Methods of Determining Glass Transition Temperature

Finally, there is the extremely important group of relaxation methods for determining T. These can be based on either mechanical (sometimes thermomechanical) or electrical relaxations occurring within the material, and, although they do not always give results that are completely consistent with those obtained by the static mechanical tests already mentioned, they are considered very reliable and are widely used. 

The relaxation methods employed are Dynamic Mechanical Thermal Analysis (DMTA) and Dielectric Thermal Analysis (DETA). Generally in both cases a single excitation frequency is used and the temperature is varied, 

Dynamic mechanical techniques for studying polymers are described in detail in Chapter 7. For the moment we will restrict ourselves to a simple outline of the method of DMTA as it is applied to the determination of Tg. 

Experimentally DMTA is carried out on a small specimen of polymer held in a temperature-controlled chamber. The specimen is subjected to a sinusoidal mechanical loading (stress), which induces a corresponding extension (strain) in the material. The technique of DMTA essentially uses these measurements to evaluate a property known as the complex dynamic modulus, , which is resolved into two component parts, the storage modulus, E and the loss modulus, E . Mathematically these moduli are out of phase by an angle 5, the ratio of these moduli being defined as tan 5, Le. 

By contrast, the technique of DETA is based on electrical measurements. In this technique polymers are exposed to an alternating current and changes 

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Rudoy VM, Dement eva OV, Yaminskii IV, Sukhov VM, Kartseva ME, Ogarev VA, Metal Nanoparticles on Polymer Surfaces 1. A New Method of Determining Glass Transition Temperature of the Surface Layer, Colloid J., 64, 746-54 (2002). 

Y. Tamai. A practical method to determine glass transition temperature in molecular dynamics simulation of mixed ionic glasses. Chem. Phys. Lett. 351 (1-2), 2002, 99-104. 

Below T polymers are stiff, hard, britde, and glass-like above if the molecular weight is high enough, they are relatively soft, limp, stretchable, and can be somewhat elastic. At even higher temperatures they flow and are tacky. Methods used to determine glass-transition temperatures and the reported values for a large number of polymers may be found in References 7—9. Values for the T of common acrylate homopolymers are found in Table 1. 

The measurements of Young s modulus in dependence of the temperature (dynamic-mechanical measurements, see Sect. 2.3.5.2) and the differential thermal analysis (DTA or DSC) are the most frequently used methods for determination of the glass transition temperature. In Table 2.10 are listed and values for several amorphous and crystalline polymers. 

The kink observed around 367 K corresponds to a change of the thermal expansion coefficient from a glassy to a liquid-like state and, by that, marks the position of the glass transition temperature. Usually, the 7g is calculated as a intersection point between two linear dependencies. Nevertheless, a more convenient method is the calculation of the first and second numerical derivatives of the experimental data (Fig. 15b,c). In this case, the Tg is defined as the minimum position in the second numerical derivative plot (Fig. 15c). Down to a thickness of 20 nm, no shifts of 7g as determined by capacitive scanning dilatometry were found (Fig. 16). 

The classic method for the experimental determination of the glass transition temperature is dilatometry. Thus, as briefly mentioned in Chapter 1, the temperature dependence of the specific volume is determined by a suitable technique, and the temperature at the change in slope upon cooling is taken as Tg. Such a plot is indicated in Figure 5-1, where it is shown that the Tg is... 

In the case of reuse of plasticized PVC, it is important to determine the residual plasticizer content. This can be obtained by extraction with ether or similar nonsolvents for PVC and determination of the chemical nature of the plasticizers by thin-layer or gas chromatographic methods. The determination of the glass transition temperature by differential thermal analysis also gives information on the efficiency of the residual plasticizers. 

Standard test method for assignment of the glass-transition temperatures hy differential scanning calorimetry or differential-thennal analysis Methods of test for determination of glass-transition temperature of electrical insulating materials... 

A method that is frequently used because of its relative simplicity is the determination of the glass-transition temperature Tg of the blend, which can be determined by any of the methods discussed in chapter 7. DSC is often used. 

