New types of phase behaviour in binary mixtures of hard rod-like particles

The phase behaviour of binary mixtures of hard rod-like particles has been studied using Parsons—Lee theory (Parsons, J. D., 1979, Phys. Rev. A, 19, 1225); Lee, S. D., 1987, J. Chem. Phys., 87, 4972). The stability of the isotropic-nematic (I-N) transition with respect to isotropic—isotropic (I-I), and nematic—nematic (N-N) demixing is investigated. The individual components in the mixtures are modelled as hard cylinders of diameters D_i and lengths L_i (i = 1,2). The aspect ratios k_i = L_i/D_i of the components are kept fixed (with values of k ₁ = 15 and k ₂ = 150), and the phase behaviour of the mixtures is studied for varying diameter ratios d = D ₁/D ₂. When the diameter ratio is relatively large, e.g., for values of d = 50, component 1 may be considered a large colloidal particle, while the second component plays the role of a weakly interacting solvent. This mixture exhibits only an I-N phase transition which is driven by the excluded volume interaction between the large particles (no I-I or N-N demixing is seen). A decrease in the diameter ratio enhances the contribution of the smaller component to the free energy (especially in terms of the unlike excluded volume term), and I-I as well as N-N demixing transitions are observed. The character of the N-N transition is rather unusual, a single region bounded by a lower critical point (in the pressure—composition plane) is seen for a diameter ratio of d = 3.2, while two demixed nematic regions bounded by lower and upper critical points are observed for d = 3.13. A further decrease in the diameter ratio (e.g., to d = 3) leads to systems with a phase behaviour in which the two demixed N-N regions meet, giving rise to a large demixed region with very strong fractionation in composition, and no N-N critical points. The I-I demixing transition is always accompanied by a lower critical point and occurs for systems with intermediate size (diameter) ratios. A diameter ratio of d = 4.5 corresponds to systems with significant like and unlike excluded volume interactions, and in this case the I-N transition takes place over the whole composition range with weak fractionation and one azeotropic point. Surprisingly, the coexisting nematic phase is of lower packing fraction than the isotropic phase for some of the compositions, i.e., an inversion of packing fraction takes place. In addition to this, the longer rods can be less ordered that the shorter rods for certain values of the composition.     

Demixed and ordered phases in hard-rod mixtures

We analyse demixing and ordering transitions in systems of hard cylindrical particles. The second virial approximation of Onsager and a bifurcation analysis, as introduced by Koda and Kimura, are used to evaluate the free energies, pressures, and density distribution functions in mixtures of equally long but differently wide cylinders. The spatial density distribution along the one relevant coordinate is of particular importance as it provides more detailed information concerning the nature of the phase transition than the bare bifurcation diagnosis. Detailed results are given for the nematic–nematic spinodal and the nematic–smectic transitions. Allowing for the absence of an isotropic phase, our results are in good qualitative agreement with those for freely orienting rods reported previously, and indicate a complex sequence of phase diagrams as the diameter dissimilarity of the two components is increased, with upper and lower critical points bounding nematic and smectic demixing regions. However, experimental results on colloidal rods show that nematic demixing occurs at a diameter ratio much smaller than ours or those for freely rotating fluids, indicating that Onsager-type theories may be insufficient to reproduce this phenomenon in a quantitative manner and, consequently, that more sophisticated approaches, presumably incorporating particle flexibility and additional interactions, are required.     

Phase transitions in lyotropic nematic gels

In this paper, we discuss the equilibrium phases and collapse transitions of a lyotropic nematic gel immersed in an isotropic solvent. A nematic gel consists of a cross-linked polymer network with rod-like molecules embedded in it. Upon decreasing the quality of the solvent, we find that a lyotropic nematic gel undergoes a discontinuous volume change accompanied by an isotropic-nematic transition. We also present phase diagrams that these systems may exhibit. In particular, we show that coexistence of two isotropic phases, of two nematic phases, or of an isotropic and a nematic phase can occur. Received 15 February 2002 and Received in final form 14 June 2002     

Demixing and nematic behaviour of oblate hard spherocylinders and hard spheres mixtures: Monte Carlo simulation and Parsons–Lee theory

