Polyacrylamide hydrogels. IV. Near-perfect elasticity and rate-dependent toughness

A polyacrylamide hydrogel exhibits near-perfect elasticity: its stress-stretch curve is rate-independent and has negligible hysteresis. The near-perfect elasticity results from the large amount of water between the polymer chains. Water has low viscosity and lubricates polymer chains. Here we report that the polyacrylamide hydrogel exhibits rate-dependent toughness when the polymer chains are long. We interpret this finding as follows. Toughness is measured by rupturing a hydrogel containing a precut crack. When the hydrogel is stretched, at the crack tip, some polymer chains slide relative to others. Before a polymer chain breaks, high tension is distributed over a long length of the chain. Breaking the chain releases the energy stored in the long length of the chain. It is this deconcentration of tension that toughens the hydrogel. When the hydrogel is stretched at a high rate, however, the polymer chain at the crack tip does not have time to slip fully, so that the high tension only transmits over a short segment of the chain. Breaking the chain will lead to a lower toughness. Consequently, the toughness decreases as the stretch rate increases. We invoke a shear lag model and find that the toughness scales with stretch rate as G_c ∼ (dλ/dt)^−1/4.