Structures, thermodynamics and dynamics of topological defects in Gay-Berne nematic liquid crystals.

Topological defects are a ubiquitous phenomenon across different physical systems. A better understanding of defects can be helpful in elucidating the physical behaviors of many real materials systems. In nematic liquid crystals, defects exhibit unique optical signatures and can segregate impurities, showing their promise as molecular carriers and nano-reactors. Continuum theory and simulations have been successfully applied to link static and dynamical behaviors of topological defects to the material constants of the underlying nematic. However, further evidence and molecular details are still lacking. Here we perform molecular dynamics simulations of Gay-Berne particles, a model nematic, to examine the molecular structures and dynamics of +1/2 defects in a thin-film nematic. Specifically, we measure the bend-to-splay ratio K3/K1 using two independent, indirect measurements, showing good agreement. Next, we study the annihilation event of a pair of ±1/2 defects, of which the trajectories are consistent with experiments and hydrodynamic simulations. We further examine the thermodynamics of defect annihilation in an NVE ensemble, leading us to correctly estimate the elastic modulus by using the energy conservation law. Finally, we explore effects of defect annihilation in regions of nonuniform temperature within these coarse-grained molecular models which cannot be analysed by existing continuum level simulations. We find that +1/2 defects tend to move toward hotter areas and their change of speed in a temperature gradient can be quantitatively understood through a term derived from the temperature dependence of the elastic modulus. As such, our work has provided molecular insights into structures and dynamics of topological defects, presented unique and accessible methods to measure elastic constants by inspecting defects, and proposed an alternative control parameter of defects using temperature gradient.

Thermodynamics of Li+-Crown Ether Interactions in Aqueous Solvent.

Lithium ion-based batteries are ubiquitous in modern technology due to applications in personal electronics and high-capacity storage for electric vehicles. Concerns about lithium supply and battery waste have prompted interest in lithium recycling methods. The crown ether 12-crown-4 has been studied for its abilities to form stable complexes with lithium ions (Li+). In this paper, molecular dynamics simulations are applied to examine the binding properties of a 12-crown-4-Li+ system in aqueous solution. It was found that 12-crown-4 did not form stable complexes with Li+ in aqueous solution due to the binding geometry which was prone to interference by surrounding water molecules. In addition, the binding properties of sodium ions (Na+) to 12-crown-4 are examined for comparison. Subsequently, calculations were performed with the crown ethers 15-crown-5 and 18-crown-6 to study their complexation with Li+ as well as Na+. It was determined that binding was unfavorable for both types of ions for all three crown ethers tested, though 15-crown-5 and 18-crown-6 showed a marginally greater affinity for Li+ than 12-crown-4. Metastable minima present in the potential of mean force for Na+ render binding marginally more likely there. We discuss these results in the context of membrane-based applications of crown ethers for Li+ separations.

Free-Energy Landscape and Isomerization Rates of Au4 Clusters at Finite Temperatures.

In metallic nanoparticles, the geometry of atomic positions controls the particle's electronic band structure, polarizability, and catalytic properties. Analyzing the structural properties is a complex problem; the structure of an assembled cluster changes from moment to moment due to thermal fluctuations. Conventional structural analyses based on spectroscopy or diffraction cannot determine the instantaneous structure exactly and can merely provide an averaged structure. Molecular simulations offer an opportunity to examine the assembly and evolution of metallic clusters, as the preferred assemblies and conformations can easily be visualized and explored. Here, we utilize the adaptive biasing force algorithm applied to first-principles molecular dynamics to demonstrate the exploration of a relatively simple system, which permits a comprehensive study of the small metal cluster Au4 in both neutral and charged configurations. Our simulation work offers a quantitative understanding of these clusters' dynamic structure, which is significant for single-site catalytic reactions on metal clusters and provides a starting point for a detailed quantitative understanding of more complex pure metal and alloy clusters' dynamic properties.

A molecular view of plasticization of polyvinyl alcohol.

