Rate Measures for Interfacial Processes

Rate Measures for Interfacial Processes Terminology used for reporting rate data can be confusing. Normally rate data are reported on a volumetric basis with transfer rate and effective area combined. For example, kLa denotes mass-transfer data per unit volume. The L subscript means it is referenced to the molar concentration difference between the interface and the bulk liquid. This is commonly used on data involving a sparingly soluble (high relative volatility) component. Note that the lowercase k means the data deal only with the resistance in the liquid phase. 

The combination of photocurrent measurements with photoinduced microwave conductivity measurements yields, as we have seen [Eqs. (11), (12), and (13)], the interfacial rate constants for minority carrier reactions (kn sr) as well as the surface concentration of photoinduced minority carriers (Aps) (and a series of solid-state parameters of the electrode material). Since light intensity modulation spectroscopy measurements give information on kinetic constants of electrode processes, a combination of this technique with light intensity-modulated microwave measurements should lead to information on kinetic mechanisms, especially very fast ones, which would not be accessible with conventional electrochemical techniques owing to RC restraints. Also, more specific kinetic information may become accessible for example, a distinction between different recombination processes. Potential-modulation MC techniques may, in parallel with potential-modulation electrochemical impedance measurements, provide more detailed information relevant for the interpretation and measurement of interfacial capacitance (see later discus-... 

The effect on the normalized approach curves of allowing to take finite values is illustrated in Fig. 5, which shows simulated data for three rate constants, for redox couples characterized by y = 1. The rate parameters considered K = 100 (A), 10 (B), and 1 (C), are typical of the upper, medium, and lower constants that might be encountered in feedback measurements at liquid-liquid interfaces. In each case, values of = 1000 or 100 yield approach curves which are identical to the constant-composition model [44,47,48]. This behavior is expected, since the relatively high concentration of Red2 compared to Red] ensures that the concentration of Red2 adjacent to the liquid-liquid interface is maintained close to the bulk solution value, even when the interfacial redox process is driven at a fast rate. 

With multiple rate controlling steps, a steady state is postulated, that is, all rates are equated to the overall rate. Equations for the individual steps are formulated in terms of variables such as interfacial concentrations and various coverages of the catalyst surface. Any such variables that are not measurable are eliminated in terms of measurable partial pressures and the rate, as well as various constants to be evaluated from the data. The solved problems deal with several cases for instance, P6.03.04 has two participants not in adsorptive equilibrium and P6.06.17 treats a process with five steps. 

Albery et al. [16] have used Marcus Theory [16] interfacial processes to calculate that an interfacial rate constant of 2p,ms-1 constitutes a free energy barrier of 44 kJ mol-1. The slowest rate here (2,4-D) gives 49kJmol-1, and rates >100jxms-1 have barriers of 34kJmol-1, still rather larger than that of diffusion itself (20 kJ mol-1). However, the RDC method is not suitable for accurate measurement of k > 20 xm s-1. 

Willig and co-workers used near-infrared spectroscopy to measure excited-state interfacial electron transfer rates after pulsed light excitation of cis-Ru(dcb)2(NCS)2-Ti02 in vacuum from 20 to 295 K [208]. They reported that excited-state electron injection occurred in less than 25 fs, prior to the redistribution of the excited-state vibrational energy, and that the classical Gerischer model for electron injection was inappropriate for this process. They concluded that the injection reaction is controlled by the electronic tunneling barrier and by the escape of the initially prepared wave packet describing the hot electron from the reaction distance of the oxidized dye molecule. It appears that some sensitizer decomposition occurred in these studies as the transient spectrum was reported to be similar to that of the thermal oxidation product of m-Ru(dcb)2(NCS)2. 

When the adsorption/desorption kinetics are slow compared to the rate of diffusional mass transfer through the tip/substrate gap, the system responds sluggishly to depletion of the solution component of the adsorbate close to the interface and the current-time characteristics tend towards those predicted for an inert substrate. As the kinetics increase, the response to the perturbation in the interfacial equilibrium is more rapid and, at short to moderate times, the additional source of protons from the induced-desorption process increases the current compared to that for an inert surface. This occurs up to a limit where the interfacial kinetics are sufficiently fast that the adsorption/desorption process is essentially always at equilibrium on the time scale of SECM measurements. For the case shown in Figure 3 this is effectively reached when Ka = Kd= 1000. In the absence of surface diffusion, at times sufficiently long for the system to attain a true steady state, the UME currents for all kinetic cases approach the value for an inert substrate. In this situation, the adsorption/desorption process reaches a new equilibrium (governed by the local solution concentration of the target species adjacent to the substrate/solution interface) and the tip current depends only on the rate of (hindered) diffusion through solution. 

To summarize, although rate constants (or, perhaps, apparent rate constants) for IT across the ITIES have been reported for more than 20 years, there is still controversy about the interpretation of this phenomenon, not least because the reported rate constants have increased over the years as experimental measurements became more and more sophisticated [127]. As noted above, a general problem has been that the characteristic timescales of the (apparent) kinetic process are often not markedly lower than the timescales of the experimental technique, a fact that has been remarked upon in the literature [128]. For example, in some of the recent data [94, 96] the time constants of the technique are frequently of the same order of magnitude as the timescales of the process they are purporting to measure. The question therefore becomes whether the rate constants reported for IT using nanopipettes [104, 107, 108] will increase in the future or whether these represent true values. Clearly at this point it is reasonable to ask whether theory predicts that a barrier to interfacial IT should exist and, if so, what the physical origin of such a barrier might be. 

Schlichthorl et al. [177] have used light modulated microwave reflectivity to derive the rates of interfacial electron transfer processes at the n-Si/electrolyte interface. In these measurements, the modulation frequency was constant, and the rate constants for charge transfer were derived from the potential dependent ARm response. Schlichthorl et al. [73] have extended the technique considerably by introducing frequency response analysis. The technique is therefore analogous to IMPS, although, as shown below, it provides additional information. 

Multicomponent systems may also involve the selective adsorption of one component at the SL interface. Since the component that lowers the interfacial tension will be preferentially adsorbed, the rate of the adsorption process can affect the local tension and the contact angle. In many systems, the rate of adsorption at the solid surface is found to be quite slow compared to the rate of movement of the SLV contact line. As a result, the system does not have time for the various interfacial tensions to achieve their equilibrium values. Most surfactants, for example, require several seconds to attain adsorption equihbrium at a LV interface, and longer times at the SL interface. Therefore, if the hquid is flowing across fresh solid surface, or over any surface at a rate faster than the SL adsorption rate, the effective values of olv and osl (and therefore 6) will not be the equilibrium values one might obtain from more static measurements. More will be said about dynamic contact angles in later chapters. 

In a paper by Kemer and Pajkossy [2002], anion adsorption rates have been measured by impedance spectroscopy at Au (111), for SO4, Cr, Br and T. Cr ion adsorption is very fast, so the equivalent circuit for the process not only has to include a Faradaic pseudocapacitance and its corresponding reaction resistance, but also a Warburg element for the anion diffusion. The interfacial capacitance is then plotted in the Nyquist plane as real vs. imaginary capacitance components, C and... 

This constant is a measure for the interfacial area, the solubility of A, the various kinetic constants that determine the rate of the process and the concentration o/ B in the liquid phase. In a mixed reactor, it may be assumed that this concentration and the effective rate constant are both constants throughout the reactor, though they do change with time. 

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