Table of contents

Volume 15

Number 48, 8 December 2003

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SPECIAL ISSUE CONTAINING ARTICLES PRESENTED AT THE CECAM WORKSHOP: EFFECTIVE MANY-BODY INTERACTIONS AND CORRELATIONS IN SOFT MATTER, LYON, 7-9 JULY 2003

SECTION A: COLLOIDAL SYSTEMS WITH STERIC INTERACTIONS

S3393

, and

Depletion forces in homogeneous and inhomogeneous binary colloidal mixtures in two dimensions are accounted for by a theoretical approach based on a contraction of the description of liquid mixtures, as well as by computer simulations. We study the depletion interactions in concentrated binary mixtures of additive and non-additive hard discs. The wall–particle depletion potential for a disc close to a hard wall with a concave curvature, or with a relief pattern, is obtained in the infinitely dilute limit, as well as the depletion potentials in mixtures of hard discs and hard plates.

S3411

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We investigate the fluid–fluid demixing phase transition of the Asakura–Oosawa model colloid–polymer mixture confined between two smooth parallel hard walls using density functional theory and computer simulations. Comparing fluid density profiles for statepoints away from colloidal gas–liquid coexistence yields good agreement of the theoretical results with simulation data. Theoretical and simulation results predict consistently a shift of the demixing binodal and the critical point towards higher polymer reservoir packing fraction and towards higher colloid fugacities upon decreasing the plate separation distance. This implies capillary condensation of the colloid liquid phase, which should be experimentally observable inside slitlike micropores in contact with a bulk colloidal gas.

S3421

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We consider the free interface between demixed fluid phases in a mixture of hard spheres and vanishingly thin hard rods using Monte Carlo simulations and density functional theory. Both approaches treat the full binary mixture and hence include all rod-induced many-body depletion interactions between spheres. The agreement between theoretical and simulation results for density and orientation order profiles across the interface is remarkable, even for states not far from the critical point. The simulation results confirm the previously predicted preferred vertical (parallel) alignment of rod orientation to the interface plane at the sphere-rich (sphere-poor) side. This ordering should be experimentally observable in phase-separated colloidal rod–sphere mixtures.

S3429

, , and

We study the Asakura–Oosawa model in the 'protein limit', where the penetrable sphere radius RAO is much greater than the hard sphere radius Rc. The phase behaviour and structure calculated with a full many-body treatment show important qualitative differences when compared to a description based on pair potentials alone. The overall effect of the many-body interactions is repulsive.

S3443

, and

Comparison of solute pair distribution functions in the true mixture and in the effective fluid is used as a diagnosis of the importance of many-body interactions in the effective fluid model of binary asymmetric hard-sphere mixtures. Results from integral equations and density functional theories are compared with simulation data for size ratios R = 3.33, 10 and 20. Small deviation from the pair interaction approximation are detected up to R = 20. The origin of these deviations suggests that many-body effects might be more important in non-hard-sphere mixtures exhibiting long range solute–solvent correlations.

SECTION B: CHARGE DCOLLOIDAL SYSTEMS

S3455

and

Understanding the interatomic interactions in noble gases remains one of the fundamental problems not completely solved to date. From small-angle neutron scattering experiments it is well-known that three-body forces exist and cannot be neglected. On the theoretical side, semi-analytic and simulation methods have been used to reveal the nature of these many-body interactions. The purpose of the present work is to provide an overview of the different three-body contributions to the interactions and their relative importance in describing the structural and thermodynamic properties for noble gases by means of the integral equation theory and molecular dynamics simulations. We examine the relevance of the effective state-dependent pair potential in this framework, as well as the self-consistency problem that we are faced with in the integral equation theory.

S3467

It is argued that a particularly simple kind of many-body interaction can be developed by making the one-body or self-energy terms in the potential depend on a local environmental factor, such as the local density, in some way. Two examples of this are considered: a toy model for macroion suspensions, and an extension to the dissipative particle dynamics simulation method.

