Surface properties of fluids of charged platelike colloids

Surface properties of mixtures of charged platelike colloids and salt in contact with a charged planar wall are studied within density functional theory. The particles are modeled by hard cuboids with their edges constrained to be parallel to the Cartesian axes corresponding to the Zwanzig model [J. Chem. Phys. 39, 1714 (1963)] and the charges of the particles are concentrated at their centers. The density functional applied is an extension of a recently introduced functional for charged platelike colloids. It provides a qualitative approach because it does not determine the relation between the actual and the effective charges entering into the model. Technically motivated approximations, such as using the Zwanzig model, are expected not to influence the results qualitatively. Analytically and numerically calculated bulk and surface phase diagrams exhibit first-order wetting for sufficiently small macroion charges and isotropic bulk order as well as first-order drying for sufficiently large macroion charges and nematic bulk order. The asymptotic wetting and drying behaviors are investigated by means of effective interface potentials which turn out to be asymptotically the same as for a suitable neutral system governed by isotropic nonretarded dispersion forces. Wetting and drying points as well as predrying lines and the corresponding critical points have been located numerically. A crossover from monotonic to nonmonotonic electrostatic potential profiles upon varying the surface charge density has been observed. Nonmonotonic electrostatic potential profiles are equivalent to the occurrence of charge inversion. Due to the presence of both the Coulomb interactions and the hard-core repulsions, the surface potential and the surface charge do not vanish simultaneously, i.e., the point of zero charge and the isoelectric point of the surface do not coincide.     

A density-functional theory study of the confined soft ellipsoid fluid

A system of soft ellipsoid molecules confined between two planar walls is studied using classical density-functional theory. Both the isotropic and nematic phases are considered. The excess free energy is evaluated using two different Ans?tze and the intermolecular interaction is incorporated using two different direct correlation functions (DCF's). The first is a numerical DCF obtained from simulations of bulk soft ellipsoid fluids and the second is taken from the Parsons-Lee theory. In both the isotropic and nematic phases the numerical DCF gives density and order parameter profiles in reasonable agreement with simulation. The Parsons-Lee DCF also gives reasonable agreement in the isotropic phase but poor agreement in the nematic phase.     

Phase behavior and interfacial properties of nonadditive mixtures of Onsager rods

Within a second virial theory, we study bulk phase diagrams as well as the free planar isotropic-nematic interface of binary mixtures of nonadditive thin and thick hard rods. For species of the same type, the excluded volume is determined only by the dimensions of the particles, whereas for dissimilar ones it is taken to be larger or smaller than that, giving rise to a nonadditivity that can be positive or negative. We argue that such a nonadditivity can result from modeling of soft interactions as effective hard-core interactions. The nonadditivity enhances or reduces the fractionation at isotropic-nematic (IN) coexistence and may induce or suppress a demixing of the high-density nematic phase into two nematic phases of different composition (N(1) and N(2)), depending on whether the nonadditivity is positive or negative. The interfacial tension between coexisting isotropic and nematic phases shows an increase with increasing fractionation at the IN interface, and complete wetting of the IN(2) interface by the N(1) phase upon approach of the triple-point coexistence. In all explored cases bulk and interfacial properties of the nonadditive mixtures exhibit a striking and quite unexpected similarity with the properties of additive mixtures of different diameter ratio.     

Structure of spherical electric double layers: a density functional approach

A density functional theory is presented for the structure of spherical electric double layers within the restricted primitive model, where the macroion is considered as a hard sphere having uniform surface charge density, the small ions as charged hard spheres, and the solvent is taken as a dielectric continuum. The theory is partially perturbative as the hard-sphere contribution to the one-particle correlation function is evaluated using suitably averaged weighted density and the ionic part is obtained through a second-order functional Taylor expansion around the uniform fluid. The theory is in quantitative agreement with Monte Carlo simulation for the density profiles and the zeta potentials over a wide range of macroion sizes and electrolyte concentrations. The theory is able to provide interesting insights about the layering and the charge inversion phenomena occurring at the interface.     

