Comparison of optical and mechanical measurements of second normal stress difference relaxation following step strain

Abstract

Relaxation of the second normal stress difference (N ₂) following step strain of a concentrated monodisperse polystyrene solution has been studied using mechanical and optical rheometry. Measurements of normal thrust in a parallel plate geometry are corrected for strain inhomogeneity and combined with independent measurements of the first normal stress difference (N ₁) to determine N ₂. Optical experiments were performed using a novel configuration where flow birefringence data collected using multiple light paths within the shear plane are combined with the stress-optical law to determine all three independent stress components for shearing deformations. This technique eliminates end effects, and provides an opportunity to oversample the stress tensor and develop consistency checks of experimental data. N ₂ is found to be nonzero at all accessible times, and relaxes in roughly constant proportion to N ₁. This reflects nonaffine distribution of chain segments, even well within the regime of chain retraction at short times. Data collected with the two techniques are reasonably consistent with each other, and with results of previous studies, generally lying between the predictions of the Doi-Edwards model with and without the independent alignment approximation. The normal stress ratio −N ₂/N ₁ shows pronounced strain thinning in the nonlinear regime.