Small-angle X-ray scattering by polymer solutions at intermediate concentrations

Abstract

SAXS by solutions of monodisperse polystyrene at intermediate concentrations has been studied for the solvents having only a small volume‐exclusion effect, such as methyl ethyl ketone (MEK) and cyclohexane (CH). Both the density‐density correlation function of segments in solution and the osmotic compressibility, as obtained from the absolute intensity at zero angle, were measured for different concentrations and the results were successfully analysed by means of the recent theory of Moore [J. Phys. (Paris), (1977), 38, 265–271] . According to the theory, in the semi‐dilute poor‐solvent regime the concentration C, dependence of the screening length ξ, and the scattered intensity at zero angle I(0) are given by = 12NA + 36N2AC and = B1 + 3NAB2C, where M is the molecular weight of a polymer molecule, NA Avogadro's number and A2M the mean square end‐to‐end distance of an unperturbed chain; m2B1 and m3B2 are respectively the binary and ternary cluster integrals (or the first and the second irreducible integrals) for segments in solution, m being the molecular weight of a segment. ΔZ is the number of excess mole electrons per unit mass of segments. The measured concentration dependences were in agreement with the above prediction and the values of B1 and B2 were obtained.

Microscopic structure of gelatin coacervates

“…Physically, S L (0) is related to the cross-link density and longitudinal osmotic modulus. Although Okano et al [35] and others [36] have found full agreement with the O-Z behavior; experiments carried out in the semi-dilute regime of polymer solutions have shown deviations from the Ornstein-Zernike function. An "excess scattering" has been reported at low wave numbers from polymeric solutions [37][38].…”

Small-Angle Neutron Scattering Studies of Chemically Cross-Linked Gelatin Solutions and Gels

“…Although Okano et al 17 and others 18 have found full agreement with the O-Z behavior, experiments carried out in the semidilute regime of polymer solutions have shown deviations from the Ornstein-Zernike function. An "excess scattering" has been reported at low wavenumbers from polymeric solutions 1,19-24 which is caused by the enhanced long wavelength concentration fluctuations in the system.…”

Static and dynamic behavior of semidilute polymer solutions

“…Values for ~s can be obtained rather straightforwardly from static light scattering (SLS) [30,31], small-angle neutron scattering (SANS) [32] or small-angle x-ray scattering (SAXS) [33]. Values for ~e can be derived as described above from the cooperative diffusion coefficient, which itself may be obtained from classical gradient diffusion (CGD) [34] or dynamic light scattering (DLS) [35].…”