EFFECTS OF MOLECULAR DISSYMMETRY 281 



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

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

 cept that due to the fact that they are attached to the heads which are con- 

 strained to remain in contact with the water. This constraint may well 

 influence the degree to which the thermal energy of agitation of the hydro- 

 carbon tails aids in spreading the film and may thus alter the relation 

 between the total energy and the free energy which should be used in con- 

 nection with the Boltzmann equation. But as a first approximation we may 

 ignore such an efifect of the thermal agitation, especially as we are willing 

 to regard the surface energies y;;, etc., as empirical quantities. 



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

 liquid having at its upper surface a surface energy 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 

 part of the surface of the water. The spreading force F (in dynes per cm.) 

 exerted by the film is measured by the mechanical force applied to the 

 piston. On one side of the piston is a surface of water which exerts a force 

 Ytf tending to cause the film to expand and on the other side is the ex- 

 panded film whose upper surface exerts a force Y/j while the lower surface 

 exerts a force which we may represent by Yl- Thus for equilibrium we have 



yw-P ^yR^lL. (7) 



If the molecules in the film did not have any active groups, the surface 

 tension Yi, would be equal to the normal interfacial energy ynw- But the 

 active groups in the interface because of their thermal agitation will tend 

 to act like a two-dimensional gas. When these active groups or heads are 

 far enough apart they will exert a force Fl following the gas law 



Fl = nkT. (8) 



When the molecules are packed as closely as in the ordinary expanded 

 film, we should, by the analogy with the h term in the van der Waals equa- 

 tion, write 



FlCo- ao) = kT (9) 



where ao is the area per molecule for a highly compressed film. 



Furthermore, the analogy with the equation of state for gases would 

 suggest that when the film is compressed sufficiently, attractive forces 

 between the active groups would come into play and that these might be 

 largely responsible for the small spreading forces observed with some 

 contracted films. In any case, however, we may place 



Jl^ Jhw-Fl (10) 