Although macromolecules such as polymers are in widespread industrial use, pure formulations rarely have precisely the properties new applications demand. Pure polymer is often too brittle and inflexible, necessitating plasticizers to soften or toughen films and bulk polymer materials. In practice, new formulations are developed by extensive trial-and-error methods, as no general molecular explanations exist for the mechanism of plasticization to aid in determining the optimal structure and concentration of plasticizers. Here, through atomistic molecular simulations augmented with advanced sampling techniques, we develop an atomic-level picture of the processes in plasticization by directly calculating free energies that govern the interaction between polymers and small-molecule plasticizers. This work focuses on the influence of two common plasticizer molecules-glycerol and sorbitol-interacting with polyvinyl alcohol (PVA), a frequently used component of polymer films. In particular, we focus on conformational and hydrogen bond structure changes induced in globules of PVA by the plasticizer molecules, with the hypothesis that hydrogen bonding plays a role in the incorporation of these plasticizers into PVA and, thus, in the observed mechanical properties. While we focus on nanoscopic systems, we observe distinct preferences in the conformational free energy that can be connected to the performance of polymer materials at laboratory and industrial scales. This work presents a new molecular perspective from which effective plasticizers can be developed and presents a firm basis from which important analyses of plasticization in complex chemical environments relevant to industry may be developed.

Surveying the free energy landscape of clusters of attractive colloidal spheres.

Controlling the assembly of colloidal particles into specific structures has been a long-term goal of the soft materials community. Much can be learned about the process of self-assembly by examining the early stage assembly into clusters. For the simple case of hard spheres with short-range attractions, the rigid clusters of N particles (where N is small) have been enumerated theoretically and tested experimentally. Less is known, however, about how the free energy landscapes are altered when the inter-particle potential is long-ranged. In this work, we demonstrate how adaptive biasing in molecular simulations may be used to pinpoint shifts in the stability of colloidal clusters as the inter-particle potential is varied. We also discuss the generality of our techniques and strategies for application to related molecular systems.

Novel elastic response in twist-bend nematic models.

Bent-shaped liquid crystals have attracted significant attention recently due to their novel mesostructure and the intriguing behavior of their elastic constants, which are strongly anisotropic and have an unusual temperature dependence. Though theories explain the onset of the twist-bend nematic phase (NTB) through spontaneous symmetry breaking concomitant with transition to a negative bend (K3) elastic constant, this has not been observed as yet in experiments. There, the small bend elastic constant has a strongly non-monotonic temperature dependence, which first increases after crossing the isotropic (I)-nematic (N) transition, then dips near the nematic (N)-twist-bend (NTB) transition before it increases again as the transition is crossed. The molecular mechanisms responsible for this exotic behavior are unclear. Here, we utilize density of states algorithms in Monte Carlo simulation applied to a variant of the Lebwohl-Lasher model which includes bent-shaped-like interactions to analyze the mechanism behind elastic response in this novel mesostructure and understand the temperature dependence of its Frank-Oseen elastic constants.

Dynamics and structure of colloidal aggregates under microchannel flow.

The kinetics of colloidal gels under narrow confinement are of widespread practical relevance, with applications ranging from flow in biological systems to 3D printing. Although the properties of such gels under uniform shear have received considerable attention, the effects of strongly nonuniform shear are far less understood. Motivated by the possibilities offered by recent advances in nano- and microfluidics, we explore the generic phase behavior and dynamics of attractive colloids subject to microchannel flow, using mesoscale particle-based hydrodynamic simulations. Whereas moderate shear strengths result in shear-assisted crystallization, high shear strengths overwhelm the attractions and lead to melting of the clusters. Within the transition region between these two regimes, we discover remarkable dynamics of the colloidal aggregates. Shear-induced surface melting of the aggregates, in conjunction with the Plateau-Rayleigh instability and size-dependent cluster velocities, leads to a cyclic process in which elongated threads of colloidal aggregates break up and reform, resulting in large crystallites. These insights offer new possibilities for the control of colloidal dynamics and aggregation under confinement.

Role of Associative Charging in the Entropy-Energy Balance of Polyelectrolyte Complexes.

