Solid-state reactions temperature dependence

If a solid state reaction is diffusion-limited, if is unlikely that we can obtain 100% of any product, and will alwa obtain a mixture of compounds whose relative ratio will depend upon their thermod3mamic stability at the firing temperature. 

Kinetics in polycrystals differ from those in solution phase, because in the former, the thermal reactions usually follow a nonexponential rate law, something that is attributed to a multiple-site problem. In contrast to a first-order reaction in solution, the rate constant of a nonexponential process in the solid state is time dependent molecules located in the reactive site will have decayed during the warmup procedure and/or the initial stage of the reaction at the given temperature. These considerations need to be taken into account when the decay of the intensity of the IR signals in a matrix at low temperature are used for kinetic measurements [70]. 

The combination of these experimental findings indicate that active bismuth molybdate catalysts undergo phase transformations when exposed to reducing conditions similar to the conditions of catalysis. The phase transformations are highly dependent upon both temperature and the severity of the reducing atmosphere. However, the occurrence of solid state reactions in the catalysts suggests that the bulk structure of the catalysts plays an important role in catalytic reaction. 

Dithiophenylbutane 66 is obtained by a radical-radical combination reaction, while 3-isopropylthiophene 67 and 3-(propen-2-yl)thiophene 68 form by a radical-radical disproportionation process. The solid-state reaction was shown to be highly temperature dependent. While irradiation of powdered samples at 20°C led to no observable product after 2 days, samples exposed to the same UV source for 24 h at ca. 45°C gave 66 as the only product in ca. 5-10% yield. Photochemical reactions were carried out with nanocrystalline suspensions of 65 in a Pyrex tube acting both as a container and a light filter (X > 290 nm). 

This entropy of activation is determined by the ratio of partition functions, which generally has a slight temperature dependence. The typical value of kc = 10-I-10 5 s 1 corresponds to a drop in AS of 65-85 cal/mol-K. Since only vibrational degrees of freedom are involved in a solid-state reaction, the sole reason for this change may be the increase in their frequencies in the transition state ... 

Thermally induced deactivation of catalysts is a particularly difficult problem in high-temperature catalytic reactions. Thermal deactivation may result from one or a combination of the following (i) loss of catalytic surface area due to crystallite growth of the catalytic phase, (ii) loss of support area due to support collapse, (iii) reactions/transformations of catalytic phases to noncatalytic phases, and/or (iv) loss of active material by vaporization or volatilization. The first two processes are typically referred to as "sintering." Sintering, solid-state reactions, and vaporization processes generally take place at high reaction temperatures (e.g. > 500°C), and their rates depend upon temperature, reaction atmosphere, and catalyst formulation. While one of these processes may dominate under specific conditions in specified catalyst systems, more often than not, they occur simultaneously and are coupled processes. 

Various fluorides may be precipitated from aqueous solution for use as constituent powders in solid state reactions. Co-precipitation offers very elegant access to intimate mixtures, but the actual products are strongly dependent on the fluoride ion activity within the solution but also on the stability constants of the respective metal complexes. Accordingly, not only anhydrous fluorides are obtained, but also hydrated fluorides or hydroxide fluorides, which may be very difficult to convert to pure fluorides. As noted already [3], reactive compounds, e.g. carbonates, acetates, oxalates, hydroxides etc., which quite easily dissolve in acidic HF solutions, are the preferred starting materials for fluoride syntheses. In contrast, many oxides which have been heated to rather high temperature are frequently unreactive and may not dissolve at all. To enhance reactivity but also improve crystallinity of the product, it has proved useful to perform reactions above the boiling point of water in adapting the hydrothermal method, which has already been shown to be useful in the recrystallisation of materials which are more or less insoluble at ambient temperatures and pressures. Up to about 240°C even PTFE vessels may be used. A number of selected examples with respective reaction conditions are listed in Table 3. 

FIGURE 5.23 Solid state reaction between silica and BaCOg, showing (a) time dependence, (b) particle size dependence, and (c) temperature dependence of reaction. From Jander [28]. 

Thus, expression (59) enables us to describe the solid-state reaction rate constant dependence on the parameters of the potential barrier and medium properties in a wide temperature range, from liquid helium temperatures when the reaction runs by a tunneling mechanism to high temperatures (naturally, not exceeding the melting point) when the transition is of the activation type. 

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