Effect of radiation transport on the kinetics of phosphor degradation

The mechanism of phosphor degradation due to ultraviolet (UV) radiation is viewed as a sum of parallel pseudo x-order photochemically induced reactions. The values of the rate constants are assumed proportional to local UV surface intensity, which produces phosphor degradation. Using the Kubelka-Monk [P. Kubelka and F. Munk, Z. Tech. Phys. 12, 593 (1931)] theory for UV propagation through a phosphor layer, it is shown that the UV radiation is exponentially decreasing through the phosphor layer. Surprisingly, the resulting form of the degradation curve is nearly independent of the order of the elementary reaction. For any pseudo x-order UV driven degradation mechanism, the decay of optically active sites takes the following form: M(t)=A+B log(t) provided the observation time is restricted to 1/k(0)less than or equal to t less than or equal to 1/k(min), where k(0) and k(min) are the largest and smallest rate constants, respectively. Here A and B are constants dependent on k(0), the equivalent fraction of the phosphor luminescent sites undergoing degradation, and the optical properties of the phosphor layer. A similarity is found between the inverse of the UV attenuation coefficient and the fraction of absorption sites with respect to the maintenance slope. In the limit of a continuous distribution of rate constants, the analytic results of the discrete model are confirmed. Also, in this limit it is found that k(min)=k(0) exp(-K(km)d), where K-km is a constant found from the Kubelka-Monk analysis and d is the phosphor layer thickness. Experimental data for fluorescent lamps is discussed in conjunction with this theory. Viewing the decay of light output over time as due to the effective decay of optically active sites in the phosphor and taking into account the distribution of UV radiation good correlation to the theory is obtained. (C) 1998 American Institute of Physics.