Substrate, heterogeneous kinetics

The effect of finite substrate heterogeneous kinetics has also been studied (Fig. 6) [33]. When the kinetics of the tip reaction are fast, the local rate of an irreversible heterogeneous reaction occurring at a substrate can be extracted by fitting an experimental approach curve to Eq. (8) [82] ... 

For the finite heterogeneous kinetics at the tip and diffusion-controlled mediator regeneration at the substrate, an approximate equation (22) was recently obtained for IT as a function of tip potential, E, and L [51]... 

Macpherson and Unwin (43) developed the theory for dissolution processes at the substrate induced by depleting of electroactive species at the SECM tip. The UME tip can oxidize or reduce the species of interest in solution at the crystal surface. If this species is one of the crystal components, the depletion of its concentration in the solution gap between the tip and substrate induces crystal dissolution. This process produces additional flux of electroactive species to the tip similarly to positive feedback situation discussed in previous sections. Unlike the desorption reaction, where only a small amount of adsorbed species can contribute to the tip current, the dissolution of a macroscopic crystal is not limited by surface diffusion. Accordingly, the developed theory is somewhat similar to that for finite heterogeneous kinetics at the substrate. Several models developed in Ref. 43a-d use different forms of the dissolution rate law applicable to different experimental systems. In general, the rate of the substrate process is (43a) ... 

The value of iT,a gives the normalizing factor for currents I = i/iT,The general solution of equations involving heterogeneous kinetics with respect to a tip above a conducting substrate can be obtained under reasonable boundary conditions in the form of two-dimensional integral equations (see Chapter 5). 

Using low-crystallinity (7% crystallinity) and biaxially oriented PET films (35% crystallinity), the T. insolens lipase showed maximum hydrolysis activity on low-crystallinity PET film between 70 and 80°C [91]. With a Tg value of 75°C, the increased chain mobility of the low-crystallinity film at this reaction temperature strongly facilitated its hydrolysis by the thermostable T. insolens PET hydrolase. The low-crystallinity PET film was almost completely hydrolyzed after 96 h at 70°C, while tenfold lower activity was detected with the semi-crystalline PET film. Degradation of the low-crystallinity PET film followed a heterogenous kinetic model considering substrate-limited conditions with a limited surface area available to the enzyme [94]. 

In deriving the latter expression we assumed that R R- Equation 196 is very fundamental, and it provides a relationship between the macroscopic rate constant k and the macroscopic processes of substrate electrode kinetics and spherical diffusion at the catalytic particle. On the rhs of Eqn. 196 the first term describes the effect of heterogeneous kinetics of the substrate at the particle surface. This rate constant k is a strong function of electrode potential. The second term describes the spherical diffusion of substrate to the catalytic particle. When ks DsIR the mass transport of S to the particle surface is rate-determining. Alternatively when k E DsiR then the electron transfer process at the particle surface is rate-determining. 

This corresponds to the situation where the substrate is consumed in a first-order reaction layer at the polymer/solution interface and the heterogeneous kinetics at the particle surface are rate-determining. Note the unusual reaction order with respect to substrate concentration of 3/4. If we consider the alternative situation where... 

Heterogeneous kinetics measurements As suggested earlier, by recording an approach curve or voltammogram with the tip close to a substrate, one can study the rates of electron transfer reactions at electrode surfaces (Chapter 6). Because mass transfer rates at the small tip electrodes are high, measurements of fast reactions withont interference of mass transfer are possible. As a rule of thumb, one can measnre kg valnes (cm/s) that are of the order of D/d, where D is the diffusion coefficient (cmVs). For example, kg for ferrocene oxidation at a Pt electrode in acetonitrile solntion was measured at a 1-pm radius tip at a... 

To simulate positive feedback situation, one has to replace the no flux condition for boundary 3 representing the substrate surface with c=1. Minor modifications in the input file allow the simulation of the SECM responses for recessed or protruding tips, and finite heterogeneous kinetics at the tip and/or substrate. 

Many semibatch reactions involve more than one phase and are thus classified as heterogeneous. Examples are aerobic fermentations, where oxygen is supplied continuously to a liquid substrate, and chemical vapor deposition reactors, where gaseous reactants are supplied continuously to a solid substrate. Typically, the overall reaction rate wiU be limited by the rate of interphase mass transfer. Such systems are treated using the methods of Chapters 10 and 11. Occasionally, the reaction will be kinetically limited so that the transferred component saturates the reaction phase. The system can then be treated as a batch reaction, with the concentration of the transferred component being dictated by its solubility. The early stages of a batch fermentation will behave in this fashion, but will shift to a mass transfer limitation as the cell mass and thus the oxygen demand increase. 

As an example the experimental results on heterogeneous recombination of CH3 radicals on glass at different temperatures are plotted on Fig. 4.1. The experimental conditions in this case are chosen in such a way that inequality (4.3) is satisfied (A < 1 cm, y is about 1(H, r = 3 cm). Thus, formula (4.1) holds in this experiment. This conclusion is supported by the fact that for all experimental series the results obtained at different temperatures of the reaction vessel walls are satisfactorily approximated by the same straight line. This means that methyl radicals on glass substrate undergo recombination governed by the first-order kinetics, and the activation energy is close to zero. 

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