Large Network Swelling and Solvent Redistribution Are Necessary for Polymer Gels to Show Negative Normal Stress

We use a statistical thermodynamic model to theoretically predict the normal stress of a polymer gel, which is twisted by a rotational rheometer in the parallel plate geometry. This theory predicts that the normal stress of the gel is positive at a short time scale. At longer time, the normal stress decreases significantly due to the redistribution of solvent, but is still positive when the polymer network is in the neo-Hookean regime. The normal stress becomes negative when the polymer network is greatly prestretched in the swelling process because large tension is generated by shearing already prestretched polymers. Our theory predicts the phase diagram with respect to the direction of normal stress as functions of the aspect ratio and swelling ratio of gels. Experimental tests on this prediction may advance our understanding of the physical mechanisms involved in the negative normal stress generated by polymer gels.