deletions | additions       diff --git a/section_Findings_from_PMF.tex b/section_Findings_from_PMF.tex  index 39b759e..356ea9b 100644  --- a/section_Findings_from_PMF.tex  +++ b/section_Findings_from_PMF.tex 
...
\section{Findings from Potential of Mean Force Calculations}  We explored the free energy landscape potential of mean force (PMF)  along the absorption path of Ag atoms from solution phase to the crystal Ag NC  surface, with the goal of gaining quantitative insight of the influence of the adsorbed PVP layer. To calculate the potential of mean force (PMF) PMF  of the  Ag atoms, atom,  we use umbrella sampling \cite{K_stner_2011} with harmonic bias potential on the molecular dynamics simulation of the previously described system for the \textit{in-silico} deposition flux calculation shown in Fig \ref{fig:sim-setup}. Umbrella sampling is used  to enhance the sampling since because  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, combine data from individual windows sampled,  also yielding a statistical error of the PMF calculated \cite{Ka_stner_2006}. Thesimulation 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 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 will present our result of the PMF profile of the Ag atom along the orthogonal axis of the Ag slab. From the PMF profile, we and  calculate therate constant of atom flux and  relative atom  fluxof deposition  to \{111\} and \{100\} facets $\frac{F_{111}}{F_{100}}$ using the framework of transition-state theory \cite{H_nggi_1990}.