Torsion, experiments pendulum

We may now express the damping term of the torsion pendulum experiment in terms of the dissipation factor by the simple equation (an approximation which holds for most cases) ... 

Surface viscosity has an important influence on the deformation of films and can also provide information about structure. Gaines [14] describes various methods of measuring this quantity. The damped torsion pendulum as developed by Langmuir and Schaefer [65] is probably the best device for making such measurements. Recent measurements of this type have been made by Buhaenko et al. [66]. Malcolm [67, 68] and Daniel and Hart [69] have carried out experiments which illustrate the important influence which viscosity has on the study of isotherms. 

Figure 5. Results of torsion pendulum experiments on (a) a natural copolymer and (b) a simulated copolymer (22 compounds)...

The stiffness modulus is, in most cases, measured in dynamical - mechanical experiments, for instance with a torsion pendulum, on a time scale of a few seconds. This experiment results in the shear modulus, G (which is related to Young s modulus, E), while the damping shows a strong maximum at Tg. 

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. 

In various experiments different elastic constants are being determined with a torsion pendulum, for instance, the shear modulus, G, is measured, with creep or vibrations in elongation or in bending the Young s modulus, (tensile modulus), E. For an isotropic material the relation between E and G is as follows ... 

The loss factor, tan 8, can be measured with the aid of dynamic-mechanical experiments (such as the torsion pendulum). The deformation in such a test varies as indicated in Figure 7.13 the damping follows from the logarithmic decrement , A, it can be easily shown that... 

The purpose of this paper is to describe an automated torsion pendulum controlled by a desktop computer, to discuss four separate methods of data analysis, and to compare the results of a torsion pendulum experiment and a TBA experiment using the same epoxy resin. 

Least Squares Method (8). A torsion pendulum specimen has a tendency to change its rotational orientation during the course of an experiment due to an uneven distribution of stresses caused by volume expansion and contraction. This results in a drift in the baseline of the wave signal which can be represented by... 

Discussion. The four methods of data reduction were used to analyze the raw data of the same TBA specimen during a slow (0.25°C/min) temperature scan (Figure 8). A comparison of the spectra indicates that they all gave similar results over the range of period (0.3 to 1.8 sec) and logarithmic decrement (0.01 to 1.08) encountered in the experiment. (The automated torsion pendulum has been used to reduce data with a range of 0.1 to 15 sec. for the period, and 0.001 to 4.0 for the... 

The G" (or E") and tan 6 peaks occuring in the temperature range from -20 to -120 C are extremely broad and skewed in both vibrating reed and torsion pendulum experiments. These peaks are considered to be the sum of two overlapping peaks—the 8 and Y relations. The highest temperature a relaxation is seen around 5 to 20 C on the tan 6 curves the drastic drop in G (or E ) and the sharpness of the tan <5g peak are characteristic of typical glass transition behavior of a neutral amorphous polymer. 

The samples were characterized by DSC-measurements and by torsional pendulum experiments. 

The measurements were performed with an automated torsion pendulum (DMA) apparatus working at a frequency of about 0.5 Hz. (varying frequency system, see Chapter 4). The use of a low-stiffness suspension wire permitted stiffness measurements as low as 5H4 N/m2. These DMA measurements were performed from 50°C up to 250°C using a heating rate of l°C/minute the samples were, during these experiments, purged with nitrogen. 

Figure 4.153 shows a schematic drawing of a torsion pendulum. It was used for some of the first DMA experiments that were carried out as a function of temperature [43]. The pendulum is set into vibrations of small amplitude ( 3°) and continues to... 

Dynamic mechanical analyzers can be divided into resonant and defined frequency instruments. The torsion pendulum just described is, for example, a resonant instrument. The schematic of a defined-frequency instrument is shown in Fig. 4.155. The basic elements are the force generator and the strain meter. Signals of both are collected by the module CPU, the central processing unit, and transmitted to the computer for data evaluation. The diagram is drawn after a commercial DMA which was produced by Seiko. At the bottom of Fig. 4.155, a typical sample behavior for a DMA experiment is sketched. An applied sinusoidal stress, o, is followed with a phase lag, 6, by the strain, e. The analysis of such data in terms of the dynamic moduli (stress-strain ratios, see Fig. 4.143) at different frequencies and temperature is the subject of DMA. 

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