Abstract
Monodisperse poly-α-methylstyrenes in benzene at 30.0°C and in cyclohexane at the theta temperature of 39.0°C have been studied. The two samples are numbered 312 for Mv=1.89×105 and 317 for Mv=4.79×105. The complex rigidity and the steady-shear viscosity have been measured by means of torsion crystals at the frequencies of 19.6kc, 39.2kc, 79.4kc and 117.7kc, and a Ubbelohde dilution type viscometer respectively. The intrinsic rigidity and the limiting relaxation time (divided by Kp) are given by the extrapolation to zero concentration.
The theory of Tschoegl, extended to partially-free-draining and non-Gaussian chains respectively through h and ε, may be summarized in the dimensionless functions of intrinsic rigidity and the relaxation time factors as follows,
[G']M/RT=Σpωs2Kp2/(1+ωs2Kp2), [G"]M/RT=ΣpωsKp/(1+ωs2Kp2)
ωs=ω(τp)0/Kp=ωηs[η]M/RT, Kp=1/λ'pΣpλ'p-1
where ωs is the generalized angular frequency and λ'p is the eigenvalue of Zimm. The numerical evaluations have been performed with a high-speed computer.
In the case of benzene solutions the ε's have been derived from the steady-shear intrinsic viscosities divided by those of theta solutions using Ptitsyn's equation, and the mean value is 0.15. The dimensionless plots of intrinsic rigidity shows that the most fitting curves for the data are the theoretical ones of Tschoegl for ε=0.15 and h=10. Consequently the degree of draining h is the order of 10, and the first relaxation time factor K1 is 0.474. Then the first limiting relaxation time(τ1)0's are estimated at 1.29×10-6sec for 312 and 5.97×10-6sec for 317.
In the theta solvent of cyclohexane, ε is zero and the dimensionless plots are explained by Zimm's dispersion curves i.e. h=∞. It is the non-draining case, so that K1=0.422, and(τ1)0=7.17× 10-7sec for 312 and (τ1)0=2.64×10-6sec for 317.
The Tschoegl theory has been quantitatively confirmed with a research in infinite dilution, and the random coil polymer is considered as partially-free-draining molecule in good solvent.
