Potential of mean force between a spherical particle suspended in a nematic liquid crystal and a substrate

Abstract

We consider a system where a spherical particle is suspended in a nematic liquid crystal confined between two walls. We calculate the liquid-crystal-mediated potential of mean force between the sphere and a substrate by means of Monte Carlo simulations. Three methods are used: a traditional Monte Carlo approach, umbrella sampling, and a novel technique that combines canonical expanded ensemble simulations with a recently proposed density-of-states formalism. The latter method offers advantages in that it facilitates good sampling of phase space without prior knowledge of the energy landscape of the system. The resulting potential of mean force, computed as a function of the normal distance between the sphere and a surface, suggests that the sphere is attracted to the surface, even in the absence of attractive molecular interactions.

Water adsorption in hydrophobic MOF channels

“…Such a quantity cannot be obtained by straightforward GCMC simulations, and requires the use of more sophisticated techniques. We have used here expanded ensemble density of states (EXEDOS) 31,32 calculations to compute the grand potential of the system, which is the thermodynamic potential of the grand canonical ensemble O(m,N), as a function of chemical potential of the adsorbate, m, and number of adsorbed molecules, N. This method, developed by Wang and Landau, calculates the density of states of the system on the fly, using biased Monte Carlo simulations. 33,34 It has been successfully used for a wide range of system, including Lennard-Jones fluids 35 and simulations of adsorption in zeolites.…”

Wang-Landau sampling of an asymmetric ising model: a study of the critical endpoint behavior

“…Wang-Landau sampling has proven very useful and efficient in many different applications, including studies of complex systems with rough energy landscapes. For example, this method has been used in studies of a Potts antiferromagnet [12], random spin systems [13], quantum systems [14][15][16], fluids [17,18], binary Lennard-Jones glass [19], liquid crystals [20], polymers [17,21], proteins [22,23], other molecular systems [24,25], atomic clusters [26], optimization problems [27], and combinatorial number theory [28]. Generalizations and further studies of this sampling technique have also been carried out by several authors [29][30][31][32][33].…”

Molecular simulation of the reversible mechanical unfolding of proteins

“…This so-called EXEDOS method has been employed for studies of suspensions of colloidal particles in liquid crystals. 30 Here we use it to examine the reversible mechanical stretching of proteins. The reaction coordinate, , is chosen to be the end-to-end distance ͑see Fig.…”

“…This scheme has been successfully applied to a variety of systems, including Ising models, 13 Lennard-Jones fluids, 26 proteins, 27,28 and glass-forming liquids. 29 In recent work 30 we have explored the use of DOS methods in the context of expanded ensembles, where intermediate states are introduced to facilitate the transition between configurations separated by large energy barriers. The expanded states are usually defined by some reaction coordinate, , and the sampling in space is governed by unknown weights.…”