S3475

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Under certain conditions ion–ion correlations play a crucial role in the description of the electrical double layer of colloidal particles. In fact, in many instances, the inclusion of the short range correlations between ions in the study of the ionic distribution leads to quite different results with respect to the classical treatment (where ions are assumed to be points). In particular, these discrepancies become more noticeable for highly charged particles in the presence of moderate or highly multivalent counterion concentrations. Moreover, it can be shown that the existence of an electrolyte mixture consisting of multi- and monovalent counterions may cause that system to become overcharged, a feature that cannot be predicted from a classical point of view based on the Boltzmann distribution function. Precisely this aspect has recently produced an enormous interest in the field of biophysics since small variations in the physiological conditions of biocolloidal systems (e.g. the addition of a multivalent salt) can induce important changes in their behaviour. In order to determine the relevance of ion correlations in electrolyte mixtures, we present some experimental results on the electrophoretic mobility of latex particles in the presence of different 1:1 and 3:1 salt mixtures. Likewise, these results are analysed within the so-called hypernetted-chain/mean spherical approximation where ion size correlations are taken into account.

S3485

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We report on a DLVO (Derjaguin–Landau–Verwey–Overbeek) theory determination of cloud and solubility temperatures as a function of the salt molarity in lysozyme solutions. The model is able to reproduce—with a fair accuracy—the experimentally observed linear dependence on the logarithm of the ionic strength, within a protein concentration range spanning from 90 to 140 g l−1. A short discussion of the results is also given in connection with previous applications of the same DLVO model to protein solutions.

S3491

, and

We calculate colloid–colloid correlations using an integral equation theory recently introduced to study charged colloidal suspensions (Anta and Lago 2002 J. Chem. Phys. 116 10514). Colloid–ion, colloid–colloid and ion–ion correlations are treated using different levels of approximation. The colloid–ion direct correlation function (DCF) is obtained initially from a given colloid–colloid pair structure by solving the corresponding hypernetted-chain (HNC) integral equation. It is then used to formulate an effective colloid–colloid pair potential for which the one-component reference hypernetted chain equation (RHNC) is solved. This strategy is used to compute self-consistent colloid–ion and colloid–colloid correlation functions. Ion–ion correlations are considered within the mean spherical approximation and are uncoupled from the others. The present method converges faster and is numerically more stable than traditional multi-component HNC/RHNC integral equation approaches, and provides accurate results for all correlation functions for a wide range of thermodynamic states. Moreover, it exhibits a larger solution region than the ordinary HNC equation for charged systems. Results in the proximity and within the 'HNC' non-solution boundary are discussed. We find that the onset of non-solution behaviour for the present theory appears when the surface charge density of the colloidal particle is very large. To understand the origin of the non-solution line and to address the effect of multi-body interactions in colloid–colloid interactions, we have extracted 'empirical' bridge functions from molecular dynamics simulations of charged colloidal suspensions with charge asymmetries 20:2 and 60:1 and states close to the non-solution region. The colloid–colloid bridge functions exhibit attractive features at intermediate colloid–colloid distances, whereas the colloid–ion bridge function is strongly attractive in the proximity of the non-solution boundary. These attractive components cannot be accounted for by either the hard-sphere bridge function or the first resummed (second order in density) bridge diagrams.

S3509

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Three-body distribution functions in classical fluids have been theoretically investigated many times, but have never been measured directly. Here we present experimental three-point correlation functions that are computed from particle configurations measured by means of video microscopy in two types of quasi-two-dimensional colloidal model fluids: a system of charged colloidal particles and a system of paramagnetic colloids. In the first system the particles interact via a Yukawa potential, in the second via a potential Γ/r3. Varying the particles' density in the charged system or the interaction strength Γ in the magnetic system, one can systematically explore how triplet correlations behave if the coupling between the particles changes. We find for both systems very similar results: on increasing the coupling between the particles one observes the gradual formation of a crystal-like local order due to triplet correlations, even though the system is still deep inside the fluid phase. These are mainly packing effects, as is evident from the close resemblance between the results for the two systems having completely different pair-interaction potentials. To demonstrate that triplet correlations are significant not only locally but also when integrated over the whole volume, we consider the Born–Green equation and show that in a strongly interacting system this equation can be satisfied only with the full triplet correlation function but not with three-body distribution functions obtained from superposing pair correlations (Kirkwood superposition approximation).

S3523

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We develop a thermodynamic description of particles held at a fixed surface potential. This system is of particular interest in view of the continuing controversy over the possibility of a fluid–fluid phase separation in aqueous colloidal suspensions with monovalent counterions. The condition of fixed surface potential allows one in a natural way to account for the colloidal charge renormalization. In a first approach, we assess the importance of the so called 'volume terms' and find that in the absence of salt, charge renormalization is sufficient to stabilize the suspension against a fluid–fluid phase separation. The presence of salt, on the other hand, is found to lead to an instability. A very strong dependence on the approximations used, however, puts the reality of this phase transition in serious doubt. To further understand the nature of the instability we next study a jellium-like approximation, which does not lead to a phase separation and produces a relatively accurate analytical equation of state for deionized suspensions of highly charged colloidal spheres. A critical analysis of various theories of strongly asymmetric electrolytes is presented, to assess their reliability as compared to the Monte Carlo simulations.

