Dilatometry, glass transition temperature

As-polymerized PVDC does not have a well-defined glass-transition temperature because of its high crystallinity. However, a sample can be melted at 210°C and quenched rapidly to an amorphous state at <—20°C. The amorphous polymer has a glass-transition temperature of — 17°C as shown by dilatometry (70). Glass-transition temperature values of —19 to — 11°C, depending on both method of measurement and sample preparation, have been determined. 

Fig. 16 Glass transition temperature of thin PS films measured by capacitive scanning dilatometry as a function of film thickness...

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). 

Empirical Relationship - Empirical relationships correlating glass transition temperature of an amorphous viscoelastic material with measurement temperature and frequency, such as the William Landel Ferry equation (17) and the form of Arrhenius equation as discussed, assume an affine relationship between stress and strain, at least for small deformations. These relationships cover finite but small strains but do not include zero strain, as is the case for the static methods such as differential scanning calorimetry. However, an infinitely small strain can be assumed in order to extend these relationships to cover the glass transition temperature determined by the static methods (DSC, DTA, dilatometry). Such a correlation which uses a form of the Arrhenius equation was suggested by W. Sichina of DuPont (18). 

Figure 23.2 Glass transition temperatures as determined by dilatometry and by DSC methods, with respect to the level of hydrogenation. Reproduced from Ref. 10, with permission of John Wiley Sons...

The glass transition temperature of thin PS films after different annealing times at 180°C in ambient air was also measured by capacitive scanning dilatometry [43,44] (Fig. 35). It provides a Tg determination on an experimental time scale much longer than in conventional dielectric measurements, since the... 

Figure 35. Glass transition temperature 7., (determined by dilatometry) and relaxation time r at 131°C as a function of annealing time in air at 180°C for a film thickness of 63 nm. The dotted lines serve as a guide for the reader. Inset Dilatometric determination of the glass transition temperature. Upper. Normalized capacitance Cn0nn versus temperature at 106Hz (the solid lines represent linear dependencies, the dotted line marks the position of the glass transition temperature). Lower. The corresponding first and second numerical derivatives of Cnonn (in arbitrary units) as a function of temperature.

A common practice is to reduce relaxation or creep data to the temperature Tg thus, the reference temperature is picked as the glass transition temperature measured by some slow technique such as dilatometry. The reason for choosing Tg as the reference temperature is founded on the idea that all amorphous polymers at their glass transition temperature will have similar viscoelastic behavior. This type of corresponding states principal is often expressed in terms of a hopefully universal mathematical relationship between the shift factor aT at a particular temperature and the difference between Tg and this temperature. Perhaps the most well known of these relationships is the WLF equation... 

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... 

Semi-empirical rules, which correlate the static glass transition temperature Ty from differential thermal analysis or dilatometry with the dynamic T(J taken from the tan 8 or E" peak, may be used with caution in analyzing two-phase systems with a dispersed rubbery phase. The dynamic Tg depends on the rubber phase volume, and it may be shifted further toward lower temperature for effectively crosslinked and grafted rubber particles because of dilatation. 

In the majority of cases the compatibility of the polymers is characterized by the glass-transition temperature Tg, determined by methods such as dilatometry, differential scanning calorimetry (DSC), reversed-phase gas chromatography (RGC), radiation thermal luminescence (RTL), dynamic mechanical spectroscopy (DMS), nuclear magnetic resonance (NMR), or dielectric loss. The existence of two... 

Either, one uses an independent method for the crystallinity determination, such as dilatometry. X-ray diffraction or infrared spectroscopy for the determination of Wc [4], or one tries to determine the amorphous fraction, Wa, from the measured increase of the heat capacity at the glass transition temperature, ACp, and the same quantity for the fully amorphous sample, ACf... 

For the dielectric measurements, sample disks were coated with silver in vaouo as electrodes. The tacticity of sample polymer was estimated by the diad analysis of NMR spectrum (18). NMR measurements were carried out in an o-dichlorobenzene solution of samples at 90 MHz and at 130 C. The density and the glass transition temperature(Tg) were measured by the floatation and the dilatometry, respectively. 

The TMA is an easy-to-use analytical instrument that measures dimensional changes in a material as a function of temperature or time under a controlled atmosphere. Its main uses in research and QC include accurate determination of coefficient of linear expansion of plastic materials. It also is used to detect transitions in materials (e.g., glass transition temperature, softening and flow information, delamination temperature, creep and stress relaxation, and melting phenomena). A wide variety of measurement modes are available (expansion, penetration, flexure, dilatometry, and tension) for analysis of solids, powders, libers, and thin film samples. 

Figure 15. Summary of glass transition temperatures of HDA P < 0.4 GPa) and VHDA (P>0.8 GPa) deduced in the literature as measured by Andersson et al. (squares) [80-84], Mishima (circle and grey bar) [41], Seidl et al. (triangles) [123], and Handle et al. (stars) [124]. Open squares from dielectric relaxation measurements [80-83] filled square from high-pressure Cp and thermal conductivity data [84] circle from high-pressure DTA [41] open triangle by DSC at Ibar [123] filled triangles by high-pressure dilatometry [123] stars from high-pressure structural relaxation times [124],...

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