The melt viscosity-molecular weight relationship for linear polymers

Colby, Ralph H.; Fetters, Lewis J.; Graessley, William W.

doi:10.1021/ma00175a030

Cited by 378 publications

(508 citation statements)

References 18 publications

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“…This is especially apparent from the inset in Figure 1 where the relative variation of the viscosity compared to its asymptotic behavior, η/M 3 , is shown. The data scatter rather unsystematically around the fit with deviations well compatible with the error bars reported in ref 61 due to uncertainties in the measurements of the molecular weight and the viscosity. The slow approach of the constraint release corrections to the asymptote, eq I.69, explains why the asymptotic η/M 3 f constant is not yet observed.…”

Section: Comparison With Melt and Solution Experimentssupporting

confidence: 85%

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Polymer-Mode-Coupling Theory of Finite-Size-Fluctuation Effects in Entangled Solutions, Melts, and Gels. 2. Comparison with Experiment

Fuchs

Schweizer

1997

Macromolecules

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The predictions of polymer mode coupling theory for the finite size corrections to the transport coefficients of entangled polymeric systems are tested in comparison with various experimental data. It is found that quantitative descriptions of the viscosities, η, dielectric relaxation time, τ , and diffusion coefficients, D, of polymer melts can be achieved with two microscopic structural fit parameters whose values are in the range expected from independent theoretical or experimental information. An explanation for the (apparent) power law behaviors of η, τ , and D in (chemically distinct) melts for intermediate molecular weights as arising from finite size corrections, mainly the self-consistent constraint release mechanism, is given. The variation of tracer dielectric relaxation times from Rouse to reptationlike behavior upon changes of the matrix molecular weight is analyzed. Self-diffusion and tracer diffusion constants of entangled polymer solutions can be explained as well, if one further parameter of the theory is adjusted. The anomalous scaling of the tracer diffusion coefficients in semidilute and concentrated polystyrene solutions, D ∼ N -2.5 , is predicted to arise due to the spatial correlations of the entanglement constraints, termed "constraint porosity". Extensions of the theory to polymer tracer diffusion through poly(vinyl methyl ether) and polyacrylamide gels provide an explanation of the observation of anomalously high molecular weight scaling exponents in a range where the size of the tracer, Rg, already considerably exceeds the gel pore size, g. IntroductionThe microscopic polymer mode coupling (PMC) theory connects the dynamics of entangled polymeric systems to the underlying equilibrium liquid structure. This description therefore naturally includes corrections arising from the finite molecular weights of tracer or matrix polymers. In the preceding paper, 1 referred to as paper I, the PMC predictions with finite size corrections have been worked out for the transport properties of entangled solutions and melts and for polymer tracer motion in gels. In the present paper these results are compared with data from many experiments. As the PMC approach has been detailed in the preceding paper, 1 it shall be summarized only shortly in this section and then compared to alternative approaches. The resulting formulas of paper I will be referenced by the equation numbers of that paper with a prefix I.The PMC approach of paper I treats the Rouseentangled crossover problem in a simple interpolative manner. The PMC contributions capturing the entanglement corrections are combined with the Rouse, unentangled quantities, see eqs I.52 and I.68 for D, eqs I.55 and I.67 for η, and eqs I.58 and I.70 for τ . Appreciable deviations from the asymptotes for high molecular weights are therefore not explained by corrections of the Rouse dynamics to the asymptotic, entangled motion. In stark contrast to the contour length fluctuation model of Doi, 2,3 the repton model of Rubinstein, 4 and the Rouse-fluc...

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Section: Comparison With Melt and Solution Experimentssupporting

confidence: 85%

“…Figure 1 shows the viscosities of PBD melts for which the highest experimental reduced molecular weights have been reported. 61 The theoretical result, eq I.74, has been used. The PMC result (at least) semiquantitatively accounts for the measured data for all molecular weights.…”

Section: Comparison With Melt and Solution Experimentsmentioning

confidence: 99%

Polymer-Mode-Coupling Theory of Finite-Size-Fluctuation Effects in Entangled Solutions, Melts, and Gels. 2. Comparison with Experiment

Fuchs

Schweizer

1997

Macromolecules

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“…Figure 9 compares the zero shear rate viscosities obtained from our PP analysis with reported experimental data [33][34][35][36][37] for a number of model PE ͓Fig. 9͑a͔͒ and PB ͓Fig.…”

