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Another useful quantity is the friction factor $f$, or the friction coefficient of a non-spherical shape divided by the friction coefficient of a sphere of equivalent volume. The nanoparticle and ellipsoidal nanorod dimensions used here were specifically chosen to create structures with equal volumes. |
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\begin{longtable}{lccccc} |
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\caption{Calculated ``slip'' interfacial friction coefficients ($\kappa$) and friction factors ($f$) of gold nanostructures solvated in TraPPE-UA hexane. The ellipsoid is oriented with the long axis along the $z$ direction.} |
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\caption{Calculated ``stick'' interfacial friction coefficients ($\kappa$) and friction factors ($f$) of gold nanostructures solvated in TraPPE-UA hexane. The ellipsoid is oriented with the long axis along the $z$ direction.} |
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\\ \hline \hline |
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{Structure} & {Axis of rotation} & {$\kappa_{VSS}$} & {$\kappa_{calc}$} & {$f_{VSS}$} & {$f_{calc}$}\\ |
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{} & {} & {\small($10^4$ Pa s m$^{-1}$)} & {\small($10^4$ Pa s m$^{-1}$)} & {} & {}\\ \hline |
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{Sphere} & {$x = y = z$} & {} & {} & {1} & {1}\\ |
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{Prolate Ellipsoid} & {$x = y$} & {} & {} & {} & {}\\ |
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{Prolate Ellipsoid} & {$z$} & {} & {} & {} & {}\\ \hline \hline |
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{} & {} & {\small($10^{-29}$ Pa s m$^{3}$)} & {\small($10^{-29}$ Pa s m$^{3}$)} & {} & {}\\ \hline |
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{Sphere} & {$x = y = z$} & {} & {5.37237} & {1} & {1}\\ |
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{Prolate Ellipsoid} & {$x = y$} & {} & {3.59881} & {} & {0.768726}\\ |
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{Prolate Ellipsoid} & {$z$} & {} & {9.01084} & {} & {1.92477}\\ \hline \hline |
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\label{table:interfacialfriction} |
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\end{longtable} |
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|
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\begin{longtable}{lccc} |
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\caption{Calculated ``slip'' interfacial friction coefficients ($\kappa$) and friction factors ($f$) of gold nanostructures solvated in TraPPE-UA hexane. The ellipsoid is oriented with the long axis along the $z$ direction.} |
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\\ \hline \hline |
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{Structure} & {Axis of rotation} & {$\kappa_{VSS}$} & {$\kappa_{calc}$}\\ |
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{} & {} & {\small($10^{-29}$ Pa s m$^{3}$)} & {\small($10^{-29}$ Pa s m$^{3}$)}\\ \hline |
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{Sphere} & {$x = y = z$} & {} & {0}\\ |
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{Prolate Ellipsoid} & {$x = y$} & {} & {0}\\ |
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{Prolate Ellipsoid} & {$z$} & {} & {7.9295392}\\ \hline \hline |
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\label{table:interfacialfriction} |
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\end{longtable} |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% **DISCUSSION** |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
