Simulation and prediction of vapour-liquid equilibria for chain molecules

Interfacial properties of binary mixtures of Lennard-Jones chains in planar interfaces by molecular dynamics simulation

Binary mixtures of fully flexible linear tangent chains composed of bonded Lennard-Jones interaction sites (monomers) were studied using the molecular dynamics simulation in the NVT ensemble. Their interfacial properties were investigated in planar interfaces by direct simulation of an explicit liquid film in equilibrium with its vapor. A method for the calculation of long-range interactions in inhomogeneous fluids was implemented to take into account the potential truncation effects. Surface tension and the pressure tensor were calculated via the classical Irving-Kirkwood method; vapor pressure, orthobaric densities, density profiles, and Gibbs relative adsorption of the volatile component with respect to the heavy component were also obtained. The properties were studied as a function of the temperature, molar concentration of the heavy component, and the asymmetry of the mixture. According to the results of this work, the temperature loses influence on the surface tension, vapor pressure, and Gibbs relative adsorption curves as the molecular length of the heavy component increases. This suggests that the universal behavior observed in pure fluids of Lennard-Jones chains also holds for binary mixtures. The contribution of the long-range interactions turned out to account for about 60%, 20%, and 10% of the surface tension, vapor pressure, and orthobaric density final values, respectively. This contribution was even larger at high temperatures and for large molecules. Strong enrichment of the volatile component at the interface was observed in the asymmetric mixtures. One of these mixtures even showed a barotropic effect at elevated pressures and a class III phase behavior.

An entropy scaling demarcation of gas- and liquid-like fluid behaviors

In this work, we propose a generic and simple definition of a line separating gas-like and liquid-like fluid behaviors from the standpoint of shear viscosity. This definition is valid even for fluids such as the hard sphere and the inverse power law that exhibit a unique fluid phase. We argue that this line is defined by the location of the minimum of the macroscopically scaled viscosity when plotted as a function of the excess entropy, which differs from the popular Widom lines. For hard sphere, Lennard-Jones, and inverse-power-law fluids, such a line is located at an excess entropy approximately equal to -2/3 times Boltzmann's constant and corresponds to points in the thermodynamic phase diagram for which the kinetic contribution to viscosity is approximately half of the total viscosity. For flexible Lennard-Jones chains, the excess entropy at the minimum is a linear function of the chain length. This definition opens a straightforward route to classify the dynamical behavior of fluids from a single thermodynamic quantity obtainable from high-accuracy thermodynamic models.

Phase Equilibria of Polydisperse Square-Well Chain Fluid Confined in Random Porous Media: TPT of Wertheim and Scaled Particle Theory

Extension of Wertheim's thermodynamic perturbation theory and its combination with scaled particle theory is proposed and applied to study the liquid-gas phase behavior of polydisperse hard-sphere square-well chain fluid confined in the random porous media. Thermodynamic properties of the reference system, represented by the hard-sphere square-well fluid in the matrix, are calculated using corresponding extension of the second-order Barker-Henderson perturbation theory. We study effects of polydispersity and confinement on the phase behavior of the system. While polydispersity causes increase of the region of phase coexistence due to the critical temperature increase, confinement decreases the values of both critical temperature and critical density making the region of phase coexistence smaller. This effect is enhanced with the increase of the size ratio of the fluid and matrix particles. The increase of the average chain length at fixed values of polydispersity and matrix density shifts the critical point to a higher temperature and a slightly lower density.

Why Do Disordered and Structured Proteins Behave Differently in Phase Separation?

Intracellular membraneless organelles and their myriad cellular functions have garnered tremendous recent interest. It is becoming well accepted that they form via liquid-liquid phase separation (LLPS) of protein mixtures (often including RNA), where the organelles correspond to a protein-rich droplet phase coexisting with a protein-poor bulk phase. The major protein components contain disordered regions and often also RNA-binding domains, and the disordered fragments on their own easily undergo LLPS. By contrast, LLPS for structured proteins has been observed infrequently. The contrasting phase behaviors can be explained by modeling disordered and structured proteins, respectively, as polymers and colloids. These physical models also provide a better understanding of the regulation of droplet formation by cellular signals and its dysregulation leading to diseases.

Vapour–liquid interfacial properties of square-well chains from density functional theory and Monte Carlo simulation

Vapour–liquid surface tension for tangent (open symbols) and vibrating (filled symbols) square-well chains.

Thermodynamic properties of Lennard-Jones chain molecules: Renormalization-group corrections to a modified statistical associating fluid theory

A modified version of the statistical associating fluid theory (SAFT), the so-called soft-SAFT equation of state (EOS), has been extended by a crossover treatment to take into account the long density fluctuations encountered when the critical region is approached. The procedure, based on White's work from the renormalization group theory [Fluid Phase Equilibria 75, 53 (1992); L. W. Salvino and J. A. White, J. Chem. Phys. 96, 4559 (1992)], is implemented in terms of recursion relations where the density fluctuations are successively incorporated. The crossover soft-SAFT equation provides the correct nonclassical critical exponents when approaching the critical point, and reduces to the original soft-SAFT equation far from the critical region. The accuracy of the global equation is tested by direct comparison with molecular simulation results of Lennard-Jones chains, obtaining very good agreement and clear improvements compared to the original soft-SAFT EOS. Excellent agreement with vapor-liquid equilibrium experimental data inside and outside the critical region for the n-alkane series is also obtained. We provide a set of transferable molecular parameters for this family, unique for the whole range of thermodynamic properties.

