Analytic formulas and numerical simulations for the dynamics of thick and non-uniform polymerization by a UV light

The kinetics of UV light photoinitiated polymerization system (PPS) with non-uniform initiator concentration is theoretically presented. Analytic formulas are derived for the cross linking time (T*), defined by the depletion level of the initiator, which is an exponentially increasing function of the thickness, whereas it is inverse proportional to the UV light intensity. Typical T* (on the surface, at z=0) is about 2 min for a UV light intensity of 20 (mW/cm(2)) and the range of T*(at z > 0) is about 3 to 5 min, for a polymer thickness of 1.0 cm. Optimal photoinitiation rate is found to be the result of the competing parameter between the UV light intensity and the initiator concentration. The roles of each of the key parameters in PPS are numerically shown including the initiator concentration and its distribution, the UV light intensity and the three absorption coefficients. Our analytic formulas and numerical results provide useful guidance for the parameters selection and optimalization in PPS with the prediction of the cross linking time in various system thickness.