Isothermal experiments

These experiments are mostly performed where the sample changes as a result of a stimulus. Examples of this may include the drying of a sample, perhaps as studied in a controlled humidity environment (see Section 4.5.6), the post-cure of a thermoset resin or the decomposition of a sample at high temperature. There is usually little restriction with regard to data collection for these experiments, as they are made over relatively long time periods. Therefore, they are frequently performed at multiple frequencies and this can be used to evaluate half-fives or relaxation times for the process under investigation (see Section 4.5.3). 

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In describing the various mechanical properties of polymers in the last chapter, we took the attitude that we could make measurements on any time scale we chose, however long or short, and that such measurements were made in isothermal experiments. Most of the experimental results presented in Chap. 3 are representations of this sort. In that chapter we remarked several times that these figures were actually the result of reductions of data collected at different temperatures. Now let us discuss this technique our perspective, however, will be from the opposite direction taking an isothermal plot apart. 

Most published studies relate only to isothermal experiments. Hence, in order to make such comparisons we modified our computations to assume isothermal conditions. Figure 11 compares our kinetic model with data by Hui and Hamielec for styrene thermal polymerization at 1A0°C. Figure 12 compares out kinetic model with data by Balke and Hamielec (7) for MMA at 90 C using 0.3 AIBN. Figure 13 compares our kinetic model with data by Lee and Turner ( ) for MMA at 70°C using 2% BPO. Our model compares quite favorably with these published experiments. The percent error was less than S% in most of the ranges of conversions. 

In conclusion, we have reviewed how our kinetic model did simulate the experiments for the thermally-initiated styrene polymerization. The results of our kinetic model compared closely with some published isothermal experiments on thermally-initiated styrene and on styrene and MMA using initiators. These experiments and other modeling efforts have provided us with useful guidelines in analyzing more complex systems. With such modeling efforts, we can assess the hazards of a polymer reaction system at various tempera-atures and initiator concentrations by knowing certain physical, chemical and kinetic parameters. 

Isothermal Decomposition Studies. An exotherm was not detected in any of the isothermal experiments that were conducted at various isotherms ranging from 100 to 225 °C. This was true even after extended periods of time and at a temperature only 21 C below the onset of the exothermic reaction as determined by the standard ARC experiments (see Table I). However, significant pressure accumulations were detected at Isotherms as low as 140 °C. In fact. 

The slope of the theoretical curve yields the zero-order rate constant. The zero-order rate constants obtained from five isothermal experiments are shown in Table III. These rate constants were used for the construction of an Arrhenious plot (Figure 4) yielding the activation energy for the reaction, Ea - 139.3 kj/mol. The activation energy for the corresponding reaction of methyl isocyanate has been reported as 132.2 kJ/mol (7). 

Empirical grey models based on non-isothermal experiments and tendency modelling will be discussed in more detail below. Identification of gross kinetics from non-isothermal data started in the 1940-ties and was mainly applied to fast gas-phase catalytic reactions with large heat effects. Reactor models for such reactions are mathematically isomorphical with those for batch reactors commonly used in fine chemicals manufacture. Hopefully, this technique can be successfully applied for fine chemistry processes. Tendency modelling is a modern technique developed at the end of 1980-ties. It has been designed for processing the data from (semi)batch reactors, also those run under non-isothermal conditions. 

Adiabatic induction times are always shorter than induction times from isothermal experiments,. see Fig. 5.4-61 (Grewer ef a/., 1989). 

A very fast testing of polymer stability is based on non-isothermal experiments (DSC, chemiluminescence) where the whole plot of the parameter followed may be visualized over a large temperature interval. The transfer of non-isothermal data to isothermal induction times involves a variety of more or less sophisticated approaches such as published in Ref. [8] or discussed later. 

L. Rychla and J. Rychly, New concepts in chemiluminescence at the evaluation of thermooxidative stability of polypropylene from isothermal and non-isothermal experiments. In A. Jimenez and G.E. Zaikov (Eds.), Polymer Analysis and Degradation, Nova Science Publishers, New York, 2000 p. 124. 

