A Deep Learning Framework Discovers Compositional Order and Self-Assembly Pathways in Binary Colloidal Mixtures

Abstract

Binary colloidal superlattices (BSLs) have demonstrated enormous potential for the design of advanced multifunctional materials that can be synthesized via colloidal self-assembly. However, mechanistic understanding of the three-dimensional self-assembly of BSLs is largely limited due to a lack of tractable strategies for characterizing the many two-component structures that can appear during the self-assembly process. To address this gap, we present a framework for colloidal crystal structure characterization that uses branched graphlet decomposition with deep learning to systematically and quantitatively describe the self-assembly of BSLs at the single-particle level. Branched graphlet decomposition is used to evaluate local structure via high-dimensional neighborhood graphs that quantify both structural order (e.g., body-centered-cubic vs face-centered-cubic) and compositional order (e.g., substitutional defects) of each individual particle. Deep autoencoders are then used to efficiently translate these neighborhood graphs into low-dimensional manifolds from which relationships among neighborhood graphs can be more easily inferred. We demonstrate the framework on in silico systems of DNA-functionalized particles, in which two well-recognized design parameters, particle size ratio and interparticle potential well depth can be adjusted independently. The framework reveals that binary colloidal mixtures with small interparticle size disparities (i.e., A- and B-type particle radius ratios of r A / r B = 0.8 to r A / r B = 0.95) can promote the self-assembly of defect-free BSLs much more effectively than systems of identically sized particles, as nearly defect-free BCC-CsCl, FCC-CuAu, and IrV crystals are observed in the former case. The framework additionally reveals that size-disparate colloidal mixtures can undergo nonclassical nucleation pathways where BSLs evolve from dense amorphous precursors, instead of directly nucleating from dilute solution. These findings illustrate that the presented characterization framework can assist in enhancing mechanistic understanding of the self-assembly of binary colloidal mixtures, which in turn can pave the way for engineering the growth of defect-free BSLs.

Multistate Dynamic Pathways for Anisotropic Colloidal Assembly and Reconfiguration

“…Based on these findings, there is significant opportunity to further maximize the assembly and reconfiguration times through optimal control methods and additional field mediated actuation and control authority. 28,30,32 Because rectangular particle anisotropy and corners contribute to increased states, defects, and dynamical complexity compared to other 2D shaped particles, 26,27,34 our findings related to achieving multiple target structures are expected to be translatable to self-assembly of other 2D particle-based materials. In addition, our findings related to multistate transitions involving liquid-glass, liquid-liquid crystal, and liquid crystal-crystal transitions have conceptually general features that can be applied to self-assembly in diverse materials and processes.…”

“…As a result, state reconfiguration as part of materials processing or device performance will have dynamic responses determined by the time evolution on landscapes depending on different field conditions. Understanding the available pathways and their dynamics provides a basis to implement open and closed loop control of such reconfiguration processes (based on pathway navigation ,, ), which we plan to explore in future work.…”

“…Colloidal self-assembly is amenable to exploration of mechanistic details including dynamic pathways based on the capability for real-space and real-time particle tracking and tunable interactions (e.g., steric, , depletion, , induced dipoles, − DNA binding, , etc.). Colloidal assembly has clear technological importance given the prevalence of colloidal particles in numerous consumer products, natural biological and environmental systems, , and emerging advanced particle-based materials and devices. − Different shaped colloidal building blocks have the potential to yield many different useful multifunctional microstructures in bulk 3D materials and in 2D surface coatings. , However, colloidal assembly pathways have been demonstrated in a limited number of simulation studies (e.g., see representative examples − ) and even fewer experimental studies where obtaining necessary spatiotemporal resolution and statistics is challenging. Examples of experimental investigations quantifying dynamic pathways include studies of spherical colloids undergoing crystal nucleation, grain boundary formation and motion, small cluster rearrangements, and crystal order–order transitions .…”

Convolutional neural network-based colloidal self-assembly state classification

“…Fourth, current machine learning-based 2-D or 3-D phase characterization approaches mainly utilize particle coordinates or neighborhood topological graph-based analysis for feature extraction, [42][43][44][45]51 which require access to the coordinates of internal particles. The framework presented in this work is designed primarily for 2-D systems and its application to 3-D systems remains to be further examined.…”

Pair-Variational Autoencoders for Linking and Cross-Reconstruction of Characterization Data from Complementary Structural Characterization Techniques

“…An autoencoder is typically trained by minimizing the mismatch (i.e., loss) between the reconstructed data and the input data. Materials scientists have applied autoencoders for multiple purposes such as reconstruction of experimental characterization data, − molecular structure, − or microscopy images; ,,, clustering , and/or classification ,,, of the latent space representations; obtaining material design parameters , or deriving order parameters − from latent space representations; and molecular or material property optimization based on the latent space representations. Some of the studies mentioned here − ,,,, used a modified version of the autoencoder called a variational autoencoder (VAE) that maps the encoded latent space to a multidimensional standard Gaussian distribution, which has the benefit of a continuous latent space compared to the sparse latent space that one would get from the encodings of an unmodified autoencoder.…”