Phase behavior of polymer mixtures with nonadditive hard-sphere potential

The phase behavior of a binary mixture of homopolymers in which macromolecules are composed of tangent hard spheres was studied. The interaction of unlike units is characterized by the contact distance (1/2)(σ_A + σ_B)(1 + Δ), where σ _i is the diameter of the ith sphere (unit) and Δ is the nonadditivity parameter. The effect of nonadditivity was taken into account by means of the perturbation theory relative to the additive system (Δ = 0) considered earlier (Polymer Science, 47, 2146 (2005)) in terms of the Percus-Yevick approximation. The theoretical consideration presented is completely analytical. It was found that a polymer mixture experiences phase separation with an increase in pressure; the two-phase region extends with an increase in both the size ratio between the units α = σ_A/σ_B and the length of the chain per se. Closed phase diagrams were first predicted for athermal mixtures; such diagrams appear at Δ < 0 and certain values of α. It was shown that the thermodynamics of an incompressible mixture of hard-chain molecules at α = 1 follows the Flory-Huggins theory with the temperature-independent interaction parameter. Phase separation in polymer solutions with the nonadditive hard-sphere potential was also analyzed.     

Phase and interfacial behavior of partially miscible symmetric Lennard-Jones binary mixtures

We have carried out extensive equilibrium molecular-dynamics simulations to study quantitatively the topology of the temperature versus density phase diagrams and related interfacial phenomena in a partially miscible symmetric Lennard-Jones binary mixture. The topological features are studied as a function of miscibility parameter, alpha = epsilonAB/epsilonAA. Here epsilonAA = epsilonBB and epsilonAB stand for the parameters related to the attractive part of the intermolecular interactions for similar and dissimilar particles, respectively. When the miscibility varies in the range 0 < alpha < 1, a continuous critical line of consolute points Tcons(rho)--critical demixing transition line--appears. This line intersects the liquid-vapor coexistence curve at different positions depending on the values of alpha, yielding mainly three different topologies for the phase diagrams. These results are in qualitative agreement to those found previously for square-well and hard-core Yukawa binary mixtures. The main contributions of the present paper are (i) a quantitative analysis of the phase behavior and (ii) a detailed study of the liquid-liquid interfacial and liquid-vapor surface tensions, as function of temperature and miscibility as well as its relationship to the topological features of the phase diagrams.     

Phase behavior and rheological properties of DNA-cationic polysaccharide mixtures

Associative aqueous mixtures over a range of concentrations of double- (ds) or single- (ss) stranded DNA with dilute or semidilute solutions of two cationic derivatives of hydroxyethyl cellulose (cat-HEC and cat-HMHEC,(1) the latter carrying grafted hydrophobic groups), were studied. The phase behavior showed an interesting asymmetry: Phase separation occurred immediately when small (sub-stoichiometric) amounts of cationic polyelectrolyte were added to the DNA solution, but redissolution into a single cat-(HM)HEC/DNA/H(2)O phase occurred already with a modest charge excess of the cationic polyelectrolyte, at a charge ratio approximately independent of the overall polyelectrolyte concentration. Cat-HEC/dsDNA/H(2)O and cat-HEC/ssDNA/H(2)O systems presented a considerable difference in the extension of the phase separation region. The one-phase samples with excess cationic polyelectrolyte were studied by rheology. The presence of DNA strengthened the viscoelastic behavior of the solutions of the cationic polyelectrolytes, reflected in an increase in storage modulus and viscosity. Differences in phase behavior and rheology were observed, particularly between systems containing cat-HEC or cat-HMHEC, but also between dsDNA and ssDNA. Thus, these systems allow for the preparation of DNA formulations with widely variable rheology and water uptake.     

Phase behavior and interfacial properties of diblock copolymer-homopolymer ternary mixtures: Influence of volume fraction of copolymers and interaction energy

We use a Monte Carlo method to study the phase and interfacial behaviors of A-b-B diblocks in a blend of homopolymers, A and B, which are confined between two asymmetric hard and impenetrable walls. Our results show that, when the interaction strength is weak, the block copolymersare uniformly distributed in the ternary mixtures under considered concentrations. Under strong interaction strength, distribution region of the block copolymers changes from a single smooth interface to a curved interface or multi-layer interface in the ternary mixtures. Furthermore, our findings show that with increasing volume fraction of A-b-B diblock copolymer(фC), copolymer profiles broaden while фC≥ 0.4, a lamellar phase is formed and by further increasing фC, more thinner layers are observed. Moreover, the results show that, with the increase of фC, the phase interface first gradually transforms from plane to a curved surface rather than micelle or lamellar phase while with the increase of the interaction between A and B segments(ε_(AB)), the copolymer chains not only get stretched in the direction perpendicular to the interface, but also are oriented. The simulations also revealthat the difference between symmetric and asymmetric copolymers is negligible in statistics if the lengths of two blocksare comparable.     

