The shear modulus G of two glass-forming colloidal model systems in d = 3 and d = 2 dimensions is investigated by means of, respectively, molecular dynamics and Monte Carlo simulations. Comparing ensembles where either the shear strain γ or the conjugated (mean) shear stress τ are imposed, we compute G from the respective stress and strain fluctuations as a function of temperature T while keeping a constant normal pressure P . The choice of the ensemble is seen to be highly relevant for the shear stress fluctuations µF(T ) which at constant τ decay monotonously with T following the affine shear elasticity µA(T ), i.e. a simple two-point correlation function. At variance, non-monotonous behavior with a maximum at the glass transition temperature Tg is demonstrated for µF(T ) at constant γ. The increase of G below Tg is reasonably fitted for both models by a continuous cusp singularity, G(T ) ∝ (1 − T /Tg) 1/2 , in qualitative agreement with some recent replica calculations. It is argued, however, that longer sampling times may lead to a sharper transition. The additive jump discontinuity predicted by mode-coupling theory and other replica calculations thus cannot ultimately be ruled out.

A hierarchical (triple scale) simulation methodology is presented for the prediction of the dynamical and rheological properties of high molecular-weight entangled polymer melts. The methodology consists of atomistic, moderately coarse-grained (mCG), and highly coarse-grained slip-spring (SLSP) simulations. At the mCG level, a few chemically bonded atoms are lumped into one coarse-grained bead. At this level, the chemical identity of the underlying atomistic system and the interchain topological constraints (entanglements) are preserved. The mCG interaction potentials are derived by matching local structural distributions of the mCG model to those of the atomistic model through iterative Boltzmann inversion. For matching mCG and atomistic dynamics, the mCG time is scaled by a time scaling factor, which compensates for the lower monomeric friction coefficient of the mCG model than that of the atomistic one. At the SLSP level, multiple Kuhn segments of a polymer chain are represented by one coarse-grained bead. The very soft nonbonded interactions between beads do not prevent chain crossing and, hence, can not capture entanglements. The topological constraints are represented by slip-springs, restricting the lateral motion of polymer chains. A compensating pair potential is used in the SLSP model to keep the static macromolecular properties unaltered upon the introduction of slip-springs. The static and kinetic parameters of the SLSP model are determined based on the lower-level simulation models. Particularly, matching the orientational autocorrelation of the end-to-end vector, we determine the number of slip-springs and calibrate the timescale of the SLSP model. As a test case, the hierarchical methodology is applied to cis-1,4-polybutadiene (cPB) at 413 K. Dynamical single-chain and linear viscoelastic properties of cPB melts are calculated for a broad range of molecular weights, ranging from unentangled to well-entangled chains. The calculations are compared, and found in good agreement, with experimental data from the literature.

The conformations and the dynamics of poly­(butadiene) (PB) chains, of various molecular weights, in PB/silica nanocomposites are studied through long-time atomistic molecular dynamics simulations at T = 413 K, well above T g. The effect of the stereochemistry of PB chains is addressed by simulation of cis-1,4-PB/silica and trans-1,4-PB/silica nanocomposites. The model systems contain 30 wt % (≈12 vol %) silica nanoparticles (NPs) of diameter ≈4 nm. The nanocomposites are characterized through analyzing (i) interfacial packing and the dimensions of the PB chains; (ii) statistics of the train, bridge, loop, and tail conformations of adsorbed chains and the coupling between segmental orientational dynamics and chain conformations; and (iii) the orientational and translational dynamics of the polymer chains and the desorption kinetics of chains and segments. The dimensions of PB chains, excluding a small fraction of chains that wrap around the NP, are not affected. The segmental and terminal dynamics of PB chains are slower in the nanocomposites than in the respective bulk melts. Moreover, the dynamics of PB chains in the nanocomposites is very heterogeneous, and a coupling between the dynamics and the conformation of PB chains is observed: the adsorbed segments (trains) and the chains that have a higher number of contacts to the NPs are more decelerated. Additionally, at long times, bridge segments exhibit a very slow orientational decorrelation. The self-diffusion coefficients, D, of PB chains in the nanocomposites are also reduced compared to the respective bulk systems. A clear crossover from the unentangled (Rouse-like) to the entangled (reptation-like) regime is observed based on the calculation of the segmental mean-square displacement and D as a function of the chain length. The effective tube diameter of entangled PB chains in the nanocomposites is estimated to be slightly smaller than in the pure melts. The deceleration of dynamics in the nanocomposites, in both Rouse and reptation-like regimes, is discussed in terms of a higher effective monomeric friction coefficient. Finally, the correlation times for the desorption of segments and chains are much larger than the segmental and end-to-end-vector correlation times, respectively.