A mathematical model for free radical polymerizations initiated by a linear bifunctional initiator was described in detail from the fundamental reactions based on the polymerization mechanism and species balance, considering the volume contraction and thermal initiation. The model presented herein utilized diffusion-controlled rate constants based on free volume theory and employed the method of moments to solve the various species concentrations, polymerization rate, molecular weight and polydispersity, considering gel effect, glass effect and cage effect. Conversion, average molecular weight and polydispersity at various initiator [2,5-dimethyl-2,5-di(2-ethylhexoylperoxy)hexane] (DMDEHPH) concentrations and temperatures were calculated with the mathematical model of styrene free radical bulk polymerizations with the linear bifunctional initiator. Model predictions agreed well with experimental data. The various species concentrations were also calculated. The model demonstrated that plot of every species concentration vs. conversion had a maximum value for either various polymer or radical concentrations. Based on model predictions, the biradical concentration was several orders of magnitude smaller than monoradical concentration while polymer concentrations were only different in several times. The plots at various initiator concentrations had no cross-points. And the higher the initiator concentration was, the higher both the radical and polymer concentrations were. The plots had cross-points at various temperatures. And the lower the temperature, the higher the radical and polymer concentrations at gel-effect phase, while the lower the temperature, the smaller the radical and polymer concentrations before and after gel-effect phase.

Key words: bifunctional, initiator, polymerization, kinetics, model