Onset of Entanglement

Juang, Jonq

doi:10.1021/ma971733f

Cited by 28 publications

(52 citation statements)

References 31 publications

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“…In comparison with experimental results of polymer melts, [3][4][5]25 the mean-field representation works very well in the long-time or entropic region of the relaxation modulus, as illustrated by the quantitative agreement of the measured viscoelastic spectra with the Rouse theory. In comparison with experimental results of polymer melts, [3][4][5]25 the mean-field representation works very well in the long-time or entropic region of the relaxation modulus, as illustrated by the quantitative agreement of the measured viscoelastic spectra with the Rouse theory.…”

Section: Comparison Of Simulation With Experimentsmentioning

confidence: 57%

“…[1][2][3][4][5] In a viscoelastic spectrum, the agreement between theory and experiment is limited to the region below the modulus level corresponding to the molecular weight of a single Rouse segment that can be assigned to the polymer system-for instance, below ϳRT / m = 3.8ϫ 10 7 dyn/ cm 2 , corresponding to the Rousesegmental molecular weight m Ϸ 850 in the case of polystyrene. [1][2][3][4][5] In a viscoelastic spectrum, the agreement between theory and experiment is limited to the region below the modulus level corresponding to the molecular weight of a single Rouse segment that can be assigned to the polymer system-for instance, below ϳRT / m = 3.8ϫ 10 7 dyn/ cm 2 , corresponding to the Rousesegmental molecular weight m Ϸ 850 in the case of polystyrene.…”

Section: Introductionmentioning

confidence: 99%

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Monte Carlo simulations of stress relaxation of entanglement-free Fraenkel chains. I. Linear polymer viscoelasticity

Das

2007

The Journal of Chemical Physics

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Shear stress relaxation modulus GS(t) curves of entanglement-free Fraenkel chains have been calculated using Monte Carlo simulations based on the Langevin equation, carrying out both in the equilibrium state and following the application of a step shear deformation. While the fluctuation-dissipation theorem is perfectly demonstrated in the Rouse-chain model, a quasiversion of the fluctuation-dissipation theorem is observed in the Fraenkel-chain model. In both types of simulations on the Fraenkel-chain model, two distinct modes of dynamics emerge in GS(t), giving a line shape similar to that typically observed experimentally. Analyses show that the fast mode arises from the segment-tension fluctuations or reflects the relaxation of the segment tension created by segments being stretched by the applied step strain-an energetic-interactions-driven process-while the slow mode arises from the fluctuations in segmental orientation or represents the randomization of the segmental-orientation anisotropy induced by the step deformation-an entropy-driven process. Furthermore, it is demonstrated that the slow mode is well described by the Rouse theory in all aspects: the magnitude of modulus, the line shape of the relaxation curve, and the number-of-beads (N) dependence of the relaxation times. In other words, one Fraenkel segment substituting for one Rouse segment, it has been shown that the entropic-force constant on each segment is not a required element to give rise to the Rouse modes of motion, which describe the relaxation modulus of an entanglement-free polymer over the long-time region very well. This conclusion provides an explanation resolving a long-standing fundamental paradox in the success of Rouse-segment-based molecular theories for polymer viscoelasticity-namely, the paradox between the Rouse segment size being of the same order of magnitude as that of the Kuhn segment (each Fraenkel segment with a large force constant HF can be regarded as basically equivalent to a Kuhn segment) and the meaning of the Rouse segment as defined in the Rouse-chain model. The general agreement observed in the comparison of the simulation and experimental results indicates that the Fraenkel-chain model, while being still relatively simple, has captured the key element in energetic interactions--the rigidity on the segment--in a polymer system.

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Section: Comparison Of Simulation With Experimentsmentioning

confidence: 57%

Section: Introductionmentioning

confidence: 99%

Monte Carlo simulations of stress relaxation of entanglement-free Fraenkel chains. I. Linear polymer viscoelasticity

Das

2007

The Journal of Chemical Physics

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“…A summary of more recent speculations based on the transition 127 from Rouse 128 to reptation chain dynamics 95,96 and its effects on chain mobility and diffusion is given in the Supporting Information. [129][130][131][132][133][134][135][136][137][138] The common assumption has been that R p • is the major terminating species. Yet the estimated inequality k < k H (F/m 0 ) (see above and below) suggests that [R s • ] > [R p • ], such that R s • should dominate termination (unless it suffers significantly greater diffusional constraints than R p • ; see next paragraph).…”

Section: Observations On Mechanistic Issuesmentioning

confidence: 99%

Reexamination of the Pyrolysis of Polyethylene: Data Needs, Free-Radical Mechanistic Considerations, and Thermochemical Kinetic Simulation of Initial Product-Forming Pathways