Nematic ordering of rigid rod polyelectrolytes induced by electrostatic interactions: effect of discrete charge distribution along the chain

Similar to the Debye-Hu?ckel plasma, charged groups in solutions of rigid rod polyelectrolytes attract each other. We derive expression for the correlation free energy of electrostatic attraction of the rods within the random phase approximation. In this theory, we explicitly take into account positions of charged groups on the chains and examine both charge and polymer concentration fluctuations. The correlation free energies and the osmotic pressures are calculated for isotropic and completely ordered nematic phase. The results of the discrete model are compared with results of a continuous model. The discrete model gives rise to a stronger attraction between the charged groups both in the isotropic and nematic phases and to a stronger orienting action of the electrostatic forces.     

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.     

Effect of discrete macroion charge distributions in solutions of like-charged macroions

The effect of replacing the conventional uniform macroion surface charge density with discrete macroion charge distributions on structural properties of aqueous solutions of like-charged macroions has been investigated by Monte Carlo simulations. Two discrete charge distributions have been considered: point charges localized on the macroion surface and finite-sized charges protruding into the solution. Both discrete charge distributions have been examined with fixed and mobile macroion charges. Different boundary conditions have been applied to examine various properties. With point charges localized on the macroion surface, counterions become stronger accumulated to the macroion and the effect increases with counterion valence. As a consequence, with mono- and divalent counterions the potential of mean force between two macroions becomes less repulsive and with trivalent counterions more attractive. With protruding charges, the excluded volume effect dominates over the increased correlation ability; hence the counterions are less accumulated near the macroions and the potential of mean force between two macroions becomes more repulsive/less attractive.     

New results from the contact theorem for the charge profile for symmetric electrolytes

In this paper the contact value of the charge profile at a charged interface is presented as the sum of the normal component of the Maxwell electrostatic tensor and a new electrostatic property defined by the integral from the product of the gradient of the electrical potential and the singlet distribution function of coions (ions with sign of the charge equal to that of the interface). On physical arguments, it is conjectured that this new property is a monotonic function of the electrical charge at the wall and is limited by the bulk electrolyte pressure for large electrical charges at the wall. Using the contact theorems for the density and the charge profiles, the exact expressions for the contact values of the profiles of coions and counterions are derived and some related general properties are discussed.     

Theory of the effect of small ions on the electrical admittance of macroion solutions

A general theory is given on the electrical admittance of a parallel plate capacitor filled with a conductive medium containing charged particles by considering both their electric atmospheres and the electric field due to charges induced on the electrodes. The theory is applied to a dilute macroion solution with added salt and it is found that the low frequency dielectric response of the solution reflects the motions of the macroion and bound small ions and the effect of motion of the ion atmosphere around the macroion is canceled out by the current due to the induced charges on the electrodes.     

Effect of Discrete Macroion Charge Distributions on Electric Double Layer of a Spherical Macroion

The effect of replacing the conventional uniform macroion surface charge density with discrete macroion charge distributions on the structure of electric double layer (EDL) of a spherical macroion has been investigated by Monte Carlo (MC) simulations. Two discrete models have been investigated in addition to the central macroion charge: point charges localized on the macroion surface and finite-sized charges protruding into the solution. Both models have been studied with fixed and mobile macroion charges. The radial functions of local densities and electrostatic potential in EDL, are calculated and compared to the results obtained for the central macroion charge distribution. It is concluded that the model of charge distribution significantly affects the EDL structure close to the macroion, while the effect is much weaker at larger distances. With point charges localized on the macroion surface, counterions become stronger accumulated to the macroion, as a result the absolute values of surface potential ?₀ and zeta ξ potential are decreased. With protruding charges, the excluded volume effect dominates over the increased correlation ability; hence the counterions are less accumulated near the macroions and the absolute values of ?₀ and ξ potentials are increased.     

Interface effects in nematic liquid-crystalline structures of polymer solutions

A solution of long semirigid linear macromolecules was considered. The liquid-crystalline nematic ordering in the solution was analyzed theoretically using an Onsager-type approach. The orientation entropy was calculated in the frameworks of Lifshits' approach, successfully developed for this system originally by Khokhlov and Semenov. For homogeneous liquid-crystalline phase using the third virial approximation for intersegmental steric interaction the orientation distribution function, the free energy density, the isotropic-nematic coexistence and the spinodal conditions were computed numerically for two types of polymer flexibility mechanism: persistent chains and chains of freely joint segments. For the asymptotically exact second virial approximation the applicability region was analyzed. We considered the general equations, which describe the concentration and orientational segment distribution for a semirigid persistent polymer chain at a surface (or interface) of any shape and orientation. These equations were numerically solved for the case when the nematic director axis was perpendicular to a planar interface boundary between the real coexisting nematic and isotropic phases. The coordinate-dependencies of the polymer concentration and of the order-parameter take the smooth two-steps form in the interface region.     

