Effect self-cooling

In Chapter 3 it was pointed out that certain rod-like polymers showed many of the attributes of liquid crystals in the melt. In particular, these molecules were oriented in shear to such an extent that interchain entanglement was small and the melts had a low viscosity. On cooling of the melt these rod-like molecules remained oriented, effectively self-reinforcing the polymer in the direction of flow. The essential differences in the properties of liquid crystal polymers... 

Somorjai and Lester [40] detail some of the problems likely to be encountered in vaporization measurements. These include (i) the effects of variations of with crystal surface, which are particularly important in the use of polycrystalline samples (ii) the self-cooling resulting from the endothermic vaporization, which may cause temperature gradients in the sample, especially at high fluxes and (iii) the complications caused by vapour-vapour collisions when measurements are made in a significant partial pressure of vapour. 

Several instances of compensation behaviour have been described, typically for endothermic, reversible decompositions. Kinetic characteristics are sensitive to reaction conditions, most notably the effects of the presence of the volatile product and heat flow to and within the reaction zones undergoing self-cooling. The following are examples of reactions studied in detail. 

More quantitative measurements of the systematic variations of dehydration rates with/7(H20), referred to as Smith-Topley behaviour, could lead to support for one or more of the several theoretical explanations that have been proposed [2,21,49,54,63] based on recrystallization of sohd product, local self-cooling and/or diffusion (effects expected to occur in all dehydration reactions) and adsorption of the volatile product. Dehydrations may also involve the intervention of a zeolitic residue and/or an amorphous phase, the formation and reciystallization of one or more lower hydrates as intermediates, and diffusive esc e of water through various channels of the barrier layer of product may be slow. 

Kinetic data measured for the decomposition of calcium carbonate under isothermal and under programmed-temperature conditions [11] and varied reaction environments influencing the ease of removal of the CO2 product, show that the apparent values of the kinetic parameters k, A and may be influenced by sample heating rate, reactant self-cooling, sample mass, geometry and particle size, which determine the rate because of the reversible nature of the decomposition [12]. These effects can lead to compensation behaviour [13]. 

Reactant temperature within the reaction zone may be appreciably different from that measured for the controlled furnace reaction vessel because of local self-cooling or self-heating as a consequence of the reaction enthalpy. The significance of self-cooling in dehydrations has been discussed by Bertrand et al. (19). L vov et al. (20) have developed a computer model to represent the effect with reference to the endothermic dehydration of Li2S04 H20. Not all research reports discuss the possible consequences of reaction enthalpy in influencing reactant temperature. 

Underestimated because of the possible catalytic effect of H2O impurity Overestimated because of the strong self-cooling effect in vacuum The E values in a and b cases are excluded from calculation... 

The mean value of the E parameter at low dehydration temperatures (<300K), applicable to eight of the reactants, was 49 10 kJ moP. This magnitude exceeds the enthalpy of evaporation of free water at 298K(Afl298 = 44.0kJ mol ). However, for three reactants the E parameter turned out to be lower than 44 kJ moP. This indicates an obvious measurement error, associated, most likely, with the self-cooling effect. If it is assumed that this systematic error affects both parameters, E and E equally then their ratio is close to the true value. 

Interpretation of Unusual Effects Modelling of the temperature distribution has allowed, for the first time, some unusual effects observed for powder decomposition to be explained quantitatively. One of these is associated with an independence of the overall decomposition rate on the powder mass, which seems to be inexplicable at first thought. However, when the self-cooling of the sample is taken into account, this effect seems obvious. Irrespective of the total number of layers, i.e., of the powder mass, the effective number of layers Ue, involved in the decomposition process should remain practically constant (the height of powder filling is assumed to be much less than its diameter). 

If the only cause of overestimation of the experimental values Eexpt, calculated by the third-law method, is the self-cooling effect, then its magnitude can be easily determined. If it is also assumed that the E magnitude at the lower temperature is free of this effect (i.e., that the sample temperature, Tg, is equal to the furnace temperature, Tf) and corresponds to the true value of the E parameter, Etrue, then it becomes possible to determine the actual value of sample temperature for any higher decomposition temperature. This temperature is equal to ... 

The above assumption, that self-cooling is the only cause of overestimation of the experimental values Texpt, is valid only for reactants decomposing to gaseous products. For decompositions with formation of a solid product, there is an additional reason for overestimation related to the condensation effect (Sect. 8.2). Therefore, it is more appropriate to call this combined effect the apparent self-cooling effect. 

Impact of Self-cooling and Condensation Effects on the E Parameters The... 

The model suggested by Bertrand et al. [11-13] assumed the existence of a spatial gradient of temperature in the reaction zone. In this model the abnormal rise of the dehydration rate with was attributed to the increase of heat transfer from the furnace to the self-cooled reactant. Model calculations and experiments on the evaporation and condensation of ethanol and water vapours provided a convincing proof of this mechanism. In the experiments [13], the temperature of the evaporating liquids turned out to be much lower than that of the heater. For instance, for ethanol the difference from the thermostat temperature (300 K) was as much as 45 K or 15%. However, this model remained unclaimed during the following 20 years of studies on the T-S effect. Such a considerable difference in temperatures between the crystalline hydrate and the furnace seemed improbable to the majority of researchers. 

The calculation results are shown below in a graphic form. As may be deduced from the shape of the curves J = f Pw) in Figs. 7.2 and 7.3, the Pw rise from 10 to 10 bar leads to the rate increase and the appearance of maxima on the curves, which is in complete agreement with experimental observations. This is due to the increase in the thermal conductivity of water vapour which results in a decrease of self-cooling. The T-S effect becomes more marked with a rise of Tf and n, which is also in good correspondence with the experimental data [12, 13] and, in particular, with an intensification of the effect with the decrease of powder grain size [13]. 

Fig. 7.6). At higher magnitudes of e the maximum disappears and only a small distortion of the J = /(PcOs) curve is observed. The self-cooling effect appears to be insignificant and, thus, some increase of CaCOs temperature... 

The T-S effect becomes apparent under extreme conditions of such kind. The temperature for experiments on the T-S effect is chosen to be much higher than temperatures typical for usual experiments on the decomposition kinetics in the absence of an excess of gaseous product. For crystalline hydrates this excess of temperature may reach 30-50 K, and for calcium carbonate, 100-150 K. This is because the decomposition in the isobaric mode is slower than in the equimolar mode. However, for initial points of the T-S curve corresponding to the absence of gaseous product or to a very low pressure of this gaseous product, this temperature is obviously much higher than the optimal value. That is why self-cooling appears to be well above the common value. 

Historically the underestimation of the role and magnitude of the self-cooling effect in kinetic studies of thermal decomposition has turned out to be one of the most important reasons which hindered interpretation of the T-S effect and, to some extent, the compensation effect, and promoted some misconceptions [19, 26-28], based on the confidence in infallibility of the second-law method in determination of thermochemical parameters (the enthalpy and entropy for decomposition reactions). 

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