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\section{Findings from Potential of Mean Force Calculations}  We explored the free energy landscape along the absorption path of Ag atoms from solution phase to the crystal surface, with the goal of gaining quantitative insight of the influence of the adsorbed PVP layer. To calculate the potential of mean force (PMF) of Ag atoms, we use umbrella sampling \cite{K_stner_2011} with harmonic bias potential to enhance the sampling since the free energy barrier of absorption is greater than $kT$. Umbrella integration \cite{Ka_stner_2005} is used to analyze the biased molecular dynamics simulation, also yielding a statistical error of the PMF calculated \cite{Ka_stner_2006}. The simulation box is set up in the same way as shown in Fig. \ref{fig:sim-setup} (a), as the equilibrated system for the \textit{in-silico} deposition flux calculation is used in the PMF calculation. The reaction coordinate of the potential of mean force is the orthogonal axis of the Ag slab, with the origin at the surface layer of the bottom slab.Fig. \ref{fig:pmf} shows the PMF of the Ag atom along the orthogonal axis of the Ag slab with Ag100 and Ag111 surfaces. At the region of $z > 25 \dot A$, the PMF is a flat maxima which is where the Ag atom is in bulk solvent. At the region of $z < 25\dot A$ and $z > 10\dot A$, the PMF is descending from the maxima towards a local minimum which traps the Ag atom from absorbing onto the Ag surface. In this latter region, the Ag atom interacts with the PVP monolayer which decreases the PMF. The energy barrier on the left side of the local minimum is from the PVP adsorbed to the Ag surface, which only allow the Ag atom to absorb onto the Ag surface when it temporarily desorbs or the Ag atom finds an opening on the Ag surface. The global minimum of the PMF profile is in the region of $z < 6\dot A$, which is the position that the Ag atom absorbs onto the Ag surface.  Results:  \begin{itemize}  \item PMF profile  \item Flux ratio  \item Reactive flux from TST  \end{itemize}  Insights:  \begin{itemize}  \item Forms sharp cube  \item Discrepancy from Xin's result: recrossing?  \item Absorbing Markov's chain model  \end{itemize}