The phase behavior of two-dimensional symmetrical mixtures

Using Monte Carlo simulation methods in the grand canonical and semigrand canonical ensembles, we study the phase behavior of two-dimensional symmetrical binary mixtures of Lennard-Jones particles. We discuss the interplay between the demixing transition in a liquid and the freezing in detail. Phase diagrams for several systems characterized by different parameters describing interactions in the system are presented. It is explicitly demonstrated that different scenarios involving demixing and freezing transitions, described in our earlier paper [A. Patrykiejew and S. Soko?owski, Phys. Rev. E, 81, 012501 (2010)], are possible. In one class of systems, the λ-line representing a continuous demixing transition in a liquid phase starts at the liquid side of either the vapor-liquid or liquid-solid coexistence. The second class involves the systems in which the λ-line begins at the liquid side of the vapor-liquid coexistence, in the lower critical end point, and then terminates at the liquid side of the liquid-solid coexistence, in the upper critical end point. It is also shown that in such systems the solid phase may undergo a demixing transition at the temperature above the upper critical end point.     

Effect of external field on phase behavior of ternary systems involving polypeptide

Phase behavior of ternary systems comprising arigid-rod polymer, a randomly coiled polymer, and asolvent was first studied by Flory on the basis of thelattice model[1]. According to the theory, above a criti-cal polymer concentration the ternary solution …     

Complete phase behavior of the symmetrical colloidal electrolyte

We computed the complete phase diagram of the symmetrical colloidal electrolyte by means of Monte Carlo simulations. Thermodynamic integration, together with the Einstein-crystal method, and Gibbs-Duhem integration were used to calculate the equilibrium phase behavior. The system was modeled via the linear screening theory, where the electrostatic interactions are screened by the presence of salt in the medium, characterized by the inverse Debye length, kappa (in this work kappasigma=6). Our results show that at high temperature, the hard-sphere picture is recovered, i.e., the liquid crystallizes into a fcc crystal that does not exhibit charge ordering. In the low temperature region, the liquid freezes into a CsCl structure because charge correlations enhance the pairing between oppositely charged colloids, making the liquid-gas transition metastable with respect to crystallization. Upon increasing density, the CsCl solid transforms into a CuAu-like crystal and this one, in turn, transforms into a tetragonal ordered crystal near close packing. Finally, we have studied the ordered-disordered transitions finding three triple points where the phases in coexistence are liquid-CsCl-disordered fcc, CsCl-CuAu-disordered fcc, and CuAu-tetragonal-disordered fcc.     

Supramolecular control of two-dimensional phase behavior

We have used directed two-component self-assembly to "pattern" organic monolayers on the nanometer scale at the liquid/solid interface. The ability of the scanning tunneling microscope to investigate structural details in these adlayers was used to gain insight into the two-component two-dimensional phase behavior. The components are symmetrically alkylated bisurea derivatives (R1-urea-spacer-urea-R2; R1, R2=alkyl, spacer=alkyl or bisthiophene). The bisthiophene unit acts as a marker and its bisurea derivative (T2) is a component in all the mixtures investigated. By varying the position of the hydrogen-bond forming urea groups along the molecule and the length of the alkyl chains of the other components, the effect of 1) hydrogen bonding, 2) molecule length, 3) odd-even effects, and 4) shape complementarity on the two-dimensional phase behavior was investigated. Insight into the effect of these parameters leads to the control of the two-dimensional patterning: from randomly intermixed systems to phase separation.     

Electric field dependence of lower critical phase separation behavior in polymer–polymer mixtures

The electric field dependence of the cloud point temperature of a poly(vinyl methyl ether)–polystyrene mixture has been experimentally measured in a laser light scattering experiment. It is found that the cloud point temperature is depressed linearly with the square of the applied electric field. A thermodynamic derivation of the electric field dependence of the spinodal temperature for polymer–polymer mixtures is also presented. A large disagreement between the experimental and theoretical findings is noted and possible explanations for this discrepancy are discussed.     

