Dilatometry Calibration

Dilatometry utilizes the volume change that occurs on polymerization. It is an accurate method for some chain polymerizations because there is often a high-volume shrinkage when monomer is converted to polymer. For example, the density of poly(methyl methacrylate) is 20.6% lower than that of its monomer. Polymerization is carried out in a calibrated reaction vessel and the volume recorded as a function of reaction time. Dilatometry is not useful for the usual step polymerization where there is a small molecule by-product that results in no significant volume change on polymerization. 

An interferometer can be used to very accurately measure the thermal expansion of solids. Although not utilized commercially to the level of dilatometry, NIST standard materials, which are in turn used to calibrate dilatometers, have had their expansion characteristics determined using interferometry. In fact, the formal definition of the meter is based on interferometric measurements. The operation of the device is based on the principle of interference of monochromatic light. The fundamental relations between wavelength and distance will first... 

One of the oldest methods employed for following the course of polymerisations with half life longer than about 15 min is based upon the volume contraction which accompanies these processes. This technique can easily be adapted to hi -vacuum manipulations and is quite reliable, provided accurate calibrations are carried out particularly when oligomers are present among the products. Apart from the limitation imposed by the initial dead time, dilatometry is also confined in scope, since it can only provide empirical kinetic relationships between the polymerisation rate and such variables as the concentrations of reactants, the temperature, the polarity of the solvent, etc. It is therefore more useful when used in conjunction with other tools devised to probe more mechanistic aspects of the process. Hi -vacuum equipment... 

Calorimetry and dilatometry were used to estimate super-high molar masses for some crystallizable polymers. For such high molar masses, crystallization is increasingly impeded and the fraction of the molecules able to crystallize has been calibrated with respect to molar mass for polytetrafluoroethylene [25,26]. 

A quantitative, isothermal measurement of the crystallization kinetics, usable for analysis by the Avrami method, is illustrated in Fig. 3.98 by the upper left curve. Similar curves can be generated by dilatometry or adiabatic calorimetry as described in Sects. 4.1 and 4.2. At time zero, one assumes that the isothermal condition has been reached. The dotted segments of the heat-flow response are then proportional to the heat of crystallization evolved in the given time intervals and can be converted directly into the changes of the mass fraction of crystallinity after calibration or normalization to the total heat evolved. An independent crystallinity determination... 

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...

Sample density can be measured using a variety of methods density-gradient column, dilatometry, pycnometry, and flotation or buoyancy. The density-gradient column approach is probably used most frequently to determine sample densities for crystallinity measurements. When thermostated and appropriately calibrated with floats, this approach permits measurements to accuracies of 0.2 mg/cm or better. Dilatometers are well suited for measuring specific volumes and following crystallization, as a function of temperature. 

The techniques discussed may be viewed as a fonn of dilatometry, and a glass dilatometer was, in fact, used by Laita (23) to study the polymerization of etl lene in benzene at pressures which were not recOTded, but must have been as h%h as about 50 atm in some cases. Here, too, recourse had to be taken to gravimetric calibration of the volume change of polymerization, particularly, since a liquid and a gas phase must have coexisted. 

In dilatometry, a sample of polymer is enclosed in mercury within a glass bulb from which a capillary tube extends. The level of mercury in the capillary is recorded as the temperature is changed. An abrupt change in volume occurs at the melting point. With appropriate calibration, a plot of polymer-specific volume against temperature can be obtained such is illustrated in Fig. 18.13. 

Dilatometry. A vitreous silica dilatometer is the basis of ASTM method D696 (27). A specimen with flat, parallel ends is placed in the bottom of an outer dilatometer tube with an inner tube resting on its upper end. A linear variable differential transformer (Ivdt) is attached to the outer tube and is in contact with the top of the inner tube. To prevent indentation of the specimen by the inner tube, thin metal plates are attached or glued to the ends of the specimen. The lower part of the dilatometer containing the specimen is allowed to equilibrate alternately in constant-temperature baths maintained at -30 and at 30°C. By measuring precisely the temperatures of the baths and the change in dimension of the specimen from the output of the calibrated Ivdt, the linear thermal expansivity may be calculated with the help of equation 6. 

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