Colloid properties Brownian diffusion

In this chapter the thermal motion of dissolved macromolecules and dispersed colloidal particles will be considered, as will their motion under the influence of gravitational and centrifugal fields. Thermal motion manifests itself on the microscopic scale in the form of Brownian motion, and on the macroscopic scale in the forms of diffusion and osmosis. Gravity (or a centrifugal field) provides the driving force in sedimentation. Among the techniques for determining molecular or particle size and shape are those which involve the measurement of these simple properties. 

As discussed in Chapters 1-7, diffusion, Brownian motion, sedimentation, electrophoresis, osmosis, rheology, mechanics, interfacial energetics, and optical and electrical properties are among the general physical properties and phenomena that are primarily important in colloidal systems [12,13,26,57,58], Chemical reactivity and adsorption often play important, if not dominant, roles. Any physical chemical feature may ultimately govern a specific industrial process and determine final product characteristics, and any colloidal dispersions involved may be deemed either desirable or undesirable based on their unique physical chemical properties. Chapters 9-16 will provide some examples. 

A second ensemble technique is DLS (Nicoli et al, 1991) - also called quasi-elastic light scattering (QELS) or photon correlation spectroscopy (PCS) — which is based on analysis of the temporal fluctuations in the scattered intensity caused by Brownian motion, or diffusion, of the particles. In recent years, it has become a popular technique for characterizing many submicron colloidal systems, including polymer lattices, because of its large size range (roughly 1 nm to 5 p,m) and approximate independence from optical properties. 

The first such relation involving the irreducible memory functions is based on a physically intuitive notion Brownian motion and diffusion are two intimately related concepts we might say that collective diffusion is the macroscopic superposition of the Brownian motion of many individual colloidal particles. It is then natural to expect that collective diffusion should be related in a simple manner to self-diffusion. In the original proposal of the SCGLE theory [18], such connections were made at the level of the memory functions. Two main possibilities were then considered, referred to as the additive and the multiplicative Vineyard-like approximations. The first approximates the difference [C(k, z) - O Kk, z)], and the second the ratio [C k, z)IO k, z)], of the memory functions, by their exact short-time limits, using the fact that the exact short-time values, C P(fe, t) and (35)SEXP( 0, of these memory functions are known in terms of equilibrium structural properties [18]. The label SEXP refers to the single exponential time dependence of these memory functions. 

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