Advances in Colloidal Assembly: The Design of Structure and

Review pubs.acs.org/CR

Advances in Colloidal Assembly: The Design of Structure and Hierarchy in Two and Three Dimensions Nicolas Vogel,*,†,‡,^ Markus Retsch,*,§,^ Charles-André Fustin,∥ Aranzazu del Campo,⊥ and Ulrich Jonas*,∇,# †

Institute of Particle Technology, Friedrich-Alexander-University Erlangen-Nuremberg, Cauerstrasse 4, 91058 Erlangen, Germany Cluster of Excellence - Engineering of Advanced Materials, University of Erlangen-Nuremberg, 91054 Erlangen, Germany § Physical Chemistry 1 - Polymer Systems, University of Bayreuth, Universitätsstraße 30, 95447 Bayreuth, Germany ∥ Institute of Condensed Matter and Nanosciences (IMCN), Bio- and Soft Matter Division (BSMA), Université catholique de Louvain, Place Louis Pasteur 1, B-1348 Louvain-la-Neuve, Belgium ⊥ Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany ∇ Macromolecular Chemistry, Cμ - The Research Center for Micro- and Nanochemistry and Engineering, University of Siegen, Adolf-Reichwein-Strasse 2, 57076 Siegen, Germany # Bio-Organic Materials Chemistry Laboratory (BOMCLab), Institute of Electronic Structure & Laser (IESL), Foundation for Research and Technology - Hellas (FORTH), Nikolaou Plastira 100, Vassilika Vouton, P.O. Box 1527, 71110 Heraklion, Crete, Greece ‡

3.1. 3D Colloidal Crystals on Planar Surfaces and Interfaces 3.1.1. Direct Assembly on Solid Substrates 3.1.2. 3D Colloidal Crystals at Liquid Interfaces 3.1.3. Defects and Cracks in Colloidal Crystals 3.2. Patterning of 3D Colloidal Crystals 3.2.1. Planar Patterned, Topography-Free Substrates 3.2.2. Colloidal Crystals on Topographically Patterned Substrates 3.2.3. 3D Patterning in Templates 3.3. Colloidal Epitaxy 3.4. Non-Close-Packed 3D Colloidal Crystals 4. Conclusion and Outlook Author Information Corresponding Authors Author Contributions Notes Biographies Acknowledgments References

CONTENTS 1. Introduction 1.1. Building Blocks 1.2. Assembly Forces 1.2.1. Repulsive Forces 1.2.2. Attractive Forces 1.2.3. External Forces 2. 2D Colloidal Assemblies 2.1. Close-Packed Colloidal Monolayers 2.1.1. Direct Assembly Methods 2.1.2. Liquid Interface-Mediated Methods 2.2. Non-Close-Packed Monolayers 2.3. Binary Monolayers 2.4. Two-Dimensional Patterning of Colloidal Crystals 2.4.1. Assembly of Monolayers on Topographically Patterned Substrates 2.4.2. “Colloids on Top of Colloids” 2.4.3. Assembly of Monolayers on Chemically Patterned Surfaces 2.4.4. Patterning without Substrate Engineering 3. 3D Colloidal Assemblies © XXXX American Chemical Society

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1. INTRODUCTION The colloidal domain is characterized by the dimensions of its constituents in the range from several nanometers to micrometers. Often, these individual entities are organized in complex structures with hierarchical order following such length scales. This hierarchical design and organization of matter is a fundamental characteristic of functional materials and living organisms that evolved in nature, and it is of key importance to achieve optimal properties and performance.1−6 One particular challenge in science and technology is the implementation of such structural hierarchies in artificial materials from the

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molecular level over mesoscopic length scales (nm and μm) to macroscopic dimensions with highest possible precision, but with the least effort and costs. The present review outlines the contributions that colloidal assembly with simple uniform, spherical particles can offer to this pivotal and highly active area of research in a tutorial style, highlighting a large number of methods and concepts in sufficient breadth but consequently in limited depth and detail. The necessary background in colloidal materials and interaction types is provided here in a qualitative manner to set the stage for the assembly methods discussed thereafter. We kindly ask the expert reader to forgive some coarse simplifications in favor of fundamental concepts for a broader audience. Furthermore, we restrict our discussions to particles larger than 10 nm for reasons outlined further below. Traditionally, the physical approach to small structures is governed by so-called “top-down” strategies, where matter is structured from larger to smaller length scales. Such methods, which are widely employed in technology and industry, are developed at the time of this writing so far as to reach sub-20 nm dimensions (e.g., in the semiconductor industry with the gate dimensions found in computer processor chips).7 Complementary to these physical strategies are the chemically inspired “bottom-up” approaches, which start at the molecular level to assemble (sub-) nanoscopic building blocks into ever larger entities. Such methods have traditionally been developed in supramolecular chemistry and have matured beyond the 100 nm range (as for example demonstrated by the intriguing 3D structure of self-organized triblock copolymers).8,9 The structural evolution in self-assembly is driven by an intricate interplay of colloidal forces directed toward an equilibrium structure.10,11 The length scales where bottom-up and top-down strategies converge relate to the colloidal domain. Colloidal objects have structural dimensions between nanometers and micrometers and are typically synthesized by chemical methods from molecular starting materials (in a bottom-up fashion). Provided that they are uniform in size, these objects can self-assemble (by “colloidal self-assembly”) into highly ordered lattices termed colloidal crystals.12−16 These crystals can be further organized into hierarchical superstructures by directing the self-assembly process via a combination of top-down and bottom-up procedures. Thus, colloidal assemblies serve well as a paradigm for structural hierarchies, and they are discussed in the present review by the emergence of structural complexity by combining elements of simplicity. Based on these features and the immense progress in particle assembly methods over the last several years, a widespread interest in this field has manifested itself in a diverse spectrum of research directions and emerging applications, including the following: (1) Fundamental Physics. Spherical colloidal particles typically crystallize in a close packed fcc lattice which is, beside the difference in size, found also in crystal structures composed of atoms, for example in metals. Building upon this analogy, one can exploit the larger size of colloidal crystals to directly observe fundamental phenomena in solid state physics, such as the formation and propagation of defects and cracks within a material,17,18 or the transition from a liquid to a glassy or crystalline state.19,20 The subject provides further insight into technologically important questions such as packing or jamming and the mutual influence of commensurate or mismatching length scales.21−23 Diffusion of mesoscopic objects can unravel fundamental concepts of confined mass transport.24

(2) Materials Science. Hierarchical structuring allows for the realization of robust, yet lightweight materials.25 Cracking, an often undesired side-effect during colloidal self-assembly, can be specifically put to use to create transparent, conducting electrodes.26 The colloidal building blocks can be programmed in such a way to add an optical response mechanism to external stimuli,27 rendering them attractive for future anticounterfeit applications.28 (3) Energy Migration. The presence of (periodic) nanostructures can severely influence the way energy or mass is transported through colloidal ensembles. Most prominent examples are the opalescent, structural colors that arise in photonic crystals from the specific interaction of light with the periodic changes in refractive index.15,29 Analogously, mechanical waves can be impeded from traveling through a phononic crystal.30,31 Furthermore, the combination of length scales and surface area can contribute to the transport of electrons and analytes in electrode materials32,33 or may improve light management in solar cells.34,35 New endeavors are emerging in the field of thermal transport through colloidally structured materials.36,37 (4) (Bio)Sensing. Colloidal assembly structures can be rendered sensitive to specific external stimuli (e.g., pH, ionic strength, surface tension), for which in many cases a change of the photonic stopband is used as easily detectable signal.38−41 The well-defined nanostructures accessible by colloidal crystals are often exploited to generate plasmonic nanoparticles for use in biosensing.42,43 The beauty of material and structure design with colloids is its simplicity and modular character; neither extensive procedures nor expensive equipment are required, yet well ordered and complex structures can be created. The characteristic features of such colloidal assembly structures are order, length scale, and porosity: (1) Order. The degree of positional order in colloidal arrangements is tunable from completely disordered, amorphous materials (colloidal glasses) to long-range ordered crystals. The presence of periodic changes in refractive index, density, and mechanical moduli gives rise to optical and vibronic bandgaps, leading to intense structural coloration44,45 and the ability to engineer photon29,46 or phonon propagation.30,31 In the case of shape-anisotropic particles, or particles with a permanent dipole or magnetic moment, an additional orientational degree of order can be introduced, which corresponds to the directional correlation of a vectorial property (like the particle’s principal axis or electric and magnetic dipoles), as it is well-known from liquid crystals. (2) Length Scale. In colloidal assemblies the dimensional features of the hierarchical structures can be viewed from two distinct angles. First, an intrinsic length scale results directly from the size of the building blocks, with the diameter of the colloidal particles typically ranging between 1 nm and 1 μm. Second, a superstructural length scale is provided by the size of the periodic unit cell of the assembly structure, which may substantially deviate from the colloidal dimensions. From a fundamental point of view, conceptual analogies between colloidal particles and atoms are often drawn to understand basic questions relating to ordering processes. As such, micron-sized colloids, which are directly observable in 3D real space, are very useful model objects to study the physics of condensed matter, for example with respect to crystallization, melting, crack propagation,17,18,47,48 stress- or confinement-induced crystallization,21,23 phase transitions, or minimum free energy arrangements.49,50 Furthermore, colloidal particles can be synthesized with nanoscale dimensions, B

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which enables the generation of defined structures with feature sizes below the wavelengths of visible light by an experimentally simple, parallel, and cheap fabrication process. The nanoscale dimensions of the particles (and lattice periodicities) provide tunability of the interaction with visible light, leading to structural color or antireflective surfaces, for example. Furthermore, they can be used as shadow masks to create very precise periodic nanoscale structures on solid substrates.51−54 (3) Porosity. Colloidal assemblies (colloidal crystals and inverse opals) inherently feature a large internal interfacial area enclosing a free continuous volume,55 which has the geometry of an interconnected network with a 3D channel structure spanning the whole sample.56,57 Colloidal assemblies are therefore wellsuited materials for many interface-related processes, e.g., as electrode materials,58,59 in catalysis,60 filtering,61,62 control of wetting properties,63,64 and sensing.41,65 As described in this review, a plethora of assembly methods have been developed in the last three decades and are being continuously optimized and refined. The vast interest in colloidal assemblies is driven by the broad applicability of such structures in very diverse research fields, as briefly introduced above. Different applications command different requirements for the assembled structures. For example, to create a liquid-repellent surface coating, it is crucial to ensure a homogeneous coverage of the surface with colloidal particles to avoid pinning, whereas long-range order of the assembly is in such a case of no importance.66,67 A sensor based on selective infiltration of liquids41 requires defined necks between the colloids and its performance can be highly sensitive to cracks.64 Cracking on the other hand may be desired for the generation of two-dimensional percolating networks.26 Finally, photonic or phononic applications relying on periodic modulations of refractive index or density, respectively, require a very high degree of order in the colloidal crystal.15,31,68,69 As a consequence of the diversity in requirements for different applications it becomes very difficult to devise generalized guidelines on what makes “the best” colloidal assembly method. In order to facilitate identification of a suitable assembly method for a specific need, we thus discuss generic characteristics of different assembly methods in the subsequent sections. Such characteristics are, for example, experimental requirements and efforts, preparation time, robustness of the process, area that can be coated, resulting homogeneity of the coating, as well as short- and long-range order of the assembly structures. The most fundamental differentiation between the assembly methods discussed in this review is based on the dimensionality of the assembly: In a 2D structure, the colloidal assembly is only one particle high but extends laterally, for ordered systems in a 2D lattice. In contrast, a 3D assembly extends along all three spatial coordinates. These two major classes are illustrated in Figure 1 together with the second feature for structural differentiation: close packed assemblies with each particle being in close contact with its direct neighbors versus open lattices, where neighboring particles may be separated by a gap. Finally, further complexity can be added to the assembly process by introducing a second type (or more types) of particles to yield binary (or higher order) assemblies or crystals. A specific case with stacks of different 2D colloidal crystals assembled on top of each other into a 3D structure with lamellar hierarchy is depicted in the center of Figure 1. With respect to the in-plane hierarchy, the two cases of continuous versus laterally patterned assembly structures can be distinguished (compare Figure 1 upper and lower part). In the

Figure 1. Types of structural hierarchies with colloidal particles in two and three dimensions.

second case an arbitrary lateral pattern or periodic superlattice may be generated by a combination of colloidal assembly methods with planar structuring or lithographic techniques. A further increase of the structural hierarchy can be achieved by the use of topographic templates, which are provided by solid substrates with 3D surface structures (Figure 2). In contrast to

Figure 2. Types of structural hierarchies with colloids employing topographic templates.

planar substrates such templates allow simultaneous control over structural elements of the colloidal assembly in the vertical and horizontal directions. The relative dimensions of the shapedetermining templates with respect to the particle size lead to the differentiation between single particle templates, where the topographic features of the template match the single particle dimensions, or to ensemble templates with many particles fitting into a single feature of the template. If the dimension of the ensemble template is a multiple of the particle dimensions, or, more precisely, of the lattice periodicity of the particle crystal, the template can induce order during colloidal assembly inside the topographic features. Otherwise, deposition of the particles in the template with particle-structure mismatch may yield disordered assemblies. Before discussing the details of colloidal self-assembly we briefly introduce the general features of colloidal particles and qualitatively describe particle interactions in suspension and at interfaces, as well as their mutual influence during the assembly process. These sections are intended to provide the necessary background for nonspecialists in the field in a concise and qualitative way, while more detailed information on these topics C

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packing (fcc and hcp), whereas monodisperse cubes tend to yield simple cubic lattice symmetries. Tailored surface modification for specific binding sites at defined regions of the colloidal particle provide a higher level of control in directed self-assembly.94−97 This interesting field is becoming increasingly active with advances being made in the synthesis of highly defined “patchy” colloids with heterogeneous surfaces composed of multiple materials.9,96,98−100 Analogies drawn from such spatially oriented binding sites with respect to atomic orbitals may provide an efficient access to more versatile crystal structures, much like the richness of crystal structures found in atomic crystals. Furthermore, a higher architectural complexity can be achieved already at the particle level, as in the case of core−shell- and hollow capsule systems,101−107 composite particles,108,109 Januslike particles,110−113 stimuli-responsive particles,114−117 nonspherical particles,93,118−120 or in defined particle clusters50,96,121 and colloidosomes.122,123 A generic overview of such particle variations is provided in Figure 3. Among the set of available colloidal building blocks,

can be found in dedicated reviews cited in the corresponding sections below. In subsequent sections, the assembly methods are critically discussed and conceptually divided into two major sections: twodimensional and three-dimensional assemblies organized at a supporting surface. Each section introduces simple assembly methods and proceeds with increasing complexity of the structural hierarchies. 1.1. Building Blocks

The range of structures that can be assembled from colloidal building blocks is vast, which to a large extent is due to the broad definition of what a colloidal particle, the constituting building block of such matter, actually is. According to the IUPAC Golden Book, a colloidal system “...refers to a state of subdivision, implying that the molecules or polymolecular particles dispersed in a medium have at least in one direction a dimension roughly between 1 nm and 1 μm, or that in a system discontinuities are found at distances of that order.”70 This classification is purely dimensional.71−73 As a consequence, apart from individual atoms or small molecules and extended objects exceeding a size of few tens of μm, anything not perceivable with the bare eyes may essentially fall under this category. Colloidal particles are characterized by their own distinct properties and dynamics situated between those of small molecules and macroscopic systems. Indeed, this behavior is reflected by the prefix “meso”, meaning “in-between”, which is often used to describe the colloidal domain. This term not only relates to a specific length scale but also to a distinct behavior, as manifested in the interparticle interactions discussed further below. In order to describe a specific system with sufficient accuracy, several categories to classify colloidal particles have to be considered: (1) type of material, (2) particle dimension, (3) shape, (4) surface functionalization, and (5) dispersion medium. Colloidal particles are available from many different materials, like clays, minerals, organic compounds (as in pigments), polymers, ceramics, semiconductors, and metals. Colloidal particles have long been used in a broad range of industrial applications such as inks, food, coatings, cosmetics, and rheological fluids. This present review excludes very small colloidal particles with dimensions below 10 nm, which may display size-tunable properties due to electron confinement and have come to be known as quantum dots, nanocrystals, or nanoparticles. The vast range of structures accessible from such sub-10 nm nanocrystalline materials are not covered here, as additional material parameters such as the nanocrystal shape, the surface functionality of individual facets, as well as additional magnetic, electronic, and dipolar forces, exceed by far the scope and limits of this review. For these assembly structures, we refer the interested reader to dedicated review articles.74−81 Instead, we intend to showcase the structural richness obtained from the most simple isotropic and spherical particles generally larger than 10 nm, with a focus on the generation of hierarchical motifs spanning several length scales. Most colloids can be produced with well-controlled size distribution, shape, and surface chemistry in macroscopic quantities, which is important for their application in the assembly methods discussed below.75,82−93 The particle size and type of material influences the range of assembly forces for a given dispersing medium. The shape of a colloidal particle can directly translate into the symmetry of the assembled structure: Monodisperse spheres for example favor hexagonal crystal

Figure 3. Evolving complexity of colloidal systems starting from simple spherical particles of a single material with varying dimension to surfacemodified and internally structured objects.

silica colloids and polymer latex systems are by far the most studied systems in colloidal assembly, and therefore these particle classes will dominate the examples presented in this review. Spherical colloids with dimensions from a few tens of nanometers up to several micrometers can be synthesized by a variety of methods and represents an intensive field of research in itself. We therefore refer the reader to respective reviews and articles for classical emulsion polymerization,92,124,125 miniemulsion polymerization,126−128 microemulsion polymerization,129,130 dispersion or precipitation polymerization,131,132 suspension polymerization, 133,134 microfluidic fabrication,135−141 or sol−gel particle formation.142−145 1.2. Assembly Forces

The balance of different forces that act on colloidal particles during their organization in an assembly process can be very complex. It is thus of essential importance to have a general understanding of this balance for obtaining the targeted structural hierarchy with desired complexity. The quantification of the various forces involved in different assembly processes is D

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Figure 4. Schematic representation of various forces and interaction motifs for colloidal particles occurring in three dimensions and at interfaces. Repulsive interparticle interactions (red): (a) dipolar repulsion by partial ionic dissociation at interfaces, (b) Coulomb repulsion, and (c) steric repulsion. Attractive interactions (blue): (d) immersion capillary forces, (e) hydrodynamic coupling/drag forces, (f) Coulomb attraction to oppositely charged surfaces, (g) bridging attraction/flocculation, (h) flotation capillary forces, (i) van der Waals (vdW) attraction, and (k) depletion attraction. External forces (black): (l) barrier compression or forced convection (effectively resulting in particle aggregation), (m) Brownian motion, and (n) gravitational sedimentation.