Molecular Dynamics Simulation of the Electrical Double Layer of Spherical Macroion

The structure of the electrical double layer (EDL) of a spherical macroion with a total charge of 60 elementary charges is studied by molecular dynamics methods. In calculations we used two models: continuous and discrete. In the continuous model, the total charge was concentrated in the center of the macroion; in the discrete model, elementary charges were randomly distributed over the surface of the macroion. The radial profiles of local densities and electric potential in EDL, as well as the degree of counterion binding by the macroion, are calculated with allowance for the Lennard-Jones and electrostatic interactions. It is established that the character of charge distribution significantly affects the EDL structure near the macroion, whereas its effect is much weaker at larger distances. The results obtained are compared with the experimental data on the surface potential and the diffuse part of EDL of sodium dodecyl sulfate micelles in aqueous solution, as well as on the micelle-bound charge. It is shown that even weak specific interaction between counterions and a macroion can substantially influence the structure of its EDL.     

Vanadium Pentoxide Sol and Gel Mesophases

Colloidal suspensions of V₂O₅ ribbon-like particles display optical textures typical of lyotropic nematic phases. Tactoids (small nematic droplets) and then isotropic phases are formed as these systems are diluted. Nematic suspensions can be oriented by applying a magnetic or an electric field. Such a liquid crystal behavior is mainly due to the highly anisotropic shape of vanadium oxide colloidal particles. Acid dissociation at the oxide/water interface gives rise to surface electrical charges and electrostatic repulsion should also be responsible for the stabilization of the nematic phases. Anisotropic xerogel layers are formed when these gels are deposited and dried onto flat substrates. X-ray diffraction patterns of such coatings exhibit a series of 00l harmonics due to the turbostratic stacking of the oxide particles. Dehydration is reversible and fluid mesophases are again obtained via a swelling process when water is added to the xerogel.     

Interfacial nematodynamics of heterogeneous curved isotropic-nematic moving fronts

The early stages of liquid crystal phase ordering upon thermal quenches of isotropic phases into unstable and metastable temperature ranges is studied using two-dimensional (2D) computational solutions of the governing Landau-de Gennes (L-dG) equations for low molar mass nematic liquid crystals and analysis based on the corresponding interfacial nematodynamic model. The early phase ordering stage, for both unstable and metastable quenches of the isotropic phase, is shown to lead to highly textured nematic spherulites through a mechanism of interfacial defect nucleation. The underlying mechanisms of interface-driven texturing are elucidated using complementary 2D computational parametric studies of the bulk L-dG equation and analysis of the IN model. It is shown that for highly curved nanodomains and realistic elastic anisotropy, sharp interfacial transitions between uniaxial and biaxial states arise and are resolved by interfacial defect nucleation, which upon subsequent migration into the spherulite's interior leads to strong texturing. This paper shows that texture formation in the early stages of phase ordering is interface driven, and due to low interface tension, elastic anisotropy, and large curvature. Interfacial defect shedding in highly curved, low tension, anisotropic interfaces is a significant defect nucleation mechanism that needs to be taken into account when considering texturing processes.     

Sol/gel and isotropic/nematic transitions in aqueous suspensions of natural nontronite clay. Influence of particle anisotropy. 1. Features of the i/n transition

The phase behavior of a natural nontronite clay was studied for size-selected particles by combining osmotic pressure measurements, visual observations under polarized light, and rheological experiments. In parallel, the positional and orientational correlations of the particles were analyzed by small-angle X-ray scattering. Aqueous suspensions of nontronite exhibit a true isotropic/nematic (I/N) transition that occurs before the sol/gel transition, for ionic strengths below 10(-3) M/L. In this region of the phase diagrams, the system appears to be purely repulsive. The I/N transition shifts toward lower volume fractions for increasing particle anisotropy, and its position in the phase diagram agrees well with the theoretical predictions for platelets. SAXS measurements reveal the presence of characteristic interparticular distances in the isotropic, nematic, and gel phases. The swelling law (separation distance vs swelling law) exhibits two regimes. For high volume fractions, the swelling law is one-dimensional as in layered systems and reveals the presence of isolated platelets. At lower volume fraction, distances scale as phi(-1/3), indicating isotropic volumic swelling. Finally, the experimental osmotic pressure curves can be satisfactorily reproduced by considering the interparticle distances between two charged planes whose effective charge is around 10% of the structural charge.     

