Dynamics of polymers in polydisperse melts

Doi, Masao; Graessley, William W.; Helfand, Eugene; Pearson, Dale S.

doi:10.1021/ma00174a035

Cited by 156 publications

(197 citation statements)

References 6 publications

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“…These results demonstrate that the jumping amplitude of fat tube segments scales as ~Ne -0.5 similar to the assumption of the tube dilation theory. 9,17 Theoretical predictions of the terminal relaxation for freely reptating chains entangled with two types of finite lifetime obstacles can be computed by assuming independence of Rouse motion of the fat tube, with respect to reptation of the thin tube and chain along the fat tube:…”

Section: Systems With Two Moving Tubesmentioning

confidence: 99%

“…Doi and co-workers in ref. 9 proposed to combine both CR pictures and defined the effective tube diameter as a crossover between mean squared displacement of the free chain and motion of the tube described by Rouse dynamics. Finally, Viovy and coworkers 28 further extended the original tube rearrangement picture for the case of binary linear melts.…”

Section: Introductionmentioning

confidence: 99%

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Understanding Effect of Constraint Release Environment on End-to-End Vector Relaxation of Linear Polymer Chains

et al. 2017

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In this study we propose and verify methods based on the slip-spring (SSp) model (Likhtman, 2005) for predicting the effect of any monodisperse, binary or ternary environment of topological constraints on the relaxation of the end-to-end vector of a linear probe chain. For this purpose we first validate the ability of the model to consistently predict both the viscoelastic 2 and dielectric response of monodisperse and binary mixtures of type-A polymers, based on published experimental data. We also report the synthesis of new binary and ternary Polybutadiene systems, the measurement of their linear viscoelastic response, and the prediction of these data by the SSp model. We next clarify the relaxation mechanisms of probe chains in these constraint release (CR) environments by analyzing a set of "toy" SSp models with simplified constraint release rates, by examining fluctuations of the end-to-end vector. In our analysis, the longest relaxation time of the probe chain is determined by a competition between the longest relaxation times of the effective CR motions of the fat and thin tubes, and the motion of the chain itself in the thin tube. This picture is tested by the analysis of four model systems designed to separate and estimate every single contribution involved in the relaxation of the probe's end-to-end vector in polydisperse systems. We follow the CR picture of (Viovy et al., 1991) and refine the effective chain friction in the thin and fat tubes based on (Read et al., 2012). The derived analytical equations form a basis for generalizing the proposed methodology to polydisperse mixtures of linear and branched polymers. The consistency between the the SSp model and tube model predictions is a strong indicator of the compatibility between these two distinct mesoscopic frameworks.

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Section: Systems With Two Moving Tubesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Understanding Effect of Constraint Release Environment on End-to-End Vector Relaxation of Linear Polymer Chains

et al. 2017

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“…As mentioned in ref 21, the influence of the tension re-equilibration process can be considered by taking into account a fully/partially coarse-grained time scale and focusing on the terminal relaxation of the components occurring in the fully/partially dilated tube. In this study, we would like to describe the evolution of the surviving tube fraction in all time scales, from the short chain relaxation time up to the terminal time of the long chain, and discuss the results with respect to the theoretical works proposed by Doi et al 40 and by Viovy et al 41 for describing the constraint release mechanisms in the case of binary blends of linear chains. While according to Doi et al the relaxed short chains are acting as a real solvent and the motions of the long chains are always considered along their fully dilated tube, Viovy et al consider both the motions of the chain within the initial tube and the motions of this initial tube within the dilated tube, which take place at the rhythm of the short chains motions.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Dilution Effect in Binary Blends of Linear Polymers with Well-Separated Molecular Weights

et al. 2014

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We investigate and model the viscoelastic properties of binary blends composed of linear chains. These systems are indeed very suitable to test the validity and the limit of the constraint release (CR) process and dynamic tube dilution and to determine the value of the dynamic dilution exponent α. We first focus on binary blends containing barely entangled short chains. In such a case, we show that the tension re-equilibration process previously observed [ van Ruymbeke van Ruymbeke Macromolecules2012452085] can be correctly described as a CR-activated contour length fluctuation (CLF) process, which takes place along the fully dilated tube and is governed by the intrinsic Rouse time of a long–long entanglement segment. In addition, reptation is considered to take place along the fully dilated tube. We also show that this CR-activated CLF process speeds up the relaxation of the long chains, which naturally leads to an effective dilution exponent α equal to 4/3, despite the fact that the modeling is based on α = 1. This result is in agreement with the experimental data. Then, we analyze the rheological behavior of binary blends containing entangled short chains. In such a case, we show that the CR-activated CLF also takes place, but with a delay time being necessary for the long chain to explore the dilated tube. This approach is tested for several binary blends, showing an improved quality of the predictions compared to previous tube modeling on the same blends. Indeed, by considering the chain motions on two different length scales, a larger fraction of the long chains relax at intermediate frequencies (through the tension re-equilibration) before their reptation, leading to an effective dilution exponent larger than 1 as determined from the low-frequency plateau modulus.

