Theory of Light Scattering by an Isotropic System Composed of Anisotropic Units with Application to the Porod–Kratky Chain

Abstract

A theory of elastic (Rayleigh-Debye) light scattering by an isotropic system composed of anisotropic units is developed. Each unit is regarded optically as a point scatterer with three different principal polarizabilities. No assumption is introduced about the radial and orientational distributions for any pair of units. The only assumption is the random orientation of the system as a whole with respect to the light-scattering framework ("isotropic" system). Theory is formally adapted to infinitely dilute solutions of polymers of completely general structure. Detailed calculations are carried out for the Porod-Kratky wormlike chain. A method is suggested for determining the parameters of the Porod-Kratky chain through comparison of the theory with experimental data on polymer chains of moderate length. Chain-length dependences of various terms in expressions for reduced intensities are inferred for general chains from those for the Porod-Kratky chain. The correspondence of the Porod-Kratky chain with general chains is thereby discussed. A detailed comparison is also made of our results for the Porod-Kratky chain and general chains with those for the random chain reported by Utiyama and Kurata.

Stiff-Chain Nature of Poly(1-phenyl-1-propyne) in Dilute Solution

“…The ci> oo values in these solvents are lower than any of the theoretical values so far calculated, 26 -29 but are comparable to those for polyamides. 4 • 5 Nagai 15 was the first present a theory for the optical anisotropy factor of a wormlike chain with cylindrical symmetry. For relatively flexible wormlike chains, his expression can be written (6) where £ is defined by (7) with a 1 and a 2 being respectively the lon- in Figure 9, which reproduces the inverse proportionality predicted by the leading term of eq 6 with reasonable accuracy; we note that the O(qML/M) term in eq 6 does not exceed 0.012 in the Mw range studied.…”

Theory of Light Scattering by an Isotropic System Composed of Anisotropic Units. Out-of-Plane Scattering

“…The vertically polarized incident light, i.e., the case of JJ/ in Figure 1, is usually employed. As is well known and can readily be shown, the out-of-plane scattering can be reduced to the in-plane scattering if JJ 1 and JJ are properly chosen. To see this, first consider a case of the in-plane scattering in which the planes of polarization of the polarizer and the analyzer make angles ¢ and w, respectively, with the vertical z direction, as shown in Figure 1.…”

“…In a previous paper 1 we developed a theory of light scattering by an isotropic system composed of anisotropic units. The treatment was restricted to the case of the in-plane scattering where the intensity of scattered light is measured in the scattering plane (the xy plane of Figure z.X Scattered 1) while the incident and scattered lights are vertically or horizontally polarized with respect to the scattering plane.…”

Studies on dilute solution of rodlike macroions: Part 4 - Aggregation with enhanced interchain orientational correlation

“…11 gives (ref. 4,[6][7][8] (13) where p is the persistence length, L the chain contour length, 6 the intrinsic anisotropy, and I the length of a chain element with molecular weight m0. For the wormlike chain where a is the chain diameter and c2, so that for small p/L, RH 2R,,/3, as expected for a flexible chain polymer.…”