Diffusion controlled uptake

For almost cubic and nearly spherical crystals, the above solution for diffusion-controlled uptake by a sphere can be used. For "coffin"-shaped crystals, the corresponding solution for diffiision in a cylinder was used. 

Many models have been suggested to describe anomalous (non-Fickian) uptake and a number of the more relevant to structural adhesives will be discussed. Diffusion-relaxation models are concerned with moisture transport when both Case I and Case II mechanisms are present. Berens and Hopfenberg (1978) assumed that the net penetrant uptake could be empirically separated into two parts, a Fickian diffusion-controlled uptake and a polymer relaxation-controlled uptake. The equation for mass uptake using Berens and Hopfenbergs model is shown below. 

One of the most important characteristics of micelles is their ability to take up all kinds of substances. Binding of these compounds to micelles is generally driven by hydrophobic and electrostatic interactions. The dynamics of solubilisation into micelles are similar to those observed for entrance and exit of individual surfactant molecules. Their uptake into micelles is close to diffusion controlled, whereas the residence time depends on the sttucture of the molecule and the solubilisate, and is usually in the order of 10 to 10" seconds . Hence, these processes are fast on the NMR time scale. 

For a step change in sorbate concentration at the particle surface (r = R) at time 2ero, assuming isothermal conditions and diffusion control, the expression for the uptake curve maybe derived from the appropriate solution of this differential equation ... 

Avena and Koopal (1999) used reflectometry to study the kinetics of adsorption of Aldrich humic acid on hematite. Uptake was fast (diffusion-controlled) at low pH, but slow at pH > 5. The rate of uptake rose with ionic strength above the iep, but decreased with ionic strength below the iep. The adsorption of humic acid onto hematite rendered its surface hydrophobic and made it a suitable sorbent for hydrophobic organic compounds (Murphy et al., 1992). 

Finally, the agitation rate does not affect the uptake rate if the particle diffusion controls the process. However, the latter criterion may be not safe the agitation in solution may have attained its limiting hydrodynamic efficiency, so that a change in the agitation rate has no effect on the uptake rate even in film diffusion-controlled systems. 

In this expression, U(t) is relative rate of uptake and Cx is relative to equilibrium, i.e. the sites available for ion exchange or adsorption for the specified ratio Vim. Thus, the absolute rate is a coupled result of kinetics and equilibrium. Note that in a solid diffusion-controlled process, U(t) is relative to the ease of movement of the incoming species in the solid phase (through Ds). 

The full extent of relaxation in the P+Qa- state spans about 120 meV over the time range from 100 ps to about 1 ms at room temperature (McMahon et al., 1998). Of this, as much as 80% is achieved prior to 1 ps. Thus, relaxations associated with diffusion-controlled net H+ uptake do not contribute more than 20-30 meV. However, proton rearrangements (intraprotein H+ transfer) can certainly be a significant part of the overall response of the protein at much shorter times. 

The uptake time-constant depends linearly on the square of the crystal size, indicating division as the dominant step in rate control. Uptake kinetics are well described by a model taking into account only diffusion without rate-controlling steps superimposed, such as sur ce barriers [19] or thermal effects [20]. 

The kinetic expressions for these reactions are given in equations 5-8. Since the reaction of oxygen with carbon-centered radicals is fast and essentially diffusion controlled, the rate of oxygen uptake is given by equation 5. 

Micelles are extremely dynamic aggregates. Ultrasonic, temperature and pressure jump techniques have been employed to study various equilibrium constants. Rates of uptake of monomers into micellar aggregates are close to diffusion-controlled . The residence times of the individual surfactant molecules in the aggregate are typically in the order of 1-10 microseconds , whereas the lifetime of the micellar entity is about 1-100 miliseconds . Factors that lower the critical micelle concentration usually increase the lifetimes of the micelles as well as the residence times of the surfactant molecules in the micelle. Due to these dynamics, the size and shape of micelles are subject to appreciable structural fluctuations. 

Studies of intramolecular ET in oxidases provide interesting examples of how pulse radiolysis is employed to obtain insights into both (1) these enzymes respective mechanisms of action and (2) electron transfer along protein polypeptide matrices that were most probably selected by evolution (9,10, 30-32). Thus, early attempts to study the electron uptake mechanism by the blue oxidase, ceruloplasmin, showed that a diffusion-controlled decay process of the eaq in solutions of this protein is paralleled by the formation of transient optical absorptions due to electron adducts of protein residues, primarily of cystine disulfide bonds (30). The monomolecular decay of the latter absorption was found to have the same rate constant as that at which the type 1 Cu(II) absorption band was reduced. These results were interpreted as being the combined result of the high reactivity of the e q and the relatively inaccessible type 1 Cu(II) site, yielding an indirect, intramolecular electron transfer pathway from surface-exposed residues (30). 

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