Think about the physical boundary of a liquid system, for example the surface of water. Clearly, the molecules of water that are found in the last layer before the air cannot form bonds in all directions. Hydrogen bonds can be formed “downward” (toward the main body of water) but not “upward” (toward the air). Given that the physical significance of the bonds is to reduce the energy of a system, we can conceive that the inability of the surface water to form all the possible hydrogen bonds leads the molecules in question to a higher energetic state than the molecules in the body of the water. This appears macroscopically as additional free energy due to the existence of a free surface. This additional free energy in the surface is called the surface tension γ:

γ = ∆G A


The factor γ is directly related to the work that must be expended by a molecule in order for it to move from the continuous phase to the surface. This energy of all the molecules that move to the surface leads to the creation of an unstable system that, at the first opportunity, will try to minimize its surface area. A simple experiment that shows this tension uses an arrangement with a wire bent to form three sides of a rectangle, on top of the legs of which is balanced another straight wire in such a manner as to form the fourth side. The structure is dipped in a liquid and removed so as to leave a film held within the rectangle. If we slowly draw the free wire away from its opposite side of the square by a distance l, thereby increasing the area enclosed, then a force will be exerted on the wire that is equivalent and opposite to the force required to move it. For every liquid, this force will differ and will be proportional to the surface

tension γ. Because the force is exerted along the whole length of the free wire, the surface tension will be

γ = = =F l

Fx lx

w A2 2


where w is the work expended by the movement of the free wire and A is the area of the rectangular frame (Figure 4.1). The “2” in the denominator means that the forces are exerted on both sides of the liquid film.