Emergence of complexity in hierarchically organized chiral particles

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Science  08 May 2020:
Vol. 368, Issue 6491, pp. 642-648
DOI: 10.1126/science.aaz7949

Complex chiral particles

Synthetic colloids are usually smooth, but nature can produce micrometer-scale particles with intricate structure and shape, such as the coccoliths produced by algae. Jiang et al. controlled the self-assembly of gold–cysteine nanoplatelets into a variety of chiral, hierarchically organized colloidal particles by changing the chiral fraction of cysteine and the nucleation temperature. Organic cations created electrostatic repulsions that favored edge assembly of the nanoplatelets, which in turn could create surfaces bearing twisted spikes.

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The structural complexity of composite biomaterials and biomineralized particles arises from the hierarchical ordering of inorganic building blocks over multiple scales. Although empirical observations of complex nanoassemblies are abundant, the physicochemical mechanisms leading to their geometrical complexity are still puzzling, especially for nonuniformly sized components. We report the self-assembly of hierarchically organized particles (HOPs) from polydisperse gold thiolate nanoplatelets with cysteine surface ligands. Graph theory methods indicate that these HOPs, which feature twisted spikes and other morphologies, display higher complexity than their biological counterparts. Their intricate organization emerges from competing chirality-dependent assembly restrictions that render assembly pathways primarily dependent on nanoparticle symmetry rather than size. These findings and HOP phase diagrams open a pathway to a large family of colloids with complex architectures and unusual chiroptical and chemical properties.

Organic-inorganic particles made by or found in living systems often display spiky, reticulated, twisted, and fractal morphologies with nanoscale structural components. They can be referred to as hierarchically organized particles (HOPs) because they possess multiscale levels of organization encompassing both molecular and nanoscale structural units. Although some topological elements of HOP geometry can be replicated in synthetic particles with different degrees of similarity (17), the physical mechanisms responsible for HOP formation remain mysterious. One unanswered question concerns the origin of their complexity, given the highly unfavorable thermodynamics of their templateless self-organization (8, 9). The Gibbs free energy of open structures with nanoscale organization (10) should be higher than that of the corresponding random, compact agglomerates (fig. S1). The latter are favored by entropy and enthalpy, and yet complex HOPs spontaneously form in multiple biological and abiological systems. Another question concerns the role of polydispersity of the nanoscale components involved in the self-assembly process. For similar thermodynamic reasons, the wide size distribution should favor disorganized structures, but numerous biological systems defy these expectations.

One mechanism guiding the assembly of nanostructures could be related to the chirality of the constituent building blocks (1114) typical for biology. However, chirality-guided self-assembly pathways are typically understood as lock-and-key mechanisms that do not permit structural variability of the components. The thermodynamic preferences of nanoparticle association based on their chirality can also be destroyed by large energy perturbations from size variations (15). Nonetheless, the role of chirality in the assembly patterns of building blocks with wide size distribution is worth investigating further because of the many fundamental implications and practical implementations of chiral HOPs.

In the search for appropriate experimental systems, we turned to noble-metal thiolates (16, 17) because they are known to exist as one- and two-dimensional nanostructures with variable surface ligands and strong chiroptical activity (1821). We prepared chiral thiolates of gold in the form of nanoplatelets with the amino acid cysteine (Cys) as surface ligands (figs. S2 and S3 and supplementary materials) and developed multiscale computational models (figs. S2, S4, and S5 and tables S1 and S2) that enabled us to evaluate their thermodynamic and optical characteristics. Au-Cys nanoplatelets are uniform in thickness but have a broad lateral size distribution with a dispersity index of 1.36 (fig. S2, B and C). When bearing nonracemic ligands, these particles display circular dichroism (CD) spectra with peaks in the far-ultraviolet (UV) range associated with the Cys ligands and those at the longer wavelengths associated with chirality of nanoplatelets themselves, according to molecular dynamics (MD) and xTB-sTDA calculations (22) (figs. S6 to S8 and movie S1).

