James M. Polson

Finite-size corrections to the free energies of crystalline solids

We analyze the finite-size corrections to the free energy of crystals with a fixed center of mass. When we explicitly correct for the leading (ln N/N) corrections, the remaining free energy is found to depend linearly on 1/N. Extrapolating to the thermodynamic limit (N → ∞), we estimate the free energy of a defect-free crystal of particles interacting through an r–12 potential. We also estimate the free energy of perfect hard-sphere crystal near coexistence: at ρσ3 = 1.0409, the excess free energy of a defect-free hard-sphere crystal is 5.918 89(4)kT per particle. This, however, is not the free energy of an equilibrium hard-sphere crystal. The presence of a finite concentration of vacancies results in a reduction of the free energy that is some two orders of magnitude larger than the present error estimate.

Integration schemes for dissipative particle dynamics simulations : from softly interacting systems towards hybrid models

We examine the performance of various commonly used integration schemes in dissipative particle dynamics simulations. We consider this issue using three different model systems, which characterize a variety of different conditions often studied in simulations. Specifically, we clarify the performance of integration schemes in hybrid models, which combine microscopic and mesoscale descriptions of different particles using both soft and hard interactions. We find that in all three model systems many commonly used integrators may give rise to surprisingly pronounced artifacts in physical observables such as the radial distribution function, the compressibility, and the tracer diffusion coefficient. The artifacts are found to be strongest in systems, where interparticle interactions are soft and predominated by random and dissipative forces, while in systems governed by conservative interactions the artifacts are weaker. Our results suggest that the quality of any integration scheme employed is crucial in all cases where the role of random and dissipative forces is important, including hybrid models where the solvent is described in terms of soft potentials. Regarding the integration schemes, the best overall performance is found for integrators in which the velocity dependence of dissipative forces is taken into account, and particularly good performance is found for an approach in which velocities and dissipative forces are determined self-consistently. Remaining temperature deviations from the desired limit can be corrected by carrying out the self-consistent integration in conjunction with an auxiliary thermostat, in a manner that is similar in spirit to the well-known Nose–Hoover thermostat. Further, we show that conservative interactions can play a significant role in describing the transport properties of simple fluids, in contrast to approximations often made in deriving analytical theories. In general, our results illustrate the main problems associated with simulation methods in which dissipative forces are velocity dependent, and point to the need to develop new techniques to resolve these issues.

Towards better integrators for dissipative particle dynamics simulations

Coarse-grained models that preserve hydrodynamics provide a natural approach to study collective properties of soft-matter systems. Here, we demonstrate that commonly used integration schemes in dissipative particle dynamics give rise to pronounced artifacts in physical quantities such as the compressibility and the diffusion coefficient. We assess the quality of these integration schemes, including variants based on a recently suggested self-consistent approach, and examine their relative performance. Implications of integrator-induced effects are discussed.

Simulation of short-chain polymer collapse with an explicit solvent

We study the equilibrium behavior and dynamics of a polymer collapse transition for a system composed of a short Lennard-Jones (LJ) chain immersed in a LJ solvent for solvent densities in the range of ρ=0.6–0.9 (in LJ reduced units). The monomer hydrophobicity is quantified by a parameter λ∈[0,1] which gives a measure of the strength of attraction between the monomers and solvent particles, and which is given by λ=0 for a purely repulsive interaction and λ=1 for a standard LJ interaction. A transition from the Flory coil to a molten globule is induced by increasing λ. Generally, the polymer size decreases with increasing solvent density for all λ. Polymer collapse is induced by changing the hydrophobicity parameter from λ=0 to λ⩾0.5, where the polymer is in a molten globule state. The collapse rate increases monotonically with increasing hydrophobicity and decreases monotonically with increasing solvent density. Doubling the length of the chain from N=20 to N=40 monomers increases the collapse time roughl...

Numerical prediction of the melting curve of n-octane

We compute the melting curve of n-octane using Molecular Dynamics simulations with a realistic all-atom molecular model. Thermodynamic integration methods are used to calculate the free energy of the system in both the crystalline solid and isotropic liquid phases. The Gibbs–Duhem integration procedure is used to calculate the melting curve, starting with an initial point obtained from the free energy calculations. The calculations yield quantitatively accurate results: in the pressure range of 0–100 MPa, the calculated melting curve deviates by only 3 K from the experimental curve. This deviation falls just within the range of uncertainty of the calculations.

CALCULATION OF SOLID-FLUID PHASE EQUILIBRIA FOR SYSTEMS OF CHAIN MOLECULES

We study the first order solid-fluid phase transition of a system of semi-flexible Lennard-Jones chains using molecular dynamics simulations. Thermodynamic integration methods are used to calculate the free energy of the solid and fluid phases. The solid phase free energy per chain can be calculated to an accuracy of ±0.03kBT with relative ease. The Gibbs-Duhem integration technique is used to trace out the complete melting curve, starting with a single point on the curve obtained from the free energy calculations. For the short chains studied here, we find that increasing the chain length stabilizes the solid phase; i.e., it raises the melting temperature at fixed pressure, and lowers the density at the transition at fixed temperature. Gibbs-Duhem integration was used also to investigate the effects of chain stiffness on the transition. We find that increasing the stiffness also acts to stabilize the solid phase. At fixed temperature, the transition is shifted to lower pressure and lower density with increasing chain stiffness. Further, we find that the density gap between solid and fluid broadens with increasing chain stiffness.

