Density-functional study of model bidisperse ferrocolloids in an external magnetic field

We present phase diagrams of a model bidisperse ferrocolloid consisting of a binary mixture of dipolar hard spheres (DHSs) under the influence of an external magnetic field. The dipole moments of the particles are chosen proportional to the particle volume to mimic real ferrocolloids, and we focus on dipole-dominated systems where isotropic attractive interactions are absent. Our results are based on density-functional theory in the modified mean-field (MMF) approximation. For one-component DHS fluids in external fields, and for corresponding mixtures dominated by one of the components, MMF theory predicts the tricritical point of the transition between an isotropic gas and a ferromagnetic liquid occurring at zero field to be changed into a critical point separating two magnetically ordered phases of different density. The corresponding critical temperature displays a nonmonotonic dependence on the field strength. Completely different behavior is found for the critical temperature related to the demixing phase transitions appearing in strongly asymmetric mixtures [G. M. Range and S. H. L. Klapp, Phys. Rev. E 70, 061407 (2004)]. For such systems, we find a monotonic decrease of the demixing critical temperature with increasing field. The field strength dependence of the critical temperature can therefore be tuned between nonmonotonic and monotonic behaviors just by changing the composition of the mixture--e.g., by adjusting the chemical potentials. This allows us to efficiently control the influence of external magnetic fields on the phase behavior over a large temperature interval.     

String formation and demixing in monolayers of dipolar colloidal mixtures

Employing hypernetted chain (HNC) integral equations and a stability analysis we investigate the structure and phase behavior of bidisperse mixtures of dipolar hard spheres with different size ratios s=σ(S)/σ(L) confined to a plane. The dipole moments of the particles are perfectly ordered along an in-plane direction, yielding anisotropic interactions favoring chain formation. Exploring a range of size ratios and compositions, our study predicts a complex interplay between aggregation phenomena, on the one hand, and volume phase transitions, on the other hand. In dilute, strongly asymmetric systems (s = 0.5), our HNC analysis indicates chain formation of the large particles, while the small particles act as a weakly correlated background. According to our fluctuation analysis, this aggregation behavior results in combined condensation-demixing transitions, with a trend towards pure demixing when the concentration of the large particles, c(L), becomes small. In dense systems, the most interesting results are found for intermediate size ratios, s ~ 0.7-0.8. Here we find signatures of a concentration-driven transition from pure chains of large particles (large c(L)) to mixed chains with alternating order of large and small particles (small c(L)). The two regimes are separated by a characteristic "jump" in the HNC non-solution line.     

Ordering transition and demixing of a binary mixture of thick and thin rodlike molecules in the presence of an external field

The effect of an external field (electric/magnetic) on the phase behavior of the binary mixture of very long thick and thin rodlike particles is studied. Both the thick and thin particles possess positive but different susceptibility anisotropics (Delta alpha). The difference in the extent of interaction between the external field and the two species is varied by means of a coupling parameter (l = Delta alpha(thick)/Delta alpha(thin)). Isotropic-nematic phase transition and demixing phase transitions taking place both in the isotropic and nematic phases are examined as a function of field strength on the level of the second virial theory of Onsager in the range of 0 < l <1. The approximate sixth order Legendre polynomial expansion method is used to represent the excluded volume interaction between the rodlike particles. It is found that the isotropic phase becomes weakly nematic (paranematic) in the presence of external field and the field orients both components in the direction of the field even if the field does not have direct interaction with the thick component (l = 0). Analytical expressions are derived for the external field induced order parameters and birefringence. The increasing field destabilizes both types of demixing transitions (isotropic-isotropic and nematic-nematic) and the paranematic-nematic phase transition. Moreover it induces closed loop immiscibility, and upper and lower critical points terminating the paranematic-nematic phase coexistence may occur for low values of the coupling parameter. It is interesting that while the phase boundaries of the paranematic-paranematic demixing and the paranematic-nematic transitions are very sensitive to the value of the coupling parameter at low pressures, the paranematic-nematic and nematic-nematic phase boundaries are practically independent of the coupling parameter at high pressures.     

Isotropic-nematic phase transition of nonaqueous suspensions of natural clay rods

A novel model system for studying the behavior of hard colloidal rods is presented, consisting of sterically stabilized particles of natural sepiolite clay. Electron microscopy and scattering results confirmed that the organophilic clay particles were individual, rigid rods when dispersed in organic solvents. With a length-to-diameter ratio of approximately 27, the particles showed nematic ordering for volume fractions phi > 0.06. Polarizing microscopy revealed that the phase separation process involved nucleation, growth, and coalescence of nematic domains. The phase volumes and particle concentrations in the coexisting phases were determined. The dependence of these quantities on the total concentration of the suspension agrees well with Onsager's [Ann. N. Y. Acad. Sci. 51, 627 (1949)] isotropic-nematic phase transition theory extended to bidisperse and polydisperse rod systems, and with previous experimental results for rigid rodlike particles. Particle size distributions were obtained by analyzing transmission electron microscopy images. A significant fractionation with respect to rod length (but not diameter) was observed in the coexisting isotropic and nematic phases. The relative polydispersity of both daughter phases was distinctly smaller than that of the parent suspension. The phase behavior of these daughter fractions agrees well with the predictions for hard spherocylinders of corresponding aspect ratios. An isotropic-nematic-nematic phase equilibrium was seen to develop in phase separated samples after 1 month standing and is ascribed to the effect of polydispersity and possibly gravity. The second nematic phase appearing is dominated by very long rods.     

