Rate-limiting diffusion control

Alkyl radicals react in solution very rapidly. The rate of their disappearance is limited by the frequency of their encounters. This situation is known as microscopic diffusion control or encounter control, when the measured rate is almost exactly equal to the rate of diffusion [230]. The rate of diffusion-controlled reaction of free radical disappearance is the following (the stoichiometric coefficient of reaction is two [233]) ... 

The thermodynamic driving force notwithstanding, the coupling of two different radicals is not an especially practical preparative method to form a new bond. This is because the preparation of precursors that directly decompose to radicals is rarely convenient, because disproportionation can often compete effectively with recombination, and especially because chemoselectivity (that is, the selective-coupling of two different radicals to the exclusion of self-coupling) is difficult to achieve if all coupling reactions occur at the same rate (the diffusion-controlled limit). 

The rates for many of the e aq reactions in Table II are very fast, exceeding 1010M-1 sec.-1, and therefore, may be limited by the rates of diffusion-controlled encounters. The equation from which the diffusion-limited rate constants may be calculated for ionic species is due to Debye... 

The upper boundary of the reaction rate is reached when every collision between substrate and enzyme molecules leads to reaction and thus to product. In this case, the Boltzmann factor, exp(-EJRT), is equal to lin the transition-state theory equations and the reaction is diffusion-limited or diffusion-controlled (owing to the difference in mass, the reaction is controlled only by the rate of diffusion of the substrate molecule). The reaction rate under diffusion control is limited by the number of collisions, the frequency Z of which can be calculated according to the Smoluchowski equation [Smoluchowski, 1915 Eq. (2.9)]. 

The slowest transport-controlled dissolution/precipitation is that governed by aqueous diffusion. Diffusion rates can be estimated (cf. Bodek et al. 1988 Fetter 1988), thus we can estimate the lower limit of rates attributable to transport control. Berner (1978) suggests that the rate of diffusion-controlled dissolution R is given by... 

There is an upper limit for the value of 2/ M which is contingent upon the rate of diffusion-controlled encounters of enzyme and substrate molecules, i.e., the rate of product formation is no longer limited by the reaction rate but by the diffusion rate. In an aqueous solution, this limiting value lies between 10 and 10 molL s (compare Sect. 20.2). Enzymes such as catalase that exhibit a value of k 2jK of this order of magnitude are considered to be (almost) catalytically perfect because (almost) every contact between enzyme and substrate leads to a reaction. 

The rate-limiting is controlled by the slowest diffusion species... 

Theory. The transport characteristics of scopolamine from the system are determined by molecular diffusion through the various elements of the multilayer laminate. During the priming dose period, drug diffusion from the contact adhesive layer dominates the temporal pattern of drug release. However, during steady-state delivery, rate-limitation, or control, is resident in the microporous membrane. 

Similarly to the response at hydrodynamic electrodes, linear and cyclic potential sweeps for simple electrode reactions will yield steady-state voltammograms with forward and reverse scans retracing one another, provided the scan rate is slow enough to maintain the steady state [28, 35, 36, 37 and 38]. The limiting current will be detemiined by the slowest step in the overall process, but if the kinetics are fast, then the current will be under diffusion control and hence obey the above equation for a disc. The slope of the wave in the absence of IR drop will, once again, depend on the degree of reversibility of the electrode process. 

Diffusion rate limited (first-order kinetics). In this case, the reaction rate is controlled by the rate of diffusion of the pollutant species into the biofilm. 

The quantity kcat/Km is a rate constant that refers to the overall conversion of substrate into product. The ultimate limit to the value of k at/Km is therefore set by the rate constant for the initial formation of the ES complex. This rate cannot be faster than the diffusion-controlled encounter of an enzyme and its substrate, which is between 10 to 10 per mole per second. The quantity kcat/Km is sometimes called the specificity constant because it describes the specificity of an enzyme for competing substrates. As we shall see, it is a useful quantity for kinetic comparison of mutant proteins. 

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