Diffusion size dependence

Diffusion in the bulk crystals may sometimes be short circuited by diffusion down grain boundaries or dislocation cores. The boundary acts as a planar channel, about two atoms wide, with a local diffusion rate which can be as much as 10 times greater than in the bulk (Figs. 18.8 and 10.4). The dislocation core, too, can act as a high conductivity wire of cross-section about (2b), where b is the atom size (Fig. 18.9). Of course, their contribution to the total diffusive flux depends also on how many grain boundaries or dislocations there are when grains are small or dislocations numerous, their contribution becomes important. 

Use of growth rate diffusivity (Randolph and White, 1977 Tavare and Gar-side, 1982) or size dependent growth (Abegg etal., 1968 Mydlarz and Jones, 1993) have both been proposed as alternative phenomenologieal means to deseribe the effeet of growth dispersion on erystal size distributions the latter being simpler mathematieally than the former, but in all probability both meehanisms ean oeeur. 

In the present chapter we shall be concerned with quantitative treatment of the swelling action of the solvent on the polymer molecule in infinitely dilute solution, and in particular with the factor a by which the linear dimensions of the molecule are altered as a consequence thereof. The frictional characteristics of polymer molecules in dilute solution, as manifested in solution viscosities, sedimentation velocities, and diffusion rates, depend directly on the size of the molecular domain. Hence these properties are intimately related to the molecular configuration, including the factor a. It is for this reason that treatment of intramolecular thermodynamic interaction has been reserved for the present chapter, where it may be presented in conjunction with the discussion of intrinsic viscosity and related subjects. 

An important result of this study is the conclusion of a particle-size-dependent COads surface mobility. The value obtained for large Ft particles is significantly smaller than Deo at a solid/gas interface. However, Kobayashi and co-workers, using solid state NMR, performed measurements of the tracer diffusion coefficient Deo at the solid/electrolyte interface and for Ft-black particles (about 5nm grain... 

Bassolino-Klimas, D. Alper, H. E. Stouch, T. R., Drug-membrane interactions studied by molecular dynamics simulation size dependence of diffusion, Drug Des. Discov. 1996,13, 135-141. 

Note that in the special case of size-independent growth, this term can be expressed as a closed function of the moments, i.e., G,t(c) = G(c)mk. Note also that when deriving Eq. (102) we have neglected the size-dependence of This is justified in turbulent flows and, in any case, to do otherwise would require a micromixing model that accounts for differential diffusion (Fox, 2003). 

Because the matrix has permeable characteristics, the ability of the molecules to diffuse will depend on the pore size of the permeable polymer and the available free space in the pores. Obviously, larger molecules would not be able to penetrate the matrix and complex with the NIR dye. As the amount of the dye-analyte complexes increase, the amount of free space into which other analytes can diffuse decreases. Therefore, a relation of the mobility with free space is defined as... 

Substituting hx = 3.6 cm and K ip/w = K - into Eq. 28 Johnson et al. calculated solute lateral diffusion coefficients in stratum corneum bilayers from macroscopic permeability coefficients. Measurements with highly ionized or very hydrophilic compounds were not performed because of the possible transport along a nonlipoidal pathway. Comparison of the computed Aat values with experimentally determined data for fluorescent probes in extracted stratum corneum lipids [47] showed a highly similar curve shape. The diffusion coefficient for the lateral transport showed a bifunctional size dependence with a weaker size dependence for larger, lipophilic compounds (> 350 Da), than... 

Growth of particles by accumulation on existing particles can be classed as two broad processes. If the precursor is supersaturated, growth will occur at a rate limited by vapor diffusion, which depends on the supersaturation, the temperature, the particle size, and the accommodation coefficient at the surface. The proportionality of particle size changes with the ratio of particle diameter to mean free path of the suspending... 

Size-dependent crystal growth is Included in the model because it can be important to describe diffusion limited growth rates or crystal attrition. As discussed in (6,X), the size reduction by attrition can be modelled by an effective growth rate G (L,t) which is the difference between the kinetic growth rate G, (L,tT and an attrition rate G (L,t) ... 

The diffusion of larger organic vapor molecules is related to absorption. The rate of diffusion is dependent on the size and shape of the diffusate molecules, their interaction with the polymer molecules, and the size, shape, and stiffness of the polymer chains. The rate of diffusion is directly related to the polymer chain flexibility and inversely related to the size of the diffusate molecules. 

Different size dependencies of thermal diffusion in aqueous and organic carriers have been reported in the literature [31] and, to date, this phenomenon is still a research topic. 

Protein transfer from the brain into CSF, and from blood into CSF, follows the law of diffusion as a function of molecular size. The diffusion-related transfer of proteins into CSF is the cause for molecular size-dependent discrimination (i.e., selectivity) of the barrier function. As a consequence, we have larger CSF/ serum quotients for the smaller molecules QAlb > QIgG > QIgA > QIgM. Again, the smaller albumin molecule equilibrates faster between blood and CSF than do the larger molecules of IgG, IgA, or IgM. 

From H NMR self-diffusion measurements, the molecular diffusion coefficients could be calculated. Since the diffusion coefficients depend on the size and... 

Figure 10 Size-dependence of the melting point and diffusion coefficient of silica-encapsulated gold particles. The dotted curve is calculated by the equation of Buffat and Borel. The bulk melting temperature of An is indicated by the double arrow as (oo). The solid curve (right-hand side axis) is a calculated An self-diffusion coefficient. (From Ref. 146.)...

The activity of polymer-supported crown ethers is a function of % RS as shown in Fig. 11 149). Rates for Br-I exchange reactions with catalysts 34, 35, and 41 decreased as % RS increased from 14-17% to 26-34%. Increased % RS increases the hydro-philitity of the catalysts, and the more hydrated active sites are less reactive. Less contribution of intraparticle diffusion to rate limitation was indicated by less particle size dependence of kohMi with the higher % RS catalysts149). 

For Am there is no evident particle size dependence. The kinetics are considerably slower than for Cs (and Sr). Possibly the sorption process is a volume dependent adsorption with contributions from ion exchange. The sorption and also the diffusion into the particles should be governed by the complicated hydrolysis reactions to be expected at environmental pH. Other tri- and tetra-valent elements would be expected to show a similar slow non-surface related sorption behaviour. 

Polyvinylchloride was the host polymer in a study of the diffusion of dimethyl-phthalate, dibutylphthalate, and dioctylphthalate, performed by Maklakov, Smechko, and Maklakov 60) between room temperature and 110 °C. Azancheev and Maklakov 61) extended this work to include polystyrene as host, and to dependences of diffusion on concentration. They concluded that the macromolecules did constrain and trap the phthalate molecules at high polymer concentration, but without inhibiting the mobility of these diluents at lower polymer concentrations, e.g., in the gel. They used a version of the free volume theory to give a semi-quantitative explanation of the temperature and molecular size dependence of phthalate diffusion. 

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