Equilibration and deformation of glass-forming polymers : molecular simulation via connectivity-altering Monte Carlo and scale-jumping methods

A deep understanding of the structure and dynamics of glasses poses a great challenge in soft condensed matter physics. On approaching the glass transition the molecular relaxation times in simple glass-formers are observed to grow to such an extent that these systems do not reach thermal equilibrium on experimentally accessible time scales. For polymers with complex microstructure the problem of the glass transition is even more difficult. While universal features of glassy dynamics should exist, superimposed chemistry-specific aspects do lead to apparently widely different behavior, such as brittle (e.g. polystyrene) vs. very ductile (e.g. polycarbonate) macroscopic failure. A better understanding of the mechanical properties of amorphous polymers is essential both for predicting the material properties after polymer processing and for the development of new materials. The objective of this thesis project is to bridge the gap between current continuum multilevel finite-element polymer modeling and coarse-grained mesoscopic network modeling of amorphous polymers on the one hand, and molecular chemistry insights on the other hand. Suitable tools for exploring the structure and properties of bulk amorphous polymers at the molecular level are molecular dynamics (MD) and Monte Carlo (MC). One serious drawback however of many detailed MD or MC simulations of chemically-specific polymers is the problem of preparing well-equilibrated initial samples when approaching the glass transition. The result is an inefficient sampling of phase space and unreliable estimations of both statistical and dynamical properties. For a few simple linear polymers this problem had been solved by the development of connectivity-altering MC (CAMC) algorithms. We use such an algorithm to obtain a well-equilibrated polyethythylene (PE) sample in the melt. Subsequently the sample is cooled into the glassy state and deformed uniaxially, see Chapter 3. Typical experimental stress-strain curves, with E-moduli, yield-stresses, Poisson ratios of the correct order of magnitude, are found. Also dependencies on temperature, strain rate and cooling rate show the right trends. In addition the simulations provide a window into the material. More insight into molecular-level processes during polymer deformation has been obtained both from separating contributions of different interactions to stress and energy at varying strain and by studying the evolution of the structure on all sub-continuum length scales. Special attention was given to the selection of a suitable implementation of deformation in the simulations; various deformation methods have been compared, see Chapter 4. In this respect also the possibility to constrain the hard degrees of freedom, in order to save CPU time, has been looked into. It is found that the combination of constrained bonds with simple deformation protocols, in which positions of monomers or chains are scaled with the sample size, are not adequate for the simulation of polymer deformation; typical features of amorphous polymer mechanical behavior are then not reproduced. Since PE is only one polymer and one of the main purposes of the project was to study and compare various chemically different polymers, we generalized the CAMC algorithm for PE to one for a broad class of linear polymers, see Chapter 5. This could be done by describing the polymers at a slightly coarse-grained (CG) level, such that the functional form of the force field becomes similar for all these polymers. By this approach the polymers are equilibrated at the CG level. Especially the distribution of intra-chain distances is important: from this we can judge whether the polymer chains adopt conformations that can be described as Gaussian chains of Kuhn segments (Flory’s theorem). After equilibration at the CG level atomistic details are reintroduced, see Chapter 6, and the polymers are equilibrated on the length scales of the atomistic details as well. In the present work this whole procedure is followed for atactic PS as an example. Extensive comparisons with literature demonstrate that our approach results in microstructures that show much similarity to those in experimentally known PS. Finally, the effect of sample preparation on the stress-strain relations for glassy polystyrene as obtained from atomistic molecular-dynamics simulations has been studied, see Chapter 7. A conventional sample-preparation method ("extended-chain condensation", ECC) that is based solely on molecular-dynamics simulations has been compared to the method ("coarse-grained end-bridging", CGEB) involving connectivity-altering (end-bridging) Monte Carlo and coarse graining. The stress-strain relations are different in the strainhardening regime. For samples prepared according to the CGEB method a stronger strain hardening is observed and the modulus is more realistic. These differences have to be attributed to the fact that screening of excluded-volume interactions is not properly taken into account in ECC, which results in too compact chain conformations.