Sticky dumbbells: from Hookean dumbbells to transient network

The Green-Tobolsky theory of transient networks is merged to the Hookean dumbbell model by considering Hookean sticky dumbbells, whose beads can randomly be stuck to a network submitted to affine deformation, or be set free from the network and undergo a free diffusive Brownian motion in the solvent. Sticking to and releasing from the network is treated as an instantaneous chemical reaction. This model has a closed-form solution, in which the stress is the sum of two (resp. three) Maxwellian codeformational relaxations for dumbbells with one (resp. two) sticking beads. When Brownian diffusion is faster than the chemical kinetics, one of the modes of two-sticking beads dumbbells is the Green-Tobolsky network relaxation, whereas the other modes correspond to fast configurational relaxations. In the opposite limit of fast chemical kinetics compared to Brownian relaxation, the effect of the network is to slow down the configurational response of Hookean dumbbells. Sticky dumbbells thus realise a continuous transition from Hookean dumbbells to transient networks.