# Thermal Quenching

For TSP where the paint layer is not oxygen-permeable such that no oxygen quenching occurs, from Eq. (2.8), the quantum yield of luminescence is simply given by

Ф = 4- = – TkT – . (2.64)

I a kr + krn

The temperature dependency of the non-radiative processes knr can be decomposed into a temperature-independent term and a temperature-dependent term modeled by the Arrhenius relation (Bennett and McCartin 1966; Song and Fayer 1991; Schanze et al. 1997)

e

knr = knr0 + knr1exp(—-ziz) , (2.65)

where k^0 = knr(T = 0) and km1 are the rate constants for the temperature – independent and temperature-dependent processes, respectively, Enr is the activation energy for the non-radiative process, R is the universal gas constant, and T is the absolute temperature in Kelvin. From Eqs. (2.64) and (2.65), we have

where I(0) = I(T = 0) is the luminescent intensity at the absolute zero temperature. For ЩТ) – I(Tf M/I(0) << 1 and I(T)I(Tf ) /[I(0)]2 << 1

over a certain temperature range, a relation between the luminescent intensity and temperature can be approximately written in the Arrhenius form

Theoretically speaking, the Arrhenius plot of ln[I(T)/ I(Tref )] versus 1/T gives

a straight line of the slope EJR. Experimental results indeed indicate that the simple Arrhenius relation Eq. (2.67) is able to fit data over a certain temperature range. However, for some TSPs, experimental data may not fully obey the simple Arrhenius relation over a wider range of temperature. Thus, as an alternative, an empirical functional relation between the luminescent intensity and temperature is

-IjTP – = f(T/Tf) , (2.68)

11ref->

where f(T /Tref) could be a polynomial, exponential or other function to fit

experimental data over a working temperature range. Either Eq. (2.67) or Eq. (2.68) can serve as an operational form of the calibration relation for TSP in practical applications.

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