We have measured the linear rheology of critically purified ring polyisoprenes, polystyrenes and polyethyleneoxides of different molar masses. The ratio of the zero-shear viscosities of linear polymer melts η0,linear to their ring counterparts η0,ring at isofrictional conditions is discussed as function of the number of entanglements Z. In the unentangled regime η0,linear/η0,ring is virtually constant, consistent with the earlier data, atomistic simulations, and the theoretical expectation η0,linear/η0,ring=2. In the entanglement regime, the Z-dependence of rings viscosity is much weaker than that of linear polymers, in qualitative agreement with predictions from scaling theory and simulations. The power-law extracted from the available experimental data in the rather limited range 1
We present an experimental investigation of the curing kinetics and viscoelasticity for a number of "vitrimers" recently developed by Leibler and coworkers. Vitrimers are covalently crosslinked networks that can relax stress at elevated temperatures due to thermoreversible bond-exchange reactions. The chosen formulations are composed of diglycidyl ether of bisphenol A, commercial fatty acid mixtures and an appropriate catalyst. The effects of the catalyst and functionality of the curing agents on the kinetics of the curing reactions were systematically investigated using rheometry. The curing kinetics followed the Arrhenius law and the catalyst drastically accelerated the reactions. Time-temperature superposition was used to construct master curves of the small-strain amplitude oscillatory shear moduli over wide ranges of frequencies for the cured networks. Terminal relaxation was not reached in oscillatory experiments for temperatures up to 130 °C and creep and stress relaxation experiments were used to probe the long-time relaxation. The shift factors displayed a Williams-Landel-Ferry dependence on temperature which could be divided into two regions, one above 70 °C, where the dynamics appeared to be controlled by the catalyst, and one below, controlled by the monomeric friction and the free volume of the network. The moduli of the vitrimers obeyed the classical rubber theory well, indicating that the curing reactions proceeded to completion. Furthermore, we systematically and reproducibly observed a double relaxation behavior for the vitrimers, i.e. next to the rubbery plateau at high frequencies, the storage modulus displayed a secondary plateau at lower frequencies before reaching terminal relaxation at even lower frequencies. Interestingly, 70 °C was found to be the transition point in agreement with the shift factors. To the best of our knowledge, the double relaxation behavior has not been previously reported in experimental works and recent theories do not incorporate an explanation for this behavior. Consequently, future investigations concerning the viscoelasticity of other "vitrimer-chemistries" are important to assess if the double relaxation is a universal fingerprint for vitrimers or if it is specific to the here-investigated formulations based on commercial fatty acid mixtures.
We present a static and quasi-elastic neutron scattering study on both the structure and dynamics of a ring polymer in a ring and linear polymer melt, respectively. In the first case, the ring structure proved to be significantly more compact compared to the linear chain with the same molecular weight. In the mixture, the ring molecules swell as was confirmed by small angle neutron scattering (SANS) in accordance with both theory and simulation work. The dynamical behavior of both systems, which for the first time has been explored by neutron spin echo spectroscopy (NSE), shows a surprisingly fast center of mass diffusion as compared to the linear polymer. These results agree qualitatively with the presented atomistic MD simulations. The fast diffusion turned out to be an explicit violation of the Rouse model.
We present results from very long (on the order of several microseconds) atomistic molecular dynamics (MD) simulations for the density, microscopic structure, conformation, and local and segmental dynamics of pure, strictly monodisperse ring and linear poly(ethylene oxide) (PEO) melts, ranging in molar mass from ∼5300 to ∼20 000 g/mol. The MD results are compared with recent experimental data for the chain center-of-mass self-diffusion coefficient and the normalized single-chain dynamic structure factor obtained from small-angle neutron scattering, neutron spin echo, and pulse-field gradient NMR, and remarkable qualitative and quantitative agreement is observed, despite certain subtle disagreements in important details regarding mainly internal ring motion (loop dynamics). A detailed normal-mode analysis allowed us to check the degree of consistency of ring PEO melt dynamics with the ring Rouse model and indicated a strong reduction of the normalized mode amplitudes for the smaller mode numbers (compared to the Rouse model scaling), combined with an undisturbed spectrum of Rouse relaxation rates. We have further measured the zero-shear rate viscosity η0 of the PEO-5k and PEO-10k rings at several temperatures and extracted their activation energies. These were compared with the activation energies extracted from the MD simulations via analysis of the temperature dependence of the corresponding Rouse relaxation times of the two rings in the same temperature range.
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