\begin{align*}
  \left\{\begin{array}{l}
    \frac{\partial C_{free}}{\partial t} = D\frac{\partial^2 C_{free}}{\partial x^2} - kC_{free}C_{polymer} \\
    \frac{\partial C_{product}}{\partial t} = kC_{free}C_{polymer} \\
    D = D_0 \exp(-K^{\prime}C_{product}) \\
    \frac{\partial C_{polymer}}{\partial t} = -kC_{free}C_{polymer} \\
  \end{array}\right. 
\end{align*}