The tendency of Au-Cys nanocolloids toward randomized agglomeration was mitigated by strong electrostatic repulsion imparted to particles by cetyltrimethylammonium bromide (CTAB). CTA+ cations increase the electrokinetic zeta potential, ζ, of nanoplatelets from –18.6 mV to +44.7 mV; nanoplatelets serve as nanoscale building blocks for most particles investigated here. Association of the Au-Cys nanoplatelets, induced by high ionic strength (0.5 M NaCl) without CTAB, led to disordered high–molecular mass agglomerates (fig. S9). Without NaCl and CTAB, half-spiked spheroids formed (fig. S10). These spheroids were largely disorganized but their shape was peculiar, revealing consistent symmetry breaking, with one side of the particle being smooth and the other spiky.

Adsorption of CTA+ on the nanoplatelets increased the electrostatic repulsion, which counteracted the close-range attraction responsible for thermodynamic minima along the high-mass pathway (fig. S1). At some point, the repulsion became strong enough to avoid stochastic agglomeration, switching the process from the high-mass agglomeration pathway to electrostatically frustrated self-assembly (23, 24). With increasing CTA+ concentration, the high ζ value should make edge-to-edge attachment of the nanoplatelets more favorable than the face-to-face alternative. When [CTA+] = 0.27 M, the use of pure l- or d-Cys enantiomers (enantiomeric excess χ = ±100%; see supplementary materials) produced HOPs (Fig. 1, A, B, D, and E) with twisted spikes radially organized around a common center (fig. S11); their formation was associated with the growth of strong CD bands in UV-visible and infrared (IR) parts of the spectrum (Fig. 2D and fig. S12). These spiky particles are denoted as Au–l-Cys and Au–d-Cys, respectively, or coccolith-like particles (CLIPs), cumulatively, in reference to their partial resemblance to spiky skeletons produced by microscale algae coccolithophores (e.g., Syracosphaera anthos HOL). Despite prior studies (8, 10, 25), the unique echinate geometry of coccoliths and silicoflagellates remains a biomineralization puzzle. Statistical analysis of 500 Au–l-Cys CLIPs showed that they were highly uniform in size, with a diameter of 3.5 ± 0.3 μm and polydispersity index of 1.02 (Fig. 1, A and B, and fig. S13).

Fig. 1 Gold thiolate hierarchically organized particles (HOPs) with cysteine surface ligands.

(A to C) SEM images of Au–l-Cys and Au–d-Cys coccolith-like particles (CLIPs) [(A) and (B)] and Au–dl-Cys kayak particles (C) with low magnification. (D to F) Enlarged SEM images of Au–l-Cys and Au–d-Cys CLIPs [(D) and (E)] and Au–dl-Cys (F) kayak particles. (G to I) SEM images and corresponding schematic illustrations of segments of Au–l-Cys (G), Au–d-Cys (H), and Au–dl-Cys (I). Statistical analysis of SEM images for 100 assembly segments indicates that the pitch of individual nanoribbons in the stacks is 1300 ± 123 nm and their average width is 16 ± 1.8 nm, whereas the average angle between two neighboring nanoribbons in the stack is 7° ± 0.7° and the pitch of nanoribbon stacks is 820 ± 10 nm. (J to M) Confocal microscopy images of Au–l-Cys CLIPs [(J) and (K)] and Au–dl-Cys kayak particles [(L) and (M)]. (N to P) Atomistic MD simulation of twisted conformation of Au–l-Cys single sheets of different lengths [(N) and (P)] and their stacks (O). The XRD, XPS, and thermogravimetry data obtained for different HOPs indicate that only Cys molecules are present in the interlamellar spacing between adjacent Au–l-Cys sheets.

Fig. 2 Chemical and optical properties of Au-Cys CLIPs.

