The Thermodynamics of Films: Energy and Entropy of Extension and Spreading of Insoluble Monolayers

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Abstract
The thermodynamic relations of insoluble monolayers on a mobile subphase are given, and equations are presented for their (a) increase of entropy, (b) heat absorbed, (c) increase of heat content, and (d) increase of internal energy, during expansion. Two different methods of expansion are considered: in spreading the decrease of area of the subphase is equal to the increase of area of the monolayer; in extension the monolayer expands but the area of the clean surface of the subphase remains constant. The two‐dimensional phases are classified as: I. gas; II. liquid (L1) expanded; III. intermediate or transition; IV. liquid (L2) condensed; and V. solid. The extreme limits of molecular area for the intermediate liquid phase are for pentadecylic acid about 22 and 44A2, while those for the liquid phases IV, III, and II, are from about 20.5 to 52A2 which indicates that, beginning with a two‐dimensional liquid in its most condensed condition, the mean molecular distances may be increased by as much as 60 percent without a destruction of the liquid state. This is very different from what is found in three dimensions. The heat absorbed in the melting of the two‐dimensional solid is zero, so this is phase change of the second order. The quantity, hs = (∂Hs/∂σ)p,T, which is the increase in heat content when the monolayer spreads over unit area, has a value of several hundred ergs cm—2 for a solid film. The increase of heat content for the other two‐dimensional phases may be illustrated by the approximate values for pentadecylic acid: it is zero for (L2), or the liquid condensed phase; rises in the intermediate phase very gradually to a nearly constant magnitude of 300 ergs cm—2 as the area is increased and decreases to about 50 erg cm—2 in the liquid expanded phase (L1). For any two‐dimensional phase spread on water or on mercury the value of h for extension is greater than that for spreading by he the total surface energy of the three‐dimensional liquid, which is about 116 erg cm—2 for water, and 540 for mercury. The increase of heat content ΔHm during the spreading of a mole of pentadecylic acid has been calculated for the case in which the film spreads from the lowest to the highest area at which the phase exists. For the solid phase this energy is of the order of about a fifth of a kcal. mole—1 at 18°C, while ΔHm for the intermediate phase is 8.3 kcal. mole—1, and for the liquid expanded (L2) phase is very small. At 25°C the value for the intermediate phase has fallen to 4.6, and that for the liquid expanded phase (L2) has increased to 1.0 kcal. mole—1.

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