Hierarchical Crystals Formed from DNA-Functionalized Janus

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Hierarchical Crystals Formed from DNA-Functionalized Janus Nanoparticles Guolong Zhu, Ziyang Xu, Ye Yang, Xiaobin Dai, and Li-Tang Yan ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.8b04753 • Publication Date (Web): 06 Sep 2018 Downloaded from http://pubs.acs.org on September 7, 2018

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Hierarchical Crystals Formed from DNAFunctionalized Janus Nanoparticles Guolong Zhu, Ziyang Xu, Ye Yang, Xiaobin Dai, and Li-Tang Yan* State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China

*Corresponding author: [email protected]

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ABSTRACT: Harnessing anisotropic interactions in DNA-mediated nanoparticle assembly holds great promise as a rational strategy to advance this important area. Here, using molecular dynamics (MD) simulations, we report the formation of novel hierarchical crystalline assemblies of Janus nanoparticles functionalized with two types of DNA chains (DNA-JNPs). We find that in addition to the primary nanoparticle crystallization into face-centered cubic (FCC) structure, sequence-specific DNA hybridization events further direct the rotational orientation of the DNAJNPs to diverse secondary crystalline phases including simple cubic (SC), tetragonally ordered cylinder (P4), and lamella (L) structures, which are mapped in the phase diagrams relating to various asymmetric parameters. The crystallization dynamics of such hierarchical crystals is featured by two consequent processes: entropy-dominated translational order for the primary crystalline structure and enthalpy-dominated rotational order for the secondary crystalline structure. For DNA-JNPs with high asymmetry in DNA sequence length, tetrahedral nanoclusters turn to be favored, which is revealed to be governed by the conformational entropy penalty caused by bounded DNA chains. This work might bear important consequences for constructing new classes of nanoparticle crystals with designed structures and properties at multiple levels and in a predictable manner.

KEYWORDS: DNA, nanoparticle crystal, hierarchical order, guided assembly, crystallization


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The rational assembly of designed building blocks opens the ways for constructing sophisticated, nanostructured materials with potential applications in medical diagnostics, catalysis, and energy conversion, and as plasmonic nanomaterials.1-6 In this respect, the use of DNA as a ligand for the crystallization of nanoparticles is a promising strategy for engineering the surface of the nanosized colloidal building blocks and for controlling their connectivity through Watson-Crick base-pairing rules.7-11 Particularly, the synthetically programmable length and recognition properties of DNA have enabled the design of interparticle distances and interactions in nanometer-scale precision, resulting in the formation of two- and threedimensional superlattice crystals.12,13 These crystalline structures depend on the size and geometry of the nanoparticles, the surface density and length of DNA strands grafted onto the particles, and the number of complementary bases available for hybridization. These diverse parameters consequently offer advantages in predictability and control of crystal stability and architecture that DNA linkers afford.14-17 Anisotropic interactions through chemical “patchiness” on the surface of building blocks are powerful tools for engineering the assembly of particular targeted structures.18-21 By replacing the spherical cores that associate through isotropic hybridization interactions with asymmetric functionalization of the nanoparticles, one could introduce the concept of valency into such structures, thereby imparting directional interactions on the nanoscale.22-24 Recently, DNA has begun to be explored for the design and assembly of anisotropic nanoparticles that have both specific and directional interactions.25-27 For instance, directionality can be enforced by direct synthesis and by chemically imprinting nanoparticles with patches of DNA.25, 28 Some examples demonstrate interesting DNA-mediated self-assembly behaviors by taking advantage of anisotropic effects resulted from the face-selective functionalization of nanoparticles, but most


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so far have focused on small nanoclusters.29-31 Despite the advantages, the crystalline structures with long-range periodicity and their formation dynamics remain underdeveloped for such unique building blocks. We therefore seek to develop an intuitive framework for predicting and analyzing the crystallization of one class of elementary but emerging anisotropic nanoparticles, that is, Janus nanoparticles consisting of two surface sites functionalized with different types of DNA chains. In this regards, MD simulations can yield insight into the effects of the interplay between specific and directional interactions on the physical processes of the self-assembly of DNA-JNPs and the resulting crystalline structures. This allows us to identify novel hierarchical crystalline assemblies of these asymmetric nanoparticles, with primary and secondary crystalline structures at different levels. Through MD simulations and theoretical analysis, we determine that the crystallization dynamics of such hierarchical crystals include two consequent processes: entropydominated translational order for the primary crystalline structure and enthalpy-dominated rotational order for the secondary crystalline structure. Moreover, entropy-mediated tetrahedral clusters are found to be favored for DNA-JNPs with high asymmetry in DNA sequence length.

