Mixtures of charged colloid and neutral polymer: influence of electrostatic interactions on demixing and interfacial tension

The equilibrium phase behavior of a binary mixture of charged colloids and neutral, nonadsorbing polymers is studied within free-volume theory. A model mixture of charged hard-sphere macroions and ideal, coarse-grained, effective-sphere polymers is mapped first onto a binary hard-sphere mixture with nonadditive diameters and then onto an effective Asakura-Oosawa model [S. Asakura and F. Oosawa, J. Chem. Phys. 22, 1255 (1954)]. The effective model is defined by a single dimensionless parameter-the ratio of the polymer diameter to the effective colloid diameter. For high salt-to-counterion concentration ratios, a free-volume approximation for the free energy is used to compute the fluid phase diagram, which describes demixing into colloid-rich (liquid) and colloid-poor (vapor) phases. Increasing the range of electrostatic interactions shifts the demixing binodal toward higher polymer concentration, stabilizing the mixture. The enhanced stability is attributed to a weakening of polymer depletion-induced attraction between electrostatically repelling macroions. Comparison with predictions of density-functional theory reveals a corresponding increase in the liquid-vapor interfacial tension. The predicted trends in phase stability are consistent with observed behavior of protein-polysaccharide mixtures in food colloids.     

Phase and mixing behavior in two-component lipid bilayers: a molecular dynamics study in DLPC/DSPC mixtures

Phase and mixing behavior of dilauroylphosphatidylcholine (DLPC)/distearoylphosphatidylcholine (DSPC) lipid mixtures are studied by molecular dynamics simulations with use of a coarse-grained model over a wide range of concentrations. The results reveal that phase transformations from the fluid to the gel state can be followed over a microsecond time scale. The changes in structure suggest regions of phase coexistence allowing us to outline the entire phase diagram for this lipid mixture using a molecular based model. We show that simulations yield good agreement with the experimental phase diagram. We also address the effect of macroscopic phase separation on the determination of the transition temperature, different leaflet composition, and finite size effects. This study may have implications on lateral membrane organization and the associated processes dependent on these membrane regions on different time and length scales.     

Phase separation of a model binary polymer solution in an external field

The phase separation of a simple binary mixture of incompatible linear polymers in solution is investigated using an extension of the sedimentation equilibrium method, whereby the osmotic pressure of the mixture is extracted from the density profiles of the inhomogeneous mixture in a gravitational field. In Monte Carlo simulations the field can be tuned to induce significant inhomogeneity, while keeping the density profiles sufficiently smooth for the macroscopic condition of hydrostatic equilibrium to remain applicable. The method is applied here for a simplified model of ideal but mutually avoiding polymers, which readily phase separate at relatively low densities. The Monte Carlo data are interpreted with the help of an approximate bulk phase diagram calculated from a simple, second-order virial coefficient theory. By derivation of effective potentials between polymer centers of mass, the binary mixture of polymers is coarse-grained to a "soft colloid" picture reminiscent of the Widom-Rowlinson model for incompatible atomic mixtures. This approach significantly speeds up the simulations and accurately reproduces the behavior of the full monomer resolved model.     

Dense orientationally ordered states of a single semiflexible macromolecule: an expanded ensemble Monte Carlo simulation

Using a coarse-grained model we perform a Monte Carlo simulation of the state behavior of an individual semiflexible macromolecule. Chains consisting of N = 256 and 512 monomer units have been investigated. A recently proposed enhanced sampling Monte Carlo technique for the bond fluctuation model in an expanded ensemble in four-dimensional coordinate space was applied. The algorithm allows one to accelerate the sampling of statistically independent three-dimensional conformations in a dense globular state. We found that the temperature of the intraglobular liquid-solid transition decreases with increasing chain stiffness. We have investigated the possible intraglobular orientationally ordered (i.e., liquid-crystalline) structures and obtained a diagram of states for chains consisting of N = 256 monomer units. This diagram contains regions of stability of coil, two spherical globules (liquid and solid), and rod-like globule conformations. Transitions between the globular states are rounded first-order ones since the states of liquid, solid, and cylinder-like globules do have different internal symmetry.     

