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\section{Findings from Potential of Mean Force Calculations}  We explored the potential of mean force (PMF) along the absorption path of an Ag atom from solution phase to the Ag NC surface, with the goal of gaining quantitative insight of the influence of the adsorbed PVP layer. To calculate the PMF profile of the Ag atom, we use umbrella sampling \cite{K_stner_2011} with a harmonic bias potential on the canonical molecular dynamics simulation. We use the same system as for the \textit{in-silico} deposition, which is shown in Fig \ref{fig:sim-setup}. Umbrella sampling is used to enhance the sampling because the free energy barrier of absorption is greater than $k_B T$. We use the umbrella integration method \cite{Ka_stner_2005} to combine data from individual windows sampled. The advantage of the umbrella integration method over the conventional weight-histogram analysis method (WHAM) is the independence of the number of grid points and one can obtain the statistical error directly through umbrella integration \cite{Ka_stner_2006}. The reaction coordinate of the PMF is the orthogonal axis of the Ag slab, with the origin at the surface layer of the bottom slab. Further description of the PMF calculation methods can be found in the supporting information. In this section, we present our result of the PMF profile of the Ag atom and calculate the relative atom flux to \{111\} and \{100\} facets $\frac{F_{111}}{F_{100}}$ usingthe framework of  transition-state theory \cite{H_nggi_1990}. theory.