Dynamic Mechanical Properties of Polystyrene Solutions from 23 to 300 MHz
Authors: Moore R. S. , McSkimin H. J. , Gieniewski C. , Andreatch P. 
Published: February 2004

Measurements of dynamic shear impedance at five frequencies from 23 to 300 MHz and at 25°C are reported for a monodisperse polystyrene as a function of concentration. The concentrations ranged from 3% to 20% polymer in di-n-butyl phthalate, a near-theta solvent, and covered the region from the start of coil overlap to well beyond entanglement. Results are reported in terms of the in-phase, G′−ν1Gs′, and quadrature, G″−υ1ωηs′, components of the dynamic shear modulus of the polymer, where Gs′ is the solvent contribution to the in-phase modulus, ω is the angular frequency, ηs′ is the dynamic solvent viscosity, and υ1 is the volume fraction of solvent. The use of dynamic values for the solvent follows from observation of relaxation and non-Newtonian behavior in the solvent beyond 100 MHz. The usual reduced variables method, even in this modified form, could not be successfully applied to superimpose data at different concentrations, indicating the need for further modification to account for finite concentration effects. The dynamic solution viscosity η′ is found to increase with increasing concentration at fixed frequency. At any one concentration, it decreases with increasing frequency above 200 MHz. This is in contrast to the nearly constant values attained at lower frequencies at concentrations to 15% polymer; the decrease is too large to be accounted for by only solvent viscosity effects. Results are also reported in terms of the reduced dynamic viscosity (η′ − υ1ηs′) / (η − υ1ηs), where η and ηs are the steady-flow values for the solution and the solvent, respectively. A high-frequency limiting value of the reduced viscosity is found to obtain for the lower concentrations at the three lowest frequencies. However, for the highest concentration the limiting value is believed to occur at frequencies lower than those measured, so that a further decrease is, in fact, being observed above 100 MHz. An estimate of 10−1.04 was obtained for the reduced high-frequency limiting viscosity in the limit of infinite dilution. From an estimate of the number of statistical segments (259) based on intrinsic viscosity measurements and on the results of Thurston, and an estimate of the extent of hydrodynamic interaction per segment, h*, of 0.2, a value of 1.97 was obtained for φ/f, the ratio of the internal to segmental friction coefficients. The concentration dependence of φ was determined assuming little or no change in h* with concentration, and an appropriate dependence of f on concentration and viscosity. It ranged from c0.26 below entanglement to c0.07 above it, approximately the one-fourth and zeroth powers, respectively. The concentration dependence of (η′ − υ1ηs′) increased by about c1 while that of (η − υ1ηs) increased by c2 on going from concentrations below to those above entanglement. Plots of the dynamic impedance against frequency indicate that departure from Newtonian behavior occurs sooner for the quadrature component than for the in-phase part. Solvent relaxation was evaluated in terms of Lamb's semiempirical theory for low-molecular-weight liquids. From a comparison of the observed frequency dependence and the reference plots of Lamb, values for G∞′ and τ, the high-frequency limiting dynamic shear modulus and the average relaxation time, were obtained of 1.97×1010 dyn/cm2 and 8.5×10−12 sec, respectively. The magnitude of the latter is discussed and is shown to be in reasonable agreement with estimates of Pinnow, Candau, and Litovitz for n-alkyl bromides. Based on values of the reduced dynamic viscosity obtained by Ferry, Holmes, Lamb, and Matheson at 73 kHz and upon the present results, it appears that the high-frequency limiting viscosity of polystyrene in a near-theta solvent persists for about 312 decades before it decreases further at a frequency in the vicinity of that for the onset of solvent relaxation. Extension of optical techniques (e.g., Brillouin scattering) to studies of polymer solutions is briefly noted.