50 PHENOMENA, ATOMS, AND MOLECULES 



characterized by the growth of crystals from nuclei and do not lead to the 

 formation of monomolecular films but rather to discrete crystal particles. 



Case 2. V2>Vi. In this case, as the pressure is gradually raised or the 

 temperature is lowered, o increases until a monomolecular film is formed, 

 but it then takes a considerable decrease in temperature or increase in pres- 

 sure before a second layer begins to form. These conditions therefore com- 

 monly lead to the formation of films which do not exceed a molecule in 

 thickness over a wide range of experimental conditions. This case therefore 

 is characterized by typical adsorbed films. 



Adsorption Isotherms. The fundamental equation governing the amount 

 of adsorbed substances on a solid surface is given by Eq. (ii). To put this 

 into a definite form relating the pressure p of the external gas and o, the 

 surface concentration, we need only to be able to express a and v as func- 

 tions of o and T. The functional relation of v to o depends not only on the 

 forces exerted by the underlying solid, but on the forces acting between 

 adatoms. Furthermore we must consider that the incident molecules corre- 

 sponding to [A cannot all go directly into elementary spaces on the bare 

 surface, but many of them will make their first contact at places already 

 occupied by adatoms. An important aspect of the problem of the adsorption 

 isotherm is the determination of the manner in which these incident atoms 

 find places in the first layer. Many atoms may temporarily be forced to 

 occupy places in the second layer from which they can either evaporate at 

 a much higher rate than from the first layer, or may migrate until they 

 drop into positions in the first layer. 



It is natural under these conditions to make assumptions which are as 

 simple as possible and to see whether the resulting equations can find a field 

 of application (24). If the adatoms do not exert appreciable forces on one 

 another, we may thus assume that the life of x of each one is independent 

 of the presence of other atoms on the surface. Thus by Eq. (12) v is pro- 

 portional to 0. 



Instead of dealing with the surface concentration of it is often con- 

 venient to use the covering fraction defined by 



Q = gIg^, (14) 



where Oi is the surface concentration in a complete monomolecular film. 

 Thus we may put 



v = rS, (15) 



where Vi represents the rate of evaporation from a completely covered 

 surface. 



When molecules incident on the surface strike a part which is un- 

 occupied by other adatoms, we may assume that the fraction ao condenses. 

 The fraction of such surface which is bare may be represented by 1 — ©. 