Results and Discussion Full technical details on the simulation method and the model of DNA-JNP are described in Method Section and also in Supporting Information I. Briefly, computer simulations are carried out using a scale-accurate coarse-grained model that has been extensively tested for robustness and reliability.32,

33

As illustrated by the schematic diagram in Figure 1, a Janus

nanoparticle consists of a gold core coated with two types of ssDNA chains, each of which contains space beads and linker beads that are self-complementary. The diameter of the core is


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10nm. The lengths of linker-bead portions in both A- and B-DNA chains are fixed at 6nm, approximating 12-20 base pair linkers.9, 32 Various values of the length of space-bead portion, ls, and the surface fraction, s , of A-DNA chains are used to tune the surface anisotropy of the DNA-JNPs, whereas the length of space-bead portion of each B-type DNA chain is kept at 16nm (about 32 bases).9 Upon thermal annealing, the thermally active hybridization can be achieved (as confirmed by different parameters in Figure S1),34, 35 which allows the Janus nanoparticles to optimize their location and orientation in order to maximize the number of DNA hybridization. Consequently, random initial configurations of nanoparticles quickly self-assemble into several types of ordered crystals, dictated by the design parameters.

Figure 1. Schematic illustration of the coarse-grained model for DNA-functionalized Janus nanoparticles and their hybridization. A Janus nanoparticle consists of a gold core coated with two types of ssDNA chains, each of which contains space beads and linker beads complementary to themselves. The bead size for the DNA chains is σ, corresponding to a diameter of 2nm. ls and

s represent the length of space-bead portion and the surface fraction of A-DNA chains. The lengths of linker-bead portions in both A- and B-DNA chains are fixed at 6nm, and the length of space-bead portion of each B-type DNA chain is kept at 16nm. The diameter of the core is 10nm. Representative events of DNA hybridization are circled in green and highlighted at bottom. Color scheme: (green) A-DNA chain and (pink) B-DNA chain.


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Hierarchical Crystals and Assembly Mechanism a

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(310)

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Figure 2. Hierarchical crystals formed by self-assembly of DNA-JNPs. (a-c) Secondary crystalline structures at different s while ls=16nm: (a) simple cubic (SC), s =0.25; (b) tetragonally ordered cylinder (P4), s =0.33; and (c) lamella (L), s =0.5. Each panel contains a model unit cell of corresponding crystal. Only A-DNA chains are displayed with chain model for clarity. (d-f) The detailed organization of DNA-JNPs in an elementary unit of the secondary crystals: (d) SC, (e) P4, and (f) L. (g-i) Primary crystal structure of DNA-JNPs. The diffraction pattern and static structure factor S(q) in (h), (i) and Figure S2 confirm that the primary crystalline structure in each system is face-centered cubic (FCC) with the model unit cell illustrated in (g). The green spheres or cylinders are used to mark the elementary units. The face-selective functionalization of nanoparticles with different types of DNA chains imparts directional interactions to the specific recognition of such DNA-encoded nanoparticles, endowing a high propensity for the thermodynamic self-assembly and structural diversity. Indeed,


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by controlling the surface anisotropy of DNA-JNPs, we find that combination of specificity and directionality can lead these asymmetric building blocks to simultaneously form primary and secondary crystalline structures at different levels. In Figure 2, we show simulation snapshots of representative cases for such hierarchical crystalline structures at three values of s . Similar with a self-complementary single-component system,15,

