Retardation electrostatic model

Morishima et al. [75, 76] have shown a remarkable effect of the polyelectrolyte surface potential on photoinduced ET in the laser photolysis of APh-x (8) and QPh-x (12) with viologens as electron acceptors. Decay profiles for the SPV (14) radical anion (SPV- ) generated by the photoinduced ET following a 347.1-nm laser excitation were monitored at 602 nm (Fig. 13) [75], For APh-9, the SPV- transient absorption persisted for several hundred microseconds after the laser pulse. The second-order rate constant (kb) for the back ET from SPV- to the oxidized Phen residue (Phen+) was estimated to be 8.7 x 107 M 1 s-1 for the APh-9-SPV system. For the monomer model system (AM(15)-SPV), on the other hand, kb was 2.8 x 109 M-1 s-1. This marked retardation of the back ET in the APh-9-SPV system is attributed to the electrostatic repulsion of SPV- by the electric field on the molecular surface of APh-9. The addition of NaCl decreases the electrostatic interaction. In fact, it increased the back ET rate. For example, at NaCl concentrations of 0.025 and 0.2 M, the value of kb increased to 2.5 x 108 and... 

In view of the approximate nature of the model, and the complete neglect of nonelectrostatic factors, no great weight should be placed on the absolute values of AW. In particular, comparisons between the anti and syn-cyclic transition states are the most suspect, since the assumptions that have to be made about them are different and are likely to introduce errors which do not cancel. Nevertheless, it appears that the crude figures do indicate that an electrostatic factor could accelerate some eliminations, e.g. 103, and retard others, e.g. in 102. Of course, whatever one might decide about the electrostatic influence of an electronegative substituent, just the opposite conclusions would apply if base-promoted elimination from onium species such as 103 were considered. Ion aggregation would, of course, favor syn elimination. 

Philipse (5) also assumed that fast hydrolysis created an active monomer bulk. He studied the growth of silica nuclei, already synthesized, after extra addition of different amounts of TES with static light scattering. To explain his growth curves (radius versus time), he used a diffusion-controlled particle growth in a finite bulk of monomers or subparticles. The model contained equations from classical flocculation theories. It takes into account the exhaustion of the monomer bulk and the retarding influence of an (unscreened) electrostatic repulsion between growing spheres and monomers. 

Since this book is dedicated to the dynamic properties of surfactant adsorption layers it would be useful to give a overview of their typical properties. Subsequent chapters will give a more detailed description of the structure of a surfactant adsorption layer and its formation, models and experiments of adsorption kinetics, the composition of the electrical double layer, and the effect of dynamic adsorption layers on different flow processes. We will show that the kinetics of adsorption/desorption is not only determined by the diffusion law, but in selected cases also by other mechanisms, electrostatic repulsion for example. This mechanism has been studied intensively by Dukhin (1980). Moreover, electrostatic retardation can effect hydrodynamic retardation of systems with moving bubbles and droplets carrying adsorption layers (Dukhin 1993). Before starting with the theoretical foundation of the complicated relationships of nonequilibrium adsorption layers, this introduction presents only the basic principles of the chemistry of surfactants and their actions on the properties of adsorption layers. 

The electrostatic retardation of the adsorption kinetics of ionic siufactants is one of these nonequilibrium surface phenomena to be described on the basis of this physical model, consisting of the electrochemical macro-kinetic equations used in theoretical and colloid electrochemistry. This approach describes the flux of ions in terms of their spatial distribution. The equations were first developed by Overbeek (1943) and later proved to be valid for the theory of different... 

From the theoretical point of view a similarity exists between electrostatic retardation of ion transport and coagulation retardation, known as slow coagulation (Fuchs, 1934). Both phenomena arise from electrostatic repulsion caused by the existence of the diffuse part of the DL. In the slow coagulation theory, the electric field if the DL is derived from the Gouy-Chapman model (cf. Chapter 2). This model does not consider a deviation of the diffuse layer from equilibrium. Initially, the same simplification was used by Dukhin et al. (1973) in describing the DL effect on the electrostatic retardation of adsorption. 

First models of electrostatic retardation of ion adsorption used the boundary condition of slow coagulation (Dukhin et al. 1973, Glasman et al. 1974, Michailovskij et al. 1974, Dukhin et al. 1976). These models are discussed in Section 7.5. In later models the derivation of the theory was performed by expressing c(0,t) through c , which is a more general case (Dukhin et al. 1983, 1990). This approach is described in detail in the following Section 7.2. The more complicated non-steady ion adsorption is considered in Section 7.3. 

Adsorption Kinetics Model, Taking Into Account the Electrostatic Retardation and a Specific Adsorption Barrier... 

In the presented theories of electrostatic retardation, very simple models are used to enable an analytical solution of the different problems and to clarify the physics of the mechanisms. The objective of further work is of course the generalisation of models with respect to the adsorption isotherm, content of background electrolyte, and ion transport properties. 

The inclusion of retardation is rather obvious in the dipole model of van der Waals attraction. There is no need to use electrostatic potentials, the electrodynamic four potential of an oscillating dipole is readily found by solving Maxwell s equations rather than Laplace s equation. 

L213DN mutant RCs. Comparison of the theoretical and experimental pH dependencies of rate constant kAB in L213DN RCs shows major discrepancies between them (i) Alteration of AspL to Asn leads to pH dependence of kAB in all regions studied, from pH 5 to > 9, while calculations predict pH dependence only at pH > 8. (ii) The model predicts that protonation of Glu n low pH leads to the disappearance of electrostatic retardation and therefore to an increase in the rate constant of electron transfer in mutant RCs in comparison with Wt RCs. However, the experimental data [12,13] do not support this prediction (Fig. 2C). The model calculations of the electron transfer rate and the experimental values differ by more than two orders of magnitude at high pH. 

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