Mean field model with active sites

Mean Field Model with Active Sites... 

The balance equations for 0, 9oh, and 6co were formulated and solved with two approaches a mean-field model with nucleation processes on active sites and kinetic Monte Carlo simulations, as illustrated in Figure 3.9. 

However, we have to reflect on one of our model assumptions (Table 5.1). It is certainly not justified to assume a completely uniform oxide surface. The dissolution is favored at a few localized (active) sites where the reactions have lower activation energy. The overall reaction rate is the sum of the rates of the various types of sites. The reactions occurring at differently active sites are parallel reaction steps occurring at different rates (Table 5.1). In parallel reactions the fast reaction is rate determining. We can assume that the ratio (mol fraction, %a) of active sites to total (active plus less active) sites remains constant during the dissolution that is the active sites are continuously regenerated after AI(III) detachment and thus steady state conditions are maintained, i.e., a mean field rate law can generalize the dissolution rate. The reaction constant k in Eq. (5.9) includes %a, which is a function of the particular material used (see remark 4 in Table 5.1). In the activated complex theory the surface complex is the precursor of the activated complex (Fig. 5.4) and is in local equilibrium with it. The detachment corresponds to the desorption of the activated surface complex. 

Our QM/MM model—the discrete (or direct) reaction field (DRF) model—treats the various terms in Eq. (3-1) separately and on the basis of their own intrinsic physical meaning [3,10,31,32,38,59,74], Historically, DRF was developed to study biochemical problems, in particular for unraveling the reaction mechanism of papain. For that we went stepwise from a model active site [75] to a model active site plus a point charge representation of an a-helix [76,77,78], then to a model with a polarizable helix [78,79], and finally to an all-atom treatment of the enzyme [41]. Furthermore, we extended these studies with an exercise—with the continuum version—to show that a solvent-exposed residue has no effect on the reaction mechanism [80], Up to then we considered the protein as a peculiar solvent the real solvents, requiring extensive MC or MD simulations, came later. 

The simulations to investigate electro-osmosis were carried out using the molecular dynamics method of Murad and Powles [22] described earher. For nonionic polar fluids the solvent molecule was modeled as a rigid homo-nuclear diatomic with charges q and —q on the two active LJ sites. The solute molecules were modeled as spherical LJ particles [26], as were the molecules that constituted the single molecular layer membrane. The effect of uniform external fields with directions either perpendicular to the membrane or along the diagonal direction (i.e. Ex = Ey = E ) was monitored. The simulation system is shown in Fig. 2. The density profiles, mean squared displacement, and movement of the solvent molecules across the membrane were examined, with and without an external held, to establish whether electro-osmosis can take place in polar systems. The results clearly estab-hshed that electro-osmosis can indeed take place in such solutions. 

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