Bulk and interfacial properties of binary polymer mixtures

A microscopic density functional theory is used to investigate a binary mixture of polymers, built of freely jointed tangent hard spheres. The difference in the chain length and in the segment diameter of polymers gives rise to a demixing transition. We evaluate the bulk fluid phase equilibria (binodal) and the limit of stability of a mixed state (spinodal) for selected systems, and analyze the decay of the critical packing fraction, critical mole fraction, and critical pressure with an increase of the chain length. The bulk results are subsequently used in the calculations of the density profiles across the fluid-fluid interface. The obtained profiles are smooth and do not exhibit any oscillations on the length scale of the segment diameter. Upon approaching the critical point the interfacial tension vanishes as (Deltarho)3, where Deltarho is the difference between bulk densities of one component in bulk phases rich and poor in that species. This indicates that the microscopic density functional theory applied here is of a mean-field type.     

Phase behavior and properties of reverse vesicles in salt-free catanionic surfactant mixtures

Salt-free 1:1 cationic/anionic (catanionic) surfactant mixture tetradecyltrimethylammonium laurate (TTAL) could be prepared by mixing equimolar tetradecyltrimethylammonium hydroxide (TTAOH) and lauric acid (LA) in water. Given the condition of suitable range of weight fraction of TTAL in total surfactant, rho=WTTAL/(WTTAL+WLA), and at existence of a small amount of water, it was found that the mixtures of so-obtained TTAL and LA could spontaneously form stable reverse vesicles in various organic solvents including toluene, tert-butylbenzene, and cyclohexane. The reverse vesicle phase shows a blue color against room light and exhibits strong birefringence under polarized microscope. The reverse vesicles are very sensitive to temperature change. Increasing temperature could make the rho values within which reverse vesicles were constructed move to higher values. In organic solvents of alkanes such as n-heptane, reverse vesicles could still form but become unstable upon time and centrifugation. Increasing temperature could accelerate phase separation, and finally a gel-like bottom phase was usually observed. Interestingly, the stable reverse vesicles formed by so-called salt-free catanionic surfactant mixtures still show some resistance against adding inorganic salts. They can trap inorganic ions such as Zn2+ and S2- into their hydrophilic layers. This opens the door for template applications of reverse vesicles to prepare inorganic nanoparticles.     

Virial coefficients and demixing of athermal nonadditive mixtures

We compute the fourth virial coefficient of a binary nonadditive, hard-sphere mixture over a wide range of deviations from diameter additivity and size ratios. Hinging on this knowledge, we build up a y expansion (Barboy, B.; Gelbart, W. N. J. Chem. Phys. 1979, 71, 3053) in order to trace the fluid-fluid coexistence lines, which we then compare with the available Gibbs-ensemble Monte Carlo data and with the estimates obtained through two refined integral-equation theories of the fluid state. We find that in a regime of moderately negative nonadditivity and largely asymmetric diameters, relevant to the modeling of sterically and electrostatically stabilized colloidal mixtures, the fluid-fluid critical point is unstable with respect to crystallization.     

Density-functional study of interfacial properties of colloid-polymer mixtures

Interfacial properties of colloid-polymer mixtures are examined within an effective one-component representation, where the polymer degrees of freedom are traced out, leaving a fluid of colloidal particles interacting via polymer-induced depletion forces. Restriction is made to zero-, one-, and two-body effective potentials, and a free energy functional is used that treats colloid excluded volume correlations within Rosenfeld's fundamental measure theory, and depletion-induced attraction within first-order perturbation theory. This functional allows a consistent treatment of both ideal and interacting polymers. The theory is applied to surface properties near a hard wall, to the depletion interaction between two walls, and to the fluid-fluid interface of demixed colloid-polymer mixtures. The results of the present theory compare well with predictions of a fully two-component representation of mixtures of colloids and ideal polymers (the Asakura-Oosawa model) and allow a systematic investigation of the effects of polymer-polymer interactions on interfacial properties. In particular, the wall surface tension is found to be significantly larger for interacting than for ideal polymers, whereas the opposite trend is predicted for the fluid-fluid interfacial tension.     

