Cooling rate effects temperature dependence

Rate effects may not be chemical kinetic ones. Benson and co-worker [84], in a study of the rate of adsorption of water on lyophilized proteins, comment that the empirical rates of adsorption were very markedly complicated by the fact that the samples were appreciably heated by the heat evolved on adsorption. In fact, it appeared that the actual adsorption rates were very fast and that the time dependence of the adsorbate pressure above the adsorbent was simply due to the time variation of the temperature of the sample as it cooled after the initial heating when adsorbate was first introduced. 

The cycle time is controlled by the heating and cooling rates, which in turn depend on the following factors the temperature of the heaters and the cooling medium, the initial temperature of the sheet, the effective heat transfer coefficient, the sheet thickness, and thermal properties of the sheet. 

Characteristics and implementation of the treatments depend on the expected results and on the properties of the material considered a variety of processes are employed. In ferrous alloys, in steels, a eutectoid transformation plays a prominent role, and aspects described by time-temperature-transformation diagrams and martensite formation are of relevant interest. See a short presentation of these points in 5.10.4.5. Titanium alloys are an example of the formation of structures in which two phases may be present in comparable quantities. A few remarks about a and (3 Ti alloys and the relevant heat treatments have been made in 5.6.4.1.1. More generally, for the various metals, the existence of different crystal forms, their transformation temperatures, and the extension of solid-solution ranges with other metals are preliminary points in the definition of convenient heat treatments and of their effects. In the evaluation and planning of the treatments, due consideration must be given to the heating and/or cooling rate and to the diffusion processes (in pure metals and in alloys). 

The reaction rate constant and the diffusivity may depend weakly on pressure (see previous section). Because the temperature dependence is much more pronounced and temperature and pressure often co-vary, the temperature effect usually overwhelms the pressure effect. Therefore, there are various cooling rate indicators, but few direct decompression rate indicators have been developed based on geochemical kinetics. Rutherford and Hill (1993) developed a method to estimate the decompression (ascent) rate based on the width of the break-dovm rim of amphibole phenocryst due to dehydration. Indirectly, decompres-... 

Transient Nucleation If a liquid is cooled continuously, the liquid structure at a given temperature may not be the equilibrium structure at the temperature. Hence, the cluster distribution may not be the steady-state distribution. Depending on the cooling rate, a liquid cooled rapidly from 2000 to 1000 K may have a liquid structure that corresponds to that at 1200 K and would only slowly relax to the structure at 1000 K. Therefore, Equation 4-9 would not be applicable and the transient effect must be taken into account. Nonetheless, in light of the fact that even the steady-state nucleation theory is still inaccurate by many orders of magnitude, transient nucleation is not discussed further. 

The onset of thermal diffusion depends on the gas concentrations, the sample surface area, the rate at which the sample cools to bath temperature, and the packing efficiency of the powder. In many instances, using a conventional sample cell, surface areas less than 0.1 m can be accurately measured on well-packed samples that exhibit small interparticle void volume. The use of the micro cell (Fig. 15.10b) is predicated on the latter of these observations. Presumably, by decreasing the available volume into which the lighter gas can settle, the effects of thermal diffusion can be minimized. Although small sample quantities are used with a micro cell, thermal conductivity detectors are sufficiently sensitive to give ample signal. 

It should be pointed out that the temperature at which the damping maximum occurs depends on the frequency of the measurement the higher the frequency, the higher the temperature. (This is quite analogous to the effect of the cooling rate on the T0 value obtained from volume-temperature measurements as discussed in the previous section). 

Figure 1.4 Differences in the temperature-time profiles for conventional and microwave dielectric heating. Particularly noteworthy are the far higher heating and cooling rates and the greater reaction temperatures achieved. Since at these higher temperatures the rate of reaction is much larger, it is not necessary to hold the reaction at this temperature for an extended period of time. Since the rate of reaction depends exponentially on temperature the translation of these profiles into product yields as a function of time will magnify these effects.

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