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.

Seven linear amylose tris(n-octadecylcarbamate) (ATODC) samples ranging in the weightaverage molar mass Mw from 2.4  10 4 to 1.5  10 6 g mol −1 and their seven cyclic analogues (cATODC) of which Mw are from 3.6  10 4 to 1.9  10 5 g mol −1 were prepared to characterize their conformation in tetrahydrohuran (THF), in 2-octanone (MHK), and in tertbutyl methyl ether (MTBE). Light and small-angle X-ray scattering and viscosity measurements in dilute solution were employed to determine the particle scattering function P(q), the z-average mean-square radius of gyration S 2 z, and the intrinsic viscosity []. The obtained data were analyzed in terms of the wormlike chain model to determine the helix pitch per residue h and the Kuhn segment length  −1 which is a measure of the chain stiffness and equal to twice the persistence length. The parameters indicate that the linear ATODC has an appreciably extended local helical structure and high chain stiffness while the latter parameter  −1 in THF is lower than those for amylose alkylcarbamates with shorter side chains. This is most likely due to the repulsion between relatively long side groups. This chain extension and less stiff main chain were more significantly observed for the cyclic chains. Lyotropic liquid crystallinity in concentrated solutions supports the high rigidity of ATODC and cATODC chains in solution.

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.

We prepared cellulose tris(ethylcarbamate) (CTEC), cellulose tris(n-butylcarbamate) (CTBC), and cellulose tris(n-octadecylcarbamate) (CTODC) samples with different molecular weight to determine their conformational properties in dilute solution. Weight average molar masses Mw, z-average mean-square radii of gyration S 2 z, particle scattering functions P(q), and intrinsic viscosities [] of the CTEC, CTBC, and CTODC samples in tetrahydrofuran (THF) at 25 C were determined by size exclusion chromatography equipped with multi-angle light scattering detectors (SEC-MALS), small angle X-ray scattering (SAXS), and viscometry. Infrared (IR) absorption measurements were also made to observe intramolecular hydrogen bonding between C=O and NH groups. The obtained S 2 z, P(q), and [] data were analyzed in terms of the wormlike chain model to determine the Kuhn segment length (stiffness parameter, or twice of the persistence length)  −1 and the helix pitch (rise) per residue h. While CTBC has the highest chain stiffness in the three cellulose derivatives as in the case of the corresponding amylose derivatives, the difference in the wormlike chain parameters is less significant for the cellulose alkylcarbamate derivatives. Indeed, intramolecular hydrogen bonding of CTEC, CTBC, and CTODC is weaker and fewer than that for the corresponding amylose derivatives owing to the main chain linkage,  or .

Lyotropic liquid crystallinity was examined for 8 linear amylose tris(noctadecylcarbamate) (ATODC) samples ranging in the weight-average molar mass (Mw) from 25 kg mol −1 to 1510 kg mol −1 and 10 cyclic ATODC (cATODC) samples, Mw of which varies between 36 kg mol −1 and 191 kg mol −1 . Appreciable cholesteric patterns were not observed in the concentration range investigated. Diffraction data from small-angle X-ray scattering both for bulk polymer samples at 160 -180 C and concentrated solutions at 25 C indicate that no characteristic peaks were found except for a broad diffraction reflecting the chain distance between the neighboring polymer molecules. The phase boundary concentrations for ATODC and cATODC in tetrahydrofuran (THF) and 2-octanone (MHK) were determined at 25 C as a function of Mw. The obtained phase diagram for ATODC was well fitted by a conventional scaled particle theory (SPT) for the wormlike spherocylinder as in the case of the other stiff polymer systems. On the other hand, when we assumed that cATODC chains form rodlike structure in the nematic phase, the experimental data were successfully explained by a modified SPT, suggesting conformation of cATODC in the nematic phase is different from that in dilute solution.