Microphase segregation in bridging polymeric brushes: Regular and singular phase diagrams

A mean-field theory of deformation-induced microphase segregation in bridging polymeric brushes anchored to two parallel surfaces is presented. Models with isotropic and orientation-dependent liquid-crystalline interactions between segments are considered. For the first model, the problem is similar to that of classical liquid-vapor phase separation, and the phase diagram in the P-T plane has a line of first-order transitions terminating at the critical point. We show that the critical pressure is negative implying that a free brush tethered only to one surface always exists at supercritical conditions and hence cannot undergo the collapse phase transition. In the second model, the free energy density depends on two coupled order parameters, one related to segment density and the other to the orientational order, which strongly modifies the phase behavior. Depending on the grafting density the system is described by a phase diagram of a regular or a singular type. In the regular phase diagram the first-order transition line terminates at the critical point. In a singular diagram, the first-order transition line extends to infinity; the critical point corresponds to infinite pressure so that the system undergoes the phase transition at arbitrary external pressures. Regular phase diagrams correspond to dense grafting, and singular ones to sparse grafting. The change from a regular phase behavior to another occurs at a certain marginal value of the grafting density. On approaching this value the critical point on the regular diagram moves to infinity, logarithmically with the deviation from the critical grafting density. We relate the analytical properties of the free energy density as a function of the segment concentration to the type of the phase diagram and the shape of the coexistence curve in the temperature- concentration plane.     

Transitions of tethered polymer chains: a simulation study with the bond fluctuation lattice model

A polymer chain tethered to a surface may be compact or extended, adsorbed or desorbed, depending on interactions with the surface and the surrounding solvent. This leads to a rich phase diagram with a variety of transitions. To investigate these transitions we have performed Monte Carlo simulations of a bond fluctuation model with Wang-Landau and umbrella sampling algorithms in a two-dimensional state space. The simulations' density-of-states results have been evaluated for interaction parameters spanning the range from good- to poor-solvent conditions and from repulsive to strongly attractive surfaces. In this work, we describe the simulation method and present results for the overall phase behavior and for some of the transitions. For adsorption in good solvent, we compare with Metropolis Monte Carlo data for the same model and find good agreement between the results. For the collapse transition, which occurs when the solvent quality changes from good to poor, we consider two situations corresponding to three-dimensional (hard surface) and two-dimensional (very attractive surface) chain conformations, respectively. For the hard surface, we compare tethered chains with free chains and find very similar behavior for both types of chains. For the very attractive surface, we find the two-dimensional chain collapse to be a two-step transition with the same sequence of transitions that is observed for three-dimensional chains: a coil-globule transition that changes the overall chain size is followed by a local rearrangement of chain segments.     

Phase diagram of supercooled water confined to hydrophilic nanopores

We present a phase diagram for water confined to cylindrical silica nanopores in terms of pressure, temperature, and pore radius. The confining cylindrical wall is hydrophilic and disordered, which has a destabilizing effect on ordered water structure. The phase diagram for this class of systems is derived from general arguments, with parameters taken from experimental observations and computer simulations and with assumptions tested by computer simulation. Phase space divides into three regions: a single liquid, a crystal-like solid, and glass. For large pores, radii exceeding 1 nm, water exhibits liquid and crystal-like behaviors, with abrupt crossovers between these regimes. For small pore radii, crystal-like behavior is unstable and water remains amorphous for all non-zero temperatures. At low enough temperatures, these states are glasses. Several experimental results for supercooled water can be understood in terms of the phase diagram we present.     

Mesoscale model parameters from molecular cluster calculations

We present an efficient, systematic, and universal method to estimate the interaction parameters used in mesoscale simulation methods such as dissipative particle dynamics and self-consistent field methods from molecular cluster calculations. The method is based on a generalized Flory-Huggins model in which molecules, or fragments thereof, are in contact with their van der Waals surface. We sample the density of states of molecular clusters in the space spanned by the coarse-grained degrees of freedom. From here, we calculate the sum over states and free energy of the cluster at a temperature of interest by histogram reweighting. The method allows to calculate the energy and entropy contributions to the cluster free energy explicitly. For two components, we then obtain the excess free energy of mixing and the Flory-Huggins chi-parameter, and their energetic and entropic contributions. We present two applications of the method: a simple liquid mixture of hexane and nitrobenzene, and a series of polymer blends. In the case of hexane/nitrobenzene, we compare to alternative simulation methods; here we find that the energy of mixing alone is too high to explain the critical point. By including the excess entropy of mixing, however, the predicted phase behavior is in reasonable agreement with experiment. The tendency of calculations based on average energy alone to overestimate the chi-parameter is also apparent in the polymer blend calculations.     

Phase behavior of a symmetrical binary fluid mixture

We have investigated the phase behavior of a symmetrical binary fluid mixture for the situation where the chemical potentials mu(1) and mu(2) of the two species differ. Attention is focused on the set of interparticle interaction strengths for which, when mu(1)=mu(2), the phase diagram exhibits both a liquid-vapor critical point and a tricritical point. The corresponding phase behavior for the case mu(1) not equalmu(2) is investigated via integral-equation theory calculations within the mean spherical approximation and grand canonical Monte Carlo (GCMC) simulations. We find that two possible subtypes of phase behavior can occur, these being distinguished by the relationship between the triple lines in the full phase diagram in the space of temperature, density, and concentration. We present the detailed form of the phase diagram for both subtypes and compare with the results from GCMC simulations, finding good overall agreement. The scenario via which one subtype evolves into the other is also studied, revealing interesting features.     

