Intrinsic nonlinearity Q
0(ω)
under medium amplitude oscillatory shear (MAOS) deformation was investigated
for monodisperse polystyrene (PS) solutions at various concentrations,
which were classified as unentangled or entangled solution in semidilute
regime. These two types of PS solutions displayed different shapes
when Q
0 was plotted as a function of frequency
(ω). Unentangled solutions showed increases of Q
0 with frequency at the low frequency region and then
plateau behavior at the high frequency region. On the contrary, entangled
solutions showed an increase of Q
0 before
the MAOS terminal relaxation time and a subsequent decrease, which
is similar to that observed for entangled linear polymer melts. The Q
0(ω) curves of each group were superposed
in a dimensionless coordinate (Q
0/Q
0,max vs De), so that transition
from the plateau of Q
0 to decreasing Q
0 at the high frequency region might indicate
the onset of entanglement in polymer solution. In particular, all
unentangled solutions had the same Q
0,max value (0.006) regardless of polymer concentration and molecular
weight because Q
0 responds to Rouse-like
relaxation process only, which is featured as no interchain interaction
and chain stretching. However, the Q
0,max values of entangled solutions were dependent on the number of entanglements
(Z). The master curve of Q
0,max as a function of Z showed that Q
0,max was constant at low entanglement numbers (few or
virtually no entanglements) and then increased with the beginning
of entanglement to approach a limiting value at high entanglement
numbers, where reptation is the dominant linear relaxation process.
In addition, the master curve of Q
0,max as a function of Z was used to quantify the degree
of tube dilation based on the dynamic tube dilution (DTD) theory.
Direct comparison of the Q
0,max values
of semidilute solutions and melts showed that they followed the same
molecular dynamics in MAOS flow like SAOS (small amplitude oscillatory
shear) flow. Comparison between static and dynamic dilutions using
the Q
0,max master curve suggested that
this curve could characterize the effective number of entanglements
per backbone chain for branched polymers. Because it was confirmed
again that Q
0(ω) is highly sensitive
to various relaxation processes, MAOS tests may provide a new means
of investigating molecular dynamics.