Prediction of Frozen-In Birefringence in Oriented Glassy Polymers Using a Molecularly Aware Constitutive Model Allowing for Finite Molecular Extensibility

Abstract

A study has been made of birefringence in oriented glassy polystyrene. The aim was to develop a methodology for the prediction of birefringence in glassy polymers with frozen-in molecular orientation. The predictive approach employed was to use a recently proposed constitutive model, consisting of a coupling between the Likhtman-Graham Rolie-Poly model for polymer melt rheology and a previously established model for polymer glasses. The methodology was validated with an experimental study of oriented glassy polystyrenes with known melt-stretching histories. It was found that, for orientation processes sufficiently far above T g (i.e., not including subentanglement stretch), birefringence could be predicted accurately in monodisperse materials.

A toolbox for parameter‐free predictions of solid‐state properties of monodisperse glassy polymers with frozen‐in molecular orientation

“…Retardation, r , was measured on the central region of all oriented specimens at room temperature using an Olympus BX51‐P transmission optical polarizing microscope fitted with strain‐free optics, polarizer, and a thick Berek (0–20λ) rotary compensator, under white light, following a previously described procedure 14. Birefringence, Δ n , was computed from measurements of retardation and specimen thickness t as Δ n = r/t .…”

“… Experimental measurements of birefringence as a function of draw temperature for specimens of BE and BB drawn at a strain rate of 0.02 s −1 to a draw ratio of λ = 3 and immediately quenched (triangles and diamonds). Also shown are measurements of birefringence on two further grades of monodisperse polystyrene AF and AG oriented under the same conditions from ref 14. (circles and squares).…”

“…Frozen‐in molecular orientation is frequently an important consideration of any design, because its presence leads to anisotropy of many material properties of practical interest. Such anisotropy has been readily observed experimentally through measurable changes of Young's modulus,1, 2 yield stress,3–6 crazing stress,7–11 optical birefringence,1, 3, 8, 12–14 strain‐hardening modulus,4–6, 15, 16 rate of ageing,17 and fracture toughness 18–21…”

“…Most of these properties are not only dependent on the direction of orientation but are also highly sensitive to both the grade of polymer used and to the flow history encountered during processing 10, 14, 15. Hence, irrespective of whether the orientation is desired or not, the design of polymeric products generally consists of three interconnected stages: (1) the selection of an appropriate type and grade of polymer; (2) the specification of processing parameters; and (3) the realization of the desired solid‐state properties in the processed product.…”

“…The authors have recently proposed a new, fully three‐dimensional constitutive model that uses the linear viscoelastic spectrum in the melt and solid states to predict the nonlinear melt‐state and solid‐state constitutive response of glassy polymers 15. By fitting this model to linear viscoelastic rheological data obtained from two monodisperse linear polystyrenes (PS), the authors demonstrated a remarkable result: that it is possible to predict the optical birefringence,14 the craze initiation stress,10 and the solid‐state mechanical response15 of a polymer of given molar mass subjected to an arbitrary process history, with a small number of molar mass‐independent material constants and experimental measurement of the molar mass‐dependent melt‐state linear viscoelastic spectrum.…”