The coexistence region in the Van der Waals fluid and the liquid-liquid phase transitions (original) (raw)
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van der Waals phase transition in protein solutions
Acta Crystallographica Section D Biological Crystallography, 2005
The van der Waals equation of state for imperfect gases is applied to solutions of macromolecules, especially to explain the fluid-fluid phase transition in protein solutions, a phenomenon of much interest in relation to protein crystallization. The van der Waals b parameter corresponds to the total excluded volume per pair of molecules and can be calculated from independently known molecular properties. It is comprised of terms resulting from hard-sphere and net chargecharge interactions. The experimentally determined second virial coefficient B 2 can then be used to obtain the equilibrium constant for dimerization K 2 , a phenomenologically accessible measure of the van der Waals a parameter. Sedimentation equilibrium is recommended as the technique for measuring B 2 most accurately. More general results are used to make a minor quantitative correction to the van der Waals prediction concerning the criterion for the fluidfluid phase transition. Calculations of the effect of inert co-solutes on the phase transition may prove useful in choosing crystallization conditions.
Nucleation, spinodal decomposition, and interface motion in the van der Waals fluid
The Journal of Chemical Physics, 1981
We discuss the predictions of the phenomenological theory of Metiu, Kitahara, and Ross for the most probable evolution of density fluctuations in the van der Waals fluid model. The knowledge of the exact (nonlocal) form for the grand potential functional n permits a precise study of the kinetics of phase change under strongly nonuniform conditions. It is shown that for every subcritical temperature and chemical potential in the spinodal region there exists an infinite family of periodic stationary states in addition to the usual uniform ones. The stability analysis of these states provides a description of spinodal decomposition in its intermediate and later stages. It is also shown that fluctuations separated in space are correlated through the nonlocality of n and that they cooperate in the nucleation process with an additional term absent in the classical and gradient theories. The solitary wave motion which describes condensation-evaporation pr~ is obtained from a perturbation on the thermodynamic conditions for.phase equilibrium.
A van der Waals-type equation of state for fluids with associating molecules
Proceedings of the National Academy of Sciences, 1976
The basic assumptions of van der Waals theory are contained in two well-known concepts: excluded volume (repulsive forces) and a homogeneous, isotropic field potential (attractive forces). We have superimposed on these, one more well-known concept: the existence of dimers, trimers, etc., at chemical equilibrium. With reasonable simplifying assumptions, we obtain a closed-form equation of state, applicable to all fluid densities, and potentially useful for fluids containing strongly polar or hydrogen-bonded molecules. At all temperatures and at high densities, the equation of state suggests a phase
The nature of the phase transition in dipolar fluids
Monte Carlo computer simulations of a quasi two dimensional (2D) dipolar fluid at low and intermediate densities indicate that the structure of the fluid is well described by an ideal mixture of self-assembling clusters. A detailed analysis of the topology of the clusters, of their internal energy and of their size (or mass) distributions further suggests that the system undergoes a phase transition from a dilute phase characterized by a number of disconnected clusters to a condensed phase characterized by a network or spanning (macroscopic) cluster that includes most of the particles in the system.
Generalized van der Waals theory of liquid-liquid phase transitions
Physical Review E, 2006
In the framework of the thermodynamic perturbation theory for fluids we study how the phase diagram of an isotropic repulsive soft-core attractive potential, where a liquid-liquid phase transition exists in addition to the standard gas-liquid phase transition, changes by varying the parameters of the potential. We show that existence of the liquid-liquid transition is determined by the interplay of the parameters of the potential and the structure of a reference liquid.
Liquid-Vapor Equilibria of Polar Fluids from a van der Waals-like Theory
1994
A van der Waals-like theory of quadrupolar and dipolar linear fluids is presented. The reference system consists of a hard polar fluid, and attractive forces are considered through the mean field approximation. The effect of polar forces on liquid-vapor equilibria and on critical properties is analyzed for a number of molecular elongations. Trends as predicted by the theory are compared with computer simulations of linear polar fluids, and good agreement is found. Polar forces increase the critical temperature and acentric factor of a fluid. Quadrupole moment increases the critical density of a fluid. However, high dipole moments decrease critical densities. Deviations from the principle of corresponding states are analyzed. Polar forces and molecular elongation provoke a broadening of the coexistence curve and an increase of the slope of the vapor pressure curve when reduced by their critical magnitudes. The presented treatment, being quite simple, describes most of the main features of vapor-liquid equilibria of linear polar fluids.
The Journal of Chemical Physics, 2015
We investigate the structural properties of liquid water at near ambient conditions using first-principles molecular dynamics simulations based on a semilocal density functional augmented with nonlocal van der Waals interactions. The adopted scheme offers the advantage of simulating liquid water at essentially the same computational cost of standard semilocal functionals. Applied to the water dimer and to ice I h , we find that the hydrogen-bond energy is only slightly enhanced compared to a standard semilocal functional. We simulate liquid water through molecular dynamics in the N pH statistical ensemble allowing for fluctuations of the system density. The structure of the liquid departs from that found with a semilocal functional leading to more compact structural arrangements. This indicates that the directionality of the hydrogenbond interaction has a diminished role as compared to the overall attractions, as expected when dispersion interactions are accounted for. This is substantiated through a detailed analysis comprising the study of the partial radial distribution functions, various local order indices, the hydrogen-bond network, and the selfdiffusion coefficient. The explicit treatment of the van der Waals interactions leads to an overall improved description of liquid water. Recently, several nonlocal formulations have been introduced which explicitly account for van der Waals interactions through a functional of the density. 15,17,19,24 Among these, the one proposed by Vydrov and Van Voorhis 19 in its revised form denoted rVV10 carries the
Molecular Simulation
Molecular dynamics (MD) simulations of a Lennard-Jones system are performed to obtain the pVT and UVT relations. An extended van der Waals equation of state (EOS) is derived by statistical mechanics on the perturbation approximation. A hard sphere system is used as the reference system. The Ree -Hoover EOS is assumed for the hard sphere system. The attraction energy term in the canonical ensemble partition function is extended by a cluster expansion. The new EOS includes three parameters, two of which are the interaction parameters in the Lennard-Jones interaction. The last parameter is the effective volume of the hard sphere system as the reference. The extended van der Waals EOS reproduces the pVT and UVT relations, at least qualitatively, whereas the original van der Waals EOS can explain only the pVT relation. The present EOS can also explain the fluctuations of the potential energy as calculated by MD simulations with 1000 molecules in the unit cell. In this sense, the present EOS gives better heat capacities at constant volume C v , even at lower temperatures than the original van der Waals EOS, which includes the attraction part of the equation, with no temperature dependence in the internal energy U.
Molecular Dynamics in Confining Space: From the Single Molecule to the Liquid State
Physical Review Letters, 1999
The transition from the dynamics of isolated molecules to that of a bulk liquid is observed for the first time by analyzing the dielectric relaxation ͑10 22 10 9 Hz͒ of ethylene glycol (EG) guest molecules confined to zeolitic host systems of different topology. Beyond a threshold channel size the liquid character is lost, indicated by a dramatically increased relaxation rate and an Arrhenius-like temperature dependence. Computer simulations of the molecular arrangement in a confining space prove that an ensemble as small as six molecules is sufficient to exhibit the dynamics of a bulk liquid. [S0031-9007(99)08701-3]