Diffusion on the Surface of a Micelle

In this section diffusion on the surface of a micelle is modelled to verify the feasibility of the exponential approximation for the scavenging and recombination kinetics (within the IRT framework). It has been assumed in the literature that both kinetic 

1 Diffusion on a Sphere Monte Ccwlo Random Flights Algorithm 

To model the diffusive motion on a sphere, the algorithm developed by Krauth [14] was used, in which for a fixed time step At a normally distributed 3D vector of mean zero and standard deviation of one is generated. At every At the vector is made orthogonal to x (3D vector containing the Cartesian coordinates of the particle s position on the unit sphere) and normalised to unit length, such that 

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Second stage The second stage involves developing the IRT algorithm to model the diffusive behaviour on the surface of a micelle, which has important applications in... 

Although the presence of buffering moieties on membrane surfaces reduces the apparent diffusion coefficient of a proton, it can enhance the probability that protons in the bulk phase will interact with groups on a membrane surface. This feature is demonstrated by the experiments presented in Figure 3. The measured parameter in these experiments was the protonation of a pH indicator adsorbed to the surface of a micelle made of uncharged detergent (Brij 58). The protons were released in the bulk from a hydrophilic proton emitter, 2-naphthol-3,6-disulfonate. The protons released in the bulk react by a diffusion-controlled reaction with the micelle-bound indicator and lead to a fast protonation phase. The perturbation then relaxes,... 

It was concluded from measurements of sedimentation, diffusion, and viscosity, that the hydration of the micelles of the dodecyl ether sulfates at m = 0 - 2 shows only a little increase, whereas a strong one was observed at m > 2. A similar trend should also exist with the distance of the terminal groups on the surface of the micelles. 

This bimodal dynamics of hydration water is intriguing. A model based on dynamic equilibrium between quasi-bound and free water molecules on the surface of biomolecules (or self-assembly) predicts that the orientational relaxation at a macromolecular surface should indeed be biexponential, with a fast time component (few ps) nearly equal to that of the free water while the long time component is equal to the inverse of the rate of bound to free transition [4], In order to gain an in depth understanding of hydration dynamics, we have carried out detailed atomistic molecular dynamics (MD) simulation studies of water dynamics at the surface of an anionic micelle of cesium perfluorooctanoate (CsPFO), a cationic micelle of cetyl trimethy-lainmonium bromide (CTAB), and also at the surface of a small protein (enterotoxin) using classical, non-polarizable force fields. In particular we have studied the hydrogen bond lifetime dynamics, rotational and dielectric relaxation, translational diffusion and vibrational dynamics of the surface water molecules. In this article we discuss the water dynamics at the surface of CsPFO and of enterotoxin. 

However, our concern is with the cationic surface which promotes a rapid exchange of an electron from dimethylaniline to pyrene, and thereafter maintains a long-lived ion which can react with further solutes added to the system. Hie concept of the experiment is, that dimethylaniline transfers the electron rapidly to pyrene via a diffusion controlled reaction, which occurs by movement of the reactants on the surface of the micelle until they encounter each other. Electron transfer then occurs, and the back reaction of the two ions is prevented by the surface of the micelle, which holds the reactants in an unsuitable configuration for back reaction to occur. However, the repulsive positive force of the micelle on the dimethylaniline cation rapidly drives it away from the micelle, and effective and efficient charge separation is achieved, with a quantum yield Q of unity for the process of charge separation. 

Polymerization starts in the micelles of the emulsifier, because a considerable part of the monomer is dissolved in its hydrocarbon moiety. At 13-20% conversion of the monomer, emulsifier micelles are completely destroyed, and the emulsifier passes into the adsorption layer on the surface of polymer particles. Polymerization continues in the polymer-monomer system, i.e. in a latex into which the monomer penetrates by diffusion from drops. 

These reductively desorbed long-chain thiols (thiolates), which are insoluble in the electrolyte, remain near the surface, probably forming micelles, and do not diffuse in the bulk solution. They can be redeposited back on the surface of the electrode as a monolayer even if there was no thiol in the electrolyte prior to desorption . The amount of material readsorbed depends directly on the solubihty of the thiol. Shorter-chain (more soluble) thiols redeposit to give monolayers with smaller coverage. Redeposition also depends strongly on the pH of solution. Thiols become less soluble at lower pH, and therefore form monolayers with higher coverage under these conditions. 

Chan et ai [31] have presented a theory of solubilization kinetics and its relation to the flow of dissolution medium, based on an analysis of five steps depicted in Fig. 7.7. Surfactant molecules diffuse to the surface as micellar species (step 1). These molecules are adsorbed on the surface of the solid (step 2) and on the surface the surfactant and solubilizate form a mixed micelle (step 3). In step 4 the mixed micelle is dissolved and it diffuses away into the bulk solution in the last step (step 5). The solubilization rate is assumed to be controlled by steps 4 and 5 in Fig. 7.7. If these steps are rate controlling... 

The diffusive behaviour of particles inside a micelle and other confined systems has been extensively studied, both experimentally and theoretically [1-9], Most simulation methods to date use Monte Carlo random flights simulation to model the diffusive motion of radicals and their subsequent recombination kinetics in confined systems. In this chapter, the possibility of using the IRT simulation to model the complete recombination kinetics and scavenging is explored (i) inside the micelle (ii) on the surface of the micelle and (iii) reversible reactions involving the micelle (i.e. adsorption and escape of solvent particles from the surface of the micelle). 

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