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The shapes of bacteria can vary widely; they may, for instance, be spherical, rod-like, string-like, or curved. In general, bacilli are highly anisotropic. For research and (bio)technological purposes, it can be useful to concentrate bacteria, which is possible by adding nonadsorbing polymers. The induced phase separation originates from a polymer-mediated depletion interaction, first understood by Asakura and Oosawa. Here, it is shown that free volume theory (FVT) can semi-quantitatively describe the phase transitions observed when adding sodium polystyrene sulfonate polymers to E. coli bacteria [Schwarz-Linek et al., Soft Matter 6, 4540 (2010)] at high ionic strength. The E. coli bacteria are described as short, hard spherocylinders. FVT predicts that the phase transitions of the mixtures result from a fluid-ABC crystal solid phase coexistence of a hard spherocylinder-polymer mixture.

We present the phase diagram of a colloid-polymer mixture in which the radius a of the colloidal spheres is approximately the same as the radius R of a polymer coil (q=R/a≈1). A three-phase coexistence region is experimentally observed, previously only reported for colloid-polymer mixtures with smaller polymer chains (q≲0.6). A recently developed generalized free-volume theory (GFVT) for mixtures of hard spheres and non-adsorbing excluded-volume polymer chains gives a quantitative description of the phase diagram. Monte Carlo simulations also agree well with experiment. Copyright © EPLA, 2008.

We study the phase behaviour of mixtures of colloidal spheres and polymers that have an excluded-volume interaction dispersed in a (background) solvent using the concept of free volume theory. The depletion layer thickness is calculated from the negative adsorption of polymer segments around a sphere. The correlation length and thermodynamic properties of the excluded-volume interacting polymer chains in solution are taken into account by using results from the renormalization group theory. For small polymer–colloid size ratios the difference from an ideal description of the polymers is small, while for larger size ratios the gas–liquid coexistence region shifts in the direction of higher polymer concentrations and at the same time the liquid–crystal coexistence region becomes more extended. Both the gas–liquid region and the gas– liquid–crystal region become less extended. These features are compared to experiment.

We have studied a system of polydisperse, charged colloidal gibbsite platelets with a bimodal distribution in the particle aspect ratio. We observe a density inversion of the coexisting isotropic and nematic phases as well as a three-phase equilibrium involving a lower density nematic phase, an isotropic phase of intermediate density, and a higher density columnar phase. To relate these phenomena to the bimodality of the shape distribution, we have calculated the liquid crystal phase behavior of binary mixtures of thick and thin hard platelets for various thickness ratios. The predictions are based on the Onsager-Parsons theory for the isotropic-nematic (I-N) transition combined with a modified Lennard-Jones-Devonshire cell theory for the columnar (C) state. For sufficiently large thickness ratios, the phase diagram features an I-N density inversion and triphasic I-N-C equilibrium, in agreement with experiment. The density inversion can be attributed to a marked shape fractionation among the coexisting phases with the thick species accumulating in the isotropic phase. At high concentrations, the theory predicts a coexistence between two columnar phases with distinctly different concentrations. In experiment, however, the demixing transition is pre-empted by a transition to a kinetically arrested, glassy state with structural features resembling a columnar phase.

Aqueous dispersions of colloidal boehmite rods turn into strong gels when the concentration of (1–1) electrolyte concentrations becomes exceeds 50 mM. However, after addition of aluminium chlorohydrate (ACH) the rods remain stable up to salt concentrations as high as 2 M. Moreover the boehmite-ACH dispersions with an aspect ratio of 19 quickly separate into an isotropic and a liquid crystal nematic phase above a typical threshold concentration of 2 v/v%. It is known that ACH forms polynuclear cations at mild acidic conditions. The anomalous stability as encountered in these dispersions is explained by assuming that these hydrolyzed poly-cations cause a shift of the charge carrying surface.

Visual observations and preliminary light scattering experiments on the crystallization process in various colloidal systems are reported. In the first place we studied the influence of the stabilizing coating of the colloidal particles on the rate of crystallization. The various coatings give rise to different ranges of the repulsive interaction. This is found to have a pronounced effect on the rate of crystallization. Furthermore we investigated the effect of free polymer added to the dispersion. It appears that addition of free polymer has a dramatic effect on the crystallization phenomena.

The interaction between two spheres in a solution of nonadsorbing polymers, with excluded volume interaction, is calculated from the depletion layers around the spheres using the generalized Gibbs adsorption equation. By combining the bulk correlation length with the curvature-dependent interfacial tension between a sphere and the surrounding polymer solution [Hanke, Eisenriegler, and Dietrich, Phys. Rev. E 59, 6853 (1999)], the depletion layer thickness around a sphere is obtained. The resulting contact potential agrees with a scaling prediction of de Gennes in the semidilute regime.

