S. Enders, B. A. Wolf and K. Binder

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

*Journal of Chemical Physics* **1995**, *103*, 3809-3819.

**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'' epsilon(tau)
of this potential in the two-phase region (tau 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, epsilon(tau)=epsilon(tau)tau(zeta).
While mean field theory implies zeta=5/2 and scaling theory zeta=3 nu+beta approximate
to 2.22 (using Ising model exponents nu approximate to 0.63,beta approximate
to 0.325), the ''effective'' exponent extracted from the data mostly falls in
between these limits (zeta(eff)approximate to 2.4). since the interfacial tension
satisfies a similar power law, sigma(tau)=sigma,tau tau(mu) (with mu=3/2 in
mean field theory or mu=2 nu approximate to 1.26 in scaling theory), we also
consider a relation between interfacial tension and free energy hump, sigma(epsilon)=sigma(epsilon)epsilon(phi).
While mean-field theory implies phi=3/5 and scaling theory phi=2(3+beta/nu)approximate
to 0.57, the empirical exponent lies in the range 0.5 less than or similar to
phi(eff)less than or similar to 0.6. we present estimates of molecular weight
dependencies of critical amplitude prefactors epsilon(tau)sigma(tau)sigma(epsilon)
and of related quantities for many different systems. We also discuss whether
the critical amplitude combination (epsilon(tau)/B-tau)(2/3)/sigma, where B-tau
describes the coexistence curve {phi(coex)((2))-phi(coex)((1))=($) over cap
B(tau)tau(beta)} 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.

preprint number: 161