THE DISTRIBUTION OF MOLECULES 97 



Thus we see thai wc should not expect the simple gas law of Equation 

 (52) to hold for expanded films, but such a law should hold only after 

 constants Fq and Qq 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 ^ show that the agreement with Equation (56) 

 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-i^)=kT 



The value of Gq 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 f 57) . 

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

 cm. The interfacial free surface energy Ybtf 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 26.7. 



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

 dynes per cm. for hexadecane. This latter value does not differ greatly 

 from that calculated from Adam's data on the myristic acid films 

 (Fo= — 13). The difference is not greater than should be expected 

 because of the uncertain part played by thermal agitation in the spreading 

 of surfaces. 



According to Equation (56) with negative values of Fo the expanded 

 film should not expand indefinitely even if the compressive force F is made 



® N. K. Adam, Proc. Royal Soc. A, 99, 336 (1921) ; loi, 452, 516 (1922) ; 103, 

 676, 686 (1923) ; 106, 694 (1924) ; Jour. Phys. Chem., 29, 87 (1925). 