Three-dimensional square water in the presence of an external electric field

In this work we study a tridimensional statistical model for the hydrogen-bond (HB) network formed in liquid water in the presence of an external electric field. This model is analogous to the so-called square water, whose ground state gives a good estimate for the residual entropy of the ice. In our case, each water molecule occupies one site of a cubic lattice, and no hole is allowed. The hydrogen atoms of water molecules are disposed at the lines connecting nearest-neighbor sites, in a way that each water can be found in 15 different states. We say that there is a hydrogen bond between two neighboring molecules when only one hydrogen is in the line connecting both molecules. Through Monte Carlo simulations with Metropolis and entropic sampling algorithms, and by exact calculations for small lattices, we determined the dependence of the number of molecules aligned to the field and the number of hydrogen bonds per molecule as a function of temperature and the intensity of the external field. The results for both approaches showed that, different of the two-dimensional case, there is no maximum in the number of HBs as a function of the electric field. However, we observed nonmonotonic behaviors as a function of the temperature of the quantities of interest. We also found the dependence of the entropy on the external electric field at very low temperatures. In this case, the entropy vanishes for the value of the external field for which the contributions to the total energy coming from the HBs and the field become the same.     

Stark and field-born resonances of an open square well in a static external electric field

The resonance positions, widths (inverse lifetimes), and wave functions of a square-potential well in the presence of a static electric field are calculated by using the outgoing boundary conditions. Our study concentrates on the field-born states that, unlike the well-known Stark resonances, are not associated with the field-free bound states. The effect of a lower cutoff of the static field on the field-born resonance phenomena is studied. The feasibility of experiments, where the isolated long-lived and overlapping short-lived field-born resonances can be explored, is discussed.     

Theory of a helicoidal cholesteric phase induced by an external field

We present a mean field theory to describe a helicoidal cholesteric phase for mixtures of a chiral nematic liquid crystal (LC) and a polymer chain as well as for pure chiral nematic LC molecules in the presence of a longitudinal external field parallel to the pitch axis of a cholesteric (Ch) phase. The free energy of the helicoidal Ch phase (Ch_H) is derived as a function of a usual orientational order parameter and an order parameter of the Ch_H phase. On increasing the strength of the external field, we find that the Ch phase changes to the nematic (N) phase through the Ch_H phase. Depending on the temperature and the strength of the external field, we find the second-order N–Ch_H and Ch_H–Ch phase transitions and the first-order paranematic (pN)–N, pN–Ch_H and pN–Ch phase transitions. We also predict phase diagrams in mixtures of a flexible polymer and a Ch LC molecule under the external field.     

Effect of external electrical field on phase behavior and morphology development of polymer dispersed liquid crystal

Phase diagrams for mixtures of liquid crystal (LC)/monomer with and without an external electrical field applied have been established using polarized light microscope (PLM).The (isotropic + nematic) coexistent phase region and (isotropic + isotropic) phase boundary of LC/monomer mixtures were observed to shift upward to higher temperatures when the external electrical field exists. It was found that the electrical field applied during the cross-linking polymerization has a significant influence on the phase diagrams for the LC/polymer mixtures by rendering the coexistent phase regions shift upward to higher temperatures. The influence of the external electrical field on the processes of the isotropic-isotropic phase separation and liquid crystal ordering in PDLC formation has also been investigated. The results revealed that both the processes could be highly accelerated by the electrical field.     

The formation of interpolymer complexes in mixtures of weak polyelectrolytes

How the specific features of the formation of interpolymer complexes in nonstoichiometric mixtures of weak and strong polyelectrolytes depend on their concentrations, their degrees of polymerization, the polyelectrolyte weakness, and the low-molecular-mass salt concentration were investigated. Theoretical results are in qualitative accordance with experimental data.     

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.     

Molecular modeling of phase behavior and microstructure of acetone-chloroform-methanol binary mixtures

Force fields based on a Lennard-Jones (LJ) 12-6 plus point charge functional form are developed for acetone and chloroform specifically to reproduce the minimum pressure azeotropy found experimentally in this system. Point charges are determined from a CHELPG population analysis performed on an acetone-chloroform dimer. The required electrostatic surface for this dimer is determined from ab initio calculations performed with MP2 theory and the 6-31g++(3df,3pd) basis set. LJ parameters are then optimized such that the liquid-vapor coexistence curve, critical parameters, and vapor pressures are well reproduced by simulation. Histogram-reweighting Monte Carlo simulations in the grand canonical ensemble are used to determine the phase diagrams for the binary mixtures acetone-chloroform, acetone-methanol, and chloroform-methanol. The force fields developed in this work reproduce the minimum pressure azeotrope in the acetone-chloroform mixture found in experiment. The predicted azeotropic composition of x(CHCl3) = 0.77 is in fair agreement with the experimental value of x(CHCl3)expt = 0.64. The new force fields were also found to provide improved predictions of the pressure-composition behavior of acetone-methanol and chloroform-methanol when compared to other force fields commonly used for vapor-liquid equilibria calculations. NPT simulations were conducted at 300 K and 1 bar for equimolar mixtures of acetone-chloroform, acetone-methanol, and methanol-chloroform. Analysis of the microstructure reveals significant hydrogen bonding occurring between acetone and chloroform. Limited interspecies hydrogen bonding was found in the acetone-methanol or chloroform-methanol mixtures.     

