Vapor-liquid phase coexistence and transport properties of two-dimensional oligomers

Grand-canonical transition-matrix Monte Carlo and histogram reweighting techniques are used herein to study the vapor-liquid coexistence properties of two-dimensional (2D) flexible oligomers with varying chain lengths (m = 1-8). The phase diagrams of the various 2D oligomers follow the correspondence state (CS) principle, akin to the behavior observed for bulk oligomers. The 2D critical density is not influenced by the oligomer chain length, which contrasts with the observation for the bulk oligomers. Line tension, calculated using Binder's formalism, in the reduced plot is found to be independent of chain length in contrast to the 3D behavior. The dynamical properties of 2D fluids are evaluated using molecular dynamics simulations, and the velocity and pressure autocorrelation functions are investigated using Green-Kubo (GK) relations to yield the diffusion and viscosity. The viscosity determined from 2D non-equilibrium molecular dynamics simulation is compared with the viscosity estimated from the GK relations. The GK relations prove to be reliable and efficient for the calculation of 2D transport properties. Normal diffusive regions are identified in dense oligomeric fluid systems. The influence of molecular size on the diffusivity and viscosity is found to be diminished at specific CS points for the 2D oligomers considered herein. In contrast, the viscosity and diffusion of the 3D bulk fluid, at a reduced temperature and density, are strongly dependent on the molecular size at the same CS points. Furthermore, the viscosity increases and the diffusion decreases multifold in the 2D system relative to those in the 3D system, at the CS points.     

Vapor-liquid coexistence in fluids of charged hard dumbbells

Vapor-liquid coexistence in fluids of charged hard dumbbells, each made up of two oppositely charged hard spheres with diameters sigma and separation d, has been studied using grand-canonical Monte Carlo simulations. In the limit d/sigma-->0, and with the temperature scaled accordingly, the system corresponds to dipolar hard spheres. For separations in the range 0.30 yield estimates of the apparent critical parameters for dipolar hard spheres.     

Communication: phase transitions, criticality, and three-phase coexistence in constrained cell models

In simulation studies of fluid-solid transitions, the solid phase is usually modeled as a constrained system in which each particle is confined to move in a single Wigner-Seitz cell. The constrained cell model has been used in the determination of fluid-solid coexistence via thermodynamic integration and other techniques. In the present work, the phase diagram of such a constrained system of Lennard-Jones particles is determined from constant-pressure simulations. The pressure-density isotherms exhibit inflection points which are interpreted as the mechanical stability limit of the solid phase. The phase diagram of the constrained system contains a critical and a triple point. The temperature and pressure at the critical and the triple point are both higher than those of the unconstrained system due to the reduction in the entropy caused by the single occupancy constraint.     

Vapor-liquid and vapor-solid phase equilibria for united-atom benzene models near their triple points: the importance of quadrupolar interactions

Gibbs ensemble Monte Carlo simulations were used to calculate the vapor-liquid and vapor-solid coexistence curves for benzene using two simple united-atom models. An extension of the Gibbs ensemble method that makes use of an elongated box containing a slab of the condensed phase with a vapor phase along one axis was employed for the simulations of the vapor-solid equilibria and the vapor-liquid equilibria at very low reduced temperatures. Configurational-bias and aggregation-volume-bias Monte Carlo techniques were applied to improve the sampling of particle transfers between the two simulation boxes and between the vapor and condensed-phase regions of the elongated box. An isotropic united-atom representation with six Lennard-Jones sites at the positions of the carbon atoms was used for both force fields, but one model contained three additional out-of-plane partial charge sites to explicitly represent benzene's quadrupolar interactions. Both models were fitted to reproduce the critical temperature and density of benzene and yield a fair representation of the vapor-liquid coexistence curve. In contrast, differences between the models are very large for the vapor-solid coexistence curve. In particular, the lack of explicit quadrupolar interactions for the 6-site model greatly reduces the energetic differences between liquid and solid phases, and this model yields a triple point temperature that is about a factor of 2 too low. In contrast, the 9-site model predicts a triple point of benzene at T = 253 +/- 6 K and p = 2.3 +/- 0.8 kPa in satisfactory agreement with the experimental data (T = 278.7 K and p = 4.785 kPa).     

Spoilt for choice: assessing phase behavior models for the evolution of homochirality

The observation of single chirality in biological systems has intrigued scientists for more than one hundred years. Here we discuss several recent experimental studies showing amplification of enantiomeric excess based on amino acid phase behavior. Comparing observations of solution-solid and gas-solid phase transitions highlights the underlying fundamental physical chemistry principles that rationalize the observed enantioenrichment in both cases.     

