Fast-diffusion limit

Surface Relaxation and Pore Size Distribution 3.6.6.1 Fast Diffusion Limit... 

The key to obtaining pore size information from the NMR response is to have the response dominated by the surface relaxation rate [19-26]. Two steps are involved in surface relaxation. The first is the relaxation of the spin while in the proximity of the pore wall and the other is the diffusional exchange of molecules between the pore wall and the interior of the pore. These two processes are in series and when the latter dominates, the kinetics of the relaxation process is analogous to that of a stirred-tank reactor with first-order surface and bulk reactions. This condition is called the fast-diffusion limit [19] and the kinetics of relaxation are described by Eq. (3.6.3) ... 

Natural rocks seldom have a single pore size but rather a distribution of pore sizes. If all pores are in the fast-diffusion limit, have the same surface relaxivity and have no diffirsional coupling, then the pores will relax in parallel with a distribution of relaxation times that corresponds to the distribution of the pore sizes. The magnetization will decay as a sum of the exponentials as described by Eq. (3.6.4). 

The binding constant Kd in the fast diffusion limit is obtained according... 

So far, attention has been focussed upon moderately small molecules, little more sizeable than a benzene ring. Studies on larger systems have been made and fluorescence depolarisation is the preferred method for molecules which luminesce. Since such molecules may also participate in fast diffusion-limited chemical reactions, they are of considerable interest. 

Let us first specify Z in the fast diffusion limit and only then clarify how this limit is approached. 

One should note that in the MF approach no second order phase transition is present. Contrary to this, MC simulations with diffusion [45,46,54-56] do show this transition, even when the results are extrapolated to infinitely fast diffusion. This means that, at least in this case, MC simulations with fast diffusion do not show the same results as MF calculations. This is remarkable since it is generally assumed that in the fast diffusion limit, both approaches should be equivalent. The MC method is certainly correct, and we believe that the discrepancies show that the MF approach is not always valid. This is the reason why we have chosen the MC approach to study CO oxidation on Pt(lOO) surfaces, as will be discussed in the next section. 

Nitric oxide and Oy metabolism in the mitochondrial matrix are linked by the very fast, diffusion limited, reaction between NO and Oy to produce peroxynitrite (ONOO ) (reaction 6 [34, 35]). This oxidative utilization of NO is the main (60-70%) pathway of NO metabolism but only a minor part (15%) of mitochondrial Oy utilization, whereas the reductive utilization of NO by ubiquinol and cytochrome oxidase provides a minor (20%) pathway of NO catabolism [12]. 

The relaxation of hydrogen nuclei in a fluid confined in pores is determined by the self-diffusion of the molecules within the pores, the bulk relaxation of the liquid, and the surface relaxation at the pore walls (Valckenborg et al. 2000, 2001). For NMR spin-echo times of a few ms, the diffusion length of the water molecules in broad pores is about 1 J.m, and hence the surface relaxation is the dominating process at pore sizes below 0.1 pm (fast diffusion limit Brownstein and Tarr 1979). In this case, a one to one correspondence exists between the observed distribution of relaxation times and the PSD (Halperin et al. 1989, Valckenborg et al. 2000). Since the transverse relaxation time of... 

Fig. 8.17 Complex plane plots of complex capacitance, C, defined using Eq. (8.28) for limiting cases of slow continuous line), fast (diffusion limited, dotted line), and intermediate (dashed line) adsorption. Insert equivalent electrical model for this process (From Ref. [367], copyright (2002), with permission from Elsevier)...

Figure 8 shows data gained from stopped-flow fluorescence experiments in which warferin s (W) fluorescence emission (excited at 330 nm and detected at 360 nm and above) is used to study its binding to human serum albumin (A). This reaction proceeds by two, consecutive reversible steps. A fast, diffusion limited bimolecular reaction by which the initial complex is formed (A.W). followed by a unimolecular conformational change in the protein following complex formation (A W). 

Isotropic translational diffusion has been simulated by a simple random walk process in which each spin — representing one or more nematic molecules — jumps to one of its nearest neighbor sites with equal probability [11]. After the diffusion jump has been performed, the spin acquires the orientation of the local director at the new coordinates. Calculating G t) we have, like in the diffusion-less case, updated from the MC data the spin configuration inside the droplet 8 times per NMR cycle. Now additional diffusion steps have been added in between these structural updates, with their number A ranging from 1 to 32. In this last case the spectra are completely motionally averaged due to dififiision effects since for A = 32 each of the spins exhibits a total of 256 jumps within the duration of one NMR cycle. This already corresponds to the fast diffusion limit with C to-... 

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