Local Molecular Field Theory Research Articles

SURFACE-DIRECTED SPINODAL DECOMPOSITION: LATTICE MODEL VERSUS GINZBURG–LANDAU THEORY

When a binary mixture is quenched into the unstable region of the phase diagram, phase separation starts by spontaneous growth of long-wavelength concentration fluctuations ("spinodal decomposition"). In the presence of surfaces, the latter provide nontrivial boundary conditions for this growth. These boundary conditions can be derived from lattice models by suitable continuum approximations. But the lattice models can also be simulated directly, and thus used to clarify the conditions under which the Ginzburg–Landau type theory is valid. This comparison shows that the latter is accurate only in the immediate vicinity of the bulk critical point, if thermal fluctuations can also be neglected (true for the late stages of phase separation). In contrast, a local kinetic molecular field theory can take full account of nonlinearities and of rapid concentration variations, and thus has a much wider validity. This enables the detailed study of phase separation processes in thin films of solid binary alloys. However, the extension to spinodal decomposition in fluid binary systems (which can be simulated by brute force large scale molecular dynamics methods, of course) remains an unsolved challenge.

Interplay of local hydrogen-bonding and long-ranged dipolar forces in simulations of confined water

Spherical truncations of Coulomb interactions in standard models for water permit efficient molecular simulations and can give remarkably accurate results for the structure of the uniform liquid. However, truncations are known to produce significant errors in nonuniform systems, particularly for electrostatic properties. Local molecular field (LMF) theory corrects such truncations by use of an effective or restructured electrostatic potential that accounts for effects of the remaining long-ranged interactions through a density-weighted mean field average and satisfies a modified Poisson's equation defined with a Gaussian-smoothed charge density. We apply LMF theory to 3 simple molecular systems that exhibit different aspects of the failure of a naïive application of spherical truncations-water confined between hydrophobic walls, water confined between atomically corrugated hydrophilic walls, and water confined between hydrophobic walls with an applied electric field. Spherical truncations of 1/r fail spectacularly for the final system, in particular, and LMF theory corrects the failings for all three. Further, LMF theory provides a more intuitive way to understand the balance between local hydrogen bonding and longer-ranged electrostatics in molecular simulations involving water.

Local molecular field theory for the treatment of electrostatics

We examine in detail the theoretical underpinnings of previous successful applications oflocal molecular field (LMF) theory to charged systems. LMF theory generally accounts forthe averaged effects of long-ranged components of the intermolecular interactions by usingan effective or restructured external field. The derivation starts from the exact Yvon–BornGreen hierarchy and shows that the approximation can be very accurate when theinteractions averaged over are slowly varying at characteristic nearest-neighbor distances.Application of LMF theory to Coulomb interactions alone allows for great simplifications ofthe governing equations. LMF theory then reduces to a single equation for arestructured electrostatic potential that satisfies Poisson’s equation defined with asmoothed charge density. Because of this charge smoothing by a Gaussian of widthσ, this equation may be solved more simply than the detailed simulationgeometry might suggest. Proper choice of the smoothing lengthσ plays a major role in ensuring the accuracy of this approximation. We examine the results of abasic confinement of water between corrugated walls and justify the simple LMF equationused in a previous publication. We further generalize these results to confinements thatinclude fixed charges in order to demonstrate the broader impact of charge smoothing byσ. The slowly varying part of the restructured electrostatic potential will be more symmetricthan the local details of confinements.

