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→ϱ), we estimate the free energy of a defect-free crystal of particles interacting through an r Ϫ12 potential. We also estimate the free energy of perfect hard-sphere crystal near coexistence: at 3 ϭ1.0409, 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. © 2000 American Institute of Physics. ͓S0021-9606͑00͒50912-X͔The earliest numerical technique to compute the free energy of crystalline solids was introduced some 30 years ago by Hoover and Ree. 1,2 At present, the ''single-occupancycell'' method of Ree and Hoover is less widely used than the so-called ''Einstein-crystal'' method proposed by Frenkel and Ladd. 3 The latter method employs thermodynamic integration of the Helmholtz free energy along a reversible artificial pathway between the system of interest and an Einstein crystal. The Einstein crystal serves as a reference system, as its free energy can be computed analytically. Since its introduction, the Einstein-crystal method has been used extensively in studies of phase equilibria involving crystalline solids. For numerical reasons-to suppress a weak divergence of the integrand-the Einstein-crystal method calculations have to be carried out at fixed center of mass. The free energy of the reference crystal is also calculated under the center-of-mass constraint, and the final calculated free energy of the unconstrained crystal is determined by correcting for the effect of imposing the constraint in the calculations. In the original paper, the fixed center-of-mass constraint was only applied to the particle coordinates, but not to the corresponding momenta. This is irrelevant as long as one computes the free-energy difference between two structures that have either both constrained or both unconstrained centers of mass. However, when computing the absolute free energy of a crystal, one needs to transform from the constrained to the unconstrained system. In the original paper, this transformation was not performed consistently. This resulted in a small but noticeable effect on the computed absolute free energy of the crystal. Below, we describe the proper approach to calculate the free energy of arbitrary molecular crystalline solids. The derivation differs from the earlier work in two respects: first, we explicitly show the effect of momentum constraints. And second, we generalize the expression to an arbitrary crystal containing atoms or molecules with different masses.The main point of interest involves the calculation of the partition function of a crystal...

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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.

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 roughly by a factor of 2, more or less independent of the hydrophobicity and solvent density. We also study the effect of conformational restrictions on polymer collapse using a chain model in which the bond angles are held near 109.5° using a stiff angular harmonic potential, but where free internal rotation is allowed, and find that the collapse times increase considerably with respect to the fully flexible polymer, roughly by a factor of 1.6–3.5. This increase is most pronounced for high solvent densities.

Articles you may be interested inMild hydration of didecyldimethylammonium chloride modified DNA by 1H-nuclear magnetic resonance and by sorption isotherm J. Appl. Phys. 113, 044702 (2013); 10.1063/1.4789011 Ultrasound-order director fluctuations interaction in nematic liquid crystals: A nuclear magnetic resonance relaxometry study J. Chem. Phys. 118, 9037 (2003); 10.1063/1.1566735Order fluctuations of the director in nematic thermotropic liquid crystals studied by nuclear magnetic resonance dipolar relaxationIn this study we use multiple-quantum 1 H-NMR spectroscopy to study butane, the simplest flexible alkane, dissolved in a nematic solvent. An analysis of the highly accurate 1 H dipolar coupling constants gives important information about conformational and orientational behavior, including the trans-gauche energy difference, E tg , 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 ͑1990͔͒ and recent versions of a model proposed by Burnell and co-workers ͓D. S. Zimmerman and E. E. Burnell, Mol. Phys. 78, 687 ͑1993͔͒. It was found that E tg 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 describe more realistically the conformational states by including torsional fluctuations about the rotational isomeric states did not significantly improve the quality of the fits or alter the results. Finally, the anisotropic component of the solute-solvent interaction was found to perturb only marginally the conformational probabilities from the isotropic values.