High-frequency viscoelasticity

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). 

The mechanical properties of polymers are of interest in all applications where they are used as structural materials. The analysis of the mechanical behavior involves the deformation of a material under the influence of applied forces, and the most important and characteristic mechanical property is the modulus. A modulus is the ratio between the applied stress and the corresponding deformation, the nature of the modulus depending on that of the deformation. Polymers are viscoelastic materials and the high frequencies of most adiabatic techniques do not allow equilibrium to be reached in viscoelastic materials. Therefore, values of moduli obtained by different techniques do not always agree in the literature. 

This result is very interesting because whilst we have shown that G(0) has been excluded from the relaxation spectrum H at all finite times (Section 4.4.5), it is intrinsically related to the retardation spectrum L through Jc. Thus the retardation spectrum is a convenient description of the temporal processes of a viscoelastic solid. Conversely it has little to say about the viscous processes in a viscoelastic liquid. In the high frequency limit where co->oo the relationship becomes... 

There are not a great number of studies on the viscoelastic behaviour of quasi-hard spheres. The studies of Mellema and coworkers13 shown in Figure 5.5 indicate the real and imaginary parts of the viscosity in a high-frequency oscillation experiment. Their data can be normalised to a characteristic time based on the diffusion coefficient given above. 

A further development is possible by noting that the high frequency shear modulus Goo is related to the mean square particle displacement (m ) of caged fluid particles (monomers) that are transiently localized on time scales ranging between an average molecular collision time and the structural relaxation time r. Specifically, if the viscoelasticity of a supercooled liquid is approximated below Ti by a simple Maxwell model in conjunction with a Langevin model for Brownian motion, then (m ) is given by [188]... 

Massa,D,J., Schrag,J.L., Ferry,J.D. Dynamic viscoelastic properties of polystyrene in high-viscosity solvents. Extrapolation to infinite dilution and high-frequency behavior. Macromolecules 4,210-214 (1971). 

Osaki, K., SchragJ.L. Viscoelastic properties of polymer solutions in high-viscosity solvents and limiting high-frequency behavior. I. Polystyrene and poly(a-methyl-styrene). Polymer J. (Japan) 2,541-549 (1971). 

The use of high-frequency technology should be especially advantageous since the efficiency of vibration effects upon rheological properties of viscoelastic materials is... 

Several studies of high frequency shear viscoelastic liquids have also been reported by Tozaki [68, 69] and Kanazawa [14] with the QCM. 

Fig. 16.9 shows the low frequency slopes of 2 and 1, respectively, as expected for viscoelastic liquids and the high frequency slopes Vi and 2/3 for Rouse s and Zimm s models, respectively. Experimentally it appears that in general Zimm s model is in agreement with very dilute polymer solutions, and Rouse s model at moderately concentrated polymer solutions to polymer melts. An example is presented in Fig. 16.10. The solution of the high molecular weight polystyrene (III) behaves Rouse-like (free-draining), whereas the low molecular weight polystyrene with approximately the same concentration behaves Zimm-like (non-draining). The higher concentrated solution of this polymer illustrates a transition from Zimm-like to Rouse-like behaviour (non-draining nor free-draining, hence with intermediate hydrodynamic interaction).

In modeling the interaction of a liquid with plate modes, the high frequency of operation necessitates the consideration of viscoelastic response by the liquid. For the simple liquids examined, good agreement was obtained by modeling the liquid as a Maxwellian fluid with a single relaxation time r. When the Maxwellian fluid is driven in oscillatory flow with cot < 1, it responds as a Newtonian fluid characterized by the shear viscosity, rj. For wt > 1, the oscillation rate approaches the rate of molecular motion in the liquid and energy ceases to be dissipated in... 

At high frequencies, the viscoelastic behavior of suspensions is primarily dissipative, as the particles are forced to move through the solvent much faster than they can relax by Brownian motion. The high-frequency behavior is characterized by a constant high-frequency viscosity = lim >oo G" jay, which has been subtracted from the data plotted in Fig. 

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