Statistical Inference of Transport Mechanisms and Long Time Scale Behavior from Time Series of Solute Trajectories in Nanostructured Membranes

Abstract

Appropriate time series modeling of complex diffusion in soft matter systems on the microsecond time scale can provide a path toward inferring transport mechanisms and predicting bulk properties characteristic of much longer time scales. In this work we apply nonparametric Bayesian time series analysis, more specifically the sticky hierarchical Dirichlet process autoregressive hidden Markov model (HDP-AR-HMM) to solute center-of-mass trajectories generated from long molecular dynamics (MD) simulations in a cross-linked inverted hexagonal phase lyotropic liquid crystal (LLC) membrane in order to automatically detect a variety of solute dynamical modes. We can better understand the mechanisms controlling these dynamical modes by grouping the states identified by the HDP-AR-HMM into clusters based on multiple metrics aimed at distinguishing solute behavior based on their fluctuations, dwell times in each state, and positions within the inhomogeneous membrane structure. We analyze predominant clusters in order to relate their dynamical parameters to physical interactions between solutes and the membrane. Along with parameters of individual states, the HDP-AR-HMM simultaneously infers a transition matrix which allows us to stochastically propagate solute behavior from all of the independent trajectories onto arbitrary length time scales while still preserving the qualitative behavior characteristic of the MD trajectories. This affords a direct connection to important macroscopic observables used to characterize performance like solute flux and selectivity. This work provides a promising way to simultaneously identify transport mechanisms in nanoporous materials and project complex diffusive behavior on long time scales. Our enhanced understanding of the diverse range of solute behavior allows us to hypothesize design changes to LLC monomers aimed toward controlling the rates of solute passage, thus improving the selective performance of LLC membranes.

Molecular insights on confined water in the nanochannels of self-assembled ionic liquid crystal

“…Nada et al (35) computed the diffusivity and stability of water and ions inside the subnanochannel divided from thermotropic ILC. Shirts and co-workers (36)(37)(38) recently reported the molecular transport mechanism of water and organic solutes inside the 1D nanochannel of the columnar nanostructures of lyotropic ILC. The formation of smectic structure of ILCs was also computationally demonstrated in the order of hundred nanoseconds (39)(40)(41).…”

Obtaining and Characterizing Stable Bicontinuous Cubic Morphologies and Their Nanochannels in Lyotropic Liquid Crystal Membranes

“…Molecular modeling has been used by several groups, including ours, to better understand the nature of nanostructured channels and to enable improved design. , For example, we have used molecular simulation to understand the chemical details of hexagonal-phase LLC pores, as well as the molecular details of transport in these pores. − Unfortunately, the nanoscale hexagonal pores are difficult to align properly with the hydrophilic channels in the direction of transport during experimental formulation, and therefore the experimental focus has most recently been on the channels in Q structures. Thus, this paper extends our molecular modeling efforts on hexagonal-phase LLC membranes to Q phase LLC membranes.…”

Obtaining and characterizing stable bicontinuous cubic morphologies and their nanochannels in lyotropic liquid crystal membranes

“…11,28 For example, we have used molecular simulation to understand the chemical details of hexagonal phase LLC pores, 29 as well as the molecular details of transport in these pores. [30][31][32] However, hexagonal pores are difficult to align properly with the hydrophilic channels in the direction of transport during experimental formulation, and therefore the experimental focus has most recently been on the channels in Q structures. Thus, this paper extends our molecular modeling efforts on hexagonal phase LLC membranes to Q phase LLC membranes.…”