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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 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 potential of mean force 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 potential of mean force 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. Results:  \begin{itemize}