Alan R. Denton (Acadia University, Canada)
"Effective Interactions in Charge-Stabilized Colloidal Suspensions"
Effective interactions between charged hard-sphere macroions in charge-stabilized colloidal suspensions are investigated using response theory methods [1]. Modeling the response of the counterion density to leading nonlinear order in the macroion charge density, effective pair and three-body interaction potentials are calculated, together with associated counterion (volume) free energies. Implications for the thermodynamic phase behaviour of highly-deionized (low-salt) suspensions will be discussed.Marjolein Dijkstra , R. van Roij, and R. Evans (University of Bristol, UK)
"Direct Simulation of the Phase Behaviour of Binary Hard-Sphere Mixtures:
Test of the Depletion Potential Description"
Understanding the stability of colloidal mixtures is relevant for many
industrial applications, but is also interesting from a fundamental
statistical physics point of view. Surprisingly, the phase behavior of
even the simplest model colloid mixture, i.e., large and small hard
spheres, is still not established and remains a topic of much debate.
For instance, it is still unclear whether a (stable) fluid-fluid
demixing transition exists for any additive binary hard-sphere mixture.
By integrating out the degrees of freedom of the small spheres in
a binary mixture of large and small hard spheres, we derive an effective
one-component Hamiltonian for the large spheres. Using this effective
Hamiltonian based on pairwise additive depletion potentials in
simulations, we do find a fluid-fluid spinodal instability for binary
hard-sphere mixtures with a size ratio 0.033<q<0.2, but this demixing
transition is metastable with respect to an extremely broad fluid-solid
transition. More surprisingly, we find a stable isostructural
solid-solid transition for q<0.05. We also studied the phase behaviour
by direct simulation of the true binary mixture and we find remarkably
good agreement with those obtained from the effective one-component
Hamiltonian, even at less asymmetric hard-sphere mixtures and even
at high packing fractions, e.g., in the solid phase. These results provide
the first justification for the effective Hamiltonian approach, based on
pairwise additive depletion potentials, for determining the phase equilibria.
Alice P. Gast and Dean C. Wang (Dept. of Chemical Engineering, Stanford University, USA)
"Soft Sphere Freezing : A Density Functional Model of Freezing in Complex Fluids"
The physical and chemical processes governing the behavior of complex fluids result from a balance of molecular forces. In this delicate balance, repulsive interactions often prevail and ordering occurs via a Kirkwood-Alder transition. Suspensions of monodisperse, charge-stabilized colloidal particles are useful model systems to study this ordering. We have found analogous ordering in nonaqueous suspensions of polymeric micelles. Some of these systems are amenable to modeling with soft repulsive potential energies such as the Yukawa and power-law potentials. We will discuss recent results from a density functional model of ordering. One such theory, the modified weighted density approximation (MWDA) of Denton and Ashcroft, can successfully model the crystallization of particles interacting via short-range, repulsive interactions. We have made an extension of this model by adding a solid reference state, the modified weighted density approximation with a solid reference state (MWDA-SRS), to explain and predict crystallization properties for longer-ranged systems and at high density. We apply the MWDA-SRS model to the power-law and Yukawa potentials, as models for charge-stabilized colloidal systems, and polymeric micelles. We focus our attention on the intriguing question of the stability of the body-centered cubic solid for long-range repulsive systems. We also look at features of the ordering process such as the Lindemann parameter at melting, the Hansen-Verlet rule for freezing and the miscibility gap between coexisting fluid and solid densities at the phase transition.Jean-Pierre Hansen (Cambridge University, UK)
"Effective Interactions Between Confined Charged Colloidal Particles"
S. Leroch, Gerhard Kahl (Technische Universität Wien, Austria) and F. Lado (North Carolina State University, USA)
"Structure and Thermodynamics of a Polydisperse Liquid Mixture"
Willem K. Kegel (Universiteit Utrecht, The Netherlands)
"Geometric Character of the Hard Sphere Freezing Transition"
A considerable fraction of the elements, when compressed, undergo a first order phase transition from a disordered state (a gas, fluid, or liquid) to a face-centred cubic (fcc) or hexagonal close packed (hcp) crystal. Computer simulations, as well as experiments show that this freezing transition is already apparent in the simplest model of interacting atoms: a collection of hard spheres subject to thermal agitation, implying that crystallisation only requires excluded volume interactions. Despite this persuasive evidence, to date, there is no theory from which this transition follows ‘naturally’, that is, without inserting properties of the coexisting phases in advance. We apply a rigorous formalism, using as input purely geometrical properties of small systems, to obtain the grand distribution function. The freezing transition appears as two peaks of this function, at a certain chemical potential, without any a priori information of the coexisting phases, and is already apparent in systems containing a number of spheres as small as 8. It is shown that, by this symmetry breaking transition, the system avoids configurations that can best be characterised as ‘defective solids’. The influence of geometrical constraints on the nature of the hard sphere freezing transition is investigated. It is found that hard spheres tend to split into a dense and a dilute phase in all geometries studied, but the transition is significantly less sharp in a box with cubic symmetry.Christos N. Likos (Universität Düsseldorf, Germany)
