THE DISTRIBUTION OF MOLECULES 73 



It will be readily recognized that this principle lies at the foundation 

 of the theory proposed by the writer in 1916, according to which the sur- 

 face tension of pure liquids and the properties of adsorbed films at inter- 

 faces depend largely upon the orientation of the molecules in the interfaces. 



Thus the surface energy - y of all the normal saturated aliphatic alco- 

 hols is the same as that of the saturated hydrocarbon hexane, namely 50 

 ergs per cm.^ The actual surface energy is that of a hydrocarbon surface 

 in both cases. The alcohol molecules should not be regarded as being 

 packed side by side and arranged with the axes of the hydrocarbon part 

 of the molecule perpendicular to the surface, for there is no force which 

 would compel them to be so arranged. The alcohol molecules which are 

 temporarily in the surface will be free to respond to thermal agitation 

 exactly as if they were in the interior of the liquid, with the single excep- 

 tion that the hydroxyl group cannot itself (for any appreciable fraction of 

 the time) form part of the actual free surface of the liquid. The interac- 

 tion between the hydroxyl groups of different molecules in the surface is 

 thereby not appreciably altered by the fact that these molecules are form- 

 ing part of the surface. 



The fact of most interest at present is that the hydroxyl group, even 

 in such a small molecule as that of methanol, does not materially alter the 

 surface energy of the CH3 group which is able to form the actual surface 

 of the liquid by the orientation of the molecule. 



The reason that the hydroxyl group avoids the surface must be sought 

 in the energy of the field surrounding this part of the molecule. But by 

 ordinary surface tension and interfacial surface tension measurements we 

 have knowledge of the forces by which hydroxyl groups and hydrocarbon 

 surfaces interact. Let us see whether from such knowledge we cannot 

 determine the energy involved in the orientation of an alcohol molecule 

 and then find from the Boltzmann equation whether this energy is suffi- 

 cient to cause the orientation indicated by the experiments. 



For this purpose let us consider a molecule of methanol. From the 

 density, molecular weight and Avogadro number we find that the volume ^ 

 per molcule is Gy.A^. Assuming close-packed spheres this gives a molecu- 

 lar surface of 65. A- and a diameter of 4.56 A. These figures would not 



^ The total surface energy y is related to the free surface energy Yf l^y the equation 

 dyt 

 Y=:Yr — ^"Tt^- ^'^'-' ^°*^' energy y is nearly independent of temperature. From the 



linear decrease of Yf with increasing temperature it is probable that the variation of 

 Yf is a direct result of the thermal agitation of the molecules rather than being due to 

 any change in the structure of the surface. The total energy y is therefore the quantity 

 which will indicate most clearly any orientation of molecules in the surface. 



^ We shall express the dimensions of molecules in terms of the Angstrom unit 

 10"^ cm. Areas will be expressed in A^ (io~^^ cm^) and volumes in A^ (lO"^* cm"''). 



