In a thermally activated delayed fluorescence (TADF) molecular system, the rate constant for each elementary process is given in the following figure, e

In a thermally activated delayed fluorescence (TADF) molecular system, the rate constant for each elementary process is given in the following figure, e.g. & is the rate of radiative transition from the S) state, k§, and kz, are the rates of non-radiative relaxation from the S; and T: states, and Asc and Jerse are the forward and reverse energy transfer rates between the Si and T) states, respectively. These processes determine the overall decay rates of the S; state and Ti state. +

4 a

i Krisc i

ke] kg, ik,

So o

QI. In the absence of exciton-formation processes, give the differential equations which describe the change rates of the [Si] and [T1] populations. ~

Q2. Develop expressions for [Si] and [Ti] by solving the rate equations in Q1] and prove that the solutions are of the form ~

[1] = Aye“*? + Age“

[T,] = Age-*!* + Agew:*

where Ai, Ao, As, and Ay are determined by the initial conditions, and the characteristic decay rates 4, and k are given by=

p= Kase + Krisc ah +key +i

. ( 1+ h- hee dei

~ (hase + kpisc + kp + Se + kB)

Q3. Assuming that Kisc, kp, KS, >> krisc, KE, in what form can h and h be approximated? —