Self-motion in glass-forming polymers: a molecular dynamics study

Dynamics theory for molecular liquids based on an interaction site model

Dynamics theories for molecular liquids based on an interaction site model have been developed over the past few decades and proved to be powerful tools to investigate various dynamical phenomena.

Are polymers standard glass-forming systems? The role of intramolecular barriers on the glass-transition phenomena of glass-forming polymers

Traditionally, polymer melts have been considered archetypal glass-formers. This has been mainly due to the fact that these systems can easily be obtained as glasses by cooling from the melt, even at low cooling rates. However, the macromolecules, i.e. the structural units of polymer systems in general, are rather different from the standard molecules. They are long objects ('chains') made by repetition of a given chemical motif (monomer) and have intra-macromolecular barriers that limit their flexibility. The influence of these properties on, for instance, the glass-transition temperature of polymers, is a topic that has been widely studied by the polymer community almost from the early times of polymer science. However, in the framework of the glass-community, the relevant influence of intra-macromolecular barriers and chain connectivity on glass-transition phenomena of polymers has started to be recognized only recently. The aim of this review is to give an overview and to critically revise the results reported on this topic over the last years. From these results, it seems to be evident that there are two different mechanisms involved in the dynamic arrest in glass-forming polymers: (i) the intermolecular packing effects, which dominate the dynamic arrest of low molecular weight glass-forming systems; and (ii) the effect of intra-macromolecular barriers combined with chain connectivity. It has also been shown that the mode coupling theory (MCT) is a suitable theoretical framework to discuss these questions. The values found for polymers for the central MCT parameter--the so-called λ-exponent--are of the order of 0.9, clearly higher than the standard values (λ ≈ 0.7) found in systems where the dynamic arrest is mainly driven by packing effects ('standard' glass-formers). Within the MCT, this is a signature of the presence of two competing mechanisms of dynamic arrest, as it has been observed in short-ranged attractive colloids or two component mixtures with dynamic asymmetry. Moreover, recent MD-simulations of a 'bead-spring' polymer model, but including intra-macromolecular potential of different strengths, confirm that the high λ-values found in polymers are due to the effect of intra-macromolecular barriers. Although there are still open questions, these results allow to conclude that there is a fundamental difference between the nature of the glass transition in polymers and in simple (standard) glass-formers.

Applicability of mode-coupling theory to polyisobutylene: a molecular dynamics simulation study

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.

Relaxation scenarios in a mixture of large and small spheres: Dependence on the size disparity

We present a computational investigation on the slow dynamics of a mixture of large and small soft spheres. By varying the size disparity at a moderate fixed composition different relaxation scenarios are observed for the small particles. For small disparity density-density correlators exhibit moderate stretching. Only small quantitative differences are observed between dynamic features for large and small particles. On the contrary, large disparity induces a clear time scale separation between the large and small particles. Density-density correlators for the small particles become extremely stretched and display logarithmic relaxation by properly tuning the temperature or the wave vector. Self-correlators decay much faster than density-density correlators. For very large size disparity, a complete separation between self- and collective dynamics is observed for the small particles. Self-correlators decay to zero at temperatures where density-density correlations are frozen. The dynamic picture obtained by varying the size disparity resembles features associated with mode coupling transition lines of the types B and A at, respectively, small and very large size disparities. Both lines might merge, at some intermediate disparity, at a higher-order point, to which logarithmic relaxation would be associated. This picture resembles predictions of a recent mode coupling theory for fluids confined in matrices with interconnected voids [V. Krakoviack, Phys. Rev. Lett. 94, 065703 (2005)].

How we can interpret the T1 dispersion of MC, HPMC and HPC polymers above glass temperature?

