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\section{Kinetic model with dynamic disorder}  As demonstrated already in first order kinetics, the Kohlrausch-Williams-Watts (KWW) stretched exponential function can measure the amount of dynamic disorder in a system.[cite] The KWW model has been widely applicable to many fields of science such as the discharge of capacitors[cite]. The KWW model adds an exponential term, $\beta$,to the survival function model. The term $\omega$ represents a time independent rate coefficient and $\beta$ represents dynamic disorder where $0<\beta\leq1$. Applying KWW to second order kinetics, the survival probability is represented as $S(t)=\frac{1}{1+(\omega t[A_0])^{\beta}}$. The time dependent rate coefficient is $k(t)=\frac{\beta([A_0]\omega t)^{\beta}}{t}$, where the second order definition of the time dependent rate coefficient was used. This time dependent rate coefficient gives statistical length and divergences of   \begin{equation}  \mathcal{L}_{KWW}(\Delta{t})=[A_0]^{\beta}\omega^{\beta}t^{\beta}\bigg|_{t_i}^{t_f}