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

Abstract

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.

Quantitative relations between cooperative motion, emergent elasticity, and free volume in model glass-forming polymer materials

“…We can understand the physical grounds for this relation from the fact that the high-frequency plateau shear modulus G p can be directly related to hu 2 i, G p = 4k B T=πσhu 2 i through a Langevin model for the Brownian motion, with a Maxwell model of viscoelasticity incorporated to describe transient caging (23). Recent simulations of a coarse-grained polymer melt, similar to the model described in the present paper, found good conformity with this relation (38). The DebyeWaller factor hu 2 i measures monomer displacements on a time scale over which the particles are caged by their neighbors, and is thus accessible from both X-ray and neutron scattering measurements (39).…”

Communication: Polymer entanglement dynamics: Role of attractive interactions

“…No detectable difference in T g is observed for cooling at a rate of 10 −6 ε/k B τ compared to 10 −7 ε/k B τ. The increase in T g with increasing k θ agrees with Schnell et al 17 for N ≤ 32. Thus the previous studies [6][7][8][9] for this model are at a temperature T = ε/k B > 2T g .…”

Shear-stress relaxation and ensemble transformation of shear-stress autocorrelation functions

“…The static equilibrium shear modulus G eq [1][2][3][4][5][6][7] is an important order parameter [8][9][10] characterizing the transition from the liquid/sol (G eq = 0) to the solid/gel state (G eq > 0) where the particle permutation symmetry of the liquid state is lost for the time window probed [6,7]. Examples of current interest for the determination of G eq include crystalline solids [11], glass-forming liquids and amorphous solids [5,[12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27], colloidal gels [28], permanent polymeric networks [2,[29][30][31], hyperbranched polymer chains with sticky end-groups [32] or networks of telechelic polymers [33]. As emphasized by the thin horizontal line in Fig.…”