Qiliang Yan

Hyper-parallel tempering Monte Carlo: Application to the Lennard-Jones fluid and the restricted primitive model

A new generalized hyper-parallel tempering Monte Carlo simulation method is presented. The method is particularly useful for simulation of many-molecule complex systems, where rough energy landscapes and inherently long characteristic relaxation times can pose formidable obstacles to effective sampling of relevant regions of configuration space. In this paper, we demonstrate the effectiveness of the new method by implementing it in a grand canonical ensemble for the Lennard-Jones fluid and the restricted primitive model. Coexistence curves and critical behavior have been explored by the new method. Our numerical results indicate that the new algorithm can be orders of magnitude more efficient than previously available techniques.

Density-of-states Monte Carlo method for simulation of fluids

A Monte Carlo method based on a density-of-states sampling is proposed for study of arbitrary statistical mechanical ensembles in a continuum. A random walk in the two-dimensional space of particle number and energy is used to estimate the density of states of the system; this density of states is continuously updated as the random walk visits individual states. The validity and usefulness of the method are demonstrated by applying it to the simulation of a Lennard-Jones fluid. Results for its thermodynamic properties, including the vapor–liquid phase coexistence curve, are shown to be in good agreement with high-accuracy literature data.

Monte Carlo simulations of diblock copolymer thin films confined between two homogeneous surfaces

Thin films of symmetric diblock copolymers confined between two hard, flat and homogeneous surfaces have been investigated by means of Monte Carlo simulations on a simple cubic lattice. For such simulations, the match between bulk lamellar period L0 and the simulation box size is crucial to obtain meaningful results. The simulations have been performed in an expanded grand-canonical ensemble, where the chemical potential and the temperature of the confined films are specified and the density is allowed to fluctuate. The dependence of morphology, density, and chain conformation in the confined films on the type of surfaces, surface separation, and the strength of surface-block interactions has been studied systematically. Our results are consistent with experimental findings.

Hyperparallel tempering Monte Carlo simulation of polymeric systems

A new hyperparallel tempering Monte Carlo method is proposed for simulation of complex fluids, including polymeric systems. The method is based on a combination of the expanded grand canonical ensemble (or simple tempering) and the multidimensional parallel tempering techniques. Its usefulness is established by applying it to polymer solutions and blends with large molecular weights. Our numerical results for long molecules indicate that the new algorithm can be significantly more efficient than previously available techniques.

Multicanonical parallel tempering

We present a novel implementation of the parallel tempering Monte Carlo method in a multicanonical ensemble. Multicanonical weights are derived by a self-consistent iterative process using a Boltzmann inversion of global energy histograms. This procedure gives rise to a much broader overlap of thermodynamic-property histograms; fewer replicas are necessary in parallel tempering simulations, and the acceptance of trial swap moves can be made arbitrarily high. We demonstrate the usefulness of the method in the context of a grand-multicanonical ensemble, where we use multicanonical simulations in energy space with the addition of an unmodified chemical potential term in particle-number space. Several possible implementations are discussed, and the best choice is presented in the context of the liquid–gas phase transition of the Lennard-Jones fluid. A substantial decrease in the necessary number of replicas can be achieved through the proposed method, thereby providing a higher efficiency and the possibility ...

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

The expanded ensemble density of states method (ExEDOS) is used to investigate the effective interaction of a spherical colloidal particle suspended in a confined liquid crystal (LC) with a substrate. The potential of mean force (PMF) is determined as a function of the normal distance between the particle and the substrates surface. The presence of the substrate induces a layered structure of the LC, which in turn greatly influences the PMF. We analyze the structure of the Saturn ring defect that accompanies the colloidal sphere, and find that the ring is displaced slightly towards the surface when the sphere is within the first LC surface layer. A transition occurs from an overall attraction of the colloid to the substrate to a global repulsion when the spheres radius is roughly twice the length of the LC molecules.

Molecular simulation of the reversible mechanical unfolding of proteins.