Parsons–Lee approach is formulated for the isotropic–nematic transition in a binary mixture of oblate hard spherocylinders and hard spheres. Results for the phase coexistence and for the equation of state in both phases for fluids with different relative size and composition ranges are presented. The predicted behaviour is in agreement with Monte Carlo simulations in a qualitative fashion. The study serves to provide a rational view of how to control key aspects of the behaviour of these binary nematogenic colloidal systems. This behaviour can be tuned with an appropriate choice of the relative size and molar fractions of the depleting particles. In general, the mixture of discotic and spherical particles is stable against demixing up to very high packing fractions. We explore in detail the narrow geometrical range where demixing is predicted to be possible in the isotropic phase. The influence of molecular crowding effects on the stability of the mixture when spherical molecules are added to a system of discotic colloids is also studied.     

Liquid-crystalline phase behavior of a colloidal rod-plate mixture

The phase behavior of rod-plate mixtures was investigated using model systems containing unambiguously rod- and plate-shaped colloids. We find that the theoretically disputed biaxial nematic phase is unstable with respect to demixing into an isotropic and two uniaxial nematic phases. The phase behavior at very high densities is exceptionally rich and includes the coexistence of up to four different liquid crystalline phases, which stem from the coupling between the employed particle shapes and polydispersity.     

Turbulence temperature spectra: Scaling theory

Grand canonical Monte Carlo, histogram reweighting and finite-size scaling methods are used to determine the phase transitions of bulk (three-dimensional) and confined (quasi-two-dimensional) neutral colloid–polymer systems. The colloids are modeled as hard spheres and the polymer molecules as hard chains, and the only attractive forces are effective ones induced by depletion effects. In contrast to the predictions of mean field and other approximate theories, the nature of the coexistence phases is found to not depend solely on the polymer-to-colloid size ratio, q, but on the colloid diameter, the polymer radius of gyration, and the polymer monomer size. The threshold values of q for the onset of liquid–liquid phase separation differ significantly from earlier predictions, and depend strongly on the dimensionality of space. Extrapolation to the “protein limit” of very small colloid and very long polymer indicates that immiscibility persists at this limit in three dimensions, while it does not always do so for confined systems.     

Demixing of amphiphile–polymer mixtures investigated using density functional theory

We construct a functional for amphiphile–polymer mixtures and investigate the demixing transition by using a proposed version of density functional theory. It is found that increase of the amphiphilic size ratio and polymer length can effectively promote phase separation of the systems. Phase diagrams are plotted to clarify these influences. The results provide an effective way of controlling the stability of the fluid–fluid phase equilibrium of the mixtures.     

Morphology and Formation Mechanism of Poly(Vinylidene Fluoride) Membranes Prepared with Immerse Precipitation: Effect of Dissolving Temperature

Poly(vinylidene fluoride) (PVDF) membranes were prepared by the immersion precipitation method. The effects of polymer dissolving temperature for the dopes on the morphology, crystallization and performance of prepared membranes were examined. Polymer dissolving temperature was varied from 50 to 120°C. N,N-dimethylacetamide (DMAc) and de-ionized water were used as solvent and non-solvent, respectively. Based on the membrane morphology and the schematic phase diagram of the ternary system, the membrane formation mechanism was analyzed theoretically. The binodal liquid-liquid demixing took place first for the nucleation and growth of droplets in the polymer poor phase; then consequently the spinodal liquid-liquid demixing occurred in the polymer rich phase. The demixings together resulted in the prepared membranes having a cross-section composed of interconnected globule-like particulates with bi-continuous structured surfaces. The dissolving temperature of the dopes had a remarkable effect on the morphology of the cross-section, even when the solution underwent a long time cooling before the demixing. The increase of the diameter of the particulates with the dissolving temperature was theoretically analyzed according to the conditions of the polymeric solution.     

Collapsed and Adsorbed States of a Directed Polymer Chain in Two Dimensions

A phase diagram for a surface-interacting long flexible partially-directed polymer chain in a two-dimensional poor solvent, where the possibility of collapse in the bulk exists, is determined using exact enumeration methods. We used a model of self-attracting self-avoiding walks and evaluated 30 steps in series. An intermediate phase between the desorbed collapsed and adsorbed expanded phases, having the conformation of a surface-attached globule, is found. The four phases, viz ., (i) desorbed expanded (DE), (ii) desorbed collapsed (DC), (iii) adsorbed expanded (AE), (iv) surface-attached globule (SAG), are found to meet at a multicritical point. These features are in agreement with those of an isotropic (or non-directed) polymer chain.     

