Molecular dynamics (MD) is used to simulate a model atactic poly(methyl methacrylate) (PMMA) system in which carbon nanotubes (CNTs) have been randomly dispersed. Our purpose is to elucidate the equilibrium structure and dynamic behavior of PMMA chains at the interface with a CNT. CNTs with different diameters and at different concentrations in the host PMMA matrix are studied, and their effect on the equilibrium squared radius-of-gyration and squared end-to-end distance of PMMA chains is examined. We have analyzed PMMA density, structure, and conformation both axially and normal to the CNT surface. Our MD simulations indicate that the presence of CNTs causes a small decrease in the size of the polymer chains, which becomes more pronounced as the concentration (volume fraction) and diameter of CNTs in the nanocomposite increases. We also provide a detailed analysis of adsorbed PMMA chain conformations in terms of trains, loops, and tails, and their statistical properties. An important finding of our work is that PMMA chains tend to penetrate significantly into the CNTs through their faces; as a result of CNT filling by PMMA chains, the area near the CNT mouths is characterized by significantly higher polymer mass density (almost by 45%) than the bulk of the nanocomposite. Additional simulation results for local and terminal relaxation in the PMMA-CNT nanocomposites reveal that due to strong PMMA-CNT attractive forces, all relaxation times in the interfacial region are significantly prolonged in comparison to the bulk, and the same happens with the diffusive (translational) motion of the chains. The density profile that develops (both axially and radially) in the vicinity of CNTs appears to significantly delay PMMA dynamics at all length scales. How this affects the glass-transition temperature of the nanocomposite is also analyzed.

Delaunay tessellation followed by Monte Carlo integration is employed in order to determine the clusters of sites where a hard-sphere penetrant of radius r p equal to a few Angstroms can reside in model carbon nanotube-atactic poly-(methyl-methacrylate) (CNT-PMMA) nanocomposite microstructures and analyze their dependence on penetrant size and temperature. Starting configurations for the geometric analysis are generated by cooling down to lower temperatures the atomistic structures fully equilibrated at a higher temperature by means of a long molecular dynamics simulation and re-equilibrating. Because the tetrahedra formed in the process of the Delaunay tessellation are irregular in space, an analytical calculation of free volume is a tough problem; to overcome this, we resort to Monte Carlo integration. By accounting for the volume occupied by polymers and CNT atoms, we obtain estimates of the unoccupied volume as well as of the volume accessible to a spherical penetrant of a given radius within each tetrahedron. From this, we calculate next the distribution of the volume and size of the corresponding cavities and of their clusters. By identifying neighboring clusters of tetrahedra that are mutually accessible to a given penetrant using a connectivity algorithm very similar to that proposed by Greenfield and Theodorou [Macromolecules, 1993, 26, 5461−5472], we quantify the network of clusters formed and determine probable pathways for diffusion for the penetrant under study.

Detailed molecular dynamics (MD) simulations of model single-walled carbon nanotube (CNT) membranes based on atactic poly­(methyl methacrylate) (aPMMA) indicate that PMMA chains significantly penetrate nanotubes through their faces. They predict very high-density values of the polymer in the interfacial area around the CNT mouths that can exceed by 50% the density of the bulk polymer at the same thermodynamic conditions. This dramatically decreases the diffusivity of relatively small penetrants (in our study, water molecules) in the nanocomposite membrane, because of the exceedingly long times needed by these small molecules to diffuse through such a dense interfacial layer before accessing the interior of the nanotubes where they can travel really fast. According to our simulations, the escape time of a confined water molecule from the blocked mouths of a CNT can exceed by several orders of magnitude the time needed by the same molecule to move through the CNT pore. Our work indicates the importance of completely avoiding (or at least minimizing) penetration of polymer chains into the CNT pores through the mouths of the tubes in enabling the efficient transport of small- to moderate-size molecules in model CNT-based polymer membranes, since this provides the highest resistance to their mobility through the membrane.