Surface tensions

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Surface tensions arise from the imbalance of molecular forces at an interface. A net force at an interface implies that work must be done to expand the surface; that is, the surface tensions can be though of as forces integrated over distances or the changes in energy between a molecule completely surrounded by molecules and a molecule only partially surrounded by others.

If the cohesion energy per molecule is inside a liquid: <math>U</math>
Then the cohesion energy per molecule at the surface is <math>\frac{U}{2}</math>
If the size of a molecule is a then it occupies an area of <math>a^{2}</math>
Therefore the surface tension is of the order <math>\sigma =\frac{U}{2a^{2}}</math>
If the liquid is near its boiling point then <math>U\approx kT</math>
Or the surface tension is about <math>\sigma =\frac{kT}{2a^{2}}</math>

<math>\text{at }25^{0}\text{ }\sigma =\frac{2\times 10^{-21}J}{a^{2}}\text{ For }a=3Ang\text{ }\sigma =20{}^{mJ}\!\!\diagup\!\!{}_{m^{2}}\;</math>

Witten (p. 155) proposes a surface-tension scaling relation, <math>\sim \frac{\alpha }{{kT}/{\delta A}\;}</math>, where <math>\delta A</math> estimates the area of each flexible unit of the liquid:

Witten, Fig. 16.7

Hydrogen bonding in water and metallic bonding in metals raise the energies of interaction considerably above kT and hence all have higher surface tensions.

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