A correction resulting from two surface tension calculations

Hsin, et al derived the surface tension increment at depletion of solute in the interface: ? σ = c k T λ. Siow and Patterson used the Prigogine-Marechal theory to get d σ / d φ2 = k T / r a in Jennings' paper. To relate these two expressions, one has to convert from c, concentration for Hsin, to c', concentration for Jennings. We have d c' / d c = MW2 / No, where MW2 is molecular weight solute and No is Avogadro's number. At the limit of vanishing solute concentration, Hsin is d σ /d c = k T λ. From dividing two of Jennings' equations, one gets d c /d φ2 = ρ2 No / MW2. The chain rule obtains (d σ / d φ2)(d φ2 / d c) = k T λ, so with algebra we eliminate k T and r (ratio of molar volume of polymer to molar volume of solvent) to get MW1 = No λ a ρ1. Both theories work best at the limit of c--->0 and they are general, so the author feels free to treat the solute in the same way for both. In Hsin, et al, they assume a value for λ, so this paper corrects that flaw. λ only depends on the solvent.