Measuring Tg

Any polymer property that changes with temperature and has different values above and below Tg can be used, in principle, to determine Tg. For example, the change in specific volume, heat capacity, or elastic modulus may be used to measure Tg. Differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA) are two common methods for such determinations. An example of the results of DSC analysis Is presented In Fig. 3.46. It is common for different methods to yield slightly different values for Tg. 

Differential scanning calorimetry trace, obtained by cooling a crystalline polymer from the melt 

An empirical relationship has been determined between Tg and T, the melting temperature, with both temperatures in Kelvin. This allows either Tg or T , to be estimated, if the other is known. 

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The glass transition temperature is generally measured- by experiments that correspond to a time scale of seconds or minutes. If the experiments are done more rapidly, so that the time scale is shortened, the apparent Tg value is raised. If the time scale is lengthened to hours or days, the apparent Tg value is lowered. Thus, as generally measured, Tg is not a hue constant but shifts with the time scale of the experiment or observation. Moreover, Tg is masked by experimental difficulties, compounded by multiple and often inaccurate definitions of Tg in the literature. The least... 

The floe rupture model may also be used to explain the maximum observed in versus temperature (figure 5). According to equation (4) Tg = f (< > H) Eg, where f(2H) is the collision frequency term. Although Eg increases with increase of temperature, f(< > H) is a decreasing function of temperature as a result of decrease of solvency of the dispersing medium which leads to the contraction of the adsorbed layer (13). The increase of Eg with increase of temperature initially outweighs any reduction of f (< > H), but at higher temperatures, the reduction in f (4> j ) as a result of chain contraction may exceed the increase in Eg and this results in reduction in the measured Tg. 

Differences in mobility of various components (e.g., starch, sucrose, water) within a food system (e.g., a cookie), as well as the inherent heterogeneity of many food systems (e.g., crust versus crumb of a cookie), suggest the need to measure more than an average Tg for a system. Ruan and Chen (1998) proposed the creation of a Tg map to capture the distribution of Tg values within a food system. Since conventional techniques used to measure Tg do not have the capacity at the present time to provide spatial information, Ruan and Chen (1998) suggested the use of MRI, as a function of temperature, to produce a Tg map. ... 

Because both Tg and water activity are functions of water content, the two parameters can be correlated to each other. This can be done in two main ways, as presented by Roos (1995). The first is to measure Tg of samples humidified to known water activity values (i.e., using saturated salt solutions) and then plot Tg values as a function of water activity (e.g., see Figure 6.2A in Roos, 1995). Over the entire nw range, a sigmoid-shaped curve was... 

Table 5. Input of measured TG-data, processing for vapor pressure determination, output of results... 

Sample Entry Oligomer Type Theory (gram/mol) Measured Tg°C... 

The problem of determining V-j in SEC is similar to that of determining zero retention time (tg) in other liquid chromatography columns. Recently, there have been several papers dealing with the determination of retention time of a retained peak in HPLC (12-19). In high-performance reversed-phase chromatography, McCormick and Karger (1 ) and Berendsen, et al., (16) have employed D2O to measure tg. Neidhart et al.,... 

The glass-transition temperatures and the corresponding specific heats were measured three times for each sample in order to enable the calculation of the standard deviations, which were in the range of 3% or lower. Apparently, the kind of substituent greatly influences the Tg values, and rigid substituents (phenyl or methyl) or flexible substituents (ethyl or nonyl) cause an increase or decrease in corresponding Tg values, respectively. The measured Tg values are plotted in Fig. 19. 

Tg of individual polymer in a blend b Measured Tg of a blend c Calculated Tg from the Fox Equation d Difference between the measured Tg and the calculated Based on temperature difference... 

For materials generally, change in expansion (or density) by dilatometry was traditionally the most often used method for measuring Tg. Thermal properties, for example specific heat, are also widely used, particularly the methods of differential thermal analysis". A method for rubbers using DSC is being developed in ISO TC 45 as ISO 22768, but is not yet published. The inflection point on the heat input - temperature curve is usually obtained automatically by the analyser s software but, if obtained manually, is best found from the derivative of the curve. 

Measuring Tg by mechanical methods is usually done with the dynamic methods, as discussed in Chapter 9, but estimates could be made from the standardised low temperature tests discussed in the next section. Indeed, these tests have been the most widely used to study the low temperature behaviour of rubbers although the transition temperature is not specifically derived. Occasionally, electrical methods have also been used. 

The relationship between flexibility and copolymer composition was explored by measuring Tg and Tgp for a series of copolymers consisting of styrene or methyl methacrylate paired with several "softer" comonomers. An example of the kind of results obtained is illustrated in Figure 11 with the methyl methacrylate/ ethyl acrylate pair. Included in this plot is a ductility, or toughness, parameter, q, defined by Wu as,... 

