Torsion pendulum data

All of the Tg data reported in Table II were obtained with the resilience method a few selected results were doubly checked with the values obtained from the torsion-pendulum data. Note the identical value of the Tg for MS/AN/MMA measured by the resilience method and that obtained with the torsion-pendulum data on Figure 12. 

Figure 11. A comparison of torsion pendulum data obtained using a film /" , shear modulus vs. T , log decrement vs. T] and TBA data obtained using a supported specimen [ 0, relative rigidity vs. T O, log decrement vs. T].

The dynamic modulus curves from torsion pendulum data (14) are reproduced in Figure 5 and show complex modulus (G ) as a function of temperature for a series of NBCs ranging in polyether content from 0 to 66%. The curves representing 9 and 18% polyether copolymers are quite similar to, but not identical with nylon 6, which is shown in the dashed curve. The copolymer curves show a deflection at -60°C, the tg for polyether. This deflection becomes much more pronounced while changes in the nylon tg region at 45 to 50°C are not apparent. 

A tube of poljKmethyl methaciylate) (PMMA) with length 200 mm, diameter 20 mm, and wall thickness 1 mm, is to be subjected to sinusoidal torsional oscillations at 1 Hz, in which the relative rotation of its ends will be by 10°. Before the oscillations commence the tube is in equilibrium with air at 20°C. Predict the initial rate of temperature rise and the final equilibrium temperature. Use the torsion pendulum data for PMMA given in Figure 4.11, and take the density and specific heat of PMMA to be 1200 kg m and 1450 J kg" K, respectivety. The heat transfer coefficient for convective beat transfer from the external surface of the tube to air at about 20 C may be assumed to be 10 W m K" . The heat loss from the inside surface can be neglected. Hint you may refer to the equation ven in Problem 4.6. 

Fig. 5. 25 Shear data for a styrene/butadiene copolymer developed using a torsional pendulum. (Data from Nielsen, (1965)).

Figure 7.46 Shear modulus (torsion pendulum data at 1 Hz) of linear polyethylenes as a function of crystallinity at different temperatures. From Boyd (1979) who used the data of Illers (1973).

Fig. 9. Torsion pendulum data for polychloroprene gum showing phase angle, 6, as a function of frequency, f, (ref. 6). Numbers on curves refer to parts of N330 carbon black in 100 parts of gum rubber.

Softening and cure is examined with the help of a torsional pendulum modified with a braid (65), which supports thermosets such as phenoHcs and epoxies that change from a Hquid to a soHd on curing. Another method uses vibrating arms coupled to a scrim-supported sample to measure storage and loss moduH as a function of time and temperature. An isothermal analytical method for phenoHc resins provides data regarding rate constants and activation energies and allows prediction of cure characteristics under conditions of commercial use (47). 

Free- Vibration Methods. Free-vibration instmments subject a specimen to a displacement and allow it to vibrate freely. The oscillations are monitored for frequency and damping characteristics as they disappear. The displacement is repeated again and again as the specimen is heated or cooled. The results are used to calculate storage and loss modulus data. The torsional pendulum and torsional braid analy2er (TBA) are examples of free-vibration instmments. 

There are several other comparable rheological experimental methods involving linear viscoelastic behavior. Among them are creep tests (constant stress), dynamic mechanical fatigue tests (forced periodic oscillation), and torsion pendulum tests (free oscillation). Viscoelastic data obtained from any of these techniques must be consistent data from the others. 

This second group of tests is designed to measure the mechanical response of a substance to applied vibrational loads or strains. Both temperature and frequency can be varied, and thus contribute to the information that these tests can provide. There are a number of such tests, of which the major ones are probably the torsion pendulum and dynamic mechanical thermal analysis (DMTA). The underlying principles of these dynamic tests have been covered earlier. Such tests are used as relatively rapid methods of characterisation and evaluation of viscoelastic polymers, including the measurement of T, the study of the curing characteristics of thermosets, and the study of polymer blends and their compatibility. They can be used in essentially non-destructive modes and, unlike the majority of measurements made in non-dynamic tests, they yield data on continuous properties of polymeric materials, rather than discontinuous ones, as are any of the types of strength which are measured routinely. 

Gel Point and Tg. The variation of Tg with ac was investigated (18, 2J5,29) for dry networks formed from system 3 of Figure 9 at different initial dilutions of reaction mixtures. Measurements were carried out at 1Hz using a torsion pendulum(26). The results were shown in Figure 10. The two limiting values of Tg for this system correspond to networks with Me = > and Mc = Me-Thus, the horizontal broken line gives the minimum Tg, that of a linear MDI/POP polymer having a repeat unit of molar mass equal to Mq, and the maximum value of Tg at ac = 0.5 was obtained by extrapolation of (1/MC, Tg) data to 1/M . 

Fig. 2. Automated torsion pendulum schematic. An analog electrical signal results from using a light beam passing through a pair of polarizers, one of which oscillates with the pendulum. The penduluin is aligned for linear response and initiated by a computer that also processes the damped waves to provide the elastic modulus and mechanical damping data, which are plotted vs. temperature or time...

In rubber-modified polystyrenes, the rubber is dispersed in the polystyrene matrix in the form of discrete particles. The two-phase nature of rubber-modified polystyrene was first suggested by Buchdahl and Nielsen [47] based on data on dynamic mechanical properties obtained with a torsion pendulum. The existence of two prominent loss peaks led to this conclusion, one at low temperatures which is due to the a relaxation of the rubber (e.g. 193 K for polybutadiene) and one at high temperatures which is due to the a relaxation of the matrix (e.g. 373 K for polystyrene). Later, microscopy provided proof of the existence of the rubber phase as a discrete dispersed phase in polystyrene [48]. 

Measurements of creep in torsion can be made very accurately. The reason is that deformation can be measured by measuring the large deflections of a light beam. A convenient way to simultaneously obtain shear dynamic and transient data is to combine both types of measurements in the same equipment (4). Usually this requires only small modifications of the experimental device. For example, the cross bar in a torsion pendulum can be removed and replaced by weights and pulleys to apply a constant torque to the upper clamp. In this way, a torsion creep apparatus is obtained (Fig. 7.8). The... 

Automated Torsion Pendulum Control and Data Collection/Reduction Using a Desktop Computer... 

A torsion pendulum interfaced with a desktop computer form an automated instrument for dynamic mechanical characterization of polymeric materials. The computer controls the initiation of the oscillations, collects the digitized data and calculates the shear modulus and loss modulus from the damped oscillations, utilizing one of four methods of analysis ... 

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. 

The data obtained from the torsion pendulum can be displayed in various modes (4) the shear modulus G is given by... 

Figure 4. Automated torsion pendulum control sequence. Key 1, previous wave decays, drift detected and correction begins II, reference level of polarizer pair reached III, wave initiating sequence begins. IV, decay of transients V, free oscillations begin VI, data collected and VII, control sequence repeated.

Data Reduction. The oscillatory motion of a freely moving torsion pendulum has been described by an equation of motion (4) ... 

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 automation of the torsion pendulum utilizing a desktop computer eliminates the tedious data analysis previously associated with that technique. Any one of four data reduction methods can be used the experimental conditions will determine which is the optimum one to employ. The torsion pendulum technique provides quantitative values of shear modulus and logarithmic decrement and in the torsion braid mode provides a qualitative analysis of materia i, especially in the liquid-to-solid transition region. 

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