(A) Dispersions of Au–l-Cys CLIPs in different solvents [methanol, ethanol, dimethyl sulfoxide (DMSO), N,N-dimethylformamide (DMF), and toluene]. Some sediment forms upon long-term standing; it redisperses upon shaking. (B) Stability study of Au–l-Cys dispersions with different pH values or concentrations of HCl or NaOH after 12 hours. Top photograph was taken under daylight illumination; bottom photo was taken under UV light (wavelength 365 nm) irradiation. (C and D) CPLE (C) and CD (D) spectra of Au–l-Cys CLIPs (blue), Au–d-Cys CLIPs (red), and Au–dl-Cys kayak particles (black). Inset in (C): Photos of Au–l-Cys, Au–d-Cys, and Au–dl-Cys dispersions under daylight (top) and UV light (bottom) illumination. (E and F) CPLE (E) and CD (F) spectra of Au–l-Cys (blue) and Au–d-Cys (red) after sonication. Inset in (F): The same spectra for the 500- to 1350-nm spectral window to confirm the absence of the CD peaks associated with differential scattering of assembled CLIPs. The helicity of the nanoribbon stacks of Au–l-Cys is left-handed, and therefore the light scattered by Au–l-Cys has left-handed polarization. After disassembly of the stacks into single right-handed nanoribbons, the light passing through these dispersions acquires right-handed circular polarization. (G and H) The computational model (G) and calculated CD spectra (H) of Au–l-Cys nanoplatelets. The corresponding peaks in the short-wavelength part of the CD spectra of CLIPs and nanoplatelet are marked in (D), (F), and (H) with green stars. (I and J) The computational model (I) and the differential extinction spectrum (J) for the differential scattering contribution to the chiroptical properties of the CLIPs at long wavelengths. The corresponding signals in the experimental and calculated spectra in (D) and (J) are marked with blue stars.

Kayak-shaped HOPs with layered architectures, denoted as Au–dl-Cys, which lack the spiky geometry but do manifest hierarchical organization (Fig. 1, C and F), were observed when a racemic mixture of Cys (χ = 0%) was used. Au–l-Cys (Fig. 1, J and K), Au–d-Cys (fig. S14, A and B), and Au–dl-Cys (Fig. 1, L and M) possess strong light emission with red and orange colors for χ = ±100% and 0%, respectively. The confocal microscopy images (Fig. 1, J to M, and fig. S14, A and B) obtained using this intrinsic particle emission show geometries consistent with the scanning electron microscopy (SEM) images.

The disassembly of HOPs into twisted nanoribbons by sonication reveals their hierarchical structure, composed of staggered thin sheets (Fig. 1, G and H, and fig. S14, C and D). Structural analysis of CLIPs and constituent twisted ribbons by means of x-ray diffraction (XRD), x-ray photoelectron spectroscopy (XPS), thermogravimetric analysis, Fourier-transform infrared spectroscopy, UV-visible spectroscopy, and time-resolved fluorescence imaging yielded results that are consistent with atomically thin layers of gold and sulfur connected by aurophilic bonds (figs. S15 to S18). The x-ray diffraction spacing between the layers is 1.23 nm; it is nearly identical to the thickness of the Au-Cys sheets of 1.26 nm and 1.37 nm, calculated according to MD simulations using either quantum chemical potential energy surfaces (fig. S19) or a classical force field (fig. S2A). The corresponding atomic structure of Au-Cys nanoribbons (fig. S2) forming nanosheets with [010] growth direction along the long axis can be proposed on the basis of density functional theory (DFT) calculations (figs. S4 and S19) and substantiated by small-angle x-ray scattering (SAXS) and XRD data (figs. S3 and S15). The preference of [010] atomic structure over [100] can also be verified for twisted states of the ribbon by coarse-grained models (fig. S5 and movie S2).

