Chain dynamics of concentrated polystyrene solutions studied by depolarized photon-correlation and viscosity measurements

Abstract

Concentrated solutions of nearly monodisperse polystyrene samples in cyclohexane in the theta condition and in the entanglement-free region have been studied by means of the depolarized photon-correlation spectroscopy and viscosity measurements. It is shown that the viscoelastic behavior of the studied systems is described by the Rouse theory and that in agreement with the theoretical analysis the main polymer dynamic process probed by the depolarized Rayleigh scattering is basically the reorientational motion associated with a Rouse segment of the polymer chain, whose relaxation is independent of the scattering angle and the molecular weight. In addition to the main dynamic process, the tail region of a very fast process associated with the sub-Rouse-segmental motions can be observed, whose existence is expected from the theoretical analysis.

Motion Associated with a Single Rouse Segment versus the α Relaxation. 2

“…It is an important contribution of ERT to bridge the gap between the Rouse and Doi−Edwards theories by showing that they have the same footing at the Rouse-segmental level. Because of this result, the frictional factor K extracted from the viscoelastic results in terms of either the Rouse theory or ERT can be used in the same way in comparing with the depolarized photon-correlation results, as done previously ,,− and in this study.…”

“…Thus, we can use the above K value at 127.5 °C and the ratio K ‘/ K = 3.3 to obtain K ‘. As explained in ref , the mass of a Rouse segment of polystyrene ( m ) being about 850 − ,− ,, leads to N e = 16. Using the value of K ‘ obtained as described above and N e = 16 or equivalently m = 850, we can calculate τ v ≈ from eq 7 or eq 5 (with K substituted by K ‘; and N r replaced by N e = 16) to be 5.1 × 10 -3 sec, which, clearly as expected, is of the same order of magnitude as the 〈 τ c 〉 value at 127.5 °C, 3.5 × 10 -3 , obtained from Patterson's results by interpolation.…”

“…For both the studies of the motion associated with a single Rouse segment and the α-relaxation, the strategy we take is to use the successful description of the slow (low-frequency) viscoelastic propertiesfor instance, the zero-shear viscosity and the viscoelastic spectrum from the low-frequency end of the transition zone to the terminal zonein terms of the molecular theories as the reference frame. − ,− The molecular theory used for analyzing the experimental results depends on whether the system is in the entanglement or entanglement-free region. Then, the frictional factor K thus determined can be used to calculate the time constant of the highest Rouse normal mode for comparison with other dynamic results or be used to “normalize” the α-relaxation time for further comparative analysis.…”

“…The depolarized photon-correlation functions of two entanglement-free concentrated solutions (∼60 wt %) of polystyrene with M w = 9100; M w / M n = 1.02, and M w = 18 100; M w / M n = 1.01 in cyclohexane at the θ condition (i.e., at 35 °C)denoted by samples S1 (59.832 wt %; 0.552 g/cm 3 ) and S2 (60.287 wt %; 0.556 g/cm 3 ), respectivelyhave been measured and analyzed. − Along with the depolarized photon-correlation measurements, two solution samples with accurately determined concentrations in the close neighborhood of the concentration of each of the two samples, S1 and S2, are prepared for viscosity measurements by the falling-ball method, which, with both the ball and solution sealed in a glass tube, is particularly good for studying solution systems as solvent evaporation can be prevented. Then, by interpolation or extrapolation, the viscosity values at the concentrations of samples S1 and S2 can be individually determined; subsequently, their τ v values can be calculated (eqs 6 and 7) for comparison with their depolarized photon-correlation results.…”

“…Furthermore, the obtained information of the concentration dependence of viscosity allows the viscosity results to be compared under the same concentration and can be used to correct for the small concentration difference between samples S1 and S2 when their depolarized photon-correlation results are compared. The discussions below are all based on the results after the corrections have been made; the details of the corrections can be found in ref .…”