Perrin Friction Factors - Translational Friction Factor

Translational Friction Factor

The frictional coefficient of an arbitrary spheroid of volume equals

$f_{tot} = f_{sphere} \ f_{P}$

where is the translational friction coefficient of a sphere of equivalent volume (Stokes' law)

$f_{sphere} = 6 \pi \eta R_{eff} = 6\pi \eta \left(\frac{3V}{4\pi}\right)^{(1/3)}$

and is the Perrin translational friction factor

$f_{P} \ \stackrel{\mathrm{def}}{=}\ \frac{2p^{2/3}}{S}$

The frictional coefficient is related to the diffusion constant D by the Einstein relation

$D = \frac{k_{B}T}{f_{tot}}$

Hence, can be measured directly using analytical ultracentrifugation, or indirectly using various methods to determine the diffusion constant (e.g., NMR and dynamic light scattering).

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