The interaction between two parallel plates due to non-adsorbing polymer chains with excluded volume is calculated using the adsorption method. The adsorption is calculated from the profile of the polymer segment concentration between the plates, which is obtained from the product function of the concentration profile near a single wall, involving the correlation length. The renormalization group theory provides expressions for the osmotic pressure and consequently for the osmotic compressibility, chemical potential and correlation length of a polymer solution. Both the local polymer concentration profiles as well as the minimum of the interaction potential between the plates agree with recently published self-avoiding random walk computer simulations.

Long-time self-diffusion in dispersions of rigid colloidal rods with an aspect ratio of 19 is studied with fluorescence recovery after photobleaching (FRAP)in isotropic and nematic phases. The long-time selfdiffusion coefficient DLs is found to decrease linearly with concentration up to (L/D)φ= 0.12 (with L the length and D the diameter of the rods, and φ the volume fraction). In the isotropic phase in coexistence with the nematic phase, DLs remains virtually constant at about 1% of its value at infinite dilution. In the nematic phase long-time self-diffusion is found to be ten times slower than in the coexisting isotropic phase. In addition, by modifying the FRAP geometry we were able to distinguish between sidewise and lengthwise diffusion in aligned nematic phases.

A closed packed system (“onion phase”) of so-called lamellar droplets, consisting of concentric surfactant bilayers which are separated from one another by water, may be obtained by subjecting a continuous lamellar phase to shear. We propose a model for the size of these lamellar droplets under shear as a function of their effective surface tension. This model fits the available experimental data quantitatively and explains the dependence of the size on surfactant volume fraction.

The isotropic - nematic (I - N) phase transition in dispersions of sterically stabilized rod-like boehmite (AlOOH) colloids is studied. We have examined the influence of the steric stabilizer, the dispersion medium and the presence of non-adsorbing polymer on the phase transition process. Dispersions in cyclohexane show an I - N phase separation that proceeds by a slow sedimentation of a pinned structure, shrinking from the meniscus, finally forming the nematic phase after weeks or months, depending on the steric stabilizer used. In toluene the onset of the I - N has shifted to higher volume fractions where individual nematic droplets grow and sediment, forming the nematic phase after one week. By adding non-adsorbing polymer to dispersions in cyclohexane the onset of the I - N phase separation shifts to lower colloid volume fractions. At polymer concentrations just above the phase boundary the same scenario as in the toluene dispersions without added non-adsorbing polymer is observed. At slightly higher polymer concentrations an abrupt change in scenario occurs. Now an interconnected network is formed which starts to sediment, resembling the process in pure cyclohexane dispersions. Clearly small variations in colloidal interactions engendered by the changes in dispersion characteristics considered in this work, have a strong influence on the I - N phase transition process.

The disorder-to-order transitions that occur in concentrated colloidal dispersions of rigid spherical and rod-like particles are reviewed. It is indicated how the wealth of theoretical work and computer simulation results on the phase behaviour of atomic and molecular fluids can be applied to colloidal dispersions. The features that make colloidal dispersions unique (controllable particle-particle interactions, convenient length- and time-scales) are emphasized throughout.

We have studied the coupling of aggregation and crystallization in a mixture of colloidal spheres and colloidal rods. Taking advantage of specially prepared fluorescent silica spheres we are able to investigate this process at the particle level by fluorescense confocal microscopy. We find that above a limiting concentration of rods in the mixture, the spheres rapidly assemble to form compact aggregates which subsequently crystallize.

A dispersion of fluorescent colloidal silica coated boehmite rods with length L'325 nm and diameter D '46 nm, dispersed in dimethylformamide, is synthesized. The concentration dependence of the long-time translational self-diffusion coefficient Ds L is measured with fluorescence recovery after photobleaching up to a rod volume fraction f50.22. A linear dependence of Ds L on concentration is found up to (L/D)f51. At higher concentration Ds L levels off and decreases to 3% of its value at infinite dilution for (L/D)f51.5. @S1063-651X~97!05110-6#

The effect of non-adsorbing, flexible polymer on the isotropic-nematic transition in dispersions of rod-like colloids is investigated. A widening of the biphasic gap is observed, in combination with a marked polymer partitioning between the coexisting phases. Under certain conditions, areas of isotropicisotropic- nematic or isotropic-nematic-nematic three-phase coexistence appear in the phase diagram of rod-polymer mixtures.

