ISSN:
1089-7690
Source:
AIP Digital Archive
Topics:
Physics
,
Chemistry and Pharmacology
Notes:
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 polymerization r as well as choosing different polymer–solvent pairs) it is shown that the data are reasonably well represented by a power law, ε(τ)=εˆττζ. 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)=σˆττμ (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)=σˆεεcursive-phi. While mean-field theory implies cursive-phi=3/5 and scaling theory cursive-phi=2/(3+β/ν)≈0.57, the empirical exponent lies in the range 0.5(approximately-less-than)cursive-phieff(approximately-less-than)0.6. We present estimates of molecular weight dependencies of critical amplitude prefactors εˆτ,σˆτ,σˆε and of related quantities for many different systems. We also discuss whether the critical amplitude combination (εˆτ/Bˆτ)2/3/σˆ, where Bˆτ describes the coexistence curve {φcoex(2)−φcoex(1)=Bˆττβ} 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. © 1995 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.470059
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