Statistics of stiff chain molecules: III. Chain length dependence of the mean square radius of gyration of cellulose‐ and amylose‐tricarbanilates

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Abstract
The unperturbed mean square radii of gyration of the two isomeric chains of cellulose‐ and of amylose‐tricarbanilates were measured over a wide range of degree of polymerisation. Both chains exhibit pronounced deviations from the Gaussian statistical conformation because of a remarkable chain stiffness. Four model calculations were performed to interpret the data: (a) the freely rotating chain model; (b) a chain with a symmetric potential of the hindered rotation around ϕ = ϕ = 0; (c) a chain with a hindrance potential symmetric around ϕ = ϕ* (d) an approximate model of (c). Because of the complicated ring conformation, the glucose units have to be approximated by a two‐bond unit, or by a one‐bond unit with variable valence angle. Model (d) differs from model (c) by the assumption that the valence angle of stiff chains is constant. Cellulose‐tricarbanilate could be reasonably interpreted by model (b), while for amylose‐tricarbanilate, helical conformations had to be taken into account. Eight helix conformations, discussed in the literature, were calculated on the basis of models (c) and (d). The experimental data could best be fitted by a helix of 4 residues per turn, a pitch height of 10.4 Å and a remarkable chain stiffness, The conception of chain stiffness is discussed, and it is shown that the chain extension or the chain expansion are not suitable stiffness parameters, while a generalised persistence length and a fluctuation parameter cos x, defined in the paper, are appropriate to describe the stiffness. The approximate model (d) appeared practically equivalent to the more elaborate model (c) for all helices considered.

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