Conditions diffuse-kinetic

The rate is inversely proportional to particle size. This is an indication of strong pore-diffusion resistance, in which t) - llcp" as " - large. Since (f>" a Le for fixed other conditions (surface kinetics, De, and c ), if we compare measured rates for two particle sizes (denoted by subscripts 1 and 2), for strong pore-diffusion resistance,... 

L channels. We assume that in all channels a situation can be prepared as illustrated in Figure 1.30, at the beginning of the experiment. Immediately after all dye molecules have entered the zeolite channels, the maximum energy transfer is observed because the donor-to-acceptor distance is short. The donor-to-acceptor distance increases, and hence the energy-transfer rate decreases, when the molecules diffuse deeper into the channels. From this, the following relation for diffusion kinetics is found under the condition that the initial distributions of the donors and the acceptors are the same, [)py+ p x+, denoted as p°. Experimental details can be found in [77],... 

Formation and stripping of a cobalt adlayer on/from a polycrystalline Au electrode have been studied [469] applying electrochemical methods under underpotential conditions. The kinetics of deposition fitted a model of a simultaneous adsorption and diffusion-controlled two-dimensional instantaneous nucleation of cobalt on the electrode surface. 

In Fig. 42, the full-width at half maximum of the (narrower) exchange propagator provides an estimate of the effective diffusion coefficient of water molecules moving between the pore space of the catalyst and the inter-particle space of the bed. In this example, the value is 2 x lO- m s which gives a lower limit to the value for the mass transfer coefficient of 4x 10 ms This value was obtained by defining a mass transfer coefficient as Djd where d is a typical distance traveled to the surface of the catalyst that we estimate as half a typical bead dimension (approximately 500 pm). This value of the mass transfer coefficient is consistent with the reaction occurring under conditions of kinetic as opposed to mass transfer control. 

Kinetic Steady-State Conditions by Assuming a Purely Diffusive Behavior for Species f and D (Diffusive-Kinetic Steady State, dkss)... 

This section deals with the solution corresponding to an EC mechanism (see reaction scheme 4.IVc) in Reverse Pulse Voltammetry technique under conditions of kinetic steady state (i.e., the perturbation of the chemical equilibrium is independent of time see Sect. 3.4.3). In this technique, the product is electrogenerated under diffusion-limited conditions in the first period (0 < t < ) and then exam-... 

For high values of the chemical rate constant, i.e., under conditions of a diffusive-kinetic steady state (dcross potentials of the ADDPV curves,... 

Diffusion current — The rate of an - electrode process is always determined by one of its consecutive steps (i.e., by the most hindered or slowest one). The - charge transfer step is always accompanied by - diffusion because, as the reagent is consumed or the product is formed at the electrode, concentration gradients between the vicinity of the interface and the bulk solution arise, which induce diffusion. When the diffusion is the rate-determining step we speak of diffusion kinetics. The - current which flows under this condition is called diffusion current. 

A simple first order reaction following reversible charge transfer is one of the few cases for which an analytical solution to the diffusion-kinetic differential equations can be obtained. For reactions (1) and (2) under diffusion-controlled charge-transfer conditions after a potential step, the partial differential equations which must be solved are (18) and (19). After Laplace transforma-... 

Beyond the instantaneous rate measurements described above, determining how enzyme activity varies with substrate concentration can provide useful information about enzyme capacity and the rates that are Hkely to be observed under different environmental conditions. These kinetic measurements probably work best in in vivo assays of exo- and ectoenzymes where substrate concentrations can be measured directly from the external environment and there are no metabolic intermediary pools or reactions to compHcate the picture. Kinetic measurements also have limitations as there can be bottle effects, diffusion boundary layers around organisms can be important, and it is often difficult to make measurements at the low substrate end-members in aU but the most oligotrophic environments. Further, kinetic parameters are physiological variables themselves, dependent on the preconditioning of cells and so can vary widely even in the same organism, across environments (see Chapter 7 by MulhoUand and Lomas, this volume). 

In principle, if polymerization under pseudo-stationary conditions is kinetically controlled and the active centres decay spontaneously, the polydispersity is independent of either yield or polymerization time . Therefore, if polymerization time is found to influence MWD, this may depend on the lack of one or more of the mentioned conditions or on eventual diffusion phenomena. 

The coupling of the flux and the time dependence of the counter-ion concentration is achieved through the material balance condition and Pick s Second Law (often termed the condition of continuity). For spherical particles and a constant interdifjusion coefficient, D, the foregoing considerations give the following partial differential equation for particle diffusion kinetics ... 

Several desirable criteria for fadlitative carriers have been described (17) (1) The carrier and its complexed form must be as water-insoluble as possible, (2) the carrier in any form must not separate out from the HC phase, (3) the carrier must ion-pair with the desired solute(s) under the selected external and internal aqueous phase conditions, (4) kinetics of ionpairing and release of the solute should be fast compared to e.g. diffusion... 

The tip-generated interfacial undersaturation is governed by the interplay between mass transport in the tip/substrate gap and the dissolution kinetics. This concept is illustrated in Figures 15 and 16. Figure 15a and b shows the radial dependence of the steady-state concentration and flux at the crystal/solution interface for a first-order dissolution process characterized by K, = 1, 10, and 100. For rapid kinetics (K, = 100), the dissolution process is able to maintain the interfacial concentration close to the saturated value and only a small depletion in the concentration adjacent to the crystal is observed over a radial distance of about one electrode dimension. Under these conditions, diffusion in the z-direction dominates over radial diffusion. As the rate constant decreases, diffusion is able to compete with the interfacial kinetics and consequently the undersaturation at the crystal surface... 

Calculations of the equilibrium conditions under which CVD of boron carbide from BCI3-CH4-H2 mixtures takes place consider the partial pressures of the gaseous species present. The method minimizes the free energy and the theoretical diagrams are compared to experimental observations . Mass-transfer and diffusion kinetics in the gas phase are related to the morphology and composition of the deposits " . 

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