Leonid Yelash

Closed-loop critical curves in simple hard-sphere van der Waals-fluid models consistent with the packing fraction limit

Two new hard-sphere equations are proposed which, in combination with a van der Waals attraction term, lead to a biquadratic, respectively a cubic, equation of state. The new equations show the correct limiting behavior at low as well as at high densities; their poles are close to the physical packing fraction of hard spheres. Both equations of state were extended towards mixtures by one-fluid mixing rules, and their global phase behavior was investigated for the special case of equal-sized molecules. Both equations are able to predict closed-loop liquid–liquid immiscibility; the topology of the phenomenenon is the same as for the Carnahan–Starling equation. It appears the occurrence of closed-loop liquid–liquid immiscibility does not depend on the location of the pole nor on the degree of the equation of state used.

Slow process in confined polymer melts: layer exchange dynamics at a polymer solid interface.

Employing Molecular Dynamics simulations of a chemically realistic model of 1,4-polybutadiene between graphite walls we show that the mass exchange between layers close to the walls is a slow process already in the melt state. For the glass transition of confined polymers this process competes with the slowing down due to packing effects and intramolecular rotation barriers.

Coarse-grained models for fluids and their mixtures: Comparison of Monte Carlo studies of their phase behavior with perturbation theory and experiment.

The prediction of the equation of state and the phase behavior of simple fluids (noble gases, carbon dioxide, benzene, methane, and short alkane chains) and their mixtures by Monte Carlo computer simulation and analytic approximations based on thermodynamic perturbation theory is discussed. Molecules are described by coarse grained models, where either the whole molecule (carbon dioxide, benzene, and methane) or a group of a few successive CH(2) groups (in the case of alkanes) are lumped into an effective point particle. Interactions among these point particles are fitted by Lennard-Jones (LJ) potentials such that the vapor-liquid critical point of the fluid is reproduced in agreement with experiment; in the case of quadrupolar molecules a quadrupole-quadrupole interaction is included. These models are shown to provide a satisfactory description of the liquid-vapor phase diagram of these pure fluids. Investigations of mixtures, using the Lorentz-Berthelot (LB) combining rule, also produce satisfactory results if compared with experiment, while in some previous attempts (in which polar solvents were modeled without explicitly taking into account quadrupolar interaction), strong violations of the LB rules were required. For this reason, the present investigation is a step towards predictive modeling of polar mixtures at low computational cost. In many cases Monte Carlo simulations of such models (employing the grand-canonical ensemble together with reweighting techniques, successive umbrella sampling, and finite size scaling) yield accurate results in very good agreement with experimental data. Simulation results are quantitatively compared to an analytical approximation for the equation of state of the same model, which is computationally much more efficient, and some systematic discrepancies are discussed. These very simple coarse-grained models of small molecules developed here should be useful, e.g., for simulations of polymer solutions with such molecules as solvent.

Investigation of a generalized attraction term of an equation of state and its influence on the phase behaviour

Abstract In this paper a generalized attraction term is investigated with respect to the resulting phase behaviour in pure substances and binary mixtures. For the calculation of phase equilibria the attraction term is combined with the van der Waals (vdW)-repulsion and the Carnahan–Starling (CS)-repulsion. The chosen parametrization of the attraction term allows a general discussion of the mathematical structure of an attraction term including a wide range of attractive virial coefficients. In the investigation of the pure substance properties it is focused on the values of the critical compressibility factor, the critical packing fraction and the close packing fraction. These properties together determine the shape of the liquid–gas coexistence curve. The performance of the attraction term for modeling binary mixtures has been traced by the liquid–liquid closed-loop immiscibility area in the global phase diagram. This phenomenon is very sensitive to changes in the equation of state and a suitable property for characterizing an equation of state with respect to its binary phase behaviour.

Interactions between polymer brush-coated spherical nanoparticles: The good solvent case

The interaction between two spherical polymer brushes is studied by molecular dynamics simulation varying both the radius of the spherical particles and their distance, as well as the grafting density and the chain length of the end-grafted flexible polymer chains. A coarse-grained bead-spring model is used to describe the macromolecules, and purely repulsive monomer-monomer interactions are taken throughout, restricting the study to the good solvent limit. Both the potential of mean force between the particles as a function of their distance is computed, for various choices of the parameters mentioned above, and the structural characteristics are discussed (density profiles, average end-to-end distance of the grafted chains, etc.). When the nanoparticles approach very closely, some chains need to be squeezed out into the tangent plane in between the particles, causing a very steep rise of the repulsive interaction energy between the particles. We consider as a complementary method the density functional theory approach. We find that the quantitative accuracy of the density functional theory is limited to large nanoparticle separation and short chain length. A brief comparison to Flory theory and related work on other models also is presented.

