the molecule or particle. Because of the random variation in conformation,
some of the polymer molecules will always be nonspherical. Larger
deviations occur with more elongated molecules, i.e., with some very stiff
polymers, which generally implies that the exponenta in Eq. (6.6) is
relatively large. The value (more precisely, the range of values) of the shear
rate where the transition occurs is inversely proportional totrot. The latter is
longer for a higher radius of gyration of the polymer molecule. This means
that the transition from high to low apparent viscosity occurs at smaller
shear rates for a larger molar mass, a better solvent quality, and a greater
stiffness of the polymer molecule.
Second,deformationof a particle like a random coil polymer molecule
may occur in a shear field. As illustrated in Figure 5.3, the particle becomes
elongated in one direction and compressed in another one. Since the particle
also rotates, this effectively means that the particle is repeatedly compressed
and elongated, which goes along with solvent locally being expelled from it
and locally being taken up. This causes additional energy dissipation and
thus an increased viscosity. The polymer molecule has a naturalrelaxation
timefor deformation: if it is deformed by an external stress and then the
stress is released, it takes a timetdeffor the deformation to be diminished to
1/eof its original value.
Note Actually, there may be a spectrum of relaxation times,
implying thattdefwould be an average value.Iftdef 41 =shear rate, the molecule cannot deform during flow, implying
that it keeps its roughly spherical shape, and the viscosity remains relatively
small. At very small shear rate, the molecule can fully deform twice during
every rotation, and viscosity is relatively large. The theory for the relaxation
time is not fully worked out, but it may be stated that the relation fortdefis
of the same form as fortrotgiven in (6.7). The same variables thus apply for
the deformation mechanism, which presumably has a larger effect on the
shear rate dependence of the viscosity than the orientation mechanism,
especially for large molecules.
Till here, only the interaction between one molecule and the solvent
has been considered. Unless polymer concentration is extremely small,
mutual interaction between polymer molecules will further affect viscosity
and its shear rate dependence. This is discussed in Section 6.4.3.
Note The reader may wonder whether the values of the apparent
viscosity at such extreme shear rates as 10^4 or 10^4 s^1 are of any
practical significance. It will be seen, however, in Chapters 11 and
13, that such velocity gradients do indeed occur and affect, for
instance, the physical stability of dispersions.