The chain dynamics in methyl cellulose (MC), hydroxypropylmethyl cellulose (HPMC) and hydroxypropyl cellulose (HPC) were studied with the aid of field-cycling NMR relaxometry technique in the temperature range from 300 to 480 K that is above the glass transition, but below thermal degradation. The frequency dependence of proton spin-lattice relaxation time was determined between 24 kHz and 40 MHz for selected temperatures. The experimental spin-lattice relaxation dispersion data were fitted with the power law relations of T(1) proportional variant omega(gamma) predicted by the tube/reptation model. The exponent's values found from the fitting procedure for MC, HPMC and HPC almost exactly match the ones predicted in tube/reptation model for limit II (gamma=0.75) and in MC also for limit III (gamma=0.50). Remarkably, this finding concerns the polymers in networks formed of the same polymer species.

Glass transition in 1,4-polybutadiene: Mode-coupling theory analysis of molecular dynamics simulations using a chemically realistic model

We present molecular dynamics simulations of the glass transition in a chemically realistic model of 1,4-polybutadiene (PBD). Around 40 K above the calorimetric glass transition of this polymer the simulations reveal a well-developed two-stage relaxation of all correlation functions. We have analyzed the time-scale separation between vibrational degrees of freedom (subpicosecond dynamics) and the alpha relaxation behavior (nanosecond to microsecond dynamics) using the predictions of mode-coupling theory (MCT). Our value for the mode-coupling critical temperature Tc agrees perfectly with prior experimental estimates for PBD. The predictions of MCT for the scaling behavior of the so-called beta relaxation, the plateau regime separating vibrational dynamics and the alpha relaxation, are well fulfilled. Furthermore, we are able to derive a consistent set of MCT exponents, completely characterizing the scaling behavior of relaxation processes in the vicinity of Tc. For the temperature dependence of the alpha relaxation we find deviations from MCT predictions which we trace to the influence of torsional barriers on the atomic motions.

Hydrogen motions in the α-relaxation regime of poly(vinyl ethylene): A molecular dynamics simulation and neutron scattering study

The hydrogen motion in poly(vinyl ethylene) (1,2-polybutadiene) in the alpha-relaxation regime has been studied by combining neutron spin echo (NSE) measurements on a fully protonated sample and fully atomistic molecular dynamics simulations. The almost perfect agreement between experiment and simulation results validates the simulated cell. A crossover from Gaussian to non-Gaussian behavior is observed for the intermediate scattering function obtained from both NSE measurements and simulations. This crossover takes place at unusually low Q values, well below the first maximum of the static structure factor. Such anomalous deviation from Gaussian behavior can be explained by the intrinsic dynamic heterogeneity arising from the differences in the dynamics of the different protons in this system. Side group hydrogens show a markedly higher mobility than main chain protons. Taking advantage of the simulations we have investigated the dynamic features of all different types of hydrogens in the sample. Considering each kind of proton in an isolated way, deviations from Gaussian behavior are also found. These can be rationalized in the framework of a simple picture based on the existence of a distribution of discrete jumps underlying the atomic motions in the alpha process.

Intramolecular caging in polybutadiene due to rotational barriers

We present molecular dynamics simulations of a chemically realistic model of 1,4-polybutadiene and a freely rotating chain model derived from the first model by neglecting all dihedral potentials. We show that the presence of energy barriers hindering dihedral rotation leads to an intermediate plateau regime in the tagged particle mean-squared displacement reminiscent of the cage effect underlying the mode-coupling description of the liquid-glass transition. This intramolecular caging, however, occurs already at temperatures well above the glass transition regime. Because of its different physical origin, it also does not comply with the theoretical predictions of the mode-coupling theory. Consequences for the applicability of the mode-coupling theory to the glass transition in polymer melts are discussed.

Mode-coupling theory for structural and conformational dynamics of polymer melts

A mode-coupling theory for dense polymeric systems is developed which unifyingly incorporates the segmental cage effect relevant for structural slowing down and polymer chain conformational degrees of freedom. An ideal glass transition of polymer melts is predicted which becomes molecular-weight independent for large molecules. The theory provides a microscopic justification for the use of the Rouse theory in polymer melts, and the results for Rouse-mode correlators and mean-squared displacements are in good agreement with computer simulation results.