The phase diagram of a single polymer chain: New insights from a new simulation method

We present simulation results for the phase behavior of a single chain for a flexible lattice polymer model using the Wang-Landau sampling idea. Applying this new algorithm to the problem of the homopolymer collapse allows us to investigate not only the high temperature coil–globule transition but also an ensuing crystallization at lower temperature. Performing a finite size scaling analysis on the two transitions, we show that they coincide for our model in the thermodynamic limit corresponding to a direct collapse of the random coil into the crystal without intermediate coil–globule transition. As a consequence, also the many chain phase diagram of this model can be predicted to consist only of gas and crystal phase in the limit of infinite chain length. This behavior is in agreement with findings on the phase behavior of hard-sphere systems with a relatively short-ranged attractive square well. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2542–2555, 2006     

Role of solvent for globular proteins in solution

The properties of the solvent affect the behavior of the solution. We propose a model that accounts for the contribution of the solvent free energy to the free energy of globular proteins in solution. For the case of an attractive square-well potential, we obtain an exact mapping of the phase diagram of this model without solvent to the model that includes the solute-solvent contribution. In particular we find for appropriate choices of parameters upper critical points, lower critical points, and even closed loops with both upper and lower critical points similar to those found before [Macromolecules 36, 5843 (2003)]. In the general case of systems whose interactions are not attractive square wells, this mapping procedure can be a first approximation to understand the phase diagram in the presence of solvent. We also present simulation results for both the square-well model and a modified Lennard-Jones model.     

Coarse-grained model for phospholipid/cholesterol bilayer

We construct a coarse-grained (CG) model for dipalmitoylphosphatidylcholine (DPPC)/cholesterol bilayers and apply it to large-scale simulation studies of lipid membranes. Our CG model is a two-dimensional representation of the membrane, where the individual lipid and sterol molecules are described by pointlike particles. The effective intermolecular interactions used in the model are systematically derived from detailed atomic-scale molecular dynamics simulations using the Inverse Monte Carlo technique, which guarantees that the radial distribution properties of the CG model are consistent with those given by the corresponding atomistic system. We find that the coarse-grained model for the DPPC/cholesterol bilayer is substantially more efficient than atomistic models, providing a speedup of approximately eight orders of magnitude. The results are in favor of formation of cholesterol-rich and cholesterol-poor domains at intermediate cholesterol concentrations, in agreement with the experimental phase diagram of the system. We also explore the limits of the coarse-grained model, and discuss the general validity and applicability of the present approach.     

Self-assembly of rod-coil block copolymers

We present a self-consistent field theory model for the self-assembly behavior of rod-coil block copolymers. The orientational interactions between the rods were modeled through a Maier-Saupe interaction, while the enthalpic interactions between rods and coils were modeled through a standard Flory-Huggins approach. We outline a "real-space" numerical approach to solve the self-consistent field equations for such rod-coil block copolymers. A major focus of our work is upon the nonlamellar phases observed in the experiments on such polymers. To develop a physical understanding of these phases and their regimes of occurrence, we compute the two-dimensional phase diagram for our model. The latter shows significant departures from the one-dimensional phase diagram, but matches qualitatively with the existing experimental results. We also present scaling arguments that rationalize the numerical results for the self-assembly behavior.     

On the mechanical properties and phase behavior of silica: a simple model based on low coordination and strong association

We present a simple and computationally efficient classical atomistic model of silica in which the silicon and oxygen are simulated as hard spheres with four and two association sites, respectively. We have performed isobaric-isothermal Monte Carlo simulations to study the mechanical and phase behavior of this model. We have investigated solid phase structures of the model corresponding to quartz, cristobalite, and coesite, as well as some zeolite structures. For the model these phases are mechanically stable and highly incompressible. Ratios of zero-pressure bulk moduli and thermal expansion coefficients for alpha quartz, alpha cristobalite, and coesite are in quite good agreement with experimental values. The pressure-temperature phase diagram was constructed and shows three solid phases corresponding to cristobalite, quartz, and coesite, as well as a fluid or glass phase, behavior qualitatively similar to that seen for silica experimentally.     