Temperature dependence of the field induced magnetization reorientation in dzialoshinsky-moriya type weak ferromagnets

Using a Hamiltonian consisting of isotropic, anisotropic, and antisymmetric exchange terms plus a Zeeman term, the temperature dependence of the weak ferromagnetic-spin-flop phase transition is calculated in the molecuar field approximation. For all temperatures less than the tricritical one, the phase transition is of first order. The stability limits of the two phases and the thermodynamic phase boundary are calculated for this temperature region. For temperatures greater than the tricritical one, the second order transition boundary between the phases is calculated. A set of equations precisely defining the tricritical point in the field-temperature plane is derived and results are presented for the location of this point as a function of the parameters of the system. The methods developed in this work are general and can be applied directly to similar problems.     

Elusiveness of fluid-fluid demixing in additive hard-core mixtures

The conjecture that when an additive hard-core mixture phase separates when one of the phases is spatially ordered, well supported by considerable evidence, is in contradiction with some simulations of a binary mixture of hard cubes on cubic lattices. By extending Rosenfeld's fundamental measure theory to lattice models we show that the phase behavior of this mixture is far more complex than simulations show, exhibiting regions of stability of several smectic, columnar, and solid phases, but no fluid-fluid demixing. A comparison with the simulations show that they are, in fact, compatible with a fluid-columnar demixing transition, thus bringing this model into the same demixing scheme as the rest of additive hard-core mixtures.     

Phase diagram of transitions from an isotropic phase to nematic and smectic (uniaxial,biaxial) phases in liquid crystals with achiral molecules

The phase diagrams of transitions from an isotropic phase to nematic and smectic phases are investigated within a simple phenomenological model of the Landau thermodynamic potential. The conditions of the isomorphic phase transition between two uniaxial smectic phases and the direct transition from the isotropic phase to the uniaxial and biaxial smectic phases are determined. The behavior of the order parameters is described along different thermodynamic paths. The theoretical results are discussed using the example of liquid-crystal phases in compounds with banana-shaped achiral molecules.     

Anomalous dielectric behavior in the nematic and isotropic phases of a strongly polar–weakly polar binary system

We report permittivity studies in the isotropic liquid and anisotropic liquid crystalline (nematic or N) phases of a binary system, in which one component has molecules with a strongly polar longitudinal group, and the other has a weakly polar transverse group. The dielectric constant in the isotropic phase as well as its anisotropy in the N phase show, surprisingly, an anomalous non-monotonic dependence with concentration having a peak-like behavior for 10.2 mol% concentration of the weakly polar constituent. The transition between the two phases, being weakly first order, exhibits pretransitional effects signifying the appearance of the N-like regions in the isotropic phase. The coordinates of the maximum point of the convex shaped temperature-dependence of the dielectric constant in the isotropic phase, characteristic of strongly polar systems, also exhibit a non-monotonic dependence with concentration. Possible causes for these observations are discussed.     

Life at ultralow interfacial tension: wetting, waves and droplets in demixed colloid-polymer mixtures

Mixtures of colloids and polymers display a rich phase behavior, involving colloidal gas (rich in polymer, poor in colloid), colloidal liquid (poor in polymer, rich in colloid) and colloidal crystal phases (poor in polymer, highly ordered colloids). Recently, the colloidal gas-colloidal liquid interface received considerable attention as well. Due to the colloidal length scale the interfacial tension is much lower than in the atomic or molecular analog (nN/m instead of mN/m). This ultra-low interfacial tension has pronounced effects on the kinetics of phase separation, the colloidal gas-liquid profile near a single wall and the thermally induced fluctuations of the interface. The amplitudes of these thermally excited capillary waves are restrained by the interfacial tension and are for that reason of the order of the particle diameter. Therefore, in molecular systems, the capillary waves can only be seen indirectly in scattering experiments. In colloidal systems, however, the wave amplitudes are on a (sub) micrometer scale. This fact enables the direct observation of capillary waves in both real space and real time using confocal scanning laser microscopy. Moreover, the real space technique enables us to demonstrate the strong influence of interface fluctuations on droplet coalescence and droplet break up.     