Controlling crystallization and its absence: proteins, colloids and patchy models

The ability to control the crystallization behaviour (including its absence) of particles, be they biomolecules such as globular proteins, inorganic colloids, nanoparticles, or metal atoms in an alloy, is of both fundamental and technological importance. Much can be learnt from the exquisite control that biological systems exert over the behaviour of proteins, where protein crystallization and aggregation are generally suppressed, but where in particular instances complex crystalline assemblies can be formed that have a functional purpose. We also explore the insights that can be obtained from computational modelling, focussing on the subtle interplay between the interparticle interactions, the preferred local order and the resulting crystallization kinetics. In particular, we highlight the role played by "frustration", where there is an incompatibility between the preferred local order and the global crystalline order, using examples from atomic glass formers and model anisotropic particles.     

Re-entrant phase behaviour of network fluids: a patchy particle model with temperature-dependent valence

We study a model consisting of particles with dissimilar bonding sites ("patches"), which exhibits self-assembly into chains connected by Y-junctions, and investigate its phase behaviour by both simulations and theory. We show that, as the energy cost ε(j) of forming Y-junctions increases, the extent of the liquid-vapour coexistence region at lower temperatures and densities is reduced. The phase diagram thus acquires a characteristic "pinched" shape in which the liquid branch density decreases as the temperature is lowered. To our knowledge, this is the first model in which the predicted topological phase transition between a fluid composed of short chains and a fluid rich in Y-junctions is actually observed. Above a certain threshold for ε(j), condensation ceases to exist because the entropy gain of forming Y-junctions can no longer offset their energy cost. We also show that the properties of these phase diagrams can be understood in terms of a temperature-dependent effective valence of the patchy particles.     

Role of solvent in protein phase behavior: Influence of temperature dependent potential

Among many factors that affect protein phase separation, solvent plays a pivotal role in the possible structuring of the solvent molecules around the protein. The effect of solvent structuring is influenced strongly by temperature because of the relative stability of hydrogen bonding at low temperatures. As a result, quantitative as well as qualitative changes in protein phase separation may be expected with change in temperature. Here, we use a temperature dependent pair potential to examine the effect of water in the phase separation of protein solutions. Using Gibbs ensemble Monte Carlo simulations, we observe both a lower critical solution temperature and an upper critical solution temperature, in good agreement with the experimental observations for a number of proteins and phenomenological, statistical thermodynamic arguments. It is found that the effect of solvent is significant at low temperatures as a result of the highly structured shell of water molecules around the protein molecules. Radial distribution functions also indicate that a thick shell of structured water exists around the protein molecules due to the formation of strong hydrogen bonds when temperature is low. The findings of this study suggest that a simple model with a reasonable physical basis can capture the general phase behavior of some proteins or biopolymers.     

Critical behavior of the Widom-Rowlinson mixture: coexistence diameter and order parameter

The critical behavior of the Widom-Rowlinson [J. Chem. Phys. 52, 1670 (1970)] is studied in d = 3 dimensions by means of grand canonical Monte Carlo simulations. The finite-size scaling approach of Kim et al. [Phys. Rev. Lett. 91, 065701 (2003)] is used to extract the order parameter and the coexistence diameter. It is demonstrated that the critical behavior of the diameter is dominated by a singular term proportional to t(1-alpha), with t the relative distance from the critical point, and alpha the critical exponent of the specific heat. No sign of a term proportional to t(2beta) could be detected, with beta the critical exponent of the order parameter, indicating that pressure mixing in this model is small. The critical density is measured to be rhosigma3 = 0.7486 +/- 0.0002, with sigma the particle diameter. The critical exponents alpha and beta, as well as the correlation length exponent nu, are also measured and shown to comply with d = 3 Ising criticality.     

