Atomistic configurations of model unentangled ring polyethylene (PE) melts ranging in chain length from C 24 up to C 400 have been subjected to detailed molecular dynamics (MD) simulations in the isothermal-isobaric statistical ensemble at temperature T = 450 K and P = 1 atm. Strictly monodisperse samples were employed in all cases. We present and discuss in detail simulation results for a variety of structural, thermodynamic, conformational and dynamic properties of these systems, and their variation with chain length. Among others, these include the mean chain radius of gyration, the pair correlation function, the intrinsic molecular shape, the local dynamics, the segmental mean square displacement (msd), the chain center-of-mass self-diffusion coefficient D G , the chain terminal relaxation time τ d , the characteristic spectrum of the Rouse relaxation times τ p , and the dynamic structure factor S(q,t). In all cases, the results are compared against the corresponding data from simulations with linear PE melts of the same chain length (the linear analogues) and the predictions of the Rouse theory for polymer rings which we derive here in its entirety. The Rouse theory is found to provide a satisfactory description of the simulation findings, especially for rings with chain length between C 50 and C 170 . An important finding of our work (from the observed dependence of D G , τ p , ζ, and η 0 on chain length N) is that PE ring melts follow approximately Rouse-like dynamics even when their chain length is as long as C 400 ; this is more than twice the characteristic crossover chain length (∼C 156 ) marking the passage from Rouse to reptation dynamics for the corresponding linear PE melts. In a second step, and by mapping the simulation data onto the Rouse model, we have managed to extract the friction coefficient ζ and the zero-shear rate viscosity η 0 of the simulated ring melts. Overall, and in agreement with previous theoretical and experimental studies, our simulation results support that the structure of ring polymers in the melt is more compact than that of their linear analogues due to their nonconcatenated configurations. Additional results for the intermolecular mer-mer and center-of-mass pair correlation functions confirm that the effective correlation hole effect is more pronounced in melts of rings than in melts of linear chains.

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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