The particle scattering function and the distribution functions in the interior of fully swollen polymer molecules

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Abstract
The particle scattering function and the distribution function for the spatial distance between two interior elements were determined by light scattering measurements on fully swollen polymers, polystyrenes in toluene, and poly (α-methylstyrenes) in benzene. Measurements were made in the large q region such that x=q2〈s2N〉 was 20 to 100. Here 〈s2N〉 is the mean-square radius of gyration and q the magnitude of the scattering vector. The distribution function is well represented by the generalized Domb–Gillis–Wilmers form W(r,n)=Cnrl exp[−(r/σn)t] with t=2.40 and l=2.80. Here n is the length of a polymer segment, r is the end-to-end distance of the segment, Cn is the normalization constant, and σn is the scaling factor, respectively. The value of l is considerably high as compared with 2.0 for a Gaussian chain and 2.27 for the end-to-end distance of the self-avoiding chain, but is favorably compared with des Cloizeaux’s estimate, 2.71, for the distance between interior elements. Thus the effect of dangling ends is detectable by the study of the particle scattering function.