Light Scattering Study of Semiflexible Polymer Solutions II. Application of an Integral Equation Theory

Abstract

ABSTRACT:The structure factor S(k) and the correlation length for semiflexible polymer solutions were formulated using the generalized Ornstein-Zernike (GOZ) integral equation for the monomer-units pair correlation functions. The derived expression for S(k) contained the Fourier transform C(k) of the direct correlation function C(r) involved in the GOZ equation. Taking advantage of the short range nature of C(r), we calculated C(k) from the scaled particle theory, which was previously shown to successfully describe thermodynamic quantities of semiflexible polymer solutions. The present theoretical approach gave S(k) and, which were favorably compared with the previously obtained experimental results for dilute through semidilute solutions of a semiflexible polymer poly(n-hexyl isocyanate) dissolved in a good solvent dichrolomethane. The spatial distribution of monomer-units (or segments) in polymer solutions is not completely random but has some regularity. Owing to the chain connectivity, this regularity ranges over a long distance in comparison with that in low-molar-mass liquids. Light scattering technique provides us with important information about the regularity in the monomerunit distribution in polymer solutions. For example, the range of regularity usually expressed in terms of the correlation length can be measured by light scattering.In Part 1 of this series, 1 we made a light scattering study on semidilute solutions of a semiflexible polymer, poly(n-hexyl isocyanate) (PHIC), dissolved in a good solvent, dichloromethane (DCM), and found that as well as the osmotic compressibility (ac/aII) obtained for these solutions exhibit polymer concentration dependences different from those of flexible polymer-good solvent systems. We succeeded in explaining the concentration 384 dependence of (ac;an) for PHIC solutions using the scaled particle theory for wormlike spherocylinders with a weak attractive interaction. On the other hand, the same theory cannot be used for the explanation of~. which is not a thermodynamic quantity. In Part 1, we did not give any theoretical interpretation of this spatial property for the semiflexible polymer solution.In the present study, we apply the generalized Ornstein-Zernike (GOZ) integral equation for the reference interaction site model (RISM) to calculate the structure factor S(k) and of semiflexible polymer solutions. The GOZ integral equation approach or the RISM theory is a standard method to deal with the structure of low-molar-mass liquids. 2 · 3 This equation however includes an unknown function, the (average) site-site direct correlation function C(r). There are different procedures to determine this function. In this study, we propose to determine the Fourier transform of C(r)

Characterization of the Micelle Formed by a Hydrophobically Modified Pullulan in Aqueous Solution: Size Exclusion Chromatography

“…Moreover, as shown in Figure 4 , aqueous PUL-OSA solutions contain a small amount of a large aggregating component. Thus, the scattering function of aqueous PUL-OSA may be written in the form [ 10 , 11 , 20 ] where M 0 is the average molar mass per glucose residue of PUL-OSA (cf. Table 1 ), N 0 is the degree of polymerization of the PUL-OSA chain, A 2 is the second virial coefficient, and w agg , M w,agg , and P z,agg ( k ) are the weight fraction, weight average molar mass, and z-average particle scattering function of the aggregating component, respectively.…”

Conformation of Pullulan in Aqueous Solution Studied by Small-Angle X-ray Scattering

“…At a finite polymer concentration, the scattering function is affected by the inter-molecular interference, and it may be written in the form [ 25 ]. where M w and A 2,app are the weight average molecular weight and the apparent second virial coefficient (including higher virial terms) for the polymer, and P ( k ) is calculated by Equation (2) or (8).…”

“…[21,24]. At a finite polymer concentration, the scattering function is affected by the inter-molecular interference, and it may be written in the form [25].…”

Light Scattering Study of Semiflexible Polymer Solutions III. Multicomponent Solutions

“…19 -24 In Part 11, 9 we utilized this equation to formulate R 0 for monodisperse polymer solutions. The extension of the equation to multicomponent polymer solutions may be given by23,24…”

“…In Part II of this series of papers, 9 we formulated the Rayleigh ratio R 8 or the light-scattering structure factor for isotropic solutions of monodisperse wormlike spherocylinders of arbitrary concentrations, by the scaled particle theory combined with the generalized Ornstein-Zernike integral equation. The formulated R8 was shown to be favorably compared with experimental data for dilute through semidilute solutions of a semiflexible polymer, poly(n-hexyl isocyanate).…”