Thermogravimetric analysis (TGA) has often been used to determine pyrolysis rates and activation energies (Ea). The technique is relatively fast, simple and convenient, and many experimental variables can be quickly examined. However for cellulose, as with most polymers, the kinetics of mass loss can be extremely complex (8 ) and isothermal experiments are often needed to separate and identify temperature effects (9. Also, the rate of mass loss should not be assumed to be related to the pyrolysis kinetic rate ( 6 ) since multiple competing reactions which result in different mass losses occur. Finally, kinetic rate values obtained from TGA can be dependent on the technique used to analyze the data. 

The interpretation of these coverage-dependent effects involves such ideas as island formation, mixed domains of CO and 0, the mobility of CO and 0 and the adsorption of CO on oxygen-covered regions (1,18,26, 27). A deeper understanding of the roles of these processes comes from isothermal experiments involving pressure transients. 

FIGURE 2.18. Rate of Heat Generation (q) of Three Isothermal Experiments as a Function of Time (t) at Three Temperatures (7). [Points of equal conversion of different isothermal experiments at different temperatures are the intersections of the isoconversion lines (A, B, or Q and the heat production lines.]... 

The RSST apparatus can be operated with its own controller or with a computer interface. Heating rates depend on the Cp of the reactive sample, and can be varied from 0.25°C/min to approximately 2°C/min. Isothermal experiments can also be run. The contents of the test cell can be mixed with a... 

FIGURE 2.18. Rate of Heat Generation (q) of Three Isothermal Experiments as a Function of Time (t)... 

A 0.5-gram mass of either the organo-treated or inorganic cation exchanged zeolite and 50 mL of 10 mM/L arsenate or chromate aqueous solutions were placed into Erlenmeyer flasks and mechanically shaken in reciprocating mode to attain equilibrium. Different equilibrium periods for individual zeolite modifications and both aqueous oxyanions species have been established. The adsorption isotherm experiments were conducted using above mass/ volume ratio of samples with an initial metal concentrations ranged from 0.5 to 100 mM/L at laboratory temperature. The... 

Even though the nonisothermal crystallization leads to just small changes in the subsequent melting behavior of different types of triblock copolymers, isothermal experiments employed to calculate the equilibrium melting temperature, T, have shown that this parameter can exhibit significant changes depending on composition. It has been reported that in PS-fc-PB-fc-PCL tri-... 

In many early experiments, hysteresis was observed for highly hydrophobic compounds such as PCBs (79, 80). Since the time to reach equilibrium can be quite long for strongly hydrophobic compounds, a solute may have never reached equilibrium during the sorption isotherm experiment. Consequently, Kj would be underestimated, which leads to the discrepancy between the sorption and desorption coefficients that was attributed to hysteresis. The case for hysteresis being an artifact is supported by recent data for tetrachlorobenzene (log K = 4.7), illustrating that sorption and desorption require approximately two days to reach equilibrium with approximately equal time constants (78). Finally, the diffusion model is consistent with the observation that the extent of hysteresis was inversely related to particle size (81). 

Experiments at a constant temperature are often carried out to investigate the kinetics of a reaction at a high temperature. The rate coefficient is a constant and the rate equation can be solved relatively easily. By var3dng the temperature of isothermal experiments, the dependence of the rate coefficient on temperature may be obtained. 

The kinetics of Reaction 2-79 has been investigated through isothermal experiments but the reaction law is not well understood. If the reaction is assumed to be an elementary reaction, the reaction rate law would be... 

Determination of the reaction rate from calorimetric measurements, using DSC technique, is very useful and was applied with success for many template polymerization systems and for blank polymerizations.Two types of calorimetric measurements were described isothermal and scanning experiments. The heat of polymerization can be measured by DSC method, measuring thermal effect of polymerization and ignoring the heat produced from decomposition of the initiator and heat of termination. In isothermal experiments sample is placed at a chosen temperature and thermogram is recorded versus time. Assuming typical relationship... 

Instead of changing the temperature it is also possible to determine lateral interactions from isothermal experiments/ or from multi-isotherm experiments in which the temperature is increased in steps. " ... 

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