\section{State Equation}
% double check this with the bits in the paper
\begin{equation}
- \frac{d C^{j}_{i_\mathrm{ves}}}{dt} = k_{fi}k_{fi\mathrm{adj}}\left[C^j_{i_\mathrm{monomer}}\right] -
- k_{bi}k_{bi\mathrm{adj}}C^j_{i_\mathrm{ves}}
+ \frac{d C_{i_\mathrm{ves}}}{dt} = k_{fi}k_{fi\mathrm{adj}}\left[C_{i_\mathrm{monomer}}\right]S_\mathrm{ves} -
+ k_{bi}k_{bi\mathrm{adj}}C_{i_\mathrm{ves}}
\label{eq:state}
\end{equation}
+For $k_{fi}k_{fi\mathrm{adj}}\left[C_{i_\mathrm{monomer}}\right]$,
+$k_{fi}$ has units of $\frac{\mathrm{m}}{\mathrm{s}}$,
+$k_{fi\mathrm{adj}}$ and $k_{bi\mathrm{adj}}$ are unitless,
+concentration is in units of $\frac{\mathrm{n}}{\mathrm{L}}$, surface
+area is in units of $\mathrm{m}^2$, $k_{bi}$ has units of
+$\frac{1}{\mathrm{s}}$ and $C_{i_\mathrm{ves}}$ has units of
+$\mathrm{n}$, Thus, we have
+
+\begin{equation}
+ \frac{\mathrm{n}}{\mathrm{s}} = \frac{\mathrm{m}}{\mathrm{s}} \frac{\mathrm{n}}{\mathrm{L}} \mathrm{m}^2 \frac{1000\mathrm{L}}{\mathrm{m}^3} -
+ \frac{1}{\mathrm{s}} \mathrm{n}
+ =
+ \frac{\mathrm{m^3}}{\mathrm{s}} \frac{\mathrm{n}}{\mathrm{L}} \frac{1000\mathrm{L}}{\mathrm{m}^3} - \frac{\mathrm{n}}{\mathrm{s}}=
+ \frac{\mathrm{n}}{\mathrm{s}} = 1000 \frac{\mathrm{n}}{\mathrm{s}} - \frac{\mathrm{n}}{\mathrm{s}}
+ \label{eq:state_units}
+\end{equation}
+
+The 1000 isn't in \fref{eq:state} above, because it is unit-dependent.
+
\subsection{Forward adjustments ($k_{fi\mathrm{adj}}$)}
\begin{equation}
\newpage
\subsubsection{Unsaturation Backward}
\begin{equation}
- un_b = 10^{\left|3.5^{-\left<un_\mathrm{ves}\right>}-3.5^{-\left<un_\mathrm{monomer}\right>}\right|}
+ un_b = 10^{\left|3.5^{-\left<un_\mathrm{ves}\right>}-3.5^{-un_\mathrm{monomer}}\right|}
\label{eq:unsaturation_backward}
\end{equation}