Molecular Theory on the Entanglement Effect of Rodlike Polymers

Teraoka, Iwao; Ookubo, Norio; Hayakawa, Ritsuko

doi:10.1103/physrevlett.55.2712

Cited by 62 publications

(50 citation statements)

References 12 publications

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“…Furthermore, a previous study by Bhave has already shown that the k =0 eigenfunction must be nonzero if ␣␤ Ͼ 0. 3 Much of the experimental work 9,10 and theoretical work [11][12][13] on this topic are aimed at describing an effective diffusivity that already includes rod-rod interaction, so these diffusivity values cannot be readily applied to an equation where rodrod interaction is considered separately through ⌽. 3 and allows infinitesimal fluctuations around the isotropic base state for all values of k ജ 0.…”

Section: Resultsmentioning

confidence: 99%

Initial stage of spinodal decomposition in a rigid-rod system

Green

Brown

Armstrong

2007

The Journal of Chemical Physics

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The initial stage of spinodal decomposition is investigated for a rigid-rod system. Spinodal decomposition proceeds through either of two mechanisms: (1) The randomly aligned rods rotate toward a common director with no inherent length scale. (2) The rods diffuse axially and segregate into regions of common alignment with a selected length scale [script-l]. Previous studies on spinodal decomposition yielded radically different conclusions about which mechanism is dominant. A computational method is employed to analyze the growth rate and properties of the dominant fluctuation mode through an eigenvalue analysis of the linearized Doi diffusion equation in Fourier space. The linearized operator is discretized in Fourier mode and orientation space (k,theta,phi) space, and the maximum eigenvalue and corresponding eigenvector of the operator are calculated. Our analysis generalizes the results of previous studies and shows that the conflicts seen in those studies are due to differences in the diffusivities for rotational motion, motion perpendicular to the rod axis, and motion along the rod axis. For a given system density, a plot of the dominant perturbation wave number k(max) as a function of the diffusivity ratios shows two separate regions corresponding to mechanisms (1) and (2). High rotational diffusivity corresponds to mechanism (1), whereas high axial diffusivity corresponds to mechanism (2). The transition between the two mechanisms depends on the ratio of diffusivities and on system density. Also, the dominant wave number increases with increasing density indicating that a deeper quench into the spinodal regime leads to a smaller characteristic length scale.

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Section: Resultsmentioning

confidence: 99%

Initial stage of spinodal decomposition in a rigid-rod system

Green

Brown

Armstrong

2007

The Journal of Chemical Physics

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“…For strong suppression, the asymptotic behavior of the self-consistent equation [Eq. (17)] is obtained as D ⊥ /D 0 ⊥ ∼ 36π(n * ) −2 , which defines the normalization n * c,⊥ = 6 √ π for comparison with our simulation results.…”

Section: B Translational Diffusionmentioning

confidence: 88%

“…As a consequence of this high entanglement, the rotational motion and the translational diffusion perpendicular to the needle slow down drastically, whereas the diffusion along the tube is unaffected. In both theory [15][16][17][18][19][20] and computer simulations [21][22][23][24][25][26] the density-dependent scaling behavior of the long-time rotational and perpendicular translational diffusion coefficients have been established and scale with the number density as n −2 . Computer simulations for two-dimensional toy models have also been performed earlier [27][28][29][30][31] and for a needle in the presence of pointlike obstacles one observes the same scaling laws of the transport coefficients as in three dimensions [29,30].…”

Section: Introductionmentioning

confidence: 99%

Dynamically crowded solutions of infinitely thin Brownian needles

2017

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We study the dynamics of solutions of infinitely thin needles up to densities deep in the semidilute regime by Brownian dynamics simulations. For high densities, these solutions become strongly entangled and the motion of a needle is essentially restricted to a one-dimensional sliding in a confining tube composed of neighboring needles. From the density-dependent behavior of the orientational and translational diffusion, we extract the long-time transport coefficients and the geometry of the confining tube. The sliding motion within the tube becomes visible in the non-Gaussian parameter of the translational motion as an extended plateau at intermediate times and in the intermediate scattering function as an algebraic decay. This transient dynamic arrest is also corroborated by the local exponent of the mean-square displacements perpendicular to the needle axis. Moreover, the probability distribution of the displacements perpendicular to the needle becomes strongly nonGaussian, rather it displays an exponential distribution for large displacements. On the other hand, based on the analysis of higher-order correlations of the orientation we find that the rotational motion becomes diffusive again for strong confinement. At coarse-grained time and length scales, the spatiotemporal dynamics of the needle for the high entanglement is captured by a single freely diffusing phantom needle with long-time transport coefficients obtained from the needle in solution. The time-dependent dynamics of the phantom needle is also assessed analytically in terms of spheroidal wave functions. The dynamic behavior of the needle in solution is found to be identical to needle Lorentz systems, where a tracer needle explores a quenched disordered array of other needles.

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“…Concentration of rods in this case is constant. The effective viscosity η of the solution can be obtained based on the general equation for the stress tensor [23]: Let us consider the regime of a thin liquid jet of radius smaller than the rod length:…”

Section: Most Of the Above Results Cover Solutions Of Flexible Chainsmentioning

confidence: 99%

Capillary-Induced Phase Separation in Ultrathin Jets of Rigid-Chain Polymer Solutions

SUBBOTIN¹,

SEMENOV²

2020

Pis'ma Zh. Eksp. Teor. Fiz.

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In the present paper, we study the terminal stage of the capillary thinning of a polymer solution jet formed with rod-like molecules. On long scales exceeding the rod length a uniform jet gets unstable according to the classical Plateau-Rayleigh pinching mechanism. We show, however, that a qualitatively different faster process, which can prevent the jet from breaking-up, generically comes into play once the jet radius becomes smaller than the rod length. Namely the solvent drains out onto the jet surface forming annular droplets there, while the rods stay trapped inside the jet polymer core. As a result, the jet core becomes more concentrated and can solidify eventually. This process can provide a universal mechanism of the capillary-induced solvent/polymer phase separation leading to fiber formation (fiber spinning) from rod-like polymer solution jets.

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Molecular Theory on the Entanglement Effect of Rodlike Polymers

Cited by 62 publications

References 12 publications

Initial stage of spinodal decomposition in a rigid-rod system

Initial stage of spinodal decomposition in a rigid-rod system

Dynamically crowded solutions of infinitely thin Brownian needles

Capillary-Induced Phase Separation in Ultrathin Jets of Rigid-Chain Polymer Solutions

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