Three-layer cellular automata model of the electrochemical oxidation of carbon Ketjen Black EC-600JD

In this paper, we consider the problem of constructing the cellular automaton model of the electrochemical oxidation of carbon. The carbon supported platinum catalyst is usually used for anode and cathode in the proton exchange membrane fuel cells which are now widely studied as alternative clean power sources with high energy efficiency. One of the main problems in the fuel cells commercialization is the low corrosion stability of carbon support which leads to detachment of large pieces of the support materials on which Pt is loaded. The mechanism of carbon corrosion, describing gradual carbon surface degradation through successive electrooxidation stages, was suggested by E.N. Gribov research group. Based on this mechanism, we construct the three-dimensional cellular automaton model of electrochemical oxidation of the carbon. According to the cellular automata approach, a space is represented as a three-dimensional Cartesian lattice L = {v = (xyz): x = 0, ...,Lx,y = 0, ..., Ly, z = 0, ..., Lz} consisting of cells. Each cell has a coordinate v e L and a state a e А. The admissible in the model states are А={0), C, COH, COOH, 0}, where C0 denotes a carbon atom inside the sample volume, C is a surface carbon atom, COH and COOH are surface carbon atoms with different oxidation degree, symbol 0 corresponds to a place without any atom. The states of cells are changed according to the transition rules which are defined by the mechanism of carbon corrosion. In this model the transition rule is a sequential composition of two operators Poxid and Psurf. The operator Poxid simulates the oxidation stages: 01(v) : {(C, v)} -- {(COH, v)}, 02(v) : {(COH, v)} --• {(COOH, v)}, 9зО) : {(COOH, v)} --• {(0, v)}. The operator Psurf finds new surface carbon atoms, i.e. the inner carbon atoms C0 that after application of Poxid have become the outer atoms C. Conductive carbon black "Ketjenblack" is currently widely used as a support for platinum catalyst in the proton exchange membrane fuel cells. So, this material is chosen for investigation in the current paper. The "Ketjenblack" consists of hollow nanospheres-granules of carbon atoms. The average diameter of carbon grains is ~ 30 nm. In the cellular automaton model, the granules are represented by spheres consisting of cells with states C0 and C. Each granule is formed by cells lying between two nested spheres with radii Rout = 15 cells and Rin = 11.3 cells. The radii are selected based on the characteristics of the "Ketjenblack". In the chemical experiments, the carbon sample is deposited on polished glass carbon rod and immersed in the electrolyte. So, in the cellular automaton model the carbon sample is supposed to be fixed from above. The carbon pieces unconnected with the upper atoms are considered as detached and disappear. To find the detached carbon atoms, all cells containing the atoms connected with upper atoms are marked by the "one scan connected component labeling technique". The atoms not marked as connected are removed, i.e., states of these cells are replaced by 0. During the simulation the following characteristics are calculated: the number of pure carbon atoms, the number of oxidized carbon atoms, the total number of surface atoms and the electrochemical capacity of the carbon sample. The results of computer simulation are compared with the experimental data. The shape of the electrochemical capacity curve obtained using the cellular automaton model is qualitatively similar to that experimentally measured. This result confirms the correctness of the cellular automaton model of carbon electrochemical oxidation.

Keywords

Authors

References