ABSTRACT:Intramolecular excluded-volume effects in stiff chains are examined by analyzing typical data of (S 2 ) (the mean-square radius of gyration) and ['7] (the intrinsic viscosity) for four different polymers with Kuhn segment lengths A. -l of 7.8-86 nm on the basis of the wormlike chain. The data are shown to be explained almost quantitatively in the YamakawaStockmayer-Shimada scheme for wormlike or helical wormlike chains, leading to the conclusion that the expansion factor versus scaled excluded-volume parameter relations established by Yamakawa, Einaga, and coworkers for (S 2 ) Molecular characterization of semiflexible polymers in dilute solution often requires knowledge of intramolecular excluded-volume effects, but our understanding of those effects in stiff chains still leaves much to be desired. The situation may be explained as follows. More than 10 years ago, Norisuye and Fujita, 1 analyzing available data for the mean-square radius of gyration (S 2 ) on the basis of the Kratky-Porod (KP) wormlike chain, 2 concluded that excluded-volume effects on (S 2 ) of various polymers become experimentally observable when the Kuhn segment number nK exceeds 50 ( ± 30).This nK value was one order of magnitude larger than that predictable from the Yamakawa-Stockmayer perturbation theory 3 for KP bead chains, suggesting that intramolecular volume exclusion in actual stiff polymers is less enhanced than predicted by the theory. Later, Yamakawa and Shimada 4 examined the discrepancy by directly comparing theoretical and experimental (S 2 ) values, and reached the conclusion that the YamakawaStockmayer scheme, now extended to helical wormlike (HW) chains 5 and called the Yamakawa-StockmayerShimada (YSS) scheme, breaks down for poly(hexyl isocyanate) (PHIC), a typical stiff chain, in hexane. 6 Little progress has since been made on the subject, though, as far as flexible polymers are concerned, the validity of the YSS scheme has been substantiated for both dimensional and hydrodynamic properties. 7 -12 Very recently Tsuboi et al.U analyzed data of (S 2 ) and [17] (the intrinsic viscosity) for cellulose tris(3,5-dimethylphenylcarbamate) (CTDC) in 1-methyl-2-pyrrolidone (NMP) to reconcile the YSS theory with Norisuye and Fujita's conclusion mentioned above. The point was that the theory was capable of explaining the observed volume effects that were practically negligible for nK < 40 and appreciable for nK >50. This motivated us to re-examine literature data of (S 2 ) and [17] including those for PHIC with a hope of deepening our understanding of the intramolecular excluded-volume effects in semiflexible polymer solutions. To make our analysis more quantitative than in the earlier work by Norisuye and Fujita, we here confine ourselves to polymers whose (S 2 ) or [17] data show both unperturbed and perturbed behaviors in the molecular weight range studied. They are CTDC in NMP, 13 • 14 sodium salt of hyaluronic acid (Na-HA) in 0.2 and 0.5 M aqueous sodium chloride/ 5 -1 7 and poly(l-phenyl-1-propyne) (PPP) i...

Nineteen fractions of cellulose tris[(3,5-dimethylphenyl)carbamate] (CTDC) ranging in weight-average molecular weight M w from 2.5 × 104 to 7.5 × 106 have been studied by static light scattering, sedimentation equilibrium, and viscometry in 1-methyl-2-pyrrolidone at 25 °C. Since this cellulose derivative exhibits pronounced optical anisotropy, light-scattering data are corrected for the anisotropy effect on the basis of Nagai theory for the Kratky−Porod (KP) wormlike chain with cylindrically symmetric polarizabilities. It is shown that the data for 〈S 2〉z (the z-average mean-square radius of gyration), δ (the optical anisotropy factor), and [η] (the intrinsic viscosity) and those reported previously for 11 fractions are described accurately by the known theories for the unperturbed KP chain if M w is lower than 7 × 105. From the comparison, the persistence length and the monomeric projection of the CTDC chain are estimated to be 7.8 and 0.52 nm, respectively. When M w exceeds 106, i.e., when n K (the Kuhn segment number) increases above 50, excluded-volume effects on 〈S 2〉z and [η] become experimentally observable. Though such a large n K value for the appearance of volume effects has been considered inconsistent with the Yamakawa−Stockmayer−Shimada (YSS) theory for KP or helical wormlike chains, the observed excluded-volume effects are found to be explained quantitatively in the YSS scheme, i.e., by the YSS perturbation theory combined with the Domb−Barrett function for the radius expansion factor and the Barrett function for the viscosity expansion factor. Thus, this theoretical scheme should have a wider applicability than what might be anticipated from earlier studies.

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The dilute-solution behavior and liquid crystal formation of cellulose tris(3,5-dimethylphenylcarbamate) (CTDC) in 1-methyl-2-pyrrolidone (NMP) at 25OC are discussed by summarizing our recent studies, and its molecular characteristics are compared with those of cellulose tris(pheny1carbamate) (CTC) in the same solvent. The molecular weight dependences of optical anisotropy factor, radius of gyration, intrinsic viscosity ([q]), and isotropic-cholesteric phase boundary concentration for CTDC are explained consistently by current theories based on the wormlike chain. An analysis of the newly measured [q] for CTC shows that the backbone conformation and chain stiffness are substantially the same for the two cellulose derivatives in NMP. However, a distinct difference in optical anisotropy is found and briefly discussed in relation to the higher optical resolution capacity of CTDC than that of CTC in chromatographic separation of racemic compounds.

The molecular weights of isopoly(L-lysine), poly(L-ornithine), and poly(L-a, }~diaminobutylic acid), the homologues of poly (L-lysine), were determined by the sedimentation equilibrium method in aqueous solutions of 1.0 M NaC1 or 0.1 M Na2CO3. In every sample the molecular weights in the presence of carbonate ions was twice that in NaC1 solution. In a previous paper we reported that poly(L-lysine) behaved as a dimer at concentrations higher than 0.4 g/dl in the presence of carbonate ions and as a monomer in dilute solution, and these two forms were related by a monomer-dimer equilibrium. The homologues did not have a monomer-dimer equilibrium relationship under the conditions of the measurements that we carried out. The CD spectrum of isopoly(L-lysine) in water showed a uniform increase with a decrease in the wave length in the presence of carbonate ions. However, in the alkaline region in NaOH solution, the spectrum changed and a small minimum at 212 nm was found. When additional carbonate ions were added a large minimum at 205 nm was observed. This result can be explained by a change in the conformation from a random coil to a regular structure. We could not compare isopoly(L-lysine) with other polypeptides, because it does not have peptide bonds. The CD spectra of poly(L-ornithine) and poly(L-a, ~-diaminobutylic acid) in NaOH or Na2CO3 solutions showed only slightly regular structures. It was also confirmed that the dimer-structures of the poly(L-lysine) homologues do not have regular structures.