Nonlinear Machine Learning of Patchy Colloid Self-Assembly Pathways and Mechanisms

Abstract

Bottom-up self-assembly offers a means to synthesize materials with desirable structural and functional properties that cannot easily be fabricated by other techniques. An improved understanding of the structural pathways and mechanisms by which self-assembling materials spontaneously form from their constituent building blocks is of value in understanding the fundamental principles of assembly and in guiding inverse building block design. We present an approach to infer systematically assembly pathways and mechanisms by nonlinear data mining of molecular simulation trajectories using diffusion maps. We have validated our methodology in applications to Brownian dynamics simulations of the assembly of anisotropic "patchy colloids" into polyhedral aggregates. For particles designed to form tetrahedral aggregates, we identify two divergent assembly pathways leading to chains of interlocking dimers and tetramers and chains of interlocking trigonal planar trimers. For particles designed to assemble icosahedral aggregates, our approach recovers two distinct assembly pathways corresponding to monomeric addition and budding from a disordered liquid phase. These assembly routes were previously reported by inspection of simulation trajectories by Wilber et al. ( J. Chem. Phys. 2007, 127, 085106 ; J. Chem. Phys. 2009, 131, 175102 ), validating the capacity of our approach to systematically recover assembly mechanisms previously discernible only by trajectory visualization.

Nonlinear machine learning and design of reconfigurable digital colloids

“…These cooperative couplings are expected to yield a separation of time scales, wherein local caged oscillations within a stable bit state give rise to highfrequency motions, and transitions between bit states are rare events with slow characteristic time scales. We anticipate that these cooperative transition pathways correspond to a small number of slow collective modes of the halo particle dynamics 15,19,37 . Extracting these slow modes from the simulation trajectory reveals the multi-body transition pathways governing the digital colloid dynamics, and also presents kinetically meaningful collective coordinates in which to construct low-dimensional free energy surface mapping out the accessible morphologies, stable states, and dynamical transition pathways 15,16,18,19,[38][39][40][41] .…”

“…Nonlinear dimensionality reduction provides a means to determine the low-dimensional hypersurface -the socalled "intrinsic manifold" -within the high-dimensional phase space to which the multi-body digital colloid dynamics are effectively restrained 15,19 . Geometrically, the intrinsic manifold is the low-dimensional phase space volume parameterized by a small number of collective variables that contains the stable colloidal bit states and the dynamic transition pathways between them 15,19,38,39 .…”

“…Excluded volume and any other interactions between the halo particles means that their motions and locations are correlated, and these cooperative couplings are expected to define an emergent low-dimensional subspace to which the digital colloid dynamics are effectively restrained 15 . This latent low-dimensional manifold supports the free energy surface containing the thermallyaccessible system configurations, stable and metastable states, and transition pathways between them.…”

“…Dimensionality reduction techniques have demonstrated good success in recovering these low-dimensional manifolds for both single molecule [16][17][18] and many-body selfassembling 15,19,20 systems. Recently, we (A.W.L.…”

“…and A.L.F.) developed an extension of the diffusion map nonlinear dimensionality reduction technique [21][22][23] for manybody colloidal systems to infer low-dimensional assembly landscapes from both simulation 15 and experimental particle tracking data 19 . Building upon these foundations, in this work we combine Brownian dynamics simulations, nonlinear machine learning, and first passage time analysis to quantify the stable and transition state morphologies and determine the transition mechanisms, free energy barriers, and transition rates for bit state switching for N=4 and N=6 digital colloids.…”