Angle between oscillators, determination

The viscoelastic parameters are generally measured by dynamic oscillatory measurements. Apparatus of three different configurations can be used cone and plate, parallel plates, or concentric cylinders. In the case of cone and plate geometry, the test material is contained between a cone and a plate with the angle between cone and plate being small (<4°). The bottom member undergoes forced harmonic oscillations about its axis and this motion is transmitted through the test material to the top member, the motion of which is constrained by a torsion bar. The relevant measurements are the amplitude ratio of the motions of the two members and the associated phase lag. From this information it is relatively simple to determine G and G". 

Dynamic Oscillatory Experiments The dynamic rheological properties of a polymeric solution can be determined by small-amplitude oscillation tests [2]. In small amplitude oscillatory measurements, a sinusoidally varying shear stress field is imposed on a fluid and the amplitude of the resulting shear strain and phase angle between the imposed stress and the strain is measured. The test is... 

The deep-channel viscometer could also be adapted for measurement of the nonlinear interfacial rheological behaviour of the film [52]. In this case several small tracer particles are placed on the fluid interface at different radial positions and the angular velocities are determined from measurements of the period of revolution. When used to measure viscoelastic properties, the deep-channel viscometer is operated in an oscillatory mode, in which case the floor of the viscometer is oscillated sinusoidally. Simultaneous measurements of the phase angle between the surface motion and the oscillating motion of the bottom dish, and the surface-to-floor amplitude ratio, may permit determination of the viscoelastic properties of the fluid interface, presuming knowledge of an appropriate rheological model [52]. 

In Eq. (12.25), 6 is the angle between the polarization of the incident radiation (A ) and the direction of propagation of the scattered wave k ), R is the position of the detector, is the dynamic polarizability of the segment, and p iv) is the density of modes of the incident radiation at frequency v (Eqs. 12.9,12.12, and B12.1.14). The factor sin(5)/IAI is the same factor that determines the amplitude of the field from an oscillating electric dipole (Figs. 3.1 and 3.2), and the fluorescence from an excited molecule whose transition dipole is oriented along a fixed axis (Sect. 5.9). The polarizability Uaa can be obtained from the difference between the dielectric constant of the solution and that of the pure solvent. 

The cone-n-plate viscometer can be used for oscillatory shear measurements as well. In this case, the sample is deformed by an oscillating 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 a stress transducer is attached. Because of the energy dissipated by the viscoelastic polymer melt, 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 t, G, G", and others [21-28]. 

Dynamic Mechanical (Low Strain Deformation). When a cyclic strain of small ampUtude is applied to a strip of material, a cyclic stress will be generated in response by the sample. If the material is ideal (Hookian) and stores all the input energy, the cyclic stress is in phase with the applied cyclic strain. Viscous components cause a finite phase lag or phase angle, 8, between the stress and strain. represents the elastic, real, or storage modulus while E" is the viscous, imaginary, or loss modulus. Tan 8 is equal to the ratio E /E" and is related to the molecular relaxations that occur in the sample. Transition temperatures and associated activation energy can be determined (72) by varying the frequency of oscillation at a fixed temperature or the temperature at a fixed frequency. 

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