Chain segments move with a definite frequency above the glass transition temperature. Consequently, the frequency of the measurement method used or the deformation time of the sample must determine the numerical value of the glass transition temperature observed. Thus, the methods of measurement are classified as static or dynamic according to the speed of the measurement. 

ASTM (1994) E1640-94. Standard Test Method for Assignment of the Glass Transition Temperature by Dynamic Mechanical Analysis, American Society for Testing and Materials, Philadelphia, PA. Tomblin, )., Salah, L., and Ng, Y. (2001) Determination of Temperature/Moisture Sensitive Composite Properties. DOT-FAA Report DOT/FAA/AR-01/40, Office of Aviation Research, Washington, DC. Bai, Y., Post, N.L, Lesko, J.J., and Keller, T. (2008) Experimental investigations on temperature-dependent thermophysical and mechanical properties of pultmded GFRP composites. Thermochim. Acta, 469, 28-35. 

The polymers were prepared by reacting five glycidyl ethers with 4, 4 -diisocyanatodiphenylmethane in the presence of 2-ethyl-4-methylimidazole. The degree of cure of the resins was followed by IR spectroscopy and DSC. The rates of the isocyanurate to oxazolidone linkages were determined quantitatively by an infrared method and the glass transition temperatures of the polymers were measured by DSC and dynamic mechanical thermal analysis. 16 refs. 

The numerical value of the glass-transition temperature depends on the rate of measurement (see Section 10.1.2). The techniques are therefore subdivided into static and dynamic measurements. The static methods include determinations of heat capacities (including differential thermal analysis), volume change, and, as a consequence of the Lorentz-Lorenz volume-refractive index relationship, the change in refractive index as a function of temperature. Dynamic methods are represented by techniques such as broad-line nuclear magnetic resonance, mechanical loss, and dielectric-loss measurements. Static and dynamic glass transition temperatures can be interconverted. The probability p of segmental mobility increases as the free volume fraction / Lp increases (see also Section 5.5.1). For /wlf = of necessity, p = 0. For / Lp oo, it follows that p = 1. The functionality is consequently... 

Several methods of Tg determination make it possible to measure the width of the glass transition temperature (TW). The value of TW can be more rehable in assessing the degree of miscibility than Tg. For example, TW of 6 °C was determined for neat polymers, TW = 10 °C for miscible blends, and TW = 32 °C for blends approaching immiscibility (Fried et al. 1978). By measuring Tg and TW for samples annealed at different temperatures and then quenched, one may be able to determine the level of miscibility and hence construct a simplified phase diagram. This has been done for numerous blends, like those listed in Table 2.26, and others, e.g., for PS/PTMPC, PVC/poly(a-methylstyrene-co-methylmethacrylate-co-acrylonitrile), and NBR/EVAc (Casper and Morbitzer 1977) vide infra. Table 2.27). 

A further important data point within the initial assessment is the determination of the glass transition temperature (Tg). Different test methods are described in more detail in Section 12.5.2. For the first assessment, one method should be selected. When choosing the method, it is important to make sure that the test procedure is compatible with the material in test... 

Because of the frequency dependence of Tg, the convention adopted for assignment of the glass transition temperature is an important consideration. Traditionally, a frequency of 1 Hz has been used as a standard value. This is based on the historic precedence, since the torsion pendulum was the most widely used DMA technique in the early days of viscoelastic property measurements. The torsion pendulum is a free vibration technique with a natural frequency of approximately 1 Hz. The 1 Hz value also is reasonably close (within 10 °C) to the Tg values determined by other widely used methods such as DSC, dilatometry, and TMA. The relation between DMA and DSC Tg values is considered further at the end of this chapter (Sircar and Drake 1990). Because of the ambiguity inherent in the kinetic nature of Tg, it is most important that the test frequency be reported along with any Tg value determined by a DMA technique. 

For many polymers, it has been determined experimentally that the ratio of the glass transition temperature to the melting temperature, TglT 0.6 (both temperatures in Kelvins). For example, for polypropylene, Tg = -19°C and T = 16°C, so TglT = 0.57. Tg can be estimated by group-contribution methods. ... 

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