Polyelectrolytes may be classified into two primary categories (strong and weak) depending on how their charge state responds to the local environment. Both of these find use in many applications, including drug delivery, gene therapy, layer-by-layer films, and fabrication of ion filtration membranes. The mechanism of polyelectrolyte complexation is, however, still not completely understood, though experimental investigations suggest that entropy gain due to release of counterions is the key driving force for strong polyelectrolyte complexation. Here we perform a comprehensive thermodynamic investigation through coarse-grained molecular simulations permitting us to calculate the free energy of complex formation. Importantly, our expanded-ensemble methods permit the explicit separation of energetic and entropic contributions to the free energy. Our investigations indicate that entropic contributions indeed dominate the free energy of complex formation for strong polyelectrolytes, but are less important than energetic contributions when weak electrostatic coupling or weak polyelectrolytes are present. Our results provide a new view of the free energy of polyelectrolyte complex formation driven by polymer association, which should also arise in systems with large charge spacings or bulky counterions, both of which act to weaken ion-polymer binding.

In Silico Measurement of Elastic Moduli of Nematic Liquid Crystals.

Experiments on confined droplets of the nematic liquid crystal 5CB have questioned long-established bounds imposed on the elastic free energy of nematic systems. This elasticity, which derives from molecular alignment within nematic systems, is quantified through a set of moduli which can be difficult to measure experimentally and, in some cases, can only be probed indirectly. This is particularly true of the surfacelike saddle-splay elastic term, for which the available experimental data indicate values on the cusp of stability, often with large uncertainties. Here, we demonstrate that all nematic elastic moduli, including the saddle-splay elastic constant k_{24}, may be calculated directly from atomistic molecular simulations. Importantly, results obtained through in silico measurements of the 5CB elastic properties demonstrate unambiguously that saddle-splay elasticity alone is unable to describe the observed confined morphologies.

Learning free energy landscapes using artificial neural networks.

Existing adaptive bias techniques, which seek to estimate free energies and physical properties from molecular simulations, are limited by their reliance on fixed kernels or basis sets which hinder their ability to efficiently conform to varied free energy landscapes. Further, user-specified parameters are in general non-intuitive yet significantly affect the convergence rate and accuracy of the free energy estimate. Here we propose a novel method, wherein artificial neural networks (ANNs) are used to develop an adaptive biasing potential which learns free energy landscapes. We demonstrate that this method is capable of rapidly adapting to complex free energy landscapes and is not prone to boundary or oscillation problems. The method is made robust to hyperparameters and overfitting through Bayesian regularization which penalizes network weights and auto-regulates the number of effective parameters in the network. ANN sampling represents a promising innovative approach which can resolve complex free energy landscapes in less time than conventional approaches while requiring minimal user input.

Weak polyelectrolyte complexation driven by associative charging.

Weak polyelectrolytes are relevant for a wide range of fields; in particular, they have been investigated as "smart" materials for chemical separations and drug delivery. The charges on weak polyelectrolytes are dynamic, causing polymer chains to adopt different equilibrium conformations even with relatively small changes to the surrounding environment. Currently, there exists no comprehensive picture of this behavior, particularly where polymer-polymer interactions have the potential to affect charging properties significantly. In this study, we elucidate the novel interplay between weak polyelectrolyte charging and complexation behavior through coupled molecular dynamics and Monte Carlo simulations. Specifically, we investigate a model of two equal-length and oppositely charging polymer chains in an implicit salt solution represented through Debye-Hückel interactions. The charging tendency of each chain, along with the salt concentration, is varied to determine the existence and extent of cooperativity in charging and complexation. Strong cooperation in the charging of these chains is observed at large Debye lengths, corresponding to low salt concentrations, while at lower Debye lengths (higher salt concentrations), the chains behave in apparent isolation. When the electrostatic coupling is long-ranged, we find that a highly charged chain strongly promotes the charging of its partner chain, even if the environment is unfavorable for an isolated version of that partner chain. Evidence of this phenomenon is supported by a drop in the potential energy of the system, which does not occur at the lower Debye lengths where both potential energies and charge fractions converge for all partner chain charging tendencies. The discovery of this cooperation will be helpful in developing "smart" drug delivery mechanisms by allowing for better predictions for the dissociation point of delivery complexes.