In this work we have combined a Wang-Landau sampling scheme [F. Wang and D. Landau, Phys. Rev. Lett. 86, 2050 (2001)] with an expanded ensemble formalism to yield a simple and powerful method for computing potentials of mean force. The new method is implemented to investigate the mechanical deformation of proteins. Comparisons are made with analytical results for simple model systems such as harmonic springs and Rouse chains. The method is then illustrated on a model 15-residue alanine molecule in an implicit solvent. Results for mechanical unfolding of this oligopeptide are compared to those of steered molecular dynamics calculations.

Molecular dynamics simulation of discontinuous volume phase transitions in highly-charged crosslinked polyelectrolyte networks with explicit counterions in good solvent

The volumetric properties of highly-charged defect-free polyelectrolyte networks with tetrafunctional crosslinks are studied through molecular dynamics simulations in the canonical ensemble. The network backbone monomers, which are monovalent, and the counterions, which are mono-, di-, or trivalent, are modeled explicitly in the simulations, but the solvent is treated implicitly as a dielectric medium of good solvation quality. The osmotic pressure of the network-solvent system is found to depend greatly on the strength of electrostatic interactions. Discontinuous volume phase transitions are observed when the electrostatic interactions are strong, and the onset of these transitions shifts to higher solvent dielectricity as the counterion valency increases. The roles of the various virial contributions to the osmotic pressure are examined. The network elasticity entropy is found to behave nearly classically. As the network contracts and collapses with increasing strength of electrostatic interactions, the loss of counterion entropy leads to increased counterion osmotic pressure contributions via two mechanisms. The reduction in available configurational space increases the counterion translational entropy contribution to the ideal part of the osmotic pressure, and the greater number of counterion-monomer contacts formed due to counterion condensation and confinement increases the counterion excluded-volume entropy contribution to the excess part of the osmotic pressure. These observations contrast the decrease in the single ideal-gas-like counterion translational entropy contribution to the osmotic pressure predicted by the counterion condensation-charge renormalization theory. An accompanying decrease in the total electrostatic energy balances the loss of counterion excluded-volume entropy as the polyelectrolyte networks collapse in low-dielectric solvents. This interplay between the electrostatic energy and the counterion excluded-volume entropy appears to be responsible for the discontinuous volume phase transitions that are observed in polyelectrolyte networks. The structure of the polyelectrolyte network is also found to be affine in the swollen state, with constituent chains nearly fully extended, and nonaffine in the collapsed state, with the chains adopting a Gaussian conformation.

Phase equilibria and clustering in size-asymmetric primitive model electrolytes

The low-temperature phase coexistence of size-asymmetric primitive model electrolyte solutions has been investigated by means of Monte Carlo simulations. A multidimensional parallel tempering method is employed and results are analyzed by means of histogram reweighting. Coexistence curves and critical constants are determined as a function of size asymmetry, λ=σ+/σ−, from 0.05 to 1. It is found that the critical temperature and the critical density decrease as λ decreases. These trends appear to contradict available integral-equation theoretical predictions. For highly asymmetric systems, we report the formation of large chain-like and ring-like structures. These clusters are much larger than those observed in symmetric electrolytes, and they are shown to give rise to considerable finite-size effects.

Critical behavior of lattice polymers studied by Monte Carlo simulations

A newly developed expanded grand-canonical formalism is applied to locate the critical point of systems of long polymeric molecules. Two polymer systems are investigated in this work; the first consists of chains in a simple cubic lattice, the second consists of bond-fluctuating molecules. For the former we simulate molecules of up to 16 000 sites, and for the latter we study molecules of up to 500 sites. These chain lengths are well above those investigated by all prior simulation studies of critical phenomena in polymer solutions. Critical parameters are determined as a function of chain length by means of field-mixing finite-size scaling techniques. Our results for the scaling behavior of the critical temperature are consistent with literature values. Our results for the scaling of the critical density, however, indicate that the corresponding critical exponent is higher than that reported by previous authors. The leading logarithmic term of the finite-chain-length correction to the critical density is...