36

in which each nanoparticle can bind to

every other one with equal affinity, the spatial arrangement of the Janus nanoparticles favors the close-packed, FCC crystal structure for all of these systems, as identified from the diffraction patterns and the static structure factor, S(q) (Figures 2g-i and S2). However, in addition to this primary crystalline structure with translational order, the anisotropic interactions caused by the asymmetric hybridization events further drive DNA-JNPs to rotate and adopt orientational order, resulting in the secondary crystalline structure at a higher level. Particularly, by tuning the surface fraction of A-DNA chains s to 0.25, 0.33, and 0.5, we obtain SC, P4, and L crystalline structures [space groups 215 ( P43m ), 132 (P42/mcm) and 129 (P4/nmm)], as demonstrated in Figure 2a-c where DNA chains are visualized by chain model for simplicity (see Figure S3 for more details). The elementary unit for each of these secondary crystalline structures is a nanocluster or a larger entity assembled by local DNA-JNPs (Figure 2d-f). At first glance, the secondary crystalline structures of DNA-JNPs resemble the microphase structures of block copolymers which can also self-assemble into spherical, cylindrical, and lamellar phases, depending on the molecular architectures.37, 38 However, a close observation reminders us that there exists nontrivial difference in the ordered structures of these both systems. For the diblock copolymers, the spherical phase prefers body-centered cubic (BCC) instead of SC; the cylindrical phase usually favors hexagonal (HEX) packing rather than the fourfold cylinder phase, P4, although P4 has only been identified in the ordered microstructure self-


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assembled from semiflexible block copolymers.39 Such difference can be attributable to the spatial confinement generated by the primary crystalline structure of DNA-JNPs, i.e., the FCC crystal of nanoparticles with translational order. Within the FCC crystal, each Janus nanoparticle can only rotate around the lattice point, restricting the formation of more-close-packed crystallographic phase for the secondary crystalline structures of DNA-JNPs. Moreover, based on the entropy-driven transition from FCC to BCC for the homogeneous DNA-nanoparticles,36 we expect that the crystal structures of Janus DNA-nanoparticles might undergo a similar transition upon making DNA much longer. The study regarding this aspect is underway. Disordered FCC

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Figure 3. Analysis of the crystallization process for the hierarchical crystal. (a) Representative structures during the formation of L-FCC at different stages: (left) disordered structure at the initial stage (t=0  ); (middle) D-FCC crystal at an interim stage (t=3.6×107  ); and (right) LFCC crystal at the late stage (t=7.2×107  ). (b) The standard deviation of orientation angle  ,

SD , (top) and mean square displacement, MSD, (bottom) as a function of time when a random configuration of DNA-JNPs at T=2.0 is linearly annealed to T=1.0. The insetting diagram schemes the definition of  . The pink dashed line indicates that the crystallization process of the primary crystal structure, i.e., D-FCC, has been completed. From time beyond the blue dashed line, the rotational dynamics results in the orientational order towards secondary crystal structure, which is completed at green dashed line. (c) The average percentage of hybridizations, pH, (top) and the height of the first peak in the pair radial distribution function, g(r1), (bottom) as a function of time when a random configuration of DNA-JNPs is annealed according to the protocol indicated by the color bar. The cyan color marks two regions of the crystallization at constant temperatures. Next we turn to the assembly mechanism of the hierarchical crystals formed by DNAJNPs. Supporting Information Videos 1-3 display the dynamical processes of various hierarchical crystals with the secondary structures of SC (S-FCC), P4 (C-FCC), and L (L-FCC) corresponding respectively to Figure 2a-c. Clearly, the assembly and organization processes in DNA-directed crystallization of Janus nanoparticles undergo both translational and rotational dynamics. To delineate the details of these dynamical processes, we present an analysis of the key steps involved in the DNA-directed assembly of Janus nanoparticles into L-FCC, which is very similar to a CuAu-FCC phase descripted by Casey et al.40

As demonstrated by the

representative snapshots in Figure 3a, annealing the system with random initial configuration first leads to disordered-FCC (D-FCC) in which the organization of DNA-JNPs possesses translational order with FCC structure but random orientation, indicating the formation of only the primary crystalline structure. This process is followed by localized reorganization through


