Local dynamics and deformation of glass-forming polymers : modelling and atomistic simulations

The research described in the present thesis is about glassy phenomena and mechanical properties in vitrifiable polymer materials. Glasses are solid materials, but, in contrast to crystals, the structure is disordered. Polymers are macromolecular chains formed by covalently linking a very large number of repeating molecular building blocks or monomers. Polymeric materials are easy to reshape and reuse. Also they are lightweight and often transparent. These characteristics make them ideal materials for commodity products such as compact discs, safety helmets, or vandal-proof glazing. Some glassy polymers are also biocompatible, so that they can be used in medical applications. For a successful usage of polymer glasses it is necessary to understand and predict their behaviour under various circumstances. Although many new insights have been acquired over the last decades still a lot of questions remain open. Upon vitrifying a polymer melt the relaxation times and the viscosity increase dramatically. Accompanied with this increase various glassy phenomena are observed — in particular dynamical heterogeneities and non-Gaussian displacements of particles. The comprehension of the striking viscosity increase and the two phenomena mentioned above is still far from complete. During the straining of a polymer glass typical mechanical characteristics are observed, of which the magnitude can vary enormously between different types of polymers. A wellknown example of a polymer glass is atactic polystyrene. In its glassy state polystyrene is usually found to be very brittle. Within a few percent of elongation the material breaks. This behaviour is caused by a relatively high yield tooth in combination with a relatively low strain-hardening modulus. Other polymers, such as bisphenol-A polycarbonate, show a tough response; a test bar can easily be extended to twice its original length. In spite of much study, the physical (molecular) origin of this difference in mechanical behaviour is still not clear. Below the glass transition rubber-elasticity theory appears to be invalid, as it fails to explain the observation that the strain-hardening modulus of polystyrene in its glassy phase is about two orders of magnitude higher than its modulus in the rubbery state. Our main goals are to acquire a better understanding at the molecular scale of heterogeneous and non-Gaussian dynamics and mechanical deformation of glassy polymers and to differentiate chemistry-specific from more universal physical properties. These goals are achieved by carrying out molecular-dynamics simulations on glass-forming systems. In addition, the results are elucidated by the usage of simple physical models. The simulations consist of solving the equations of Newton, a coupled set of differential equations with a given force field and initial conditions. The force field describes the interactions between the various particles. As the main interest is in glassy polymers, most simulations are done for a united-atom model of polystyrene. In the simulation run several characteristics of the glass transition are identified. As is typical for other vitreous systems as well, anomalous, non-Gaussian displacements play an important role near the glass transition for polystyrene; the same observation has been made for a dendritic melt and a colloid-like system. For all these systems of different architecture we have described some essential features of this non-Gaussian behaviour with a simple one-particle model in an effective field. The non-Gaussian behaviour is mainly caused by the cage-to-cage motion of the constituent particles, whereby the cage is formed by interactions with neighbouring particles. By means of the model the height of the so-called non-Gaussian parameter can be interpreted as a measure for the ratio of the root-mean-square displacement within the cage and the effective jump length between cages, without the assumption of any heterogeneity of glassy dynamics in the sense of sitespecific relaxation times. The maximum of the non-Gaussian parameter occurs in each case at the crossover from the cage regime to the (sub)diffusive regime and is connected to the cage-escape time. For the colloid-like system also the shape of the time-dependent non-Gaussian parameter is described well by the model (chapter 3). Dynamical heterogeneity, a phenomenon observed in many experiments on glasses, is also found in the simulation result of the polystyrene phenyl-ring-flip movement (to which the mechanical gamma relaxation is ascribed). This means that some phenyl rings behave very differently than others within a typical simulation run. Different relaxation times and activation enthalpies associated with the flip are determined using various methods. A particular result of the study of the phenyl flip is that an enthalpy barrier determined solely from structural properties is in accordance with an activation enthalpy acquired by analyzing the dynamics of the phenyl rings, even in the presence of dynamical heterogeneity. The heterogeneity arises because of the following mechanism. The conformation of the backbone determines to a large extent the barrier of the phenyl-ring flip. Eventually the relaxation of the backbone is becoming so slow upon cooling down that the phenyl ring is unable to access the conformation-dependent state with the lowest flip barrier within the corresponding barrier-jump time. The phenyl rings are trapped instead in various other states with accompanying different energy barriers. These states are available because of the disordered nature of the material. The mechanism just described for the heterogeneous dynamics in the phenyl-ring flip movement becomes stronger upon cooling down towards the glass transition; eventually the relaxation becomes more Arrhenius-like below the glass transition temperature because only the fastest phenyl flips occur within the accessible observation time (chapter 4). By doing uniaxial-stress extension and compression simulations the stress-strain relation of polystyrene has been measured under various conditions. Although the cooling and deformation velocities in the simulations differ many orders of magnitude from their values in usual experiments, the characteristic features of the experimental stress-strain relation are well reproduced, which allows one to study the origin of the yield tooth and strain hardening. It is observed that the strain-hardening modulus increases with increasing pressure, an effect not described by rubber-elasticity theory. Also it is observed that the thermal history is not completely erased by the mechanical deformation. The picture arising from this study is that the yield peak in polystyrene is mostly mediated by interchain energetic interactions. A net debonding of these interactions is likely causing this yield peak and the subsequent strain softening. The positiveness of the strain-hardening modulus in polystyrene is mainly due to intrachain interactions (chapter 5). From our comparative study of polystyrene and polycarbonate it can be concluded that strain hardening in polymer glasses such as these two polymers is likely caused mainly by the following mechanism. During uniaxial extension a glassy chain adopts a more stretched and hence more inflexible state, also at a local scale. Due to interactions with other particles non-affine displacements take place. The non-affine response is stronger at shorter length scales, but as the deformation proceeds and the effective flexibility decreases also longer length scales are affected. This is accompanied with more bond-altering processes and implies an increase in the rate of energy dissipation, causing in turn an increase in stress upon straining the polymer material further (chapter 6). All these results show that simple physical models supported and tested by results of molecular-dynamics simulations (in which typical physical phenomena observed in real experiments can be reproduced) provide a fruitful approach in understanding glassy materials