THE DISTRIBUTION OF MOLECULES 95 



area of about io8 A^. Clearly then the expanded fihns occupying an area 

 of at most 50 A- must consist of molecules which are only slightly in- 

 clined from the vertical. As a matter of fact there is no reason at all why 

 the flexible hydrocarbon chains should orient themselves at any particular 

 angle. They will be quite free to respond to thermal agitation and arrange 

 themselves nearly in the same random manner as in a liquid hydrocarbon, 

 the only restriction upon their motion being imposed by the condition that 

 the lower end of each molecule must remain in contact with the under- 

 lying water. We can thus readily see why the expanded films are ahvays 

 liquid while the contracted or fully compressed films of vertically oriented 

 molecules are frequently solid. Taking the volume of the hydrocarbon chain 

 in the palmitic acid molecule as 450 A""^ we see that the thickness of the 

 hydrocarbon layer (in A units) will be 450-^ a where a is the area of 

 the film per molecule (in A- units). Thus when a = 20 A^ the thickness is 



22.5 A while for an expanded film for which o = 33 A^ the thickness is 



13.6 A. 



Consider an expanded film as covering a definite area of a water sur- 

 face. If additional palmitic acid molecules are introduced into the film there 

 is no change in the area of the free hydrocarbon surface. The energy of 

 transfer of a molecule from any given location to an expanded film is thus 

 the same as the energy of transfer of the molecule to an interface between 

 hydrocarbon and water. The total surface energy "k for a molecule of 

 palmitic acid at the edge of a condensed film is — 17 while for a molecule 

 in an expanded film X is — 37. This would indicate that the expanded film 

 should form in preference to the condensed film. However the difiference of 

 20 in the values of A, is not greater than the probable error so that the 

 sign of the difference is somewhat uncertain. In considering the stability of 

 expanded films we must take into account the applied compressive force 

 and the effect of the forces acting between the heads of the molecules 

 which are located in the interface between the hydrocarbon film and the 

 water. To understand these relationships better let us analyze the problem 

 as follows. 



Let n molecules of a substance (which spreads on water) be present 

 per unit area as an expanded film on the surface of the water. The flexible 

 hydrocarbon tails of the molecules are subject to little or no constraint 

 except that due to the fact that they are attached to the heads which must 

 remain in contact with the water. 



The expanded film may thus be looked upon as a layer of hydrocarbon 

 liquid having at its upper surface a surface energ}^ y and having adsorbed 

 in its interface with the water n active groups, or heads per unit area. 

 Consider now that by means of a two-dimensional piston (for example a 

 paper strip on the surface) the expanded film is allowed to cover only a 



