Plasma immersion ion implantation (PIII) is a promising technique for immobilizing biomolecules on the surface of polymers. Radicals generated in a subsurface layer by PIII treatment diffuse throughout the substrate, forming covalent bonds to molecules when they reach the surface. Understanding and controlling the diffusion of radicals through this layer will enable efficient optimization of this technique. We develop a model based on site to site diffusion according to Fick's second law with temperature activation according to the Arrhenius relation. Using our model, the Arrhenius exponential prefactor (for barrierless diffusion), D0, and activation energy, EA, for a radical to diffuse from one position to another are found to be 3.11 × 10^-17 m² s^-1 and 0.31 eV, respectively. The model fits experimental data with a high degree of accuracy and allows for accurate prediction of radical diffusion to the surface. The model makes useful predictions for the lifetime over which the surface is sufficiently active to covalently immobilize biomolecules and it can be used to determine radical fluence during biomolecule incubation for a range of storage and incubation temperatures so facilitating selection of the most appropriate parameters.