Borchardt and Daniels

A study of benzocyclobutene polymerization kinetics and thermodynamics by differential scanning calorimetry (DSC) methods has also been reported in the literature [1]. This study examined a series of benzocyclobutene monomers containing one or two benzocyclobutene groups per molecule, both with and without reactive unsaturation. The study provided a measurement of the thermodynamics of the reaction between two benzocyclobutene groups and compared it with the thermodynamics of the reaction of a benzocyclobutene with a reactive double bond (Diels-Alder reaction). Differential scanning calorimetry was chosen for this work since it allowed for the study of the reaction mixture throughout its entire polymerization and not just prior to or after its gel point. The monomers used in this study are shown in Table 3. The polymerization exotherms were analyzed by the method of Borchardt and Daniels to obtain the reaction order n, the Arrhenius activation energy Ea and the pre-exponential factor log Z. Tables 4 and 5 show the results of these measurements and related calculations. 

Figure 3.8 Borchardt and Daniels DTA [3]. Stirring rods maintain temperature uniformity within the sample and reference containers. The sample consisted of both reactive and reference fluid. Mixing in this way allowed the heat capacities and thermal conductivities of sample and reference to closely approach.

Differential scanning calorimetry (DSC) was used to determine the kinetics of polymerization and the glass transition temperature of the solid polymer. Preliminary results indicate the dependence of kinetics on the microstructure as determined using Borchardt and Daniels method (26). The reaction order, rate constant, and conversion were observed to be dependent on the initial microstructure of the microemulsions. The apparent glass transition temperature (Tg) of polystyrene obtained from anionic surfactant (SDS) microemulsions is significantly higher than the Tg of normal bulk polystyrene. In contrast, polymers from nonionic microemulsions show a decrease in Tg. Some representative values of Tg are shown in Table I. 

A basic assumption in Kissinger s analysis is that reaction occurs equally in all parts of the specimen. Disagreement between the results of various authors shows that this assumption is not generally true and the results are particularly influenced by particle size and sample geometry. Borchardt and Daniels have derived an expression for the rate coefBcient k) derived from a dta curve... 

The original work extends the discussion to more complex reactions and the determination of activation energies and heats of reaction. However, the equations were developed for homogeneous reactions in solution and required twelve assumptions some of which are very difficult to satisfy when applied to dta studies of solid state reactions. These assumptions 2u e (/) the heat transfer coefficients and heat capacities of reactants and products are equal and constant, and (ii) that the temperature is uniform throughout the sample and reference material. Freeman and Carroll and Wendlandt have suggested simplifications in Borchardt and Daniels procedure. 

Borchardt and Daniels [70,71] developed a method for DTA studies of homogeneous liquid-phase reactions, that involves the calculation of the rate coefficient, k, from the expression [72] ... 

Perhaps the most widely used kinetic method in DTA has been that derived by Borchardt and Daniels f 185) in 1957. The method is based on the following assumptions (1) The temperature in the sample and reference materials is uniform obviously, this only can be applied to stirred liquids and not to solids (2) the heat is transferred by conduction only, a condition easily met with liquids and the temperature ranges usually employed (the heat transfer through the thermocouple is neglected) (3) the heat transfer coefficients are identical for the sample and reference materials and (4) the heat capacities of the sample and reference materials must also be identical, a condition approached if dilute sample solutions are investigated. 

The kinetic method of Borchardt and Daniels (185) was subjected to an exhaustive examination by Reed el al. (120) in 1965. The equations were... 

Using the decomposition of benzenediazonium chloride, Reed et al. (120) compared the kinetic results obtained by several different methods these comparisons are shown in Table 5.12. They concluded that the Borchardt and Daniels method can be used for the quantitative determination of kinetic parameters if the experimental conditions closely approximate the assumptions of the theory, namely, reaction order, n. with respect to only one component, and the absence of temperature gradients and overlapping peaks. 

For studying the kinetics of homogeneous reactions in solution, Borchardt and Daniels (91) used the glass apparatus illustrated schematically in Figure 6.31. The cells consisted of two Pyrex tubes, 1.25 in. in diameter and 5 in. 

Figure 6.31 - Solution DTA apparatus used by Borchardt and Daniels 191).

Nearly all the computer applications to DTA have been concerned with the calculations of reaction kinetics where they find the ideal means of simulating the DTA curve of a chemical reaction of known kinetics. One of the first of these applications was that by Reed et al. (25) in which the quantitative determination of kinetics by the methods of Borchardt and Daniels (26) and Kissinger (27) were evaluated and compared. The DTA curve was generated numerically by use of equations such as... 

As described in section B, DTA and DSC data may also be acquired and processed by the systems previously discussed (5,6,54,56). Vernon (56) used the Borchardt and Daniels (26) and Kissinger (27) methods to calculate and Z of explosive materials from nonisothermai DSC data. Roger s method (57) was used for these calculations from isothermal DSC data. 

The experimental study of kinetics, as mentioned earlier, has as its basis the identification of the rate of reaction with instrument signal and the extent of reaction with fractional area of the peak. Analysis of experimental data often makes use of named approaches which exploit the advantages of dynamic experiments to achieve results without recourse to protracted experimental effort. Two popular but very different methods are those of Borchardt and Daniels and Ozawa and both appear in ASTM methods. Both are supported by commercial software. The concern here is with the Borchardt and Daniels method [ASTM E 2041 (1999)] which had a considerable impact on kinetic evaluation both by DTA and subsequently DSC. The analysis was devised originally for DTA experiments in which the thermocouples were in large volumes of stirred liquids. This is in direct contrast to the current application of the method to DSC studies of solids. A number of assumptions were made which were met more readily in stirred liquid systems than with solids. As a result there are a number of caveats associated with its application to solids. In particular the analysis assumed the absence of temperature... 

The Borchardt and Daniels approach is usually associated with an analysis based on equation (15) ... 

The methods according to ASTM E 689-79, and to Borchardt and Daniels apply data from DSC or DTA test runs, whereas the methods according to Flynn and Wall, and to McCarty and Green are based upon the use of data fi om thermogravimetty. For the... 

The Borchardt and Daniels method [3-19] permits the calculation of activation energy E, frequency (pre-exponential) factor A, heat of reaction AH, and order of reaction n from a single DSC or DTA scan of a reaction isotherm. In principle it relies on a comparison between a partial area and the total area of an exothermic peak (Fig. 3-50). This will... 

Experiments on model substances were not carried out. A comparison of the oxidation and pyrolysis kinetics according to Borchardt and Daniels with the other three methods will be made in chapter 4.10. 

Borchardt and Daniels Flynn and Wall McCarty and Green Version C 4.20... 

Software only for the Simultaneous Thermal Analyzer STA 780 was available for kinetics according to Borchardt and Daniels. Similarly to the kinetics program according to ASTM E 698-79, only separately sampled DTA data can be processed using the Borchardt and Daniels program. The DTA data from simultaneous TGA/DTA experiments cannot be... 

Fig. 4-195 P5TOlysis of Bitumen B80 STA Diagram DTA Heating Rate )3 lOK/min Atmosphere Argon 30 + 20 cm /min Kinetics according Borchardt and Daniels Integration Limits 400 C and 500 °C...

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