Depletion induced isotropic-isotropic phase separation in suspensions of rod-like colloids

When non-adsorbing polymers are added to an isotropic suspension of rod-like colloids, the colloids effectively attract each other via depletion forces. We performed Monte Carlo simulations to study the phase diagram of such rod-polymer mixture. The colloidal rods were modeled as hard spherocylinders; the polymers were described as spheres of the same diameter as the rods. The polymers may overlap with no energy cost, while the overlap of polymers and rods is forbidden. Large amounts of depletant cause phase separation of the mixture. We estimated the phase boundaries of isotropic-isotropic coexistence both in the bulk and in confinement. To determine the phase boundaries we applied the grand canonical ensemble using successive umbrella sampling [J. Chem. Phys. 120, 10925 (2004)], and we performed a finite size scaling analysis to estimate the location of the critical point. The results are compared with predictions of the free volume theory developed by Lekkerkerker and Stroobants [Nuovo Cimento D 16, 949 (1994)]. We also give estimates for the interfacial tension between the coexisting isotropic phases and analyze its power-law behavior on the approach of the critical point.     

Determination of fluid-phase behavior using transition-matrix Monte Carlo: binary Lennard-Jones mixtures

We present a novel computational methodology for determining fluid-phase equilibria in binary mixtures. The method is based on a combination of highly efficient transition-matrix Monte Carlo and histogram reweighting. In particular, a directed grand-canonical transition-matrix Monte Carlo scheme is used to calculate the particle-number probability distribution, after which histogram reweighting is used as a postprocessing procedure to determine the conditions of phase equilibria. To validate the methodology, we have applied it to a number of model binary Lennard-Jones systems known to exhibit nontrivial fluid-phase behavior. Although we have focused on monatomic fluids in this work, the method presented here is general and can be easily extended to more complex molecular fluids. Finally, an important feature of this method is the capability to predict the entire fluid-phase diagram of a binary mixture at fixed temperature in a single simulation.     

Study of percolation and clustering in supercritical water-CO2 mixtures

The microscopic structure of supercritical water-CO(2) mixture is investigated by neutron diffraction experiments exploiting the isotopic HD substitution. The investigated water reach mixtures are in the liquidlike region of the phase diagram, according to the behavior of the radial distribution functions, yet a reduction of the average number of hydrogen bonds, compared to equivalent states of pure water, is found. As a consequence, the average dimension of water clusters is reduced and the system stays below the percolation threshold. These results, along with the shift of the main peaks of the site-site radial distribution functions, suggest that the excess volume in these supercritical mixtures is likely associated with the CO(2) solvation shell.     

Coarse-grained polyethylene: 1. The simplest model for the orthorhombic crystal

The coarse-grained model of polyethylene and alkanes (the united-atom model, in which each CH₂ group is represented by a single bead) was proposed several decades ago. It is widely applied in molecular dynamics simulations. For different tasks, the models with different geometrical and force parameters are used. Until now, it was thought that the coarse-grained model of polyethylene cannot reproduce the orthorhombic crystalline phase, which is typical of this polymer. In the present study, we analyze the simplest coarse-grained model of polyethylene. In this model, the Lennard-Jones potential (6–12) is adopted for van der Waals interactions between the beads of different chains. Of the bonded interactions, only the “valence” bonds between beads and the “bond” and “torsion” angles are taken into account, whereas the cross terms between them are disregarded. We consider the model variation in which the bead (the force center with the mass of a CH₂ group) is displaced from the center of the carbon atom and all the interactions, both bonded and nonbonded, are defined by the positions of these beads. For this model, we find the area of geometrical parameters (the displacement value and the van der Waals radius of the bead) in which all the three known crystalline phases of polyethylene are at equilibrium at low temperatures. We choose the force field constants for the model so that its oscillation spectrum reproduces the low-frequency part of the inelastic neutron scattering spectrum of the orthorhombic polyethylene. It proved to be that this choice can be made unambiguously. We compare the dispersion curves in the terahertz range with experimental data on the Raman scattering and infrared spectroscopy, and discuss the advantages and disadvantages of the analyzed simplest coarse model.     

Phase coexistence in polydisperse athermal polymer-colloidal mixture

A theoretical scheme developed earlier [Y. V. Kalyuzhnyi et al., Chem. Phys. Lett. 443, 243 (2007)] is used to calculate the full phase diagram of polydisperse athermal polymer-colloidal mixture with polydispersity in both colloidal and polymeric components. In the limiting case of bidisperse polymer-colloidal mixture, theoretical results are compared against computer simulation results. We present the cloud and shadow curves, critical binodals, and distribution functions of the coexisting phases and discuss the effects of polydispersity on their behavior. According to our analysis polydispersity extends the region of the phase instability, shifting the critical point to the lower values of the pressure and density. For the high values of the pressure polydispersity causes strong fractionation effects, with the large size colloidal particles preferring the low-density shadow phase and long chain length polymeric particles preferring the high-density shadow phase.