Pressure dilatometry

Fig. 4.42 A schematic drawing of a high-pressure dilatometry apparatus (1) high-pressure pipe, (2) a sheathed Alumel-Chromel thermocouple, (3) a sheathed heater, (4) a support, (5) a liquid medium (silicon oil), (6) the sample, (7) a bellows cell, (8) steel wire, (9) high-pressure vessel, and (10) a differential transformer. (Reprinted with permission from Polymer J. 1992, 24, 778.)...

Pressure, Volume, and Temperature. The pressure-volume-temperature (PVT) diagrams of linear macromolecules in different states provide another set of important thermodynamic functions, as is shown in Figure 6, for polypropylene. Using high pressure dilatometry, macromolecules have been analyzed in their liquid states, as shown in Table 4. All data can be fitted to the empirical Tait equation listed in Figure 6. Both constants of the Tait equation are exponential functions of temperature. 

Another means of examining fundamental thermodynamic phenomena is the use of high pressure dilatometry to measure the pressure-volume-temperature dependence of polymers. This results in the development of an equation of state describing the variation of specific volume with temperature and pressure. As with DSC, these curves show thermodynamic as... 

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],...

Figure 21. Dual dilatometry effect of ram pressure on isothermal propellant cure...

I continue to feel that the study of the volume changes in protein reactions is sorely neglected. They may be determined by dilatometry and by the effects of pressure on protein equilibrium constants. The results complement the results of the determination of enthalpy changes as measured by calorimetry and the effects of temperature on equilibrium constants. Much useful insight at the molecular level can be obtained from a knowledge of volume changes... 

The typical form in which dilatometry data are reported is in terms of a volume difference and a relative volume as a function of temperature and pressure. 

The analogue of measurement of pressure change at constant volume for a gas phase reaction is the measurement of volume change at constant pressure for a reaction in the liquid phase by dilatometry ". This is used extensively in polymerisation studies. 

An increase in pressure results in an increase in T. When the polymer chains are subjected to pressure, more therma energy is required to activate the energy loss mechanisms. Heydemann and Guicking (23) determined the specific volume of unplasticized and DOP plasticized PVC by dilatometry over the temperature range of -80 to 150 °C at hydrostatic pressures of 1-1000 atm. Figure 19 shows... 

The presence of dissolved CO2 molecules in a polymer results in the plasticization of the amorphous component of the matrix. In this respect CO2 mimics the effect of heat but with the important distinction that the Tg is depressed. The extent of the Tg depression is dependent on the wt% of CO2 in the matrix. As previously mentioned, one of the characteristics of plasticization is the enhancement of segmental motion, which has been observed spectroscopically for the ester groups of PMMA [20] and the phenyl rings of polystyrene [21]. The consequential increase in free volume of the matrix has been studied by methods such as laser dilatometry [22], in situ FTIR spectroscopy [20], high-pressure partition chromatography [23], and inverse gas chromatography [24]. 

The dilatometry at different pressures leads to a full p-V-T phase diagram. Linear macromolecules in the liquid state can reach equilibrium and have then been successfully described by a single p-V-T diagram. The semicrystalline and glassy... 

The reaction volume can be determined by dilatometry, by measuring the effect of pressure on the equilibrium constant K, or by a combination of separately determined partial molar volumes of all reactants and products using Equation (2.25). 

The truly impressive feature of NELF is that it is a completely predictive model of small molecule sorption in glassy polymers, if information about the polymer partial density, P2, is known. Unfortunately, P2 is obtained firom dilatometry data, and these data exist for only a very small number of penetrant-polymer systems, which limits the general practical applicability of the model. In light of this shortcoming, two approaches have been used to make NELF more widely applicable. The first approach assumes that the pol5mier partial density is equal to the density of the pure polymer, p2° (96). This approach limits NELF to low pressures, where no polymer swelling occurs however, in this pressure range, NELF is still completely predictive. The second approach to increase the applicability of NELF introduces one or two adjustable parameters (95). In this approach, the poljnner partial density is assumed to vary linearly with pressure such that... 

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