(474j) Predicting the Yield Stress of Solvent-Free Nanoparticle Fluids Resulting From Configurational Entropy of Tethered Space-Filling Oligomers

The yield stress is determined for a solvent-free nanoparticle fluid system known as nanoparticle-organic hybrid materials (NOHMs). These materials consist of inorganic spherical nanoparticle cores (with diameters of about 10 nm) with dense brushes of tethered oligomers and no unattached molecular solvent. Despite their solvent-free nature, these materials have been observed to flow when subject to stresses exceeding a yield stress. In this paper we will derive the yield stress resulting from the oligomer mediated many-core interactions. The oligomers are modeled as bead-soft-springs tethered to the surfaces of cores which form an incompressible liquid filling the interstices between the cores. The configuration of the oligomers for a given core configuration is determined by minimizing the configurational free energy of the oligomers subject to the constraint that the number of oligomer beads per unit volume be nearly constant. For simplicity we consider a periodic array of cores with an initial face centered cubic configuration which is then subjected to affine core motion in a simple shearing motion. The yield stress can be determined as the maximum slope of a plot of the free energy per volume with respect to strain. The predicted yield stress is high on the order many kPa and is intermediate between nk_BT and nMk_BT where n is the number of cores per unit volume and M is the number of oligomers per core and is thus intermediate between the entropic free energy of the particles and that of the oligomers. The theory predicts that the yield stress decreases with increasing core volume fraction and with increasing molecular weight. These surprising trends arise because oligomers can more easily fill the interstitial space when the interparticle spacing is smaller and when oligomer’s radius of gyration is larger. The predicted yield stress is compared with estimates based on oscillatory shear rheology by Agarwal et al. (Nano Lett. 2010, 10, 111-115) for core volume fraction of 0.111 and oligomer radii of gyration of 2.71 and 3.63 nm.