The dilatometric method

For kinetic investigations of homogeneous polymerizations, a variety of methods and apparatus has been developed. The dilatometric method is especially worthy of mention on account of its simplicity and general applicability (Fig. 2.3). 

Dilatometric technique can also be used for determination of polymerization rate in the case of multimonomer polymerization. However, in this case calibration of the dilatometric method is more complex. The substrates and products are both polymers with similar molecular weights. Difference in density during the course of polymerization is connected only with the conversion of double bonds to the single bonds. It is difficult to obtain a macromolecular product in which double bonds are fully converted to single bonds. Calibration must be based on simultaneous measurements of Ah and independent method (e.g., IR spectroscopy) and calculation of (1/dp l/d]vi). 

Rate coefficients of hydrolysis and other nucleophilic reactions of epoxides have been measured by various authors (49, 150—154]. The data are reviewed insofar as they are of interest with respect to acid—base catalysis. Measurements have been done mainly by the dilatometric method or by continuous titration of the base formed in the reaction. Table 9 contains rate coefficients, referring to rate eqn. (44), and... 

The SFC and SFI values can be determined by dilatometric methods or by pulsed NMR. The dilatometric method is still considered the most accurate, but NMR provides reliable information much more quickly. 

The dilatometric method is time-consuming and subject to the bias introduced by the convention described. More recently pulsed Nuclear Magnetic Resonance (pNMR) has been used to measure the relative amounts of liquid and solid fat in a sample, based upon the difference in rates of relaxation of protons in the two phases after the sample has been pulsed (AOCS Method Cd 16-81). With proper calibration this gives a direct determination of the percentage of solid fat, and the results are termed sohd fat content (SFC). The analysis takes less time than dilato-metry, but the equipment is more expensive. 

The dilatometric method evidently gives no indication whatever of critical points in this alloy. On the expansion curve there is no sign of any definite irregularity. 

Experimental Measurement of Rate of Cure. The rate of cure was measured experimentally in several studies (54-58). Three of these (54, 57, 58) used the dilatometric method to determine the rate of... 

I. The Dilatometric Method.—Since, in the majority of cases, transformation at the transition point is accompanied by an appreciable change of volume, it is only necessary to ascertain the temperature at which this change of volume occurs, in order to determine the transition point. For this purpose the dilatometer is employed, an apparatus which consists of a bulb with capillary tube attached, and vrhich constitutes a sort of large thermometer (Fig. 159). Some of the substance to be examined is passed into the bulb A through the tube B, which is then sealed off. The rest of the bulb and a small portion of the capillary tube is then filled with some liquid, which, of course, must be without chemical action on the substance under investigation. A liquid, however, may be employed which dissolves the substance, for, as we have seen (p. 58), the transformation at the transition point is, as a rule, accelerated by the presence of a solvent. On the other hand, the liquid must not dissolve in the substance under examination, for the temperature of transformation would be thereby altered. 

If the melt were contained in a crucible, expansion would continue to occur to the highest temperature of the experiment. However, the sample used in thermal expansion measurements is actually under a small load introduced by the push rod. Eventually, deformation will occur as the push rod sinks into the sample or the sample bends under the load. The temperature of maximum expansion is called the dilato-metric softening temperature, or T (Figure 7.8). This temperature is an artifact of the dilatometric method used to measure the thermal expansion coefficient. As a result, it is slightly dependent upon the load applied by the push rod and the cross-sectional area of the sample, which, in combination, determine the stress on the sample. Values obtained from most laboratories, surprisingly, agree within a few degrees. 

The glass transition temperature was determined using the dilatometric method. Volume dependence on temperature was measured on a rising temperature scale with a heating rate of 2° K/min. The films were carefully degassed at room temperature before filling the dilatometer with mercury. 

The dilatometric methods for detecting phase changes utilize volume changes in the same way as the calorimetric methods utilize thermal effects. Dilatometry is widely used in the analysis of melts and particularly of fats and waxes (Bailey, 1950 Swern, 1979). The techniques and equipment are usually quite simple. 

The bound water content can be determined by methods such as dilatometric determination, vacuum filtration, expression, drying, and thermal analysis. The dilatometric method is based on the assumption that free water can be frozen at 20°C. By placing a known amount of sludge into a scaled container called a dilatometer and measuring the volume of expansion at 20°C, the free water content can be calculated [18]. The part that does not freeze is the bound water. The sludge is usually mixed with a fluid that does not freeze at 20°C, is immiscible with water, has specific gravity less than 1.0, and shows... 

The most widely used way to study the kinetics of pol5mierization is the dilatometric method. It allows to carry out the measurements on a continuous basis and provides precise and reproducible results. 

The quantities measured in the dilatometric method are the changes in the height of the liquid column (h) during the reaction time (t). The degree of transformation (W), which is a measure of the decrease of meniscus of the reaction mixture in the capillary of dilatometer, is obtained fi om the following formula ... 

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