How Dilute are Dilute Solutions in Extensional Flows?

Abstract

We investigate the concentration-dependence of the characteristic relaxation time of dilute polymer solutions in transient uniaxial elongational flow. A series of monodisperse polystyrene solutions of five different molecular weights (1.8×10^6 ≤ M ≤ 8.3×10^6 g/mol) with concentrations spanning five orders of magnitude were dissolved in two solvents of differing solvent quality (diethyl phthalate and oligomeric styrene). Optical measurements of the rate of filament thinning and the time to break-up in each fluid are used to determine the characteristic relaxation time. A lower sensitivity limit for the measurements was determined experimentally and confirmed by comparison to numerical calculations.

Above this sensitivity limit we show that the effective relaxation time of moderately dilute solutions (0.01 ≤ c/c* ≤ 1) in transient extensional flow rises substantially above the fitted value of the relaxation time extracted from small amplitude oscillatory shear flow and above the Zimm relaxation time computed from kinetic theory and intrinsic viscosity measurements. This effective relaxation time exhibits a power-law scaling with the reduced concentration (c/c*) and the magnitude of the exponent varies with the thermodynamic quality of the solvent. This scaling appears to be roughly consistent to that predicted when the dynamics of the partially elongated and overlapping polymer chains are described within the framework of blob theories for semi-dilute solutions.