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“…In contrast to earlier extensions of the DE theory [4][5][6][7] and double reptation theories [8][9][10], the present model does not assume that in general the stress relaxation function of i-polymers (which is proportional to the fraction of the initial tube survived at time t), cannot be presented as the product of a pure "reptational" and a "constraint release" part. In fact, as is seen from eq.…”

Section: -P1mentioning

confidence: 91%

“…It breaks down because a low molecular weight polymer imposing a constraint on a high molecular weight test chain can diffuse away much faster than the test chain reptates. Clearly, any realistic model for polydisperse systems must provide a rigorous treatment of constraint release along with thermal fluctuations.In a number of attempts one has tried to adjust the original DE model through inclusion of constraint release [4][5][6][7]. Most of these extensions led to models, that were mathematically complicated and still had restricted predictive capability and thus limited practical utility.…”

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confidence: 99%

Relaxation spectra of binary blends: Extension of the Doi-Edwards theory

et al. 2007

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-A molecular model is presented which allows the calculation of the stress relaxation function G for binary blends consisting of two monodisperse samples with arbitrary molecular weights. It extends the Doi-Edwards reptation theory (Doi M. and Edwards S. F., The Theory of Polymer Dynamics (Oxford Press, New York) 1986) to highly polydisperse melts by including constraint release (CR) and thermal fluctuations (CLF), yet making use of the same input parameters. The model reveals an explicit nonlinear dependence of CR frequency in the blend on the blend's molecular weight distribution (MWD). It provides an alternative way to quantify polydisperse systems compared to the widely used "double-reptation" theories. The results of the present model are in a good agreement with the experimental data given in Rubinstein M. and Colby R. H., J. Chem. Phys., 89 (1988) 5291. Copyright c EPLA, 2007The molecular model of Doi and Edwards (DE) [1] proved to be remarkably successful in predicting the rheological response of linear monodisperse polymer melts in the linear viscoelastic regime. Some initial shortcomings in this regime could be eliminated by including a rigorous treatment of thermal fluctuations [2]. However, already in an early stage it was realized that its straightforward extensions to polydisperse systems, such as binary blends, did not adequately describe the observed rheological behavior [3]. This discrepancy between theory and experiment strongly suggested that the fundamental postulate of the DE model that the surrounding network of polymers constitutes a time-independent mean field of topological constraints is not applicable in case of polydisperse materials. It breaks down because a low molecular weight polymer imposing a constraint on a high molecular weight test chain can diffuse away much faster than the test chain reptates. Clearly, any realistic model for polydisperse systems must provide a rigorous treatment of constraint release along with thermal fluctuations.In a number of attempts one has tried to adjust the original DE model through inclusion of constraint release [4][5][6][7]. Most of these extensions led to models, that were mathematically complicated and still had restricted predictive capability and thus limited practical utility. Alternatively to the DE theory, des Cloizeaux and Tsenoglou independently developed a network model [8,9] for linear viscoelastic materials based on the concept of "double reptation". Their formalism allows one to express the stress relaxation function of a polydisperse melt in terms of relaxation spectra of each of its monodisperse components and a so-called "mixing rule". Double reptation theory shows a good agreement with observed data on polydisperse melts with rather narrow molecular weight distribution (MWD). The broader the MWD, the larger the disagreement between theoretical predictions and data. Recently, Mead [10] extended the "double reptation" theory to non-linear flows by introducing convective constraint release and stretch in the model.

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Dynamics of polymers in polydisperse melts

Cited by 156 publications

References 6 publications

Understanding Effect of Constraint Release Environment on End-to-End Vector Relaxation of Linear Polymer Chains

Understanding Effect of Constraint Release Environment on End-to-End Vector Relaxation of Linear Polymer Chains

Dynamic Dilution Effect in Binary Blends of Linear Polymers with Well-Separated Molecular Weights

Relaxation spectra of binary blends: Extension of the Doi-Edwards theory

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