Hyperfine coupling constants (hfcs) are a sensitive means of examining the electronic structure of a radical in solution and monitoring how this is altered through solvent interactions. The hfcs of the cyclohexadienyl radical's methylene proton and muon are altered by the partial ordering of the quadrupole moments of the neighboring solvent molecules around the dipole of the muoniated cyclohexadienyl radical. The methylene hfcs of the muoniated cyclohexadienyl radical were measured by avoided level crossing muon spin resonance (ALC-µSR) in a series of benzene/cyclohexane mixtures. The methylene hfcs were found to be directly proportional to the concentration of solvent quadrupole moments, which contradicts the model of Vujosevic et al. [J. Phys. Chem. B 111 (2007) 199] where the hfc shift was predicted to be proportional to the quadrupole concentration to the ⁴⁄₃ power. In this work the model of Vujosevic et al. has been extended and an analytical method for calculating the internal field was developed. This extended model reproduces the observed linear relationship between the hfcs and the quadrupole concentration. It was found that the diameter of solvents and solute molecules is of great importance.