Computer simulation study of the global phase behavior of linear rigid Lennard-Jones chain molecules: Comparison with flexible models

The global phase behavior (i.e., vapor-liquid and fluid-solid equilibria) of rigid linear Lennard-Jones (LJ) chain molecules is studied. The phase diagrams for three-center and five-center rigid model molecules are obtained by computer simulation. The segment-segment bond lengths are L = sigma, so that models of tangent monomers are considered in this study. The vapor-liquid equilibrium conditions are obtained using the Gibbs ensemble Monte Carlo method and by performing isobaric-isothermal NPT calculations at zero pressure. The phase envelopes and critical conditions are compared with those of flexible LJ molecules of tangent segments. An increase in the critical temperature of linear rigid chains with respect to their flexible counterparts is observed. In the limit of infinitely long chains the critical temperature of linear rigid LJ chains of tangent segments seems to be higher than that of flexible LJ chains. The solid-fluid equilibrium is obtained by Gibbs-Duhem integration, and by performing NPT simulations at zero pressure. A stabilization of the solid phase, an increase in the triple-point temperature, and a widening of the transition region are observed for linear rigid chains when compared to flexible chains with the same number of segments. The triple-point temperature of linear rigid LJ chains increases dramatically with chain length. The results of this work suggest that the fluid-vapor transition could be metastable with respect to the fluid-solid transition for chains with more than six LJ monomer units.

An accurate density functional theory for the vapor-liquid interface of associating chain molecules based on the statistical associating fluid theory for potentials of variable range

A Helmholtz free energy density functional is developed to describe the vapor-liquid interface of associating chain molecules. The functional is based on the statistical associating fluid theory with attractive potentials of variable range (SAFT-VR) for the homogenous fluid [A. Gil-Villegas, A. Galindo, P. J. Whitehead, S. J. Mills, G. Jackson, and A. N. Burgess, J. Chem. Phys. 106, 4168 (1997)]. A standard perturbative density functional theory (DFT) is constructed by partitioning the free energy density into a reference term (which incorporates all of the short-range interactions, and is treated locally) and an attractive perturbation (which incorporates the long-range dispersion interactions). In our previous work [F. J. Blas, E. Martin del Rio, E. de Miguel, and G. Jackson, Mol. Phys. 99, 1851 (2001); G. J. Gloor, F. J. Blas, E. Martin del Rio, E. de Miguel, and G. Jackson, Fluid Phase Equil. 194, 521 (2002)] we used a mean-field version of the theory (SAFT-HS) in which the pair correlations were neglected in the attractive term. This provides only a qualitative description of the vapor-liquid interface, due to the inadequate mean-field treatment of the vapor-liquid equilibria. Two different approaches are used to include the correlations in the attractive term: in the first, the free energy of the homogeneous fluid is partitioned such that the effect of correlations are incorporated in the local reference term; in the second, a density averaged correlation function is incorporated into the perturbative term in a similar way to that proposed by Toxvaerd [S. Toxvaerd, J. Chem. Phys. 64, 2863 (1976)]. The latter is found to provide the most accurate description of the vapor-liquid surface tension on comparison with new simulation data for a square-well fluid of variable range. The SAFT-VR DFT is used to examine the effect of molecular chain length and association on the surface tension. Different association schemes (dimerization, straight and branched chain formation, and network structures) are examined separately. The surface tension of the associating fluid is found to be bounded between the nonassociating and fully associated limits (both of which correspond to equivalent nonassociating systems). The temperature dependence of the surface tension is found to depend strongly on the balance between the strength and range of the association, and on the particular association scheme. In the case of a system with a strong but very localized association interaction, the surface tension exhibits the characteristic "s shaped" behavior with temperature observed in fluids such as water and alkanols. The various types of curves observed in real substances can be reproduced by the theory. It is very gratifying that a DFT based on SAFT-VR free energy can provide an accurate quantitative description of the surface tension of both the model and experimental systems.

Molecular simulation of ultrathin polymeric films near the glass transition

Properties such as the glass transition temperature ( T(g)) and the diffusion coefficient of ultrathin polymeric films are shown to depend on the dimensions of the system. In this work, a hard-sphere molecular dynamics methodology has been applied to simulate such systems. We investigate the influence that substrates have on the behavior of thin polymer films; we report evidence suggesting that, depending on the strength of substrate-polymer interactions, the glass transition temperature for a thin film can be significantly lower or higher than that of the bulk.