No abstract

Recently reported data of the particle scattering function P(q) with the magnitude q of the scattering vector for rigid cyclic amylose tris(phenylcarbamate) (cATPC) and cyclic amylose tris(n-butylcarbamate) (cATBC) in different solvents were analyzed in terms of a novel simulation method based on the Kratky-Porod wormlike chain model. Although similar wormlike chain parameters were evaluated for both relatively flexible cyclic chains and the corresponding linear polymers, an appreciable decrease in the chain stiffness and slight extension of the local helical structure were found for cyclic chains with a higher chain stiffness. The difference in the wormlike chain parameters between the cyclic and linear chains cannot be realized in the previously reported molar mass dependence of the radius of gyration. This suggests that analyses of P(q) are decisively important to understand the conformational properties of rigid and/or semiflexible cyclic chains in solution if the molar mass range of the cyclic polymer samples is limited.

Conformational properties of rigid and semiflexible cyclic chains are still unclear owing to few experimental researches on dilute solution properties. Five cyclic amylose tris(3,5dimethylphenylcarbamate) (cADMPC) samples ranging in the weight-average degree of polymerization from 23 to 150 were prepared from enzymatically synthesized cyclic amylose. Light scattering and small-angle X-ray scattering measurements were made on the samples to determine the weight-average molar mass Mw, the particle scattering function P(q), and the zaverage mean-square radius of gyration S 2 z in methyl acetate (MEA), 4-methyl-2-pentanone (MIBK), and tetrahydrofuran (THF) at 25 C. The obtained P(q) and S 2 z data were analyzed on the basis of the cyclic wormlike chain model to determine the wormlike chain parameters, that is, the helix pitch (or helix rise) per residue h and the Kuhn segment length  −1 (the stiffness parameter or twice of the persistence length) as a function of Mw. Although the chain stiffness parameter  −1 for the corresponding linear polymer was reported to be 22 nm and 73 nm in MEA and MIBK, respectively, those for cADMPC in the three solvents were determined to be about 20 nm, this value being still significantly larger than that for cyclic amylose in aqueous sodium hydroxide. On the other hand, the former parameter h is somewhat larger than those for the linear ADMPC. The extended main chain of cADMPC by the topological constraint does not retain the chain stiffness as high as the corresponding linear chain. This phenomenon only becomes significant when the corresponding linear polymer behaves as a stiff chain with a small value of the Kuhn segment number NK. The threshold value of NK to achieve the significant difference in NK between the linear and cyclic chains is about less than 1.0 -1.5 at which the probability to link the both ends (ring closure probability) of the linear wormlike chain significantly decreases with decreasing NK.

A Monte Carlo (MC) study is made of the scattering function P(k) of the discrete Kratky−Porod (KP) wormlike ring as a function of the magnitude k of the scattering vector, and an approximate formula is also derived for P(k) of the continuous (original) KP ring in the Daniels approximation. It is found from MC results that the peak appearing in the reduced Kratky plot, which is characteristic of the KP ring, lowers continuously from the random-coil-ring limit to the rigid-ring limit with decreasing reduced contour length (increasing chain stiffness), and that the intramolecular topological constraint to keep the KP ring having the tivial knot lowers the peak. It is then shown that the formula in the first Daniels approximation may reproduce well the MC results except for very large k. A comparison is also made of the formula with literature data for ring atacic polystyrene in cyclohexane-d 12 near Θ.