Granular Matter

, 20:9 | Cite as

Granular sphere-chain relaxation dynamics to interpret polymer-nanocomposite glass transition temperatures

  • Ahmad Mohaddespour
  • Reghan J. Hill
Original Paper


Free volume and polymer chain architecture play important roles in controlling the glass transition temperature \(T_g\) of polymer nanocomposites. Various changes in \(T_g\) with respect to nanoparticle (NP) loading have been reported, depending, in part, on whether there are attractive or repulsive interactions between the polymer and NPs. However, even with no enthalpic interaction, there are ostensible changes in \(T_g\) that must be attributed to topological factors, such as chain stiffness and nanoparticle size. Here we adopt a macroscopic granular model to help understand frustrated dynamics in glassy polymer nanocomposites. Mixtures of granular chains with spherical inclusions were prepared with prescribed sphere size, chain length, and mixture composition. We measured the time to reach a close–packed, jammed state when these composites were subjected to controlled mechanical shaking. The compaction dynamics reveal that spherical inclusions profoundly influence the chain relaxation dynamics. In the long-chain limit, increasing the NP loading furnishes a minimum in the chain relaxation time, which may be loosely associated with an intermediate minimum in \(T_g\) with respect to nanoparticle loading for polymer nanocomposites. This minimum occurs for spheres having different sizes, but only at concentrations where the characteristic sphere separation is comparable to the chain loop size. This observation may explain the variety of contrasting trends that have been found in the literature for the dependence of \(T_g\) on nanoparticle loading in polymeric nanocomposites.



Funding was provided by Natural Sciences and Engineering Research Council of Canada (Grant No. RGPIN 262785-08).

Funding R.J.H. gratefully acknowledges support from the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Canada Research Chairs program. A.M. thanks the Faculty of Engineering, McGill University, for support through a McGill Engineering Doctoral Award (MEDA).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Authors and Affiliations

  1. 1.Department of Chemical EngineeringMcGill UniversityMontrealCanada

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