Poutsma

2003

Macromolecules

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Gaps in the voluminous data on pyrolysis of polyethylene that impede mechanistic understanding are highlighted, especially for H:C material balances, product distributions at varying conversions in isothermal closed systems, and inconsistencies between GC and FIMS analyses of products with lower volatility. Thermochemical kinetic estimates are made for the rates of various initiation processes; these suggest that molecular disproportionation contributes to chain initiation, along with homolysis, at lower Mn. Simulations indicate that the standard statistical test for random scission, a linear relationship between log Nc and c for volatile products, is not generally valid in open systems, and its empirical observation implies restrictions on the dependence of the rate of volatilization on c.Simulations of the initial distributions of volatile products and residue functionalities were performed based on propagation rate constants estimated by thermochemical kinetic procedures. The practice of deducing the amount of backbiting from positive deviations at lower c from the linear log N c-c relationship established for higher c values is shown to underestimate the fraction of backbiting because the latter will give some products at every c so long as the 1,5-shift is not exclusive (k15 . k16 > k14). Compositions of volatiles at finite conversions were simulated by formal superposition of (a) backbiting and unzipping products predicted from this kinetic model and (b) random scission products, which form only after multiple bond cleavages, predicted from a statistical model. Comparisons with experimental data showed some success but were limited by data gaps and inconsistencies.

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“…Moreover, the very low molecular weights (M -w a 2M e ) which are contained in the MWD for molecular weight M -w a 10 M e induce a decrease of entanglement density and then a decrease of the viscosity. Therefore, the relationship g 0 against M -w is only an apparent behavior in a given range of molecular weights, which means that the different data must be compared defining the entangled domain M Note that pertinent rheological studies on the transition from low molecular weights to the entangled regime have been only recently published (Majesté et al 32) , Lin and Juang 33) ). The same agreement is observed between experimental and calculated values in the case of the elastic compliance (Tab.…”

Section: The Forward Calculationmentioning

confidence: 99%

Structure and dynamics of melt poly(ɛ-caprolactone) from inverse rheological calculation

Gimenez¹,

Cassagnau²,

Fulchiron³

et al. 2000

Macromol. Chem. Phys.

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IntroductionThe correlation of the flow curves of a melt polymer and its molecular weight distribution (MWD) has long been a subject of discussion. The first papers on the inverse problem were published by Tuminello 1) and Malkin et al. 2)Within the last ten years, the resolution of the inverse problem has been extensively treated because the forward problem of the calculation of the dynamic moduli has received interesting new developments from a molecular point of view. For example, the concept of double reptation proposed by Tsenoglou 3) and Des Cloizeaux 4) is now viewed as the reference model for the calculation of dynamic moduli from known MWDs.Two different approaches to the inverse solution were generally used. The first one tries to solve the ill-posed problem by using either a numerical algorithm based on a Tikhonov regularization procedure (Wasserman 5) , Leonardi et al. 6) ) or a regularization method using quadratic programming (Ramkumar and Wiest 7) ). Wasserman used various relaxation spectra with a mixing rule based on the double reptation concept, whereas Leonardi et al.6) used an empirical blending law on complex viscosities. This second method also uses numerical methods but these methods postulate the shape of the MWD, giving its analytical form as some typical shapes of the MWD which are generally assumed in the case of a particular polymerization process. Different works can be cited: Tuminello 1,8,9) , Malkin and Teishev 2) , Wood-Adams and Dealy 10) . Carrot and Guillet 11) proved that a reasonable solution to the inverse problem, i. e., the determination of the MWD from dynamics experiments in the linear viscoelastic domain, can be found using simple molecular dynamics together with additional information concerning the shape of the MWD. Full Paper:The linear viscoelastic behavior of poly(ecaprolactone) (PCL) in situ synthesized between the plates of the rheometer was investigated. The polymerization of e-caprolactone was initiated and catalyzed by titanium tetrapropoxide. These polymers are very sensitive to hydrolysis of the alkoxy-titanium bonds included in the polymer chains. Two different forms of PCL can be studied: hydrolyzed or non-hydrolyzed PCL. However, only the molecular weight distribution (MWD) of the hydrolyzed chains can be accessed from size exclusion chromatography (SEC) analysis. The MWD of the in-situ synthesized poly(e-caprolactone) was calculated by solving the inverse problem of determination of the MWD from rheological data. A continuous form of the relaxation function was derived and an a priori shape (Wesslau or bi-modal Wesslau ) of the MWD was assumed. Then MWDs calculated from complex moduli curves were used to investigate the structure of the poly(e-caprolactone) at the end of the polymerization process. About 85% of the polymer chains consist of a single branched linear structure. The remaining 15% are assumed to be mainly two fold branched. The presence of star structures cannot be precluded. The present work describes an illustrative example of the s...

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Onset of Entanglement

Cited by 28 publications

References 31 publications

Monte Carlo simulations of stress relaxation of entanglement-free Fraenkel chains. I. Linear polymer viscoelasticity

Monte Carlo simulations of stress relaxation of entanglement-free Fraenkel chains. I. Linear polymer viscoelasticity

Reexamination of the Pyrolysis of Polyethylene: Data Needs, Free-Radical Mechanistic Considerations, and Thermochemical Kinetic Simulation of Initial Product-Forming Pathways

Structure and dynamics of melt poly(ɛ-caprolactone) from inverse rheological calculation

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