"Structure and Thermodynamics of Star Polymers"
Star polymers are macromolecular aggregates consisting of f linear polymers, one end of which is attached to a common center. Stars offer, due to their peculiar architecture, a natural "bridge" between colloidal and polymer science. Based on (a) results from scaling theory, (b) explicit simulation calculations on the effective force between two stars and (c) direct comparison with SANS-data, we propose a new effective potential between two stars in a good solvent. This interaction is then the basis for theoretical calculations regarding the structure in the fluid state and phase transformations from the fluid to the solid state. New phenomena, e.g., an "anomalous structure factor" for the fluid as well as an unusual topology of the phase diagram result from this interaction. Moreover, there exists a "critical arm number" f_c = 33 such that, for f <= f_c the system never crystallizes, at any density.Gerhard Nägele (Universität Konstanz, Germany)
"Viscoelasticity and Generalized Stokes-Einstein Relation in Colloidal Dispersions"
Using a recently developed scaled mode coupling theory (MCT), we investigate the linear viscoelastic properties of colloidal model suspensions and discuss possible relations between the (dynamic) shear viscosity and various diffusion coefficients. Results are presented for hard sphere suspensions and for particle dispersions with long-ranged screened Coulomb interactions. The scaled MCT predicts that the shear viscosity of hard sphere suspensions obeys nearly quantitative generalized Stokes-Einstein relations (GSE) both with the long-time self-diffusion coefficient and the long-time collective diffusion measured at the principle peak of the static structure factor. In contrast, the MCT predicts that the same GSE relations are violated in case of suspensions of highly charged particles. We further investigate another empirical GSE due to Mason and Weitz, which relates the frequency dependent elastic storage and viscous loss moduli to the particle mean squared displacement. According to our MCT results, the Mason and Weitz GSE is fullfilled fairly well for concentrated hard sphere suspensions, but strong deviations are found for charge-stabilized dispersions. However, remarkably good agreement is observed between the frequency dependence of the Laplace-transformed normalized viscoelastic relaxation function and the Laplace-transformed normalized time-dependent self-diffusion coefficient of strongly correlated particles.Roland Roth, B. Götzelmann, and S. Dietrich (University of Wuppertal, Germany); M. Dijkstra and R. Evans (University of Bristol, UK)
"Depletion Potential in Hard Sphere Mixtures"
In several experimentally interesting systems, such as mixtures of colloids or mixtures of colloids and polymers, the particle interaction is almost hard-core-like. In these systems entropy plays an important role and gives rise to so-called depletion forces. We present a new versatile approach for calculating the depletion potential in a hard sphere mixture within density functional theory. Our approach is valid for any number of components and for arbitrary densities of all components. This approach, when applied to binary mixtures in the dilute limit, in which the density of one component goes to zero, is in excellent agreement with simulations. The flexibility of our approach allows us to make contact to some recent experiments.Daniel Rudhardt, C. Bechinger, P. Leiderer (Universität Konstanz, Germany)
"Direct Measurements of Entropic Forces in Colloid/Polymer Mixtures"
The mutual interaction of colloidal particles is well known to be strongly influcenced by the presence of smaller uncharged particles, e.g. polymer coils. This phenomenon, which is usually termed depletion interaction, is very important for the phase behavior and flocculation of polydisperse mixtures. We have studied the depletion forces between a single colloidal sphere immersed in a solution of smaller, uncharged polymer coils close to a flat glass surface by means of total internal reflection microscopy (TIRM). This method which was originally invented by Prieve et al. [1] allows the precise measurement of particle-wall interaction potentials and has prooven to be a powerful tool for the investigation of depletion forces. We present experiments where both the polymer concentration and the ratio h=R/r between the radii of the colloids (R) and the polymer coils (r) are changed. For small h we obtain entirely attractive depletion forces which are in agreement with an ideal gas theory [2]. For large h, however, in addition repulsive contributions are observed. We discuss the role of van der Waals forces to account for this effect.Matthias Schmidt (Universität Düsseldorf, Germany)
