; (2) sections through plant shoots (conifer Araucaria excels) showing spiral divergence left- and right-handed; (3) shells of the snail Linnaean showing left and right orientation; (4) identical twins Monica and Gird. Monica is left-handed and has the forelock to the right. Gird is right-handed and has the forelock to the left. They are mirror images of each other. (Reprinted with permission from ref 343. Copyright 1997 Elsevier Ltd.) (B) Continuum of critical hierarchical design parameters (CHDPs) and associated new emerging properties.

Figure 99. Illustration of hierarchical dimensions influenced by the traditional elemental periodic system and the proposed nanoperiodic system, respectively. (Reprinted with permission from ref 24. Copyright 2010 The Royal Society of Chemistry.)

support a unifying central paradigm for nanoscience, as well as

AUTHOR INFORMATION

provide important insights and optimism for extending these

Corresponding Authors

CHDP-based principles beyond the nanoscale to the micron and

*E-mail: [email protected]. *E-mail: [email protected].

macroscale levels as illustrated in Figure 99.346 2765


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Notes

extensive studies on dendrimers provided a conceptual window to his recent work concerning the development of a systematic framework and nanoperiodic concept for defining and unifying nanoscience.

The authors declare no competing financial interest. Biographies

Shiv N. Khanna is a Commonwealth Professor of Physics at Virginia Commonwealth University (VCU), having been a visiting associate professor at Northeastern University (1983−1984) and a scientific collaborator at the Swiss Federal Institute of Technology in Switzerland (1980−1983). He served as Chair of the Physics Department during 1995−1998. Dr. Khanna is internationally recognized for his work on clusters (groups containing few atoms) and nanoscale materials. One of his significant contributions is the “superatoms”, where he and coworkers discovered that selected clusters can take on the chemical behavior of atoms in the periodic table and that materials with novel characteristics could be developed using such clusters, named “superatoms”, as building blocks. They proposed that the conventional periodic table of elements, which has remained at the heart of chemistry and material science for nearly a century, may finally need modification with “superatoms” forming a third dimension. These developments have opened a pathway to novel nanomaterials, and have been featured in more than 200 reports by various news agencies, including Chemical & Engineering News, Scientific American, Nature, Science, and New Scientist. His current work focuses on forming materials where clusters serve as the building blocks. He has coauthored more than 300 research publications in refereed journals, including prestigious journals such as Science and Nature Chemistry, and has edited six monographs. These publications have been cited more than 8000 times. Dr. Khanna has delivered more than 130 lectures at national and international conferences, universities, and industry. Dr. Khanna has been a recipient of the Outstanding Faculty Award from the State Council of Higher Education in Virginia. This is the highest honor bestowed by the Commonwealth of Virginia. Dr. Khanna is a fellow of the American Physical Society and of the American Association for the Advancement of Science. He has been the recipient of the University Distinguished Scholarship Award of the VCU. He has also twice been the recipient of the Distinguished Scholar Award from the College of Humanities and Sciences at VCU.

Donald A. Tomalia is the CEO and Founder of NanoSynthons LLC, National Dendrimer & Nanotechnology Center, Distinguished Visiting Professor (Chemistry Department) Columbia University, NY; Adjunct Professor (Department of Chemistry), University of Pennsylvania, and Affiliate Professor (Department of Physics) Virginia Commonwealth University. He received his B.A. in chemistry from the University of Michigan and Ph.D. in physical−organic chemistry from Michigan State University while working at The Dow Chemical Company (1962− 1990). In 1990, he moved to Michigan Molecular Institute as Professor and Director of Nanoscale Chemistry and Architecture and subsequently became Scientific Director of the Biological Nanotechnology Center, University of Michigan, School of Medicine (1998−2001). He has founded two previous dendrimer-based nanotechnology companies, namely, Dendritech, Inc. (1992) and Dendritic Nanotechnologies, Inc. (2001). Other positions currently held by Tomalia include the following: Advisory Board, European Foundation for Clinical Nanomedicine (CLINAM); Faculty Member, Faculty 1000 Biology; Associate Editor, Journal of Nanoparticle Research (Springer); and Honorary Editorial Board, Nanomedicine (Elsevier). He is the pioneering scientist and lead inventor associated with the discovery of poly(oxazolines) (Industrial Research-100 Awards in 1978 and 1986) and dendrimers. His 1979 discovery of dendrimers (dendritic polymer architecture) led to a third R&D-100 Award in 1991 and the Leonardo da Vinci Award (Paris, France) in 1996. He received the International Award of The Society of Polymer Science Japan (SPSJ) (2003) for discovery of the fourth major macromolecular architectural class, namely, dendritic polymers. Tomalia’s recent lectureships have included the Dow/ Karabatsos Distinguished Alumni Lectureship, Michigan State University (2005); Chevron Lecture Series, Texas A&M University (2009); Linus Pauling Memorial Lecturer, Portland, Oregon (2010); L. W. Busse Lecture Series, University of WisconsinMadison (2011); and the 38th W. H. Rauscher Memorial Lecturer, Rensselaer Polytechnic Institute (2012). He was the recipient of the Wallace H. Carothers Award (American Chemical Society) (2012). He has authored/ coauthored over 265 peer-reviewed publications with >33203 citations and been granted >128 U.S. patents. His article entitled, “Starburst Dendrimers: Molecular Level Control of Size, Shape, Surface Chemistry, Topology and Flexibility from Atoms to Macroscopic Matter”, by D. A. Tomalia, A. M. Naylor, and W. A. Goddard, III (Angew. Chem. Int., Ed. Engl. 1990, 29 (2), 138) received >2790 citations. Tomalia was inducted into the Thomson Reuters Hall of Citation Laureates in Chemistry (2011) (i.e., 40 most highly cited scientists in the field of chemistry). Tomalia is recognized as a pioneer in dendritic polymers, dendrimer-based nanotechnology, and nanomedicine. His

ACKNOWLEDGMENTS The authors are grateful to Ms. Linda S. Nixon, MBA, for critical graphics and editing, as well as the assembly of the review manuscript. D.A.T. is grateful to the National Science Foundation for initial encouragement and support of this work through NSF Award No. 0707510 and would especially like to acknowledge important discussions with Dr. M. Roco (NSF), Prof. N. J. Turro, Columbia University (deceased), Prof. P.-G. de Gennes, Collège de France (deceased), as well as many others associated with the NSF Workshop (2007) entitled “Periodic Patterns, Relationships and Categories of Well-Defined Nano2766


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scale Building Blocks.”176 S.N.K. is grateful to the U.S. Department of Energy (DOE) through Award No. DESC0006420 to the Basic Research Initiative Grant from the Air Force Office of Scientific Research, AFOSR FA9550-12-1-0481.

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