Nonideal Two-Dimensional Gases

The deviation of Gibbs monolayers from the ideal two-dimensional gas law may be treated by plotting xA// 7 versus x, as shown in Fig. III-15c. Here, for a series of straight-chain alcohols, one finds deviations from ideality increasing with increasing film pressure at low x values, however, the limiting value of unity for irAfRT is approached. 

This behavior suggests the use of an equation employed by Amagat for gases at high pressure the two-dimensional form is 

This form is obeyed fairly well above x values of 5-10 dyn/cm in Fig. Ill-15c. Limiting areas or a values of about 22 per molecule result, nearly independent of chain length, as would be expected if the molecules assume a final orientation that is perpendicular to the surface. Larger A values are found for longer-chain surfactants, such as sodium dodecyl sulfate, and this has been attributed to the hydrocarbon tails having a variety of conformations [127]. 

Various other non-ideal-gas-type two-dimensional equations of state have been proposed, generally by analogy with gases. Volmer and Mahnert [128, 

The varying actual orientation of molecules adsorbed at an aqueous solution-CCU interface with decreasing A has been followed by resonance Raman spectroscopy using polarized light [130]. The effect of pressure has been studied for fatty alcohols at the water-hexane [131] and water-paraffin oil [132] interfaces. 

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