Glassy dynamics of simulated polymer melts: Coherent scattering and van Hove correlation functions

Abstract

We report results of molecular-dynamics simulations of a model polymer melt consisting of short non-entangled chains in the supercooled state above the critical temperature Tc of mode-coupling theory (MCT). To analyse the dynamics of the system, we computed the incoherent, the collective chain and the collective melt intermediate scattering functions as well as their space Fourier transforms, the van Hove correlation functions. In this first part of the paper we focus on the dynamics in the β-relaxation regime. The final structural relaxation, the α-relaxation, will be studied in the following second part. The results can be summarized as follows: Without using any fit procedure we find evidence for the space-time factorization theorem of MCT in real and reciprocal space, and also for polymer-specific quantities, the Rouse modes. The critical amplitudes in real space are determined directly from the simulation data of the van Hove correlation functions. They allow to identify the typical length scales of the β-dynamics, and illustrate that it is a localized process. In a quantitative analysis the wave vector dependences of the β-coefficients, i.e., of the non-ergodicity parameter, the critical amplitude, and the next-to-leading order correction coefficients, are studied for all correlators. The β-coefficients show indications of polymerspecific effects on the length scale of the chain's radius of gyration. The agreement between simulation and the leading-order MCT description is found to be good in the central β-regime. Next-to-leading order corrections extend the validity of the MCT approximations to a greater time window and become more important at large wave vectors.

Polymer-specific effects of bulk relaxation and stringlike correlated motion in the dynamics of a supercooled polymer melt

“…The small amplitude of ␣ 2 p (t) may be attributed to the difference in packing of the monomers and of the chains. The monomers of our model exhibit an oscillatory pairdistribution function g(r) 35 whose shape and range are very similar to those found in simple dense liquids. In contrast to that, the pair-distribution function g cm (r) for the centers-ofmass is fairly structureless, and resembles the g(r) of a gas.…”

“…This is the signature of the slowing down of structural relaxation. Second, the curves collapse in the time window of the minimum which deepens and evolves into a protracted plateau with decreasing T. Previous analysis 34,35,37,38 showed that this time window corresponds to the MCT ␤-process where one expects temporary intermittence of particle motion due to the cage effect. 2, 56 In the ␤-regime, g n (t) is close to the localization length 6r n,c 2 , 2,39,56…”

“…The plateau reflects a temporary localization of the monomers by their nearest neighbors ͑''cage''͒ because g 0 is of the order of 10% of the monomer diameter (g 0 is close to 6r 0,c 2 with r 0,c Ӎ0.095 34,35 ͒. The intermediate time window encompassing the plateau and initial relaxation away from it is known as the ''␤-regime'' in MCT.…”

“…Thus, we may replace g(r) by its large-r limit. This limit is 0 for the polymer pair-distribution function 35 so that ͗s seg ͘ϭ1, whereas it is 1 in the case of the melt. Furthermore, since G s is a normalized Gaussian, the integral over r i j just gives 1.…”

Local polymer dynamics under strong connectivity constraints: The dendrimer case

“…In the past studies in linear polymers, 17 it was noted that the mean localization length r sc calculated from ⌬r 2 ͑t * ͒ϳ6r sc 2 , when expressed in terms of the intermolecular distance d =2 / Q max ͑Q max represents the magnitude of the first peak of the static structure factor͒ it yields a value of r sc / d Ӎ 0.094 very close to a value of 0.095 that was also found in linear bead-spring models. 9,41,42 A similar estimation of the mean localization length based on the value of r * as calculated from the present models at the low temperature limit results to a value of r sc / d Ӎ 0.109 nearly identical to the Lindemann criterion for melting. 44 To examine the dependence of r * on the location of the beads within the dendrimer structure for a constant dendrimer size, we followed the procedure described above for the g = 1 and g = 2 shells of the G3 model at all the temperatures for which reliable estimations could be performed.…”