Interfacial tension of phase-separated polymer solutions and relation to their equation of state

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Abstract
Using an effective (coarse‐grained) thermodynamic potential describing the excess free energy of mixing of a polymer solution and fitting its parameters to measured critical point data, we obtain the ‘‘hump’’ ε(τ) of this potential in the two‐phase region (τ being the reduced distance from the critical temperature T of unmixing). For 30 different systems (varying the degree of polymerizationr as well as choosing different polymer–solvent pairs) it is shown that the data are reasonably well represented by a power law, ε(τ)=ε̂ττζ. While mean field theory implies ζ=5/2 and scaling theory ζ=3ν+β≊2.22 (using Ising model exponents ν≊0.63,β≊0.325), the ‘‘effective’’ exponent extracted from the data mostly falls in between these limits (ζeff≊2.4). Since the interfacial tension satisfies a similar power law, σ(τ)=σ̂ττμ (with μ=3/2 in mean field theory or μ=2ν≊1.26 in scaling theory), we also consider a relation between interfacial tension and free energy hump, σ(ε)=σ̂εεφ. While mean‐field theory implies φ=3/5 and scaling theory φ=2/(3+β/ν)≊0.57, the empirical exponent lies in the range 0.5≲φeff≲0.6. We present estimates of molecular weight dependencies of critical amplitude prefactors ε̂τ,σ̂τ,σ̂ε and of related quantities for many different systems. We also discuss whether the critical amplitude combination (ε̂τ/B̂τ)2/3/σ̂, where B̂τ describes the coexistence curve {φcoex (2)−φcoex (1)=B̂ττβ} is universal. Contrary to some theoretical expectations, our data imply that this combination is not universal, and hence it cannot be used to predict interfacial tensions from equation of state data.

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