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the rotation of DNA-JNPs at the lattice points, which maximizes the number of hybridization events and eventually results in the secondary crystalline structure with both translational and orientational order. Previous experimental results obtained by the Mirkin group showed localized reorganization in DNA-directed crystallization of homogeneous nanoparticles.41 Our simulations further reveal that the rotational dynamics driven by asymmetric hybridization events plays a crucial role in the reorganization of the DNA-JNPs with heterogeneous surface. To quantitatively capture these successive processes, we examine the translational and rotational dynamics through calculating respectively the mean square displacement (MSD) and the standard deviation of orientation angle  , SD , defined as SD   i 1i2 / N with N



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i = arccos ( ei , e0 ) (for more details, see Supporting Information II). Here ei and e0 denote the orientation of a Janus nanoparticle and the ensemble-averaged orientation, as schemed by the insetting diagram in Figure 3b; N is the total number of Janus nanoparticles. A lower value of SD , a higher orientational order for the secondary crystalline structure with L-FCC. Figure 3b shows the plots of MSD and SD as a function of the simulation time step. As the temperature linearly decreases to T=1.6, the MSD of Janus nanoparticles reaches a steady state at ~2.8×107 time steps, when the disordered liquid instantaneously transforms into the primary crystalline structure, as also identified from the bond order parameter (Figure S4).42 In contrast, a decrease of SD occurs at a later time with a lower temperature, i.e., ~4.2×107 time steps when T=1.4, corresponding to the initiation of the localized reorganization for the secondary crystalline structure. For the sake of pinpointing the inner nature underpin the translational and rotational order in the crystallization dynamics of the hierarchical crystal, we provide a deeper insight into the


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thermodynamic interactions underlying such two consequent processes. Although an annealing process with a decrease of the initial temperature can trigger the crystallization events, crystals can also be obtained via a constant simulation temperature, which eliminates the effects exerted by the temperature change and allows us to examine the translation and rotation processes respectively through choosing certain temperatures in light of Figure 3b. As described by the color bar in Figure 3c, we thereby adopt a protocol of the temperature control including two sections of constant temperatures: one keeps at T=1.6 where only translational order occurs and the other at T=1.1 for the solely rotational order.

In the first section, the percentage of

hybridizations of the total DNA chains, pH, remains stable at about 0.23 which is so small that hybridization strength is not enough to serve as an appropriate stabilizing interaction between the DNA-JNPs and guide them into crystal.35 However, the peaks in the pair radial distribution function, g(r), whose separations and heights are characteristics of the FCC crystal structure, do become sharp, as demonstrated in Figure S5a and indicated by the height of the first peak, g(r1), in Figure 3c. In theory, the thermodynamically preferred structure can be determined based on the enthalpic differences and the entropies of the constituent DNA chains.15 Due to the stable and low hybridization strength, the enthalpic contribution to the formation of D-FCC structure is really trivial. Although it is not feasible to calculate the DNA conformational entropy exactly, it can be estimated through considering the volume accessible to the DNA chains (Vf), as N

S  kB  ln Vi , where Vi represents the free volume of a Janus nanoparticle and kB is the i 1

Boltzmann’s constant.43,44 In view of the well-known results of statistical mechanics, the maximum value of the entropy of N nanoparticles in volume V can be reached when Vi is equal for each particle, i.e., S m  NkB ln(V /N ) .45 As observed for g(r), the formation of D-FCC structure leads to more uniformly distributed Janus nanoparticles and thereby increases the 11 ACS Paragon Plus Environment

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conformational freedom for the DNA chains. As such, it is the conformational entropy of the DNA chains that dominates the translational order for the primary crystalline structure. In sharp contrast, in the second section with lower temperature, hybridization becomes more thermodynamically favorable (as clarified by the evident increase of pH), while the peaks in g(r) keep almost unchangeable (Figures 3c and S5b). This indicates that the enthalpic contribution caused by the hybridization turns to governing the reorganization and rotational order for the secondary crystalline structure. Phase Diagrams

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DNA-JNPs, as depicted by the insetting image, fT depending on ls and s , where ls  12nm. The color bar shows the color code for the values of fT. (b) Phase diagram of the hierarchical crystalline structures, where ls>12nm. Open circles on the graph indicate that corresponding crystal structures form while filled circles indicate that crystalline structure does not show in the simulations. The open circles are colored and grouped according to the crystalline structures at different levels. Color scheme is presented in the right region where the secondary structures are: SC (S-FCC), P4 (C-FCC), L (L-FCC), and disordered (D-FCC).