an important and active research field, yet it is very difficult to generalize.146,147 As this review is intended to provide an overview on the vast field of colloidal assembly structures, we restrict the discussion to a qualitative description of the most relevant forces necessary to understand colloidal self-assembly processes. Generally, a subtle balance between attractive and repulsive interactions is required to allow probing of local thermodynamic minima by the particles and to overcome activation barriers by the energy provided from the environment to assemble into an ordered structure. The forces involved in colloidal assembly processes can be divided into three main classes: (1) repulsive forces resulting from interparticle interactions between two and more particles (or with extended interfaces) that prevent a colloidal dispersion from spontaneous aggregation and flocculation, (2) attractive interparticle forces that can counteract repulsive forces and may yield specific assembly structures as a result of this (im)balance, and (3) external forces acting on individual particles or particle ensembles. Details of these forces have been described in previous publications and are reviewed here only in brief to give a qualitative flavor of the large variety of different parameters that have to be taken into account and that can be tuned experimentally to yield the desired structures and order (Figure 4). For further reading reference is given to authoritative overviews in the literature.146−149 1.2.1. Repulsive Forces. Dipolar interactions (Figure 4a): At the air−water interface ionic groups at the particle surface can only dissociate inside the water phase, which results in an asymmetric charge distribution around the particle.150 The resulting dipoles on all particles are oriented parallel to each other and lead to a repulsive force if the ionic surface groups are isotropically distributed around the particle. A similar scenario is found at the water−oil interface, but partial wetting of the particle surface with water droplets in the oil phase may lead to partial ion dissociation in the oil phase, resulting in stronger particle−particle repulsion by an additional electrostatic component. Furthermore, the presence of an oil− water interface instead of an air−water interface may reduce the counteracting attractive forces given by flotation capillary attraction (which are described below).151,152

Coulomb interactions (Figure 4b): They are governed by the charges distributed over the colloidal object and are repulsive between like-charged particles. Charge densities and spatial distribution functions are expressed by the Poisson−Boltzmann formalism and are approximated by the linearization of Debye. The electrostatic repulsion scales with e−κx, where κ represents the inverse Debye length. Electrostatic repulsion can be of longrange order; however, due to the self-dissociation of water, it is limited to a maximum of 680 nm.148 Electrostatic repulsion is one of the major contributors to colloidal stabilization and is summarized in the DLVO theory.153,154 The magnitude of electrostatic repulsion can often be tuned by the pH of the dispersion medium or by the addition of salt, which changes the ionic strength of the dispersion medium and thus the Debye length. Steric stabilization (Figure 4c): In the case of colloidal particles with a solvated polymer corona, colloidal stability is attained by steric stabilization. The aggregation of colloidal particles is prevented by the evolution of an osmotic pressure in the region of polymer chain overlap (therefore local polymer concentration increase), as well as by mechanical spring forces, which result from an unfavorable decrease in entropy due to compression and restriction of the solvated polymer chains.155,156 The range of this interaction force is given by the spatial extension of the stabilizing layer. The use of theta-solvent conditions for the corona polymer eliminates the evolution of an osmotic pressure in the overlap region and thereby may be exploited to reduce the stabilizing effect. The repulsive forces between particles in liquid media are the major contributors in the stabilization of colloidal dispersions. They are crucial to guarantee a long shelf life and processability. 1.2.2. Attractive Forces. When a colloidal particle comes into contact with an interface between two liquid media it can be energetically stabilized or “trapped” there with a degree of stabilization up to 107 kBT (at room temperature) for a particle diameter of one micrometer and equal wetting by the two liquid phases. This interfacial stabilization was explained by Pieranski as the change of the interfacial energy between the two mobile phases in the presence of the particle and the increased contact area of the particle with both phases.148,150 This effect is the basis for Ramsden and Pickering emulsions, where dispersions of E

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The presence of much smaller objects, such as individual dissolved polymer chains or smaller nanoparticles, can lead to depletion forces (Figure 4k), which drive aggregation of the larger particles. Thereby the overall system reduces its total energy by an increase in the degrees of translational freedom and entropy.167 The combination of surface roughness with depletion interaction can lead to aggregation discrimination between rough and smooth particles, with the smooth colloids showing preferential depletion attraction.168 1.2.3. External Forces. Particles trapped at a liquid interface and restricted to 2D translational diffusion can be manipulated by external forces to yield colloidal assemblies. For example, mechanical barriers known from the Langmuir−Blodgett (LB) technique can be used to compress the floating colloid ensemble and induce two-dimensional phase transitions from a gaseous state to an ordered, crystalline state (Figure 4l).164,169,170 Compaction and crystallization can also be affected by external drag forces such as air flow.171 Brownian motion (Figure 4m) is a fundamental property of colloidal particles dispersed in a liquid or gaseous medium. It represents an omnipresent source of kinetic energy and is related to the thermal energy kBT of the system.146,172 Any assembly process has to overcome this randomizing energy to result in a thermodynamically stable superstructure, and counteract erratic diffusion, which can be described with the help of the Stokes− Einstein formalism.173 Gravitational forces (Figure 4n), which lead to particle sedimentation, are generally low and increase with the size of the colloidal object and its density difference with the dispersing medium.174 However, increasing the accelerating forces in a (disk or ultra) centrifuge can be easily used to speed up particle sedimentation or to separate colloidal objects by size or density. Furthermore, experiments carried out under microgravity conditions revealed a change in the aggregation kinetics and crystal structure.175,176 From the considerations above a differentiation can be made between “intrinsic” parameters, which control the particle interactions and “external” experimental parameters that influence the assembly behavior and the resulting structures. The intrinsic parameters result from the immanent nature of the particle itself, such as material, size, and surface modification. These factors determine the mutual interactions between particles, the interplay of particles with an interface, and more generally with its environment. The balance of interactions, which result from intrinsic parameters, is responsible for the classical self-assembly of particles into (local) free energy minimum structures. External parameters are given by the choice of the dispersion medium (pH, ionic strength), the solid substrate (material, shape, surface modification), which supports the colloidal assembly, and the assembly conditions (e.g., temperature, mode of particle deposition, particle volume fraction in the assembly medium). External parameters also allow the exertion of forces onto the particles through tailored fields and confinements, which provides the basis for directed self-assembly to drive the particles into structural organizations beyond the thermodynamic free energy minimum.81 The formation of self-assembled structures necessitates a high degree of control over the balance of attractive and repulsive forces. How this is achieved in a wide range of processes will be discussed in the following sections of this review.

water and oil are stabilized by solid particles located at the water− oil interface. It also plays an important role in the stabilization of food emulsions, foams, as well as in the industrial flotation process.157,158 The presence of a liquid or solid interface strongly affects the mode of interaction between colloidal particles. Confinement of the particles at an interface usually leads to slower particle dynamics. It is associated with a reduction of the free translational motion in the bulk to a planar random walk at the plane of the interface. Specific interfacial interactions of particles have been discussed in the literature and are only briefly sketched in the following.81,148,159−162 When the particles deform the liquid interface, the surface tension of the liquid causes an effective interaction between the particles. If the deformation between two particles is in the same direction (which means the particles are wetted in the same way) the interaction is attractive and the resulting capillary forces will pull the particles together. For floating particles, this effect takes place if their diameter and density difference to the liquid medium is large enough to cause an interfacial deformation by gravitational and buoyancy forces (typically for particle dimensions larger than one micrometer). The extent of interfacial deformation further depends on the wettability of the colloidal object with the liquid medium and the particle shape. The resulting interaction is known as the flotation capillary force (Figure 4h).162,163 For very small nonisotropic particles this flotation capillary force can be significant, due to the meniscus deformation by other mechanisms such as electrostatic stresses.164 When particles are trapped at a solid interface in a liquid film with a thickness below the particle diameter, a deformation of the liquid surface can take place even for particles much smaller than one micrometer. The resulting immersion capillary forces drag the particles together (Figure 4d) and are often encountered in drying latex dispersions.162,163 Hydrodynamic coupling (Figure 4e) can lead to deviations from the random Brownian motion by the presence of a convective flow of the liquid medium or from viscous coupling between the particles. For charged particles dispersed in a liquid medium, which are in contact with an oppositely charged solid surface (permanent surface charges or a conducting electrode), electrostatic attraction can lead to particle adsorption (Figure 4f). When attractive forces are present between dissolved polymer chains and the colloidal object, bridging flocculation can occur (Figure 4g). Depending on the size ratio between the polymer chain and the colloids, two or more particles can interact with an individual polymer chain. Furthermore, with increasing polymer concentration, this effect can also switch to steric stabilization, when the particle surface is fully saturated with polymer chains.165 Van der Waals (vdW) forces (Figure 4i) are generally attractive multibody dipolar interactions. Their magnitude and range depend on the size and shape of the colloidal object. This behavior is captured by the Hamaker formalism. Colloidal vdW forces act over much larger distances (force ∝ (1/d2), for two spheres with R ≫ d) compared to intermolecular vdW interactions. An interesting feature, which can be inferred from the Hamaker formalism, is the fact that vdW forces can be effectively screened by refractive index matching of the dispersion medium to the colloidal objects.166 This fact can be experimentally exploited to tune the particle−particle interaction. F

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Table 1. Overview of 2D Crystallization Methods for Close-Packed Colloidal Monolayers

2. 2D COLLOIDAL ASSEMBLIES Two-dimensional assemblies of colloids on solid substrates are typically referred to as colloidal monolayers. In this section, we briefly introduce different methodologies to assemble homogeneous two-dimensional crystals and discuss differences, advantages, and challenges of individual techniques as well as the key interparticle forces that need to be controlled to yield highly ordered structures. Subsequently, we outline existing strategies to generate more complex assembly types, consisting of nonclose-packed monolayers that feature particle arrays with the colloids not in direct contact with each other, and binary monolayers with ordered assemblies of large and small particle populations. Following this general introduction, we discuss in detail strategies to create more complex, hierarchical assemblies, such as patterns of colloidal monolayers, clusters of individual colloids on surfaces, and assemblies on topographically structured substrates.

The possibility to assemble nanoscale elements in an experimentally simple, inexpensive, and highly parallel fashion has allowed colloidal monolayers to be widely applied to create functional surface patterns.14,177−181 Predominantly, colloidal monolayers have been used as shadow masks to create arrays of metal nanoparticles. Since first reports in the 1990s to create triangular metal nanoparticles,182 increasingly sophisticated process designs have led to the development of a whole zoo of available shapes and structures,183 described in detail in a number of review articles.14,54,177,178,184 Such metal nanoparticles support localized surface plasmon resonances and have been used to design nanoscale sensing units based on shifts in the resonance wavelengths upon binding events and by surface enhanced Raman scattering.43,185,186 Further, two-dimensional colloidal assemblies have been exploited to create and understand structural color187,188 and mimic colorations occurring in nature,44,189,190 and to create surface coatings that show G

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Figure 5. Convective assembly processes for the two-dimensional crystallization of colloids. (a) Vertical deposition process. (b) Horizontal deposition process. (c) Typical problems arising from convective assembly processes as reported by Dimitrov et al. Reprinted with permission from ref 198. Copyright 1996 American Chemical Society. (d) Optical micrograph showing the growth of a monolayer by the horizontal deposition process. Arrows indicate particles being dragged to the growing front.201 (e,f) Assembly of mono- and bilayers by carefully controlling experimental conditions. Reprinted with permission from ref 201. Copyright 2007 American Chemical Society.

sional and fluid by nature, thus allowing the compression of the formed monolayer to avoid voids or incomplete fillings. Table 1 provides an overview of the different preparation methods described in the following. 2.1.1. Direct Assembly Methods. 2.1.1.1. EvaporationInduced Methods. Most predominantly, direct assembly methods take advantage of solvent evaporation to control the deposition of colloids. Such techniques are usually referred to as convective assemblies and are based on the formation of a very thin liquid film in the meniscus region of at the three-point contact line. The dominating forces governing the crystallization mechanism are immersion capillary forces that push the particles together once the height of the liquid film falls below the colloid diameter (Figure 5a).163 A convective flow is consequently created as water evaporates in the formed monolayer. This flow opposes random Brownian motion and continuously drags particles from the bulk dispersion to the monolayer nucleus and causes its continuous growth (Figure 5a,b).163,196,197,221 Evaporation induced deposition methods that rely on capillary forces require low particle-surface interactions so that particles can freely diffuse across the substrate, seeking their lowest energy configuration. This is often achieved via electrostatic repulsion by chemically modifying the colloid and substrate surface with negatively charged functionalities (such as carboxylate or sulfate moieties). These are repelled by negatively charged substrate surfaces, present for example on glass. In addition, the ordering

antireflective,191 and self-cleaning63,192 properties, as well as repellency toward water193 and low-surface tension liquids.63 2.1. Close-Packed Colloidal Monolayers

A number of recent reviews12,14,16,179 discusses two-dimensional assemblies of colloids in great detail. We limit ourselves to the discussion of general crystallization methods to obtain closepacked colloidal monolayers along with selected examples. Conceptually, existing techniques can be classified in two main approaches:14 (1) direct assembly on solid substrates and (2) liquid interface-mediated assembly. There are certain key differences between these two approaches. In direct assembly methods the colloids are immediately deposited and assembled on the substrate of choice without intermediate transfer steps. Additionally, the introduction of topographic features onto the substrate can be used to control the assembly process and produce assembly structures with more complex symmetries. However, the choice of substrates is partially limited as certain criteria essential to the respective assembly process need to be fulfilled (for example hydrophilicity of the substrate). In contrast, liquid interface-mediated assembly processes allow the transfer of the monolayer to a much wider range of solid substrates, as the monolayer formation step and the immobilization step on the target substrate are decoupled. Therefore, interface-mediated processes are capable to coat hydrophobic or topographically structured substrates. As a liquid interface is used to assemble the particles, the resulting arrangement is exclusively two-dimenH

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surfaces. Sedimentation of colloids has been mainly employed for the fabrication of 3D silica colloidal crystals225,226 but can be employed for the fabrication of monolayers if the cell volume is properly controlled to prevent the formation of multilayers.208 Spin-coating has also been applied to crystallize colloidal monolayers. The main advantage of spin-coating is the high throughput of the technique that can be operated with minimal amount of time and effort to cover wafer-scale areas. The quality of the resulting monolayer can be seriously compromised by the high shear forces and fast solvent evaporation rate. Forcing the colloidal particles into a thin wetting layer of the same height as the particle size triggers attractive immersion capillary forces. When the colloid concentration and the centripetal and capillary forces are matched on the appropriate time scale, this can lead to ordered arrays. While small domains of crystalline monolayers can be produced with standard preparation protocols,53,182 the preparation of large area monolayers with a high degree of order requires more sophisticated protocols.207 Electrostatic attraction between a charged surface and oppositely charged colloids can be used to deposit colloids to the charged surface.209,210,227,228 However, the strong electrostatic interactions fix the particles very tightly to the substrate upon contact. The adsorption mechanism follows the “random sequential adsorption” (RSA) theory229 and is driven by the competition of the attractive forces between the charged substrate and the oppositely charged particles with repulsive forces between the equally charged colloids. Once a particle has adsorbed onto the substrate it is immobilized with respect to its thermal energy (Brownian motion) and shows no lateral motion. Consequently, any space between adsorbed particles that is smaller than one particle diameter remains inaccessible for further adsorption since no reordering within the layer is possible. The resulting particle assembly at the substrate is disordered with a surface coverage usually below 50%. Similar to electrostatic assembly processes, electrophoretic deposition processes take advantage of attractive electrostatic interactions to immobilize colloidal particles onto a substrate. While charges are permanently present on the substrate in the first case, the latter process uses conducting substrates as electrodes to generate a variable electric field by applying a distinct voltage. The characteristic features for electrophoretic deposition processes should, in principle, be similar to the electrostatic deposition: The strong electrostatic attraction should impede ordering of the colloids at the electrode, as the assembly should follow a random sequential adsorption process. However, it has long been observed that colloids assembling at an electrode are subjected to interparticle attractive forces that induce ordering and lead to the formation of crystalline monolayers.230,231 This attraction cannot be explained by classical colloidal forces (section 1.2). In principle, like-charged particles and parallel dipoles (induced by the polarization of the ion cloud around the particle in proximity to the electrode) would lead to a mutual repulsion. The unexpected attractive force between the colloids has been attributed to convective flows caused by electrohydrodynamic movement of ions.232−234 and electroosmosis.235,236 Electrohydrodynamic forces are created by the presence of a dielectric colloid at an electrode: When a voltage is applied, the electrode attracts oppositely charged ions to form a concentration gradient at the electrode. A nonconducting colloid disturbs this gradient and induces an ion flow toward the electrode. Once a second colloid is in proximity, the flows generated by the two colloids interact with each other and result in an attractive convective flow.232,233 An electro-

process is dramatically influenced by the surface energy and wetting properties of the particle and substrate surfaces: to allow for the assembly process to take place, a very hydrophilic substrate with low water contact angles (i.e., below 20°) is crucial.201 A higher contact angle prevents the formation of monolayers on flat substrates as the water film dewets before the height of the water layer becomes small enough for immersion capillary forces to act effectively.201,205 Evaporation induced methods can be performed with different levels of sophistication. In the experimentally simplest case, a droplet of water is left to evaporate on a hydrophilic substrate (drop casting). Pioneered by Nagayama in the 1990s, this method has been valuable to study the fundamental mechanisms of the crystallization process that is driven by immersion capillary forces.196,197 Although ordered patches of monolayers (∼mm2 dimensions) will form upon evaporation of solvent, a homogeneous coverage of large areas with well-ordered monolayers is impeded by the coffee-stain effect, leading to multilayers at the drying front and submonolayer in the central part of the droplet. The circumvention of coffee-stain effects requires more elaborate process designs, including the addition of surfactants222 or polymers223 to the deposition solution or the use of anisotropically shaped particles.224 In 1996, a vertical deposition method was introduced to form homogeneous, well-ordered monolayers over larger areas.198 The assembly mechanism is conceptually similar to the drop casting method. However, control over the deposition is gained by slowly removing the substrate from a colloidal dispersion. This enables the formation of a straight meniscus line at which the assembly process takes place (Figure 5a). To achieve homogeneous growth of the monolayer, the substrate is slowly moved in the opposite direction to the growth front and a convective flow of particles toward the growth front induces crystallization (convective assembly). Both, evaporation rate and withdrawal speed, have to be matched carefully. Though the technique leads to assembly structures of high order, the uniform coverage over large areas may be hampered as precise control over evaporation conditions can be difficult to achieve. Figure 5c shows typical heterogeneities (voids and multilayers) that are related to the difficulties of exactly controlling the process conditions. The addition of surfactants (such as sodium dodecyl sulfate (SDS)) beyond its critical micelle concentration to the particle dispersion has shown to result in a more rapid and robust colloidal monolayer formation, though this has been only demonstrated on a gold surface.200 Another variation of the process is the horizontal deposition technique201,205,206 shown schematically in Figure 5b. A receding meniscus is formed by a confining glass slide mounted on top of a translational stage. The particle monolayer is formed during horizontal displacement of the target substrate. The advantage of the horizontal technique is the possibility to directly observe the deposition process by optical microscopy (Figure 5d). The solvent evaporation rate, which is controllable by the substrate temperature, the target substrate velocity, and the suspension particle concentration need to be mutually matched for homogeneous monolayer growth. If carefully controlled, the size of the colloidal crystal (i.e. the number of layers) can be adjusted as demonstrated in Figure 5e,f for a single monolayer (e) and a double layer (f).201 2.1.1.2. External Force-Induced Assembly Methods. External forces that can be applied to crystallize colloids into twodimensional crystals include gravity, shear forces, as well as electrostatic and electrophoretic forces acting on electrode I

