Anomalous Segment Diffusion in Polymer Melts

Appel, Matthias; Fleischer, G.; Kaerger, Joerg; Fujara, F.; Chang, I.

doi:10.1021/ma00093a031

Cited by 40 publications

(37 citation statements)

References 4 publications

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“…The simplified diffusive center-of-mass relaxation of the entanglement constraints as described by the memory func-tionsΣ andM , eqns. (36) and (37), leads to the identical results as the reptation tube model, i.e. eqn.…”

Section: A Tracer Shape Fluctuationsmentioning

confidence: 76%

Polymer-Mode-Coupling Theory of Finite-Size-Fluctuation Effects in Entangled Solutions, Melts, and Gels. 1. General Formulation and Predictions

Fuchs

Schweizer

1997

Macromolecules

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The transport coefficients of dense polymeric fluids are approximately calculated from the microscopic intermolecular forces. The following finite molecular weight effects are discussed within the Polymer-Mode-Coupling theory (PMC) and compared to the corresponding reptation/ tube ideas: constraint release mechanism, spatial inhomogeneity of the entanglement constraints, and tracer polymer shape fluctuations. The entanglement corrections to the single polymer Rouse dynamics are shown to depend on molecular weight via the ratio N/N e , where the entanglement degree of polymerization, N e , can be measured from the plateau shear modulus. Two microscopically defined non-universal parameters, an entanglement strength 1/α and a length scale ratio, δ = ξ ρ /b, where ξ ρ and b are the density screening and entanglement length respectively, are shown to determine the reduction of the entanglement effects relative to the reptation-like asymptotes of PMC theory. Large finite size effects are predicted for reduced degrees of polymerization up to N/N e ≤ 10 3 . Effective power law variations for intermediate N/N e of the viscosity, η ∼ N x , and the diffusion constant, D ∼ N −y , can be explained with exponents significantly exceeding the asymptotic, reptation-like values, x ≥ 3 and y ≥ 2, respectively. Extensions of the theory to treat tracer dielectric relaxation, and polymer transport in gels and other amorphous systems, are also presented.Macromolecules, accepted (May 1997).

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Section: A Tracer Shape Fluctuationsmentioning

confidence: 76%

Polymer-Mode-Coupling Theory of Finite-Size-Fluctuation Effects in Entangled Solutions, Melts, and Gels. 1. General Formulation and Predictions

Fuchs

Schweizer

1997

Macromolecules

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“…64 The same Gaussian approximation also simplifies the single molecule coherent dynamic structure factor to…”

Section: ͑9͒mentioning

confidence: 99%

Mode-coupling theory of the slow dynamics of polymeric liquids: Fractal macromolecular architectures

Fuchs

Schweizer

1997

The Journal of Chemical Physics

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Recently a mode coupling theory for the dynamics of solutions and melts of entangled linear chain polymers has been developed. We report the extension of this approach to macromolecular architectures different from linear chains. Specifically, this work addresses recent experimental findings on melts of ring shaped polymers, small spherical micro-networks, and linear chains in two dimensions. The mechanical and dielectric response, diffusion, and molecular relaxation times of macromolecules modeled by fractal mass distributions are studied. The distribution is chosen to be Gaussian and then is uniquely determined from the experimentally measured scaling of macromolecular size (R g ) with degree of polymerization (N), i.e., R g ϰ N . The exponent and the spatial dimension d determine the large N scaling of the transport coefficients and the exponents describing intermediate time anomalous diffusion. Within the theory, entanglement corrections to the single polymer Rouse dynamics are effective for Ͻ2/d only. There, we find D ϰ N 2dϪ5 for the diffusion coefficient and that the ratio D D /R g 2 is almost constant, where D is the terminal relaxation time. Using independent input from equilibrium liquid state theories, the magnitude and scaling with macromolecular density and segment length of the dynamical properties is determined. It is also found that macromolecular interpenetration requires progressively higher densities and consequently entanglements become less effective with fractal dimension 1/ approaching the spatial dimension. © 1997 American Institute of Physics. ͓S0021-9606͑97͒50901-9͔

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“…For a more precise determination of the time exponent of D,, and of the prefactor (see eq 9) more experiments, in particular with narrower distributed samples, are to be done. Such investigations are in progress 12. …”

mentioning

confidence: 95%

Investigation of the chain length dependence of self-diffusion of poly(dimethylsiloxane) and poly(ethylene oxide) in the melt with pulsed field gradient NMR

Appel¹,

Fleischer²

1993

Macromolecules

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106

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The chain length dependence of the self-diffusion coefficients of PDMS and PEO has been measured with pulsed field gradient NMR (PFG NMR). With PDMS the maximum molar mass region attainable with PFG NMR could be investigated. For molar masses larger than about lOM, the proportionality D -M-2 according to the strict reptation picture was observed; at small M Rouse-like diffueion is observed separated from the reptation part by a D(M) dependence characterized by a strong slowing down of the self-diffusion coefficient. The monomeric friction coefficients for PDMS derived from diffusion with the Doi-Edwards theory agree satisfactorily with those obtained from viscosity and also neutron scattering. Quantitatively, a discrepancy remains between the high molar mass part of D(M) where the monomeric friction coefficient is by a factor of about 0.5-0.6 smaller than that determined from the Rouse part of D(M) at low molar masses. Within experimental accuracy, for PDMS the activation energy of diffusion is equal to the activation energy of viscosity. For PEO the activation energy decreases from 24 to 18 kJ/mol at a molar mass of about 20 OOO g mol-'.

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Anomalous Segment Diffusion in Polymer Melts

Cited by 40 publications

References 4 publications

Polymer-Mode-Coupling Theory of Finite-Size-Fluctuation Effects in Entangled Solutions, Melts, and Gels. 1. General Formulation and Predictions

Polymer-Mode-Coupling Theory of Finite-Size-Fluctuation Effects in Entangled Solutions, Melts, and Gels. 1. General Formulation and Predictions

Mode-coupling theory of the slow dynamics of polymeric liquids: Fractal macromolecular architectures

Investigation of the chain length dependence of self-diffusion of poly(dimethylsiloxane) and poly(ethylene oxide) in the melt with pulsed field gradient NMR

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