46 PHENOMENA, ATOMS, AND MOLECULES 



(which should be proportional to a/p) increases about 3-fold for each 

 CH2. When this is interpreted in accord with Gibbs' and Boltzmann 

 equations, we conclude that the energy X involved in the adsorption of 

 these molecules increases linearly with the length of the chain. This means 

 that each CH2 group in the molecule must be similarly situated in the 

 surface film. In other words, in these dilute films where there is much 

 free water surface available, the hydrocarbon molecules must lie flat on 

 the surface. With the concentrated films in which o is constant so that 

 Eq, (8) applies, there is no available free surface of water and the mole- 

 cules must stand nearlv erect on the surface. 



These two cases given by Eqs. (6) and (8) are only limiting cases 

 and the complete equation of state for the whole range from dilute to 

 concentrated films would be more complicated, since it must involve the 

 intermediate states between those in which the molecules lie flat on the 

 surface and stand erect on the surface. The experimental difficulties of 

 the accurate measurements of the surface tensions of solutions are such, 

 that relatively little work has been done on the equation of state of these 

 adsorbed films on solutions as compared with the large amount of work 

 done by N. K. Adam (22) and others on the equations of state of films 

 of insoluble substances on water. 



The molecules in adsorbed films on liquids are of course free to move 

 over the surface of the liquid except in so far as the film itself may pos- 

 sess the properties of a solid. 



Adsorbed Films on Solids. Adsorbed films on solids may exist in three 

 states corresponding to 2-dimensional gases, liquids or solids. A new fac- 

 tor now appears, however, which was not present in the case of adsorbed 

 films on liquids. The forces exerted by the underlying solid on adsorbed 

 atoms or molecules tend to hold the molecules in definite positions fixed 

 by the lattice of the solid. The solid surface is thus to be looked upon as 

 a type of checkerboard containing definite numbers and arrangements of 

 elementary spaces (13) (24), each of which is capable of holding an 

 adsorbed molecule. To move a molecule from one elementary space to 

 another thus presumably requires something analogous to an activation 

 energy ; only those molecules possessing sufificient kinetic energy to pass 

 over a potential barrier can succeed in hopping from one elementary space 

 to another (25). On this basis we should expect a surface mobility at 

 high temperatures which would disappear at low temperatures. The 

 logarithm of the rate of mobility, or the surface dififusion coefficient, 

 should vary linearly with the reciprocal of the absolute temperature and 

 the slope of this line should be proportional to the activation energy. 



In general the surface diffusion coefficient increases with a, for the 

 ability of adatoms to cross the potential barrier is not determined solely 