Nematic-nematic phase equilibria and an isotropic-nematic-nematic triple point are located in the phase diagram of a bidisperse solution of rigid hard rods. To this end, the formulation of the Onsager second virial theory for bidisperse systems using Gaussian trial functions is applied. It appears that-within this approximation-the nematic-nematic transition is not caused by excluded-volume effects but by a balance between orientational entropy and entropy of mixing. Below a length ratio of 3.167 there is only a simple isotropic-nematic transition present

The Onsager theory for the isotropic–anisotropic phase separation in a solution of rodlike particles is extended to the case of mixtures of such particles with different lengths. The concentration, composition, order parameters, and orientation dependent thermodynamic quantities of the coexisting phases are calculated for the case of a mixture of rods of two different lengths for different length ratios. It is found that there is a significantly higher mole fraction of the longer rods in the anisotropic phase than in the isotropic phase. The order parameter of the longer rods is higher than in the one component case, whereas the order parameter of the shorter rods first increases and then decreases as the mole fraction of the longer rods is increased. All these features are accentuated as the length ratio of the two kinds of rods increases.

We use a recently developed method to obtain tight bounds on multipole dispersion coefficients for the interaction of helium atoms.

We review stochastic descriptions of the dynamics of colloidal particles, suspended in a liquid, which interact both directly and hydrodynamically. The equivalence of approaches based on Smoluchowski and Langevin equations is established. Particular attention is paid to the Ito and Stratonovich interpretations of stochastic differential equations with multiplicative noise. The short time behaviour of the correlation between two functions of particle position is discussed in some detail and compared with that found for a simple liquid. Finally the non-gaussian statistical properties of particle displacement are considered in the presence and absence of hydrodynamic interactions.

The dynamic structure factor for concentrated dispersions of small polydisperse hard spherical particles has been measured and compared with theoretical predictions. Experimental evidence for the occurrence of a slowly decaying mode has been found. The dynamic structure factor is analyzed in terms of two independent modes, associated with collective diffusion and exchange diffusion. Calculations of the mode amplitudes are extended to the case of combined optical and size polydispersity. The correspondence between measurements and theory is quite satisfactory.

An analysis is presented of the behavior of the hydrodynamic modes in a horizontal fluid layer subject to a downward-directed temperature gradient which, when reaching a critical value, drives the system into convective instability. It is found that the combination of this thermal constraint and gravity gives rise to a coupling between the heat-diffusion mode and the transverse mode (curl curl v→)z, with v→, the velocity field, and the z axis pointing in the vertical direction. As a result of this mode coupling, which is absent in a fluid at equilibrium, the damping factor of one of the coupled modes goes to zero when the temperature gradient increases to its critical value. On the basis of this mode analysis, the spectral distribution of the light scattered by the nonequilibrium fluid is then computed. The main features of the light-scattering spectrum consist of the appearance of an additional central component and the respective narrowing and broadening of the spectral components corresponding to the coupled modes as the instability critical point is approached. © 1974 The American Physical Society., SCOPUS: ar.j, info:eu-repo/semantics/published

The short‐time self‐diffusion coefficient of two types of monodisperse colloidal particles differing only in interparticle interactions were measured by dynamic light scattering both in dilute as well as in concentrated dispersions. The results indicate that the short‐time self‐diffusion is remarkably insensitive to direct particle interactions. The dependence on concentration is in good agreement with the theoretical predictions.

The cluster variation theory for the Maier–Saupe model of the isotropic–nematic phase transition is extended to the four‐particle level. As in the case of the Heisenberg ferromagnet, the irregularities of the three‐particle cluster approximation applied to cubic lattices, where there are no triangles of nearest neighbors, disappear. The extension from three‐ to four‐particle clusters yields improved values of all quantities, characteristic for the phase transition.

The coefficients of the R−6 and R−8 terms in the series representation of the dispersion interaction between two hydrogen molecules and between two nitrogen molecules are calculated by a simple variation method. The agreement with available calculations is encouraging.

A simple derivation and extension of the bounds on dynamic polarizabilities obtained by Langhoff, Karplus, and Gordon are given. A new matrix method to solve the relevant moment equations is presented.

We consider two ways to calculate the self‐diffusion coefficient of interacting Brownian particles. The first approach is based on the calculation of the mean square displacement of a Brownian particle starting from the Smoluchowski equation. In the second approach the self‐diffusion coefficient is obtained as the product of the thermodynamic driving force and the mobility. The advantages and limitations of the two methods are discussed.

The dispersion polymerization of methylmethacrylate stabilized by poly(12-hydroxy-stearic acid) in hydrocarbon media has been investigated. Unlike earlier results [7] it was found that stable latex particles can be prepared in the initial monomer concentration range 8.5 % to 34 %. To obtain stable particles varying amounts of stabilizer were used.