S3537

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The low-density phase diagrams of charge-stabilized colloidal suspensions of the Derjaguin–Landau–Verwey–Overbeek theory with an approximate effective one-component Hamiltonian given by the volume term and effective pair interactions, and of the classical theory (without including the volume term), are obtained from the hypernetted-chain integral equation at low colloidal charges. In the salt-free case both phase diagrams exhibit a vapour–liquid transition with short-ranged colloid–colloid correlations. This phase separation is compared to the vapour–liquid transition found in binary mixtures of highly asymmetrical hard spheres.

S3549

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We study, by simulation, the effect of attractive triplet interactions on the phase behaviour of suspensions of charged colloidal particles at low ionic strength, i.e. in the regime where the pair interactions are purely repulsive. We use the pair and triplet interactions that were obtained recently from a numerical, nonlinear Poisson–Boltzman study (Russ et al 2002 Phys. Rev. E 66 011402). Our simulations tentatively explain, for the first time, experimental observations of a rather large density difference between coexisting body centred cubic and face centred cubic crystal phases.

S3557

and

Using computer simulations we study the phase behaviour of hard spheres with repulsive Yukawa interactions and with the repulsion set to zero at distances larger than a density-dependent cut-off distance. Earlier studies based on experiments and computer simulations in colloidal suspensions have shown that the effective colloid–colloid pair interaction that takes into account many-body effects resembles closely this truncated Yukawa potential. We present a phase diagram for the truncated Yukawa system by combining Helmholtz free energy calculations and the Kofke integration method. Compared to the non-truncated Yukawa system we observe (i) a radical reduction of the stability of the body centred cubic (BCC) phase, (ii) a wider fluid region due to instability of the face centred cubic (FCC) phase and due to a re-entrant fluid phase and (iii) hardly any shift of the (FCC) melting line when compared with the (BCC) melting line for the full Yukawa potential for sufficiently high salt concentrations, i.e. truncation of the potential does not affect the location of the solid–fluid line but replaces only the BCC phase with the FCC at the melting line. We compare our results with earlier results on the truncated Yukawa potential and with results from simulations where the full many-body Poisson–Boltzmann problem is solved.

S3569

We combine hydrostatic equilibrium with Donnan equilibrium to identify three different regimes of sedimentation equilibrium in suspensions of highly charged colloids. In the low-density regime the familiar exponential (barometric) distribution is recovered, in an intermediate density regime the profile is found to be linear with height, and in the high-density regime it is exponential again but with a gravitational length that is increased by a factor Z+1, where Z is the colloidal charge number. The nonbarometric distributions are explained in terms of macroscopic electric fields, generated by macroscopic charge separation as calculated by Poisson–Boltzmann theory.

S3581

, and

We present quantitative three-dimensional real space measurements by confocal microscopy on fluorescently labelled and sterically stabilized dispersions of polymethylmethacrylate spheres dispersed in index and density-matched solvent mixtures with a relative dielectric constant 5<εr<10 . In this new model system Debye screening lengths (κ−1) comparable to the particle size (diameter σ) can be realized even for particles with sizes of several micrometres. Moreover, by addition of salt (tetrabutylammonium chloride) κ−1 can be varied and the surface charge of the particles can be set roughly in between the values +100 and −100 mV, as determined by electrophoresis. By a comparison of radial distribution functions and displacements from lattice positions with Monte Carlo computer simulations we found that both the structure in the liquid and the crystallization volume fraction could be described with a Yukawa potential characterized by one set of parameters, a surface potential of 36 mV and κσ = 5, where the particle diameter σ = 2 µm . Anomalous ('phase') behaviour such as extreme long-range repulsions, 'coexistence' of high-density and low-density colloidal crystals and void formation, previously observed for deionized dispersions in water, was observed as well, and can now be studied in a different system without ion exchange resin. These anomalous effects are seen relatively soon after preparing the systems and are absent or short-lived in systems with grounding and at higher salt concentrations.