(356h) Deep Learning for Characterizing and Modeling the Dynamics of Complex Colloidal Self-Assembly Systems

Self-assembly (SA) is the process by which discrete components (e.g., nanoparticles in solution) spontaneously organize into an ordered structure [1]. The spontaneous self-organization central to SA enables “bottom-up” materials synthesis, which allows for manufacturing advanced, highly ordered crystalline structures in an inherently parallelizable and cost-effective manner. Thus, SA can create new avenues for highly scalable, economical manufacturing of novel metamaterials with unique optical, electrical, or mechanical properties [2-4].

SA is an inherently stochastic (i.e., random) process prone to kinetic arrest [2]. This leads to variability in materials manufacturing and possibly high defect rates, which can severely compromise the viability of using SA to reproducibly manufacture advanced materials. However, creating a systematic methodology to characterize and understand the highly nonlinear and stochastic SA dynamics responsible for kinetic arrest remains an open grand challenge. Previous attempts to characterize kinetically arrested states have either relied on physics-based order parameters that cannot accurately resolve structures in the face of thermal fluctuations or unsupervised learning techniques based on diffusion maps that provide incomplete physical interpretations of the underlying kinetics [5-7]. Moreover, all attempts to model SA dynamics either involve physics-based strategies based on the chemical master equation or parameter estimation strategies based on Bayesian Inference, neither of which are computationally tractable for practically sized SA systems [7-8]. Due to their strong adaptability and generalization properties in learning, strong noise tolerance, and ability to solve exceptionally large problems, deep neural networks (DNNs) are ideal candidates for investigating the complex, stochastic, nonlinear dynamics of SA systems [9].

In this work, we develop a type of DNN called a variational autoencoder [10] to translate the positions of individual SA particles into an easily interpretable low-dimensional space. The autoencoder provides an explicit mapping between the particle positions and the low-dimensional space. We extrapolate the knowledge from this mapping to understand the relevant symmetries that distinguish the different environments possibly present in the system and determine a rigorous physical interpretation of the low-dimensional space. We calculate low-dimensional free energy landscapes from SA trajectory data and use the relative free energies to identify the kinetically arrested states into which the system may assemble. We leverage a second DNN to model the evolution of the SA over time and predict the likelihood that SA systems avoid kinetic traps or reach target states under certain external conditions (e.g., temperature). The main contribution of this work is the development of a systematic framework to not only fully characterize kinetic traps, but also analyze exactly how these kinetic traps can be avoided in order to reproducibly reach high-value structures.

We demonstrate the efficacy of the proposed framework on an in-silico three-dimensional system of self-assembling DNA functionalized colloids that have shown enormous promise for sensing and photonics applications [11,12]. The system is especially prone to kinetic arrest due to the complexity of its underlying (and often competing) free energy surface, which includes repulsive interactions among the underlying silica particles, repulsive interactions due to ssDNA chain overlap, and attractive interactions due to ssDNA hybridization. We characterize and analyze the relative importance of these kinetic traps and demonstrate how changes in temperature (which turn ssDNA bonds “on” or “off”) can be used to avoid kinetic traps and reach target structures.

References

[1] Whitesides, G. M., & Grzybowski, B. (2002). Self-assembly at all scales. Science, 295(5564), 2418-2421.

[2] Paulson, J. A., Mesbah, A., Zhu, X., Molaro, M. C., & Braatz, R. D. (2015). Control of self-assembly in micro-and nano-scale systems. Journal of Process Control, 27, 38-49.

[3] Grzelczak, M., Vermant, J., Furst, E. M., & Liz-Marzán, L. M. (2010). Directed self-assembly of nanoparticles. ACS nano, 4(7), 3591-3605.

[4] Liddle, J. A., & Gallatin, G. M. (2016). Nanomanufacturing: a perspective. ACS nano, 10(3), 2995-3014.

[5] Long, A. W., & Ferguson, A. L. (2019). Landmark diffusion maps (L-dMaps): Accelerated manifold learning out-of-sample extension. Applied and Computational Harmonic Analysis, 47(1), 190-211.

[6] Reinhart, W. F., & Panagiotopoulos, A. Z. (2018). Automated crystal characterization with a fast neighborhood graph analysis method. Soft matter, 14(29), 6083-6089.

[7] Tang, X., Rupp, B., Yang, Y., Edwards, T. D., Grover, M. A., & Bevan, M. A. (2016). Optimal feedback-controlled assembly of perfect crystals. ACS nano, 10(7), 6791-6798.

[8] Lakerveld, R., Stephanopoulos, G., & Barton, P. I. (2012). A master-equation approach to simulate kinetic traps during directed self-assembly. The Journal of chemical physics, 136(18), 184109.

[9] Jain, A. K., Mao, J., & Mohiuddin, K. M. (1996). Artificial neural networks: A tutorial. Computer, 29(3), 31-44.

[10] Ohno, H. (2019). Auto-encoder-based generative models for data augmentation on regression problems. Soft Computing, 1-11.

[11] Pretti, E., Zerze, H., Song, M., Ding, Y., Mahynski, N. A., Hatch, H. W., ... & Mittal, J. (2018). Assembly of three-dimensional binary superlattices from multi-flavored particles. Soft matter, 14(30), 6303-6312.

[12] Pretti, E., Mao, R., & Mittal, J. (2019). Modelling and simulation of DNA-mediated self-assembly for superlattice design. Molecular Simulation, 45(14-15), 1203-1210.