Statistical Mechanics of Colloidal Suspensions

To relate macroscopic observables to forces acting between particles is the objective. The relevant measurable properties are (a) the phase diagram, (b) scattering of photons, neutrons, and X-rays, (c) the osmotic equation of state, and (d) rheological behaviour. This Report covers (a), (b), and (c) with emphasis on the transition between ordered and disordered states. Discussion of (b) is limited to light-scattering. Current problems in relation to (d) are set out (up to mid-1980). 

Five types of forces between colloidal particles may be identified (i) repulsive forces, from the overlap of electrical double-layers (ii) dispersion forces, from long-range van der Waals attraction between molecules in neighbouring particles (iii) steric forces, from interaction of macromolecules adsorbed at the particle surface (iv) structural and Brownian forces, from interaction with solvent molecules of the dispersion medium and (v) hydrodynamic forces. 

In an electrostatically-stabilized dispersion in which the particles do not approach within a distance of about 10 or 15 solvent diameters, the equilibrium behaviour depends only on the double-layer repulsion and van der Waals attraction. The interaction energy between pairs of spherical particles i and / a distance r apart is split into two parts, arising respectively from repulsive and 

In equation (2), is the relative dielectric constant of the continuous phase, is the absolute permittivity of free space, a is the particle radius, tjf is the surface potential, and d is the closest surface-to-surface separation. The quantity k, the reciprocal of the Debye length, is defined by 

This Report places emphasis on the time-averaged behaviour of assemblies with pair-wise DLVO-t5qje potentials given by equations (1)—(4). This reflects the strong current interest in the phase equilibria of electrostatically-stabilized dispersions of spherical latex particles. Pair-wise additivity, in which the total excess potential energy of N particles is given by 

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Other review articles relating to colloidal suspensions and containing discussions of numerical calculations (Monte Carlo simulations) include contributions by van Megen and Snook (1984) and Castillo et al. (1984). The scope of these articles is not, however, limited to numerical techniques they also provide general reviews of the statistical mechanics of colloidal suspensions. 

Statistical Mechanics of Colloidal Suspensions attractive forces,... 

Ray Kapral came to Toronto from the United States in 1969. His research interests center on theories of rate processes both in systems close to equilibrium, where the goal is the development of a microscopic theory of condensed phase reaction rates,89 and in systems far from chemical equilibrium, where descriptions of the complex spatial and temporal reactive dynamics that these systems exhibit have been developed.90 He and his collaborators have carried out research on the dynamics of phase transitions and critical phenomena, the dynamics of colloidal suspensions, the kinetic theory of chemical reactions in liquids, nonequilibrium statistical mechanics of liquids and mode coupling theory, mechanisms for the onset of chaos in nonlinear dynamical systems, the stochastic theory of chemical rate processes, studies of pattern formation in chemically reacting systems, and the development of molecular dynamics simulation methods for activated chemical rate processes. His recent research activities center on the theory of quantum and classical rate processes in the condensed phase91 and in clusters, and studies of chemical waves and patterns in reacting systems at both the macroscopic and mesoscopic levels. 

D. Ronis, Phys. Rev. E, 49,5438 (1994). Statistical Mechanics of Ionic Colloids Interparticle Correlations and Conformational Equilibria in Suspensions of Polymer Coated Colloids. 

Prediction of the stability of colloidal suspensions has been analysed in two ways. The first sums the above energy changes due to London attraction and double layer repulsion respectively as particles approach each other with the net effect passing through a maximum (Figure 6.9). This is known as the DLVO (Derjaguin-Landau and Verwey-Overbeek) model and its development forms a major part of the statistical mechanical theory of colloid stability (Derjaguin... 

The statistical mechanical approach, density functional theory, allows description of the solid-liquid interface based on knowledge of the liquid properties [60, 61], This approach has been applied to the solid-liquid interface for hard spheres where experimental data on colloidal suspensions and theory [62] both indicate 0.6 this... 

Statistical mechanics was originally formulated to describe the properties of systems of identical particles such as atoms or small molecules. However, many materials of industrial and commercial importance do not fit neatly into this framework. For example, the particles in a colloidal suspension are never strictly identical to one another, but have a range of radii (and possibly surface charges, shapes, etc.). This dependence of the particle properties on one or more continuous parameters is known as polydispersity. One can regard a polydisperse fluid as a mixture of an infinite number of distinct particle species. If we label each species according to the value of its polydisperse attribute, a, the state of a polydisperse system entails specification of a density distribution p(a), rather than a finite number of density variables. It is usual to identify two distinct types of polydispersity variable and fixed. Variable polydispersity pertains to systems such as ionic micelles or oil-water emulsions, where the degree of polydispersity (as measured by the form of p(a)) can change under the influence of external factors. A more common situation is fixed polydispersity, appropriate for the description of systems such as colloidal dispersions, liquid crystals, and polymers. Here the form of p(cr) is determined by the synthesis of the fluid. 

The phase behavior of nonaqueous colloidal suspensions containing nonadsorbing polymer was investigated by Gast et al. [3] on the basis of statistical mechanics. In their theory, a second-order perturbation approach was used to calculate the free energy. Rao and Ruckenstein [4,5] examined the phase behavior of systems involving steric, depletion, and van der Waals interactions. 

There are three chapters in this volume, two of which address the microscale. Ploehn and Russel address the Interactions Between Colloidal Particles and Soluble Polymers, which is motivated by advances in statistical mechanics and scaling theories, as well as by the importance of numerous polymeric flocculants, dispersants, surfactants, and thickeners. How do polymers thicken ketchup Adler, Nadim, and Brenner address Rheological Models of Suspensions, a closely related subject through fluid mechanics, statistical physics, and continuum theory. Their work is also inspired by industrial processes such as paint, pulp and paper, and concrete and by natural systems such as blood flow and the transportation of sediment in oceans and rivers. Why did doctors in the Middle Ages induce bleeding in their patients in order to thin their blood ... 

Later methods made adjustments to external forces to account for periodic boundary conditions and introduced suitable modifications of the Hamiltonian or the Newtonian equations of motion [75-78]. Considerable progress has been made since those early efforts, both with the original [79-83] and modified Hamiltonian approaches [84]. However, many subtle issues remain to be resolved. These issues concern the non-Hamiltonian nature of the models used in NEMD and the need to introduce a thermostat to obtain a stationary state. Recently Tuckerman et al. [25] have considered some statistical mechanical aspects of non-Hamiltonian dynamics and this work may provide a way to approach these problems. Although the field of NEMD has been extensively explored for simple atomic systems, its primary applications lie mainly in treating nonequilibrium phenomena in complex systems, such as transport in polymeric systems, colloidal suspensions, etc. We expect that there will be considerable activity and progress in these areas in the coming years [85]. 

Albert Einstein (1879-1955). .. was a German-bom theoretical physicist who is mainly renowned for his special theory of relativity and its extension to the general theory of relativity. In addition to this, he worked on statistical mechanics and quantum theory and investigated the thermal properties of light. At the beginning of his scientific career he also set important landmarks for colloid science. This applies particularly to his explanation of Brownian motion, but is also valid for the calculation of suspension viscosity as well as his theory of critical opalescence. In 1921, he was given the Nobel Prize in Physics Tor his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect . 

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