MATHEMATICAL SOLUTION OF SOME MODEL MATERIALS SCIENCE BOUNDARY VALUE PROBLEMS AND THEIR COMPARISON WITH EXPERIMENTAL RESULTS (SALPST, CURRENT DENSITY, COMPUTERIZATION, CORNER EFFECT, ABSOLUTE EQUIVALENT CIRCUIT).

摘要

Mathematical solutions of some model material science boundary value problems and their comparison with experimental results are presented. They include surface film formation on copper alloys in aerated 3.4wt% NaCl solution, and current density distribution in an electrolytic cell. The mathematical models and experimental results are compared. The small amplitude linear potential sweep technique (SALPST) is fully analyzed by mathematical methods and for the first time used systematically in polarization resistance, R(,p), and interfacial capacitance, C(,p), measurements for an electrochemical system. The impedance measurements include various electrochemical methods and the theoretical analyses apply to time-domain and frequency-domain methods for the study of various mechanisms of electrochemical reactions. The interfacial models describing the solution/electrode interface during electrochemical processes are obtained by using transmission line equations, the differential method, and reaction mechanisms. The resultant absolute equivalent circuits are shown in detail. Computerization in impedance measurements is introduced to the frequency-domain analysis and several systems are calculated by computer and compared with experimental results. Surface film formation on copper alloys is observed by EDX and SEM. Different alloys show different corrosion resistance and interfacial capacitance values. Surface film formation can be described in terms of an initial time period. During this period, a relatively stable R(,p), C(,p), and E(,corr) are obtained, corresponding to the formation of an uniform surface film on copper alloys. The defined initial time period takes an important position in the application of the technique to engineering systems.;Mathematical modeling of the current density distributions on an electrode is set up by using potential theory and Green's theorem. The resultant integral equations are solved by computer. Edge effects are obtained from two-dimensional modeling. Corner effects are for the first time obtained mathematically and experimentally in the three-dimensional problem. Local variation of the polarization parameter is analyzed for the two-dimensional and three-dimensional problems. The application of these models is extended to different shapes of the electrode, the dealloying problem, pitting corrosion, different crystallographic faces under activation polarization, different reaction mechanisms, different surface control processes and other engineering problems.