Mechanical response of networks formed by end-functionalised spherical polymer grafted nanoparticles

Via computer simulations we examine the mechanical response of hybrid polymer-particle networks composed of rigid spherical nanoparticles with long flexible polymer chains grafted onto their surface. The canopy of grafted polymer arms are end-functionalised such that interacting polymer-grafted nanoparticles (PGNs) form labile bonds when their coronas overlap. In the present study, the number of grafted arms, f, are such that the PGN brushes are in the small (f = 600) and intermediate curvature (f = 900 and 1200) regime with stable bonded interactions. To investigate the mechanical response of networks formed by these PGNs, controlled uniaxial elongation at a specified pulling rate is imposed on a 2-D network of PGNs placed on a hexagonal lattice. In the simulations, the force required to deform the network is measured as a function of the elongation and pulling rate imposed on the network until the network fails. By analysis of the force-strain curves and the rearrangement of the PGNs in the network we show that an increase in the number of grafted arms, pulling velocity and energy of the bonded interactions alters both the toughness and the mode of failure of the networks. In particular, we show that an increase in the number of grafted arms results in a reduction of toughness. Furthermore, analysis of the simulations of force relaxation after rapid extension indicates that the relaxation in deformed networks can be characterised by one or two time scales that depend on the number of grafted arms. The analysis of force-strain curves and force relaxation demonstrate the role of Deborah number, De, and the limitations in the use of a unique De in understanding the mechanical response of the networks respectively.