Excluded Volume Model for the Reduction of Polymer Diffusion into Nanocomposites

Abstract

An analytic model for the slowing down of polymer chain diffusion in nanocomposites attributable to excluded volume effects is presented. The nanocomposite is modeled as an ensemble of cylinders through which the polymer chains diffuse. The reduction of polymer diffusion in each cylinder is equated with the reduction of diffusion for a sphere through a cylinder. The distribution of cylinder diameters within the ensemble is determined from statistical mechanical theories based on the packing of spherical particles. For low loadings of spherical particles in nanocomposites, this model results in a master curve for the reduced diffusion coefficient. With no adjustable parameters, the model agrees with recent data for tracer diffusion measurements in polymer nanocomposites at low loading.

Modeling of Entangled Polymer Diffusion in Melts and Nanocomposites: A Review

“…An excluded volume analytical model predicts the decrease of polymer diffusion in nanocomposites, in agreement to experiments at low nanoparticle loading (lower I-0.166667emD/2Rg values) [215]. However, at higher loading (low I-0.166667emD/2Rg values), the model predicts a slower polymer diffusion than that observed in experiments as can be seen in Figure 17.…”

Polymer and spherical nanoparticle diffusion in nanocomposites

“…In a simplified model where polymer chains were modeled as spheres diffusing down cylindrical pores 95 , it was shown that excluded volume effects can account for the observed reduction in polymer diffusion for values of ID/2R g > 5. In that region, the excluded volume model predicted a pseudomaster curve for the reduced diffusion coefficients, in good agreement with experimental results 23,92 at higher nanoparticle loading.…”

Effect of Crosslinker Length and Architecture on the Thermomechanical Properties of CNT‐Loaded Elastomeric Polymer Matrix Composites

“…Various approaches to improve the particle‐matrix compatibility have been explored, including surface functionalization reactions to match the surface chemistry of the nanoparticles to the matrix (e.g., small molecules or short polymer chains) and covalent attachment of the particle to the polymer matrix . Several pioneers in this area, including Winey and co‐workers, have demonstrated that the nanoparticles stiffen their local surroundings, impact chain entanglements and excluded volume effects, and impart unique temperature dependence to polymer mobility and diffusion . The above strategies have experienced varying success, and all have the drawback of potentially 1) limiting the nanofiller function (e.g., the added surface groups can alter the intended function of the particle), 2) reducing the mechanical stability of the system (e.g., grafting short polymer chains can dramatically reduce the matrix glass transition temperature ( T g )), or 3) increase the system complexity beyond any practical implementation.…”