The gold-thiolate nanoribbons in Au-l-Cys HOPs are right-handed (RH, twisted clockwise). The stacks of the corresponding nanoribbons are, however, left-handed (LH, twisted counterclockwise, Fig. 1G). The handedness of the nanoribbons and their stacks is inverted (i.e., to LH and RH, respectively) if d-Cys is used instead (Fig. 1H). The twist of individual nanoribbons is reproduced well in atomistic MD models (Fig. 1, N to P). The staggered configuration of the ribbons assembled in a stack originates from the minimization of electrostatic repulsive forces observed previously for gold nanorods (26, 27).

Strong bonding of sulfur atoms to two Au atoms and the spiky geometry associated with the molecular and submicrometer organization of CLIPs leads to chemical properties that are unusual for both colloidal particles and two-dimensional nanostructures. Typical gold thiolates are known to aggregate rapidly and form precipitates (28), but this is not the case for CLIPs. The spiky geometry and charged surface ligands allow this type of HOPs to form dispersions in hydrophilic and hydrophobic media with high colloidal stability (Fig. 2A and fig. S20) (29). They also display remarkable chemical stability, with both their geometry and bright red luminescence observed from pH 0 to 11 (Fig. 2B and figs. S21 and S22).

The dispersibility and strong luminescence of CLIPs enables elucidation of their chiroptical properties and self-assembly pathways. The spectroscopic measures for different levels of organization in CLIPs are needed as experimental order parameters to understand how self-assembly pathways to complexity depend on the chirality and polydispersity (fig. S1). Unlike small chiral molecules, nanoparticles, and biological and (bio)inorganic nanoassemblies (30), HOPs of this type display strong chiroptical activity in absorption, luminescence, and differential scattering simultaneously. Separation of HOPs into structural components by ultrasonication (Fig. 1, G and H, and fig. S14, C and D) as well as a diverse set of computational techniques make possible the comprehensive identification of spectral signatures of all these optical processes.

The CD spectra for CLIPs show nearly perfect mirror symmetry for all the bands. Sharp peaks at 250, 310, 350, and 380 nm (Fig. 2D and fig. S23A) correspond to electronic transitions matching those calculated for model Au–l-Cys nanoplatelets (Fig. 2, G and H, and figs. S7 and S8). The broad 650- to 1350-nm band in Fig. 2D is attributed to the circularly polarized differential scattering (31) from the spiky particles (Fig. 2, I and J). Disassembly of these HOPs into nanoribbon stacks (Fig. 2F and fig. S23B) leads to disappearance of the peaks with maxima at 420, 560, and 830 nm, indicating that these bands are specific to the fully assembled CLIPs.

Circularly polarized light emission (CPLE) spectra of Au–l-Cys and Au–d-Cys display mirror-symmetrical strong bands at 620 nm, whereas their racemic counterparts, kayak-like HOPs, are CPLE-silent (Fig. 2C). Emission from HOPs acquires circular polarization by two mechanisms. First, photons are emitted in the circularly polarized state as a result of angstrom-scale chirality of the excited states in the Au-Cys nanosheets (fig. S18). The chirality and a more general case of asymmetry of the different excited states can be visualized by quantum chemical calculations (movie S1). Second, the emitted photons acquire additional circular polarization as the result of scattering on dispersed particles with submicrometer-scale chirality. The second mechanism modifies the polarization of photons emitted by Au-Cys sheets and can revert the polarization rotation of the photons acquired during the emission. The stage of assembly and the geometry of the HOPs affect the contribution of scattering, which results in the variable sign of CPLE spectra. As such, the polarity of the CPLE peak of Au–l-Cys switches from positive (left-handed photons dominate) to negative (right-handed photons dominate) after disassembly of CLIPs into individual ribbons (Fig. 2, C and E, and fig. S24) because CLIPs contribute more of the differential scattering in CPLE. The same is observed for Au–d-Cys and constituent twisted ribbons, albeit with opposite signs of the CPLE peaks. The CD peaks in the 500- to 1200-nm region (Fig. 2, D and F) disappear for the constituent nanoribbons. The positive and negative CPLE peaks are therefore spectroscopic signatures of CLIPs, as was also confirmed by electrodynamics simulations (Fig. 2, I and J).