Phase behavior and interfacial properties of symmetric polymeric ternary blends A/B/AB

In this paper, the phase behavior and interfacial properties of symmetric ternary polymeric blends A/B/AB are studied by dissipative particle dynamics (DPD) simulations. By using the structure factor and nematic order parameter, we carefully characterized the diversified phases and phase transitions, and established the phase diagram of such symmetric ternary blends. It can be generally divided into four regions: disordered phase (DIS) region at high temperature, ordered lamellar phase (LAM) region, bicontinuous microemulsion (BµE) channel and phase-separated phase (2P) region at low temperature with the increase of the total volume fractions of homopolymers Φ _H, which shows good accordance with that in previous experimental and theoretical reports. Furthermore, we calculated the elastic constants of 2P and LAM phase, and discussed the transition mechanisms from 2P and LAM to BμE phase, respectively. The results show a direct relevance between the phase transitions and the change of interfacial properties. Finally, we also demonstrate that the BμE channel becomes narrower in lower temperature caused by the temperature dependence of interfacial properties of ternary blends.     

Equation of state of nonadditive d-dimensional hard-sphere mixtures

An equation of state for a multicomponent mixture of nonadditive hard spheres in d dimensions is proposed. It yields a rather simple density dependence and constitutes a natural extension of the equation of state for additive hard spheres proposed by us [A. Santos, S. B. Yuste, and M. Lopez de Haro, Mol. Phys. 96, 1 (1999)]. The proposal relies on the known exact second and third virial coefficients and requires as input the compressibility factor of the one-component system. A comparison is carried out both with another recent theoretical proposal based on a similar philosophy and with the available exact results and simulation data in d=1, 2, and 3. Good general agreement with the reported values of the virial coefficients and of the compressibility factor of binary mixtures is observed, especially for high asymmetries and/or positive nonadditivities.     

Phase behavior of carbon dioxide-aromatic hydrocarbon mixtures

Occhiogrosso, R.N., Igel, J.T. and McHugh, M.A., 1986. Phase behavior of carbon dioxide-aromatic hydrocarbon mixtures. Fluid Phase Equilibria, 26: 165–179.Vapor-liquid-equilibria experiments are conducted at 299.25, 305.65, 316.25, 338.35, 363.15, and 383.15 K and for pressures up to 175 bar for the CO₂-isopropyl benzene (cumene) system. Pressure-composition information is obtained. The resulting experimental data are modeled using the Peng-Robinson equation-of-state. Two temperature-independent model parameters, δ_ij, which accounts for molecular interactions between CO₂ and cumene, and η_ij, which accounts for the size difference between CO₂ and cumene, are used to obtain good agreement between calculated and experimental data.The results for the CO₂-cumene system are compared to the CO₂-toluene and CO₂-m-xylene systems which are available in the literature. The CO₂-toluene and CO₂-m-xylene systems can be modeled using the same δ_ij and η_ij values used for the CO₂-cumene system.     

Fourth virial coefficients of asymmetric nonadditive hard-disk mixtures

The fourth virial coefficient of asymmetric nonadditive binary mixtures of hard disks is computed with a standard Monte Carlo method. Wide ranges of size ratio (0.05 ≤ q ≤ 0.95) and nonadditivity (-0.5 ≤ Δ ≤ 0.5) are covered. A comparison is made between the numerical results and those that follow from some theoretical developments. The possible use of these data in the derivation of new equations of state for these mixtures is illustrated by considering a rescaled virial expansion truncated to fourth order. The numerical results obtained using this equation of state are compared with Monte Carlo simulation data in the case of a size ratio q = 0.7 and two nonadditivities Δ = ±0.2.     

Critical behavior and interfacial tension of mixtures of propylene glycol and ethylene glycol oligomers

This investigation presents an analysis of the critical behavior of mixtures of oligomers of propylene glycol, PG₁₇, and ethylene glycol, EG_n, withn=3, 4, 5, 6.4, 8.7, 12.1 and 22.1. The critical coordinates, _c andT _c were determined from the phase diagrams. The critical compositions compare very well with the Huggins-Flory predictions. The interaction parameter _n is around one for EG₃, EG₄ and EG₅ and it increases up to two for the higher oligomers. The break in the interaction parameter also corresponds to a minimum in the critical temperature. The phase diagrams and the interfacial tension were used to get the critical exponents and , respectively. The data were analysed with two approaches. First, from the temperature dependence of the length of the tie-lines and of the interfacial tension up to the upper critical solution temperature, UCST. Second, with the data at 30°C using the critical temperature of the systems as the variable. The first method led to =0.39±0.05 in good agreement with the result of the second method, =0.37±0.04. The exponents for the interfacial tension, , determined with the first method for PG₁₇ with EG_6.4, EG_8.7 and EG_12.1 are =1.66±0.11, 1.46±0.25 and 1.73±0.18, respectively. The second method led to =1.17±0.14. The critical exponents are compared to mean field and ising-3D predictions.     

