Whole Range of Chain Dynamics in Entangled Polystyrene Melts Revealed from Creep Compliance:  Thermorheological Complexity between Glassy-Relaxation Region and Rubber-to-Fluid Region. 1

Abstract

The rubber(like)-to-fluid region of the creep compliance J(t) results reported by Plazek of two nearly monodisperse polystyrene melts in the entanglement region have been quantitatively analyzed in terms of the extended reptation theory (ERT), giving the frictional factor K (= zetab2kTpi2m2) in quantitative agreement with the values obtained previously from analyzing the relaxation modulus Gt line shapes as well as calculated from the viscosity and diffusion data-a quantity shown independent of molecular weight as expected from the theory. Using the successful description of Jt in terms of ERT in the rubber(like)-to-fluid region as the reference frame in time, the glassy-relaxation process microG(t) that occurs in the small-compliance short-time region of J(t) can be studied in perspective. As shown from the analysis in terms of a stretched exponential form for microG(t) incorporated into ERT, the temperature dependence of the energetic interactions-derived microG(t) process being stronger in a simple manner than that of the entropy-derived ERT processes accounts fully for the uneven thermorheological complexity occurring in J(t) as initially observed by Plazek. When the results of analysis being displayed in the G(t) form, the relative roles of the energetic interactions-derived dynamic process and the entropy-derived ones in polystyrene are clearly revealed. It is shown that at the calorimetric glass transition temperature (Tg) the contribution from energetic interactions among segments to G(t) at the time scale of the highest Rouse-Mooney normal mode greatly exceeds that derived from entropy, indicating vitrification at the Rouse-segmental level. At the same time the Rouse-Mooney normal modes provide an internal yardstick for estimating the characteristic length scale of a polymer at Tg, giving approximately 3 nm for polystyrene. On the basis of the obtained results, the basic mechanism for the thermorheological complexity occurring in polystyrene is analyzed. It is shown that this basic mechanism should be also responsible for the breakdown of the Stoke-Einstein equation in relating the translational diffusion constant and viscosity as observed in glass-forming liquids, such as OTP and TNB, in approaching Tg from above.

Reinforcing mechanisms in amorphous polymer nano-composites

“…In high molecular weight polymers the rubbery plateau can be detected. The rubbery region exhibits primarily entropy driven behavior and the elastic modulus, G rubber , in entangled polymers can be approximated as [8]:…”

The Rouse–Mooney model for coherent quasielastic neutron scatterings of single chains well entangled in polymer melts

“…2,[7][8][9][10][11][12] This also represents a support on the microscopic level for the mechanism of chain slippage through entanglement links as embodied in the Doi-Edwards theory. This strongly supports that the Rouse-Mooney model is applicable microscopically as it has been shown to be so macroscopically in the studies of viscoelastic-response functions.…”

“…[1][2][3][4][5] Various techniques have been used to study different aspects of polymer dynamics. [7][8][9] The physical pictures as contained in these models may provide the approaches for analyzing the coherent quasielastic ͑or dynamic͒ neutron scattering results. 6 Successful models have been developed describing the viscoelastic responses quantitatively over the whole range: From the glassy-relaxation region to the flow region.…”

“…The relaxation modulus G͑t͒ functional forms have been given [7][8][9] by incorporating a stretched exponential Kohlrausch, Williams, and Watts ͑KWW͒ form for the glassyrelaxation process G ͑t͒ into the extended reptation theory 2,10-12 ͑ERT͒ ͑for entangled systems͒ or the Rouse theory 2,13-16 ͑for entanglement-free systems͒ as the frame of reference. The creep compliance J͑t͒ curves [17][18][19] and viscoelastic spectra G * ͑͒ ͑Ref.…”

Methods for probing the long-range dynamic of confined polymers in nanoparticles using small-angle neutron scattering

“…((0.36 -3(t))/(0.36 -3(0)) 2 we found t & 44 s. The polystyrene dynamic in the glassy regime near the T g is more likely to be a stretched exponential (G(t) = exp(-(t/t) b )) with an exponent b = 0.4. 30,39 In this case, we estimated the average relaxation time, <t > (<t > = $exp(-(t/t) b )dt), by numerically resolving eq. [3] with 3(t) from I(t)/I(0) !…”