Intramolecular caging in polybutadiene due to rotational barriers

Role of torsional potential in chain conformation, thermodynamics, and glass formation of simulated polybutadiene melts

For polymer chains, the torsional potential is an important intramolecular energy influencing chain flexibility and segmental dynamics. Through molecular dynamics simulations of an atomistic model for melts of cis-trans-1,4-polybutadiene (PBD), we explore the effect of the torsions on conformational properties (bond vector correlations and mean-square internal distances), fundamental thermodynamic quantities (density, compressibility, internal energy, and specific heat), and glass transition temperature T_g. This is achieved by systematically reducing the strength of the torsional potential, starting from the chemically realistic chain (CRC) model with the full potential toward the freely rotating chain (FRC) model without the torsional potential. For the equilibrium liquid, we find that the effect of the torsions on polymer conformations is very weak. Still weaker is the influence on the monomer density ρ and isothermal compressibility κ_T of the polymer liquid, both of which can be considered as independent of the torsional potential. We show that a van der Waals-like model proposed by Long and Lequeux [Eur. Phys. J. E 4, 371 (2001)] allows us to describe very well the temperature (T) dependence of ρ and κ_T. We also find that our data obey the linear relation between 1/k_BTρκ_T and 1/T (with the Boltzmann constant k_B) that has recently been predicted and verified on the experiment by Mirigian and Schweizer [J. Chem. Phys. 140, 194507 (2014)]. For the equilibrium liquid, simulations result in a specific heat, at constant pressure and at constant volume, which increases on cooling. This T dependence is opposite to the one found experimentally for many polymer liquids, including PBD. We suggest that this difference between simulation and experiment may be attributed to quantum effects due to hydrogen atoms and backbone vibrations, which, by construction, are not included in the classical united-atom model employed here. Finally, we also determine T_g from the density-temperature curve monitored in a finite-rate cooling process. While the influence of the torsional potential on ρ(T) is vanishingly small in the equilibrium liquid, the effect of the torsions on T_g is large. We find that T_g decreases by about 150 K when going from the CRC to the FRC model.

Relaxation processes and glass transition of confined polymer melts: A molecular dynamics simulation of 1,4-polybutadiene between graphite walls

Molecular dynamics simulations of a chemically realistic model for 1,4-polybutadiene in a thin film geometry confined by two graphite walls are presented. Previous work on melts in the bulk has shown that the model faithfully reproduces static and dynamic properties of the real material over a wide temperature range. The present work studies how these properties change due to nano-confinement. The focus is on orientational correlations observable in nuclear magnetic resonance experiments and on the local intermediate incoherent neutron scattering function, F_s(q_z, z, t), for distances z from the graphite walls in the range of a few nanometers. Temperatures from about 2T_g down to about 1.15T_g, where T_g is the glass transition temperature in the bulk, are studied. It is shown that weakly attractive forces between the wall atoms and the monomers suffice to effectively bind a polymer coil that is near the wall. For a wide regime of temperatures, the Arrhenius-like adsorption/desorption kinetics of the monomers is the slowest process, while very close to T_g the Vogel-Fulcher-Tammann-like α-relaxation takes over. The α-process is modified only for z≤1.2 nm due to the density changes near the walls, less than expected from studies of coarse-grained (bead-spring-type) models. The weakness of the surface effects on the glass transition in this case is attributed to the interplay of density changes near the wall with the torsional potential. A brief discussion of pertinent experiments is given.

Dielectric α-relaxation of 1,4-polybutadiene confined between graphite walls : Molecular dynamics investigations through numerical simulations of polymer molecules relaxation

We present results of Molecular Dynamics (MD) simulations of a chemically realistic model of 1,4-polybutadiene confined by crystalline graphite walls. The simulations cover a large range of temperatures from T ≈ 2T g to T ≈ 1.15T g, where relevant time scales are accessible using such computational methods. We investigate the dielectric relaxation close to the walls in comparison to the one in the center of the film, and study the latter as a function of the film thickness from the walls. The segmental dynamics in the film is slowed down close to the walls, in comparison to the bulk. In addition to the α-process, the relaxation exhibits an additional long time decay, the so-called wall desorption process. We focus here on the α-process and find no significant shift of the dielectric T g as a function of layer thickness, in agreement with recent dielectric experiments. These findings can be correlated with the importance of the dihedral dynamics for all relaxation processes in polymers, which is unaltered except for the first nanometer next to the walls.

