In a recent paper [V. N. Novikov, K. S. Schweizer, and A. P. Sokolov, J. Chem. Phys. 138, 164508 (2013)] a simple analytical ansatz has been proposed to describe the momentum transfer (Q) dependence of the collective relaxation time of glass-forming systems in a wide Q-range covering the region of the first maximum of the static structure factor S(Q) and the so-called intermediate length scale regime. In this work we have generalized this model in order to deal with glass-forming systems where the atomic diffusive processes are sub-linear in nature. This is for instance the case of glass-forming polymers. The generalized expression considers a sub-linear jump-diffusion model and reduces to the expression previously proposed for normal diffusion. The generalized ansatz has been applied to the experimental results of the Q- and temperature-dependence of polyisobutylene (PIB), which were previously published. To reduce the number of free parameters of the model to only one, we have taken advantage of atomistic molecular dynamics simulations of PIB properly validated by neutron scattering results. The model perfectly describes the experimental results capturing both, Q- and temperature-dependences. Moreover, the model also reproduces the experimental Q-dependence of the effective activation energy of the collective relaxation time in the temperature range of observation. This non-trivial result gives additional support to the way the crossover between two different relaxation mechanisms of density fluctuations is formulated in the model.

We present a study of the static and dynamic structure factor of polyisobutylene (PIB) by fully atomistic molecular dynamics simulations. The reliability of the simulated cell is first assured by computing the magnitudes measured by diffraction and neutron spin echo techniques on a fully deuterated sample and directly comparing the results with those previously obtained from experiments [B. Farago et al., Phys. Rev. E 2002, 65, 051803]. Taking advantage of the validated simulations, we have disentangled the contributions to the static and dynamic structure factor by using a suitable grouping of the partial correlation functions based on specific molecular groups in PIB: main-chain (MC) atoms and methyl-group (MG) atoms. Regarding the structural features, we can attribute the temperature dependence of the first structure factor peak-which is dominated by inter-chain correlations mainly from backbone atoms-predominantly to the evolution of the MC/MG cross-correlations. Paradoxically, in the momentum transfer region where the MG/MG correlations present their main peak, the total structure factor displays a minimum due to a strong negative feature of the MC/MG cross-correlations. Concerning the dynamics, the decay of the intra-molecular correlations takes place through highly correlated motions relating pairs of MGs and MG and MC atoms. At inter-molecular level, the difference between pair and self-correlations for MC atoms is enhanced as the system approaches the glass-transition, indicating a gradual increase of collectivity. This collectivity of the backbones is ultimately the responsible for the modulation of the activation energy with the structure factor found in the experiments and reproduced by the simulations. Finally, we analyze the contributions of the analytical ansatz recently proposed to describe the collective relaxation time [J. Colmenero et al., J. Chem. Phys. 2013, 139, 044906] in order to identify the key ingredient leading to the above mentioned modulation of the activation energy, which is successfully accounted for by the model.

The applicability of Mode Coupling Theory (MCT) to the glass-forming polymer polyisobutylene (PIB) has been explored by using fully atomistic molecular dynamics simulations. MCT predictions for the so-called asymptotic regime have been successfully tested on the dynamic structure factor and the self-correlation function of PIB main-chain carbons calculated from the simulated cell. The factorization theorem and the time-temperature superposition principle are satisfied. A consistent fitting procedure of the simulation data to the MCT asymptotic power-laws predicted for the α-relaxation regime has delivered the dynamic exponents of the theory-in particular, the exponent parameter λ-the critical non-ergodicity parameters, and the critical temperature T(c). The obtained values of λ and T(c) agree, within the uncertainties involved in both studies, with those deduced from depolarized light scattering experiments [A. Kisliuk et al., J. Polym. Sci. Part B: Polym. Phys. 38, 2785 (2000)]. Both, λ and T(c)/T(g) values found for PIB are unusually large with respect to those commonly obtained in low molecular weight systems. Moreover, the high T(c)/T(g) value is compatible with a certain correlation of this parameter with the fragility in Angell's classification. Conversely, the value of λ is close to that reported for real polymers, simulated "realistic" polymers and simple polymer models with intramolecular barriers. In the framework of the MCT, such finding should be the signature of two different mechanisms for the glass-transition in real polymers: intermolecular packing and intramolecular barriers combined with chain connectivity.

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