(471f) Deep Learning for Characterizing the Structure of Three-Dimensional, Binary, Self-Assembled Colloidal Lattices

The introduction of multiple components into colloidal mixtures allows for decoupling self- and cross-interactions among species and thus greatly enhances the diversity of accessible self-assembled structures [1-2]. Such systems have been realized in both simulations and experiments and have exhibited a rich variety of three-dimensional binary superlattice structures with applications in photonics, sensing, and catalysis. Despite the abundance of intriguing three-dimensional binary lattice structures, the mechanistic details of how binary crystals transform and critical controlling parameters for these transformations are still poorly understood [3]. Creating a systematic framework to characterize the structural states of colloidal binary self-assembly systems is crucial for unraveling the fundamental understanding of these systems’ stochastic and non-linear behavior.

Although many methods for characterizing self-assembled colloidal structures exist in the literature [4-8], the most common methods either (1) heavily rely on the concept of “cut-off” radiuses to determine local structure and are thus sensitive to thermal fluctuations, (2) fail to provide quantitative information about particles whose local structure does not correspond to well-defined reference structures or templates, and/or (3) rely on diffusion mapping methods that can become intractable for systems with large configurational phase spaces. Most importantly, to our knowledge, only two reported characterization methods explicitly account for particle type in multi-component lattices. These two methods depend on cut-off radiuses, diffusion maps, and characterize either two-dimensional or extremely simple three-dimensional lattices [4, 7].

We present a four-step framework for characterizing the “total” and “compositional” structure of three-dimensional, binary, colloidal lattices, where total structure is defined as the structure to which all particles contribute and compositional structure refers to the lattices’ individual components. In the first step, we extend a previously reported methodology [8-10] that has been shown to be robust to thermal fluctuations to quantify local compositional and total structure in the form of neighborhood graphs. The second step uses tractable deep learning techniques to reduce the dimensionality of the neighborhood graphs to create total and compositional structure low-dimensional spaces. The third step employs agglomerative hierarchical clustering to partition the low-dimensional space and assign physically meaningful classifications to the resulting partitions (e.g., ordered FCC, disordered FCC, compositionally disordered FCC). The final step supplements the discrete classification analyses by using low-dimensional distances to assess relative total and compositional structural order.

We demonstrate the efficacy of the proposed framework on two in-silico three-dimensional systems of self-assembling DNA functionalized colloids that have shown enormous promise for sensing and photonics applications [3]. The colloids are functionalized according to the popular multi-flavored motif, wherein multiple distinct strands of DNA are grafted in different ratios to different colloids. The first system involves colloids of identical sizes where each half of the colloids have different DNA strand grafting ratios. The second system involves particles with different grafting ratios and a 25% size difference. In each case, the proposed framework discovers a myriad of “defective” and “ordered” structures that current methods cannot reveal. In the case of particles with multiple sizes, the framework even helps uncover previously unknown nucleation pathways.

References

(1) Shevchenko, E. V., Talapin, D. V., Kotov, N. A., O'Brien, S., & Murray, C. B. (2006). Structural diversity in binary nanoparticle superlattices. Nature, 439(7072), 55-59.

(2) Macfarlane, R. J., Lee, B., Jones, M. R., Harris, N., Schatz, G. C., & Mirkin, C. A. (2011). Nanoparticle superlattice engineering with DNA. Science, 334(6053), 204-208.

(3) 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.

(4) Boattini, E., Dijkstra, M., & Filion, L. (2019). Unsupervised learning for local structure detection in colloidal systems. The Journal of Chemical Physics, 151(15), 154901.

(5) Reinhart, W. F., & Panagiotopoulos, A. Z. (2017). Multi-atom pattern analysis for binary superlattices. Soft Matter, 13(38), 6803-6809.

(6) 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.

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

(8) Larsen, P. M., Schmidt, S., & Schiøtz, J. (2016). Robust structural identification via polyhedral template matching. Modeling and Simulation in Materials Science and Engineering, 24(5), 055007.

(9) O’Leary, J., Mao, R., Pretti, E. J., Paulson, J. A., Mittal, J., & Mesbah, A. (2021). Deep learning for characterizing the self-assembly of three-dimensional colloidal systems. Soft Matter, 17(4), 989-999.

(10) Milenković, T., & Pržulj, N. (2008). Uncovering biological network function via graphlet degree signatures. Cancer Informatics, 6, CIN-S680.