Oscillatory shear measurements

Of the techniques used to characterise the linear visco-elastic behaviom displayed by many non-Newtonian fluids, the oscillatory shear technique which involves either an applied stress or shear rate which varies harmonically with time, is perhaps the most convenient and widely used. 

The definition of linear visco-elasticity may be expressed in the following form the ratio of the applied stress to strain for any shear histoiy is a function of time alone, and independent of stress magnitude each stress applied to a material produces a strain which is independent of that produced by any other stresses. However, the total strain experienced by a material is equal to the sum of all the changes induced in the material by the applied stress throughout its history. 

The foregoing is an expression of the Boltzmann superposition principle [Bird et al., 1977] which may also be expressed in the following terms  

These constitutive equations, involving G(t), describe the response of linear visco-elastic materials to various time-dependent patterns of stress and strain in 

Within the region of linear visco-elastic behaviour, an imposed stress of angular frequency, u , results in a harmonic strain of amplitude proportional to the stress amplitude, and with phase lag 8 relative to the stress, which is independent of the applied stress amplitude [Ferry, 1980], 

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Brown, W Schillen, K Hvidt, S, Triblock Copolymers in Aqueous Solution Studied by Static and Dynamic Light Scattering and Oscillatory Shear Measurements. Influence of Relative Block Sizes, Journal of Physical Chemistry 96, 038, 1992. 

Small an jlitude oscillatory shear measurements have been widely used to follow the gelation process of biopolymers [9] because of their non-destroying character and the great variability of procedures, which allow simultaneous investigations of various features of a single sample. 

Dynamic oscillatory shear measurements of polymeric materials are generally performed by applying a time dependent strain of y(t) = y0sin(cot) and the resultant shear stress is a(t) = y0[G sin(a)t) + G"cos(cot)], with G and G" being the storage and loss modulus, respectively. 

Mills,N.J., Nevin,A. Oscillatory shear measurements on polystyrene melts in the terminal region. J. Polymer Sci. Pt. A-2 9,267-281 (1971). 

The loss and storage moduli of small amplitude oscillatory shear measurements [1, 3] follow from (5b) in the linear response case at y = 0 ... 

Rahalkar, R. R., Javanaud, C.. Richmond, P., Melville, I., and Pethrick, R. A. (1985). Oscillatory shear measurements on concentrated dextran solutions Comparison with Doi and Edwards theory reptation. J. Rheol. 29(6), 955-970. 

Brown, W., Schillen, K. and Almgren, M., 1991. Micelle and gel formation in a poly(ethylene oxide)/poly(propylene oxide)/poly(ethylene oxide) triblock copolymer in water solution. Dynamic and static light scattering and oscillatory shear measurements. Journal of Physical Chemistry, 95, 1850-1858. 

Brown, W. Schillen, K. Hvidt, S. Triblock copolymers in aqueous-solution studied by static and dynamic light-scattering and oscillatory shear measurements-influence of relative block sizes. J. Phys. Chem. 1992,96, 6038-6044. 

A number of experimental methods have been applied to measure the melt viscosity of polymers (53-55,65), but capillary extrusion techniques probably are generally preferred. Rotational methods are also used, and some permit the measurement of normal stress effects resulting from elasticity as well as of viscosity. Slit rheometers can also be used to measure normal stress (66). Oscillatory shear measurements are useful for measuring the elasticity of poljmier melts (57,58). Controlled stress methods have also been applied (59). Squeeze film flow has also been proposed as a geometry suitable for processibility testing of polymer melts... 

Branched polyesters Entanglements Oscillatory shear measurement 124, 125... 

The shear rate-dependent viscosity of pure PLA and various PLACNs at 175°C was also measured by Sinha Ray and Okamoto [69]. While the pure PLA exhibits almost Newtonian flow behavior at all shear rates tested, PLACNs exhibited non-Newtonian flow behavior. All PLACNs showed a very strong shear thinning behavior at all measured shear rates and this behavior is analogous to the results obtained in the case of oscillatory shear measurements. 

Steady and oscillatory shear measurements were performed at a temperature of 20 °C with a Rheo-Stress RSI50 rheometer (Haake) using a Couette cell geometry for the glycerol and Sterocoll FD solutions and a cone-plate geometry (60 mm in diameter, 1° cone angle) for the Sterocoll D. 

The cone and plate viscometer can be used for oscillatory shear measurements as well. In this case, the sample is deformed by an oscillatory driver which may be mechanical or electromagnetic. The amplitude of the sinusoidal deformation is measured by a strain transducer. The force deforming the sample is measured by the small deformation of a relatively rigid spring or tension bar to which is attached a stress transducer. On account of the energy dissipated by the viscoelastic polymer system, a phase difference develops between the stress and the strain. The complex viscosity behavior is determined from the amplitudes of stress and strain and the phase angle between them. The results are usually interpreted in terms of the material functions, p, G, G" and others [33-40]. 

Oscillatory shear measurements can be done with the parallel-disc arrangement in a similar manner as in the case of the cone and plate viscometer and similarly the material functions, and others... 

Transmission IR spectra were recorded using a Perkin-Elmer model 577 spectrometer, NMR spectra were taken at 32.442 MHz by means of a Bruker WP-80-SY spectrometer. An external deuteriated lock was used. The reference was 85% orthophosphoric acid. Oscillatory shear measurements were made with a Bohlin CS-10 rheometer using a double-gap cell with concentric cylinder geometry. 

Oscillatory shear measurements can be done with the parallel-disk arrangement in a manner similar to the case of the cone-n-plate viscometer and, similarly, the material fimcdons i), G, C, and others can be generated. However, a slightly different tedinique [36] is at times used wherein the polymer melt sample is deformed between two oscillating parallel eccentric disks as shown in Fig. 3.2. In this case, too, it has been shown that the fluid elements undergo a periodic sinusoidal deformation and the forces exerted on the disk are thus interpreted in terms of G and G" [4]. 

It was clear that low concentrations of hnear contaminants had a large influence on the melt rheology of rings. The extent to which this is tme was revealed in a recent report on the stress-relaxation behavior of PS rings (161 and 198 kg/mol) that were purified by LCCC (Section 26.1) and characterized as pure as currently possible (Kapnistos et al, 2008). Kapnistos et al conducted small-amphtude oscillatory shear measurements at different... 

To more thoroughly investigate the effect of chain interactions in the spinning solution prior to fiber extrusion on the properties of the formed fiber, the spinning solution must be characterized. One method of doing this is to perform mechanical measurements commonly referred to as oscillatory shear measurements. 

The temperature independence of log G versus log G" plots can be explained as follows. Recall that in Chapter 4 we presented the Doi-Edwards theory for entangled, monodisperse, linear flexible homopolymers (i.e., for M > Af ). In the terminal region of oscillatory shear measurements, using Eqs. (4.114) and (4.115) for -c 1,... 

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