deletions | additions       diff --git a/Kinetic model with dynamic disorder.tex b/Kinetic model with dynamic disorder.tex  index 6c1e8d2..2c33f48 100644  --- a/Kinetic model with dynamic disorder.tex  +++ b/Kinetic model with dynamic disorder.tex 
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\section{Second-order kinetic model with dynamical disorder}  to To  study the effect of dynamical disorder on higher-order kinetics, we adapt the Kohlrausch-Williams-Watts (KWW) model for stretched exponential decay. In first-order kinetics, stretched exponential decay involves a two-parameter survival function $\exp(-\omega t)^\beta$ and associated time-depedent rate coefficient, $k_{1,KWW}(t) = \beta(\omega t)^{\beta}/t$. The parameter $\omega$ is a characteristic rate or inverse time scale and the parameter $\beta$ is a measure of the degree of stretching. We showed in Reference~1 Reference~[citation]  that stretching the exponential with $\beta$ increases  the degree of dynamic disorder when stretching the exponential varies nonlinearly with $\beta$. nonlinearly.  Assuming an overall second order process with a time depedent rate coefficient the survival function is written as $S_2(t) = 1/\left(1+(\omega tC_A(0))^{\beta}\right)$. Through the time-derivative of the inverse of the survival function the time depedent rate coefficient characterizing the decay is expressed as $k_{2,KWW}(t) = \beta(C_A(0)\omega t)^{\beta}/t$. We see this definition of the rate coefficient maintains a dependence on the initial concentration of the reactants which is a unique result when comapared to the first-order result. Integrating the time-depedent rate coefficient gives the statistical length  \begin{equation}