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To further assess how DNA-directed assembly of Janus nanoparticles relates to the surface anisotropy of the DNA-JNPs, we systematically simulate the assembled structures as a function of the space-bead portion ls and the surface fraction s of A-DNA chains (recall that the length of space-bead portion of B-type DNA chains is fixed at 16nm), which allows us to construct the phase diagram in the s -ls plane, as displayed in Figure 4. In order to ensure that the obtained structures correspond to the thermodynamic equilibrium, we performed a large scale of independent simulation runs for each point shown in the phase diagrams. For very short A-type chains (ls  12nm), the large periodic structure can never be identified; rather, the extreme anisotropy leads the DNA-JNPs to assemble into nanoclusters with different numbers of nanoparticles (for example, see Figure S6a). As the tetrahedral nanocluster bears the particular interest for the potential applications,46-48 in Figure 4a we present the colored contour map for the fraction of the tetrahedral nanoclusters, fT, with respect to ls and s . The details regarding this map and the formation mechanism of the tetrahedral nanoclusters will be discussed in the next section. Figure 4b shows the phase diagram of the hierarchical crystalline structures where

ls>12nm, and the characteristic regions are approximately bounded by shaded sections and symbols. We note that increasing the fraction of A-DNA chains s significantly narrows the region for the formation of the primary crystalline structure (D-FCC). The secondary crystalline structures are expected to occur only when the length of A-type DNA chains is commensurate with that of the B-type chains, as the FCC-arranged nanoparticles in the primary crystalline structure restrains the hybridization events for the DNA chains with much shorter length. Particularly, the hierarchical crystals of S-FCC, C-FCC, and L-FCC occur with ls between 14nm and 18nm, and the boundaries among these three crystals lie at about s =0.30 and 0.40,


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respectively. The Mirkin group developed a rule, the complementary contact model, to explain which crystal should form in equilibrium.12, 14 This rule states that the equilibrium crystal is the one that maximizes the contact between DNA-nanoparticles that have complementary strands. By employing this model, we also get a phase diagram regarding aforementioned hierarchical crystalline structures depending on ls and s , as demonstrated in Figure 5. A comparison between the simulated and modeled phase diagrams shows that the model faithfully reproduces the ranges and boundaries for each simulated crystal, corroborating that these simulated hierarchical crystalline structures indeed correspond to the thermodynamic equilibrium.

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different secondary crystal structures are determined as a function of ls and s . (b) Twodimensional “slice” through the plot at ls=16nm in (a).


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Entropy-Mediated Tetrahedral Nanoclusters

As the simplest cluster with highly uniform and isotropic dipolar symmetry, tetrahedral nanoclusters are of particular interests for some potential applications, such as metafluids.46-48 Figure 4a demonstrates that such a unique structure can be obtained through self-assembly of DNA-JNPs within a large parameter window for the surface anisotropy. The test runs regarding the melting temperature indicate that tetrahedral nanoclusters possess high stability (Figure S6b). Such energetically stable nanoclusters that are not commensurate with an equilibrium crystal may provide some clues about the nucleation and growth of the hierarchical crystalline structures.47 It is thereby essential to elucidate the mechanism for the formation of the tetrahedral nanoclusters. For this purpose, we consider two neighboring DNA-JNPs with the normal configuration in a tetrahedral nanocluster, as illustrated by the schematic diagrams in Figures 6a. Upon the binding on interaction between these both DNA-JNPs, the difference of the DNAmediated interaction free energy, F , is attributable to the conformational entropy penalty and the reduced potential energy.15 In view of the implicit solvent model, F can be estimated using F =U -T S , where U is the energetic (enthalpic) contribution and S can be estimated as k B ln V f .43, 44 In principle, U approximates to 3pH N m ,34 with   6.0k BT being the bond strength. pH and Nm are the change in pH and the maximum number of hybridizations, respectively. As pH keeps almost unchangeable for a certain temperature ( pH ≈0.35 at T=1.0, Figure S7), U per bonding prefers a constant value of about -2.1kBT, independent of ls and s (Figure 6b). However, the changes of ls and s will remarkably modify Vf and thereby the conformational entropy of DNA chains. Depending on the interaction geometry of the present systems, Vf includes V1, V2 and V3, V4 before and after the hybridization events, as marked by


