282 PHENOMENA, ATOMS, AND MOLECULES 



and thus from Equation 7 we get 



F ^ yw-yB — ynw + Fl. ( i i ) 



For very low compressive forces we may neglect the attractive forces be- 

 tween the heads and thus by combining Equations (11) and (9) we get 



(F-Fo) (a-ao)=kT (12) 



as our equation of state for expanded films. Here Fq is used as an abbrevia- 

 tion for the three y terms in (11) so that 



Fo = yw — yn — yRw- (13) 



Thus we see that we should not expect the simple gas law of Equation 6 

 to hold for expanded films, but such a law should hold only after constants 

 Fo and Oo have been subtracted from the observed values of F and a. 



Examination of the experimental data on expanded films in my 191 7 

 paper, and in Adam's papers, shows that the agreement with Equation (12) 

 is very satisfactory. For large compressive forces deviations occur which 

 are of the kind that are to be expected as a result of attractive forces 

 between the heads of the molecules.* For example, Adam's curve (in this 

 3rd paper) for a film of myristic acid on water at 32.5° C. gives the 

 equation 



(F + 13) (a-i8)=kT 



The value of Qq is thus 18. A^ while Fq has the value — 13 dynes per cm. 



Let us compare this value of Fq with that calculated by Equation (13). 

 For water at 32.5° the free energy (surface tension) yw is 71.0 dynes 

 per cm. The interfacial free surface energy ynw of octane is 50.4. Since 

 the temperature coefficient is very low the total interfacial energy is about 

 the same as the free energy. Our theory of the structure of the interface 

 leads to the conclusion that the total energy is independent of the length of 

 the hydrocarbon chain and since in this case the free energy and total 

 energies are nearly the same the free energy will also be independent of the 

 chain length. Thus for tetradecane (the hydrocarbon corresponding to 

 myristic acid) we may put yuw = 50.4. 



The free surface energy of octane at 32.5° is 20.4 and the total energy 

 is 48.4. For tetradecane the theory indicates that the total energy will also 

 be 48.4. The free surface energy is a linear function of temperature and 

 becomes zero at the critical temperature. Taking the critical temperature of 

 tetradecane as 680° K. we can thus estimate that the free surface energy at 

 32.5° C. should be 26.8. 



These values for the y's give Fq = + 0.2 for octane and Fq = — 6.2 



* See 3rd Colloid Symposium Monograph (Chemical Catalog Co., 1925). 



