Simulated glass-forming polymer melts: glass transition temperature and elastic constants of the glassy state

By means of molecular-dynamics simulation we study a flexible and a semiflexible bead-spring model for a polymer melt on cooling through the glass transition. Results for the glass transition temperature T(g) and for the elastic properties of the glassy state are presented. We find that T(g) increases with chain length N and is for all N larger for the semiflexible model. The N dependence of T(g) is compared to experimental results from the literature. Furthermore, we characterize the polymer glass below T(g) via its elastic properties, i.e., via the Lamé coefficients λ and μ. The Lamé coefficients are determined from the fluctuation formalism which allows to split λ and μ into affine (Born term) and nonaffine (fluctuation term) contributions. We find that the fluctuation term represents a substantial correction to the Born term. Since the Born terms for λ and μ are identical, the fluctuation terms are responsible for the different temperature dependence of the Lamé coefficients. While λ decreases linearly on approaching T(g) from below, the shear modulus μ displays a much stronger decrease near T(g). From the present simulation data it is not possible to decide whether μ takes a finite value at T(g), as would be expected from mode-coupling theory, or vanishes continuously, as suggested by recent work from replica theory.