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Figure 6. Two-dimensional colloid assembly structures created by electrohydrodynamic flow on an electrode surface under varying confinement, which was characterized by the ratio of colloid diameter over cell gap dimension, as reported by Gong et al.237 With decreasing cell height, attractive electrohydrodynamic flows are decreased, leading to stronger contributions of repulsive dipole−dipole interactions. This causes a change in the assembly structures from close-packed (a) to chain-like (b) and non-close-packed (c). Reprinted with permission from ref 237. Copyright 2002 American Chemical Society.

osmotic flow is generated by the polarization of the ion cloud of the colloid near the electrode. As the colloid is attracted to the electrode by the opposing charges, its counterion cloud will bear charges with a similar sign as the electrode. Consequently, the ions are repelled from the electrode and result in an electroosmotic flow. This flow is directed away from the electrode near the particle and pulls fluid toward the particle. Consequently, a second particle in the vicinity is dragged toward the first particle.235,236 Additionally, confinement of colloids close to the electrode has a dramatic effect on the resulting assembly structures as investigated by Gong et al.237 (Figure 6). They created a phase diagram of the assembly structures of 4 μm polystyrene (PS) colloids under varying confinement in a wedge cell. With little confinement, close-packed structures similar to nonconfined experiments were found (Figure 6a). At very strong confinements, dipole repulsion forces become stronger than the electrohydrodynamic attractive forces and the colloids assemble into a non-close-packed monolayer (Figure 6c). Between these two extreme situations, a rich variety of morphologies was observed, including honeycomb and wormlike assemblies (Figure 6b) as a result of the colloids attempting to minimize their dipole repulsion while still being dragged together by electrohydrodynamic flows. Electrophoretic assembly can also be conducted in alternating electric fields.213,232,238 Compared to constant electric fields more highly ordered monolayers are obtained here as the nucleation rate of ordered patches can be better controlled.213 The electrophoretic assembly also provides a convenient method for the creation of superstructures by introducing patterns to the electrode-substrate239,240 and has been used to control the crystal orientation with respect to the electrodes.241 Kleinert et al. combined the application of alternating electric fields with an evaporative assembly process. The electric field enhances the spreading of the colloidal dispersion by polarization of the substrate (electrowetting-on-dielectrics phenomenon).242 Thus, a more uniform coating with large crystallite domains can be achieved. Another interesting phenomenon is the potential to anneal defects by the application of electric fields. Aubry et al. reported on the use of electromagnetic fields to increase the order and heal defects in a monolayer assembled at the oil−water interface. The electric field was used to increase the strength of the dipole repulsion of the particles trapped at the interface.243 Xie et al. used one-dimensional colloidal lines for an epitaxial assembly of a monolayer and applied alternating electric fields to anneal grain boundaries in order to produce macroscopic monolayer domains.244 2.1.2. Liquid Interface-Mediated Methods. The possibility to assemble colloids at liquid interfaces is a consequence of the general tendency of colloidal particles to be trapped at such

interfaces. As Ramsden and Pickering observed, colloidal particles possess a large tendency to adsorb to interfaces between liquid−air or liquid−liquid, and thereby lead to a stabilization of the respective interface. By means of surface energy arguments one can deduce that colloidal particles are typically strongly immobilized at liquid interfaces depending on their wettability.148 The maximum arrestment at the liquid interface appears for equal wetting conditions of the immobilized particle (contact angle = 90°). In such a scenario a PS particle of 100 nm diameter is trapped by ≈106 kBT at the air−water interface.150 Thus, liquid interfaces can become stabilized by attachment of colloidal particles due to the reduction of interfacial energy. Colloids present at a liquid interface are not subjected to 3D convective bulk flows, but still possess a high degree of lateral mobility which can be beneficial to induce in-plane order. The two-dimensional nature of an interface effectively confines the colloids and enables their crystallization into purely two-dimensional monolayers, thus avoiding problems with multilayer formation occurring in direct assembly methods. Four key forces dominate the crystallization process (for details see section 1.2): Capillary forces (flotation capillary force) cause long-range attractions, van-der-Waals forces induce short-range attraction while electrostatic, and dipole forces add repulsive character. The balance of these forces is crucial for the assembly of high quality monolayers: Disorder in monolayers assembled at the liquid interface is often caused by a lack of sufficient electrostatic repulsion. Capillary forces will inherently bring individual particles in close proximity. Electrostatic repulsion acts as a contact barrier to prevent the particles from random aggregation by van der Waals forces. This separating barrier force enables particles to arrange into their minimum free energy position in a hexagonal lattice and thus introduce order toward the twodimensional crystal. The magnitude of the electrostatic interactions can be manipulated by changing the subphase, e.g., by addition of electrolytes or changing the pH value.217 This allows for an additional degree of control of the crystallization process. The balance of forces is fundamentally different when changing from air−water to oil−water interfaces. While closepacked monolayers are the typical result in the former case,164,220,245 the appearance of non-close-packed structures prevails at oil−water interfaces, indicating significantly stronger repulsive forces alongside with lower capillary attraction.151,245,246 The classical protocol to assemble particles at the air−water interface employs Langmuir troughs, where the assembly can be followed by optical microscopy and surface pressure−area isotherms.169,170,247−250 Typically, incompressible spheres (polystyrene, poly(methyl methacrylate), silica) are used in monolayer crystallization processes. After spreading the particles from appropriate dispersions at the air−water interface, barrier J

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Figure 7. Air-water interface mediated two-dimensional assembly of colloids. (a−d) Crystal formation on a Langmuir trough in dependence of the pH value of the subphase.217 SEM images and Fourier transformations (shown as insets) of the assembly of sodium carboxylate functionalized particles at different pH values (a: 2.3; b:3.3; c: 4.5; d:5.3). Blue arrows indicate the direction of the principle axes within the crystal domains. Red marked areas demonstrate the boundaries of ordered domains. The sample shown in (d) for pH 5.3 has been analyzed with blue-laser diffraction (λ = 325 nm) with a spot size of 3 mm. A clear hexagonal pattern can be seen, indicating the presence of a single crystal domain. Reprinted with permission from ref 217. Copyright 2010 American Chemical Society. (e−i) Direct assembly of colloidal monolayers at the air−water interface and subsequent manual transfer to a substrate. Adapted with permission from ref 220. Copyright 2011 Wiley. (e) Schematic illustration of the process. (f,g) Photograph of the manual transfer of the interfacial monolayer to a wafer substrate (f) and the same wafer after drying (g). (h,i) SEM images of a monolayer of 422 nm carboxylic acid surface-functionalized polystyrene particles transferred to a flat substrate (h) and to an array of photoresist micropillars (i). (j−m) Monolayer floating process. Adapted with permission from ref 219. Copyright 2009 Wiley. (j) Schematic illustration of the process: colloids are spin-coated onto a solid substrate to create a sparsely distributed particle film (i,ii), which is then slowly immersed into a water subphase. The colloids assemble into a closepacked monolayer at the three-phase contact line (iii). The floating monolayer (iv) can subsequently be transferred to a solid substrate (v). (k−m) Characterization results from the different process steps. (k) Photographs of a glass slide covered with loosely packed colloids and close-packed monolayer resulting from the process. (l) SEM images showing a high degree of order in transferred film. (m) Hierarchical assembly of individual monolayers stacked into a three-dimensional structure.

compression first reduces the free interfacial area without lateral pressure increase until the individual particles come into contact. Continued barrier movement increases the surface pressure, leading to densely packed particle domains, and subsequently pushes these domains into close contact to yield an interface completely covered with colloids. The rigid character of the individual particles allows for only very little compressibility. Thus, once a complete monolayer is formed, the surface pressure rises sharply as the monolayer is compressed. Further compression induces buckling and collapse of the monolayer. The surface pressure−area isotherm typically shows a step function with a very steep rise of the surface pressure upon particle contact, followed by an abrupt collapse.169,170,249,250 When using softer colloids, such as hydrogels, the interfacial properties drastically change as soft particles can be significantly compressed before buckling occurs.251,252 Transfer to a solid substrate can be performed either manually by immersion of a

substrate and withdrawal under a shallow angle,214 by lowering of the water level,164,217 or by a classical, vertical Langmuir− Blodgett253,254 transfer.215 The latter technique has also been used to deposit three-dimensional crystals with precise control of the number of colloidal layers.255 The surface functionalities of the colloids have been recognized to be a crucial factor for the quality of the monolayer as they control key properties of the particles at the interface, such as surface charge density and contact angle. As examples, high quality monolayers were reported for partially hydrophobized silica monolayers obtained by surface methylation250 or surface modification with allyl groups.216 The addition of various surfactants was proposed to tune the interfacial properties of the colloids as well.215,256 A conceptually simple approach leading to monolayers with excellent order was introduced by Weekes et al.,164 who used a glass slide at an angle of 45° with respect to the water surface and allowed the dispersion to gently float onto the subphase via the K

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Table 2. Overview of Methods to Create Non-Close-Packed Monolayers

and assembled into a highly ordered monolayer upon drying. Adding an additional external force to an already immobilized monolayer film at the air−water interface can lead to a quasimelting and recrystallization of the 2D crystal. This was recently demonstrated by Meng et al.,171 who obtained single crystalline domains over several square centimeters by application of a shear flow of compressed nitrogen gas over the floating particle layer. A concept coined “floating monolayers” was introduced by Retsch et al.219 The technique uses a two-phase assembly process: First, a diluted colloidal dispersion is spin-coated onto a glass slide with high speed in order to create a substrate with sparsely distributed particles. This slide is then slowly immersed into the water subphase. At the three-phase contact line between air, water, and glass, the colloid particles detach from the glass slide and are trapped at the air−water interface. A small amount of surfactant present at the subphase surface acts as a soft barrier that prevents rapid diffusion after detachment of the colloids from the three-phase contact line. As more and more particles are deposited at the interface, a close-packed monolayer forms that can be manually transferred to a solid support (Figure 7j). The process yields highly ordered monolayers on hydrophilic and hydrophobic substrates,259−261 can be employed to create monolayers consisting of patches of differently sized or composed particles, and it allows for stacking of individual layers into hierarchical three-dimensional structures (Figure 7k−m).

glass slide, reducing disturbance of the interface to a minimum. Tuning of the pH of the subphase allowed for a further increase in long-range order, with single crystal domains reaching macroscopic dimensions (Figure 7a−d).217 Beyond tuning of the subphase or particle properties, the method of LB compression can also significantly contribute to yield large area monolayers with high quality. Kim et al. demonstrated the effect of stress relaxation in monolayers of Au nanoparticles and showed a substantial increase in order upon multiple compression-relaxation cycles.257 More recently, several techniques have been introduced to simplify the assembly of colloids using the air−water interface. These techniques might lead to a more widespread use of colloidal monolayers in different fields of science and technology as they are straightforward yet reliable and can easily be performed by nonspecialists and without the need of sophisticated equipment, which puts them ahead of the Langmuir−Blodgett technique for the fast fabrication of large area colloidal monolayers. A direct assembly process at the air− water interface was established by Vogel et al. (Figure 7e).220 Similar to the technique reported by Weekes et al.,164 a glass slide was used to spread polystyrene colloids to the interface from a dispersion containing 50% ethanol. Directly upon spreading, close-packed monolayer patches crystallized at the air−water interface, triggered by immersion and flotation capillary forces. By this method colloids can be added until the complete interface is covered with a close-packed monolayer, which can be subsequently transferred manually simply by “fishing” the monolayer with a solid substrate immersed into the subphase (Figure 7f). Highly ordered monolayers over large areas only limited by the dimensions of the accessible air−water interface can be obtained and transferred onto topographically structures surfaces (Figure 7g−i). A variation of this method has been described recently by Dai et al., where the particle dispersion was directly injected into a wetting water film on top of the target substrate.258 The spheres were trapped at the air−water interface

2.2. Non-Close-Packed Monolayers

We define a non-close-packed monolayer here as an array of colloidal particles with a hexagonal symmetry but, in contrast to a close-packed crystal, with spatial separation between the individual spheres. Monolayers with different symmetries (i.e., square packing) or clusters of monolayers will be discussed in the next section in the context of patterned colloidal monolayers. Non-close-packed monolayers with separated spheres are of high interest for applications in colloidal lithography as they allow preparation of complex nanostructures by applying angular evaporation or etching steps.177,179,183,262−264 Conceptually, two L

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Figure 8. Fabrication of non-close-packed colloidal monolayers from close-packed arrangements. (a) Schematic illustration of a plasma-assisted size reduction of the colloids, adapted with permission from ref 14. Copyright 2012 Royal Society of Chemistry. (b) Example of non-close-packed monolayers produced by exposure of a close-packed monolayer to oxygen plasma. Reprinted with permission from ref 262. Copyright 2009 Wiley. (c) Change of the monolayer color upon size reduction can be used as an easy means to control the etching process optically. Reprinted with permission from ref 220. Copyright 2011 Wiley. (d) Illustration of the stretching of an elastomeric substrate to yield non-close-packed monolayers, adapted with permission from ref 14. Copyright 2012 Royal Society of Chemistry. (e) Examples of non-close-packed monolayers produced by stretching protocols of the substrate. Reprinted with permission from ref 278. Copyright 2010 American Chemical Society.

air−water interface.103,148,245 The repulsive nature has been shown to arise from strong dipole repulsion, reduced capillary forces and possibly unscreened charges at the particle surface in the oil phase.151,159,245 Chemical modification of the particle surface allows controlling the wetting and consequently the vertical position (immersion depth) at the oil−water interface which has a substantial influence on the particle ordering in nonclose-packed structures. A less polar particle surface (larger water contact angle) pushes the particle more into the oil phase and the resulting larger repulsion induces a higher order in the particle layer.279 More recently, colloidal alloy structures comprising large and small spheres, have been investigated, where also a discrepancy between kinetically formed and thermodynamically stable structures has been noticed.280 When combining hydrophilic and hydrophobic particles, well-defined cluster structures have been observed, which arrange in a hexagonal superlattice at the oil−water interface. The internal structure of the colloidal clusters is governed by induced dipole attraction.152 Transfer of such monolayers from the liquid interface to solid substrates is challenging as viscous drag and capillary forces arise upon drying of the monolayer on a solid substrate, which will lead to a loss of the original positions of the colloids.151,281 Therefore, successful transfer requires additional forces (e.g., electrostatic attraction between substrate and particles) to conserve the particle positions upon drying.151 Spin-coating has been employed as well to create non-closepacked monolayers. To allow particles to have sufficient time required for proper ordering, the spin-coating protocol as well as the choice of solvents needs to be carefully optimized.282,283 Whereas the direct spin-coating protocol seems to be a fast method to access wafer-scale areas of non-close-packed structures, further control on the interparticle distance is difficult to achieve. Recently, Yang et al. devised a multistep method that introduces some control over the lattice spacing, based on the immobilization of the non-close-packed spheres on a poly(vinyl alcohol) (PVA) film, which can be shrunk at elevated temperatures.284 Table 2 summarizes the existing techniques to prepare non-close-packed monolayers.

approaches for the preparation of non-close-packed colloidal monolayer arrangements can be distinguished (see Table 2).14 First, a close-packed monolayer can be transformed into a nonclose-packed arrangement by spatially separating the particles in a symmetric fashion. Second, a direct crystallization of non-closepacked arrangements can be achieved, either by exploiting the repulsive character of particles at the oil−water interface or by sophisticated spin-coating protocols. To prepare non-closepacked monolayers from previously assembled close-packed monolayers, four methods have been established (Figure 8): (i) Plasma treatment of the monolayers can isotropically reduce the size of the individual colloids without affecting their lattice position (Figure 8a−c).220,262,265−268 Arrays of non-close-packed, extremely small metal nanoparticles with adjustable distance can be created similarly by complete combustion of metal-complex containing colloid arrays.269−271 (ii) Heat treatment can be used in the case of hybrid core− shell particles with a noncombustible core such as silica or metal.252,272 Retaining the particle position can be more challenging compared to plasma treatment due to various forces originating from depolymerization, carbonization, and combustion. (iii) Inherent particle shrinking after immobilization as a close packed monolayer on the target substrate by loss of the swelling solvent during drying. Prominent examples are water swellable poly(N-isopropylacrylamide) particles251,273,274 or hybrid core−shell spheres with a polystyrene251,275 or gold core.114,252,276 (iv) An elastomeric substrate can be stretched in order to separate the individual particles (Figure 8d,e).277,278 Once the desired separation distance is reached upon stretching, the colloids can be transferred to a desired substrate modified with a polymeric adhesion layer. More sophisticated elongation protocols can be used to create monolayer crystals with nonhexagonal symmetries as, e.g., square arrangements.278 Direct assemblies of non-close-packed monolayers are possible using oil−water interfaces for the colloid assembly. The self-assembly of latex particles at such oil−water interface leads to non-close-packed arrangements of the particles due to an increased repulsive character as compared to the assembly at the