Vapor-liquid equilibrium and critical behavior of the square-well fluid of variable range: a theoretical study

The vapor-liquid phase behavior and the critical behavior of the square-well (SW) fluid are investigated as a function of the interaction range, lambdain [1.25, 3], by means of the self-consistent Ornstein-Zernike approximation (SCOZA) and analytical equations of state based on a perturbation theory [A. L. Benavides and F. del Rio, Mol. Phys. 68, 983 (1989); A. Gil-Villegas, F. del Rio, and A. L. Benavides, Fluid Phase Equilib. 119, 97 (1996)]. For this purpose the SCOZA, which has been restricted up to now to a few model systems, has been generalized to hard-core systems with arbitrary interaction potentials requiring a fully numerical solution of an integro-partial differential equation. Both approaches, in general, describe well the liquid-vapor phase diagram of the square-well fluid when compared with simulation data. SCOZA yields very precise predictions for the coexistence curves in the case of long ranged SW interaction (lambda>1.5), and the perturbation theory is able to predict the binodal curves and the saturated pressures, for all interaction ranges considered if one stays away from the critical region. In all cases, the SCOZA gives very good predictions for the critical temperatures and the critical pressures, while the perturbation theory approach tends to slightly overestimate these quantities. Furthermore, we propose analytical expressions for the critical temperatures and pressures as a function of the square-well range.     

Gas-liquid phase coexistence in quasi-two-dimensional Stockmayer fluids: A molecular dynamics study

The Maxwell construction together with molecular dynamics simulation is used to study the gas-liquid phase coexistence of quasi-two-dimensional Stockmayer fluids. The phase coexistence curves and corresponding critical points under different dipole strength are obtained, and the critical properties are calculated. We investigate the dependence of the critical point and critical properties on the dipole strength. When the dipole strength is increased, the abrupt disappearance of the gas-liquid phase coexistence in quasi-two-dimensional Stockmayer fluids is not found. However, if the dipole strength is large enough, it does lead to the formation of very long reversible chains which makes the relaxation of the system very slow and the observation of phase coexistence rather difficult or even impossible.     

Polyethylene glycol adsorption on silica: from bulk phase behavior to surface phase diagram

A characterization of the bulk-phase diagram from literature data and new NMR and DSC measurements provided us with valuable elements that are helpful for gaining, from aqueous solution, better insight into the surface behavior of polyethylene glycol on Aerosil 200. Adsorption isotherms built further to measurements by a depletion method showed a strong and temperature-dependent variation of the isotherm shape in agreement with the variations of interactions already evidenced in the bulk. In temperature-concentration areas, where water is behaving as a helix-promoting solvent, the finding of positive PEG adsorptions and stairlike isotherms agrees with observations reported in the literature. We identified some of the vertical parts as corresponding to the formation of monolayers of helix-shaped PEG molecules. In poor-solvent zones, adsorptions were null or negative, and the isotherms exhibited oscillations suggesting very different surface behavior. Our data analysis evidenced the presence of a much greater amount of water than in the previous surface states; however, the similar analysis of PEG behavior remains relevant. Indeed, the occurrence of first-order transitions in the surface layer implies some water reorganization, permitting the PEG molecules to move closer to the surface and become helix-shaped to rearrange in a monolayer. The surface phase diagram confirmed this analysis in a very satisfying way.     

Viscoelastic properties of polymers: From molecular models to non-linear behavior

The molecular models of polymer physics (reptation, tube renewal) give a reasonable picture of the diffusion and relaxation of long and flexible chains: the concept of “tube renewal” (constraint release) added to the reptation idea explains the polydispersity effects for multimodal blends as well as for commercial linear polymers. The real issue now is to introduce these concepts in the formalism of non-linear viscoelasticity in order to explain the experimental data, as a first step in the range of moderate rates of deformation, then at very high strains.     

Theoretical and numerical study of the phase diagram of patchy colloids: ordered and disordered patch arrangements

We report theoretical and numerical evaluations of the phase diagram for a model of patchy particles. Specifically, we study hard spheres whose surface is decorated by a small number f of identical sites ("sticky spots") interacting via a short-ranged square-well attraction. We theoretically evaluate, solving the Wertheim theory, the location of the critical point and the gas-liquid coexistence line for several values of f and compare them to the results of Gibbs and grand canonical Monte Carlo simulations. We study both ordered and disordered arrangements of the sites on the hard-sphere surface and confirm that patchiness has a strong effect on the phase diagram: the gas-liquid coexistence region in the temperature-density plane is significantly reduced as f decreases. We also theoretically evaluate the locus of specific heat maxima and the percolation line.     