Combining SEM images and CPLE data, which serve as spectroscopic order parameters for this thermodynamic system, we constructed phase diagrams (Fig. 3, A to C, and fig. S25) and found a diverse spectrum of HOP phases and degrees of organization for different values of χ and the building-block nucleation temperature tn (see supplementary materials). Besides the CLIPs and kayak particles, χ-tn diagrams include several other phases with different packing of Au-Cys sheets (Fig. 3B) and CPLE activity (Fig. 3C).

Fig. 3 Phase diagram and diversity of HOPs from chiral nanoplatelets.

(A) SEM images of Au-Cys particles assembled at different nucleation temperatures tn and χ values. (B) Phase diagram based on the geometrical description of the assembled particles. (C) Phase diagram based on the CPLE intensity and sign. Both types of phase diagrams display the distinct top-bottom symmetry with respect to the middle line (χ = 0). (D) CI-based phase complexity map for HOPs. GT models for phases DSP, SPP1, SPP2, bow bundles 1 (BB1), and BB2 are placed for tn and χ values where the specific phase is observed. (E and F) SEM images of Au/Cu–d-Cys (E) and Au/Ag–l-Cys HOPs (F). Inset in (F): An enlarged view of the HOP surface. (G) UV-visible and photoluminescence (PL) spectra of Au-Cys (red), Au/Cu-Cys (orange), and Au/Ag-Cys (green) samples. Solid line, HOPs obtained from l-Cys; dashed line, HOPs obtained from d-Cys. Inset: photos of Au-Cys, Au/Cu-Cys, and Au/Ag-Cys samples (right to left) under UV light. Numerous CD peaks were observed corresponding to molecular, nanoscale, and mesoscale levels of chirality (fig. S42). The handedness of the nanoribbons and their stacks in Au/Ag-Cys and Au/Cu-Cys was the same as those in Au-Cys CLIPs. (H and I) CPLE spectra of Au/Cu-Cys (H) and Au/Ag-Cys (I) HOPs. Solid line, before sonication; dotted lines, after sonication. The anisotropy factors for emitted photons were 0.0016 and 0.005 for Au/Cu-Cys and Au/Ag-Cys, respectively.

The CPLE peaks mark the evolution of the nanoscale system toward complex HOPs. However, CPLE and other chiroptical characteristics such as optical dissymmetry factor (g-factor) have difficulties as general enumerators of complexity because they require similarity in materials and/or geometries of the particles. For example, the g-factor of complex porous particles from BaCO3 (1), CaCO3 (3), or FeSe (9) with centrosymmetric geometry is ~0. The g-factor of solid particles from gold with noncentrosymmetric geometry is ≥0.2 (4), but their complexity can be comparable to that of the previous particles. To address this problem, we enumerated particle complexity using graph theory (GT), extending GT approaches from chemistry (32) to nanomaterials (see supplementary materials). We calculated a GT-based complexity index (CI) as an augmented valence sum (33) with modifications ensuring its applicability across a wide range of self-assembled structures (see supplementary materials). CI values for a variety of particles indicate that this parameter adequately ranks them according to information content and structural sophistication (table S3). Note that other common GT indices reveal little or no correlations with particle complexity (table S4).

For typical assemblies of nanoparticles studied earlier, CI is in the range of 1.5 to 38.25 (fig. S26 and table S3). Analogous calculations for HOPs with the morphology of reticulated supraparticles, kayak particles, and CLIPs (Fig. 1 and fig. S11) give CI values of 6.0, 40.0, and 87.0, respectively (Fig. 4, A to F). Within the knowledge of nanoscale structure available for spiky coccoliths representing one of the complex biological HOPs, their CI is 49.0 (Fig. 4, G and H).