Many body effects on the phase separation and structure of dense polymer-particle melts

Liquid state theory is employed to study phase transitions and structure of dense mixtures of hard nanoparticles and flexible chains (polymer nanocomposites). Calculations are performed for the first time over the entire compositional range from the polymer melt to the hard sphere fluid. The focus is on polymers that adsorb on nanoparticles. Many body correlation effects are fully accounted for in the determination of the spinodal phase separation instabilities. The nanoparticle volume fraction at demixing is determined as a function of interfacial cohesion strength (or inverse temperature) for several interaction ranges and nanoparticle sizes. Both upper and lower critical temperature demixing transitions are predicted, separated by a miscibility window. The phase diagrams are highly asymmetric, with the entropic depletion-like lower critical temperature occurring at a nanoparticle volume fraction of approximately 10%, and a bridging-induced upper critical temperature at approximately 95% filler loading. The phase boundaries are sensitive to both the spatial range of interfacial cohesion and nanoparticle size. Nonmonotonic variations of the bridging (polymer-particle complex formation) demixing boundary on attraction range are predicted. Moreover, phase separation due to many body bridging effects occurs for systems that are fully stable at a second order virial level. Real and Fourier space pair correlations are examined over the entire volume fraction regime with an emphasis on identifying strong correlation effects. Special attention is paid to the structure near phase separation and the minimum in the potential of mean force as the demixing boundaries are approached. The possibility that nonequilibrium kinetic gelation or nanoparticle cluster formation preempts equilibrium phase separation is discussed.     

Comparing the morphology and phase diagram of H-shaped ABC block copolymers and linear ABC block copolymers

By using a combinatorial screening method based on the self-consistent field theory (SCFT) for polymers, we have investigated the morphology of H-shaped ABC block copolymers (A2BC2) and compared them with those of the linear ABC block copolymers. By changing the ratios of the volume fractions of two A arms and two C arms, one can obtain block copolymers with different architectures ranging from linear block copolymer to H-shaped block copolymer. By systematically varying the volume fractions of block A, B, and C, the triangle phase diagrams of the H-shaped ABC block copolymer with equal interactions among the three species are constructed. In this study, we find four different morphologies (lamellar phase (LAM), hexagonal lattice phase (HEX), core-shell hexagonal lattice phase (CSH), and two interpenetrating tetragonal lattice (TET2)). Furthermore, the order-order transitions driven by architectural change are discussed.     

Theory of volume phase transitions of side-chain liquid crystalline gels

We present a mean field theory to describe volume phase transitions of side-chain liquid crystalline gels. Three different uniaxial nematic phases (N(1), N(2), and N(3)) are defined by using orientational order parameter S(m) of side-chain liquid crystals (mesogens) and S(b) of backbone chains. We derive the free energy for the three nematic phases of side-chain liquid crystalline gels dissolved in isotropic solvents and calculate the swelling curve of the gel, the order parameters of a backbone chain and of side-chain liquid crystals, and the deformation of the gel as a function of temperature and an electric field. We find isotropic-nematic (N(1), N(2), and N(3)) and N(1)N(2) phase transitions of the gels, depending on the interaction between a backbone chain and a side-chain liquid crystal.     

Crystal-liquid crystal binary phase diagrams

We propose a new theoretical scheme for the binary phase diagrams of crystal-liquid crystal mixtures by a combination of a phase field model of solidification, the Flory-Huggins theory for liquid-liquid mixing and Maier-Saupe-McMillan (FH-MSM) model for nematic and smectic liquid crystal orderings. The phase field theory describes the crystal phase transition of anisotropic organic crystal and/or side chain liquid crystalline polymer crystals while the FH-MSM model explains isotropic, nematic and smectic-A phase transitions. Self-consistent calculations reveal several possible phase diagram topologies of the binary crystal-liquid crystal mixtures. The calculated phase diagrams were found to accord well to the reported experimental results.     

