Dynamic oscillation measurements

The linear visco-elastic range ends when the elastic modulus G starts to fall off with the further increase of the strain amplitude. This value is called the critical amplitude yi This is the maximum amplitude that can be used for non-destructive dynamic oscillation measurements... 

In dynamic (oscillator) measurements, a sinusoidal strain, with frequency v in Hz or CO in rad s (concentric cylinder) or plate (of a cone and plate) and the stress is measured simultaneously on the bob or the cone, which are connected to a torque bar. The angular displacement of the cup or the plate is measured using a transducer. For a viscoelastic system, such as the case with a cosmetic emulsion, the stress oscillates with the same frequency as the strain, but out-of-phase [11). Figure 12.4 illustrates the stress and strain sine waves for a viscoelastic system. 

In our studies, critical Deborah numbers are rather constant (around 1) for different relaxation times at constant permeability, whereas for constant fluid properties and different permeabilities the critical Deborah numbers vary between 1 and 2. This suggests that the longest relaxation time obtained from dynamic oscillation measurements for practical solutions may successfully be used in calculations indicating the onset of an excess pressure increase, but that the approximations of the stretching rate, as given in equation 2, is somewhat dubious. 

Fig. ni-19. Trough for dynamic surface measurements A, stainless-steel dish B, aluminum mantle C, inlet thermostatting water D, lower PTFE bars E, oscillating bars F, attachment lower bars G, Wilhelmy plate. (From Ref. 140.)... 

A technique for performing dynamic mechanical measurements in which the sample is oscillated mechanically at a fixed frequency. Storage modulus and damping are calculated from the applied strain and the resultant stress and shift in phase angle. 

With a new software program it is possible to measure the Texture Constant" of pectins. This Texture Constant K is calculated by the ratio of the maximum force during the time interval of the measurement and the measured area below the force-time curve. The resulting constants K correlate well with the dynamic Weissenberg number of oscillating measurements carried through with the same pectin gels. 

Dynamic rheological measurements have recently been used to accurately determine the gel point (79). Winter and Chambon (20) have determined that at the gel point, where a macromolecule spans the entire sample size, the elastic modulus (G ) and the viscous modulus (G") both exhibit the same power law dependence with respect to the frequency of oscillation. These expressions for the dynamic moduli at the gel point are as follows ... 

Cohen, R.E., Tschoegl,N.W, Dynamic mechanical properties of block copolymer blends—a study of the effects of terminal chains in elastomeric materials. I. Torsion pendulum measurements. Intern. J, Polymeric Mater. 2, 49-69 (1972) II. Forced oscillation measurements. Ibid 2, 205-223 (1973) III. A mechanical model for entanglement slippage. Ibid (in press). 

Various types of vibration experiments can be carried out to measure E and E2 at a certain frequency. An example is the torsion pendulum, in which the sample, connected to an auxiliary mass, is brought into a free torsional oscillation. From the frequency of the pendulum (around 1 to 10 sec) E is calculated, from the rate of damping tan 8 and E2. Other types of dynamic mechanical measurements can be carried out at higher frequencies, such as bending vibrations with or without extra mass, wave propagation, etc. By combining a number of these different techniques, a time scale ranging from 10 to 10"8 sec can be covered. 

The bulk rheological properties of the PFPEs, including the melt viscosity (p), storage modulus (G ), and loss modulus (G"), were measured at several different temperatures via steady shear and dynamic oscillation tests. Note that we denoted p as melt viscosity and r as solution viscosity. An excellent description of the rheology is available in Ferry [99]. 

Dynamic (oscillatory) measurements A sinusoidal stress or strain with amphtudes (Tjj and is appHed at a frequency a> (rads ), and the stress and strain are measured simultaneously. For a viscoelastic system, as is the case with most formulations, the stress and strain amplitudes oscillate with the same frequency, but out of phase. The phase angle shift S is measured from the time shift of the strain and stress sine waves. From a, y and S, it is possible to obtain the complex modulus j G, the storage modulus G (the elastic component), and the loss modulus G" (the viscous component). The results are obtained as a function of strain ampHtude and frequency. 

Dynamic shear rheology involves measuring the resistance to dynamic oscillatory flows. Dynamic moduli such as the storage (or solid-like) modulus (G ), the loss (or fluid-like) modulus (G"), the loss tangent (tan 8 = G"IG ) and the complex viscosity ( / ) can all be used to characterize deformation resistance to dynamic oscillation of a sinusoidally imposed deformation with a characteristic frequency of oscillation (o). 

Dynamic-shear measurements are of the complex viscosity rj ) as a function of the dynamic oscillation rate (o), at constant temperature. These tests are defined as isothermal dynamic frequency sweeps. Since the dynamic frequency sweeps are conducted at a given amplitude of motion, or strain, it is necessary to ensure that the sweeps are conducted in the region where the response is strain-independent, which is defined as the linear viscoelastic region. This region of strain independence is determined by an isothermal strain sweep, which measures the complex viscosity as a function of applied strain at a given frequency. This ensures that a strain at which the dynamic frequency sweep may be conducted in the linear viscoelastic region is selected. 

The complex viscosity as a function of frequency, maximum strain and temperature is generally determined with one rheometer. Standard ASTM 4440-84/90 defines the measurement of rheological parameters of polymer samples using dynamic oscillation. This standard reiterates the importance of determining the linear viscoelastic region prior to performing dynamic frequency sweeps. 

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". 

FIGURE 5.9 Illustration of dynamic (oscillatory) measurement of rheological properties. In (a) the applied shear strain (y) is shown as a function of time t oscillation frequency. In (b d) the resulting shear stress a is given for an elastic, a viscous, and a viscoelastic response. 5 is the phase or loss angle. See text. 

In dynamic mechanical tests, the response of a material to periodie stress is measured. There are many types of dynamic mechanical test instruments. Each has a limited Irequency range, but it is generally possible to cover frequencies from 1(E to 10 cycles per second. A popular instrument for dynamic mechanical measurements is the torsion pendulum (Figure 13.6A). A polymer sample is elamped at one end, and the other end is attaehed to a disk that is free to oscillate. As a result of the damping characteristics of the test sample, the amplitude of oscillation decays with time (Figure 13.6B). 

Dynamic mechanical measurements can mostly be divided into two groups. The reaction of a sample to a once applied light torque can be measured with the torsion pendulum. The sample oscillates freely, whereby the amplitude decreases steadily with each cycle for viscoelastic materials. The ratio of two successive amplitudes is constant for ideal viscoelastic materials. This procedure yields shear moduli. The torsion pendulum allows measurements to be relatively easily made the disadvantage is that the frequency is not an independent variable with this method. 

Mixes of S13TMSx and T30TMSx silylated silicas and a silicone oil (Wacker-Chemie AKIOOO) were submitted to dynamic rheological measurements using an oscillating cone/plane rheometer. In Fig. 14, the evolution of the viscosity, measured at 25°C and 0.278 Hz, with the silica surface coverage ratio is shown. 

Figure 5.53. Illustration demonstrating the necessity of using a pretension in DMA tensile measurements of fibers and thin films sample buckhng will take place below a certain pretension level is the static pretension force, and Fi is the variable dynamic oscillating force imposed during the test (from Grehlinger and Kraft, 1988b, with permission of the Society of Plastics Engineers).

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