Chemically Selective Transport in a Cross-Linked HII Phase Lyotropic Liquid Crystal Membrane

Aquatic Functional Liquid Crystals: Design, Functionalization, and Molecular Simulation

Aquatic functional liquid crystals, which are ordered molecular assemblies that work in water environment, are described in this review. Aquatic functional liquid crystals are liquid-crystalline (LC) materials interacting water molecules or aquatic environment. They include aquatic lyotropic liquid crystals and LC based materials that have aquatic interfaces, for example, nanoporous water treatment membranes that are solids preserving LC order. They can remove ions and viruses with nano- and subnano-porous structures. Columnar, smectic, bicontinuous LC structures are used for fabrication of these 1D, 2D, 3D materials. Design and functionalization of aquatic LC sensors based on aqueous/LC interfaces are also described. The ordering transitions of liquid crystals induced by molecular recognition at the aqueous interfaces provide distinct optical responses. Molecular orientation and dynamic behavior of these aquatic functional LC materials are studied by molecular dynamics simulations. The molecular interactions of LC materials and water are key of these investigations. New insights into aquatic functional LC materials contribute to the fields of environment, healthcare, and biotechnology.

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

Amphiphilic monomers in polar solvents can self-assemble into lyotropic liquid crystal (LLC) bicontinuous cubic structures under the right composition and temperature conditions. After cross-linking, the resulting polymer membranes with three-dimensional (3D) continuous uniform channels are excellent candidates for filtration applications. Designing such membranes with the desired physical and chemical properties requires molecular-level understanding of the structure, which can be obtained through molecular modeling. However, building molecular models of bicontinuous cubic structures is challenging due to their narrow regime of stability and the difficulty of self-assembly of large unit cells in molecular simulations. We developed a protocol for building stable bicontinuous cubic unit cells involving both parameterization and assembly of the components. We validate the theoretical structure against experimental results for one such LLC monomer and provide insight into the structure missing in experimental data, as well as demonstrate the qualitative nature of water and solute transport through these membranes.

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

Self-assembled ionic liquid crystals can transport water and ions via the periodic nanochannels, and these materials are promising candidates as water treatment membranes. Molecular insights on the water transport process are, however, less investigated because of computational difficulties of ionic soft matters and the self-assembly. Here we report specific behavior of water molecules in the nanochannels by using the self-consistent modeling combining density functional theory and molecular dynamics and the large-scale molecular dynamics calculation. The simulations clearly provide the one-dimensional (1D) and 3D-interconnected nanochannels of self-assembled columnar and bicontinuous structures, respectively, with the precise mesoscale order observed by x-ray diffraction measurement. Water molecules are then confined inside the nanochannels with the formation of hydrogen bonding network. The quantitative analyses of free energetics and anisotropic diffusivity reveal that, the mesoscale geometry of 1D nanodomain profits the nature of water transport via advantages of dissolution and diffusion mechanisms inside the ionic nanochannels.

Capturing Subdiffusive Solute Dynamics and Predicting Selectivity in Nanoscale Pores with Time Series Modeling

Fitting mathematical models with a direct connection to experimental observables to the outputs of molecular simulations can be a powerful tool for extracting important physical information from them. In this study, we present two new approaches that use stochastic time series modeling to predict long-time-scale behavior and macroscopic properties from molecular simulation, which can be generalized to other molecular systems where complex diffusion occurs. In our previous work, we studied long molecular dynamics (MD) simulation trajectories of a cross-linked H_II phase lyotropic liquid crystal (LLC) membrane, where we observed subdiffusive solute transport behavior characterized by intermittent hops separated by periods of entrapment. In this work, we use our models to parameterize the behavior of the same systems, so we can generate characteristic trajectory realizations that can be used to predict solute mean-squared displacements (MSDs), solute flux, and solute selectivity in macroscopic length pores. First, using anomalous diffusion theory, we show how solute dynamics can be modeled as a fractional diffusion process subordinate to a continuous time random walk. From the MD simulations, we parameterize the distribution of dwell times, hop lengths between dwells, and correlation between hops. We explore two variations of the anomalous diffusion modeling approach. The first variation applies a single set of parameters to the solute displacements and the second applies two sets of parameters based on the solute's radial distance from the closest pore center. Next, we present an approach that generalizes Markov state models, treating the configurational states of the system as a Markov process where each state has distinct transport properties. For each state and transition between states, we parameterize the distribution and temporal correlation structure of positional fluctuations as a means of characterization and to allow us to predict solute MSDs. We show that both stochastic models reasonably reproduce the MSDs calculated from MD simulations. However, qualitative differences between MD and Markov state-dependent model-generated trajectories may in some cases limit their usefulness. With these parameterized stochastic models, we demonstrate how one can estimate the flux of a solute across a macroscopic length pore and, based on these quantities, the membrane's selectivity toward each solute. This work therefore helps to connect microscopic, chemically dependent solute motions that do not follow simple diffusive behavior with long-time-scale behavior, in an approach generalizable to many types of molecular systems with complex dynamics.

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

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.