Diffusing molecule

Deniz A A, Dahan M, Grunwell J R, Ha T, Faulhaber A E, Chemla D S, Weiss S and Schultz P G 1999 Single-pair fluorescence resonance energy transfer on freely diffusing molecules observation of Forster distance dependence and subpopulations Proc. Natl Acad. Sc/. USA 96 3670-5... 

Micropore Diffusion. In very small pores in which the pore diameter is not much greater than the molecular diameter the diffusing molecule never escapes from the force field of the pore wall. Under these conditions steric effects and the effects of nonuniformity in the potential field become dominant and the Knudsen mechanism no longer appHes. Diffusion occurs by an activated process involving jumps from site to site, just as in surface diffusion, and the diffusivity becomes strongly dependent on both temperature and concentration. 

Activated diffusion of the adsorbate is of interest in many cases. As the size of the diffusing molecule approaches that of the zeohte channels, the interaction energy becomes increasingly important. If the aperture is small relative to the molecular size, then the repulsive interaction is dominant and the diffusing species needs a specific activation energy to pass through the aperture. Similar shape-selective effects are shown in both catalysis and ion exchange, two important appHcations of these materials (21). 

The lowest diffusion rates occur with crystalline polymers below the Tj, since there is very little space through which diffusing molecules may pass. 

For amorphous polymers above the T, i.e. in the flexible and rubbery states there is more space available through which diffusing molecules may pass, and so these materials show comparatively high diffusion rates with diffusing fluids. 

Diffusion Molecules of a fluid already inside a polymer at a high-concentration region compared with surrounding regions will diffuse over a finite time away from the high concentration until an equilibrium situation is achieved. If the high concentration is at the surface, diffusion occurs into the bulk. The diffusant molecules move stepwise into free volume holes as they form according to kinetic theory. 

The hydrodynamic drag experienced by the diffusing molecule is caused by interactions with the surrounding fluid and the surfaces of the gel fibers. This effect is expected to be significant for large and medium-size molecules. Einstein [108] used arguments from the random Brownian motion of particles to find that the diffusion coefficient for a single molecule in a fluid is proportional to the temperature and inversely proportional to the frictional coefficient by... 

The Stokes-Einstein equation can be successfully used to explain diffusion under the following conditions [401], where (a) the diffusing molecule is large with respect to the molecules defining the medium, (b) the medium has a very low viscosity, and (c) no solute-solvent interactions occur. 

When using the microporous zeolite membrane (curve 3) the N2 permeance decreases when the pressure increases such a behaviour can be accounted for by activated diffusion mechanisms [21], which are typical of zeolite microporous systems. In such systems the difflisivity depends on the nature and on the concentration of the diffusing molecule which interacts with the surface of the pore. For gases with low activation energies of diffusion, a decrease of the permeability can be observed [22]. 

The negative sign in Fick s first law suggests that diffusion occurs in the opposite direction to increasing concentration. In other words, diffusion occurs in the direction of decreasing concentration of diffusing molecules. 

The net contribution to the rate of accumulation of diffusing molecules in the element from these two faces is thus equal to... 

If neither convection nor chemical reaction occurs within the element, the rate of accumulation of diffusing molecules is then equal to the net contribution by diffusion ... 

Although these examples demonstrate the feasibility of using calculated values as estimates, several constraints and assumptions must be kept in mind. First, the diffusant molecules are assumed to be in the dilute range where Henry s law applies. Thus, the diffusant molecules are presumed to be in the unassociated form. Furthermore, it is assumed that other materials, such as surfactants, are not present. Self-association or interaction with other molecules will tend to lower the diffusion coefficient. There may be differences in the diffusion coefficient for molecules in the neutral or charged state, which these equations do not account for. Finally, these equations only relate diffusion to the bulk viscosity. Therefore, they do not apply to polymer solutions where microenvironmental viscosity plays a role in diffusion. 

Various diffusion coefficients have appeared in the polymer literature. The diffusion coefficient D that appears in Eq. (3) is termed the mutual diffusion coefficient in the mixture. By its very nature, it is a measure of the ability of the system to dissipate a concentration gradient rather than a measure of the intrinsic mobility of the diffusing molecules. In fact, it has been demonstrated that there is a bulk flow of the more slowly diffusing component during the diffusion process [4], The mutual diffusion coefficient thus includes the effect of this bulk flow. An intrinsic diffusion coefficient, Df, also has been defined in terms of the rate of transport across a section where no bulk flow occurs. It can be shown that these quantities are related to the mutual diffusion coefficient by... 

The tortuosity factor appears as a squared term because it decreases the concentration gradient and increases the diffusive path length. Using a cubic lattice model and inquiring how many steps a diffusing molecule needs to take to get around an obstacle, 0 was derived to be... 

Permeation of small molecules through polymers takes place in four steps. In the first stage, the permeating molecules, know as the diffusants, wet or adsorb onto the polymer s surface. Secondly, the diffusant molecules dissolve in the polymer. In the third step, the molecules diffuse down a concentration gradient towards the opposing surface. Finally, the diffusant molecules desorb or evaporate from the surface, or are absorbed into another material. 

In the above discussion, we have presumed that the tortuosity factor t is characteristic of the pore structure but not of the diffusing molecules. However, when the size of the diffusing molecule begins to approach the dimensions of the pore, one expects the solid to exert a retarding influence on the flux and this effect may also be incorporated in the tortuosity factor. This situation is likely to be significant in dealing with catalysis by zeolites (molecular sieves). 

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