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.

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

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 β relaxation and for the time-temperature superposition principle (TTSP) of the α relaxation, and we also discuss deviations from these predictions for T ≈ 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 β regime. Within MCT a key quantity, in addition to T c, is the exponent parameter λ. For the fully flexible polymer models studied we find that λ is independent of N and has a value (λ = 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 (∞) . This increase can be described by T c (∞) - T c(N) ∼ 1/N and may be interpreted in terms of the N dependence of the monomer density ρ, if we assume that the MCT glass transition is ruled by a soft-sphere-like constant coupling parameter Γ c = ρ c T c (-1/4), where ρ 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.

Slow process in confined polymer melts: layer exchange dynamics at a polymer solid interface

Employing Molecular Dynamics simulations of a chemically realistic model of 1,4-polybutadiene between graphite walls we show that the mass exchange between layers close to the walls is a slow process already in the melt state. For the glass transition of confined polymers this process competes with the slowing down due to packing effects and intramolecular rotation barriers.

Influence of the torsional potential on the glass transition temperature and the structure of amorphous polyethylene

The effect of the torsional potential on several thermodynamic and structural properties of a system of polyethylene chains has been analyzed. To this end, molecular dynamics simulations of a coarse-grained model, whose sites interact through a force field with bending, torsional, and nonbonded terms, have been considered. The torsional potential has three stable configurations: gauche-, trans, and gauche+ . It has been modeled using a simple functional form with only two parameters: the trans-gauche and the gauche-gauche energy barriers. In order to analyze the influence of these parameters on the properties considered in this work, five models with different values of the torsional barriers have been considered. We have observed that the glass transition temperature, the intrachain radial distribution function, the radius of gyration, and the end to end distribution functions are very sensitive to the changes in the trans-gauche torsional barrier. Moreover, at low temperatures, the interchain radial distribution function, the orientational correlation function, and the volume distribution functions of the Voronoi polyhedra, that surround every site of the polymeric chains, also depend on the trans-gauche torsional barrier. On the contrary, the gauche-gauche energy barrier has a minor influence in the properties considered in this work.

Structural properties of crystallizable polymer melts: Intrachain and interchain correlation functions

We present results from constant pressure molecular-dynamics simulations for a bead-spring model of a crystallizable polymer melt. Our model has two main features, a chemically realistic intrachain rigidity and a purely repulsive interaction between nonbonded monomers. By means of intrachain and interchain structure factors we explore polymer conformation and melt structure above and below the temperature T{crys}{hom} of homogeneous crystallization. Here, we do not only determine average spatial correlations, but also site-specific correlations which depend on the position of the monomers along the polymer backbone. In the liquid phase above T{crys}{hom} we find that this site dependence can be well-accounted for by known theoretical approximations, the Koyama distribution for the intrachain structure and the polymer reference interaction site model (PRISM) for the interchain structure. This is no longer true in the semicrystalline phase. Below T{crys}{hom} short chains fully extend upon crystallization, whereas sufficiently long chains form chain-folded lamellae which coexist with amorphous regions. The structural features of these polymer crystals lead to violations of premises of the Koyama approximation or PRISM theory so that both theoretical approaches cannot be applied simultaneously. Furthermore, we find a violation of the Hansen-Verlet freezing criterion; our polymer melt crystallizes more easily than a simple liquid. This hints at the importance of the coupling between conformation (backbone rigidity) and density (packing constraints) for polymer crystallization.

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.

General relationships between the mobility of a chain fluid and various computed scalar metrics

We performed molecular dynamics simulations of chain systems to investigate general relationships between the system mobility and computed scalar quantities. Three quantities were found that had a simple one-to-one relationship with mobility: packing fraction, potential energy density, and the value of the static structure factor at the first peak. The chain center-of-mass mobility as a function of these three quantities could be described equally well by either a Vogel-Fulcher type or a power law equation.