Shaping the Future of Solid-State Electrolytes through Computational Modeling.

Advances and progress in computational research that aims to understand and improve solid-state electrolytes (SSEs) are outlined. One of the main challenges in the development of all-solid-state batteries is the design of new SSEs with high ion diffusivity that maintain chemical and phase stability and thereby provide a wide electrochemical stability window. Solving this problem requires a deep understanding of the diffusion mechanism and properties of the SSEs. A second important challenge is the development of an understanding of the interface between the SSE and the electrode. The role of molecular simulations and modeling in dealing with these challenges is discussed, with reference to examples in the literature. The methods used and issues considered in recent years are highlighted. Finally, a brief outlook about the future of modeling in studying solid-state battery technology is presented.

Influence of Constraints within a Cyclic Polymer on Solution Properties.

Cyclic polymers with internal constraints provide new insight into polymer properties in solution and bulk and can serve as a model system to explain the stability and mobility of cyclic biomacromolecules. The model system used in this work consisted of cyclic polystyrene structures, all with a nearly identical molecular weight, designed with 0-3 constraints located at strategic sites within the cyclic polymer, with either 4 or 6 branch points. The total number of branch points (or arms) within the cyclic ranged from 0 to 18. Molecular dynamic (MD) simulations showed that as the number of arms increased within the cyclic structure, the radius of gyration and the hydrodynamic radius generally decreased, suggesting the greater number of constraints resulted in a more compact polymer chain. The simulations further showed that the excluded volume was much greater for the cyclics compared to a linear polymer at the same molecular weight. The spirocyclic, a structure consisting of three rings joined in series, showed significant excluded volume effects in agreement with experimental data; the reason for which is unclear at this stage. Interestingly, under a size exclusion chromatography flow, the radius of hydration for all the cyclic structures increased compared with the DLS data, and could be explained from the greater swelling of the rings perpendicular to the flow found from previous simulations on rings. This data suggests that the greater compactness, greater excluded volume and structural rearrangements under flow of constrained cyclic polymers could be used to provide a physical basis for understanding greater stability and activity of cyclic biological macromolecules.

Free Energy Calculations with Reduced Potential Cutoff Radii.

The Jarzynski Equality, the Crooks Fluctuation Theorem, and the Maximum Likelihood Estimator use a nonequilibrium approach for the determination of free energy differences due to a change in the state of a system. Here, this approach is used in combination with a novel transformation algorithm to increase computational efficiency in simulations with interacting particles, without losing accuracy. The algorithm is shown to work well for a Lennard-Jones fluid undergoing a change in density over three very different density ranges, and for the systems considered the algorithm demonstrates computational savings of up to approximately 90%. The results obtained directly from the Jarzynski Equality and from the Maximum Likelihood Estimator are also compared.

A local dissipation theorem.

The transient time correlation function is a standard method for measuring transport properties in simulations. It represents a special case of a more general theorem, the dissipation theorem, that indirectly calculates phase function averages though the use of the dissipation function. These indirect averages often have significantly less statistical error than direct averages. Recently, it has been demonstrated that a local version of the fluctuation theorem can be derived with a well defined deviation from the global result at sufficiently low fields. Here we show that a similar local expression can be obtained for the dissipation theorem, providing a way of determining values of phase functions by monitoring the fluctuations of phase functions in a small region of the system.

The free energy of expansion and contraction: treatment of arbitrary systems using the Jarzynski equality.

Thermodynamic integration, free energy perturbation, and slow change techniques have long been utilised in the calculation of free energy differences between two states of a system that has undergone some transformation. With the introduction of the Jarzynski equality and the Crooks relation, new approaches are possible. This paper investigates an important phenomenon - systems undergoing a change in volume/density - and derives both the Jarzynski equality and Crooks relation of such systems using a statistical mechanical approach. These results apply to systems with arbitrary particle interactions and densities. The application of this approach to the expansion/compression of particles confined within a vessel with a piston and within a periodic system is considered.

Communication: Beyond Boltzmann's H-theorem: demonstration of the relaxation theorem for a non-monotonic approach to equilibrium.

Relaxation of a system to equilibrium is as ubiquitous, essential, and as poorly quantified as any phenomena in physics. For over a century, the most precise description of relaxation has been Boltzmann's H-theorem, predicting that a uniform ideal gas will relax monotonically. Recently, the relaxation theorem has shown that the approach to equilibrium can be quantified in terms of the dissipation function first defined in the proof of the Evans-Searles fluctuation theorem. Here, we provide the first demonstration of the relaxation theorem through simulation of a simple fluid system that generates a non-monotonic relaxation to equilibrium.

Different approaches for evaluating exponentially weighted nonequilibrium relations.

The Kawasaki identity (KI) and the Jarzynski equality (JE) are important nonequilibrium relations. Both of these relations take the form of an ensemble average of an exponential function and can exhibit convergence problems when the average of the exponent differs greatly from the log of the average of the exponential function. In this work, we re-express these relations so that only selected regions need to be evaluated in an attempt to avoid these convergence issues. In the context of measuring free energies, we compare our method to the JE and the literature standard approach, the maximum likelihood estimator (MLE), and show that in a system with asymmetric work distributions it can perform as well as the MLE. For the KI, we derive an analog to the MLE to compare with our relation and show that these two new relations improve on the KI and are complimentary to each other.