Large-scale self-diffusion

Figure 9.8 Isolated-boundary (Type-B) self-diffusion associated with a stationary grain boundary, (a) Grain boundary of width 6 extending downward from the free surface at y = 0. The surface feeds tracer atoms into the grain boundary and maintains the diffusant concentration at the grain boundary s intersection with the surface at the value cB(y = 0, t) = 1. Diffusant penetrates the boundary along y and simultaneously diffuses transversely into the grain interiors along x. (b) Diffusant distribution as a function of scaled transverse distance, xi, from the boundary at scaled depth, yx, from the surface. Penetration distance in grains is assumed large relative to 5.

The "laminar" macroscopic flow equations contain phenomenological terms which represent averages over the macroscopic dynamics to include the effects of turbulence. Examples of these terms are eddy viscosity and diffusivity coefficients and average chemical heat release terms which appear as sources in the macroscopic flow equations. Besides providing these phenomenological terms, the turbulence model must use the information provided by the large scale flow dynamics self-consistently to determine the energy which drives the turbulence. The model must be able to follow reactive interfaces on the macroscopic scale. 

In many structured products, water management includes several mass transport mechanisms such as hydrodynamic flow, capillary flow and molecular self-diffusion depending on the length scale. Hydrodynamic flow is active in large and open structures and it is driven by external forces such as gravity or by differences in the chemical potential, that is, differences in concentrations at different locations in the structure. Capillary flow also depends on surface tension and occurs in channels and pores on shorter length scales than in hydrodynamic flow. A capillary gel structure will hold water, and external pressures equivalent to the capillary pressure will be needed to remove the water. 

Local motions which occur in macromolecular systems can be probed from the diffusion process of small molecules in concentrated polymeric solutions. The translational diffusion is detected from NMR over a time scale which may vary from about 1 to 100 ms. Such a time interval corresponds to a very large number of elementary collisions and a long random path consequently, details about mechanisms of molecular jump are not disclosed from this NMR approach. However, the dynamical behaviour of small solvent molecules, immersed in a polymer melt and observed over a long time interval, permits the determination of characteristic parameters of the diffusion process. Applying the Langevin s equation, the self-diffusion coefficient Ds is defined as... 

Very recently, a novel Fourier transform NMR method was employed by Lindman, et al. (21) to obtain multicomponent self-diffusion data for some single phase microenulsion systems. Because of the large values obtained for the self-diffusion coefficients of water, hydrocarbon, and alcohol, over a wide range of concentrations, the authors concluded that there are no extended, well-defined structures in these systems. In other words, the Interfaces which separate the hydrophobic from the hydrophilic regions appear to open up and reform at a short time scale. 

Let us start the description of the principles with a simple case. Assume a dispersion of one solvent in another. If the (discrete) drops of the dispersed phase are large, i.e., considerably larger than the distance over which diffusion is monitored, then the self-diffusion of both components will be unrestricted on the relevant time scale and we will observe high D values for both solvents. In fact, except for an obstruction correction, which may amount to at most about 30%, the D values will be the same as for the neat solvents. If the diffusion distance and the drop sizes match each other, the observed diffusion will be critically dependent on the (variable) diffusion time chosen. These cases are not applicable to microemulsions but give the basis for a very important general and noninvasive technique of monitoring drop sizes (and fusion processes) in (macro)emulsions [13,20-27]. 

The experimental methods for measurement of transport and self-diffusion in zeolite crystals (and in other microporous materials) are reviewed. Large discrepancies between distent techniques are commonly observed and appear to be related to the scale of the measurements, suggesting that structural defects may be more important than is generally believed. 

The Brownian motion of a polymer chain for self-diffusion is carried out by the integration of Brownian motions of monomers. Therefore, the entropic elasticity of chain conformation in a random coil allows a large-scale deformation, with its extent subject to the external stress for polymer deformatiOTi and flow, and hence exposes the characteristic feature of a mbber state in a temperature window between the glass state and the fluid state. 

When multiple scattering is discarded from the measured signal, DLS can be used to study the dynamics of concentrated suspensions, in which the Brownian motion of individual particles (self-diffusion) differs from the diffusive mass transport (gradient or collective diffusion), which causes local density fluctuations, and where the diffusion on very short time-scales (r < c lD) deviates from those on large time scales (r c D lones and Pusey 1991 Banchio et al. 2000). These different diffusion coefficients depend on the microstructure of the suspension, i.e. on the particle concentration and on the interparticle forces. For an unknown suspension it is not possible to state a priori which of them is probed by a DLS experiment. For this reason, a further concentration limit must be obeyed when DLS is used for basic characterisation tasks such as particle sizing. As a rule of thumb, such concentration effects vanish below concentrations of 0.01-0.1 vol%, but certainty can only be gained by experiment. 

The sloping solid line shows the reported temperature variation of T2 between 13 K and 17 K for unconstrained solid D2 with an x = 0.33 p-D2 fraction. The dashed curve shows the coefficient of self-diffusion (on the right hand scale) reported for liquid n-H2 at SVP. Liquid D2 diffusion must follow a similar curve. It is probable that the observed temperature variation of T2 for the narrow central DMR component in a-Si D,F (325) reflects the melting of bulk solid and diffusion in dense fluid D2 in microvoids. Either the presence of F produces unusually large voids (which does not seem likely) or else void surfaces are rendered less effective in controlling the relaxation properties of the contained D2 than was the case in a-Si D,H (circles). 

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