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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 along the orthogonal axis from the Ag surface, we used umbrella sampling with harmonic bias potential to enhance the sampling since the free energy barrier of absorption is $> kT$. greater than $kT$.