By Tess R.W. (ed.)
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Example text
If the new method’s primary purpose, for example, is simply greater efficiency, then a simple model like the Cottrell system and chronopotentiometry may be enough to demonstrate that; these two differ fundamentally in their boundary conditions, the Cottrell system having a socalled Dirichlet boundary condition (given concentrations at the boundary), while chronopotentiometry has a derivative or Neumann condition, where gradients are specified at the boundary. If a method under development is expected to give high resolution (small intervals) along x—usually at the boundary—a model that provides marked concentration changes very close to the boundary is the best for testing that.
By using more points, higher-order approximations can be achieved. In the context of this book, forward and backward multi-point formulae are of special interest, as well as some asymmetric and central multi-point ones. To this end, a notation will be established here. 2 shows the same Fig. 3 Multi-Point First Derivative Approximations 43 curve as Fig. 1 but now seven points are marked on it. The notation to be used is as follows. n/ (for a second derivative). 14) This is done by writing the Taylor expansions around the point at index i for all the other (n 1) points, to a sufficient number of terms, and solving for the derivatives, discarding all but the numbers for the first derivative.
102) or, in dimensionless terms, with B D bc . It may be that while the state of adsorption is in momentary equilibrium with c0 , there are nevertheless concentration gradients in the solution. The isotherms take many forms; a large list was presented by Mohilner [48]. Â/ D Â 1 Â exp. 105) with a the attraction parameter. 106) There are other, more complicated isotherms but the above examples suffice. 5 Adsorption Kinetics 33 In order to reach a certain surface concentration or fractional coverage Â, the substance in question must first arrive at the electrode by some transport process.