Generalized solutions to the Kisenschitz and London perturbation equations are derived. It is pointed out that the results obtained in the formalisms proposed by Hirschfelder (HAV), by Hirschfelder and Silbey, by Murrell and Shaw, and by Musher and Amos are special cases of the generalized treatment.

The effect of direct interactions between suspended particles on their diffusion coefficient is investigated starting from the generalized Einstein relation. It is shown that an attractive potential added to the hard core repulsion leads to a decrease of the diffusion coëfficiënt, whereas a repulsive term has the opposite effect. Simple examples of attractive and repulsive potentials are considered in some detail. Using these results the possibility to obtain information on the interaction potential between suspended particles from their diffusion coefficient is discussed.

We present a thermodynamic analysis of inverted bifurcation in binary mixtures heated from below. From this analysis it follows that an inverted bifurcation is caused by the competition between a stabilizing effect with a long relaxation time and a destabilizing effect with a short relaxation time. These conditions are precisely the same as those that give rise to overstability. This might explain why overstability and inverted bifurcation occur in the same systems.

Recently there has been a growing interest in pretransitional effects in hydrodynamic regime transitions2. Particular emphasis is put on the interesting resemblance that these pretransitional effects bear to those occurring in equilibrium phase transitions. One of the most striking analogies is the amplification of thermal fluctuations near the transition point.

The onset of convection in a horizontal layer of fluid heated from below, the so-called Rayleigh-Benard instability, has been extensively investigated for a long time 1,2. In recent years there has been considerable interest in the new phenomena that occur in systems in which two competing stability influencing effects with different relaxation times are present. The first example of such systems that was studied in detail is the case of thermal convection in binary mixtures3,4. More recently it has been pointed out that thermal convection in nematic liquid crystals can also be advantageously considered from the same point of view 5. It has been found that under certain conditions both binary mixtures 3,4 and nematic liquid crystals 6,7, when heated from below, show oscillatory and finite amplitude instabilities. In this contribution I will discuss the common physical mechanism underlying these phenomena from the point of view of the energy balance of convective disturbances.

New upper and lower bounds for Van der Waals coefficients using even and odd oscillator-strength sum rules are derived.

Since there exists in the literature some discrepancies in the formulation of the relation between diffusion, sedimentation, and friction of colloidal particles in solution, we rederive the relation between these transport phenomena in this paper. From the application of irreversible thermodynamics it is shown, that the relation between the experimentally accessible quantities like diffusion coefficient, sedimentation velocity, and osmotic compressibility can be obtained unambiguously. The relation between sedimentation velocity and frictional coefficient is discussed in detail, where we give an argumentation for the right expression between these two quantities.

The Onsager theory for the isotropic-nematic phase transition in a solution of rodlike particles is extended to the case of mixtures of such rods with different lengths. For the case of a mixture of particles with two different length to diameter ratios (L/D) it is found that there is a significantly higher molefraction of long rods in the anisotropic phase than in the isotropic phase. This is clear from the Π-x diagram (Π: osmotic pressure) of the coexisting phases presented in Fig. 1. Further the orientational order of the long rods in the anisotropic phase is considerably enhanced compared to the monodis perse system of such rods. This is illustrated in Fig.2. The relevance of these results for the explanation of the isotropic-hexagonal transition in soap solutions is indicated.

The equilibrium thermodynamic and structural properties of colloidal dispersions may be treated in the same way as in the case of simple liquids by considering the colloidal particles as “supramolecules” dispersed in a continuous (but fluctuating) back-ground. The potential which for the case of fluctuating forces replaces the interaction potential between molecules (in vacuo) is the potential of the average forces which act between the dispersed particles. This effective interaction is the input for statistical mechanical theories. Therefore statistical mechanical theories developed for simple fluids can be applied to colloidal dispersions. The theoretical basis for such a treatment was given by Onsager1 and Mc Millan and Mayer2. In recent years concepts of liquid state theory have been applied successfully to understand the behavior of concentrated colloidal dispersions3,4.

We present a simple matrix solution for the moment equations that occur in recently discovered bounds on van der Waals coefficients. Using this matrix solution it is possible to express these new bounds directly in terms of the oscillator strength sum rules of the interacting systems.

Calculations of the interaction energy between non-bonded hydrogen atoms in the fragments A—H---H'—A' for selected displacements of the hydrogen atoms enable one to evaluate corrections to the force field due to the non-bonded interactions and to discuss the changes in the stretching vibration frequencies of the interacting fragments.

The diffusion coefficient of suspended Brownian particles diverges near a hydrodynamicregime transition point. © 1976 The American Physical Society.

The special features of the light scattering spectrum of disparate-mass gas mixtures are analyzed via the dispersion equation for the hydrodynamic modes.