Colloids short-time diffusion

Short-time Brownian motion was simulated and compared with experiments [108]. The structural evolution and dynamics [109] and the translational and bond-orientational order [110] were simulated with Brownian dynamics (BD) for dense binary colloidal mixtures. The short-time dynamics was investigated through the velocity autocorrelation function [111] and an algebraic decay of velocity fluctuation in a confined liquid was found [112]. Dissipative particle dynamics [113] is an attempt to bridge the gap between atomistic and mesoscopic simulation. Colloidal adsorption was simulated with BD [114]. The hydrodynamic forces, usually friction forces, are found to be able to enhance the self-diffusion of colloidal particles [115]. A novel MC approach to the dynamics of fluids was proposed in Ref. 116. Spinodal decomposition [117] in binary fluids was simulated. BD simulations for hard spherocylinders in the isotropic [118] and in the nematic phase [119] were done. A two-site Yukawa system [120] was studied with... 

Section 10.3 treated mutual diffusion of colloidal spheres. To summarize significant results the low-concentration dependence of D on (j) is close to zero, in reasonable agreement with models based on the assertion that Dm 4>) of colloidal spheres is determined by the direct and hydrodynamic interactions of the spheres, and that (as also found for Ds) dynamic friction corrections are not large at short times. The value of Dmiinitial slope ko decreases markedly with increasing q at large Dm (q) approaches Ds, as expected theoretically. 

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. 

The dynamics of all our fluid-like, ergodic systems is characterized by a two-step decay, which is a typical characteristic of the dynamics of colloidal suspensions at larger effective volume fractions the short-time dynamics is associated to the diffusion of the spheres within the cages of nearest neighbors, while the long-time dynamics is due to the structural rearrangement of the cages themselves. 

As one would expect, the understanding of the mechanism of the formation of monodispersed colloids by precipitation has been of major concern to workers in the field. For a long time the concept developed by LaMer was generally accepted that is, such dispersions should be generated, if a short lived burst of nuclei in a supersaturated solution is followed by controlled diffusion of constiment solutes onto these nuclei, resulting in the final uniform particles. This mechanism is indeed operational in some, albeit limited, cases, and more often only at the initial stage of the precipitation process. 

Shortly after this study, Graham discovered that certain substances, such as lime, diffuse much more slowly than, say, common salt, and do not readily permeate a membrane. Since this behavior was characteristic of limelike, noncrystalline substances, whereas the crystalline substances known at that time all diffused and permeated rapidly, Graham differentiated between crystalloids and colloids (from the Greek Kokka = lime). He thus attributed the colloidal behavior to the structure of the colloids and not to their state. 

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