Mathematical models and calculation methods for optimally distributed electrical conductivity and reaction surface area of 3D carbon cathodes in galvanic metallization of composite and nanocomposite materials

Introduction. The task of uniformly coating carbon-graphite fibers with metal as a base for composite materials is a pressing issue. Galvanic metallization is preferred due to the ability to control the parameters of the electrochemical system. Materials and methods. To determine the effective values of specific electrical conductivity and reactive surface area of a carbon flow three-dimensional electrode (FTE), as well as to identify rational metal electrodeposition modes, mathematical modeling and a combination of calculated and experimental data regarding the feasibility of producing carbon fiber materials (CFM) and FTEs with desired properties are useful. Proper selection of electrolyzer operating modes and parameters allows for intensification of the metallization process and facilitates the production of the desired composites. Results. Mathematical models of electrolysis using a CFM were developed in the form of systems of differential equations for the potential distribution functions, polarizing current density, and deposited metal concentration across the electrode thickness. Boundary value problems were formulated. An optimal control problem was posed with control actions in the form of distributed values of the resistivity and specific surface area of the electrode and an optimization criterion – an indicator of the uniformity of metal distribution across the electrode thickness. The solution was based on S.L. Pontryagin's maximum principle and direct selection of control parameters using the equations of the mathematical model. Discussion. The proposed mathematical models and methods are consistent with the modern electrochemical theory of metal electrodeposition in FTEs. Accounting for dynamic changes in electrode properties and the metallization process of the carbongraphite filaments that comprise it expands the applicability of mathematical models to describe real-world electrolysis processes in FTEs and improves the adequacy of the models for real-world physicochemical processes. Conclusion. The presented mathematical modeling methods and computational algorithms 1) are used both to study the theoretical principles of electrolysis processes in FTEs and to analyze the properties of actual carbon-graphite material metallization processes; 2) allow one to determine the effective values of the distributed specific electrical conductivity and the reactive surface area of the carbon-graphite material to improve the uniformity of electrodeposition across the TFE thickness and to produce carbon-graphite fibers with desired properties.