2.3. Binary Monolayers

Binary monolayers consist of large (L) and small (S) colloids that are cocrystallized to form an ordered lattice structure (see Table 3). Typically, a binary two-dimensional crystal is based on a M

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Table 3. Overview of Crystallization Methods to Yield Binary Monolayer Assemblies

(Figure 9a). The elastic nature of PDMS allowed stretching the mold before replication to obtain anisotropically shaped monolayer structures (Figure 9b). Subsequent filling of the interstitial sites with smaller colloids via convective assembly created complex arrangements with decreased symmetry (Figure 9c). The second strategy consists of a one-step codeposition process296 in which the two types of particles are assembled in situ from mixed dispersions. Besides convective assembly techniques,296−298 the coassembly process allows to employ the air-water170,258,299 or oil-water280 interface to crystallize binary mixtures of colloids in an ordered fashion. To ensure proper crystallization, exact control over the stoichiometry of the two particle populations at the interface is crucial. Often this cannot be achieved trivially by simply applying stoichiometric spreading mixtures, as different types of particles have different tendencies to be transferred from the spreading solution to the interface. The surface fraction after spreading of a given type of particles at the interface has to be determined individually and can be deduced from surface pressure−area isotherms on a Langmuir trough. Knowledge of this surface fraction for each particle type provides a high degree of control over the

close-packed monolayer of large spheres. The interstitial sites of the monolayer are occupied by a distinct number of small spheres, forming superlattices typically denoted LSn structures, with n indicating the stoichiometry of the small particles with respect to the large ones. The combination of two particle types for the preparation of binary colloidal monolayers increases the complexity of the experimental procedure and the number of parameters that need to be controlled in order to achieve a satisfactory long-range order and stoichiometry. Two strategies have evolved:14 In two-step sequential assemblies,288 a homogeneous close-packed monolayer is crystallized prior to depositing small particles. The interstitial sites of the largeparticle monolayer provide energetically favorable locations for the small particles that can form a superlattice by occupying these sites in a regular fashion. The small particles can be deposited via convective assembly,288−291 electrophoretic assembly of likecharged particles on electrodes,292,293 electrostatic attraction of oppositely charged particles294 and spin-coating.295 An interesting approach to generate more complex binary crystal structures was reported by Choi et al.285,286 who combined colloid templating with soft lithography techniques by creating a poly(dimethylsiloxane) (PDMS) mold of a colloidal monolayer N

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Figure 9. Sequential assembly of binary monolayers into complex structures using prestretched substrates according to Choi et al.285,286 (a) Schematic illustration of the process to create anisotropic nanostructures by colloidal templating and their decoration with colloids to form binary assemblies. A colloidal monolayer is replicated with PDMS (i) which is subsequently stretched (ii) and replicated with photoresist (iii) to produce anisotropic surface patterns (iv). These are used as a substrate to crystallize smaller colloids into the interstitial sites provided by the template (v). (b) SEM images of examples of surface structures prepared by replication of deformed PDMS replicas of colloidal monolayers.286 (c) Deposition of smaller colloids lead to complex binary assembly structures.285 All scale bars are 1 μm. Adapted with permission from refs 285 and 286. Copyright 2009 and 2010 American Chemical Society.

Figure 10. Co-crystallization of binary monolayers on a Langmuir trough. Reprinted with permission from ref 170. Copyright 2011 Wiley. The stoichiometry of large and small colloidal particles present at the air-water interface directly translates into different binary configurations of the assembled monolayer, which can be adjusted from LS2 to LS9. Scale bars are 1 μm.

stoichiometry in coassembled binary monolayers (Figure 10).170 An overview of existing approaches, classified by the applied techniques, the reported crystal structures and the accessible size ratios is given in Table 3.

surface regions that will be reviewed in detail in the following sections. The most commonly applied patterning method defines the desired structural confinement by surface modifications of the substrate prior to the assembly process. Two main approaches can be distinguished: physical and chemical patterning. Physical patterning processes structure the substrate topographically to provide regions of confinement at which colloids will assemble. Such templates can consist of channels or stripe patterns, small holes that accommodate individual colloids or patches of monolayers or regions with a materials contrast, e.g., substrate with electrodes and insulating regions. Chemical patterning methods apply surface chemistry in combination with micro-

2.4. Two-Dimensional Patterning of Colloidal Crystals

The specific integration of nanoscale building blocks into complex, hierarchical assemblies is necessary to fully exploit the potential of colloidal particles in the design of future devices. One main goal is to precisely confine the deposition of colloids onto selected regions of a substrate, e.g., microengineered, functional parts of a device. Several approaches have been established to create patterns of colloidal monolayers at defined O

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Table 4. Methods to Generate Hierarchical 2D Structures with Colloidal Crystals

Figure 11. Classification of colloidal monolayer patterns with respect to the relative template dimensions. (a) The dimension of the pattern is much larger than the colloid size (Dpattern ≫ Dcolloid). Ordered monolayer patches result. Adapted with permission from ref 325. Copyright 2000 Nature Publishing Group. (b) The dimension of the pattern matches multiples of the colloid diameter (Dpattern = nDcolloid [n = 1, 2, ...]): high ordering or the creation of symmetric clusters is achieved. Adapted with permission from ref 239, copyright 2002 Wiley, and from ref 303, copyright 2001 American Chemical Society. (c) The dimension of the pattern is comparable to the size of the colloids applied (Dpattern = Dcolloids): nonequilibrium symmetries result by defining each colloid position in the lattice307 through the topographic template.277 Reprinted with permission from ref 307. Copyright 2009 American Chemical Society.

patterning, either by external force fields, such as optical or electric fields or by precisely controlling experimental conditions in the assembly process itself. Table 4 provides an overview of experimental methodologies to create hierarchical 2D colloidal assembly structures. Besides differentiation of the methodologies to create colloidal surface structures, it is further possible to classify such twodimensional patterns according to their dimensions with respect

structuration processes resulting in regions with higher and lower affinities for the colloids to be deposited. Typically, silane- or thiol chemistry is used for oxide-based substrates or gold surfaces, respectively. Another approach to generate surface patterns consists of mechanical removal or deposition of colloids starting from homogeneous monolayers. The archetypal example of this method is the use of microcontact printing300 processes to generate the patterns. Finally, lateral colloid structures can also be created on substrates without any predefined substrate P

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Figure 12. Hierarchical assembly of colloidal particles or monolayers on patterned substrates. (a) Binary monolayer deposited onto a micropillar array. Reprinted with permission from ref 170. Copyright 2011 Wiley. (b) Square symmetry induced by a pyramidal groove. Reprinted with permission from ref 68. Copyright 2001 Wiley (c) Assembly of colloidal monolayers in electroconductive grooves. Only if the width of the groove is commensurate with a distinct number of colloids, a high degree of order is present. Reprinted with permission from ref 239. Copyright 2002 Wiley. (d) Assembly of colloidal clusters with a high degree of precision into a prestructured substrate. Reprinted with permission from ref 303. Copyright 2001 American Chemical Society. (e) Square symmetry monolayer assembled on a substrate prepatterned with extended grooves. Spacing and assembly direction were chosen to match the square symmetry as indicated in the inset. Reprinted with permission from ref 306. Copyright 2008 Wiley. (f,g) Dry assembly of particles into prestructured silicon wafer substrates to induce line-patterns (f) and complex symmetries (g). Reprinted with permission from ref 307. Copyright 2009 American Chemical Society.

2.4.1. Assembly of Monolayers on Topographically Patterned Substrates. The guided assembly of particles by surface templates is a fundamental process to prepare hierarchically patterned colloid structures, and a wide variety of process conditions exist in the literature to produce such structures. In general, one distinction can be made in the way the monolayer is assembled. Most often the deposition processes utilize convective assembly mechanisms (section 2.1.1.1). The presence of surface patterns thus provides nucleation and deposition sites for the colloids in this process, which has been used with an immense variety of structures of all sizes.68,201,301,303,306,327−329 Alternatively, patterns can be generated by the aid of electric fields on patterned electrodes.239,304,324 Conceptually different are techniques that preassemble close-packed monolayers at the air−water interface and transfer them onto structured substrates in a subsequent step. Such processes allow deposition on a variety of substrate topographies and yield hierarchical order. However, as the packing of the two-dimensional crystal is decoupled from the surface structures, only minimum-free energy crystal lattices (i.e., close-packed monolayers) can be obtained.170,219,220,309 An interesting deposition technique was recently demonstrated by Khanh et al.307 They used dry colloidal particles and manually rubbed them into surface patterns, thus circumventing a variety of problems that arise from the drying process in liquid-based assembly processes, most prominently viscous drags and capillary forces acting on particles. Figure 12 presents a selection of different surface hierarchies using surface topographies of different feature sizes. Macroscopic substrate structures have been applied to create patterns of ordered colloidal monolayers. As an example, Figure 12a illustrates the decoration of micropillars with a binary colloidal monolayer.170 The assembly of colloidal mono- and multilayers into extended surface grooves has been studied for their

to the size of the respective colloidal building blocks. One may distinguish three distinct categories (compare Figures 2 and 11): (i) The surface structures used for patterning can be much larger than the colloid dimensions (Dpattern ≫ Dcolloid) (ii) The pattern dimensions can be commensurate with a few integer multiples of the colloid diameters (Dpattern = nDcolloid [n = 1, 2, ...]) (iii) The pattern can be of the same size as the individual colloids (Dpattern = Dcolloids). This classification is of relevance as different surface morphologies will result depending on the selected structuring process. When the dimensions of the pattern are much larger than the particle size, extended patches of colloidal monolayers result with superstructures reflecting the respective pattern (Figure 11a). Such hierarchical assemblies of close-packed colloidal monolayers are of interest, e.g., for the combination with microstructures in devices;302,324,325 or to add a nanoscale surface pattern to microstructural assemblies.220 Patterns with dimensions that are commensurate with a distinct number of particles are depicted in Figure 11b. They can be either utilized to induce superior ordering of particles,68,239 or to precisely prepare clusters with a distinct number of colloids.303,310 Patterns which are commensurable to the lattice periodicity are a tool to generate different crystal symmetries and lattice orientations with colloidal particles. This method, termed graphoepitaxy326 gives access to patterns or crystal structures not accessible by classic crystallization approaches on nonpatterned substrates.211,240,306,307 Exemplarily, Figure 11c shows a monolayer with square symmetry induced by placing colloidal particles into individual voids arranged with the desired lattice symmetry. Q

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Figure 13. “Colloids on top of colloids”: A hierarchy is introduced by the assembly of colloids on top of differently sized colloids: (a) Ternary hierarchy with a binary monolayer deposited on top of a very large particles. Reprinted with permission from ref 170. Copyright 2011 Wiley. (Size ratios of up to 2 orders of magnitude.) (b) A monolayer of 180 nm deposited on a monolayer of 1.1 μm particles. Reprinted with permission from ref 219. Copyright 2009 Wiley. (c) Monolayer patterns created by using micron-sized particles as etching mask: A monolayer of micrometer sized particles is deposited onto a monolayer of smaller particles, reduced in size by a plasma treatment and used as a mask to remove parts of the underlying monolayer. After removal of the large particle monolayer mask, symmetric patterns of the underlying small particle monolayer are created. Reprinted with permission from ref 308. Copyright 2008 American Chemical Society.

2.4.2. “Colloids on Top of Colloids”. Structural hierarchy can also be achieved by the deposition of colloids on top of colloids of different sizes. While this has mostly been applied in two-step crystallization processes of binary monolayers (section 2.3) with relatively small size ratios usually less than one order of magnitude, a number of reports exist on the creation of a more pronounced degree of hierarchy.170,309,316 Figure 13a shows an example of a ternary colloidal assembly consisting of a binary monolayer on top of a very large colloid with a size of 50 μm.170 Similarly, close-packed latex particles,316 non-close-packed silica monolayers,309 and hybrid Au@poly(N-isopropylacrylamide) microgels252 have been successfully transferred to larger spherical particles. The decoration of micron-sized particles by 200 nm sized particles (Figure 13b) was used as a template to grow additional inorganic nanostructures to yield highly hierarchical surface structures that are interesting for a number of different applications, e.g., to control wetting.219,331 Finally, colloids have also been used as etching masks to create patterns in an underlying monolayer of smaller particles, as illustrated in Figure 13c.308 2.4.3. Assembly of Monolayers on Chemically Patterned Surfaces. The combination of micro- and nanopatterning techniques (usually photolithography or microcontact printing) with the ability of functionalized thiols or silanes to form self-assembled monolayers (SAMs) onto gold or silica surfaces provides a platform to generate chemically patterned substrates. The chemical contrast between neighboring regions in the pattern can be exploited for site-selective attachment of colloids, and therefore for the fabrication of hierarchical colloid patterns. Selective particle deposition can be achieved either by enhancing the adhesion of the particles at the desired substrate region or by tailoring the wetting properties of the substrate to allow contact of the colloidal dispersion during the deposition process only at the desired areas. 2.4.3.1. Particle Attachment on Patterns with a Surface Charge Contrast. The attachment of colloids to selected regions of a substrate is strongly enhanced by attractive interactions between the surface groups of the particles and those of the substrate, and the effect of the capillary forces upon drying.228,310 Reversible intermolecular interactions of various origins (electrostatic, hydrogen-bonding, and van der Waals) can be exploited for such purposes.147,148 In general, lateral mobility is required to achieve a high packing order of the colloids at the substrate.210 Electrostatic attachment of charged colloids to oppositely

possibility to guide light.68,301 If the size of the surface grooves approaches the dimensions of the individual colloids, a precise placement of a defined number of colloids can be achieved. Figure 12b,d illustrates this effect. Figure 12b shows a squaresymmetric assembly of colloids in a 4 × 4 matrix by confinement in a quadratic surface groove.68 Systematic variation of the size of voids in a surface has also shown to lead to the defined assembly of colloidal clusters with an adjustable number given by the ratio of diameters between surface structures and colloids.303,330 Examples shown here are clusters of two to five colloids assembled in circular hole patterns (Figure 12d).303 The effect of confinement on the ordering process of colloidal monolayers is further illustrated in Figure 12c. It shows colloids deposited into electroconductive surface grooves.239 A high degree of ordering is achieved only when the size of the groove is commensurate with a distinct number of colloids. The same effect can be exploited to create crystals with a superior long-range order of the constituting colloids, which is also often referred to as grapho or colloidal epitaxy.304 The ordering effect does not depend on the deposition process or the nature of the surface grooves and comparable results have been reported for the deposition of colloids in surface wrinkles327 or the patterned polycarbonate surface of a DVD.329 An interesting experiment was reported by Sun et al.,306 who assembled colloids on substrates with linear grooves and realized that the orientation of the grooves with respect to the deposition front crucially affects the crystal structure of the monolayer. If the grooves are oriented diagonal to the drying front (i.e., by an angle of 45° with respect to the water meniscus) and if the pitch was chosen to match the colloid spacing in the square lattice, a highly ordered square symmetry monolayer was deposited (Figure 12e). Substrates with feature sizes matching the dimensions of the individual colloids have been extensively applied to design novel 2D and 3D crystal structures. The aforementioned dry assembly process allowed the creation of lines of single-particle width (Figure 12f), as well as complex monolayer geometries determined by the surface patterns (Figure 12g).307 Square symmetry mono- and multilayers have also been fabricated by Dziomkina et al. with the help of nanostructured electrodes to electrodeposit colloids at individually designed surface spots.211,240 Similarly, the creation of non-close-packed monolayers with hexagonal symmetry328 and the controlled placement in complex surface geometries201,302 was achieved by convective assembly and printing305 techniques (this is also discussed in section 2.4.3.3). R

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charged surface regions, induced by creating a contrast of positive and negative charges on the surface, induces a very strong adhesion between the substrate and the colloids.227,228 As a consequence, thermally activated, lateral Brownian motion of individual colloids required for reorganization into increasingly ordered structures is impeded, resulting only in the formation of disordered monolayers by a random sequential adsorption process (compare section 1.2). However, if high lateral ordering of the colloids is not required, electrostatically induced pattern generation is an experimentally simple and fast method and has been demonstrated for a variety of patterning processes and feature sizes. Large structural features in the micrometer regime have been realized using photodegradable, self-assembled silane monolayers,228,332 microcontact printing of thiols310 and by selective assembly on polyelectrolyte multilayers.209,311 High resolution patterns capable of attracting individual colloids have been prepared by atomic force microscopy based techniques, i.e., using dip-pen nanolithography333 or by writing charge patterns in a hydrophobic fluoropolymer thin film using a conductive atomic force microscopy tip.334 The controlled placement of individual colloidal particles, as well as the generation of defined colloidal clusters by assembling a restricted number of colloidal particles on patterns (with their size matching the cross-section of the desired cluster geometry), is not compromised by the strong electrostatic binding forces or like charge repulsion between particles. Consequently, the precise placement of one to four colloids has been demonstrated (Figure 14a).311 Immersion capillary forces acting during the drying process lead to focusing of the individual nanoparticles in the center of each attractive spot in the pattern, which adds to the precision of the method.310 Recently, an approach to improve the limited order in electrostatically driven assemblies has been proposed by Zhang and co-workers (Figure 14d) by tuning the charge density on the substrate, and thus decoupling the assembly process from the subsequent strong electrostatic fixation of the colloid monolayer.210 Such control over the charge density is achieved by assembling the particles in ethanol, where the polyelectrolyte layer remains undissociated. Subsequent exchange of the solvent to water switches the electrostatic attraction between the adsorbed colloids and the substrates. After washing, only a single layer of colloids, electrostatically attached to the surface, remains on the substrate. Lateral structuring of the polyelectrolyte film provides binding sites for the colloidal monolayer, thus allowing for a precise patterning with high order. Figure 14c,d compares patterns created by the conventional electrostatic attraction process (Figure 14c)209 and the two-step process proposed by Zhang et al. (Figure 14d). The order in the pattern increases drastically if the deposition is decoupled from the electrostatic attraction. 2.4.3.2. Wettability Contrast-Induced Pattern Formation. Patterns of colloidal monolayers can also be created by tailoring the surface chemistry of the substrate in such a way as to confine the wetting with colloidal dispersions, to defined sites on the surface. Here, immersion capillary interactions are the main forces governing the ordering process. The long-range attractive character of this force generally induces a high degree of order in the monolayers (see section 1.2). The relevance of the capillary forces in colloidal assembly on chemical patterns with regions of different wettability has been shown by Guo et al.312 A drop of a suspension with negatively charged PS colloids was allowed to dry on mica substrates, which

