Intrinsic Viscosity of Flexible Ring Polymers with Small Excluded Volume

Tanaka, Genzo; Yamakawa, Hiromi

doi:10.1295/polymj.4.446

Cited by 9 publications

(4 citation statements)

References 16 publications

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“…Using the prescription for combs of section III.B, the L matrix for a regular comb is for i = I(n0 + 1), I(n0 + 1) + 1, ..., f(n0 + 1) + n0 -1 (29) with column index j varying from 1 to nb for each submatrix. Finally, the elements of the f -1 submatrices denoted W7 are defined by W7(íJ) = -ad + j + I(n0 + 1)) i, j =1, 2, 3.....nb (30) This submatrix represents the hydrodynamic interaction occurring between submolecules on arms separated by I(n0 + 1) backbone springs. In general, the Ns eigenvalues of the L matrix for these regular combs vary between 0 and 5 for values of h* between 0.00 and 0.25.…”

Section: Qk = (I)mentioning

confidence: 99%

Bead-spring model predictions of solution dynamics for flexible homopolymers incorporating long-chain branches and/or rings

Sammler¹,

Schrag²

1988

Macromolecules

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A generalization of the model of Zimm is presented which predicts solution dynamics for chains composed of any assortment of identical spherical beads connected by identical Hookean springs. The model is formulated in a coordinate system that translates with the chain to ensure that the predicted dynamic properties may be computed, regardless of chain size or degree of hydrodynamic interaction, with the efficient eigenvalue algorithm applied by Lodge and Wu to linear chains. Several new block-diagonal matrices, which further improve the computation efficiency for linear, ring, and regular H structures, also arise from this formulation. All three features enable new quantitative predictions of the effects of long-chain branches, combinations of rings and branches, chain size, and hydrodynamic interaction on dilute-solution, low-shear-rate, dynamic properties of flexible homopolymers. Numerical results for selected chain geometries will be presented in a subsequent paper.

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Section: Qk = (I)mentioning

confidence: 99%

Bead-spring model predictions of solution dynamics for flexible homopolymers incorporating long-chain branches and/or rings

Sammler¹,

Schrag²

1988

Macromolecules

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“…The Kirkwood-Riseman formalism gives where $o(x,x) and rc/l(x,x) are the unknown functions to be determined by solving the set of integral equations Here Ko(x,t) and K1 are the same as defined by eqs. (7) and (8). In the same way as employed in the intrinsic viscosity problem, these equations can be solved analytically, yielding…”

Section: Intrinsic Viscositymentioning

confidence: 99%

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

Norisuye

Fujita

1978

J. Polym. Sci. Polym. Phys. Ed.

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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.

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“…When the parameter ß is negative, the segments tend to attract each other to lower the free energy, and if ß is much less than zero the polymer chain collapses.47,63-66 It is necessary to introduce higher than pairwise short-range interaction terms63-66 to prevent a prediction of collapse to a point. The binary cluster approximation is meaningful if the interaction energy is bounded67 by *ß > -AN (19) where A is a positive constant. Equation 19 leads to…”

Section: Comparison With Experimentsmentioning

confidence: 99%

Intrinsic viscosity and friction coefficient of flexible polymers

Tanaka¹

1982

Macromolecules

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Padé approximants, assuming Flory's limiting exponent and utilizing the first-order perturbation results for the intrinsic viscosity [77] and the friction coefficient / of a flexible polymer, are shown to agree well with experimental data over a wide range of the interaction parameter z. Based on these approximants, it is shown that the unperturbed dimension (R2)0 and the polymer-solvent interaction parameter B can be estimated from viscosity or friction coefficient data in good solvents by a linear extrapolation of a plot of (M/M1/2)6/3 or (//tjoM1/2)5 against AÍ1/2, where M is the polymer molecular weight and 0 is the solvent viscosity coefficient. Values of (R2)o and B determined from viscosity plots are in good agreement with that of experiment and that from mean-square radii, respectively.

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Intrinsic Viscosity of Flexible Ring Polymers with Small Excluded Volume

Cited by 9 publications

References 16 publications

Bead-spring model predictions of solution dynamics for flexible homopolymers incorporating long-chain branches and/or rings

Bead-spring model predictions of solution dynamics for flexible homopolymers incorporating long-chain branches and/or rings

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

Intrinsic viscosity and friction coefficient of flexible polymers

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