Large-scale self-diffusion coefficient

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. 

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. 

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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