A new approach for efficient simulation of Coulomb interactions in ionic fluids

We propose a simplified version of local molecular field (LMF) theory to treat Coulomb interactions in simulations of ionic fluids. LMF theory relies on splitting the Coulomb potential into a short-ranged part that combines with other short-ranged core interactions and is simulated explicitly. The averaged effects of the remaining long-ranged part are taken into account through a self-consistently determined effective external field. The theory contains an adjustable length parameter sigma that specifies the cutoff distance for the short-ranged interaction. This can be chosen to minimize the errors resulting from the mean-field treatment of the complementary long-ranged part. Here we suggest that in many cases an accurate approximation to the effective field can be obtained directly from the equilibrium charge density given by the Debye theory of screening, thus eliminating the need for a self-consistent treatment. In the limit sigma-->0, this assumption reduces to the classical Debye approximation. We examine the numerical performance of this approximation for a simple model of a symmetric ionic mixture. Our results for thermodynamic and structural properties of uniform ionic mixtures agree well with similar results of Ewald simulations of the full ionic system. In addition, we have used the simplified theory in a grand-canonical simulation of a nonuniform ionic mixture where an ion has been fixed at the origin. Simulations using short-ranged truncations of the Coulomb interactions alone do not satisfy the exact condition of complete screening of the fixed ion, but this condition is recovered when the effective field is taken into account. We argue that this simplified approach can also be used in the simulations of more complex nonuniform systems.

Attraction Between Like-Charged Walls: Short-Ranged Simulations Using Local Molecular Field Theory

Effective attraction between like-charged walls mediated by counterions is studied using local molecular field (LMF) theory. Monte Carlo simulations of the "mimic system" given by LMF theory, with short-ranged "Coulomb core" interactions in an effective single particle potential incorporating a mean-field average of the long-ranged Coulomb interactions, provide a direct test of the theory, and are in excellent agreement with more complex simulations of the full Coulomb system by Moreira and Netz [Eur. Phys. J. E 8, 33 (2002)]. A simple, generally applicable criterion to determine the consistency parameter sigma(min) needed for accurate use of the LMF theory is presented.

Local molecular field theory for effective attractions between like charged objects in systems with strong Coulomb interactions

Strong, short-ranged positional correlations involving counterions can induce a net attractive force between negatively charged strands of DNA and lead to the formation of ion pairs in dilute ionic solutions. However, the long range of the Coulomb interactions impedes the development of a simple local picture. We address this general problem by mapping the properties of a nonuniform system with Coulomb interactions onto those of a simpler system with short-ranged intermolecular interactions in an effective external field that accounts for the averaged effects of appropriately chosen long-ranged and slowly varying components of the Coulomb interactions. The remaining short-ranged components combine with the other molecular core interactions and strongly affect pair correlations in dense or strongly coupled systems. We show that pair correlation functions in the effective short-ranged system closely resemble those in the uniform primitive model of ionic solutions and illustrate the formation of ion pairs and clusters at low densities. The theory accurately describes detailed features of the effective attraction between two equally charged walls at strong coupling and intermediate separations of the walls. Analytical results for the minimal coupling strength needed to get any attraction and for the separation at which the attractive force is a maximum are presented.

Connecting Systems with Short and Long Ranged Interactions: Local Molecular Field Theory for Ionic Fluids

Structural and thermodynamic properties of ionic fluids are related to those of a simpler “mimic” system with short ranged intermolecular interactions in a spatially varying effective field by use of local molecular field (LMF) theory, already successfully applied to nonuniform simple fluids. By consistently using the LMF approximation to describe only the slowly varying part of the Coulomb interaction, which we view as arising from a rigid Gaussian charge distribution with an appropriately chosen width σ, exceptionally accurate results can be found. In this paper we study a uniform system of charged hard spheres in a uniform neutralizing background, where these ideas can be presented in their simplest form. At low densities the LMF theory reduces to a generalized version of the Poisson−Boltzmann approximation, but the predicted structure factor satisfies the exact Stillinger−Lovett moment conditions, and with optimal choice of σ the lowest order approximation remains accurate for much stronger couplings....

Multicritical behaviour of disordered Heisenberg antiferromagnets with mixed uniaxial anisotropy

Magnetic phase diagrams of disordered Heisenberg antiferromagnets with mixed uniaxial anisotropy are calculated within a local molecular field theory. The phase diagrams numerically obtained for sets of parameters relevant for the system Fe1-xNixCl2 are in very good agreement with recent experimental results. It is demonstrated that by changing the concentration x, or the ratio of the anisotropies, a rich variety in the physical behaviour of these systems can be expected.