Adaptive enhanced sampling by force-biasing using neural networks.

A machine learning assisted method is presented for molecular simulation of systems with rugged free energy landscapes. The method is general and can be combined with other advanced sampling techniques. In the particular implementation proposed here, it is illustrated in the context of an adaptive biasing force approach where, rather than relying on discrete force estimates, one can resort to a self-regularizing artificial neural network to generate continuous, estimated generalized forces. By doing so, the proposed approach addresses several shortcomings common to adaptive biasing force and other algorithms. Specifically, the neural network enables (1) smooth estimates of generalized forces in sparsely sampled regions, (2) force estimates in previously unexplored regions, and (3) continuous force estimates with which to bias the simulation, as opposed to biases generated at specific points of a discrete grid. The usefulness of the method is illustrated with three different examples, chosen to highlight the wide range of applicability of the underlying concepts. In all three cases, the new method is found to enhance considerably the underlying traditional adaptive biasing force approach. The method is also found to provide improvements over previous implementations of neural network assisted algorithms.

SSAGES: Software Suite for Advanced General Ensemble Simulations.

Molecular simulation has emerged as an essential tool for modern-day research, but obtaining proper results and making reliable conclusions from simulations requires adequate sampling of the system under consideration. To this end, a variety of methods exist in the literature that can enhance sampling considerably, and increasingly sophisticated, effective algorithms continue to be developed at a rapid pace. Implementation of these techniques, however, can be challenging for experts and non-experts alike. There is a clear need for software that provides rapid, reliable, and easy access to a wide range of advanced sampling methods and that facilitates implementation of new techniques as they emerge. Here we present SSAGES, a publicly available Software Suite for Advanced General Ensemble Simulations designed to interface with multiple widely used molecular dynamics simulations packages. SSAGES allows facile application of a variety of enhanced sampling techniques-including adaptive biasing force, string methods, and forward flux sampling-that extract meaningful free energy and transition path data from all-atom and coarse-grained simulations. A noteworthy feature of SSAGES is a user-friendly framework that facilitates further development and implementation of new methods and collective variables. In this work, the use of SSAGES is illustrated in the context of simple representative applications involving distinct methods and different collective variables that are available in the current release of the suite. The code may be found at: https://github.com/MICCoM/SSAGES-public.

Elastic response and phase behavior in binary liquid crystal mixtures.

Utilizing density-of-states simulations, we perform a full mapping of the phase behavior and elastic responses of binary liquid crystalline mixtures represented by the multicomponent Lebwohl-Lasher model. Our techniques are able to characterize the complete phase diagram, including nematic-nematic phase separation predicted by mean-field theories, but previously not observed in simulations. Mapping this phase diagram permits detailed study of elastic properties across the miscible nematic region. Importantly, we observe for the first time local phase separation and disordering driven by the application of small linear perturbations near the transition temperature and more significantly through nonlinear stresses. These findings are of key importance in systems of blended nematics which contain particulate inclusions, or are otherwise confined.

Sculpting bespoke mountains: Determining free energies with basis expansions.

The intriguing behavior of a wide variety of physical systems, ranging from amorphous solids or glasses to proteins, is a direct manifestation of underlying free energy landscapes riddled with local minima separated by large barriers. Exploring such landscapes has arguably become one of statistical physics's great challenges. A new method is proposed here for uniform sampling of rugged free energy surfaces. The method, which relies on special Green's functions to approximate the Dirac delta function, improves significantly on existing simulation techniques by providing a boundary-agnostic approach that is capable of mapping complex features in multidimensional free energy surfaces. The usefulness of the proposed approach is established in the context of a simple model glass former and model proteins, demonstrating improved convergence and accuracy over existing methods.

DNA shape dominates sequence affinity in nucleosome formation.