Self-motion and the alpha relaxation in a simulated glass-forming polymer: crossover from Gaussian to non-Gaussian dynamic behavior

We present fully atomistic molecular dynamics simulations for a realistic model of a glass-forming polymer: polyisoprene. The simulations are carried out at 363 K and extend until 20 ns. We calculate the self-part of the Van Hove correlation function G(s)(r,t), the mean-squared displacement <r(2)(t)>, the second-order non-Gaussian parameter alpha(2)(t), and the incoherent intermediate scattering function F(s)(Q,t) for the main chain protons. In addition, we also calculate the density-density correlation function F(Q,t)/F(Q,0) and the second-order autocorrelation function M2(t) for different C-H bonds of the main chain. alpha(2)(t) shows a broad maximum centered at a time t(*) approximately 4 ps, which corresponds to the intermediate region of <r(2)(t)> between microscopic dynamics and sublinear diffusion. The analysis of F(s)(Q,t), F(Q,t)/F(Q,0), and M2(t) focuses on the second slow step which is associated to the alpha relaxation. Following the usual experimental procedure this decay is described in terms of a Kohlrausch-Williams-Watts (KWW) function: A exp[-(t/tau)(beta)]. In the Q range below Q(max), where Q(max) is the value at which the static structure factor shows its first maximum, the Q dependence of the KWW relaxation time of F(s)(Q,t) follows a law tau approximately Q(-2/beta). This kind of Q dependence corresponds to a Gaussian behavior of G(s)(r,t) and F(s)(Q,t). This law has been experimentally found in this Q range for different polymers. In the higher Q range-not easily accessible experimentally-strong deviations from the Gaussian behavior manifest. This crossover from Gaussian to non-Gaussian behavior can be understood in the framework of the mode coupling theory as well as in terms of a crossover from homogeneous to heterogeneous dynamics. This last interpretation opens a possible way of rationalizing the apparent contradiction between the neutron scattering and relaxation techniques results concerning dynamical heterogeneity of the alpha relaxation.

Relaxation dynamics of a viscous silica melt: the intermediate scattering functions

We use molecular dynamics computer simulations to study the relaxation dynamics of a viscous melt of silica. The coherent and incoherent intermediate scattering functions, F(q,t) and F(s)(q,t), show a crossover from a nearly exponential decay at high temperatures to a two-step relaxation at low temperatures. Close to the critical temperature of mode-coupling theory (MCT) the correlators obey in the alpha regime the time temperature superposition principle (TTSP) and show a weak stretching. We determine the wave-vector dependence of the stretching parameter and find that for F(q,t) it shows oscillations that are in phase with the static structure factor. The temperature dependence of the alpha-relaxation times tau shows a crossover from an Arrhenius law at low temperatures to a weaker T dependence at intermediate and high temperatures. At the latter temperatures the T dependence is described well by the power law proposed by MCT with the same critical temperature that has previously been found for the diffusion constant D and the viscosity. We find that the exponent gamma of the power law for tau are significantly larger than the one for D. The wave-vector dependence of the alpha-relaxation times for F(q,t) oscillates around tau(q) for F(s)(q,t) and is in phase with the structure factor. Due to the strong vibrational component of the dynamics at short times the TTSP is not valid in the beta-relaxation regime. We show, however, that in this time window the shape of the curves is independent of the correlator and is given by a functional form proposed by MCT. We find that the value of the von Schweidler exponent and the value of gamma for finite q are compatible with the expression proposed by MCT. Finally we discuss the q dependence of the critical amplitude and the correction term and find that they are qualitatively similar to the ones for simple liquids and the prediction of MCT. We conclude that, in the temperature regime where the relaxation times are mesoscopic, many aspects of the dynamics of this strong glass former can be rationalized very well by MCT.