Both in the lab and in nature (molecules responsible for biomineralization processes are homochiral), the highest structural complexity is observed for χ = 100%. One might infer that complexity increases as χ increases, which might be compelling given the amazing complexity of biological systems. However, the relationship between χ and CI is nonmonotonic, as reflected by the CI calculation for different HOP phases (Fig. 3D). For example, supraparticle phases 1 and 2 (SPP 1 and 2), observed for 45% < χ < 70%, have CI values of 6 to 20; these are smaller than the CI values of both CLIP and kayak-like particles, which may confirm the initial concerns about the ability of nanoparticle chirality to guide the assembly of complex systems. Nonetheless, the strong dependence of structural complexity on chirality can be substantiated by replacement of l-Cys with achiral thioglycolic acid (TGA; Fig. 4, A and B). With an increasing amount of TGA, Au-thiolate particles gradually lose their organization, transitioning to random agglomerates, porous dumbbells, and spheroidal particles (figs. S27 and S28) with CI ≤ 6 (Fig. 4). Additionally, Au-S nanoplatelets with chiral penicillamine produce CLIPs with twisted spikes (fig. S29) similar to those from l- and d-Cys, with CI = 87.

Fig. 4 SEM images of different HOPs, their GT models, and corresponding complexity indexes (CI).

(A and B) SEM image of supraparticle Au-thiolate with achiral TGA as surface ligands (A) and its GT model (B). (C and D) SEM image of the Au–dl-Cys kayak-like particle (C) and its GT model (D). (E and F) SEM image of the Au–l-Cys CLIP (E) and its GT model (F). (G and H) SEM image of a skeleton of Syracosphaera anthos HOL reproduced from the depository of SEM images of coccoliths found at (G) and its GT model (H). The graph segments marked with the purple stars in (B) and (D) are minimal topological contracts (MTCs) for the flat Au-S sheets with continuous crystallinity. The graph segments marked with the orange stars in (F) and (H) are the MTC for twisted sheets.

The relationship between chirality and complexity in this system can be understood in the context of different restrictions on the association patterns for nanoparticles traversing the thermodynamic landscapes (fig. S1). One of the exemplary restrictions is due to electrostatic repulsion (13, 23, 24). Gradually increasing electrostatic forces in self-assembled structures leads to self-limitation of particle aggregation. Note that electrostatic restrictions result in self-limited particles exceeding 100 nm, and therefore the size variations of individual nanoparticles (2 to 5 nm) become insignificant (fig. S2, B and C). The resulting spheroids, however, have high size uniformity but not high complexity (see SPP1 and SPP2 phases in figs. S25, S27, and S28) with CI = 2 to 20.

The complex particle architectures emerge only when restrictions on the assembly size are multiple, anisotropic, and competitive (13, 24, 34). They may be associated with different types of interactions and can be anisotropic; that is, the restrictions for assembly of Au-Cys nanoplatelets along their normal or in-plane axes can also vary. What is essential is that energy gains and penalties associated with these restrictions on the assembly of building blocks must be comparable. When none of the competing interactions and restrictions dominate, the nanoparticle assembly acquires complex architectures to negotiate these conflicting requirements. In the case of chiral nanoplatelets, anisotropic restrictions associated with electrostatic repulsion are intertwined with those from supramolecular and elastic ones. Surface energy, Frank chiral energy (34), and Casimir forces (35) contribute to the overall ΔG, but the gains and penalties associated with these interactions may not be sufficiently high to compete with restrictions from other interactions.

The comparable ΔG contribution from multiple interactions and associated restrictions on the assembly patterns force the system to acquire complex geometries. The first-order assessment of energy penalties related to electrostatic, elastic, and supramolecular interactions for two chiral nanoplatelets, based on MD and experimental data, gives a range of 50 to 150 kJ/mol (36, 37). For instance, the energy penalties for twisting nanoribbons (fig. S5 and movie S2) and separating two chiral nanoparticles coated with l-Cys are both ~50 to 60 kJ/mol (36).