Nucleosomes provide the basic unit of compaction in eukaryotic genomes, and the mechanisms that dictate their position at specific locations along a DNA sequence are of central importance to genetics. In this Letter, we employ molecular models of DNA and proteins to elucidate various aspects of nucleosome positioning. In particular, we show how DNA's histone affinity is encoded in its sequence-dependent shape, including subtle deviations from the ideal straight B-DNA form and local variations of minor groove width. By relying on high-precision simulations of the free energy of nucleosome complexes, we also demonstrate that, depending on DNA's intrinsic curvature, histone binding can be dominated by bending interactions or electrostatic interactions. More generally, the results presented here explain how sequence, manifested as the shape of the DNA molecule, dominates molecular recognition in the problem of nucleosome positioning.

Basis function sampling: a new paradigm for material property computation.

Wang-Landau sampling, and the associated class of flat histogram simulation methods have been remarkably helpful for calculations of the free energy in a wide variety of physical systems. Practically, convergence of these calculations to a target free energy surface is hampered by reliance on parameters which are unknown a priori. Here, we derive and implement a method built upon orthogonal functions which is fast, parameter-free, and (importantly) geometrically robust. The method is shown to be highly effective in achieving convergence. An important feature of this method is its ability to attain arbitrary levels of description for the free energy. It is thus ideally suited to in silico measurement of elastic moduli and other material properties related to free energy perturbations. We demonstrate the utility of such applications by applying our method to calculate the Frank elastic constants of the Lebwohl-Lasher model of liquid crystals.

Measuring liquid crystal elastic constants with free energy perturbations.

A first principles method is proposed to calculate the Frank elastic constants of nematic liquid crystals. These include the constants corresponding to standard splay, twist and bend deformations, and an often-ignored surface-like contribution known as saddle-splay. The proposed approach is implemented on the widely studied Gay-Berne (3, 5, 2, 1) model [J. G. Gay and B. J. Berne, J. Chem. Phys., 1981, 74, 3316], and the effects of temperature and system size on the elastic constants are examined in the nematic phase. The results of simulations for splay, twist, and bend elastic constants are consistent with those from previous literature reports. The method is subsequently applied to the saddle-splay elastic constant k24 which is found to exist at the limits of the Ericksen inequalities governing positive definite free energy. Finally, extensions of the method are discussed that present a new paradigm for in silico measurements of elastic constants.

Coarse-grained modeling of DNA curvature.

The interaction of DNA with proteins occurs over a wide range of length scales, and depends critically on its local structure. In particular, recent experimental work suggests that the intrinsic curvature of DNA plays a significant role on its protein-binding properties. In this work, we present a coarse grained model of DNA that is capable of describing base-pairing, hybridization, major and minor groove widths, and local curvature. The model represents an extension of the recently proposed 3SPN.2 description of DNA [D. M. Hinckley, G. S. Freeman, J. K. Whitmer, and J. J. de Pablo, J. Chem. Phys. 139, 144903 (2013)], into which sequence-dependent shape and mechanical properties are incorporated. The proposed model is validated against experimental data including melting temperatures, local flexibilities, dsDNA persistence lengths, and minor groove width profiles.

Calculating Binding Free Energies in Model Host-Guest Systems with Unrestrained Advanced Sampling.

Host-guest interactions are important to the design of pharmaceuticals and, more broadly, to soft materials as they can enable targeted, strong, and specific interactions between molecules. The binding process between the host and guest may be classified as a "rare event" when viewing the system at atomic scales, such as those explored in molecular dynamics simulations. To obtain equilibrium binding conformations and dissociation constants from these simulations, it is essential to resolve these rare events. Advanced sampling methods such as the adaptive biasing force (ABF) promote the occurrence of less probable configurations in a system, therefore facilitating the sampling of essential collective variables that characterize the host-guest interactions. Here, we present the application of ABF to a rod-cavitand coarse-grained model of host-guest systems to acquire the potential of mean force. We show that the employment of ABF enables the computation of the configurational and thermodynamic properties of bound and unbound states, including the free energy landscape. Moreover, we identify important dynamic bottlenecks that limit sampling and discuss how these may be addressed in more general systems.