Two different approaches were used to model the insertion of lithium ions into a single carbon particle fiber under potentiodynamic control. In the first approach, volume changes in the particle due to lithium intercalation/deintercalation were neglected (NVCP model) while in the second approach the volume changes were included (VCP model). Modeling discrimination techniques were used to determine the statistical significance of the different models when fitting experimental cyclic voltammetry data. It was found that the VCP model is a better fit of the experimental cyclic voltammetry data than the NVCP model. The VCP model predicts significant changes in the radius of the particle due to lithium intercalation/deintercalation. It is recommended to extend the application of the VCP model to a complete lithium ion cell. Incorporation of volume changes into the model along with the formation of the SEI layer may be the key to understanding and predicting capacity fade in a lithium ion battery during cycling.