Density functional theory of freezing of a system of conjugated oligomers parameterised via Gay–Berne potential

Density functional theory (DFT) of freezing is used to study the isotropic–nematic, isotropic–smectic A and nematic–smectic A phase transitions in a system of large, semi-flexible conjugated oligomers parameterised within Gay–Berne (GB) potential. The pair correlation functions of the isotropic fluid, used as structural inputs in the DFT, are calculated by solving the Percus–Yevick integral equation theory. Large number of spherical harmonic coefficients of each orientation-dependent functions has been considered to ensure the numerical accuracy at different densities and temperatures for the system of these model GB ellipsoids having large aspect ratio (length-to-breadth ratio). We found that the system of GB ellipsoids parameterised for conjugated oligomers shows stable isotropic, nematic and smectic A phases. At low temperatures, on increasing the density, isotropic fluid makes a direct transition to smectic A phase. Nematic phase get stabilised in between the isotropic and smectic A phases on increasing the temperature. Using the transition parameter obtained through the DFT, we have plotted the temperature–density and pressure–temperature phase diagrams which are found to be qualitatively similar to the one obtained in simulations for the systems with low aspect ratio GB particles.     

Phase behavior of binary symmetric mixtures in pillared slit-like pores: a density functional approach

Density functional approach is applied to study the phase behavior of symmetric binary Lennard-Jones(12,6) mixtures in pillared slit-like pores. Our focus is in the evaluation of the first-order phase transitions in adsorbed phases and lines delimiting mixed and demixed adsorbed phases. The scenario of phase changes is sensitive to the pore width, to the energy of fluid-solid interaction, the amount, and the length of the pillars. Quantitative trends and qualitative changes of the phase diagrams topology are examined depending on the values of these parameters. The presence of pillars provides additional excluded volume effects, besides the confinement due to the pore walls. The effects of attraction between fluid species and pillars counteract this additional confinement. We have observed that both the increasing surface pillar density and the augmenting strength of fluid-solid interactions can qualitatively change the phase diagrams topology for the model with sufficiently strong trends for demixing. If the length of pillars is sufficiently large comparing to the pore width at low temperatures, we observe additional phase transitions of the first and second order due to the symmetry breaking of the distribution of chain segments and fluid species with respect to the slit-like pore center. Re-entrant symmetry changes and additional critical points then are observed.     

Electrokinetic demixing of aqueous two-phase polymer/salt systems

Electrokinetic demixing of aqueous two-phase polymer/salt systems is demonstrated, resulting in significant enhancement in demixing rates by about 1-4-fold. The effect of field polarity, field strength, volume ratio, and phase composition on phase demixing has been studied. Further the influence of these parameters on phase demixing could be explained based on the hydrodynamic flow-electroosmotic flow (HEF) model.     

Orientational ordering in hard rectangles: The role of three-body correlations

We investigate the effect of three-body correlations on the phase behavior of hard rectangle two-dimensional fluids. The third virial coefficient B3 is incorporated via an equation of state that recovers scaled particle theory for parallel hard rectangles. This coefficient, a functional of the orientational distribution function, is calculated by Monte Carlo integration, using an accurate parametrized distribution function, for various particle aspect ratios in the range of 1-25. A bifurcation analysis of the free energy calculated from the obtained equation of state is applied to find the isotropic (I)-uniaxial nematic (N(u)) and isotropic-tetratic nematic (N(t)) spinodals and to study the order of these phase transitions. We find that the relative stability of the N(t) phase with respect to the isotropic phase is enhanced by the introduction of B3. Finally, we have calculated the complete phase diagram using a variational procedure and compared the results with those obtained from scaled particle theory and with Monte Carlo simulations carried out for hard rectangles with various aspect ratios. The predictions of our proposed equation of state as regards the transition densities between the isotropic and orientationally ordered phases for small aspect ratios are in fair agreement with simulations. Also, the critical aspect ratio below which the N(t) phase becomes stable is predicted to increase due to three-body correlations, although the corresponding value is underestimated with respect to simulation.     

Bidisperse electrorheological fluids using hydrolyzed styrene-acrylonitrile copolymer particles: synergistic effect of mixed particle size

Monodisperse micron-sized styrene-acrylonitrile copolymer (SAN) particles with three different sizes (about 5, 10, and 15 microm) were prepared by a two-step seeded polymerization and used for a study of bidisperse electrorheological (ER) suspensions. The effect of the particle size and the size-mixing fraction on ER properties was studied with varying the size of these monodisperse copolymer particles. When the two particle sizes were mixed, the suspension generally showed a decrease in the shear yield stress, reaching a minimum value. However, a bidisperse ER suspension of large particles containing a small fraction of fine particles showed an interesting synergy effect of size mixing on ER response, giving enhanced yield stresses over the other size-mixing fractions. This synergistic ER suspension also showed a great increase in the viscoelastic property. The current density of suspensions was maximum at the synergistic bidisperse suspension. This synergy effect in a particular bidisperse suspension was investigated in view of the structure model consideration and was concluded to be due to a close packing and a peculiar structural ordering at an optimum size ratio and mixing fraction.     

