Direct calculation of the functional inverse of realistic interatomic potentials in field-theoretic simulations.

We discuss the functional inverse problem in field-theoretic simulations for realistic pairwise potentials such as the Morse potential (widely used in particle simulations as an alternative to the 12-6 Lennard-Jones one), and we propose the following two solutions: (a) a numerical one based on direct inversion on a regular grid or deconvolution and (b) an analytical one by expressing attractive and repulsive contributions to the Morse potential as higher-order derivatives of the Dirac delta function; the resulting system of ordinary differential equations in the saddle-point approximation is solved numerically with appropriate model-consistent boundary conditions using a Newton-Raphson method. For the first time, exponential-like, physically realistic pair interactions are analytically treated and incorporated into a field-theoretic framework. The advantages and disadvantages of the two approaches are discussed in detail in connection with numerical findings from test simulations for the radial distribution function of a monatomic fluid at realistic densities providing direct evidence for the capability of the analytical method to resolve structural features down to the Angstrom scale.

Field-theoretic simulations beyond δ-interactions: Overcoming the inverse potential problem in auxiliary field models.

Modern field-theoretic simulations of complex fluids and polymers are constructed around a particle-to-field transformation that brings an inverse potential u-1 in the model equations. This has restricted the application of the framework to systems characterized by relatively simple pairwise interatomic interactions; for example, excluded volume effects are treated through the use of δ-function interactions. In this study, we first review available nonbonded pair interactions in field-theoretic models and propose a classification. Then, we outline the inverse potential problem and present an alternative approach on the basis of a saddle-point approximation, enabling the use of a richer set of pair interaction functions. We test our approach by using as an example the Morse potential, which finds extensive applications in particle-based simulations, and we calibrate u-1 with results from a molecular dynamics simulation. The u-1 thus obtained is consistent with the field-theoretic model equations, and when used in stand-alone self-consistent field simulations, it produces the correct fluid structure starting from a random initial state of the density field.

Microphase separation and the formation of ion conductivity channels in poly(ionic liquid)s: A coarse-grained molecular dynamics study.

We study generic properties of poly(ionic liquid)s (PILs) via coarse-grained molecular dynamics simulations in bulk solution and under confinement. The influence of different side chain lengths on the spatial properties of the PIL systems and on the ionic transport mechanism is investigated in detail. Our results reveal the formation of apolar and polar nanodomains with increasing side chain length in good agreement with previous results for molecular ionic liquids. The ion transport numbers are unaffected by the occurrence of these domains, and the corresponding values highlight the potential role of PILs as single-ion conductors in electrochemical devices. In contrast to bulk behavior, a pronounced formation of ion conductivity channels in confined systems is initiated in close vicinity to the boundaries. We observe higher ion conductivities in these channels for increasing PIL side chain lengths in comparison with bulk values and provide an explanation for this effect. The appearance of these domains points to an improved application of PILs in modern polymer electrolyte batteries.

Excluded-Volume Interactions in Field-Theoretic Simulations: Multiconvolutions and Model Equivalence.

To deal with divergences of functional integrals in field-theoretic simulations (FTS) of complex fluids, the microscopic density is often smeared by being replaced by a convoluted one, typically using a Gaussian masking function. The smearing changes radically the nature of nonbonded interactions of the original microscopic density and results in a regularized model that is free of ultraviolet (UV) divergences. In this work, we first resolve a few fundamental issues related with the use of masking functions for δ-interactions in FTS and then we detail a new methodology that builds on the concept of multiconvoluted inverse potentials and a principle of model equivalence for statistical weights to accommodate more physically relevant interactions in FTS. The capabilities of the new approach are highlighted by examining the Gaussian-regularized Edwards model (GREM) and the Yukawa potential. A successful test calculation of the excess chemical potential of a polymer chain in a good solvent with the GREM illustrates the power of the new theoretical framework.