Effects of colloid polydispersity on the phase behavior of colloid-polymer mixtures

We study theoretically the equilibrium phase behavior of a mixture of polydisperse hard-sphere colloids and monodisperse polymers, modeled using the Asakura-Oosawa model [S. Asakura and F. Oosawa, J. Chem. Phys. 22, 1255 (1954)] within the free volume approximation of H. N. W. Lekkerkerker, W. C. K. Poon, P. N. Pusey, A. Stroobants, and P. B. Warren [Europhys. Lett. 20, 559 (1992)]. We compute full phase diagrams in the plane of colloid and polymer volume fractions, using the moment free energy method. The intricate features of phase separation in pure polydisperse colloids combine with the appearance of polymer-induced gas-liquid coexistence to give a rich variety of phase diagram topologies as the polymer-colloid size ratio xi and the colloid polydispersity delta are varied. Quantitatively, we find that polydispersity disfavors fluid-solid against gas-liquid separation, causing a substantial lowering of the threshold value xi(c) above which stable two-phase gas-liquid coexistence appears. Phase splits involving two or more solids can occur already at low colloid concentration, where they may be kinetically accessible. We also analyze the strength of colloidal size fractionation. When a solid phase separates from a fluid, its polydispersity is reduced most strongly if the phase separation takes place at low colloid concentration and high polymer concentration, in agreement with experimental observations. For fractionation in gas-liquid coexistence we likewise find good agreement with experiment, as well as with perturbative theories for near-monodisperse systems.     

Added surfactant can change the phase behavior of aqueous polymer-particle mixtures

The phase behavior of aqueous mixtures of the "clouding" polymer ethyl(hydroxyethyl)cellulose (EHEC) mixed with colloidal particles and surfactants has been studied. These types of mixtures are important in many technical formulations. Two types of particles, polystyrene latex and silica, and two types of EHEC, nonmodified EHEC (N-EHEC) and hydrophobically modified EHEC (HM-EHEC), were studied. The EHECs adsorb to both kinds of particles. Both the amount and the type of added surfactant were seen to dramatically influence the partitioning of the particles between the EHEC-rich and EHEC-poor phases of phase-separated mixtures (above the cloud point temperature). Surfactants that are known not to associate with the EHEC backbone, that is, nonionic surfactants and short-chain cationic surfactants, changed the interaction between EHEC and the colloidal particles from attraction to repulsion above a specific surfactant concentration, resulting in a change in the partitioning of the particles from the EHEC-rich to the EHEC-poor phase. No such particle inversion was observed for ionic surfactants that bind to the EHEC backbone. An analysis considering both the binding of surfactant to EHEC and the competitive adsorption of surfactant to the particle surfaces could rationalize all observations, including the large variations observed, among the studied mixtures, in the surfactant concentration required for particle inversion.     

Fluid phase separation inside a static periodic field: an effectively two-dimensional critical phenomenon

When a fluid with a bulk liquid-vapor critical point is placed inside a static external field with spatial periodic oscillations in one direction, a new phase arises. This new phase-the so-called "zebra" phase-is characterized by an average density roughly between that of the liquid and vapor phases. The presence of the zebra phase gives rise to two new phase transitions: one from the vapor to the zebra phase, and one from the zebra to the liquid phase. At appropriate values of the temperature and chemical potential, the latter two transitions become critical. This phenomenon is called laser-induced condensation [I. O. Go?tze, J. M. Brader, M. Schmidt, and H. Lo?wen, Mol. Phys. 101, 1651 (2003)]. The purpose of this paper is to elucidate the nature of the critical points, using density functional theory and computer simulation of a colloid-polymer mixture. The main finding is that critical correlations develop in two-dimensional sheets perpendicular to the field direction, but not in the direction along the field: the critical correlations are thus effectively two-dimensional. Hence, static periodic fields provide a means to confine a fluid to effectively two dimensions. Away from criticality, the vapor-zebra and liquid-zebra transitions become first-order, but the associated surface tensions are extremely small. The consequences of the extremely small surface tensions on the nature of the two-phase coexistence regions are analyzed in detail.     

