1. Modeling of reactant concentration in electrocatalytic processes at conducting polymer modified electrodes Valdas Jasaitis, Albertas Malinauskas, Feliksas Ivanauskas valdas.jasaitis@gmail.com Vilnius University, Institute of Mathematics and Informatics, Institute of Chemistry, Lithuania

2. Layout Introduction Mathematical model of electrocatalysis at conducting polymer modified electrodes Results of calculations Conclusion

3. What are conducting polymers? Novel synthetic materials (plastics) that conduct electricity. Ability to catalyze some electrochemical oxidation and/or reduction (redox) processes of solution species. Low cost and ease of preparation. Can be simply obtained in appropriate form like thin films covering electrodes.

4. Electrocatalytic conversion processes The diffusion of solute species through the porous conducting polymer film placed at electrode surface, toward the reaction zone. Chemical redox reaction between the diffusing species and catalytically active centers within the polymer film. The diffusion of charge carriers, from the underlying electrode surface through the polymer layer to reaction zone. The diffusion of reaction products out of polymer layer into the bulk of solution.

5. Schematic diagram

6. Assumptions (1) Limited electric conductivity of conducting polymers. Considering the net kinetics of electrocatalytic processes at conducting polymer modified electrodes. Rate of charge carries: High – reaction occurs at polymer/solution interface; Limited – reaction should occur within the conducting polymer.

7. Assumptions (2) Flat surface of electrode is covered with a uniform layer of conducting polymer (thickness d). The modified electrode is immersed into a reactant solution of unlimited volume. Process proceeds under ideal stirring conditions.

8. Subject of investigation The location of the mean reaction zone during electrochemical redox process. The choice between the two reaction mechanisms: “metal-like catalysis” “a redox catalysis”

9. Mathematical modeling The Fick law describes the diffusion of reactant into a polymer layer: The electrochemical charge transfer process: The rate of this reaction is described by simple equation of chemical kinetics

10. Mathematical modeling The rate equations for R, P, and n could be expressed as follows:

11. Initial conditions (t=0) The electrocatalytic processes starts when the reactant appears over the surface of a polymer layer.

12. Boundary conditions (t > 0) Reactant Product Charge carrier

13. Numerical values for parameters ParameterDimensionNumerical value d (thickness of polymer layer)(m)10 -6, 10 -5, 10 -4 D (diffusion coefficient for reactant and product) (m 2 /s)10 -9 D n (diffusion coefficient for charge carrier within polymer film) (m 2 /s)10 -9, 10 -8, 10 -7 k (second –order reaction rate constant)(m 3 ×mol/s)10 1,10 0,10 -1,10 -2 R 0 (concentration of reactant in the bulk of solution) (mol/m 3 )10 2, 10 1, 10 0 n 0 (initial concentration of charge carriers within polymer) (mol/m 3 )4 × 10 3

14. Reactant concentration Calculated time and space profiles for reactant concentration (~4000 graphs) d = 10 -5 m k = 10 -2 m 3 × mol/s D n = 10 -8 m 2 /s R 0 = 10 1 mol/m 3

15. Half conversion of reactant Polymer thickness d = 10 -6 m Fast chemical redox reaction (k = 10 0.. 10 1 m 3 × mol/s) near polymer/solution interface The lowest reaction rate constant values (k = 10 -2.. 10 -1 m 3 × mol/s) near electrode/polymer interface

16. Half conversion of reactant Polymer thickness d = 10 -5 m Fast chemical redox reaction (k = 10 0.. 10 1 m 3 × mol/s) near polymer/solution interface The lowest reaction rate constant values (k = 10 -2.. 10 -1 m 3 × mol/s) near polymer/solution interface

17. Half conversion of reactant Polymer thickness d = 10 -4 m Fast chemical redox reaction (k = 10 0.. 10 1 m 3 × mol/s) near polymer/solution interface The lowest reaction rate constant values (k = 10 -2.. 10 -1 m 3 × mol/s) near polymer/solution interface

18. Conclusions Electrocatalysis of solute species at conducting polymer modified electrodes proceeds within the polymer film rather than at the outer polymer/solution interface. Electrocatalytic conversion follows a redox-mechanism rather than metal-like one. Based on the proposed model, optimization of reaction system parameters could be made for any particular case to get an optimum efficiency or reaction to product conversion.