# Theoretical Description of Carbon Felt Electrical Properties Affected by Compression
## 1 Introduction  
Carbon Felt (CF) is used as electrode material in a variety of electrochemical applications [1; 2; 3; 4; 5; 6; 7]. Currently, its most prominent utilization is in the vanadium redox and other flow type batteries owing to its good electrical conductivity, hydraulic permeability, and durability in strong acid and alkali electrolytes. In particular, good electrical conductivity arises from the movement of electrons through the carbon filaments to reach the electrolyte [8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20]. CF conductivity is determined by the carbon fibers comprising the felt structure and which connect simultaneously to both electrodes. Conductivity is well known to be improved by felt compression. With slight pressure on a felt, the density of the fibers is increased, producing additional self-interconnections of fibers and better contact with the substrate of the electrodes. However, felt compression also decreases the interstitial volume, and therefore, reduces the average cross-section of micro-channels linking pores inside a felt framework. The result is an increase in the CF hydraulic resistance obstructing electrolyte flow through the electrode. Electrochemical researchers, designengineers, and others need to consider both the electrical and physical properties of CF for optimal performance in many electrochemical applications. A tremendous amount of research work [21; 22; 23; 24; 25; 26; 27; 28; 29; 30] has been carried out to investigate and measure the properties of CF. [PERSON] et al. [31], for example, suggested a ladder circuit comprising multiple equal resistances that model resistivity for the explanation CF conductivity. However, this model does not explain sufficiently the decrease of CF resistivity during its compression. [PERSON] et al. [32] measured physical parameters of rayon-based CF manufactured by Mersen Co in large sheets with a width of several mm to a few cm. The structure of CF exhibits a significant stochastic framework; therefore, theoretical analyses previously developed, as a rule, used many simplifying assumptions. Thus, results and conclusions required correction coefficients and frequently differed from experimental test results. Moreover, it proved difficult to generalize results to other similar cases. Therefore, many investigations concerning electrical conductivity of CF were conducted for specific applications with the generalization obtained by results from mathematical formulations. For example, measurements of CF electrical resistivity (conductivity) were carried out for furnace heating elements [3]. Among the reports, work by [PERSON] et al. [26] was the first to examine conductivity of CFs used in electrochemical applications. These authors studied a new bipolar cell with a proton-exchange membrane, where flat electrodes were made of long carbon fiber assemblies like CF structure to facilitate electrical current flow. The main aim of the investigation was the amplification of the cell current that could be enhanced by the increase of electrodes conductivity. They found a two-fold increase of stress on the electrodes which causes a 2.5-times increase of CF conductivity and current, which in turn led to enhanced electrochemical reactions. At the same time, oxidative reactions are enhanced at the anode electrode, and reduction reactions are enhanced at the cathode. Accordingly, electrodes resistivity were measured based on the area-specific resistance (ASR), which represents the specific resistance in the perpendicular-plane direction of CF electrodes. ASR was found to be a function of the compression of felt, and it allows the resistance estimation of any electrode having its own specific dimensions. It is important to emphasize the usefulness of ASR for describing CF conductivity appearing in this work for the first time. The usefulness of ASR is witnessed by its usage in multiple published studies [27; 28; 29; 30]. The sharp decrease of CF ASR during compression was observed in all experiments.