Systematic investigation of global phase behavior of polymer mixtures in the pressure-temperature plane

We investigate the critical lines of polymer mixtures in the presence of their vapor phase at the mathematical double point, where two critical lines meet and exchange branches, and its environment. The model used combines the lattice gas model of Schouten, ten Seldam and Trappeniers with the Flory-Huggins theory. The critical line structure is displayed for various combinations of the chain length and system parameters in the pressure (P)-temperature (T) plane, as is usually done with experimental results. This type of work sheds light on the essential transition mechanism involved in the phase diagram's change of character, such as multi-critical points and mathematical double points, which are of great practical importance in supercritical fluid extraction processes. The P, T diagrams are discussed in accordance with the Scott and van Konynenburg binary phase diagram classification. We found that our P, T plots were in agreement with type II, type III, or type IV phase diagram behaviors. We also found that some of our phase diagrams represent the liquid-liquid equilibria in polymer solutions and mixtures.     

Investigation of the global phase behavior of polymer mixtures in the shield region

This paper is a contribution of our systematic investigation of the global phase behaviors of the chain molecules mixtures, i.e., polymer mixture solutions. The phase behavior of fluid mixtures is understood by the critical lines in fluid-gas diagrams. The critical lines of binary fluid system may, under circumstances, exhibit closed loops in the critical lines. A distinction is made between free critical loops, as described by type VI in the Scott and van Konynenburg classification, and "rooted" critical loops, as found in the shield region. We define rooted loops as closed critical lines that are attached to the critical line structure by means of unstable critical line. We obtain the rooted loops in the global phase diagrams of the polymer mixture solutions within the framework of a model that combines the lattice gas model of Schouten, ten Seldam and Trappeniers with the Flory-Huggins theory, and we present the influence of the chain length of long molecules on the rooted critical loops. We present the results in the density-density and the temperature (T)-pressure (P) planes in detail.     

Monolayer,bilayer, multilayers: evolving magnetic behavior in Langmuir-Blodgett films containing a two-dimensional iron-nickel cyanide square grid network

The assembly of two-dimensional cyanide-bridged Fe(III)-Ni(II) square grid networks at the air-water interface and subsequent transfer of these networks as isolated monolayer, isolated bilayer, and multiple bilayer (multilayer) films via the Langmuir-Blodgett technique results in novel low-dimensional systems in which the effects of dimensionality on magnetic behavior in molecule-based materials can be observed. The magnetic response of these films between 2 < T < 300 K in dc fields from -50 < H < 50 kG and in 4 G ac fields from 1 Hz to 1 kHz are reported. The results show the presence of ferromagnetic domains with characteristic hysteresis in each of the three systems. The magnetic response for all three samples is anisotropic with a stronger field-cooled magnetization observed when the planes of the films are aligned parallel to the applied field. Additionally, each of the three samples shows frequency dependence in both the real and imaginary components of the ac susceptibility. This behavior is interpreted as being characteristic of spin glass-type ordering of ferromagnetic domains to form a cluster glass. A lower glass temperature (T(g)) is observed in the isolated monolayer film relative to the bilayer and multilayer samples. The bilayer sample shows two glass transitions at T(g1) = 3.8 K and T(g2) = 5.4 K, whereas only one transition at T(g) = 5.4 K is observed in the multilayer sample. The different magnetic responses of the three films are attributed to different in-plane, interplane, and long-range dipolar exchange interactions.     

Unusual phase behavior of decane-dodecane mixtures confined in SBA-15:Size effect on binary phase diagram

Phase behavior of normal decane-dodecane(n-C₁₀H₂₂-C₁₂H₂₆,C₁₀-C₁₂) system confined in SBA-15（Santa Barbara Amorphous,pore diameters 3.8,7.8,and 17.2 nm） has been studied by using differential scanning calorimetry.It has been found solid-liquid phase diagram of the C₁₀-C₁₂/SBA-15 system is composed of a straight line（3.8 nm）,a curve（7.8 nm） and a loop line （17.2 nm）.The growth of the phase diagram clearly shows the size effect on phase behavior of binary alkanes.Phase behavior has been compared among the systems C₁₀H₂₂-C₁₂H₂₆/SBA-15,C₁₂H₂₆-C₁₄H₃₀/SBA-15 and C₁₄H₃₀-C₁₆H₃₄/SBA-15.