Effects of Excluded Volume on Light Scattered from Flexible Macromolecules

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Abstract
The effect of the non‐Gaussian behavior of the chain‐segment distribution in flexible polymer coils on the angular distribution of scattered light is discussed. The explicit form of a general spherical‐segment distribution function, W(r, N)dr = t Γ(3/t) ( Γ(5 / t) Γ(3 / t) 〈R N 2 〉 ) 3/2 exp − ( Γ(5 / t)r 2 Γ(3 / t) 〈R N 2 〉 | t/2 r 2 dr, with different values of t , is used to evaluate the general scattering equation for the particle scattering factor P(θ) . P(θ) = (1 / N 2 ) ∑ i ∑ j ( sin ksr ij / ksr ij ). In addition, the effects of excluded volume on the mean end‐to‐end chain separation 〈R N 2 〉 is taken to be of the form 〈R N 2 〉≈N 1+ε , where N is the number of chain steps and ε is a parameter which measures the excluded volume effect on the 〈R N 2 〉 . In this paper, an expansion of the P(θ) function to the first few terms is carried out and numerically evaluated for the dependence of P(θ) on the variable x , where x = ks〈R exptl ,〉 k is the wavenumber of the incident light, s is related to the scattering angle, and 〈R exptl 〉 is the radius of gyration determined from experimental data of the scattering cross section. The computations were carried out for the polymer in good solvent, for which data for ε and t were adopted, based on the lattice model of nonself‐intersecting chain, and for polymer in theta solvent, for which Gaussian chain model was adopted. The computations were carried out for various degrees of polydispersity. A comparison was made between the theoretical and the experimental results on a polystyrene sample of molecular weight of 4 × 106 in cyclohexane at 35°, 45°, 55°C and in benzene at 40°C.

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