Figure 14. Structured particle films by chemical substrate patterning. (a) Placement of individual colloids and colloidal clusters by electrostatic attraction to defined substrate spots. The colloid size is 4.3 μm. Reprinted with permission from ref 311. Copyright 2002 Wiley. (b) Patterns created by a wettability contrast that confines the colloid dispersion to selected substrate regions. Reprinted with permission from ref 315. Copyright 2005 American Chemical Society. (c) Patterns introduced by electrostatic attachment of colloidal films. The strong electrostatic interaction hinders lateral mobility of the colloids and thus impedes high ordering. Reprinted with permission from ref 209. Copyright 2000 American Chemical Society. (d) Decoupling the deposition from the attachment process circumvents the sequential random absorption mechanism. Thus, it is possible to achieve patterns with a high order by electrostatic attraction. Reprinted with permission from ref 210. Copyright 2010 American Chemical Society.

had been patterned with gold stripes by photolithography. Despite the repulsive Coulomb interaction between the negatively charged mica and the PS particle surfaces, a selective colloidal assembly onto the mica regions in a loosely packed arrangement was observed. This result suggests that the assembly is not driven by the intermolecular interactions between the particles and the surface but by the interaction between the hydrophilic mica surface and the water layer. During evaporation, dewetting of the surface starts at the places where the watersurface interaction is weak, i.e., the gold regions. The water film retracts to the hydrophilic mica regions, thus forcing the colloidal particles to assemble onto the mica stripes. This tendency can be modified by addition of surfactants, which change the wetting properties of the substrate and particle surfaces. In particular, addition of SDS led to the formation of drops onto the hydrophobic regions during evaporation and therefore the colloids assemble onto the gold stripes.312 Wettability contrast patterns can be introduced by various methods such as photolithographic patterning of two different thiols,335 photoinduced cleavage of hydrophobic surface modifications on titania,313 application of photodegradable silane molecules,228 photolithographic patterning with silanes,336 microcontact printing,314 or assembly of thiols and silanes on surfaces with a gold/silicon materials contrast.259 S

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The deposition of the colloids has been performed by simple drop casting,312,314 convective assembly processes,313,336 or by phase separation of two immiscible liquids.315 The latter process, introduced by Masuda et al.315 confines a hydrophilic liquid (i.e., the colloid dispersion in methanol) to hydrophilic surface regions by the addition of a continuous layer of a hydrophobic liquid (hexane in the example). The second liquid induces dewetting of the hydrophilic liquid from all nonhydrophilic surface regions and leads to a more accurate confinement of the colloid dispersion by increasing the contact angle at the borders of the pattern. Upon slow dissolution of the methanol in the hexane phase, the colloids are subjected to strong immersion capillary forces that induce mutual attraction and lead to highly ordered structures with a surprisingly low line-edge roughness, not exceeding the size of a single particle diameter. Figure 14b shows an example of a surface pattern generated by this method. In general, this flow induced particle aggregation leads to 3D colloidal crystal formation rather than pure colloidal monolayers (as discussed in section 3). The transition from 2D to 3D structures depends on the pattern size.336 2.4.3.3. Patterns Generated by Micro-Contact Printing of Colloidal Monolayers. Microcontact printing has been established as a fast, low-cost and precise technique to create surface micro- and nanostructures.300,337 In brief, it uses soft stamps to transfer material by mechanical contact. The use of microcontact printing to create patterned colloidal monolayer patches as well as applications of such patterns has recently been reviewed by Zhang et al.316 and will be discussed here only in brief. The key point to successfully print and transfer particle monolayers is the control over the balance of adhesion between the colloidal particles and the different substrates in order to selectively remove single colloidal layers from the donor substrate, while allowing the deposition of the same colloids on the transfer substrate. In practice, the adhesion can be tuned by modifying the surface chemistry of the elastomer (often polydimethylsiloxane, PDMS) stamp,338 by promoting adhesion to the second substrate,317,318,339 by actively controlling contact via inflatable stamps, and by exploiting contact rate-dependent adhesion strengths.340 Figure 15a schematically illustrates the microcontact printing process.317 A homogeneous, three-dimensional crystal or monolayer is used as the “ink pad” for the starting material. A soft, patterned stamp is applied and a single layer of particles is transferred to the stamp. This colloidal monolayer can subsequently be transferred as pattern to a second substrate, carrying a thin polymeric adhesion layer. The process is capable of printing arbitrary structures with a fair resolution in the micrometer regime and reasonably welldefined line edges (Figure 15b). The soft character of the elastomer stamp allows for coverage of curved surfaces as well (Figure 15c)317 and multiple deposition steps can be used to deposit defined multilayer patches (Figure 15d).318 By directly depositing gold nanoparticles into tailored voids in a PDMS template and controlling the adhesion to a desired substrate, Kraus et al. significantly advanced the methodology toward printing with single particle resolution in arbitrary patterns and with high fidelity.305 The patterning process can also be combined with mechanical deformation of the substrate, leading to complex structural pattern designs (Figure 15e).277,278 2.4.4. Patterning without Substrate Engineering. The creation of patterns without a substrate-engineering step preceding the actual deposition process is of technological

Figure 15. Patterning of colloidal monolayers by microcontact printing.317 (a) Schematic process description.317 (b,c) Line patterns by microcontact printing; (c) Demonstration of the possibility to pattern curved surfaces, such as a glass vial. Reprinted with permission from ref 317. Copyright 2004 American Chemical Society. (d) Complex pattern geometry by multiple successive printing steps. Scale bar: 10 μm, inset: 2 μm. Reprinted with permission from ref 318. Copyright 2004 Wiley. (e) Combination of microcontact printing with PDMS stretching provides opportunities to create different crystal structures and pattern them into arbitrary shapes. Scale bar: 2 μm.Reprinted with permission from ref 277. Copyright 2005 American Chemical Society.

interest and can either be achieved by the application of external fields, or by sophisticated deposition process designs. Properly fashioned electromagnetic fields generated by focused laser beams have been exploited to create an optical pattern by which microscopic dielectric (polarizable) objects can be trapped and manipulated.320 The radiation pressure from the incident laser light moves the colloidal particles to the positions of the maximum intensity of the standing wave field.341 The energy to completely trap a sphere is just that required to overcome its thermal motion, and hence depends on the temperature.342 By these means, periodic crystals of micrometer size particles have been generated by creating an optical standing wave pattern with a regular array of intensity antinodes at the positions where the colloids are ultimately desired.343 Through intensity modulation of the periodic light field it is possible to induce changes in the phase behavior of the colloidal lattice.319 The use of such optical tweezers has the advantage of not requiring mechanical contact with a probe, of not being limited in particle number or morphology, and of offering precise control over particle position with rapid reconfiguration of the pattern. However, the controlled transfer of liquid-based assemblies to solid substrates is challenging, as strong hydrodynamic drag- and capillary forces act during the drying process. Further developments are being directed toward a more rapid manipulation of several particles at the same time by the generation of multiple light traps. Methods to achieve this are, e.g., time-sharing, holographic, or interferometric trapping, as well as splitting of an individual laser beam into an array of traps by micromirror- and microlens arrays. Quite interestingly, not only can colloidal particles be manipulated by light but also the colloidal particles themselves are capable to manipulate light and have been shown T

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Figure 16. Patterning of colloidal monolayers without substrate engineering. (a−c) Periodic contact line pinning in convective assembly processes can be used to create stripe patterns of a colloidal monolayer. Adapted with permission from ref 321. Copyright 2009 American Chemical Society. (d−f) Floatation of printed particles with different sizes at the air−water interface and subsequent deposition to solid substrates can be used to create structural patterns in colloidal monolayers. Reprinted with permission from ref 323. Copyright 2010 Royal Society of Chemistry.

to act as microlens arrays for projection photolithography.344 The periodicity of colloidal monolayers of micron-sized spheres can also directly be exploited as phasemask for the threedimensional patterning of photoresists.180,181 Complex patterns of colloidal particles on electrodes are accessible by superimposing optical and electrical fields. The additional introduction of electrostatic attraction binds the particles to the substrate more strongly, and thus overcomes problems of stability of the patterns during drying. Hayward et al. described a method that combines the electric-field-induced assembly of colloidal particles with the photochemical sensitivity of the indium tin oxide (ITO) electrode (Figure 11a).325 Illumination of the ITO electrode by UV light results in a small increase in the current density within the cell, as a result of an increased charge transfer rate between solution and electrode due to generation of hole−electron pairs at the ITO-water interface by UV light. If the ITO electrode is illuminated through a mask, different regions of higher and lower current density will be generated across the electrode according to the light intensity pattern. The colloidal particles will be swept from dark areas into bright regions (with higher current density), reproducing the pattern of the irradiation mask. Despite the presence of charges, the quality of the monolayer patterns is high as a consequence of electroosmotic and electrohydrodynamic flows (compare section 2.1.1.2). The creation of colloid patterns purely by the design of the deposition process is advantageous both in terms of simplicity and reduction of production steps (and consequent costs) for technological applications. On the other hand, it requires careful mechanistic insight and understanding of the assembly process resulting from a balance between various types of fundamental interactions in colloidal matter. Recently, two interesting approaches have been demonstrated, and are highlighted in Figure 16. Watanabe et al. set out to understand stripe pattern formation in convective assembly processes (Figure 16a).321 If properly balanced, the evaporation of solvent induces a particle flux toward the crystal growth front and a steady-state is achieved, leading to a homogeneous growth of a well-ordered colloidal monolayer (Figure 16a/i). If the concentration of particles is reduced, the equilibrium is disturbed and the growth rate cannot compete with the evaporation. As a result, the meniscus of the

liquid bends toward the substrate (Figure 16a/ii). The reduced height of the meniscus at the curved interface further reduces the particle flux toward the growth front and leads to an increase in concentration at the lower surface region B. As the meniscus continues to bend, the height of the water level finally drops as low as to completely impede the flux of particles toward region A (Figure 16a/iii) and the particles accumulated in region B start to assemble in a new crystal front (Figure 16a/iv). By adjusting several experimental parameters, the authors gained control over size and distance of the stripes and reported full control over the two-dimensional growth of stripes consisting of pure monolayers. By rotating the substrate by 90°, network patterns with a square symmetry can be prepared as well.322 The assembly of colloids at the air−water interface has been exploited by Retsch et al. to prepare heterogeneous monolayers consisting of ordered patterns of colloids with different sizes (Figure 16d).323 Patterns of sparsely distributed particles with different sizes were inkjet-printed on a substrate (Figure 16d/i) and carefully floated onto the air−water interface by immersion of the substrate under a shallow angle (Figure 16d/ii). As for the nonpatterned particle layers described in section 2.1.2 and Figure 7, the floating process leads to well-ordered colloidal monolayers. The pattern printed on the template is reproduced during the floatation process and can be controlled by taking into account the shrinkage of the monolayer in the direction of immersion during the assembly process (Figure 16d/iii). Subsequent transfer to solid substrates (Figure 16d/iv) immobilizes the patterned monolayer, which is comprised of individual domains of close-packed particles. This can be seen by uniform colors in the optical photograph, shown in Figure 16e. The high order and relatively sharp line boundaries are revealed by electron microscopy (Figure 16f).

3. 3D COLLOIDAL ASSEMBLIES Expanding colloidal monolayers by a further dimension in space and complexity leads to three-dimensional structures. Such 3D colloid structures have attracted a very broad range of interests from various fields and disciplines over the last 30 years.12,345,346 The potential of well-defined nanoparticles to organize into regular nanostructures fueled intense research and application U

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Table 5. Methods for 3D Colloidal Assembly

developments in chemistry, physics, biology, and engineering. Foremost, the self-assembly of nano- and microscopic particles into colloidal crystals has been investigated exhaustively and a range of excellent reviews cover these and related topics in great detail.13,15,75,92,347−349 Established techniques to fabricate 3D colloidal crystals and films are comprehensively summarized in Table 5 with references to the different methods and approaches.

The focus of the following section goes beyond 3D systems with simple geometry, and targets the assembly of uniform spheres into more sophisticated hierarchical structures with organizational features at several length scales. Access to such hierarchically structured assemblies are discussed in the context of many methods already introduced for the fabrication of 2D systems (section 2), which can also be applied to 3D structures. V

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Figure 17. (a) Convective assembly for the fabrication of 2D and 3D colloidal crystals. Reprinted with permission from ref 198. Copyright 1996 American Chemical Society. (b) Simultaneous deposition of two different types of particle crystals on opposite faces of a glass slide facilitated by a fluorinated solvent subphase. Adapted with permission from ref 372. Copyright 2006 American Chemical Society.

prevalence of inhomogeneities in the colloidal crystal film thickness, which are caused by pinning and slipping of the meniscus at the three phase contact line between the substrate, the dispersion, and air.371 Furthermore, even if colloidal crystal films on rigid substrates can feature single-crystalline monoliths of several tens of μm in width and up to hundreds of μm in length, their quality is limited by μm sized cracks as a result of stress release upon drying (which will be discussed in section 3.1.3). With the simple approach of withdrawing a target substrate from the particle dispersion, one will typically obtain a colloidal crystal on either side of the substrate, unless one side has been hydrophobized. Takeda et al. demonstrated a method to grow colloidal crystals with different types of particles on each of the two sides of a glass substrate.372 The self-assembly is achieved via vertical lifting deposition, but the glass slide is immersed into a fluorinated solvent and on either side of the hydrophilic glass slide, an aqueous droplet of the desired particle dispersion is placed. By subsequent substrate withdrawal the colloids assemble on both sides of the target (Figure 17b). Transmission spectra of a sample carrying 240 and 466 nm PS particle crystals on each side revealed two distinct stop bands. 3D binary colloidal crystals can be crystallized from dispersions containing two particle populations of different sizes, and in analogy to 2D binary assembly structures, the coexistence of two particle types increases the parameters space, since tight control has to be maintained over the relative particle sizes and ratios. The smaller particles need to be chosen such that they fit into the tetrahedral and octahedral voids between the large spheres of the templating fcc crystal lattice. Such binary 3D crystals can be inverted to porous structures with a well-defined hierarchy of mesopores.373,374 3.1.2. 3D Colloidal Crystals at Liquid Interfaces. The air−water interface itself can provide a flexible support for floating colloidal monolayers, so that they can be successively deposited on top of each other.255 This method has been demonstrated by Reculusa et al.,216 who used the LB method to assemble colloidal crystals with well-defined thickness by repetitive transfer of particle monolayers from the air−water interface. The advantage of this method is clearly the great control over the number of particle layers within the crystal, which is simply given by the number of repetitions of the transfer process. In addition, this method enables to incorporate various

Further processing by replication and transformation of 3D colloidal crystals into porous materials and inverse opals by particle coassembly or backfilling of interstitial sites is generally not included in this review. Only some instructive examples are highlighted for certain types of assembly processes. A detailed introduction to the field of inverse opals, their assembly, material choices, and applications can be found in recent review articles.13,55,56,59,350 3.1. 3D Colloidal Crystals on Planar Surfaces and Interfaces

Various assembly techniques to prepare colloidal crystals of high order without additional superstructure are discussed first in this section, more intricate pattern features are described in subsequent sections. Such methods yield colloidal films directly on planar solid substrates or at the liquid−air interface. 3.1.1. Direct Assembly on Solid Substrates. One of the most widespread and simplest methods for colloidal crystal fabrication is based on convective particle aggregation, which was introduced by Denkov et al.,197 initially used for the fabrication of colloidal monolayers (compare to section 2.1.1.1). The interplay of convective drag force, electrostatic repulsion, and capillary attraction caused by the evaporation of solvent at the liquid meniscus in contact with the solid substrate leads to highly ordered structures. Two preconditions need to be fulfilled for a successful crystal formation: (a) the solvent has to wet the surface of the solid substrate to ensure a low contact angle at the meniscus (b) the interaction between the substrate and the particles needs to be small to provide enough mobility allowing the particles in contact with the substrate to organize into a hexagonal array. The thickness of the resulting crystal film is then determined by a range of parameters such as temperature, humidity and colloid concentration, and can be tuned from single monolayers to several tens of micrometers. In practical terms, the colloidal crystals are fabricated either by the method of convective assembly or by vertical lifting deposition (Table 5). In the first case the liquid of the particle dispersion evaporates in the presence of the static substrate, which can be fixed perpendicular to the solvent surface359 or at an inclined angle.369 In the latter case the target substrate is continuously removed from the particle dispersion at a slow speed (Figure 17a).198,370 A common drawback of the convective assembly method is the W

