Solutions of Flexible Polymers. Neutron Experiments and Interpretation

Abstract

We present small angle neutron scattering data on polystyrene (normal or deuterated) in a good solvent (carbon disulfide). All data are taken in the semidilute regime where the chains overlap strongly, but the solvent fraction is still large. We have measured the following, (a) The radius of gyration RG(c) for one deuterated chain in a solution of normal chains with concentration c. We find that RG²(c) is proportional to the molecular weight and that RG² decreases with concentration like c^–x where x = 0.25 ± 0.02. (b) The screening length ξ(c) (introduced, but not quite correctly calculated by Edwards) giving the range of the 〈c(r)c(r’)〉 correlations. We find ξ ~ c^–z, with z = 0.72 ± 0.06. (c) The osmotic compressibility χ(c) (through the scattering intensity of identical chains in the small angle limit). From an earlier light-scattering experiment, we find χ ~ c^-y with y = 1.25 ± 0.04. These results are to be compared with the predictions of the mean field (Flory-Huggins-Edwards) theory which are: R_G independent of c, χ ~ c^–1, and ξ ~ c^-1/2 in the semidilute range. We show in the present paper that the measured exponents can all be interpreted in terms of a simple physical picture. The underlying basis is the analogy, recently found by Des Cloizeaux, between the semidilute system and a ferromagnet under an external field. However, in this paper, we emphasize mainly the polymer aspects. At short distances (r < ξ) the correlations are determined by excluded volume effects. At large distances (ξ < r < R_G) the chains are gaussian and the effective interaction between subunits of the same chain are weak.