deletions | additions       diff --git a/Mechanistic Studies.tex b/Mechanistic Studies.tex  index e56b2f5..d87f8b9 100644  --- a/Mechanistic Studies.tex  +++ b/Mechanistic Studies.tex 
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The shape of the nanocrystal will be determined by the relative magnitudes of the atom deposition rate ($V_{deposition}$) and the surface diffusion rate ($V_{diffusion}$).  The relative magnitudes can be concisely represented by the ratio between the rates for atom deposition and surface diffusion ($V_{deposition}/V_{diffusion}$) \cite{Xia_2013}.  When $V_{deposition}/V_{diffusion} << 1$, atoms deposited adatoms  at the active region are able to diffuse quickly to the more stable sites, and thus the synthesis is under thermodynamic control. The thermodynamic product is the nanocrystal shape with the minimum surface free energy.  The surface free energy is different for each crystallographic planes.  Among the low-index planes of an fcc metal, the surface free energies in vacuum increase in the order of (111) < (100) < (110). 
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In the synthesis of nanocrystals, capping agents such as ionic species, small molecules, and polymers can selectively bind to different facets and alter their specific surface free energies.  The final shape of the nanocrystal can be altered by capping agents through this mechanism if the synthesis is under thermodynamic control.  In contrast when $V_{deposition}/V_{diffusion} >> 1$, most deposited atoms adatoms  stay at the high surface energy region since they do not diffuse fast enough. In this case, the synthesis is under kinetic control.  Kinetically controlled shapes depend on the relative deposition rates to different facets of the nanocrystal, which the shape can be predicted by the kinetic Wulff construction \cite{Zhang_2006}.  Various experimental parameters can influence the rates for atom deposition and surface diffusion. 
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Solvent effects in experiments  Fichthorn solvent