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types of particle layers375 and any kind of particles within each layer. The floating monolayer technique described above in section 2.1.2 represents another interface-mediated monolayer fabrication method that can potentially be used to build 3D structures.219 A limitation of these methods may be the propagation and accumulation of defects from the bottom layer through the whole layer stack with each individual transfer steps. Furthermore, the lack of registry between the individually transferred layers leads to a random close-packed structure rather than a single-domain fcc crystal. A method to directly immobilize 3D multilayered colloidal crystal films at the air−water interface by convective flow was introduced by Im et al.363 The 3D crystal is simply formed at the interface by heating a colloidal dispersion to 90 °C in a convection furnace. The induced convection leads to a drag force on the suspended PS particles from the hot plate at the bottom of the dispersion to the top of the container, and the colloids eventually become trapped at the air−water interface. The interplay of capillary attraction and electrostatic repulsion between the particles at the interface leads to nucleation and formation of ordered islands, which successively grow larger. The authors postulate that due to the lower effective density of the 3D colloidal crystal composed of PS particles and air relative to bulk water, the ordered array floats at the water surface and continues to grow by the particle supply from the subphase. Finally, the floating colloidal crystal can be transferred to a target substrate. The importance of the relative densities in this procedure has been pointed out by Liu et al. in experiments where they fabricated ordered arrays of μm sized PS spheres. By adding ethylene glycol to the aqueous suspension, they adjusted the subphase density and only ordered crystals formed as long as the subphase exceeded the density of PS (Figure 18a).376 A further

enhance evaporation at room temperature.378 However, their method differs from the original concepts as it was conducted in thin films of particle dispersions on a glass substrate. Homogenous films and suppression of the coffee-stain effect were reported, which may also be attributed to the high volume fraction of particles in the employed dispersions (30 vol %).379 In an effort to directly obtain free-standing colloidal crystal films, Gu et al. exploited colloidal self-assembly at adjacent air− water−air interfaces in thin dispersion films using a soap-bubble technique.380 In the reported experiments a colloidal suspension was picked up with a copper ring of 1 cm diameter - just as one would pick up a soap solution for soap bubbles (Figure 18b). The colloidal dispersion was left to dry under ambient conditions, which ultimately yielded a well-ordered, free-standing colloidal film of macroscopic dimensions (Figure 18c). The water subphase can also be exchanged by another liquid, like molten metals such as Ga or Hg. The immiscibility with the aqueous medium allows direct placement of a particle dispersion droplet onto the liquid metal surface. Upon drying large crackfree colloidal crystals are obtained.381 However, environmental and health concerns about the toxic Hg limits the widespread use of this method. A great advantage of fluid interface-mediated assembly methods lies in the efficient reduction of crack defects in the resulting colloidal crystals by sustained particle mobility during aggregation. While on solid supports the lateral extension of the crystal monolith is limited to tens or hundreds of μm2 due to pinning on the substrate, crystal monoliths up to cm2 can be realized at liquid interfaces. 3.1.3. Defects and Cracks in Colloidal Crystals. Defects are an intrinsic problem in crystallization processes and can seriously compromise quality and applicability of colloidal crystals. However, the formation of defectsif properly controlledcan be exploited to deliberately create a hierarchical organization. The research efforts in this field can be classified into three major categories: (1) study of fundamental physics and analysis of intrinsic defects and cracks in the crystal structure, (2) method development to reduce intrinsic defects and cracks, and (3) engineered defect generation. 3.1.3.1. Intrinsic Defects. The concentration and types of defects in a colloidal crystal depend on the specific assembly method, the type of colloidal particles, and their size dispersity. The predominant defect types are point and line defects. Using convective assembly with hard spheres, Rengarajan et al. found a direct relation between the particle size dispersity and the defect density, which deteriorated the optical properties.382 Consequently, by exploiting the flexibility of soft particles, 3D colloidal assemblies with very low intrinsic line and point defects can be obtained. The reduced defect density is directly reflected in remarkably sharp and tunable Bragg peaks in the optical absorption, as demonstrated for Au@PNIPAM (poly(Nisopropylacrylamide)) core−shell colloidal crystals featuring a high refractive index contrast.383 The influence of stacking faults between an fcc crystal (ABC layer progression) and a hcp crystal (ABA layer progression) on the optical properties were investigated by Vekris et al.384 No effect of these stacking faults were found for the optical stop band with light propagating perpendicular to the (111) plane, but higher bands and complete photonic band gap bands are affected. The characterization of defect sites was achieved with thin films (few particle layers) via SEM and micro-optical spectroscopy,384,385 or by using confocal microscopy, which limits the accessible size range to spheres of several 100 nm.17,18,386 Thicker samples of 15−20 layers have

Figure 18. (a) 3D colloidal crystal assembly at the air−water interface, adapted with permission from ref 376. Copyright 2005 American Chemical Society. (b) Crystal formation at adjacent air−water−air interfaces. A homogeneous free-standing colloidal crystal film was obtained after dipping a copper ring into a dispersion of PS particles. (c) High magnification SEM images of the resulting colloidal crystal, adapted with permission from ref 380. Copyright 2007 Royal Society of Chemistry.

extension of this method allowed fabrication of a 3D silica crystal, which is remarkable due to the considerably higher density of SiO2 spheres compared to PS.377 Wang et al. investigated a strategy to reduce the high temperatures required during the selfassembly process to induce the convective flow to the air−water interface. They mixed cosolvents like EtOH into the subphase to X

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Figure 19. Control of crack formation in colloidal crystals. (a and b) Low and high magnification images of crack-free inverse opals obtained from codeposition of poly(methyl methacrylate) (PMMA) particles and tetraethoxysilane (TEOS). Scale bars: 10 μm (a) and 1 μm (b) adapted with permission from ref 399. Copyright 2010 National Academy of Sciences of the United States of America. (c) Concept of crack engineering using a patterned substrate with varying wettability. (d) Cracks forced into a checkerboard pattern after colloidal crystal formation and annealing. Adapted with permission from ref 407. Copyright 2011 American Chemical Society. (e−g) Assembly of colloidal crystals on superhydrophobic surfaces. Adapted with permission from ref 357. Copyright 2012 American Chemical Society. (e) Schematic illustration of the difference in assembly between high adhesive force (left) and low adhesive force substrates (right). The elimination of pinning on low adhesive force substrates leads to a crack-free assembly of the colloids. (f) SEM and optical images of a crack-free opal assembled on a low adhesive force substrate. (g) Comparison of the optical properties of colloidal crystals assembled on substrates with varying adhesive force. A narrowing of the peak width of the Bragg reflection indicates higher order on lower adhesive force substrates.

been investigated by microradian X-ray diffraction, where line defects at the crystal surface could be attributed to double stacking faults.387 3.1.3.2. Cracks. Besides point and line defects within the colloidal crystal lattice, the formation of extended cracks (often larger than several particle diameters) represents an additional challenge for the fabrication of high quality materials. Such macroscopic cracks inevitably evolve during the drying of the colloidal particles on rigid substrates due to compressive stresses perpendicular and tensile stresses parallel to the plane of the

support material. A comprehensive review on cracking and evaporation in drying colloidal films has been recently published by Routh.48 Russel and Tirumkudulu have carried out a detailed study on the complex drying and cracking behavior.388 The evolution of macroscopic cracks strongly depends on the shear modulus of the colloidal particles as well as the layer thickness of the drying film.389,390 The driving force for crack nucleation is controlled by the interplay between a minimum capillary pressure for crack formation and the maximum sustainable capillary pressure within a colloidal particle aggregate. The Y

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flexible substrate, has been used by Zhou et al. to demonstrate cm2 sized filled colloidal crystal and inverse polymer opals.404 The combination of infiltration and substrate bending allows for sufficient tensile stress release to result in a crack-free colloidal crystal, which possesses sharper photonic band gaps. Ultimately, Huang et al. exploited the low-adhesive properties of superhydrophobic substrates to prepare crack-free, high quality opal films.357 Once the adhesive force to the substrates dropped below a critical value (determined as 156 μN), pinning of the colloidal dispersion is no longer energetically favorable. Instead, the colloidal film maintained its mobility during drying and continuously receded with the contact line of the colloid dispersion to form a homogeneous, crack-free film (Figure 19e,f). The absence of cracks led to crystals featuring much narrower Bragg reflection peaks, indicating that the optical properties can serve as an indicator for the quality and homogeneity of the opal film. Figure 19g shows optical reflectance spectra of films assembled on substrates with varying surface energy. A strong narrowing of the reflection band is visible for films grown on substrates with an adhesive force lower than 171 μN, indicating the transition from a Wenzel-type wetting405 and a Cassie state406 that supports a receding contact line (Figure 19e). It should be noted that simple drying of an aqueous colloidal dispersion in a hydrophobic container is also a viable route toward macroscopic, free-standing colloidal crystals with low crack-density and good crystallinity. This way Ruckdeschel et al. fabricated monoliths from hollow silica spheres with several 100 μm in thickness.37 3.1.3.3. Engineered Defects and Cracks. Cracks and defects in colloidal crystals do not necessarily deteriorate the materials properties, but when intentionally designed, they can be exploited to introduce patterns and structural features at larger length scales.408,409 Putting random cracks to use has been shown by Rao et al. by assembling a film of acrylic based colloidal particles on a glass substrate. Random cracking was spontaneously observed along with the formation of a continuous, sparse network. Using metal evaporation, this template could be converted into a transparent, conducting electrode after removal of the cracked colloidal film layer.26 Crack engineering targets the predetermination of the location and the pattern shape of cracks. Sun et al. presented a detailed study of how patterns of varying surface tension can induce defined crack patterns in colloidal crystal films of several μm thickness, which are confined between two substrates.407 The inherent crack density of the colloidal film had to be matched to the crack spacing of the template pattern. Parameters governing this dependency are film thickness, particle size, and evaporation rate.410 The pattern is then transferred into the colloidal crystal by stresses due to wettability mismatch, and by differences in the confinement and mobility (Figure 19c,d). Defect engineering in general deals with the designed introduction of point-, line-, or plane defects into the lattice of a crystalline material. Point defects can be randomly introduced by adding a different type of spheres to a dispersion of the crystalforming colloids followed by particle crystallization.411 If control over the spatial position of the defects is required, a sequential fabrication technique has to be chosen, which is also typically employed for line- and plane defects. After assembly of a colloidal crystal distinct particles in the top layer can be modified by an electron beam and then selectively removed in a developer solution.412 The generated point defects are then integrated at defined positions into the interior of the colloidal crystal by

critical pressure for crack formation increases with decreasing shear modulus of the constituting spheres, since the tensile stress in the film can be accommodated by deformation of the particles. Therefore, soft colloidal particles can ultimately lead to void-free and crack-free films.391 Similarly, colloidal films with a decreasing layer thickness increasingly resist the critical capillary pressure, which results in a maximum thickness below which the drying front can recede into the colloidal film without causing cracking or peeling.389 These two regimes have been termed “strainlimited”, and “stress-limited” by Singh and Tirumkudulu. In the case of hard particles, which are mostly featured in the literature discussed in this review, the capillary pressure at the onset of crack formation is independent of the particle size. The occurrence of cracks can be further complicated by the presence of flaws during the dispersion drying as these can nucleate cracks. The maximum flaw size, which will not initiate an infinite crack, depends on the maximum possible capillary pressure. This is the reason why colloidal systems consisting of large spheres with high shear modulus feature a lower tendency toward cracking.392−394 An additional source of cracking can originate from the constituting particles themselves, in case they can undergo shrinkage upon complete drying. This volume reduction leads to the generation of a free volume, which is accommodated by the opening of cracks in an otherwise close-packed crystal. Repeated calcination of silica spheres prior to convective assembly from ethanol reduced this particle shrinking and led to larger crackfree areas.395,396 Whereas sintering is not a viable route for polymeric particles, the addition of cosolvents can lead to a partial swelling of the particles and thereby avoid crack formation.397 The resulting crystals are not in a completely dry state, which affects their optical properties and long-term stability. Other methods deliberately deposit filler material in the interstices between the spheres and thereby reduce crack formation upon drying. After crystallization the filler material can be removed without compromising the order in the assembled material, for instance silica etching via hydrofluoric acid vapors.398 Quite often, instead of removing the filler material from the interstitial space, the lattice-constituting colloid particles are removed, for example by calcination of polymeric spheres. Thereby large areas of crack-free inverse opals can be obtained (Figure 19a,b),399 and by proper choice of calcination temperature, the geometry of the pore can be tailored from spherical to anisotropic.400 However, even with these methods cracks start to occur when a certain film thickness (∼16 particle layers) is exceeded. In an effort to fabricate free-standing crackfree films Kanai and Sawada fixed the regular arrangement of dispersed particles, ordered in a shear field, by photopolymerization of a hydrogel matrix.401 Subsequently, by a gradual solvent exchange from water to ethanol, which does not dissolve the hydrogel polymer, a collapsed hydrogel composite with retained crystallinity was obtained. Even after complete drying no cracks were observed. This material represents a composite where the polystyrene spheres are embedded in a polymer matrix. Such swellable colloidal crystals have been used as sensing platform402 and for tunable lasers.403 Further approaches to reduce defects address the rigidity of the supporting substrate or the pinning of the colloidal particles to the substrate. Exchanging the solid support with liquid interfaces enables the growth of mm2 sized colloidal monoliths. However, the necessary transfer to a solid target substrate can introduce cracks.381 A combination of both, interstitial infiltration and Z

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Figure 20. (a) Defect mode (middle gray area) in the (111) photonic stop band caused by the introduction of a defect layer in a colloidal crystal of 650 nm silica spheres. Reprinted with permission from ref 418. Copyright 2005 Wiley. (b) Introduction of defined point-defect into the top layer of a PMMA colloidal crystal by e-beam lithography. Reprinted with permission from ref 413. Copyright 2005 Elsevier. (c and d) Concept and realization of line defects inside colloidal crystals. A photoresist is patterned on top of a crystal, after growth of an additional crystal layer the structure can be inverted and the photoresist is removed. Reprinted with permission from ref 416. Copyright 2005 Wiley. (e) Concept of 3D defects inscribed into colloidal crystals and inverse opals using multiphoton polymerization. (f) Side-view SEM image of a line defect inscribed into an inverse opal. Adapted from references.408,429 Reprinted with permission from ref 408. Copyright 2006 Wiley.

or variations of the refractive index and can be exploited for sensing of various physical conditions, such as pressure,422 temperature,417 or to detect the presence of analyte molecules, as for DNA hybridization.423 Other applications include lowthreshold lasing by a fluorescent dye-doped layer in the cavity of a flexible colloidal crystal sandwich.424 When using a photosensitive polymer for the defect layer further structuring can be performed by conventional photolithography. In this way defined patterns and lines can be written into the polymer layer, followed by colloidal crystal overgrowth to yield air channels416,425 and colloidal heterochannels416 in colloidal crystals or their inverse opal counterparts after replication (Figure 20c,d). Such channels can have dimensions of several particle diameters in width and height. In order to approach the minimum feature limit of line defects in colloidal crystals, Jun et al. employed direct writing with two-photon polymerization inside a colloidal crystal.426 The minimum width of the defect line was found to be about 1 μm, limited by the size of the confocal spot. Braun et al.427 pioneered the fabrication of fully three-dimensional defects within a colloidal crystal by multiphoton polymerization after monomer infiltration to write

successive growth of additional layers on top of the crystal (Figure 20b).413 Using plasma etching Ding et al. modified the volume fraction of the entire top layer of a polymeric colloidal crystal to introduce a defined 2D layer defect after continued colloid crystal growth.414 Quite commonly an additional layer of a specific polymer or photoresist is deposited on top of an assembled colloidal crystal, which can serve as defect layer itself, but also leaves ample degrees of freedom to apply nanoimprinting415 or photolithography416 for further structuring. Typical ways to deposit such defect layers are spin-coating,415 transfer printing,417 layer-by-layer assembly,418 chemical vapor deposition,419 or Langmuir−Blodgett transfer.420,421 Depending on the wettability, it may be necessary to protect the first layer of the colloidal crystal from infiltration by the defect layer material. This can be achieved for instance by prior infiltration with a sacrificial material such as ribose, which can be removed after deposition of the second colloidal crystal layer.422 2D defect layers sandwiched between colloidal crystals permit the existence of otherwise forbidden modes inside the periodic material (Figure 20a).418−420 These characteristic dips in the optical stop band of the photonic crystal are sensitive to dimensional changes AA

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Table 6. Methods to Generate Hierarchical 3D Structures with Colloidal Crystals

pattern formation on structured substrates with feature sizes substantially larger than the particle diameter will be reviewed. Finally, colloidal crystals with a periodic superlattice in three dimensions will be discussed. Table 6 provides an overview of the methods to prepare 3D structured colloidal crystals, which are reviewed in this section. 3.2.1. Planar Patterned, Topography-Free Substrates. Three main strategies to prepare patterned 3D colloidal crystals can be distinguished. In the first top-down approach a pattern is cut into a continuous, preassembled particle layer by photolithography. In the second top-down approach a continuous colloidal crystal film is dissected by microimprint lithography. In the third bottom-up approach, as reviewed in sections 3.2.2 and 3.2.3 below, the colloidal crystals are self-assembled directly at prepatterned substrates. An elegant example for the top-down approach has been demonstrated by Jiang and McFarland.430 by applying wellestablished photolithography. First, a crystalline composite layer of colloidal silica particles and photopolymer was deposited with defined thickness on a standard silicon wafer by spin-coating a concentrated particle dispersion in a photoreactive monomer

complex 3D patterns with lines and planes (Figure 20e). After development of the photoresist, the entire structure could be replicated by chemical vapor deposition. Removal of the colloidal spheres and the photopolymer yielded an inverse opal with defined 3D defects (Figure 20f). With this method the waveguiding capabilities of such air channels in the IR range were demonstrated (Figure 20f),428 which further reflects the potential of these materials to become important elements in future optoelectronic devices. 3.2. Patterning of 3D Colloidal Crystals

Whereas the controlled generation of defects within a colloidal crystal, as discussed above, provides access to functional hierarchical assemblies, the following section introduces approaches to the formation of patterns of colloidal crystals as spatially separated entities, leading to hierarchical superstructures. By such methods the size and shape of the individual colloidal crystal monoliths are to be controlled. Following the conceptual blue print for structural hierarchies of Figures 1 and 2, we will present a range of routes to structured 3D colloidal crystals, beginning with 2D patterning on plain substrates. Then, AB

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Figure 21. (a) Array of colloidal crystal pixels toward a reflection-mode display. The colors originate from inverse opals with different lattice parameter obtained by photolithographic patterning. Reprinted with permission from ref 431. Copyright 2014 Wiley. (b) Patterned colloidal crystal with PS (green areas) and SiO2 spheres (violet areas). The pattern was formed by microimprinting of a PS colloidal crystal and ensuing convective assembly of SiO2 particles. Reprinted with permission from ref 437. Copyright 2015 Royal Society of Chemistry. Discrete colloidal crystal dome formation using inkjet printing (c) and dispersion plotting on a hydrophilic dot array on a hydrophobic substrate (d). Adapted with permission from ref 355, Copyright 2006 Elsevier, and ref 438, Copyright 2007 American Chemical Society. Patterning of colloidal crystal by differences in the wettability: (e) Defined colloidal crystal lines by convective assembly on hydrophilic stripes on an otherwise hydrophobic substrate. Reprinted with permission from ref 336. Copyright 2004 American Chemical Society. (f) A and B are complementary parts after cleavage of a colloidal crystal that was sandwiched between two substrates. The substrate was hydrophobically modified in the empty square of B, leading to the transfer of the pattern to the hydrophilic substrate A upon cleavage. Adapted with permission from ref 435. Copyright 2005 American Chemical Society.

