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Preparation of Polymeric Membranes 83
G', G'', G* (Pa)
10.000
1.000
100
10
1
0.1 1.0 10.0
frequency (w)
100.0 1000.0
Fig. 2.30 Dynamic frequency sweep test of a dope solution at the same strain (polymer solution: 24 wt
% 6FDA-ODA/NDA; 3 wt% EtOH; 22 C; strain = 20%) [adapted from ref. (99)].
test of a spinning polymer solution at 20% strain at room temperature (99). At a low
frequency, the loss shear modulus G 00 is almost the same as the complex modulus G and
the storage shear modulus G 0 is much lower than G 00 . It can be concluded that the rheology of
the dope solution is mainly influenced by viscosity in low shear rates. However, with an
increase in frequency, the influence of elasticity of the dope solution on the rheology of the
dope solution will increase. This can be reflected according to the decrease of loss tangent,
tan d. The influence of frequency on the dynamic viscosity and complex viscosity is indicated
in Fig. 2.31 (99). At a low frequency, the dynamic shear viscosity 0 is a constant, 0. The
dynamic relaxation viscosity 00 is much lower as compared to the dynamic shear viscosity,
0 . With the increase of frequency, 0 experiences the transition from 0 to a power-law
behavior and decreases. But 00 increases with the increase of frequency and then is kept
almost the same at a high frequency. So it can be concluded that the rheological characteristics
of the dope solution also change from viscosity to elasticity with the increase of shear
rate. Viscoelasticity of the polymer solution related to the relaxation time, which is the
characteristic time of the exponential strain decay curve and indicates the level of viscoelasticity
of polymer solutions.
The relaxation time is an important parameter in the membrane fabrication. It indicates the
level of molecular orientation of the polymer dope induced under shear, which will finally
influence the membrane performance (68, 100). With the progress of the phase separation
process of the polymeric solution, the relaxation time of the polymer chains will actually
increase due to the onset of solidification. In the instantaneous phase separation process, the
shear-induced molecular orientation will be frozen quickly into the nascent skin layer of the
membrane because the polymer solution has no chance of relaxing (101, 102). Even for some
delayed demixing processes, certain level of orientation would still be kept because the
relaxation times become progressively longer at low levels of residual strain. Generally, the
G'
G''
G*
tan