Stress and birefringence measurements during the uniaxial elongation of polystyrene melts

Abstract

A rheometer for generating uniaxial elongations in molten polymers has been modified to allow for the simultaneous measurement of stress and flow-induced birefringence. Tensile stress σ and birefringence Δn′ data in flows at constant strain rates up to 1 s−1 were collected on a polydisperse polystyrene melt at temperatures of 160 and 170 °C. From these data, the stress-optic rule was followed for stresses below roughly 1 MPa. For stresses less than 1 MPa, the stress-optic coefficient |C|=|Δn′|/σ was found to have a value of 4.8×10−9 Pa−1, which was independent of strain, strain rate, and temperature. At stress levels higher than 1 MPa, |C| decreased indicating a failure of the stress-optic rule. A criteria for failure of the stress-optic rule was formulated using simple arguments from network models and characteristic times suggested by the tube model. This criteria, which is based on the hypothesis that failure of the stress-optic rule is the result of significant chain stretching, was found to be consistent with the data reported in this study and with data from previous studies on polystyrene melts.

Validity of the linear stress optical rule in mono-, bi- and polydisperse systems of entangled linear chains

“…Experimentally, the validity of the SOR has been verified in shear and uniaxial flows [4,9,10,[13][14][15][16][17]. In shear flows, the SOR is observed to hold for different polymer systems, based on the mechanically and optically measured viscosity (although the fully non-linear regime could not be reached optically).…”

“…[5,7] or a cross-slot flow [2,7]. However, a deviation from the linear relationship between the refractive index tensor and the stress tensor occurs for a large degree of stretch in the chain [6,[8][9][10], at temperatures well above the glass transition [11,12].…”

Welding Flow of Low Density Polyethylene Melt

“…There are many reports on viscoelastic flow birefringence phenomenon [5][6][7][8][9], while not many studies treat welding flows. Baaijens et al [10] studied viscoelastic flows past a cylinder by both flow birefringence experiments using low density polyethylene melts and a numerical simulation.…”

Correction of Doi-Edwards' Green function for a chain in a harmonic potential and its implication for the stress-optic rule

“…If the polymer chain is stretched beyond the Gaussian regime, SOR is violated because of the breakdown of the linear relation between the traction and the end-to-end length of the strand. 3,4 The tube model of entangled polymers assumes that the lateral motion of the polymer chain in the melt is prohibited, as if the chains were confined in a tube-like domain. 6 The origin of the stress of the material is usually assumed to be the traction force of the chain strand along the tube.…”

“…[1][2][3][4] This linear relation is called the stress-optic rule (SOR). 2 For Gaussian chains, the traction force of a chain strand whose ends are constrained by entanglements is a linear function of the strand's end-to-end vector, so that the stress tensor of the polymer melt is proportional to the second-moment of the strand's orientation vector.…”