liquid. Subsequent photopolymerization fixed the composite structure, whereas the unexposed regions can be removed by dissolution. The patterned composite can finally be transformed into a macroporous inverse polymer opal by HF etching of the silica spheres. This field has matured tremendously over the past years with the realization of full color photonic displays. These were either realized by different exposure times432 or by successive steps of convective assembly of differently sized particles with ensuing lithographic fixture in a photopolymer (Figure 21a).431 In many cases the templating colloidal spheres are finally removed to yield inverse opals of high optical contrast. Building upon the refractive index match between particle and matrix, however, paves the way to transparent coatings with distinct reflection properties for future security applications.433 The combination of a coassembly process of polymer colloids with tetraethylorthosilicate, yielding highly oriented, nearly crack free inverse opals, with photolithographic techniques can be used to control the crystal orientation of the underlying inverse opal matrix within the hierarchical superstructure.434 In very recent work the direct patterning of colloidal crystals with a microimprint technique has been demonstrated.437 In this method a preformed PDMS stamp is pressed onto a colloidal ensemble. This can have two consequences: either the lattice constant is reduced upon the compression with the PDMS stamp, which lead to a blue-shift of the stop-band, or the entire region can adhere to the stamp and subsequently be lifted off (Figure 21b). Clearly, the key parameter to control in this process is the adhesion between the spheres of the colloidal crystal and the adhesion to the interface of the substrate and the PDMS stamp. When using a combination of hard-core and softshell particles as photonic crystal films a predefined pattern can be embossed into it. Along with the topographic pattern, the interplay of compression, shear, and extrusion can lead to a rearrangement of the colloidal spheres in the film to result in better crystallinity and different lattice spacing.436 Mask-free techniques to access patterned colloidal crystals comprise inkjet printing and dispersion plotting.439 While these techniques do not require the time- and cost-intensive

preparation of photomasks, they suffer from some limitations in the minimum feature size, which is typically several tens of μm. A decisive parameter to be controlled during colloidal crystal printing is the spreading of the dispersion on the target substrate. This can be adjusted by rendering the entire substrate hydrophobic using aliphatic silanes (Figure 21c)438 or by generating hydrophilic patterns, that are wetted by the colloid dispersion, on an otherwise nonwetting substrate (Figure 21d).355 The easiest accessible structures are hemispheres of colloidal crystal by printing of individual droplets.356,447 To mitigate the coffee-stain effect,448 which is caused by meniscus pinning and convective flow, the composition of colloidal dispersion is adapted by addition of high boiling point cosolvents (e.g., formamide or ethylene glycol)449 or by high particle concentrations.450 It is worth mentioning here that the coffee-ring effect is also suppressed with elliptical particles224 or by the addition of appropriate surfactants222 or water-soluble polymers.223 A bottom-up approach taking advantage of the wetting contrast of the colloid dispersion on a substrate surface pattern has been investigated by Fustin et al. for convective assembly.336,440 Selective immobilization of a perfluorinated silane in hydrophilic/hydrophobic patterns on a glass substrate causes the meniscus to undulate between wetting and dewetting surface regions. Neglecting the height of the immobilized silane layer in the nanometer range, the substrates are topographically flat at the length scale of the colloidal particles. As a consequence of the wetting contrast, colloidal crystal layers form only in hydrophilic regions, whereas the hydrophobic areas remain uncovered. A cross section through the colloidal crystal stripes features a variation in layer thickness with thin edges and thick centers, following the curvature of the wetting dispersion film (Figure 21e). This structuring concept by selective wetting was not only applicable to continuous stripe patterns, but could also be applied to discontinuous patterns (like dots of colloidal crystals). To circumvent the variation in crystal thickness caused by the meniscus, Parikh et al. developed a sandwich method to prepare crystal stripes with homogeneous thickness.435 Here, a AC

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Figure 22. (a) Colloidal heterostructures successively deposited on a laterally patterned substrate. Reprinted with permission from 441. Copyright 2007 Elsevier. Linear stripes comprising two different particles were obtained. (b) SEM image of inverted opal patterns, obtained by capillary infiltration of a PDMS mold with a latex dispersion and a silica sol. Reprinted with permission from ref 443. Copyright 1998 American Association for the Advancement of Science. (c,d) Fabrication of prismatic colloidal crystal stripes by solvent evaporation under a wrinkled, flexible PDMS stamp. Reprinted with permission from ref 452. Copyright 2010 Royal Society of Chemistry. (e,f) Hierarchical inverse opals from coassembly of silica precursor and colloids onto photolithographically patterned substrates. Reprinted with permission from ref 442. Copyright 2012 Wiley.

(discussed above in section 3.2.1). This method also improves the limits for the minimum feature size down to 5 μm. Li et al. selected silica nanoparticles and removed the photoresist by dissolution in acetone.441 Surface passivation of the patterned silica colloidal crystal by chemisorption of a perfluoroalkyl silane allowed them to repeat the colloidal crystal deposition process after resist removal with a different particle type. The particles assembled in the hydrophilic trenches between the lines of the already deposited and passivated colloidal array. In this way, patterned heterocolloidal crystals were obtained, which feature bifrequency Bragg diffraction (Figure 22a). In a very similar approach Ding et al. deposited a homogeneous colloidal crystal film on top of a patterned photoresist. The colloidal crystal structure with the inverse shape of the resist pattern was developed by dissolution of the photoresist in acetone and brief sonication to selectively remove the colloidal particles from the resist regions.451 Hierarchical assemblies featuring tailor-made hole structures in a continuous inverse opal film were recently reported by Mishchenko et al. by using a photolithographically structured substrate for coassembly of tetraethoxysilane (TEOS) with colloidal particles.442 Since the colloids preferentially adsorb in a close-packed layer onto the imposed walls, the crystal domain orientation can be fully controlled over large length scales by the relative orientation of the templating wall to the crystal growth direction. By cotransferring the TEOS silica precursor with the polymer particles, the interstitial sites can be filled to form an inverse silica opal matrix. In a subsequent step, the templating resist pattern can be removed together with the colloidal particles by orthogonal chemistry or calcination to yield the inverted silica structure. Figure 22e and f show an optical microscopy image of triangular holes and a SEM image of cylindrical holes in a continuous inverse opal film, respectively. Very high order with a fixed lattice orientation over the entire crystal film resulted from pillar structures matching the symmetry of the crystal lattice, as can be seen by the uniform coloration of the film with triangular pillars (Figure 22e). A micromolding methodology to prepare hierarchically structured porous metal oxides was introduced by Yang et al.,443 where a patterned colloidal crystal was assembled inside a PDMS mold via capillary forces and solvent evaporation. The influence of geometric constraints on the colloidal crystal was

highly concentrated colloidal dispersion was confined and slowly dried between two glass slides with one plain hydrophilic and one hydrophilic/hydrophobically patterned face. After drying a colloidal crystal film fills the gap between the two faces. Upon separation of the two glass slides the colloidal crystal film splits into two complementary parts, with the crystal film patches being transferred from the hydrophobic substrate regions to the opposite unstructured, hydrophilic glass slide. (Figure 21f). 3.2.2. Colloidal Crystals on Topographically Patterned Substrates. Topographically patterned substrates or adjuvant molds can guide and shape the assembly of colloidal particles into designed hierarchical 3D structures. In analogy to the patterning of colloidal monolayers (Figure 11), an important distinction has to be made with respect to the relative size feature of the surface topography in comparison to the particle dimensions (see Figure 2). The features of the templating structure can be “large” in relation to the dimensions of the colloidal particles and thus do not affect the lattice geometry of the assembled crystal, typically an fcc or hcp structure. On the other hand, the pattern dimensions can fall in the range of the size of a single or multiple particles. In such a case the geometric constraints force the particles to arrange themselves in lower-symmetry arrangements. In analogy to atomic crystals, when the feature dimensions of the template are commensurate with the lattice spacing of the colloid crystal, the induction of a predefined packing symmetry by the supporting substrate to the self-assembled colloid structure is referred to as graphoepitaxy. This phenomenon is often also termed “colloidal epitaxy” when the colloidal particles themselves serve as nuclei and lattice-orientating sites, this will be covered in the subsequent section 3.3. Micrometer-sized colloid patterns can be conveniently obtained by convective deposition of colloidal particles into trenches that are prepared by photolithography. In analogy to patterned crystals on planar substrates with different regions of wettability336 the water contact angle difference between the hydrophilic trenches and the hydrophobic photoresist ensures selective deposition of the particles only in the desired trench areas.441 The spatial confinement between the discrete resist walls forces the colloidal crystal to grow with a rectangular cross section, homogeneous thickness, and a flat top surface, which is in contrast with the colloidal stripes with a convex cross section from deposition on planar, chemically patterned substrates AD

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Figure 23. (a) 3D shaping of hierarchical colloidal crystal structures by backfilling of an inverse opal with colloidal particles. Subsequent infiltration with a gel precursor followed by removal of the polymer particles yields a double-periodic inverse opal. Further replication generates a double-periodic porous polymer film. Adapted with permission from ref 445. Copyright 2013 Wiley. (b, c) SEM image of a backfilled metal oxide skeleton with colloidal particles, and (d, e) its TiO2 inverted counterpart after removal of the PS particles by calcination. Reprinted with permission from ref 444. Copyright 2011 Wiley. (f) Tubular colloidal assemblies after removal of the templating silicon membrane. (g) Close-up of a colloidal wire with helical particle packing. Reprinted with permission from ref 454. Copyright 2005 American Chemical Society.

Rhee do et al. managed to decorate each void in an inverse opal with one single mobile sphere, that is smaller than the void diameter. They achieved this by selectively etching the SiO2 shell after backfilling the colloidal ensemble with a photocurable polymer.446 A method to prepare tubular colloidal crystal arrays was introduced by Li et al. by particle infiltration into silicon membranes.454 Depending on the ratio between the particle and tube diameter, the packing geometries within a single particle strand ranged from hexagonal to cubic and helical arrangement (Figure 23f,g). An interesting symbiosis of two-dimensional colloidal monolayers and three-dimensional structuring was theoretically postulated by Cates and co-workers in 2005, which they termed “bijels” - bicontinuous interfacially jammed emulsion gel.455 Soon after this prediction Herzig et al. experimentally realized such systems as three-dimensional interpenetrating, bicontinuous emulsions that were stabilized by the immobilization of colloidal particles at the interface between the water and the oil phase.456 Starting from a homogeneous particle dispersion at low temperatures, spinodal demixing of the components in the liquid medium leads to a phase-separated, bicontinuous fluid system (oil−water), which was stabilized by the colloidal spheres adsorbing at the water−oil interface. Such systems feature a longterm stability, but the critical role of the surface chemistry of the stabilizing colloidal particles still needs to be clarified.457−459 Further advances of this method resulted in the selective polymerization of one phase, leading to bicontinuous macroporous templates that could be replicated by infiltration with a ceramic precursor and pyrolysis or it could be coated with Cu or Ni metal by an electroless plating procedure.460 When conducting this type of spinodal demixing of a colloid suspension in a lutidine-water phase within the confined geometry of two parallel plates, the particle attraction can be sensitively tuned by a temperature gradient parallel to the gap plane. Heating close to the demixing temperature of the two liquid components strongly enhances particle attraction and leads to crystallization into a very large single-domain 2D lattice and the formation of high quality colloidal monolayers.461

inferred from the differences in packing symmetry between the large triangular objects and the thin bridges. The patterned structure was finally inverted by infiltration with silica and calcination of the polymer particles (Figure 22b). Schweikart et al. demonstrated a conceptually different method to prepare a templating line pattern in a flexible PDMS stamp via controlled wrinkle formation by stamp stretching, plasma treatment and stretch release.452 The wrinkled PDMS stamp was then placed on top of a droplet of the particle dispersion, which yielded after drying a regular line pattern with a periodicity defined by the PDMS stamp (Figure 22c,d). The architecture of the colloidal line itself could be tuned from single particle chains to multiparticle prismatic ridges by adjusting the initial volume fraction of the particles in the dispersion. 3.2.3. 3D Patterning in Templates. Most methods for patterning 3D colloidal crystals reported so far either generate 2D structural features (according to structure lattice vectors in the x−y plane parallel to the substrate), or they control the specific orientation of the crystal lattice vectors with respect to the support (i.e., by epitaxy, which will be discussed further below in section 3.3). Surprisingly, only few reports describe full control over structure formation in colloidal crystals along all three space dimensions, i.e. including a periodic or arbitrary pattern along the z-axis normal to the supporting substrate surface in addition to the in-plane structure. Cho et al. developed a dual-templating method for generating meso- and macroscale pores, which combines the macroscale template from multibeam interference lithography in a SU8 photoresist layer with the mesoscale template from a colloidal particle assembly.444 The hierarchical structure was obtained by inversion of the colloid assembly as porous TiO2 scaffold by sol−gel infiltration and calcination (Figure 23a−e). The authors further extended this method to an all-colloidal crystal-templating strategy, where an inverse TiO2 opal was first formed from large particles and then backfilled with smaller particles, followed by a second TiO2 infiltration and removal of the templating colloids.453 In these particular examples the mesoporous-in-macroporous inverse opals were used as structured TiO2 electrodes in dye-sensitized solar cells, but the possibility to combine macro- and mesopores is also important for a range of applications such as catalysis, filtering, or drug delivery. This concept was further expanded by demonstrating a range of double-periodic porous composite materials and hierarchically structured, porous polymer films.445 By synthesizing a sacrificial silica shell around a polystyrene core,

3.3. Colloidal Epitaxy

Probably the lowest level of control, which needs to be mastered in order to realize by design the hierarchical structures with colloids, lies at the level of the crystal lattice parameters. In an effort to specifically tune the size, orientation, and growth of the AE

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Figure 24. (a) Method to grow an fcc colloidal crystal with its (100) plane parallel to the substrate surface using a topographic template pattern. Left inset: confocal image of dye labeled spheres in the pitches; right inset: confocal image of the empty template. Adapted with permission from ref 462. Copyright 1997 Nature Publishing Group. (b) Precise control of the deposition parameters allows the defect-free fabrication of large area, oriented fcc crystals. Reprinted with permission from ref 466. Copyright 2005 American Chemical Society. (c) Confocal image of the first (100) lattice plane in an fcc crystal including an unpatterned substrate area of 7 sphere diameters in the center. Scale bar: 5 μm. Adapted with permission from ref 462. Copyright 1997 Nature Publishing Group. (d) Top and (e) side view confocal images of a binary colloidal crystal with NaCl structure. The octahedral sites between the large spheres (green) are occupied by smaller particles (red). Scale bars: 5 μm. Reproduced with permission from 470. Copyright 2009 National Academy of Sciences of the United States of America. (f) Epitaxial growth on substrates with topographic features larger than the single particle dimensions. Growth of an fcc crystal from prismatic grooves with the (100) lattice plane parallel the substrate plane. Reproduced with permission from ref 468. Copyright 2000 Royal Society of Chemistry. (g and h) Growth of an fcc crystal from square pyramidal holes in a silicon wafer with the (100) plane parallel to the substrate. Reproduced with permission from ref 469. Copyright 2002 Wiley.

colloidal crystal types with defined crystal structures and lattice orientations could been grown.463,464 Whereas the initial studies relied on slow gravitational sedimentation for colloidal crystal growth, more efficient colloidal assembly techniques, such as convective assembly, were later successfully applied to colloidal epitaxy as well.465 Further improvements of the particle deposition procedure by variation of the substrate angle, the temperature, and the evaporation rate pushed the boundaries to thick (>10 layers) and defect-free as well as crack-free colloidal crystals with their (100) plane parallel to the substrate (Figure 24b).466 Similarly, it was shown that very rapid crystal growth by centrifugation of a colloidal dispersion was possible on an etched silicon template matching the fcc (100) plane of a colloidal crystal.467 The strong shear forces during centrifugation prevent the formation of a high order, but the structured substrate with an epitaxial (100) template helps to guide the colloids into their well-defined minimum free energy position. However, if the (111) or (110) plane is presented by the substrate template, two degenerate minimum free energy positions for the subsequent particle layer are available (leading to ABAB or ABCABC stacking respectively). This degeneracy of free energy states

lattice structure in 3D colloidal crystals, van Blaaderen et al. coined the term “colloidal epitaxy”.462 They demonstrated this strategy with a patterned substrate featuring a hole pattern with commensurate spacing and a predefined symmetry, on which it was possible to grow a perfect fcc crystal with its (100) plane oriented parallel to the substrate (Figure 24a, c). This result demonstrated the impressive degree of epitaxial control over the colloid crystallization process by this template approach, since regular crystallization at unpatterned substrates usually leads to orientation of the (111) lattice plane of multidomain fcc and hcp structures parallel to the substrate wall. In the colloidal epitaxy process the first layer of particles assembles into the predefined hole pattern, in this case the (100) plane of the respective colloidal crystal, and directs the assembly of the next layer in the same defined lattice geometry. This lattice-dictating process repeats with each subsequent particle layer that forms on top of the crystal. The template structure needs to exactly match the size of the colloidal spheres, since even tiny deviations will lead to a gradual increase of defects and ultimately results in the growth of randomly stacked hexagonal layers. This concept was further demonstrated to be of more general applicability as various AF

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eventually leads to formation of disordered particle sediments under continued centrifugation.467 In the examples above, the individual features in the latticedictating pattern shared the same dimensions as the colloidal particles. This restriction limits the minimum particle sizes that can be used in the assembly process, as they need to match the spatial resolution of the photolithographic process. Yang et al. introduced an alternative route, in which V-shaped channels were used to direct colloidal particle assembly into an fcc crystal with its (100) lattice plane being oriented parallel to the substrate plane (Figure 24f).468 V-shaped trenches can be conveniently obtained by anisotropic etching of a Si wafer with KOH, resulting in grooves with 70.6° apex angles. When the Si wafer is patterned with squares instead of lines, the same etching procedure leads to pyramidal holes, which are also suitable to direct an fcc crystal growth at the (100) plane (Figure 24g,h).469 Colloidal epitaxy can also be applied to binary colloidal systems, as demonstrated by Vermolen et al. for a binary colloidal crystal with NaCl structure grown by sedimentation.470 Application of an external electric field gradient during crystallization induced an additional dielectrophoretic force onto the particle array and thereby further improved the crystal quality. The internal structure was revealed by confocal microscopy of the differently fluorescence labeled particles. Large areas of defect-free NaCl type colloidal crystals were found with 73% occupancy of the smaller particles in the octahedral vacancies of the large sphere lattice (Figure 24d,e). 3.4. Non-Close-Packed 3D Colloidal Crystals

Unperturbed crystallization of spherical colloids with uniform size leads to relative simple close-packed crystals with fcc or hcp lattice geometry and particle volume fraction of 74%. A very strong motivation for the designed fabrication of non-closepacked colloidal crystals and more complex lattice architectures results from calculations that show that a reduced volume fraction or a change in the crystal structure can increase the width of a photonic stop band. By this strategy, full photonic bandgaps are potentially accessible for a specific combination of lattice type, particle volume fraction, and refractive index contrast between particles and surrounding medium.471,472 We distinguish two types of non-close-packed (ncp) colloidal crystals: ncp colloidal crystals with an fcc or hcp lattice but reduced volume fraction, and ncp colloidal crystals with a lower crystal lattice symmetry. In fcc or hcp ordered colloidal crystals, the sizes of the constituting spheres within the lattice can be reduced after crystal assembly under the precondition that connecting trusses exist between the spheres to maintain the 3D particle arrangement and crystalline order. Synthetic approaches toward such fcc-based systems are sintering of silica sphere lattices with ensuing HF etching,473 annealing of polystyrene sphere lattices followed by hyperthermal neutral beam etching (Figure 25d),474 fixation of ordered dispersed sphere lattices in suspension via photopolymerization and structure inversion,475 spin-coating of a photopolymer/nanoparticle composite,430 or double-inversion techniques from opal to inverse opal to non-close-packed opals.476 The reflectance spectra of such ncp lattices typically feature a blue shift,473,474,476 which is caused by the removal of high refractive index material from the constituting spheres and thus reducing the effective refractive index of the overall structure.