Landau model of the direct isotropic to smectic-C*A phase transition in antiferroelectric liquid crystals

An orientational order parameter is proposed for the isotropic to smectic C*A phase transition in antiferroelectric liquid crystals. A phenomenological theory is developed to describe the direct isotropic to smectic-C*A phase transition on the basis of a free energy expansion. The free energy is written in terms of the coupled order parameters including the antipolar correlations. We present a detailed analysis of the different phases that can occur and analyze the question: under which conditions a direct isotropic to smectic-C*A phase transition is possible when compared to other phase transitions? The theoretical results are compared with experimental results.     

Phase behaviour of poly-(λ-benzyl-L-glutamate) in benzyl alcohol

Polarized optical microscopy has been used to investigate phase transitions in the poly-(λ-benzyl-L-glutamate) benzyl alcohol system and these have been compared with the predictions of Flory. All of the samples studied form gels at room temperature. The behaviour of the lowest concentration studied, 5 per cent by volume, shows transitions in the optical microscope compatible with the Flory phase diagram, becoming isotropic at elevated temperatures. Gels of higher concentrations exhibit bulk phase separation into an isotropic liquid phase and an anisotropic phase at room temperature, also in accord with the Flory predictions; the texture of the anisotropic phase varies with concentration. At higher temperatures these concentrations exhibit two coexistent anisotropic phases.     

Surface phase transitions in athermal mixtures of hard rods and excluded volume polymers investigated using a density functional approach

Using fundamental measures' density functional framework based on Wertheim's first order perturbation theory [J. Chem. Phys. 87, 7323 (1987)] we study the surface phase transitions in athermal polymer-needle mixtures, which demix in bulk into the isotropic polymer-rich (rod-poor) and polymer-poor (rod-rich) phases. We find that the polymer-rich (rod-poor) phase wets the hard wall at coexistence and the wetting transition is of first order. In the partial wetting regime we find a sequence of layerings but these transitions are gradually suppressed as the chain length increases. For long enough chains we detect the prewetting line. Rods exhibit pronounced ordering at the wall in the polymer-rich phases. Our results imply that experiments on the (isotropic) wetting transition for colloidal rod-polymer mixtures should be easier to carry out than those for the colloidal rod-sphere mixtures because the wetting transition occurs at lower rod densities. On the other hand, layerings in sphere-needle mixtures may turn out to be difficult to observe experimentally because some of them will be metastable with respect to the freezing transition, whereas the remaining ones are located very close to the binodal.     

Is there a relation between excess volume and miscibility in binary liquid mixtures?

Molecular dynamics computer simulations of various symmetrical Lennard-Jones (LJ) models are used to elucidate how the excess volume in dense binary liquids is related to the microscopic interactions between the particles. Both fully miscible systems and systems with a liquid-liquid phase separation are considered by varying systematically the parameters of the LJ potentials. The phase diagrams with the critical points of the demixing systems are determined by means of Monte Carlo simulations in the semigrandcanonical ensemble. The different LJ models are investigated by computing Bhatia-Thornton structure factors, enthalpy of mixing, and excess volume. For the demixing systems, the LJ models show a positive enthalpy of mixing while it is negative for the systems without miscibility gap. In contrast to that, the excess volume can be negative and positive for both demixing and fully miscible systems. This behavior is explained in terms of the interplay between the repulsive and attractive terms in the LJ potential. Whereas repulsions dominate the packing of particles as reflected by the number-density structure factor, the chemical ordering and thus the concentration structure factor are strongly affected by attractive interactions, leading to the "anomalies" of the excess volume.     

A theoretical and simulation study of the self-assembly of a binary blend of diblock copolymers

Pure diblock copolymer melts exhibit a narrow range of conditions at which bicontinuous and cocontinuous phases are stable; such conditions and the morphology of such phases can be tuned by the use of additives. In this work, we have studied a bidisperse system of diblock copolymers using theory and simulation. In particular, we elucidated how a short, lamellar-forming diblock copolymer modifies the phase behavior of a longer, cylinder-forming diblock copolymer. In a narrow range of intermediate compositions, self-consistent field theory predicts the formation of a gyroid phase although particle-based simulations show that three phases compete: the gyroid phase, a disordered cocontinuous phase, and the cylinder phase, all having free energies within error bars of each other. Former experimental studies of a similar system have yielded an unidentified, partially irregular bicontinuous phase, and our simulations suggest that at such conditions the formation of a partially transformed network phase is indeed plausible. Close examination of the spatial distribution of chains reveals that packing frustration (manifested by chain stretching and low density spots) occurs in the majority-block domains of the three competing phases simulated. In all cases, a double interface around the minority-block domains is also detected with the outer one formed by the short chains, and the inner one formed by the longer chains.