Conformational equilibrium and orientational ordering: 1H‐nuclear magnetic resonance of butane in a nematic liquid crystal

In this study we use multiple‐quantum 1H‐NMR spectroscopy to study butane, the simplest flexible alkane, dissolved in a nematic solvent. An analysis of the highly accurate 1H dipolar coupling constants gives important information about conformational and orientational behavior, including the trans–gauche energy difference, Etg, and the conformer probabilities and order parameters. An essential component of the analysis involves the use of mean‐field models to describe the orientational ordering of solutes in a nematic solvent. Several models were found to adequately describe the molecular ordering, including the chord model of Photinos et al. [D. J. Photinos, E. T. Samulski, and H. Toriumi, J. Phys. Chem. 94, 4688 (1990)] and recent versions of a model proposed by Burnell and co‐workers [D. S. Zimmerman and E. E. Burnell, Mol. Phys. 78, 687 (1993)]. It was found that Etg lies in the range 2.1–3.0 kJ/mol, which is significantly below most experimental estimates of the gas–phase value. An attempt to describ...

Simulation study of the coil-globule transition of a polymer in solvent

Molecular dynamics simulations are used to study the coil-globule transition for a system composed of a bead-spring polymer immersed in an explicitly modeled solvent. Two different versions of the model are used, which are differentiated by the nature of monomer-solvent, solvent-solvent, and nonbonded monomer-monomer interactions. For each case, a model parameter lambda determines the degree of hydrophobicity of the monomers by controlling the degree of energy mismatch between the monomers and solvent particles. We consider a lambda-driven coil-globule transition at constant temperature. The simulations are used to calculate average static structure factors, which are then used to determine the scaling exponents of the system in order to determine the theta-point values lambdatheta separating the coil from the globule states. For each model we construct coil-globule phase diagrams in terms of lambda and the particle density rho. The results are analyzed in terms of a simple Flory-type theory of the collapse transition. The ratio of lambdatheta for the two models converges in the high density limit exactly to the value predicted by the theory in the random mixing approximation. Generally, the predicted values of lambdatheta are in reasonable agreement with the measured values at high rho, though the accuracy improves if the average chain size is calculated using the full probability distribution associated with the polymer-solvent free energy, rather than merely using the value obtained from the minimum of the free energy.

Polymer translocation dynamics in the quasi-static limit

Monte Carlo (MC) simulations are used to study the dynamics of polymer translocation through a nanopore in the limit where the translocation rate is sufficiently slow that the polymer maintains a state of conformational quasi-equilibrium. The system is modeled as a flexible hard-sphere chain that translocates through a cylindrical hole in a hard flat wall. In some calculations, the nanopore is connected at one end to a spherical cavity. Translocation times are measured directly using MC dynamics simulations. For sufficiently narrow pores, translocation is sufficiently slow that the mean translocation time scales with polymer length N according to ∝ (N - N(p))(2), where N(p) is the average number of monomers in the nanopore; this scaling is an indication of a quasi-static regime in which polymer-nanopore friction dominates. We use a multiple-histogram method to calculate the variation of the free energy with Q, a coordinate used to quantify the degree of translocation. The free energy functions are used with the Fokker-Planck formalism to calculate translocation time distributions in the quasi-static regime. These calculations also require a friction coefficient, characterized by a quantity N(eff), the effective number of monomers whose dynamics are affected by the confinement of the nanopore. This was determined by fixing the mean of the theoretical distribution to that of the distribution obtained from MC dynamics simulations. The theoretical distributions are in excellent quantitative agreement with the distributions obtained directly by the MC dynamics simulations for physically meaningful values of N(eff). The free energy functions for narrow-pore systems exhibit oscillations with an amplitude that is sensitive to the nanopore length. Generally, larger oscillation amplitudes correspond to longer translocation times.

Modeling lipid-sterol bilayers: applications to structural evolution, lateral diffusion, and rafts.

Publisher Summary This chapter describes the off-lattice models for lipid–cholesterol and lipid–lanosterol bilayers. The difference in behavior between the two sterols was modeled on the basis of their specific molecular characteristics and in terms of their differential interactions with lipid molecules. The Metropolis Monte Carlo method and the algorithm used in the MMC simulations of the model are analyzed. The simulated equilibrium phase diagrams for the lipid–cholesterol and the lipid–lanosterol membranes are shown. It is found that the small modification in the lipid–sterol interaction strength leads to considerable differences in the overall topologies of the two-phase diagrams. To characterize quantitatively, the differential effects of the two sterols on the physical properties of lipid–sterol bilayer membranes, the calculated conformational order parameter is presented. The lipid tracer diffusion coefficient in a model lipid–cholesterol binary mixture was calculated as a function of cholesterol concentration and temperature.