Free energy of semiflexible polymers and structure of interfaces

The free energy of semiflexible polymers is calculated as a functional of the compositional scalar order parameter and the orientational order parameter of second-rank tensor S_ij on the basis of a microscopic model of wormlike chains with variable segment lengths. We use a density functional theory and a gradient expansion to evaluate the entropic part of the free energy, which is given in a power series of .The interaction term of the free energy is derived with a random phase approximation. For the rigid rod limit, the nematic-isotropic transition point is given by , N and w being the degree of polymerization and the anisotropic interaction parameter, respectively, and the degree of ordering at the transition point is 0.33448. We also find that the contour length of polymer chains becomes larger in a nematic phase than in an isotropic phase. Interface profiles are obtained numerically for some typical cases. In the neighborhood of isotropic-isotropic interfaces, polymer chains tend to align parallel to the interface on the polymer-rich side and perpendicular on the poor side. When an isotropic region and a nematic region coexist, orientational order parallel to the interface is preferred in the nematic region. Received: 28 May 1998 / Revised: 12 August 1998 / Accepted: 8 September 1998     

Entropy-driven triple point wetting in hard-rod mixtures

We theoretically study binary mixtures of thin and thick hard rods with diameter ratio more extreme than 1:4. The bulk phase diagram of these systems exhibits a triple point, where an isotropic (I) phase coexists with two nematic phases ( N1 and N2) of different composition. Using density functional theory, we predict that the I-N2 interface is completely wet by N1 upon approach of the the I-N1-N2 triple point. This entropic triple point wetting should be experimentally observable in colloidal suspensions of rodlike particles.     

Quantum criticality between topological and band insulators in 3+1 dimensions

Four-component massive and massless Dirac fermions in the presence of long range Coulomb interaction and chemical potential disorder exhibit striking fermionic quantum criticality. For an odd number of flavors of Dirac fermions, the sign of the Dirac mass distinguishes the topological and the trivial band insulator phases, and the gapless semimetallic phase corresponds to the quantum critical point that separates the two. Up to a critical strength of disorder, the semimetallic phase remains stable, and the universality class of the direct phase transition between two insulating phases is unchanged. Beyond the critical strength of disorder the semimetallic phase undergoes a phase transition into a disorder controlled diffusive metallic phase, and there is no longer a direct phase transition between the two types of insulating phases.     

Isotropic to nematic liquid crystalline phase transition of F-actin varies from continuous to first order

We report that the properties of the isotropic to nematic liquid crystalline phase transition of F-actin depend critically on the average filament length. For average filament lengths longer than 2 microm, we confirm previous findings that the phase transition is continuous in both alignment and concentration. For average filament lengths shorter than 2 microm, we show for the first time a first order transition with a clear discontinuity in both alignment and concentration. Tactoidal droplets of coexisting isotropic and nematic phases, differing in concentration by approximately 30%, form over the course of hours and appear to settle into near equilibrium metastable states.     

Morphology,Crystallization and Formation Mechanism of Poly(Vinylidene Fluoride) Membranes Prepared with Immersion Precipitation: Effect of Maturation Time

Poly(vinylidene fluoride) (PVDF) membranes were prepared by the immersion precipitation method. Effects of the maturation time of dopes on the morphology and crystallization of the prepared membranes were investigated. The analysis showed that the maturation time played an important role in determining the morphology of the prepared membranes. For the dope prepared in the initial day, liquid–liquid demixing preceded solid–liquid demixing in the process of the membrane formation. The morphology of the cross section of the prepared membrane (M1) was finger-like structures with a sponge substrate beneath the porous skin. During the maturation, the dopes underwent a microscopic phase separation and the PVDF crystallized, which resulted in the existence of micro-liquid phases and micro-solid phase crystalline areas in the dopes. In the process of the membrane formation, liquid–liquid demixing took place by nucleation and growth of droplets of the polymer rich phase in the micro-liquid phase. The micro-solid phase crystallites were connected together by the polymer chains, and formed a three-dimensional network gelation morphology. The crystal structure of M1 was mainly β crystals. With increasing maturation time of the dopes, the proportion of β decreased crystals, but that of α crystals increased for the prepared membranes.