Efficient prediction of thermodynamic properties of quadrupolar fluids from simulation of a coarse-grained model: the case of carbon dioxide.

Monte Carlo simulations are presented for a coarse-grained model of real quadrupolar fluids. Molecules are represented by particles interacting with Lennard-Jones forces plus the thermally averaged quadrupole-quadrupole interaction. The properties discussed include the vapor-liquid coexistence curve, the vapor pressure along coexistence, and the surface tension. The full isotherms are also accessible over a wide range of temperatures and densities. It is shown that the critical parameters (critical temperature, density, and pressure) depend almost linearly on a quadrupolar parameter q=Q(*4)T*, where Q* is the reduced quadrupole moment of the molecule and T* the reduced temperature. The model can be applied to a variety of small quadrupolar molecules. We focus on carbon dioxide as a test case, but consider nitrogen and benzene, too. Experimental critical temperature, density, and quadrupolar moment are sufficient to fix the parameters of the model. The resulting agreement with experiments is excellent and marks a significant improvement over approaches which neglect quadrupolar effects. The same coarse-grained model was also applied in the framework of perturbation theory in the mean spherical approximation. As expected, the latter deviates from the Monte Carlo results in the critical region, but is reasonably accurate at lower temperatures.

Prediction of the critical locus in binary mixtures using equation of state: II. Investigation of van der Waals-type and Carnahan–Starling-type equations of state

Abstract The ability to predict critical lines of members of the methane–, perfluoromethane– and water–alkanes homologous series is compared for van der Waals (vdW)-type and Carnahan–Starling (CS)-type equations of state. A temperature dependent combining rule for the binary attraction parameter is discussed and employed. It is found that the appropriate choice of the adjustable parameters yields quite accurate results for both equations. A new application of global phase diagrams is proposed for the quantitative description of real mixtures. In this diagram, the boundaries of the different types of phase behavior are presented in the k12–l12 plane. Analysis of this diagram has allowed us to reach conclusions that cannot be obtained by a simple fit of data points. In particular, it is demonstrated that the global phase diagrams shape defines the correlative ability of the equations. It is found that CS-type equations tend to predict a larger region of liquid–liquid immiscibility, the accuracy of the result depends on the particular experimental system. Changes in the density dependence of the attraction term of the two-parameter equations influence mostly the predicted critical volumes and not their qualitative performance. In addition, the development of a CS-type equation suitable for engineering calculations is discussed.

Three-step decay of time correlations at polymer-solid interfaces

Two-step decay of relaxation functions, i.e., time scale separation between microscopic dynamics and structural relaxation, is the defining signature of the structural glass transition. We show that for glass-forming polymer melts at an attractive surface slow desorption kinetics introduces an additional time scale separation among the relaxational degrees of freedom leading to a three-step decay. The inherent length scale of this process is the radius of gyration in contrast to the segmental scale governing the glass transition. We show how the three-step decay can be observed in incoherent scattering experiments and discuss its relevance for the glass transition of confined polymers by analogy to surface critical phenomena.

A generic equation of state for the hard-sphere fluid incorporating the high density limit

Based on an analysis of the virial coefficients of some hard-sphere fluid models a generic equation for the hard-sphere fluid is developed. This equation reproduces the correct high density limit. The generic equation provides the basis of a hierarchy of hard-sphere terms for different levels of simplification. As a result of this investigation a new hard-sphere term is developed by a simple linear regression of the virial coefficients in suitable coordinates. This term accurately represents the virial coefficients from B2 to B10 and gives the nearly correct pole packing fraction.

Adaptive discontinuous evolution Galerkin method for dry atmospheric flow

We present a new adaptive genuinely multidimensional method within the framework of the discontinuous Galerkin method. The discontinuous evolution Galerkin (DEG) method couples a discontinuous Galerkin formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of multidimensional hyperbolic systems, such that all of the infinitely many directions of wave propagation are considered explicitly. In order to take into account multiscale phenomena that typically appear in atmospheric flows, nonlinear fluxes are split into a linear part governing the acoustic and gravitational waves and a nonlinear part that models advection. Time integration is realized by the IMEX type approximation using the semi-implicit second-order backward differentiation formula (BDF2). Moreover in order to approximate efficiently small scale phenomena, adaptive mesh refinement using the space filling curves via the AMATOS function library is employed. Four standard meteorological test cases are used to validate the new discontinuous evolution Galerkin method for dry atmospheric convection. Comparisons with the Rusanov flux, a standard one-dimensional approximate Riemann solver used for the flux integration, demonstrate better stability and accuracy, as well as the reliability of the new multidimensional DEG method.