Glass transition specific volume

For a property which manifests a change at the glass transition (specific volume for example), the experimentally determined value below T is dependent on the sample thermal history. For example, for faster cooling rates, the glass is observed to have a greater specific volume. In addition, for... 

The thermophysical properties, such as glass transition, specific heat, melting point, and the crystallization temperature of virgin polymers are by-and-large available in the literature. However, the thermal conductivity or diffusivity, especially in the molten state, is not readily available, and values reported may differ due to experimental difficulties. The density of the polymer, or more generally, the pressure-volume-temperature (PVT) diagram, is also not readily available and the data are not easily convertible to simple analytical form. Thus, simplification or approximations have to be made to obtain a solution to the problem at hand. 

Polymeric materials are unique owing to the presence of a glass-transition temperature. At the glass-transition temperatures, the specific volume of the material and its rate of change changes, thus, affecting a multitude of physical properties. Numerous types of devices could be developed based on this type of stimuli—response behavior however, this technology is beyond the scope of this article. 

As the temperature is decreased, free-volume is lost. If the molecular shape or cross-linking prevent crystallisation, then the liquid structure is retained, and free-volume is not all lost immediately (Fig. 22.8c). As with the melt, flow can still occur, though naturally it is more difficult, so the viscosity increases. As the polymer is cooled further, more free volume is lost. There comes a point at which the volume, though sufficient to contain the molecules, is too small to allow them to move and rearrange. All the free volume is gone, and the curve of specific volume flattens out (Fig. 22.8c). This is the glass transition temperature, T . Below this temperature the polymer is a glass. 

Fig. 14. The variation of the specific heat jumps at glass-transition temperatures of elacc-epoxy composites, versus the fiber volume content, uf. The values for the factor X and the mesophase, (uj and matrix, (nm) volume fractions, versus uf, as derived from the values of the respective AC, s are also plotted...

Glass transition temperature (Tg), measured by means of dynamic mechanical analysis (DMA) of E-plastomers has been measured in binary blends of iPP and E-plastomer. These studies indicate some depression in the Tg in the binary, but incompatible, blends compared to the Tg of the corresponding neat E-plastomer. This is attributed to thermally induced internal stress resulting from differential volume contraction of the two phases during cooling from the melt. The temperature dependence of the specific volume of the blend components was determined by PVT measurement of temperatures between 30°C and 270°C and extrapolated to the elastomer Tg at —50°C. 

FIGURE 24.6 Specific volume as a function of temperature at the indicated pressures for 1,2-PB network (molecular weight between cross-hnks 8 kg/mol) [81]. The solid squares denote the glass transition defined from the intersection of the glassy and liquid data. 

Figure 3 Curves of specific volumes vs. temperature for poly(vinyl acetate) measured on cooling. Equilibrium values measured 0.02 h and 100 h after cooling, as indicated. Tg and Tg are glass transitions respectively at fast and slow cooling rate. Reproduced from Ref. [2] with permission of John Wiley Sons, Inc.

Fig. 1 9 Determination of glass transition and crystalline melting temperatures by changes in specific volume.

Figure 17. Specific volume Vt and isothermal compressibility (at the glass transition temperature Tg) calculated from the LCT as a function of the inverse number l/M of united atom groups in single chains for constant pressure (P = I atm 0.101325 MPa) F-F and F-S polymer fluids. Both quantities are normahzed by the corresponding high molar mass limits (i.e., by...

Frequency-Dependent Specific Heat. We mention measurements of volume relaxation through the frequency-dependent specific heat Cn(co) as in fluids near the glass transition [52]. This is feasible when the experimental frequency co is of the order fi0 in small gels. The deviations of the entropy, temperature, and volume are related by SS = CV5T + (dH/dT)v8Vand the relaxation equation reads... 

Below T0 the material is in the glassy state. Compared with the crystal the glass shows a larger specific volume and heat content, but both quantities have a smaller temperature coefficient than in the melt (< ). The transition from melt to glass is often called a transition of the second order (2, 3) since it is not accompanied by finite changes of volume and enthalpy, but only by changes of their temperature coefficients. 

---