Complex modulus dilute solutions

With appropriate caUbration the complex characteristic impedance at each resonance frequency can be calculated and related to the complex shear modulus, G, of the solution. Extrapolations to 2ero concentration yield the intrinsic storage and loss moduH [G ] and [G"], respectively, which are molecular properties. In the viscosity range of 0.5-50 mPa-s, the instmment provides valuable experimental data on dilute solutions of random coil (291), branched (292), and rod-like (293) polymers. The upper limit for shearing frequency for the MLR is 800 H2. High frequency (20 to 500 K H2) viscoelastic properties can be measured with another instmment, the high frequency torsional rod apparatus (HFTRA) (294). 

Figure 10. Real and imaginary part of complex modulus, G and G —cut/j, vs. loor for atactic polystyrene in dilute solution Oj- is shift factor. Experimental points are from refs. 102 and 103 best-fit continuous lines [from Eqn. (34) of ref. 12] superimposed on experimental points after rigid, parallel shift. [Model assumptions and parameters unperturbed periodic chain, N = 8000 (left) and N = 1300 (right), to/to = 47, R ff = 0.125 A.] (Reprinted with permission from ref. 12, Copyright 1981, American Chemical Society.)...

For fluids of low viscosity such as dilute polymer solutions, it is customary to describe the viscoelasticity with the complex modulus and the experiments have been performed in simple shear flow. The sinusoidally oscillating simple shear flow employed in this paper is illustrated in Fig. 1.1. The velocity of the fluid in the cartesian coordinate... 

In this section we will define several quantities which are convenient for the discussion of the viscoelasticity of dilute polymer solutions. As mentioned above, the two quantities G and G — o)t s related to the complex modulus as functions of to, are the measurable quantities. In order to make comparisons with theory, one has to extrapolate these quantities to infinite dilution, i.e.,... 

Semi-dilute polymer solutions are viscoelastic liquids which have a very complex mechanical behavior, intermediate between viscous and elastic. After a mechanical perturbation such as the application of stress, a semi-dilute polymer solution behaves as a solid over short time intervals, with a well-defined elastic modulus, and as a liquid over long time intervals, characterized by a macroscopic viscosity. The elastic modulus is related to the transient network made by the chains. This elastic behavior lasts until chains can disentangle and then the solution flows. The characteristic time separating viscous and elastic behavior is thus the reptation time. 

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