Colloidal dispersions description

In Sec. 3 our presentation is focused on the most important results obtained by different authors in the framework of the rephca Ornstein-Zernike (ROZ) integral equations and by simulations of simple fluids in microporous matrices. For illustrative purposes, we discuss some original results obtained recently in our laboratory. Those allow us to show the application of the ROZ equations to the structure and thermodynamics of fluids adsorbed in disordered porous media. In particular, we present a solution of the ROZ equations for a hard sphere mixture that is highly asymmetric by size, adsorbed in a matrix of hard spheres. This example is relevant in describing the structure of colloidal dispersions in a disordered microporous medium. On the other hand, we present some of the results for the adsorption of a hard sphere fluid in a disordered medium of spherical permeable membranes. The theory developed for the description of this model agrees well with computer simulation data. Finally, in this section we demonstrate the applications of the ROZ theory and present simulation data for adsorption of a hard sphere fluid in a matrix of short chain molecules. This example serves to show the relevance of the theory of Wertheim to chemical association for a set of problems focused on adsorption of fluids and mixtures in disordered microporous matrices prepared by polymerization of species. 

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. 

Equation (6.4) is applicable to a description of the flow behaviour of ideal fluids, or Newtonian fluids. Examples include water, mineral oils, bitumen, and molasses. However, many fluids, especially colloidal dispersions, do not obey Eq. (6.4), usually due to the mutual orienting and even structure formation of the dispersed species in the flow. 

Attempts to describe the unlimited increase of the viscosity of dispersions and emulsions observed when their concentrations approach the maximum values (tPmax) meet great theoretical difficulties. Various approaches were developed to overcome these difficulties. Thus, for example, Russel et al. [58] suggested that account should be taken of the Brownian motion of particles in colloidal dispersions in the form of a hydrodynamic contribution. They showed that this contribution which is to be taken into account in considering a slow flow (with slow shear rates y), increases considerably with increasing dispersion concentration. For a description of the dependence of viscosity on concentration the above authors obtained an exact equation only in the integral form. At low shear rates it gives the following power series ... 

The MCT-ITT approach thus provides a microscopic route to calculate the generalized shear modulus g t, y) and other quantities characteristic of the quiescent and the stationary state under shear flow. While MCT has been reviewed thoroughly, see, e.g., [2, 38, 39], the MCT-ITT approach shall be reviewed here, including its recent tests by experiments in model colloidal dispersions and by computer simulations. The recent developments of microscopy techniques to study the motion of individual particles under flow and the improvements in rheometry and preparation of model systems, provide detailed information to scrutinize the theoretical description, and to discover the molecular origins of viscoelasticity in dense colloidal dispersions even far away from thermal equilibrium. 

Consequently, this approach reflects in the most general way the specifics of the colloidal dispersed state, and introduces into the thermodynamic description of disperse systems two terms different in nature... 

Gouy-Chapman Theory A description of the electric double layer in a colloidal dispersion in which one layer of charge is assumed to exist as a uniform charge distribution over a surface and the counterions are treated as point charges distributed throughout the continuous dielectric phase. 

This process is, however, not as simple as this brief description implies, and stable colloidal dispersions are obtained only if the conditions are properly controlled. 

In the W century the description of materials could be based for the first time on an experiment-based atomic theory. This permitted an easy recognition of the differences between phases and molecules. Phases are macroscopic, homogeneous volumes of matter, separated from other phases by well-defined boundaries, and molecules are the constituent smallest particles that make up the phases. As research progressed, microphases were discovered, initially in the form of colloidal dispersions. More recently, it was recognised that phase-areas may be of nanometer dimensions (nanophases). On the other hand, flexible macromolecules have micrometer lengths or larger. Particularly the nanophases may then have structures with interfaces that frequendy intersect macromolecules, giving the materials unique properties. 

