Chain Stiffness and Excluded-Volume Effects in Dilute Polymer Solutions:  Cellulose Tris[(3,5-Dimethylphenyl)carbamate]

Abstract

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.

Scattering function of semiflexible polymer chains under good solvent conditions

“…Thus, it is a clear advantage of our model calculations that via Eqs. (20), (21) accurate direct estimates of ℓ p are possible, unlike in experiment. These estimates for ℓ p are tabulated in Ref.…”

“…In view of an apparent conflict of the estimate [12] n * K = 50 with the Yamakawa-Stockmayer-Shimata theory [16][17][18][19] for worm-like chains the result n * K = 50 was considered as a very fundamental problem [20,21]. However, Tsuboi et al [21] confirmed this estimate for another stiff polymer and concluded that the result n * K = 50 is compatible with the theory. We also note that in d = 2 there occurs a single crossover from rods to self-avoiding walks, any regime of Gaussian-like behavior is completely absent [13,22].…”

Solution properties of cellulose tris(3,5‐dimethyl‐phenylcarbamate)

“…Very recently, we have investigated dilute-solution behavior and liquid crystal formation of this cellulose derivative in 1-methyl-2-pyrrolidone (or N-methyl-2-pyrrolidone, NMP) by light scattering, sedimentation equilibrium, viscometry, and polarized microscopy (Refs. [5][6][7][8], and analyzed the experimental results on the basis of the Kratky-Porod wormlike chain (Ref. 9) with or without excluded volume.…”

Remarks on 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) in toluene/ 8 in addition to PHIC in hexane. 6 No polyelectrolyte in aqueous solution of low ionic strength is included.…”