A remark on an equation of state for linear polymers in monolayers

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Abstract
A few years ago, Singer, following Huggins' method of treatment of high polymer in bulk phase, derived an equation of state for monolayers of large, threadlike molecules. Davies and his co‐worker defined a quantity ω as a measure of flexibility of a polymer chain in the interface, where ω =z– 2 (zis the coordination number of the unit in the postulated two‐dimensional quasi‐lattice in the interface), assuming that each segment in a chain has exactly two positions in which its two neighbors in the chain must fit whenz= 2. Using this definition, they have developed their discussion as to flexibility of polymer chains at the interface. It is one of the purposes of this note to point out that their definition of ω is lacking in its theoretical background. Nevertheless, the values ofzobtained from the observed force‐area relations seem to afford a reasonable order of magnitudes for various types of polymer molecules, in accordance with other data on the flexibility of the polymer chains. Another purpose of this note lies in clarifying the origin of the just‐mentioned contradiction. The reason why the values ofzappear, at first sight, to give a good representation of the degree of flexibility of polymer chains, lies in the remarkable difference in molecular configurations between the “condensed” and “expanded” states at the interface. In conclusion,zor ω resembles the empirical parameter μ often used in the discussion on thermodynamic properties of polymer solutions. Careful analysis of this value is necessary before conclusions can be drawn about the structural characteristics of polymer molecules and the intra‐ and intermolecular cohesions acting on them.

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