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different colors in Figure 6a. Explicit expressions of V1-V4 are derived in Supporting Information III and summarized in Method Section. Thus, the entropic free energy contribution caused by a bonding can be determined as T S  kBT ln(V1 / V3 )  kBT ln(V2 / V4 ) . b 0.60 R1 R2

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Figure 6. Entropy-mediated formation of the tetrahedral nanoclusters of DNA-JNPs. (a) Schematic diagrams illustrating the estimation of conformational-entropy change caused by the formation of a tetrahedral nanocluster. Color scheme: (cyan), the surface section with linker beads, (blue, red) V1, (pink, green) V2, (blue) V3, and (pink) V4. The enthalpic (b) and entropic (c) free energy contributions per bonding as a function of ls and s upon the formation of a tetrahedral nanocluster. The color bars indicate the color codes for the values of U and T S , respectively. Figure 6c shows the colored contour map of the entropic free-energy landscape with the same scales of ls and s in Figure 4a. It can be found that the entropic free energy evidently decreases within the primary range corresponding to the formation of tetrahedral nanoclusters (Figure 4a), in striking contrast to the mild fluctuation of U around -2.1kBT (Figure 6b). Although the reduced potential energy as a result of hybridization favors the formation of the tetrahedral nanoclusters, such a free energy gain is opposed by the entropic free-energy penalty incurred by the conformation loss of bounded DNA chains. As a consequence, the DNA-JNPs


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can self-assemble into a tetrahedral nanocluster only when the conformational entropic freeenergy penalty cannot offset or even overwhelm the reduced potential energy. Hence, the conformational entropy of the DNA chains acts as the predominant factor mediating the formation of tetrahedral nanoclusters. These results may allow guides for exploiting variations in the anisotropic parameters of DNA-JNPs to control the formation of tetrahedral nanoclusters.

Conclusions In summary, we have demonstrated novel hierarchical crystalline structures assembled by DNA-functionalized Janus nanoparticles which effectively impart directionality to the specific recognition of such important building blocks. By controlling the surface anisotropy of DNAJNPs, we find that in addition to the primary crystalline structure of FCC-arranged nanoparticles, sequence-specific DNA hybridization events further direct the rotational orientation of DNAJNPs to diverse secondary crystalline phases including SC, P4, and L structures. In contrast to corresponding phase structures of diblock copolymers, such secondary crystalline structures are less-close-packed due to the spatial confinement generated by the primary crystalline structure. Through systematic simulations and theoretical analysis, we determine that the crystallization dynamics of the hierarchical crystals include two consequent processes: entropy-dominated translational order for the primary crystalline structure and enthalpy-dominated rotational order for diverse secondary crystalline structures. The phase diagrams regarding the assembled structures of DNA-JNPs are mapped, which detail the characteristic regions for the primary and secondary crystalline structures and demonstrate that tetrahedral nanoclusters turn to be favored upon high asymmetry in DNA sequence length. Furthermore, a quantitative analysis of the relative importance of enthalpy vs entropy in the assembly process is performed, revealing that the conformational entropy penalty caused by bounded DNA chains dominates the formation of the tetrahedral nanoclusters. The motif and findings described in this paper might bear important 17 ACS Paragon Plus Environment

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consequences for constructing new classes of nanoparticle crystals in a predictable manner, wherein material structures and properties can be designed at multiple levels. Recalling the exquisite surface functionalities of nanoparticles (such as patchy particles18), more complex structural organizations, such as linear and chiral superstructures, may be realized by designing more heterogeneous building blocks modified by DNA. We thereby expect that this work would promote further efforts towards fundamental research and the wide applications of designed assemblies of multifunctionalized DNA-nanoparticles in new types of functional nanomaterials and beyond.

