Thermodynamic properties of liquids,including solutions

Summary A new theoretical treatment of the dependence of surface pressure on the concentration of linear polymer molecules in a monolayer is presented. The development follows closely that in the author's new theory of the thermodynamic properties of three-dimensional solutions.

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Zusammenfassung Es wird eine neuartige theoretische Untersuchung vorgelegt über die Abhängigkeit des Oberflächendruckes von der Konzentration an linearen Makromolekülen in einer monomolekularen Schicht. Die Entwicklung schließt sich eng an des Autors neue Theorie der dynamischen Eigenschaften von dreidimensionalen Lösungen an.

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Glossary A Area of the monolayer surface - B ₁,B ₂ Functions in the expansion of in powers ofm/A. See 38] - E Intermolecular energy in the monolayer. See 2]. It is negative for attraction energy - G Gibbs energy. See 1] - H Enthalpy. See 1] - K Equilibrium constant, defined by 3]. Equal to 1 for perfect randomness of segment contacts - K A constant, related toK by 8] - M ₁,M ₂ Molar masses (molecular weights) of substrate and polymer - N _a Avogadros number=6.0225×10²³ mol^–1 - R Molar gas constant=8.3143 JK^–1 mol^–1 - S Entropy. See 1] - S _cc Correction to the combinatorial entropy to allow for imperfect randomness - S _or Contribution to the entropy of mixing to allow for concentration dependence of entropy of orientation, vibration and rotation of molecules and segments - S _rm Combinatorial entropy of mixing, assuming perfect randomness - T Temperature in kelvins - a ₀ ,a ₀ Areas in monolayer occupied by one mole (Avogadros number) of solvent and polymer segments, respectively. See 10] - g _K A function ofK and the concentration, defined by 7] - m Mass of polymer in the monolayer - m/A Mass/area ratio. Related to area fractions by 14] - n Average number of segments per polymer molecule - r _a =a ₀ /a ₀ Segment area ratio. See 16] - r = ₀ / ₀ Contacting segment outline ratio. See 16] - r _a/ =r _a /r See 16] - r _/a =r /r _a See 16] - x ₁,x ₂ Mole fractions of solvent and polymer in the monolayer - z ,z Contacting segment outline fractions, defined by 9] - Surface pressure required to keep monolayer in areaA - , Designating solvent and polymer segments, respectively - , , Energy per unit length of contact between pairs of segments of the type indicated. See 6] - Energy change when two unit lengths of contacts between like segments are replaced by two unit lengths of contacts between unlike segments. Defined by 6] - Energy parameter, defined by 5] - ₁, ₂ Densities of the pure components (mass/volume) - _m Surface density of polymer in a completely filled monolayer (mass/area) - , Sum of the contacting outlines, for segments of the type indicated, in the monolayer - ⁰ , ⁰ Average contacting outline per segment, of the type indicated - , , Sum of the contact lengths, for contacts of the type indicated, in the monolayer - ₁, ₂ Area fractions, measuring the fractions of the monolayer area occupied by solvent and polymer molecules, respectively.