Figure 25. (a−c) Schematic and experimental realization of non-closepacked colloidal crystal films starting from close-packed SiO2@PMMA core−shell particles. SEM images (b) before and (c) after removal of the PMMA shell by plasma etching. Scale bars: 1 μm (main images), 250 nm (inset b), and 500 nm (inset c). Adapted with permission from ref 477. Copyright 2010 American Chemical Society. (d) Non-close-packed fcc PS particle crystal via hyperthermal neutral beam etching. Trusses between the particles retain the crystal structure. Reprinted with permission from ref 474. Copyright 2005 American Chemical Society. (e and f) Nanorobotic fabrication of a mixed bcc crystal comprising two interpenetrating diamond lattices of polymer and silica particles, respectively. Plasma etching selectively removes the (darker) latex spheres, exposing a diamond lattice of silica spheres. Reprinted with permission from ref 482. Copyright 2002 Wiley.

Another simple route has been demonstrated by Ding et al.477 by self-assembly of SiO2@PMMA core−shell particles into an fcc crystal, followed by plasma etching to remove the PMMA shell. Taking advantage of an anisotropic etching effect from top to bottom during the plasma etching, the top layer particles were sinking into the interstices of the bottom layer during size reduction, which was accompanied by a change in lattice symmetry (Figure 25a−c). Depending on the initial particle architecture (shell to core dimensions) simple cubic (sc) and body-centered cubic (bcc) crystal lattices could be obtained. A number of very different methods have been investigated to obtain ncp colloidal crystals of lower symmetry. Following the concepts of epitaxial growth, Dziomkina et al. managed to obtain thin layers of bcc colloidal crystals by a combination of surface structuring, electrodeposition, and convective assembly.478 Similar results have been reported by Hoogenboom et al. during particle deposition onto topographically patterned substrates with lattice match by evaporation, but without the aid of an electric field.479 AG

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structural hierarchies covering the mesoscopic realm by comparably simple and fast processes, while utilizing cheap starting materials and simple building blocks. Certainly, at the heart of structure formation with colloidal objects is the knowledge and control over the various forces governing such particle assembly processes. This review highlights the methods for controlling these forces and provides a qualitative understanding on how these forces need to be balanced in order to target a specific architecture. The simplicity of many experimental methods has led to widespread application of colloidal assembly in a range of research fields and consequently created a tremendous body of literature. It is therefore by far not trivial to select from this wealth of knowledge the proper technique for a desired architecture. With this review we aim to provide convenient access to this literature and help to identify the proper assembly method for a desired application. Originally, colloidal crystals were used to mimic atomic crystals and to fundamentally understand structure formation at small length scales. From these niche applications, researchers have extended the application of colloidal crystals to many fields. Some prominent examples are • Photonic crystals, where light is modulated by the periodicity of the colloidal assembly. • Sensing of external stimuli by visible changes in the stop band due to changes of the lattice spacing. • Flexible lasers. • Masks for the generation of periodic plasmonic resonators that can be used in sensing of (biological) binding events. • Design of repellent surface coatings. To name but a few. Many further applications are expected to arise from a deeper understanding and increased control over the self-assembly and structure formation processes. Advances in characterization techniques, computational power, and synthetic capabilities will continue to push the boundaries of hierarchically structured materials. We have highlighted how simple spherical building blocks are used to create assembly structures with properties not inherent to the individual particles. The use of more complex building blocks with nontrivial shapes and made from functional materials will enable access to particle lattices with even more sophisticated symmetries and properties arising from the combination of the inherent material properties themselves with structural features over multiple length scales. Further quantitative understanding of forces at work during the particle assembly processes is needed to achieve the highest possible control over the interactions between the building blocks in order to guide them into a desired target structure in the best possible way. Access to nonequilibrium structures has become of increasing interest during recent years, which adds additional demand on the kinetic control over the assembly processes, but will extend the arsenal of assembly methods to even more elaborate structural motifs. Tailoring disorder will be an emerging field to create novel materials with properties significantly differing from those of the highly ordered structures primarily covered in this review. Finally dynamic aspects of colloidal material will need to be increasingly considered, which carry tremendous potential for the development of advanced materials. Here are to mention active swimmers that by their motile nature can alter their

Theoretical concepts to generate open architectures from Laves- or bcc binary crystals with interpenetrating diamond or pyrochlor structures were proposed, exploiting the coassembly of two different types of particles into well-defined binary lattices.480,481 Selective removal of one particle type would leave the other type in a ncp lattice, which should feature a full photonic bandgap.471,472 The proof of principle of this idea has been realized by a nanorobotic pick-and-place approach with 1.2 μm silica and PS spheres (Figure 25e,f).482 The beads were assembled on a prepatterned substrate into a colattice, with the PS spheres being finally removed via plasma etching. Autonomous self-assembly attempts toward this goal are based on a layer-by-layer growth of binary colloidal crystals with repeated alternating deposition of a layer of smaller spheres in the interstices of the underlying layer of large particles. When the particle deposition process and assembly conditions (like particle volume fractions in the suspensions) are well controlled, defined multilayers can be obtained, which yields non-close-packed lattices of the large spheres after removal of the smaller beads.288 In extension of this concept, alternating deposition of silica and PS particles on top of a topographic template with square lattice geometry was attempted by controlling interparticle charge repulsion via the Debye length in the aqueous dispersion medium.483 This approach led to the first realization of a half unit cell of a diamond cubic structure. However, the vast range of parameters that need to be controlled during each single layer deposition currently limits the size, quality, and scalability of the proposed concept.

4. CONCLUSION AND OUTLOOK Driven by the continuous demand of size reduction of modern devices, a paradigm shift emerges in production technologies from traditional pick-and-place of individual components to assembly methods based on self-organization concepts prevalent in nature. With decreasing dimensions of the building blocks the conceptual border between devices with a specific set of functions starts to merge with the realm of functional matter that is characterized by a range of complex properties, which potentially change in response to environmental stimuli. In particular, the functionality and diversity of the properties in such complex materials increase with the complexity of their internal structure. The length scale where the critical dimensions of the device building blocks and the structural features in advanced materials overlap, corresponds to the colloidal domain, or mesoscopic realm, with feature size ranging from nano- to micrometers. Both, technical devices and functional matter are characterized by a complex hierarchy of their structural organization and dynamical features at different length scales, which interrelate with each other and form the basis for their richness of functional properties. The interplay between the constituting units across different structural levels leads to a sophisticated and often unforeseeable property profile, which, in the words of Aristotle, is greater than the sum of its parts. As the essential length scales for the design and fabrication of such hierarchically structured systems relate to the colloidal domain, fundamental insights into the general working principles and valuable knowledge about preparation and characterization techniques can be drawn from the existing body of research in colloidal sciences. In this aspect the current review provides a comprehensive overview on the technological developments for hierarchical nano- and microstructure formation in 2D and 3D. It is the great strength and beauty of colloidal self-assembly to create complex materials with AH

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organization in a swarm-like behavior to switch from one hierarchical configuration to another. Closely related is the field of reconfigurable matter, where the chemical, physical and functional properties can be switched between well-defined states by the action of external stimuli. Such systems may become accessible by marrying hierarchical colloidal assemblies with stimuli responsive materials. A general denominator linking all aspects of hierarchical assembly with colloidal particles is the interdisciplinary character of this research. It is a key factor for further developments in this field and to expand into future applications of colloidal crystals. The fundamental science is cross-fertilized by synthetic knowhow from polymer, organic, inorganic, and biochemistry concerning the building blocks of colloidal matter and by methods and knowledge from physics, physical chemistry, colloid sciences, and engineering regarding the assembly and structuring processes. Future developments will draw even stronger on the interdisciplinary collaboration of experts with very different background and this particular challenge renders hierarchical colloidal assemblies such an attractive topic for the foreseeable future.

Markus Retsch studied Polymer and Colloid Chemistry at the University of Bayreuth (2001−2006) and graduated in 2006 with a diploma thesis in the group of Prof. A. H. E. Müller. He conducted his Ph.D. (2006−2009) at the Max-Planck-Institute for Polymer Research in Mainz in the group of Prof. W. Knoll, where he began to work on colloidal assembly structures. After that he spent 2.5 years as a postdoc in

AUTHOR INFORMATION

the group of Prof. E. L. Thomas at the Massachusetts Institute of

Corresponding Authors

Technology, MIT, in Cambridge, MA, U.S.A. In August 2012, he was

*E-mail: [email protected]. Phone: +49 9131 852 0357. *E-mail: [email protected]. Phone: +49 921 55 2776. *E-mail: [email protected]. Phone: +49 271 740 4713.

appointed Juniorprofessor for Polymer Systems at the University of

Author Contributions

accessible with colloidal assembly strategies. Throughout his career, he

^

received numerous awards and scholarships: a Bavarian scholarship for

Notes

his undergraduate studies, a Kekulé mobility stipend for his Ph.D., and a

The authors declare no competing financial interest.

Feodor Lynen fellowship for his postdoctoral research.

Bayreuth. In 2013 he received a Lichtenberg professorship from the Volkswagen foundation. His current research interests lie in the investigation of materials for energy conservation and conversion,

Equal contribution.

Biographies

Charles-André Fustin got his Ph.D. in 1999 from the University of Namur (Belgium). From 2000 to 2001 he was a postdoctoral researcher

Nicolas Vogel studied chemistry at the Johannes Gutenberg-University in Mainz and Seoul National University in Seoul, Republic of Korea. In 2011, he received his Ph.D. at the Max Planck Institute for Polymer Research in Mainz, Germany in the group of Prof. Katharina Landfester. He then joined the group of Prof. Joanna Aizenberg at the School of Engineering and Applied Sciences at Harvard University as a postdoctoral fellow. In 2014, he was appointed associate professor in the Department of Chemical and Biological Engineering at the Friedrich-Alexander-University Erlangen-Nuremberg. He likes to apply colloidal assembly methods to create functional materials and surface coatings, for example to create structural color or to tailor the wetting properties of liquids.

at the Université Catholique de Louvain (Belgium). He then moved to the group of Prof. H. W. Spiess in the Max-Planck Institute for Polymer Research in Mainz (Germany) where he got a European Marie-Curie Fellowship. In 2003 he obtained a Chargé de Recherches position of the FNRS at the Université Catholique de Louvain. Since October 2007, he is a Research Associate of the FRS-FNRS and Professor at the Université Catholique de Louvain. His research interests include supra- and macromolecular chemistry, self-assembly of block copolymers, stimuli responsive polymers, and mechanically linked polymeric architectures. AI

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Advanced Materials” at University Erlangen-Nuremberg. We thank Benoit Loppinet, George Fytas, Dimitris Vlassopoulos, and George Petekidis very much for helpful discussions and valuable insights. CAF is Research Associate of the FRS-FNRS. U.J. acknowledges partial support by the European Commission (ITN “Comploids”, FP7-234810, and NMP SMALL “Nanodirect”, CP-FP7-213948-2).

REFERENCES (1) Pan, N. Exploring the significance of structural hierarchy in material systems-A review. Appl. Phys. Rev. 2014, 1, 021302. (2) Lakes, R. Materials with structural hierarchy. Nature 1993, 361, 511−515. (3) Fratzl, P.; Weinkamer, R. Nature’s hierarchical materials. Prog. Mater. Sci. 2007, 52, 1263−1334. (4) Fratzl, P. Biomimetic materials research: what can we really learn from nature’s structural materials? J. R. Soc. Interface 2007, 4, 637−642. (5) Sanchez, C.; Arribart, H.; Giraud Guille, M. M. Biomimetism and bioinspiration as tools for the design of innovative materials and systems. Nat. Mater. 2005, 4, 277−288. (6) Aizenberg, J.; Weaver, J. C.; Thanawala, M. S.; Sundar, V. C.; Morse, D. E.; Fratzl, P. Skeleton of Euplectella sp.: Structural Hierarchy from the Nanoscale to the Macroscale. Science 2005, 309, 275−278. (7) International Technology Roadmap for Semiconductors, 2013. (8) Gröschel, A. H.; Schacher, F. H.; Schmalz, H.; Borisov, O. V.; Zhulina, E. B.; Walther, A.; Müller, A. H. E. Precise hierarchical selfassembly of multicompartment micelles. Nat. Commun. 2012, 3, 710. (9) Gröschel, A. H.; Walther, A.; Löbling, T. I.; Schacher, F. H.; Schmalz, H.; Müller, A. H. E. Guided hierarchical co-assembly of soft patchy nanoparticles. Nature 2014, 503, 247−251. (10) Whitesides, G. M.; Grzybowski, B. Self-Assembly at All Scales. Science 2002, 295, 2418−2421. (11) Halley, J. D.; Winkler, D. A. Consistent concepts of selforganization and self-assembly. Complexity 2008, 14, 10−17. (12) Li, F.; Josephson, D. P.; Stein, A. Colloidal Assembly: The Road from Particles to Colloidal Molecules and Crystals. Angew. Chem., Int. Ed. 2011, 50, 360−388. (13) Stein, A.; Wilson, B. E.; Rudisill, S. G. Design and functionality of colloidal-crystal-templated materials-chemical applications of inverse opals. Chem. Soc. Rev. 2013, 42, 2763−2803. (14) Vogel, N.; Weiss, C. K.; Landfester, K. From soft to hard: the generation of functional and complex colloidal monolayers for nanolithography. Soft Matter 2012, 8, 4044−4061. (15) von Freymann, G.; Kitaev, V.; Lotschz, B. V.; Ozin, G. A. Bottomup assembly of photonic crystals. Chem. Soc. Rev. 2013, 42, 2528−2554. (16) Velev, O. D.; Gupta, S. Materials Fabricated by Micro- and Nanoparticle Assembly − The Challenging Path from Science to Engineering. Adv. Mater. 2009, 21, 1897−1905. (17) Schall, P.; Cohen, I.; Weitz, D. A.; Spaepen, F. Visualization of dislocation dynamics in colloidal crystals. Science 2004, 305, 1944− 1948. (18) Schall, P.; Cohen, I.; Weitz, D. A.; Spaepen, F. Visualizing dislocation nucleation by indenting colloidal crystals. Nature 2006, 440, 319−323. (19) Bartsch, E.; Antonietti, M.; Schupp, W.; Sillescu, H. Dynamic Light-Scattering Study of Concentrated Microgel Solutions As Mesoscopic Model of the Glass-Transition in Quasi-Atomic Fluids. J. Chem. Phys. 1992, 97, 3950−3963. (20) Kozina, A.; Sagawe, D.; Diaz-Leyva, P.; Bartsch, E.; Palberg, T. Polymer-enforced crystallization of a eutectic binary hard sphere mixture. Soft Matter 2012, 8, 627−630. (21) Bausch, A. R.; Bowick, M. J.; Cacciuto, A.; Dinsmore, A. D.; Hsu, M. F.; Nelson, D. R.; Nikolaides, M. G.; Travesset, A.; Weitz, D. A. Grain boundary scars and spherical crystallography. Science 2003, 299, 1716− 1718. (22) Meng, G.; Paulose, J.; Nelson, D. R.; Manoharan, V. N. Elastic instability of a crystal growing on a curved surface. Science 2014, 343, 634−637.

Aránzazu del Campo received her Ph.D. in Chemistry in 2000 at the ́ Instituto de Ciencia y Tecnologiá de Polimeros in Madrid (Spain). After postdoctoral stays at the Max Planck Institute for Polymer Research in Mainz (Germany) and the Universitá degli Studi di Urbino (Italy), she built up her research group in 2004 at the Max Planck Institute for Metals Research in Stuttgart in the field of bioinspired adhesives. Since February 2009 she heads the Minerva independent research group ‘“Dynamic Biointerfaces”’ at Max Planck Institute for Polymer Research, with a strong focus on bioinspired materials design.

Ulrich Jonas studied Chemistry (1987−1993) at the Johannes Gutenberg University of Mainz, Germany and UCSB, Santa Barbara, U.S.A. He received his diploma (1993 in Mainz) in Organic Chemistry, and after a six-month research visit at the ETH Zurich, Switzerland, obtained his Ph.D. in 1996 with Prof. H. Ringsdorf at the University in Mainz. From 1996 to 1999 he was a postdoctoral Feodor Lynen fellow (of the Alexander von Humboldt Foundation) in the group of Dr. D. Charych at the Lawrence Berkeley National Laboratory in Berkeley, U.S.A. In 1999 he joined the Max Planck Institute for Polymer Research, Mainz as project leader and became permanent staff in 2004. In 2007 he was appointed as affiliated scientist at FORTH in Crete, Greece, active in the Polymer & Colloid Science Group, and in 2009 he was elected there as director of research. Since 2012 he has been professor for Macromolecular Chemistry at the University of Siegen, Germany. His current research activities include advanced polymeric materials synthesis and characterization, responsive hydrogel layer systems for biosensor and biomedical applications, hierarchical structure formation in colloidal systems, and 2D organization of semifluorinated alkane derivatives at the air−water interface.

ACKNOWLEDGMENTS M.R. acknowledges funding from the German Research Foundation (DFG) within the SFB840. N.V. acknowledges support from the Cluster of Excellence “Engineering of AJ

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