**Simulated glass-forming polymer melts: Dynamic scattering functions,
chain length effects, and mode-coupling theory analysis**

S Frey and F Weysser and H Meyer and J Farago and M Fuchs and J Baschnagel, EUROPEAN PHYSICAL JOURNAL E, 38, 11 (2015).

DOI: 10.1140/epje/i2015-15011-x

We present molecular-dynamics simulations for a fully flexible model of polymer melts with different chain length N ranging from short oligomers (N = 4) to values near the entanglement length (N = 64). For these systems we explore the structural relaxation of the supercooled melt near the critical temperature T-c of mode-coupling theory (MCT). Coherent and incoherent scattering functions are analyzed in terms of the idealized MCT. For temperatures T > T-c we provide evidence for the space-time factorization property of the beta relaxation and for the time-temperature superposition principle (TTSP) of the a relaxation, and we also discuss deviations from these predictions for T approximate to T-c. For T larger than the smallest temperature where the TTSP holds we perform a quantitative analysis of the dynamics with the asymptotic MCT predictions for the late beta regime. Within MCT a key quantity, in addition to T-c, is the exponent parameter lambda. For the fully flexible polymer models studied we find that. is independent of N and has a value (lambda = 0.735) typical of simple glass-forming liquids. On the other hand, the critical temperature increases with chain length toward an asymptotic value T-c(infinity). This increase can be described by T-c(infinity) - T-c(N) similar to 1/N and may be interpreted in terms of the N dependence of the monomer density., if we assume that the MCT glass transition is ruled by a soft-sphere-like constant coupling parameter Gamma(c) = rho T-c(c)-1/4, where rho(c) is the monomer density at T-c. In addition, we also estimate T-c from a Hansen-Verlet- like criterion and MCT calculations based on structural input from the simulation. For our polymer model both the Hansen-Verlet criterion and the MCT calculations suggest T-c to decrease with increasing chain length, in contrast to the direct analysis of the simulation data.

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