Casing: dilatometry

For the first case, as the sample is heated, there will be a change in the volume of the sample that can be followed by a technique known as dilatometry. For changes in entropy, use can be made of the fact that AG = 0, and from Eq. (8.51) we find that... 

These graft copolymerizations became heterogeneous almost immediately, but in the case of MAN this did not lead to difficulties in measuring the rate of polymerization via dilatometry 36). 

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). 

VS c to c = 0. (Scheme 2) (c) from the direct measurement of the difference between the volumes of reactants and products employing dilatometry. To a first approximation the molar volume of neat liquid compounds (Tm = M/d) and, hence, the reaction volumes can be calculated with additive group increments which were derived empirically by Exner for many groups such as CH3, CH2, or CH from the molar volumes, Tm. easily determined from the known densities for many different types of compounds. This method is comparable to that of the calculation of enthalpies of formation by the use of Franklinor Benson group increments. In all cases where the volume of reaction could be determined by at least two independent methods, the data were in good agreement. ... 

Reactions in the pure liquid phase, typically the cyclopentadiene dimerisa-tion, have been sometimes studied by refractometry" " " or dilatometry". In other cases, eithei determination of product and/or reactants has been preferred"" " or the same methods as for reactions in solution were employed. It is worth mentioning that kinetics of a few Diels-Alder reactions were determined by gas-chromatographic analysis of diene, the dienophile being the stationary phase inside the column" . 

Choi et al. [S] used dilatometry to monitor the kinetics of styrene miniemulsion polymerizations employing not only varying KPS concentrations but, in addition, the oil-soluble initiator 2,2 -azobis(2-methyl butyronitrile) (AMBN). The latter was initially thou t to provide an increased probability of nucleating all monomer droplets considering that the main locus of initiator decomposition and subsequent ch growth would be in the monomer droplets. This, however, did not prove to be the case. 

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... 

Combining Eq. (1) with (2) results in Eq. (3). One can see that in this case the change of heat, dQ, can be expressed in three terms the first is due to the change in temperature, the second due to the change in volume, and the third due to the change of the number of moles of substance in the system. A full characterization by thermal analysis would, thus, require calorimetry, dilatometry, and also thermogravimetry. 

The quantitative influence of self-nucleation is shown in Fig. 3.66 for the case of crystallization of poly-l-butene with crystal form 11 when followed by dilatometry. 

At sufficient supercooling, the sphemhtic superstmcture may be described with only one growth rate, v, as shown in Fig. 3.83. The increase in crystal volume, V, is given by the second equation and allows the computation of the enthalpy evolved by multiplication with the product of density and specific heat of fusion (Ahf in 1 g ). With nucleation data, the crystallization rate of the whole sample can be computed and linked to growth rates measured by dilatometry or calorimetry. Results for the LiPOj crystallization, which is discussed in Sect. 3.1.6, are also listed in Fig. 5.83 [15]. The changes of the growth rale with temperature are given in the table. Note that the crystallization of the polymer is in this case coupled with the polymerization reaction [1], and increases with temperature. 

Figure 4.67[A] shows a typical isothermal experiment carried out with a DSC. Similar experiments could be carried out with isothermal calorimeters, dilatometry and other teehniques sensitive to crystallinity changes. After attainment of steady state at point 0, the experiment begins. At point 1, the first heat flow rate is observed, and when the heat flow rate reaches 0 again, the transition is complete. The shaded area is the time integral of the heat flow rate, and if there is only a negligible instrument lag, it represents the overall kinetics. In case of an excessive heat flow-rate amplitude, lag calibrations with sharply melting substances of similar thermal conductivity may have to be made (see Figure 4.22). Processes faster than about 1 min...

Dilatometry and thermomechanical analysis (TMA) are also techniques used to monitor the thermal behavior of fibers. They both employ a sensitive probe in contact with the surface of the sample, and the thermal transitions are detected either by a change in volume or modulus of the sample, respectively. In the latter case, the probe necessarily penetrates the sample surface. A variable transformer records the voltage output that is directly proportional to the degree of displacement of the probe during a thermally induced transition. TMA is a more sensitive technique than either DTA or DSC for detecting thermal transitions. 

The overall crystallization rate is used to follow the course of solidification of iPP. Differential scanning calorimetry (DSC), dilatometry, dynamic X-ray diffraction and light depolarization microscopy are then the most useful methods. The overall crystallization rate depends on the nucleation rate, 1(0 and the growth rate of spherulites, G(0. The probabilistic approach to the description of spherulite patterns provides a convenient tool for the description of the conversion of melt to spherulites. The conversion of melt to spherulites in the most general case of nonisothermal crystallization is described by the Avrami equation ... 

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