Intrinsic viscosity and translational friction coefficient of nondraining flexible rings with small excluded volume

Abstract

First‐order excluded‐volume effects on the intrinsic viscosity and translational friction coefficient of nondraining flexible ring polymers were calculated on the basis of the Kirkwood–Riseman formalism of polymer hydrodynamics. The cube of the viscosity expansion factor αη,r was found to be represented by α 3η,italicr = 1 + 1.18z + …, where z is the usual excluded‐volume parameter. Combination of this result with the corresponding calculation by Fujita et al., for nondraining linear polymers, yielded α 3η,italicr/α 3η,italicl = 1 – 0.11z + … (αη,l denotes the viscosity expansion factor for linear chains). The negative coefficient of the z term contradicts the conclusion by Tanaka and Yamakawa who used the Zimm–Hearst theory of polymer dynamics. The friction expansion factor αf,r, for ring polymers, was obtained in powers of z as αf,r/αf,l = 1 + 0.773z + …. The earlier evaluation of αf,r by Fukatsu and Kurata was in error. The ratio αf,r/αf,l (αf,l is the friction expansion factor for linear chains) was given by 1 ± 0.182z ± … when the corresponding result on αf,l was used. This expansion compares well with Casassa's result αs,r/αs,l = 1 ± 0.147z + … for the ratio of the radius expansion factors of ring and linear chains.

Monte Carlo study of cycloamylose: Chain conformation, radius of gyration, and diffusion coefficient

“…Such an experimental g H should not be interpreted as due to small excluded‐volume effects on R H of ring polymers compared to those in linear chains. In fact, our g H is always greater for a larger a , consistent with the first‐order perturbation prediction18, 30 that the hydrodynamic‐radius expansion factor α H (≡ R H / R H0 ) is larger for a ring molecule than for the corresponding linear chain; note that g H / g H0 = α H ( r )/α H ( l ).…”

“…They exhibit damped oscillation for x smaller than 30, manifesting the locally helical conformation of amylose. The ratios of 〈 S 2 〉 and R H for a perturbed cyclic chain to the respective radii for the corresponding linear chain can be slightly lower than or comparable to the (asymptotic) Gaussian‐chain values unless x is sufficiently large, while excluded‐volume effects on these properties of cycloamylose are always larger than those in linear amylose with the same x , consistent with the predictions from the first‐order perturbation calculations18, 30, 31 and earlier simulations22, 23 on ideally flexible chains. The relation between the radius expansion factors for the two types of amylose is accurately represented by the one derived from the first‐order perturbation expressions or by the interpolation expression constructed in this work.…”

“…Such relations are illustrated with the simulation data for x ≥ 15 in Figures 6 and 7, which show α( r ) to be a function only of α( l ) or α( r ) in a first approximation. The straight lines in the figures represent the following relations derived from the first‐order perturbation expressions30, 31 [α( r ) = 1 + 1.571 z ; α( l ) = 1 + 1.276 z ; α( r ) = 1 + 1.545 z ] for flexible chains by eliminating z : They come close to the respective data sets, though that in Figure 7 deviates for α( r ) > 1.6. Close examination reveals that the plotted points for small x in both graphs tend to deviate slightly upward from the lines probably owing to some effect of the local‐helical nature of amylose.…”

Translational diffusion coefficient of cycloamylose in aqueous sodium hydroxide

“…In previous work, 6 we found that the following relations derived from the first-order perturbation equations 24,25 approximately hold for Monte Carlo data for the expansion factors ␣ H (r), ␣ s 2 (r), and ␣ s 2 (l ) if ␣ s 2 (r) is smaller than 1.6:…”