Small angle neutron and X-ray scattering by poly(methyl methacrylate) chains

The intensity of radiation scattering by poly(methyl methacrylate) (PMMA) chains is computed as a function of scattering angle over the range $\text{0 < μ = (}\text{4π}\text{λ)}\text{sin}\text{(}\text{υ}\text{2}\text{) < 0.3}\text{A}\text{?}{}^{\mathrm{?1}}$, on the basis of a realistic rotational isomeric state model. The scattering functions F_x(μ), corresponding to Iμ², are developed for chains of x units in terms of the even moments 〈r^2p_ij〉 of the separation distance between pairs of the monomer units i and j. Whereas the theoretical scattering function F_x(μ) for isotactic PMMA increases monotonically with μ, for predominantly syndiotactic PMMA it exhibits a maximum at $\text{μ ≈ 0.05}\text{A}\text{?}{}^{\mathrm{?1}}$. This is in agreement with experimental results on small angle neutron and X-ray scattering by PMMA (in bulk and in solution, respectively). The appearance of the maximum in F_x(μ), heretofore considered anomalous, is shown to be a direct consequence of the preference of racemic diads of PMMA for the trans, trans conformation and of the inequality of the skeletal bond angles at CH₂ and at the doubly substituted C^α.