Ionic Liquids

Abstract

The probability that a hole in a liquid will have a radius between r and r + dr is P dr and is given by

$$ P\,dr=(16{a^{7/2}}r^{6}/15{\pi^{1/2}})\, {\rm exp}(-ar^{2})dr $$

(6.1.1)

where

$$ a=4\pi \gamma /kT $$

(6.1.2)

and γ is the surface tension of the liquid. Show that the mean hole volume v _h is given by

$$P \,dr=(16{a^{7/2}}r^{6}/15{\pi^{1/2}})\, {\rm exp}(-ar^{2})dr $$

(6.1.3)

Use the data of Table 6.1.1 to calculate the mean size of holes in molten salts and compare these values with the volumes of the ions concerned. Comment on the conclusion.