Phase behavior of palmitic acid/cholesterol/cholesterol sulfate mixtures and properties of the derived liposomes

The phase behavior of mixtures formed by palmitic acid (PA), cholesterol (Chol), and sodium cholesteryl sulfate (Schol) has been characterized by differential scanning calorimetry and infrared and 2H NMR spectroscopy. It is reported that it is possible to form, with PA/sterol mixtures, fluid lamellar phases where the sterol content is very high (a sterol mole fraction of 0.7). As a consequence of the rigidifying ability of the sterols, the PA acyl chains are very ordered. The stability of these self-assembled bilayers is found to be pH-dependent. This property can be controlled by the Chol/Schol molar ratio, and it is proposed that this parameter modulates the balance between the intermolecular interactions between the constituting species. A phase-composition diagram summarizing the behavior of these mixtures as a function of pH, at room temperature, is presented. It is also shown that it is possible to produce large unilamellar vesicles (LUVs) from these mixtures, using standard extrusion techniques. The resulting LUVs display a very limited passive release of the entrapped material. In addition, these LUVs constitute a versatile vector for pH-triggered release.     

Phase behavior of diisobutyl adipate–carbon dioxide mixtures

Phase equilibrium data are reported for diisobutyl adipate (DiBA) in CO₂ at temperatures from 25 to 150 °C. This system exhibits a continuous mixture-critical curve with a maximum near 200 °C and 260 bar. The phase behavior of the DiBA–CO₂ system is well characterized and modeled with the Peng–Robinson equation of state using a single, fixed binary interaction parameter, k_ij. The DiBA–CO₂ data are compared to other solute–CO₂ systems with structures similar to DiBA to demonstrate the impact of the diester end groups in DiBA, which enhance DiBA solubility in CO₂ at low temperatures, relative to a single (ethyl laurate) or no ester end groups (tetradecane), and a single acid end group (tetradecanoic acid). DiBA–CO₂ data are also compared to data for two compounds each with diester groups but one containing an interior aromatic group (dibutyl phthalate) and the other containing the same number of interior carbon groups but with two less carbon groups at either end of the chain (divinyl adipate).     

Liquid-vapor interfacial properties of water-ammonia mixtures: dependence on ammonia concentration

The equilibrium and dynamical properties of the liquid-vapor interfaces of water-ammonia mixtures are investigated by means of molecular-dynamics simulations. Altogether, we have simulated seven different systems of different concentration of ammonia. The inhomogeneous density, anisotropic orientational profiles, surface tension, and the pattern of hydrogen bonding are calculated for both water and ammonia molecules in order to characterize the location, width, thermodynamic aspects, and microscopic structure of the liquid-vapor interfaces of each of the water-ammonia systems. The dynamical aspects of the interfaces are investigated in terms of the anisotropic diffusion and dipole orientational relaxation of water and ammonia molecules. The properties of the interfaces are compared with those of the corresponding bulk phases. The present theoretical results are also compared with experimental findings wherever available.     

Phase behavior in thin films of confined colloid-polymer mixtures

Using self-consistent-field and density-functional theories, we first investigate colloidal self-assembly of colloid-polymer films confined between two soft surfaces grafted by polymers. With increasing colloidal concentrations, the film undergoes a series of transitions from disordered liquid --> sparse square --> hexagonal (or mixed square-hexagonal) --> dense square --> cylindrical structures in a plane, which results from the competition between the entropic elasticity of polymer brushes and the steric packing effect of colloidal particles. A phase diagram displays the stable regions of different in-layer ordering structures as the colloidal concentration is varied and layering transitions as the polymer-grafted density is decreased. Our results show a new control mechanism to stabilize the ordering of structures within the films.     

Phase behavior of undecane-tetradecane mixtures confined in SBA-15

Phase behavior of undecane-tetradecane (n-C11H24-C14H30, C11-C14) mixtures in bulk and confined in SBA-15 have been studied using differential scanning calorimetry. The bulk C11-C14 system shows multiple phase regions due to rotator phase. Confined in the pores of SBA-15 (pore diameters 3.8-7.8 nm), the mixtures only show a melting boundary of a straight line and a curve, respectively. In SBA-15 (17.2 nm), phase behavior of themixtures has some similarity to that of the bulk. Under confinement, the phase diagrams of the mixtures vary with the pore size, temperature, and compositions.