Surface tension and vapor-liquid phase coexistence of confined square-well fluid

Phase equilibria of a square-well fluid in planar slit pores with varying slit width are investigated by applying the grand-canonical transition-matrix Monte Carlo (GC-TMMC) with the histogram-reweighting method. The wall-fluid interaction strength was varied from repulsive to attractive such that it is greater than the fluid-fluid interaction strength. The nature of the phase coexistence envelope is in agreement with that given in literature. The surface tension of the vapor-liquid interface is calculated via molecular dynamics simulations. GC-TMMC with finite size scaling is also used to calculate the surface tension. The results from molecular dynamics and GC-TMMC methods are in very good mutual agreement. The vapor-liquid surface tension, under confinement, was found to be lower than the bulk surface tension. However, with the increase of the slit width the surface tension increases. For the case of a square-well fluid in an attractive planar slit pore, the vapor-liquid surface tension exhibits a maximum with respect to wall-fluid interaction energy. We also report estimates of critical properties of confined fluids via the rectilinear diameter approach.     

Mechanical stability of micropipet-aspirated giant vesicles with fluid phase coexistence

Micropipet aspiration of phase-separated lipid bilayer vesicles can elucidate physicochemical aspects of membrane fluid phase coexistence. Recently, we investigated the composition dependence of line tension at the boundary between liquid-ordered and liquid-disordered phases of giant unilamellar vesicles obtained from ternary lipid mixtures using this approach. Here we examine mechanical equilibria and stability of dumbbell-shaped vesicles deformed by line tension. We present a relationship between the pipet aspiration pressure and the aspiration length in vesicles with two coexisting phases. Using a strikingly simple mechanical model for the free energy of the vesicle, we predict a relation that is in almost quantitative agreement with experiment. The model considers the vesicle free energy to be proportional to line tension and assumes that the vesicle volume, domain area fraction, and total area are conserved during aspiration. We also examine a mechanical instability encountered when releasing a vesicle from the pipet. We find that this releasing instability is observed within the framework of our model that predicts a change of the compressibility of a pipet-aspirated membrane cylinder from positive (i.e., stable) to negative (unstable) values, at the experimental instability. The model furthermore includes an aspiration instability that has also previously been experimentally described. Our method of studying micropipet-induced shape transitions in giant vesicles with fluid domains could be useful for investigating vesicle shape transitions modulated by bending stiffness and line tension.     

Effect of added alpha-lactalbumin protein on the phase behavior of AOT-brine-isooctane systems

We have found that the presence of <1 wt% of the globular protein alpha-lactalbumin has a significant impact on the equilibrium phase behavior of dilute sodium bis(ethylhexyl) sulfosuccinate (AOT)/brine/isooctane systems. Nuclear magnetic resonance (NMR), Karl Fischer titration, and ultraviolet spectroscopy were used to determine the surfactant, oil, water, and protein content of the organic and aqueous phases as a function of the total surfactant and protein present. As a small amount of alpha-lactalbumin is added to the mixture, there is a substantial increase (up to 80%) in the maximum water solubility in the water-in-oil microemulsion phase. Dynamic light scattering measurements indicate that this increase is due to a decrease in the magnitude of the (negative) spontaneous curvature of the surfactant monolayer, as droplets swell in size. As the molar ratio of alpha-lactalbumin to AOT surpasses approximately 1:300, the partitioning of water, protein, and surfactant shifts to the excess aqueous phase, where soluble assemblies with positive curvature are detected by dynamic light scattering. Significant amounts of isooctane are solubilized in these aggregates, consistent with the formation of oil-in-water microemulsion droplets. Circular dichroism studies showed that the tertiary structure of the protein in the microemulsion is disrupted while the secondary structure is increased. In light of these findings, the protein most likely expands to a molten-globule type conformation in the AOT interfacial environment, but does not substantially unfold to become an extended chain.     

The use of two-phase molecular dynamics simulations to determine the phase behavior and critical point of propane molecular models

Molecular dynamics simulations were performed to determine two-phase configurations of model propane molecules below the critical point and in the near-critical, two-phase region. A postprocessor that uses a Monte Carlo method for determination of volumes attributable to each molecule was used to obtain density histograms of the particles from which the bulk coexisting equilibrium vapor and liquid densities were determined. This method of analyzing coexisting densities in a two-phase simulation is straightforward and can be easily implemented for complex, multisite models. Various degrees of internal flexibility in the propane models have little effect on the coexisting densities at temperatures 40 K or more below the critical point, but internal flexibility (angle bending and bond vibrations) does affect the saturated liquid densities in the near-critical region, changing the critical temperature by approximately 20 K. Shorter cutoffs were also found to affect the phase dome and the location of the critical point.