deletions | additions       diff --git a/section_Findings_from_PMF.tex b/section_Findings_from_PMF.tex  index 5bee800..073c514 100644  --- a/section_Findings_from_PMF.tex  +++ b/section_Findings_from_PMF.tex 
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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. 3 shows the PMF of the Ag atom along the orthogonal axis of the Ag slab with Ag100 and Ag111 surfaces. At $z > 25 \dot A$ where the Ag atom is in bulk solvent phase, the PMF of the Ag atom is a flat maxima. As the position is closer to the surface At $z < 25\dot A$ and $z > 10\dot A$  where there is interactions between the PVP monolayer and the Ag atom, the PMF is below the flat maxima, with a local minima Results:  \begin{itemize}