Terre Trupp's JCE Classroom Activity #36 in the May 2001 issue of J. Chem. Educ. (1) provides a nice visual demonstration of steady-state photochemical kinetics. In Part II of the activity, UV-sensitive beads at different temperatures are exposed to the same amount of light. It is observed that the intensity of the color varies inversely with temperature--less of the colored form of the photochromic dye is formed at higher temperatures. This is just what is expected if the rate of formation of the colored form is independent of temperature and the rate of thermal return to the colorless form increases with temperature.

The rate of formation of the colored form is

dC/dt = (aI₀f)L (1)

Here C and L are the concentrations of the Colored and colorLess forms of the dye, I₀ is the flux of photons, a is the fraction of photons absorbed by a unit concentration of the dye in the bead, and f is the quantum yield for formation of the colored form of a photo-excited dye molecule. The factors inside the parentheses are essentially independent of temperature over the short range of interest for these beads.

The rate of loss of the colored form by thermal return to the colorless form is

-dC/dt = kC (2)

Here k is the temperature-dependent (via the Arrhenius activation energy factor) rate constant for the thermal return. The activation energy for the thermal return can be obtained by exposing flattened, room-temperature beads to the same light source for a specified time and then placing them on metal surfaces at different temperatures and noting the time required to return to the colorless form. The times range from 120 to 20 seconds over the range from 0 to 40 °C (private communication with Silberman, R.; Radcliffe, K. SUNY-Cortland, Jul 2000). The activation energy derived from these measurements is about 37 kJ mol^-1.

When the rates (eqs 1 and 2) are equal, the steady state, the ratio of the colored to colorless forms of the dye in the bead is

C/L = aI₀f/k (3)

Since k increases with temperature (the thermal return times get shorter), the steady-state ratio decreases with temperature. The intensity of color developed is lower at higher temperatures, which provides a visual demonstration of the steady-state kinetics. A further experiment would be to change the flux of photons (brightness of the light source) to test whether the steady-state color intensity is a function of this variable, as eq 3 predicts.

In an article that accompanies the Classroom Activity, Prypsztejn and Negri outline a photochromic experiment with a spiropyran dye (2). In ethanol solution, they find a large temperature dependence for the thermal decay with an activation energy of 112 kJ mol^-1. The decay time for their dye is strongly dependent on solvent effects and decreases dramatically in less polar solvents. If the dye(s) in the UV-sensitive beads are similar to these spiro dyes, we can infer that their environment in the beads is relatively nonpolar.

Literature Cited

1. Trupp, T. J. Chem. Educ. 2001, 78, 648A-648B.
2. Prypsztejn, H. E.; Negri, R. M. J. Chem. Educ. 2001, 78, 645-648.