Kirkwood-Buff integrals: From fluctuations in finite volumes to the thermodynamic limit

What is the best simulation approach for measuring local density fluctuations near solvo-/hydrophobes?

Measurements of local density fluctuations are crucial to characterizing the interfacial properties of equilibrium fluids. A specific case that has been well-explored involves the heightened compressibility of water near hydrophobic entities. Commonly, a spatial profile of local fluctuation strength is constructed from the measurements of the mean and variance of solvent particle number fluctuations in a set of contiguous subvolumes of the system adjacent to the solvo-/hydrophobe. An alternative measure proposed by Evans and Stewart [J. Phys.: Condens. Matter 27, 194111 (2015)] defines a local compressibility profile in terms of the chemical potential derivative of the spatial number density profile. Using Grand canonical Monte Carlo simulation, we compare and contrast the efficacy of these two approaches for a Lennard-Jones solvent at spherical and planar solvophobic interfaces and SPC/E water at a hydrophobic spherical solute. Our principal findings are as follows: (i) the local compressibility profile χ(r) of Evans and Stewart is considerably more sensitive to variations in the strength of local density fluctuations than the spatial fluctuation profile F(r) and can resolve much more detailed structure; and (ii) while the local compressibility profile is essentially independent of the choice of spatial discretization used to construct the profile, the spatial fluctuation profile exhibits a strong systematic dependence on the size of the subvolumes on which the profile is defined. We clarify the origin and nature of this finite-size effect.

Effect of the Ion, Solvent, and Thermal Interaction Coefficients on Battery Voltage

In order to increase the adoption of batteries for sustainable transport and energy storage, improved charging and discharging capabilities of lithium-ion batteries are necessary. To achieve this, accurate data that describe the internal state of the cells are essential. Several models have been derived, and transport coefficients have been reported for use in these models. We report for the first time a complete set of transport coefficients to model the concentration and temperature polarization in a lithium-ion battery ternary electrolyte, allowing us to test common assumptions. We include effects due to gradients in chemical potentials and in temperature. We find that the voltage contributions due to salt and solvent polarization are of the same order of magnitude as the ohmic loss and must be taken into account for more accurate modeling and understanding of battery performance. We report new Soret and Seebeck coefficients and find thermal polarization to be significant in cases relevant to battery research. The analysis is suitable for electrochemical systems, in general.

Calculating Thermodynamic Factors for Diffusion Using the Continuous Fractional Component Monte Carlo Method

Thermodynamic factors for diffusion connect the Fick and Maxwell-Stefan diffusion coefficients used to quantify mass transfer. Activity coefficient models or equations of state can be fitted to experimental or simulation data, from which thermodynamic factors can be obtained by differentiation. The accuracy of thermodynamic factors determined using indirect routes is dictated by the specific choice of an activity coefficient model or an equation of state. The Permuted Widom's Test Particle Insertion (PWTPI) method developed by Balaji et al. enables direct determination of thermodynamic factors in binary and multicomponent systems. For highly dense systems, for example, typical liquids, it is well known that molecular test insertion methods fail. In this article, we use the Continuous Fractional Component Monte Carlo (CFCMC) method to directly calculate thermodynamic factors by adopting the PWTPI method. The CFCMC method uses fractional molecules whose interactions with their surrounding molecules are modulated by a coupling parameter. Even in highly dense systems, the CFCMC method efficiently handles molecule insertions and removals, overcoming the limitations of the PWTPI method. We show excellent agreement between the results of the PWTPI and CFCMC methods for the calculation of thermodynamic factors in binary systems of Lennard-Jones molecules and ternary systems of Weeks-Chandler-Andersen molecules. The CFCMC method applied to calculate the thermodynamic factors of realistic molecular systems consisting of binary mixtures of carbon dioxide and hydrogen agrees well with the NIST REFPROP database. Our study highlights the effectiveness of the CFCMC method in determining thermodynamic factors for diffusion, even in densely packed systems, using relatively small numbers of molecules.

Eliminating finite-size effects on the calculation of x-ray scattering from molecular dynamics simulations

Structural studies using x-ray scattering methods for investigating molecules in solution are shifting focus toward describing the role and effects of the surrounding solvent. However, forward models based on molecular dynamics (MD) simulations to simulate structure factors and x-ray scattering from interatomic distributions such as radial distribution functions (RDFs) face limitations imposed by simulations, particularly at low values of the scattering vector q. In this work, we show how the value of the structure factor at q = 0 calculated from RDFs sampled from finite MD simulations is effectively dependent on the size of the simulation cell. To eliminate this error, we derive a new scheme to renormalize the sampled RDFs based on a model of the excluded volume of the particle-pairs they were sampled from, to emulate sampling from an infinite system. We compare this new correction method to two previous RDF-correction methods, developed for Kirkwood-Buff theory applications. We present a quantitative test to assess the reliability of the simulated low-q scattering signal and show that our RDF-correction successfully recovers the correct q = 0 limit for neat water. We investigate the effect of MD-sampling time on the RDF-corrections, before advancing to a molecular example system, comprised of a transition metal complex solvated in a series of water cells with varying densities. We show that our correction recovers the correct q = 0 behavior for all densities. Furthermore, we employ a simple continuum scattering model to dissect the total scattering signal from the solvent-solvent structural correlations in a solute-solvent model system to find two distinct contributions: a non-local density-contribution from the finite, fixed cell size in NVT simulations, and a local contribution from the solvent shell. We show how the second contribution can be approximated without also including the finite-size contribution. Finally, we provide a "best-practices"-checklist for experimentalists planning to incorporate explicit solvation MD simulations in future work, offering guidance for improving the accuracy and reliability of structural studies using x-ray scattering methods in solution.

Reduced-variance orientational distribution functions from torque sampling

We introduce a method to sample the orientational distribution function in computer simulations. The method is based on the exact torque balance equation for classical many-body systems of interacting anisotropic particles in equilibrium. Instead of the traditional counting of events, we reconstruct the orientational distribution function via an orientational integral of the torque acting on the particles. We test the torque sampling method in two- and three-dimensions, using both Langevin dynamics and overdamped Brownian dynamics, and with two interparticle interaction potentials. In all cases the torque sampling method produces profiles of the orientational distribution function with better accuracy than those obtained with the traditional counting method. The accuracy of the torque sampling method is independent of the bin size, and hence it is possible to resolve the orientational distribution function with arbitrarily small angular resolutions.