Editing Surface tension (section)

====Influence of particle size on vapor pressure====
{{See also|Gibbs–Thomson effect}}
The [[Clausius–Clapeyron relation]] leads to another equation also attributed to Kelvin, as the [[Kelvin equation]]. It explains why, because of surface tension, the [[vapor pressure]] for small droplets of liquid in suspension is greater than standard vapor pressure of that same liquid when the interface is flat. That is to say that when a liquid is forming small droplets, the equilibrium concentration of its vapor in its surroundings is greater. This arises because the pressure inside the droplet is greater than outside.<ref name="moore"/>

<math display="block">P_\mathrm{v}^\mathrm{fog}=P_\mathrm{v}^\circ e^{V 2\gamma/(RT r_\mathrm{k})}</math>

[[Image:TinyDropletMolecules.png|thumb|[[Molecule]]s on the surface of a tiny droplet (left) have, on average, fewer neighbors than those on a flat surface (right). Hence they are bound more weakly to the droplet than are flat-surface molecules.]]

*{{math|''P''<sub>v</sub>°}} is the standard vapor pressure for that liquid at that temperature and pressure.
*{{mvar|V}} is the molar volume.
*{{mvar|R}} is the [[gas constant]]
*{{math|''r''<sub>k</sub>}} is the Kelvin radius, the radius of the droplets.

The effect explains [[supersaturation]] of vapors. In the absence of [[nucleation]] sites, tiny droplets must form before they can evolve into larger droplets. This requires a vapor pressure many times the vapor pressure at the [[phase transition]] point.<ref name="moore"/>

This equation is also used in [[catalyst]] chemistry to assess [[Mesoporous material|mesoporosity]] for solids.<ref name="Handbook">Ertl, G.; Knözinger, H. and Weitkamp, J. (1997). ''Handbook of heterogeneous catalysis'', Vol. 2, p. 430. Wiley-VCH, Weinheim. {{ISBN|3-527-31241-2}}</ref>

The effect can be viewed in terms of the average number of molecular neighbors of surface molecules (see diagram).

The table shows some calculated values of this effect for water at different drop sizes:

{| class="toccolours" border="1" style="float: center; margin: 0 0 1em 1em; border-collapse: collapse;"
|-
! style="text-align:center; background:#c0c0f0;" colspan="5"|{{math|{{sfrac|''P''|''P''<sub>0</sub>}}}} for water drops of different radii at [[Standard temperature and pressure|STP]]<ref name="adam"/>
|- style="text-align:center;" 
| style="width:120px; "|Droplet radius (nm)
| style="width:120px; "|1000
| style="width:120px; "|100
| style="width:120px; "|10
| style="width:120px; "|1
|- style="text-align:center;" 
|| {{math|{{sfrac|''P''|''P''<sub>0</sub>}}}}|| style="text-align:center;"| 1.001|| style="text-align:center;"| 1.011|| style="text-align:center;"|1.114|| style="text-align:center;"| 2.95
|}

The effect becomes clear for very small drop sizes, as a drop of 1&nbsp;nm radius has about 100 molecules inside, which is a quantity small enough to require a [[quantum mechanics]] analysis.