Theoretical descriptions of such behavior have been given in terms of a mechanism first put forward by Ostwald around the turn of the centory, namely that a critical local supersaturation is required to initiate local precipitation (see Henisch, 1988 Klueh and Mullins, 1969 Prager, 1956 Wagner, 1950). But subsequent experimental studies have raised questions concerning the applicability of this mechanism (Kai et al., 1982). In particular, the solid has been observed to form as a colloidal dispersion before the appearance of bands. Also it has been found that bands sometimes develop, in contrast to predictions of the above theory, in systems of uniform initial composition (Hicker and Ross, 1974). 

For rapid coagulation induced by the addition of 1.0 mol dm KQ, the Smoluchowski kinetic scheme gave an excellent description for the rapid coagulation of colloidal dispersions (Figures 12 and 13). This was shown by the linearity of the second order rate constant plots the lack of any concentration effects the closeness of the final rate constants to the diffusion-limited value of 6.1 X 10" cm s ... 

In this chapter we discuss the basics of the phase behaviour of hard spheres plus depletants. Phase transitions are the result of physical properties of a collection of particles depending on many-body interactions. In Chap. 2 we focused on two-body interactions. As we shall see, depletion elfects are commonly not pair-wise additive. Therefore, the prediction of phase transitions of particles with depletion interaction is not straightforward. As a starting point a description is required for the thermodynamic properties of the pure colloidal dispersion. Here the colloid-atom analogy, recognized by Einstein and exploited by Perrin in his classical experiments, is very useful. Subsequently, we explain the basics of the free volume theory for the phase behaviour of colloids -I- depletants. In this chapter we treat only simplest type of depletant, the penetrable hard sphere. 

In the vast literature that covers the subject of polymer brushes, one may find numerous studies concerning brush formation and properties on flat surfaces. Since the introduction of the concept, polymer brushes have been studied traditionally on flat macroscopic surfaces due to the applicability of well-established experimental techniques and also because of the relative simplicity of the theoretical description on a flat geometry. However, the properties of polymer brushes grown on curved interfaces (especially on the surface of micro- and nanoparticles) have also received interest because of early-suggested applications in the stabilization of colloid dispersions [1]. 

In the 1940s, a scientific theory describing the delicate balance of colloidal dispersion and aggregation was developed by Derjaguin and Landau and by Verwey and Overbeek. The theory is usually called the DLVO theory for short. In this theoretical description, a potential V is used to describe the different interactions between colloidal particles in solution and we can simply write... 

This chapter deals mainly with the thermodynamic and rheological properties of aqueous colloidal dispersions of complexes of polyelectrolytes (PE) with ionizable organic molecules, in particular model drugs. In addition, it follows with a description of a survey of several appUcations based on the unique properties of... 

Historically, the bulk lubricant has been studied by dielectric spectroscopy and interpreted according to the Debye relaxation theory [3,4]. In impedance terms the system can also be represented according to a theory of colloidal dispersions or polycrystalline media composed of spheres of vastly different conductivities, where the contaminants become a more conductive phase suspended inside the less conductive additive/base oil matrix [6, 34]. Alternatively, when the contaminants are absent, the polar additives can be considered as a conductive discontinuous phase suspended inside insulating continuous base oil. Initially the description of the impedance representation of the fresh, uncontaminated oil will be provided, and then the effects of oxidative degradation and contaminants will be discussed. 

In this article we will focus on systems which comprise particles, with or without internal degrees of freedom, suspended in a simple fluid. We will first outline the necessary ingredients for a theoretical description of the dynamics, and in particular explain the concept of hydrodynamic interactions (HI). Starting from this background, we will provide a brief overview of the various simulation approaches that have been developed to treat such systems. All of these methods are based upon a description of the solute in terms of particles, while the solvent is taken into account by a simple (but sufficient) model, making use of the fact that it can be described as a Newtonian fluid. Such methods are often referred to as mesoscopic. We will then describe and derive in some detail the algorithms that have been developed by us to couple a particulate system to a LB fluid. The usefulness of these methods will then be demonstrated by applications to colloidal dispersions and polymer solutions. Some of the material presented here is a summary of previously published work. 

Let us now apply the general concepts above to the description of the Brownian motion of a tracer particle that interacts with the other particles of a colloidal dispersion [23,55]. In this manner we will derive an exact result for the time-dependent friction function A (t), which is later given a useful approximate expression. 

---