Dynamic Mechanical Properties of Polystyrene Solutions from 23 to 300 MHz

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, ${\mathrm{G\prime -\nu }}_1{G}_s\prime$ , and quadrature, ${\mathrm{G″-\upsilon }}_1{\mathrm{\omega \eta }}_s\prime$ , components of the dynamic shear modulus of the polymer, where $G_s\prime$ is the solvent contribution to the in‐phase modulus, $\omega$ is the angular frequency, ${\eta }_s\prime$ is the dynamic solvent viscosity, and ${\upsilon }_1$ 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 $\mathrm{\eta \prime }$ 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 ${\mathrm{(\eta \prime \hspace{0.17em}-\hspace{0.17em}\upsilon }}_1{\eta }_s{\mathrm{\prime )\hspace{0.17em}/\hspace{0.17em}(\eta \hspace{0.17em}-\hspace{0.17em}\upsilon }}_1{\eta }_s)$ , where $\eta$ and ${\eta }_s$ 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, $\mathrm{h*}$ , of 0.2, a value of 1.9₇ was obtained for $\mathrm{\phi /f}$ , the ratio of the internal to segmental friction coefficients. The concentration dependence of $\phi$ was determined assuming little or no change in $\mathrm{h*}$ with concentration, and an appropriate dependence of $f$ on concentration and viscosity. It ranged from $c^{{\text{0.2}}^6}$ below entanglement to $c^{\text{0.07}}$ above it, approximately the one‐fourth and zeroth powers, respectively. The concentration dependence of ${\mathrm{(\eta \prime \hspace{0.17em}-\hspace{0.17em}\upsilon }}_1{\eta }_s\mathrm{\prime )}$ increased by about $c^1$ while that of ${\mathrm{(\eta \hspace{0.17em}-\hspace{0.17em}\upsilon }}_1{\eta }_s)$ increased by $c^2$ 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 $G_{\infty }\prime$ and $\tau$ , 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...