Electrokinetics of diffuse soft interfaces. 1. Limit of low Donnan potentials

The current theoretical approaches to electrokinetics of gels or polyelectrolyte layers are based on the assumption that the position of the very interface between the aqueous medium and the gel phase is well defined. Within this assumption, spatial profiles for the volume fraction of polymer segments (phi), the density of fixed charges in the porous layer (rho fix), and the coefficient modeling the friction to hydrodynamic flow (k) follow a step-function. In reality, the "fuzzy" nature of the charged soft layer is intrinsically incompatible with the concept of a sharp interface and therefore necessarily calls for more detailed spatial representations for phi, rho fix, and k. In this paper, the notion of diffuse interface is introduced. For the sake of illustration, linear spatial distributions for phi and rho fix are considered in the interfacial zone between the bulk of the porous charged layer and the bulk electrolyte solution. The corresponding distribution for k is inferred from the Brinkman equation, which for low phi reduces to Stokes' equation. Linear electrostatics, hydrodynamics, and electroosmosis issues are analytically solved within the context of streaming current and streaming potential of charged surface layers in a thin-layer cell. The hydrodynamic analysis clearly demonstrates the physical incorrectness of the concept of a discrete slip plane for diffuse interfaces. For moderate to low electrolyte concentrations and nanoscale spatial transition of phi from zero (bulk electrolyte) to phi o (bulk gel), the electrokinetic properties of the soft layer as predicted by the theory considerably deviate from those calculated on the basis of the discontinuous approximation by Ohshima.     

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.     

Phase equilibrium of poly(n-butyl acrylate) and E7

The experimental equilibrium phase diagram of mixtures of linear poly(n-butyl acrylate) of molecular mass M_w = 112000 g mol^-1 and the low molecular mass LC mixture E7 has been established using polarized optical microscopy and light scattering techniques. The diagram is found to be reminiscent of an upper critical solution temperature system. Two independent series of samples with the same composition were studied, yielding consistent results. A region of nematic and isotropic coexisting phases and a region of a single isotropic phase were identified in the composition-temperature phase diagram. The results were analysed within a theoretical model combining the Flory-Huggins lattice theory for isotropic mixing and the Maier-Saupe theory for nematic ordering. Interestingly, no region of isotropic coexisting phases was observed in our experiments. This is probably due to the fact that the nematic interaction overwhelms the isotropic interaction in the region where (I + I) coexisting phases could appear. A preferential solubility of certain constituents of the LC mixture in the polymer could possibly be a reason for this behaviour.     

Induced phase separation in cellulose nanocrystal suspensions containing ionic dye species

Suspensions of negatively charged cellulose nanocrystal are obtained by sulfuric acid hydrolysis of cotton cellulose. Within a specific concentration range, the suspensions spontaneously phase separate to give isotropic and chiral nematic phases. Added anionic dyes of varying charge cause separation of an isotropic phase from the highly concentrated, completely anisotropic suspensions; these dyes have a much greater effect on the suspensions than the equivalent ionic strength of a simple 1:1 electrolyte (sodium chloride). Neutral, cationic and cellulose-binding anionic dyes do not cause phase separation in the anisotropic cellulose suspensions.     

Liquid-vapor phase diagram and cluster formation of two-dimensional ionic fluids

Direct molecular dynamics simulations on interfaces at constant temperature are performed to obtain the liquid-vapor phase diagram of the two-dimensional soft primitive model, an equimolar mixture of equal size spheres carrying opposite charges. Constant temperature and pressure simulations are also carried out to check consistency with interface simulations results. In addition, an analysis of the cluster formation of mixtures of particles with charge asymmetry in the range 1:1 to 1:36 at low and high densities is performed. The number of free ions, when plotted as a function of the positive ion charge, Z(+), has an oscillatory behavior and is independent of the density. The formation of aggregates is analyzed in terms of the attraction and repulsion between ions.