To better understand how the competitive restrictions can produce the entire spectrum of HOP phases (Fig. 3 and fig. S25) and the origin of nonmonotonous dependence between chirality and complexity, an additional factor needs to be considered. Although the assembly of nanoparticles can be quasi-reversible, the formation of early nanoparticles (i.e., the building blocks) is irreversible. The shape of these building blocks varies for different HOPs. The early particles found at different points on the phase diagram have diverse shapes with twisted, flat, and spheroidal geometries (Fig. 1N and figs. S30 to S33) depending on both χ and tn. When the initial d/l-Au-S nanoplatelets are flat and thin, as for the kayak particles, where χ = 0% (fig. S31A), the elastic energy becomes small. The structure-defining competing restrictions for these particles are electrostatic and supramolecular, related to edge-to-edge and face-to-face attachment of the nanoplatelets. Instead of random agglomerates, uniformly sized ribbons whose widths and stacking heights are restricted by electrostatic repulsion are formed. The kayak-like particles made from them are fairly complex, but CI can be increased further when elastic restrictions become more pronounced.

As χ reaches 30 to 60%, chiral asymmetry at the molecular scale increases, but particle dissymmetry and elastic restrictions disappear because the initial building blocks are large, amorphous, and spherical (fig. S32). The nearly isotropic electrostatic repulsion dominates over other restrictions, and so do the spheroidal assemblies with low CI represented by the SPP1, SPP2, and discoid supraparticles (DSP) phases. The analogous conclusions can be made from the nanoassemblies made with mixed TGA/Cys surface ligands (fig. S33). When the initial particles are chiral nanoplatelets, electrostatic and elastic restrictions compete with those supramolecular ones (fig. S34). Consequently, complex HOPs with the highest CI emerge.

Finally, one of the key factors driving the formation of self-assembled structures with high complexity from polydispersed building blocks can be particle-particle correlations that favor a specific mutual orientation of nanoparticles, such as stacking of nanoplatelets. The particle-particle correlations can originate from long-range ion correlations (38) and criticality of phase transitions (39). A phase diagram with numerous phase transitions indicates a possibility of irreversible near-critical states that can enhance interparticle correlation and dominance of particle symmetry over polydispersity (39).

The interplay between the different restrictions and the self-assembly pathways toward complex particles can be further visualized in HOPs obtained by doping Au–l-Cys with other coinage metals, such as Cu and Ag (Fig. 3, E and F, and figs. S35 to S38). The possibility for gradual “tuning” of the competitive interactions through doping also offers the opportunity to engineer the HOP complexity. The constituent twisted nanoribbons in Au/Cu and Au/Ag HOPs displayed a pitch of 4 μm and 10 μm, respectively, indicating increased stiffness of the metal-thiolate nanosheets after doping. The elastic restrictions dominate the assembly process, which results in the formation of simple microscale nanosheets to minimize stored mechanical energy. Consequently, a morphological transition from HOPs to long, individual nanoribbons was observed upon increasing the Ag/Au ratio (figs. S38 to S41).

Doping with Cu and Ag also enables the chiroptical properties to be tuned. The emission peaks shifted from red (620 nm) to orange (580 nm) and yellowish-green (550 nm) upon Cu and Ag doping (Cu/Au = 3.3% and Ag/Au = 16.5%; fig. S35), respectively (Fig. 3G and table S5), with concomitant changes in the CD and CPLE spectra (Fig. 3, H and I, and figs. S42 to S44) due to quantum mechanical conjugation of atomic orbitals of the coinage metals with the electronic levels of Au-Cys nanosheets.