Model and Methods Coarse-Grained Molecular Dynamics. In this study, we have modified a scale-accurate coarsegrained model developed for isotropy ssDNA-nanoparticle assemblies32 to include effects of asymmetry in DNA sequence length and surface fraction. Using MD simulations, we directly study the guided assembly and crystallization of DNA-JNPs. Each nanoparticle is modeled as a Janus spherical core of radius 2.5, where ≈2.0nm and two types of ssDNA chains (with the total chain number N=60) are distributed randomly on the nanoparticle surface. An ssDNA is modeled as spacer beads and linker beads, and each bead with a diameter of  represents about 4-7 bases (Figure 1).32,34,35 Actually, the thermally active hybridization (i.e., a DNA hybridization process in which bonds between complementary DNA bases form and break as a result of thermal fluctuations) is the key to achieving successful crystallization.34 Here we realize a thermally active hybridization by carefully tuning the bond strength,  0 , of the sticky ends and temperature of the system. Particularly,  0  6.0k BT and an annealing process from T=2.0 to

T=1.0 (linearly decreasing temperature) serve as suitable values that enable crystallization while achieving a fully active hybridization (Figure S1).


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The attractive interactions between central beads are modeled via shifted Lennard-Jones (SLJ) potential and the short-range repulsive interactions between any other pair of beads are modeled with shifted Weeks-Chandler-Anderson (SWCA) potential.49 To mimic the stiffness of ssDNA chains, harmonic angle potential is also applied along the ssDNA chains. The MD simulation is performed in an NVT ensemble with constant number of particles, volume, and temperature. The temperature is controlled by a Langevin thermostat50 in a three dimensional

Lx×Ly×Lz lattice which is determined based on the system volume fraction  (=1.16) defined as 4 4 N (  r13S   R13 (1  S )) 3  3 Lx  Ly  Lz

(1)

Thirty-two JNPs coated with DNA chains are placed in a simulation box with periodic boundary conditions.33 More details on the simulation methods and models are given in Supplementary Information I.

Free Volumes Accessible to DNA Chains upon Formation of Nanocluster. Due to the complexity of DNA-JNPs lattices and the vast number of possible microstates, it is not feasible to calculate the DNA conformational entropy exactly. Instead, we calculate the volume accessible to the DNA chains, Vf, as an estimation of conformational entropy.44 Depending on the interaction geometry of the present systems, Vf includes V1, V2 and V3, V4 before and after the hybridization events, as marked by different colors in Figure 6a. Explicit expressions of V1-V4 are derived in Supporting Information III. Briefly, V1-V4 can be calculated by volume integrals as follow:

V1  



0

2

r1

0

r2

 

r 2 sin( )drd d

(2)


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V2 

2 3 R1  R23    3

V3  2



0

V4  2



0

r1

0

r1 cos( )/cos( )

sin(   ) sin(   ) sin(   ) -arccos sin(   )



(3)

2

  arccos

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


R1

R1

sin(   ) sin(   )cos( )


(4)

(5)

Here, r1 and r2 are respectively the average distances between the center of a nanoparticle and the end of the relaxed DNA chain, and between the center of a nanoparticle and the end of the space-bead portion for the A-DNA chains; R1 and R2 for the B-DNA chains. The definitions of  and  can be found in Supporting Information III.  and  represent the zenith and azimuth angles used for the volume integrals.

ASSOCIATE CONTENT Supporting Information The detailed derivation of the models, additional simulation results, and videos. This material is available free of charge on the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Authors * Email: [email protected]

ACKNOWLEDGEMENTS We thank stimulating discussions with Zihan Huang and Pengyu Chen. L. T. Y. acknowledges financial support from Ministry of Science and Technology of China (Grant No. 2016YFA0202500). We acknowledge support from NSFC (Grant Nos. 21873053 and 51633003).


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TOC Graphics


Hierarchical Crystals Formed from DNA-Functionalized Janus

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