Subject self-diffusivity

It will be noted that because of the low self-diffusion coefficients the numerical values for representations of self-diffusion in silicon and germanium by Anhenius expressions are subject to considerable uncertainty. It does appear, however, that if this representation is used to average most of the experimental data the equations are for silicon... 

The self-diffusion coefficient is determined by measuring the diffusion rate of the labeled molecules in systems of uniform chemical composition. This is a true measure of the diffusional mobility of the subject species and is not complicated by bulk flow. It should be pointed out that this quantity differs from the intrinsic diffusion coefficient in that a chemical potential gradient exists in systems where diffusion takes place. It can be shown that the self-diffusion coefficient, Di, is related to the intrinsic diffusion coefficient, Df, by... 

In polymers, the field-gradient spin-echo methods of measuring self-diffusion have been useful in three more or less distinct areas, the diffusion of polymers in their own melt and in concentrated solutions, in dilute and semidilute solutions, and the diffusion of penetrants and diluents in polymer hosts. A fourth category, the diffusion of bulky or flexible molecules in polymer hosts, is useful for subject matter not closely associated with the first and third category. It should be noted that the work reviewed here represents only a small fraction of the diffusion studies in polymers, including those using other NMR methods. 

While there have been efforts to polymerize other surfactant mesophases and metastable phases, bicontinuous cubic phases have only very recently been the subject of polymerization work. Through the use of polymerizable surfactants, and aqueous monomers, in particular acrylamide, polymerization reactions have been performed in vesicles (4-8). surfactant foams ), inverted micellar solutions (10). hexagonal phase liquid crystals (111, and bicontinuous microemulsions (121. In the latter two cases rearrangement of the microstructure occured during polymerization, which in the case of bicontinuous microemulsions seems inevitable b ause microemulsions are of low viscosity and continually rearranging on the timescale of microseconds due to thermal disruption (131. In contrast, bicontinuous cubic phases are extremely viscous in genei, and although the components display self-diffusion rates comparable to those... 

If the viscosity N itself fluctuates to a small extent according to N = A/o[l 4- (n/No) sin jx ], clearly will not vary with x if s /Sq = h/Nq. In other words, if a fluctuation n is prescribed and the material is subjected to uniform constriction, a stress fluctuation s will result when j is small, s is adequately approximated by 6ne (self-diffusion negligible), but for large values of j the complete expression 6ne /(l + j R /2) is needed it leads to smaller magnitudes for s than the approximate form. 

At box (6), V S affects if the stress state is more strongly nonhydro-static at some points than at others, volume-loss by self-diffusion will not be isotropic and change of shape will occur. [Boxes (5) and (6) are the subject of Chapter 13.]... 

At present, no reported data on ring self-diffusion in polymer concentrates are available other than those of Mills et al. and no theory of this subject exists other than Klein s. Thus we see a virgin field of research open before us. What seems most needed is experimental data for self-diffusion in the melt and concentrated solutions of rings. Diffusion of linear chains in ring chain matrices should also be instructive, as pointed out by Mills et al. The reptation idea now dominating the study of polymer self-diffusion will face crucial tests when accurate and systematic diffusion data on these systems become available. 

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. 

The initial motivation for the study of self-diffusion in the bcc phases of the rare earth elements is connected to the problem of so-called anomalous diffusion in bcc metals. Any discussion of self-diffusion in the bcc rare earth metals must be viewed against the background of this anomalous diffusion. This subject has received extensive coverage and has been summarized by Le Claire (1965), Lazarus (1965), Peterson (1968) and Seeger (1972). 

To start with, NMR is a very powerful tool for the study of surface and colloid chemistry in general and several good reviews on this subject have been produced (1-5). As far as micelle size and shape are concerned, two main experiments prevail in the literature, namely NMR relaxation and self-diffusion measurements. The technique of NMR self-diffusion is a relative tool for the study of micellar size and shape since it uses the Stokes-Einstein relationship (or modifications to it) to... 

Interdiffusion may be discerned from a macroscopic perspective by changes in concentration that occur over time, as in the example for the Cu-Ni diffusion couple. There is a net drift or transport of atoms from high- to low-concentration regions. Diffusion also occurs for pure metals, but all atoms exchanging positions are of the same type this is termed self-diffusion. Of course, self-diffusion is not normally subject to observation by noting compositional changes. 

Self-diffusion involves the motion of atoms that are all of the same type therefore, it is not subject to observation by compositional changes, as with interdiffusion. Suggest one way in which selfdiffusion may be monitored. 

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