Thus, anisotropic electrostatic and elastic interactions place combined restrictions on the assembly pathways of chiral nanoparticles, such that the evolution of multiparticle systems becomes strongly dependent on particle symmetry and asymmetry rather than on particle size (40). The described phase diagrams open the door to further studies of phase transitions in systems with high dispersity and may allow comprehensive explorations of the roles of particle chirality and asymmetry in a variety of assembly pathways. The unique optical, chemical, and colloidal properties of some of the HOPs suggest their broad application in asymmetric catalysis and polarization-based optoelectronics. Assembly mechanisms involving those observed for HOPs may help us to understand the origins of the astounding diversity and sophistication of biological nanocomposites.

Supplementary Materials

Materials and Methods

Figs. S1 to S44

Tables S1 to S5

Movies S1 and S2

References (4149)

References and Notes

Acknowledgments: We thank National Laboratory for Scientific Computing, LNCC/MCTI, Brazil ( for the access to the SDumont supercomputer and the Cloud@UFSCar ( for the HPC resources, and the Michigan Center for Materials Characterization (MC)2 for its assistance with electron microscopy. N.A.K. thanks D. Lioi from Universal Technology Corporation, Wright Patterson Air Force Base, and S. Glotzer of the University of Michigan for insightful discussions. S.R.M. thanks S. Pratavieira and F. Guimarães at IFSC/USP for technical assistance and discussions. Funding: Supported by the Vannevar Bush DoD Fellowship to N.A.K. titled “Engineered Chiral Ceramics” ONR N000141812876, NSF project “Energy- and Cost-Efficient Manufacturing Employing Nanoparticles” (NSF 1463474, ONR N000141812876); NSF 1566460 “Nanospiked Particles for Photocatalysis”; NSF grant 1538180; NSF grant DMR-9871177 for funding the JEOL 2010F analytical electron microscope used in this work; and the Brazilian funding agencies CAPES (finance code 001), CNPq, and FAPESP (process 2009/54035-4, 2012/15147-4, 2013/07276-1, 2013/07296-2, and 2017/12063-8). Support for the Dual Source and Environmental X-ray Scattering Facility at the University of Pennsylvania was provided by the Laboratory for Structure and Matter which is funded in part by NSF MRSEC 1720530. Also supported by Office of Naval Research Multidisciplinary University Research Initiative Award ONR N00014-18-1-2497 (E.M. and C.M.); an MEC/PET fellowship (2014–2020) and a CNPq Fellowship of Research Productivity (2020) (A.F.d.M.); and the China Scholarship Council and Shanghai Jiao Tong University (W.J.). Author contributions: N.A.K. conceived the project. W.J. and N.A.K. designed the experiments. W.J. did the design, synthesis, and characterization of the supraparticles and studied their chemical and chiroptical properties. S.R.M. designed, carried out, and analyzed the experiments combining time and spectrally resolved fluorescence. Z.Q. performed the MD simulations of the Au-Cys nanosheets. Y.W. and P.K. studied the phase diagram of Au-Cys supraparticles. Y.M. helped W.J. with some synthesis and characterizations. J.H.B. did the FDTD simulations of the CD spectra. K.B., W.R.G., F.M.C., A.L.-B., and A.F.d.M. carried out the DFT MD simulations, calculations of CD spectra, and coarse-grained simulations of nanoparticle assemblies. N.A.K. conceived and calculated the GT models for the characterization of the complexity of different structures. E.M. measured and analyzed the SAXS data. W.J. and N.A.K. co-wrote the paper. All authors contributed to data analysis, discussion, and writing. Competing interests: Authors declare no competing interests. Patents: N.A.K. and J.Y., Synthesis of Chiral Nanoparticles Using Circularly Polarized Light, #14/940,845, filed 13 November 2015, granted 29 January 2019. N.A.K., Self-Assembly Methods for Forming Mesoscale Hedgehog-Shaped Particles, application no. 62/563,966, filed 27 September 2017. Data and materials availability: All data are available in the main text or the supplementary materials.

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