Rate limiting diffusion

SOME IMPLICATIONS OF A RATE-LIMITING DIFFUSION 7.5.1 Bioavailability of Colloidal Bound Metal... 

The cross-linked aggregates of MeHNL also showed themselves to be highly active and robust catalysts. Optimized procedures give MeHNL CLEAs with activity recoveries up to 93% measured by a synthetic assay [75]. As observed earlier for PaHNL CLEAs [74], this result is in contrast with the photometric assay, indicating that a fast assay severely underestimates the recovery of initial activity because of rate-limiting diffusion [75]. 

The reductive nitrosylation of a synthetic iron porphyrin by HNO (193) proceeds with a reported rate constant of 1 x 107 A/-1 s However, this value was estimated based on a HNO dimerization rate constant of 8 x 109 M-1 s-1 (210), which is now considered to be 1000-fold lower [(8 x 106 A/-1 s-1 (106)]. The recalculated constant for the reaction of HNO with the porphyrin (3 x 10s AT V1) is similar to the estimated value of HNO addition to metMb. Synthetic porphyrins generally react 30-fold faster with NO (1 x 109M 1 s-1) than ferrous Mb [for a recent, thorough review see (44)] due to rate-limiting diffusion of NO through the protein. The similarity in rate constants for HNO with metMb and the ferric porphyrin suggests that the rate-limiting step in reductive nitrosylation is likely addition of HNO to the ferric metal, with little influence from the protein structure. 

The purpose of in vitro diffusion studies is to determine the flux rates of particular molecules through the rate-limiting diffusion layer of skin, the stratum corneum. Often, it is... 

Hence, as observed for oxygen and nitrogen acids, the proton transfer step may not be rate-limiting in the overall ionization or isotope exchange of these carbon acids. For the isotope exchange of phenylacetylene, mechanism (88), which involves a rate-limiting diffusion step, has been proposed [143], and a similar mechanism may apply to the isotope exchange of chloroform [171]. It should be noted that the fast proton transfers observed for cyanocarbons, sulphones, phenylacetylene, and chloroform were discovered comparatively recently. Carbon acids studied up to that time, and the majority of carbon acid systems which have been... 

In contrast with intermittent hemodialysis in which dialyzer blood flow is rate limiting/ diffusive drug clearance during continuous renal replacement therapy is limited by dialysate flow (Qd)/ which typically is only 25 mL/min. Accordingly/ diffusive drug clearance (CLd) is calculated from the equation ... 

During the falling rate phase of drying, models based on rate-limiting diffusion within the particles and also from external vapor diffusion on the particles have been proposed, but the primary energy transfer mechanisms remain the same. 

If transport occurs much faster than sorption, sorption processes may not reach equilibrium conditions. Nonequilibrium sorption may result from physical causes such as intraparticle rate-limited diffusion, chemical causes such as rate-limiting reaction kinetics, or a combination of the two. One approach used to model rate-limited sorption is bi-continuum models consisting of one region where transport is described by the advection-dispersion equation with equilibrium sorption, and another region where transport is diffusion limited with equilibrium sorption, or another region where sorption is chemically rate limited. 

The problem of crystal reactivity and diffusion limitations has been considered in detail by Makinen and Fink [170]. They provide a simple treatment for crystals approximated as a plane sheet of material which leads to the definition of a limiting crystal thickness below which kinetic measurements of second-order rate constants are not affected by rate-limiting diffusion processes. For papain [172], ribonuclease A [173] and deoxyhaemoglobin [174], where the crystal thicknesses are comparable to the critical crystal thickness, reactivities are the same in the crystal and solution. In the case of glycogen phosphorylase b Kasvinsky and Madsen [175] demonstrated that the values for both substrates, glucose 1-phosphate (37 + 8mM) and malto-heptaose (176 + 20 mM), were the same in the crystal and solution. The 10-100-fold reduction in rate, despite the fact that crystal thickness was only twice the critical thickness, may be attributable partly to the allosteric nature of this enzyme and partly to the fact that the large substrate maltoheptaose (molecular weight, 1152) may not obey the simple diffusion rules in the crystal. 

The dialytic regime is characterized by high surface reaction rate coefficients and by rate-limiting diffusion. The Sherwood number (Sh) characterizes the regimes. Sh is defined as the ratio of the driving force for diffusion in the boundary layer to the driving force for surface reaction alternatively, it is the ratio of the resistivity for diffusion to the resistivity for chemical reaction (reciprocal reaction rate coefficient). Diffusion limitation is the regime at Sh 1 and reaction limitation means Sh 1. The Sherwood number is closely related to the Biot, Nusselt, and Damkohler II numbers and the Thiele modulus. Some call it the CVD number. In the boundary-layer model it is a simple function of the thickness of the boundary layer, the diffusion coefficient, and the reaction rate coefficient. For simplicity a first-order reaction will be considered in the derivation below. 

The rate-limiting diffusion of an electrode reaction can also be incorporated into the Chang-Jaffd boundary conditions by a similar approach. In this case, assuming, for example, diffusion through a semiinfinite electrode, the result obtained is... 

Suggest how you might use a marker (e.g. a Pt wire) to identify the rate limiting diffusion process. 

The interest of the facilitated transport is to decrease the resistances due to rate-limiting diffusion layers (or membrane) where forced convection is impossible. In other terms this means the diminishing of the concentration-polarization at the inter-... 

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