Most methods to measure Tg are, respectively, based on the jump in specific heat and on the sharp decrease of the modulus of elasticity, accompanied by a maximum in the damping. 

Differential scanning calorimetery (DSC) was used to measure heat capacity as a function of temperature. The DSC used in this study was a Perkin-Elmer model DSC-2. Liquid nitrogen was used as a heat sink and helium was used as the purge gas. Samples were usually about 30 mg, and a heating rate of 20°C/min was used for measuring Tgs and Tms. 

Nonetheless, the correlations they obtained with product structure are very informative. The melt penetration was defined as the temperature above the 7) /moisture curve at the point of extrusion. (Note that from the arguments presented above, this parameter will correlate positively with both the steam-driving pressure for expansion and inversely with melt elasticity and viscosity, that is, conditions for rapid bubble expansion.) The second parameter measured was the moisture and temperature of the expanded product immediately after the die, and its value was compared to the midpoint of the measured Tg of the ingredient mix at the same water content. 

The characteristic temperature, T0, is usually located about 30-70°C below the experimentally measured Tg and in various thermodynamic theories it represents an equilibrium value. We will not discuss these theories, but the existence of such a thermodynamic transition remains in dispute, with some arguing that the T is purely a kinetic phenomenon. Certainly, the experimentally observed quantity is kinetic in character. One manifestation of this is the shift in T... 

In Figure 21.8, a softening temperature for the polystyrene endblock is shown as a function of endblock molecular weight (ranging from about 6000 to 30000). The softening temperature is characterized as the onset of test specimen creep (in a small-strain dynamic mechanical test in tensile mode), the creep point occurring when strain extension becomes considerable in order to maintain the appropriate stress level to continue the test. This softening temperature lies below the measured Tg, and it is an indication of the... 

Many relatively slow or static methods have been used to measure Tg. These include techniques for determining the density or specific volume of the polymer as a function of temperature (cf. Fig. 11-1) as well as measurements of refractive index, elastic modulus, and other properties. Differential thermal analysis and differential scanning calorimetry are widely used for this purpose at present, with simple extrapolative eorrections for the effects of heating or cording rates on the observed values of Tg. These two methods reflect the changes in specific heat of the polymer at the glass-to-rubber transition. Dynamic mechanical measurements, which are described in Section 11.5, are also widely employed for locating Tg. 

If in relationship (124) the fuzzy similarity measure Sg is replaced by either one of the unsealed similarity measures tg and Zg or the scaled similarity measures s, tf, and Zf, then the fuzzy symmorphy element 5( )3) is specified in terms of the corresponding fuzzy Hausdorff-type similarity measure. 

Actual weighed composition of sample, expressed as monohydrate (%) Anticipated TG weight loss of sample (%) Experimentally measured TG weight loss (%) Calculated monohydrate content, based on weight loss of 5.0% for the monohydrate (%)... 

IMA and RIA are the two main methods used for the measurement of Tg. The IMA assays have the advantage of having a shorter incubation time and are automatable however, they suffer from greater interferences. The main interferants in both assays are antithyroglobulin antibodies, which cause an underestimation of Tg levels in the IMA. Antithyroglobulin antibodies can either be measured directly in all patients or if both IMA and RIA are used to measure Tg, a discordant result suggests the presence of anti-thyroglobulin antibodies. 

Crystallinity can be measured using the same thermal and dynamic mechanical methods used for measuring Tg however, the melting transition (Tm) is much sharper and is at a higher temperature than the Tg. The majority of the PB is used as an elastomer for which... 

Applications of TMA are in many ways the simplest of the thermal techniques. Only the change in the size or position of a sample is being measured. However, they are also incredibly important in supplying information needed to design and process everything from chips to food products to engines. A sample of ASTM methods for TMA is shown in Table 1. Because of the sensitivity of modern TMA, it is often used to measure Tg s that are difficult to obtain by DSC, for example, those of highly cross-linked thermosets. 

Oxygen deficiency in a series of doped SrTiOs+g perovskites was measured using thermo-gravity measurement (TG, Mac Science, TG-DTA-5000S). A flow rate of 50 ml/min H2 gas was used in the TG measurements after the gas had been bubbled through pure water at 283K. The partial pressure of oxygen observed was almost the same as that calculated (3.6 10 atm for the calculated value versus 4.2 10 atm for the observed value). 

The Tg of the resulting polymers can be steered in this way to any desired value between the Tg of the two homopolymers involved by adjusting the level of co-mono-mer employed. The Tg of homo(polynorbornene) is around 370-390 °C. The measured Tg of 5-decylnorbornene homopolymer is around 150-160 °C. Longer alkyl substituents (e.g. hexadecylnorbornene) have a more pronounced impact on Tg. 

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