Film forming Finite elements

Approximate vs. Numerical Solution. The accuracy of the approximate reaction factor expression has been tested over wide ranges of parameter values by comparison with numerical solutions of the film-theory model. The methods of orthogonal collocation and orthogonal collocation on finite elements (7,8) were used to obtain the numerical solutions (details are given by Shaikh and Varma (j>)). Comparisons indicate that deviations in the approximate factor are within few percents (< 5%). It should be mentioned that for relatively high values of Hatta number (M >20), the asymptotic form of Equation 7 was used in those comparisons. 

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When the polymer flhn is oxidized, its electronic conductivity can exceed the ionic conductivity due to mobile counterions. Then, the film behaves as a porous metal with pores of limited diameter and depth. This can be represented by an equivalent circuit via modified Randles circuits such as those shown in Figure 8.4. One Warburg element, representative of linear finite restricted diffusion of dopants across the film, is also included. The model circuit includes a charge transfer resistance, associated with the electrode/fllm interface, and a constant phase element representing the charge accumulation that forms the interfacial double... 

In a broad sense a parallel combination of charge transfer resistance and CPE elements, in series with finite diffusion element typically represent the circuit. When potential modulation is introduced, charge-transfer-related impedances decrease with increases in electrochemical potential and capacitance for the metal-polymer interface. The capacitance is usually nonideal due to film or electrode porosity [13] and typically is represented by the CPE element. If the film is formed as a reflective boundary, the angle is sometimes different from -90° because of inhomogeneity of the film and distributed values for diffusion coefficients. If two films are formed on the electrode, two RI CPE semicircles are often observed. 

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