Stable Monolayers of Bile Acids

In order to understand this isotherm, it is worthwhile to apply Gibbs phase rule (93) which, at constant temperature and pressure, states that the number of degrees of freedom (F) in a system at equilibrium is equal to the number of components (C) in the system minus the number of phases (solid, liquid, gas) present in the system, or F — C — P. Crisp (94) has derived a two-dimensional phase rule to apply to a single plane surface containing q surface phases. The rule predicts that the number of degrees of Freedom (F) will he F = C — Ph — q — ), where C is the total number of components in the system, F is the number of bulk phases, and q is the number of surface phases. In the case of deoxycholic acid spread on aqueous substrate the number of components (C) can be considered to be two, the water of the aqueous phase and the deoxycholic acid. The number of bulk phases, that is the substrate, can be 1 or 2 and the number of surface phases can be 1 or 2. When the area per molecule is very large, for instance 10,000 A- molecule (right side of Fig. 11), the surface pressure is very low ( 0.1 dynes/cm) but 

Finally, at very small surface areas there is again an increase in surface pressure which suggests that no surface phase (monolayer) remains and we are now dealing with the compression of two bulk phases, and F again equals one. 

Cholanic acid (Fig. 12) shows a very steep isotherm from 44 to 40 A-/molecule. The viscosity of the film remains liquid up to the collapse point of the monolayer at about 20 dynes/cm. Lithocholic acid spread (Fig. 12) on water at pH 2 obviously has a different isotherm. At about 119 A molecule there is a sudden rise in pressure to a first collapse point at 81 A Vmolecule. Thus, between 119 and 81 A molecule the film is a single liquid phase. This range of surface areas corresponds to a monolayer of molecules lying flat 

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