Electrochemical electrodes comprise multiple phenomena at different scales. Several works have tried to model such phenomena using statistical techniques. This paper proposes a novel process to work with reduced size images to reconstruct microstructures with the Simulated Annealing method. Later, using the Finite Volume Method, it is verified the effect of the image resolution on the effective transport coefficient (ETC). The method can be applied to synthetic images or images from the Scanning Electron Microscope. The first stage consists of obtaining the image of minimum size, which contains at least 98% of the statistical information of the original image, allowing an equivalent statistical study. The image size reduction was made by applying an iterative decimation over the image using the normalized coarseness to compare the amount of information contained at each step. Representative improvements, especially in processing time, are achieved by reducing the size of the reconstructed microstructures without affecting their statistical behavior. The process ends computing the conduction efficiency from the microstructures. The simulation results, obtained from two kinds of images from different materials, demonstrate the effectivity of the proposed approach. It is important to remark that the controlled decimation allows a reduction of the processor and memory use during the reconstruction and ETC computation of electrodes.

The study of the microstructure of random heterogeneous materials, related to an electrochemical device, is relevant because their effective macroscopic properties, e.g., electrical or proton conductivity, are a function of their effective transport coefficients (ETC). The magnitude of ETC depends on the distribution and properties of the material phase. In this work, an algorithm is developed to generate stochastic two-phase (binary) image configurations with multiple geometries and polydispersed particle sizes. The recognizable geometry in the images is represented by the white phase dispersed and characterized by statistical descriptors (two-point and line-path correlation functions). Percolation is obtained for the geometries by identifying an infinite cluster to guarantee the connection between the edges of the microstructures. Finally, the finite volume method is used to determine the ETC. Agglomerate phase results show that the geometry with the highest local current distribution is the triangular geometry. In the matrix phase, the most significant results are obtained by circular geometry, while the lowest is obtained by the 3-sided polygon. The proposed methodology allows to establish criteria based on percolation and surface fraction to assure effective electrical conduction according to their geometric distribution; results provide an insight for the microstructure development with high projection to be used to improve the electrode of a Membrane Electrode Assembly (MEA).

The influence of topological entropy (TS) on the effective transport coefficient (ETC) of a two-phase material is analyzed. The proposed methodology studies a system of aligned bars that evolves into a stochastic heterogeneous system. This proposal uses synthetic images generated by computational algorithms and experimental images from the scanning electron microscope (SEM). Microstructural variation is imposed for statistical reconstruction moments by simulated annealing (SA) and it is characterized through TS applied in Voronoi diagrams of the studied systems. On the other hand, ETC is determined numerically by the Finite Volume Method (FVM) and generalized by a transport efficiency of charge (ek). The results suggest that our approach can work as a design tool to improve the ETC in stochastic heterogeneous materials. The case studies show that ek decreases when TS increases to the point of stability of both variables. For example, for the 80% surface fraction, in the particulate system of diameter D = 1, ek = 50.81 ± 0.26% @ TS = 0.27 ± 0.002; when the system has an agglomerate distribution similar to a SEM image, ek = 45.69 ± 0.60% @ TS = 0.32 ± 0.002.

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