Rheology and Dynamics of Associative Polymers in Shear and Extension: Theory and Experiments
Division of Engineering, Brown University, Providence, Rhode Island 02916; School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore; and Department of Mechanical Engineering, M.I.T., Cambridge, Massachusetts 02139
Received July 22, 2005
Revised Manuscript Received November 16, 2005
We investigate the steady and transient shear and extensional rheological properties of a series of model hydrophobically modified ethoxylate-urethane (HEUR) polymers with varying degrees of hydrophobicity. A new nonlinear two-species network model for these telechelic polymers is described which incorporates appropriate molecular mechanisms for the creation and destruction of elastically active chains. Like other recent models we incorporate the contributions of both the bridging chains (those between micelles) and the dangling chains to the final stress tensor. This gives rise to two distinct relaxation time scales: a short Rouse time for the relaxing chains and a longer network time scale that depends on the aggregation number and strength of the micellar junctions. The evolution equations for the fraction of elastically active chains and for the conformation tensors of each species are solved to obtain the total stress arising from imposed deformations. The model contains a single adjustable nonlinear parameter and incorporates the nonlinear chain extension, the shear-induced enhancement of associations, and the stretch-induced dissociation of hydrophobic chains. In contrast to earlier closed-form models, we are able to obtain quantitative agreement between experimental measurements and the model predictions for three different series of telechelic polymers over a range of concentrations. The scaling of both the zero shear viscosity and the effective network relaxation time shows good agreement with those measured in experiments. The model also quantitatively captures both the shear thickening and subsequent shear thinning observed in the rheology at high deformation rates and predicts transient extensional stress growth curves in close agreement with those measured using a filament stretching rheometer.