The Elastic Response of Wire Frame Glasses.

This talk considers the elastic response of concentrated suspensions of rigid wire frame particles to a step strain. These particles are constructed from infinitely thin, rigid rods of length L. We specifically compare straight rod-like particles to bent and branched wire frames. In dense suspensions the wire frames are frozen in a disordered state by the topological entanglements between their arms. We present a simple, geometric method for finding the scaling of the elastic stress with concentration in these glassy systems. The behaviour of wire frames is found to be strikingly different from that of rods. The linear elasticity scales like ρ³L⁶ for wire frames, whereas it scales proportional to ρ for rods, where ρ is the number density. The character of the non-linear response is also markedly different.  Wire frame suspensions shear harden below a critical density dependent on the bending modulus of the particles. Suspensions of rods, on the other hand, always shear thin. The reason for these differences is that wire frames can be forced to bend by the entanglements with their surroundings, whereas rods always remain straight. This is found to be very important even for small strains, with most particles being bent above a critical strain γ_c ∼(ρL³)^-1.