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.

Poly(methyl-methacrylate), PMMA, is a disubstituted vinyl polymer whose properties depend significantly on its tacticity. Here we present a detailed study of the structure, conformation, and dynamics of syndiotactic, atactic, and isotactic PMMA melts at various temperatures (580, 550, 520, and 490 K) via all-atom molecular dynamics simulations. The calculated volumetric properties are close to experimental data. The T and chain dimensions of PMMA model systems are found to depend strongly on tacticity in agreement with experimental findings. The backbone bonds in trans (t), diads in tt, and inter-diads in t|t torsional states are the most populated for all PMMA stereo-chemistries and their fractions increase with the number of syndiotactic sequences. Also, the effective torsional barrier heights for the backbone, ester side group, and α-methyl group are larger for syndiotactic PMMA compared to the isotactic one. The structure of the PMMA chains is studied by computing the intra- and inter-chain static structure factors, S(q), and the radial pair distribution functions. In the first peak of S(q), both intra- and inter-chain components contribute, whereas the second and third peaks mainly come from inter- and intra-chain parts, respectively. For all PMMA stereo-isomers a clear tendency of ester-methyl groups to aggregate is observed. The local dynamics are studied by analyzing torsional autocorrelation functions for various dihedral angles. A wide spectrum of correlation times and different activation energies are observed for the motions of different parts of PMMA chains. The stereo-chemistry affects the backbone, ester side group, and α-methyl motions, whereas the ester-methyl rotation remains unaffected. The dynamic heterogeneity of the PMMA chains is also studied in detail for the different stereo-chemistries via the temperature dependence of the stretching exponent. Furthermore, the reorientational dynamics at the chain level and translational dynamics for monomer and chain centers-of-mass are analyzed.

A detailed analysis of the structure and conformation of stereoregular and atactic poly­(methyl methacrylate) (PMMA) chains confined between oxidized graphene sheets is provided through long-time atomistic molecular dynamics simulations. Low-molecular-weight isotactic-, atactic-, and syndiotactic-PMMA chains confined between graphene oxide (GO) and reduced graphene oxide (RGO) sheets have been simulated at different temperatures ranging from 520 to 580 K. The interfacial properties of PMMA/pristine graphene (PG) are also discussed. GO and RGO structures have been generated based on the Lerf–Klinowski structural model of graphite oxide with carbon-to-oxygen ratios of 3 and 10, respectively. The interfacial packing and adsorption of PMMA chains on PG, RGO, and GO model surfaces are studied through the calculation of interfacial mass density profiles and distribution of monomer/surface distance. Furthermore, the arrangement of PMMA atoms in the vicinity of functional groups of nanosheets and their hydrogen bond formation are investigated. The conformations of adsorbed chains, that is, chains with at least one adsorbed monomer, are analyzed in detail as trains, loops, and tails. It is observed that the number of adsorbed monomers and the average size of trains, that is, consecutive adsorbed monomers of a chain, increase with the concentration of functional groups of the nanosheets. This is related to the strength of the polymer/substrate interactions and the increase of the roughness of model nanosheets which enhances the probability of polymer/surface contacts. The tacticity-dependent adsorption of PMMA chains is also examined in detail. Isotactic-PMMA chains, compared to atactic and syndiotactic ones, exhibit a better interfacial packing and form longer trains. i-PMMA chains are stiffer and, moreover, become more extended in the vicinity of model surfaces. The formation of longer trains by isotactic stereoisomers is found to be consistent with their higher stiffness, that is, higher characteristic ratio and gyration radius. Results reported here suggest a clear correlation between chain dimensions, size of trains, and interfacial packing of the adsorbed PMMA chains.