Detection of hexagonal fluid crystalline phase in polymer suspensions as suggested by de Gennes via anomalous small-angle x-ray scattering. I. Theory and results from semi-dilute concentration of 25 mM polyacrylate suspensions

Element specific scattering techniques known as anomalous small-angle x-ray scattering have been employed in the analysis of the thallium counterion distribution in aqueous salt-free polyacrylate solutions with the molar concentration of 25 mM. The pure-resonant scattering contribution of the Tl+-counterions was deduced explicitly, thereby revealing the existence of a hexagonal lattice structure, as suggested by de Gennes et al. About 75% of the Tl+-counterions are localized in the cylinders of the hexagonal lattice structure. A cylinder axis of 12.1 nm was deduced, giving, in combination with the amount of monomer units inside the cylinder, a length of the monomer unit of 0.66 nm, indicating strong stretching of the polyanions. The stability criterion of Lindemann is served, thus explaining the stability of the liquid crystalline phase. From the mixed-resonant and the non-resonant scattering contribution, the monomer volume of 0.1111 nm3 was deduced.