44 PHENOMENA, ATOMS, AND MOLECULES 



strip of paper, it is possible to measure directly the spreading force F in 

 dynes per cm. exerted by an oil film having a given number of molecules 

 of oil per square cm. of surface. This surface concentration we shall 

 denote by the symbol o. Such measurements as these, by which F can be 

 expressed as a function of o and T, give us then the 2-dimensional equa- 

 tion of state of the oil film which corresponds exactly to the 3-dimensional 

 equation of state which characterizes ordinary gases and liquids. In fact, 

 the movable paper strip in these experiments is the equivalent of a piston 

 which, compresses the gas in a cylinder. 



The oil films observed on water may exist as 2-dimensional solids, 

 liquids or, gases. The film on water obtained from stearic acid C17H35 = 

 COOH is solid. If it is compressed by a force of 10 dynes per cm. exerted 

 against the paper strip, this solidity is manifested if particles of talc are 

 dusted on to the surface and the effects of air currents directed against 

 the surface are watched. The talc particles do not move freely over the 

 surface; if a strong wind displaces them, they return to their original 

 positions when the wind stops, proving a surface rigidity and elasticity 

 characteristic of solids. Other substances such as cetyl alcohol or oleic 

 acid give films which are liquid, since talc particles circulate freely when 

 small forces are exerted by the wind. 



By slightly increasing the area available for these films of saturated 

 fatty acids, it is found that the spreading force decreases very nearly to 

 zero, which proves that these films do not act as 2-dimensional gases but 

 rather as 2-dimensional liquids which have an unmeasurably small 2- 

 dimensional vapor pressure. With myristic acid (22), however, a definite 

 2-dimensional vapor pressure of about 0.2 dyne cm~^ is observed. Still 

 lower fatty acids give typical gaseous films, but they cannot be studied 

 by this method because the films are so easily soluble in water that the 

 force exerted by a moving barrier causes, them to go into solution. 



Adsorbed Films on Solutions (18.) (21). The foregoing method for 

 studying the properties of oil films on water is inapplicable if the film is 

 soluble or is volatile. In such cases measurements must be made in the 

 presence of saturated vapor or saturated solution. Gibbs' equation, Eq. 

 (i), gives us a means of determining the relation between the amount 

 adsorbed on the solution and the spreading force F, in terms of the par- 

 tial pressure p of the vapor of the adsorbed substance over the liquid or 

 the partial osmotic pressure p of the dissolved substance in the underly- 

 ing solution. Experimentally F can be measured as the decrease in the 

 surface tension of the pure liquid produced by the presence of the dis- 

 solved substance. By the integration of this equation, using the experi- 

 mentally determined values of F, one can obtain the equation of state of 

 the 2-dimerisional film whether this is gaseous or liquid or solid. 