"Density-Functional Theory for Penetrable Spheres"
Density-functional theory is a powerful tool for the investigation of liquid and solid properties. We use it to study a system of penetrable colloids. Their effective interaction is modeled by a step function that is zero outside the core and has some finite value once two particles overlap. For this pair potential an ab-initio density functional is presented. An overview of the derivation that only requires the geometrical properties of the particles and the exactly known statistical behaviour of the system under strong confinement is given. The functional predicts the bulk fluid structure, in satisfactory agreement with liquid integral theories and simulation, as well as the freezing transition into an fcc crystal with multiply occupied lattice sites. We discuss various limits: For both strong confinement and high temperature the theory becomes exact. Rosenfeld's hard-sphere functional is recovered for zero temperature.An-Chang Shi (Xerox Research Centre of Canada)
"Nature of Anisotropic Fluctuation Modes in Ordered Systems"
The nature of anisotropic fluctuation modes in an ordered structure is analyzed using general symmetry arguments. It is shown that the anisotropic fluctuation modes in a periodic phase can be classified using a wave vector within the irreducible Brillouin zone and a band index. The spatial profiles of the fluctuation modes are described by Bloch functions which are plane waves modulated by periodic functions. These general statements enable the study of the stability and kinetic pathway of complex ordered structures. The utility of the theory is illustrated by the Landau-Brazovskii theory of weak crystallization.Moises Silbert (University of East Anglia, UK)
"Sterically Stabilised Colloidal Dispersions: Beyond Hard Spheres"
Sterically stabilised colloidal dispersions, such as PMMA, have long been regarded as archetypal realisations of hard spheres and hard sphere mixtures. Indeed this is precisely what is found in studies of these systems as a function of the volume fraction, at constant temperature. However, as a function of both volume fraction and temperature, a much richer phase behaviour is found which goes beyond to what is expected from just hard spheres. For instance, sterically stabilised colloids are known to exhibit both upper (high-T) and lower (low-T) two phase behaviour, such that the former is temperature sensitive but the latter is not. We present model calculations, based on a double Yukawa potential, which exhibits some of the rich phase behaviour found experimentally in these systems. We specifically show that, if we assume the exponential coefficient of the repulsive Yukawa to be temperature dependent, the concave up and concave down phases referred to above do appear in our phase diagram. We also present preliminary results for the phase behaviour of binary mixtures of model sterically stabilised colloids.Mark Stevens (Sandia National Laboratories, USA)
"Attraction Between Like-Charged Macroions"
Interactions between charged macroions can be quite complex. One of the intriguing and controversial issues has been whether like-charged macroions exhibit attractive interactions and whether the source of this attraction is due to the Coulomb interactions. Even the basic issue of determining the degree of counterion screening is a computationally difficult task. I will present simulation results of charged macroions with explicit, discrete counterions focused on these issues. Recent algorithms have significantly reduced the cost of Coulomb calculations. Using such an algorithm, attraction between charged rods with divalent counterions are found and studied. Similar simulations for charged spheres find no such attraction. To understand better the nature of the macroion interactions, counterion screening, determined in the simulations, will be compared to various theoretical predictions.René van Roij (University of Bristol, UK)
"Gas-Liquid and Gas-Solid Coexistence in Low-Salt Suspensions of Mutually Repelling Charged Colloids"
Experimental observations of gas-liquid and gas-solid coexistence in low-salt suspensions of charged colloidal particles have led to the proposition that these charged particles (with the same charge sign) must attract each other at long distances. This proposition contrasts the standard DLVO theory which, in accordance with recent experimental measurements of the pair-wise interactions, predicts screened-Coulomb repulsions. In my contribution I will describe my attempts to resolve these apparently contradicting results: a simple (but systematic) density functional theory shows the existence of (i) pair-wise screened-Coulomb repusions between the colloidal particles, and (ii) a so-called volume term that can drive liquid-vapour coexistence at low salt concentrations. These two findings not only explain the experimental observations, but also close an apparent gap between the Debye-Hückel theory for simple electrolytes and the DLVO theory for charged colloidal suspensions.Last updated June 18, 1999