On the N-scaling of the Ginzburg number and the critical amplitudes in various compatible polymer blends

D. Schwahn; G. Meier; K. Mortensen; S. Janßen

doi:doi:10.1051/jp2:1994168

Numéro		J. Phys. II France Volume 4, Numéro 5, May 1994


Page(s)		837 - 848
DOI		https://doi.org/10.1051/jp2:1994168

DOI: 10.1051/jp2:1994168
J. Phys. II France 4 (1994) 837-848

On the N-scaling of the Ginzburg number and the critical amplitudes in various compatible polymer blends

D. Schwahn¹, G. Meier², K. Mortensen³ and S. Janßen¹

¹ Forschungszentrum Jülich GmbH, Institut für Festkörperforschung, Postfach 1913, D-52425 Jülich, Germany
² Max-Planck-Institut für Polymerforschung, Postfach 3148, D-55021 Mainz, Germany
³ Risø National Laboratory-DK-4000 Roskilde, Denmark

(Received 3 November 1993, received in final form 17 January 1994, accepted 2 February 1994)

Abstract
The susceptibility related to composition fluctuations in polymer blends can be described by a crossover function derived by Belyakov et al. [2, 3] near and far from the critical temperature $T_{\rm c}$ . This has quite recently been demonstrated by us using neutron and light scattering data [1]. In this paper we discuss consequences of this analysis with respect to the accomplishment of the mean-field approximation far from $T_{\rm c}$ and the N scaling ( N is the degree of polymerization) of the critical amplitudes of the bare correlation length and susceptibility respectively and the Ginzburg number, Gi. A quite unexpected N dependence of Gi was found : polymer blends with N < 30 give the same Gi as low molecular liquids and at about N = 30 an increase of Gi of more than one order of magnitude which is synonymous to an increase of the 3d-Ising regime is observed. For $N \gtrsim 30$ a Gi $\propto 1/N^2$ scaling is found in a range up to $N \cong 400$ . The observed N scaling of Gi can be explained by the large entropic contribution of the Flory-Huggins parameter $\Gamma_\sigma$ related to the compressibility or free volume of the system in comparison with the combinatorial entropic term, which was obtained from the analysis of the scattering results with the crossover function.