Rouse mode analysis of chain relaxation in polymer nanocomposites.

Jagannathan T Kalathi,Sanat K Kumar,Michael Rubinstein,Gary S Grest

doi:10.1039/c5sm00754b

Abstract

Large-scale molecular dynamics simulations are used to study the internal relaxations of chains in nanoparticle (NP)/polymer composites. We examine the Rouse modes of the chains, a quantity that is closest in spirit to the self-intermediate scattering function, typically determined in an (incoherent) inelastic neutron scattering experiment. Our simulations show that for weakly interacting mixtures of NPs and polymers, the effective monomeric relaxation rates are faster than in a neat melt when the NPs are smaller than the entanglement mesh size. In this case, the NPs serve to reduce both the monomeric friction and the entanglements in the polymer melt, as in the case of a polymer-solvent system. However, for NPs larger than half the entanglement mesh size, the effective monomer relaxation is essentially unaffected for low NP concentrations. Even in this case, we observe a strong reduction in chain entanglements for larger NP loadings. Thus, the role of NPs is to always reduce the number of entanglements, with this effect only becoming pronounced for small NPs or for high concentrations of large NPs. Our studies of the relaxation of single chains resonate with recent neutron spin echo (NSE) experiments, which deduce a similar entanglement dilution effect.

Highlights

In our previous studies, using molecular dynamics (MD) simulations, we showed that the shear viscosity of a polymer melt can be significantly reduced when it is filled with small energetically neutral NPs.[19]
The Rouse mode results on effectively athermal nanocomposites show that, in the case of short chains, the NPs only affect the monomer friction, and that too only for NPs that are comparable in size to a solvent molecule or a monomer
As in the case of the short chains, we find a renormalization of the monomer friction on the addition of small NPs, but no such modification for NPs larger than half the entanglement mesh size

Summary

Introduction

Adding nanoparticles (NPs) to polymer matrices can substantially enhance their optical, mechanical and thermal properties.[1,2,3] The resulting polymer nanocomposites (PNCs) have found widespread use in e.g., packaging[4,5] and solar cells.[6,7,8] As a consequence there have been many investigations[9,10,11,12,13,14,15,16,17,18] to understand the dynamics of polymers in nanocomposites to optimize properties and to facilitate their processing. Since polymer chains relax over a wide range of time and length scales, it is important to understand how the presence of NPs in polymer composites affects their relaxations across these different length and time scales. The diffusivities of the NP in a polymer melt are found to be strongly dependent on their size.[21] For NPs smaller than the polymer’s entanglement mesh size, the relaxation times and NP diffusivity are described by the Stokes–Einstein relationship, where the viscosity is set by the segment of polymer chain with end-to-end distance comparable to the NP diameter. For NPs with diameters larger than the entanglement mesh size it appears that the competition of full chain relaxation vs NP hopping through entanglement gates controls NP diffusion22 – there is no ready means to apply the Stokes–Einstein formula here

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Conclusion