Section: -8mentioning

confidence: 99%

Quantifying chain reptation in entangled polymer melts: Topological and dynamical mapping of atomistic simulation results onto the tube model

Stephanou

Baig

Tsolou

et al. 2010

The Journal of Chemical Physics

106

153

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Articles you may be interested inTemperature dependent micro-rheology of a glass-forming polymer melt studied by molecular dynamics simulation J. Chem. Phys. 141, 124907 (2014) The topological state of entangled polymers has been analyzed recently in terms of primitive paths which allowed obtaining reliable predictions of the static ͑statistical͒ properties of the underlying entanglement network for a number of polymer melts. Through a systematic methodology that first maps atomistic molecular dynamics ͑MD͒ trajectories onto time trajectories of primitive chains and then documents primitive chain motion in terms of a curvilinear diffusion in a tubelike region around the coarse-grained chain contour, we are extending these static approaches here even further by computing the most fundamental function of the reptation theory, namely, the probability ͑s , t͒ that a segment s of the primitive chain remains inside the initial tube after time t, accounting directly for contour length fluctuations and constraint release. The effective diameter of the tube is independently evaluated by observing tube constraints either on atomistic displacements or on the displacement of primitive chain segments orthogonal to the initial primitive path. Having computed the tube diameter, the tube itself around each primitive path is constructed by visiting each entanglement strand along the primitive path one after the other and approximating it by the space of a small cylinder having the same axis as the entanglement strand itself and a diameter equal to the estimated effective tube diameter. Reptation of the primitive chain longitudinally inside the effective constraining tube as well as local transverse fluctuations of the chain driven mainly from constraint release and regeneration mechanisms are evident in the simulation results; the latter causes parts of the chains to venture outside their average tube surface for certain periods of time. The computed ͑s , t͒ curves account directly for both of these phenomena, as well as for contour length fluctuations, since all of them are automatically captured in the atomistic simulations. Linear viscoelastic properties such as the zero shear rate viscosity and the spectra of storage and loss moduli obtained on the basis of the obtained ͑s , t͒ curves for three different polymer melts ͑polyethylene, cis-1,4-polybutadiene, and trans-1,4-polybutadiene͒ are consistent with experimental rheological data and in qualitative agreement with the double reptation and dual constraint models. The new methodology is general and can be routinely applied to analyze primitive path dynamics and chain reptation in atomistic trajectories ͑accumulated through long MD simulations͒ of other model polymers or polymeric systems ͑e.g., bidisperse, branched, grafted, etc.͒; it is thus believed to be particularly useful in the future in evaluating proposed tube models and developing more accurate theories for entangled systems.

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“…25 The corollary is that for a fixed annealing temperature the viscosity of the P3HT matrix is invariant. Thus, for the same polymer matrix at a fixed temperature, a particle's mobility decreases as R −1 and, consequently, the diffusion constant for molecular PCBM (R = 0.5 nm) will be 50 times greater than that of the PCBM crystallites (R = 25 nm).…”

mentioning

confidence: 97%

Molecular versus crystallite PCBM diffusion in P3HT:PCBM blends

Berriman¹,

Holdsworth²,

Zhou³

et al. 2015

AIP Advances

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The diffusion of PCBM in P3HT:PCBM blend films has been investigated using multi-wavelength scanning absorption microscopy (MWSAM). By studying the depletion of PCBM in the vicinity of the phase segregated PCBM-rich regions that form upon thermal annealing, we are able to measure the diffusion constant and activation energy for PCBM diffusion in P3HT:PCBM blend films. The measured kinetic parameters are consistent with the diffusion of nanoscale PCBM crystallites rather than molecular PCBM. We show that the presence of two distinct diffusion processes in these blend materials provides an explanation for the large differences that have been reported for PCBM diffusion in P3HT:PCBM blends. This insight allows us to develop a unified model for PCBM mass transport in these materials.

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The melt viscosity-molecular weight relationship for linear polymers

Cited by 378 publications

References 18 publications

Polymer-Mode-Coupling Theory of Finite-Size-Fluctuation Effects in Entangled Solutions, Melts, and Gels. 2. Comparison with Experiment

Polymer-Mode-Coupling Theory of Finite-Size-Fluctuation Effects in Entangled Solutions, Melts, and Gels. 2. Comparison with Experiment

Quantifying chain reptation in entangled polymer melts: Topological and dynamical mapping of atomistic simulation results onto the tube model

Molecular versus crystallite PCBM diffusion in P3HT:PCBM blends

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