Decomposition of a solid

If the flow is accompanied with CBA decomposition, the G value in Eq. (5) should be substituted with its time function, G(t). In the general case, thermal decomposition of a solid substance with gas emission is a heterogeneous topochemical reaction [22]. Kinetic curves of such reactions are S -shaped the curves representing reaction rate changes in time pass a maximum. At unchanging temperature, the G(t) function for any CBA is easily described with the Kolrauch exponential function [20, 23, 24] ... 

The thermal decomposition of a solid, which necessarily (on the above definition) incorporates a chemical step, is sometimes associated with the physical transformations to which passing reference was made above melting, sublimation, and recrystallization. Aspects of the relationships between physical transitions and decomposition reactions of solids are discussed in a book by Budnikov and Ginstling [1]. Since, in general, phase changes exert significant influence upon concurrent or subsequent chemical processes, it is appropriate to preface the main survey of the latter phenomena with a brief account of those features of melting, sublimation, and recrystallization which are relevant to the consideration of thermal decomposition reactions. 

Kabanov and Zingel [352] have recently published a comprehensive review of studies of the effect of application of continuous or periodic electric fields on the reactant during thermal decomposition of a solid. They comment on the superficiality of most of the work discussed. The application of an electric field is contrasted with the effect of selected additives as a means of obtaining information on the mechanism of a decomposition reaction. Both may alter the concentration of free electrons in the solid, but the effect of the field is more apparent in the vicinity of the surface. An example of an investigation of the effect of an electric field on a reaction is to be found in the work of the Panafieu et al. [373] on KN3. 

Other factors have been identified as rate controlling in other types of solid—solid interaction, and some of these are described in subsequent sections. These include, for example, the decomposition of a solid catalyzed by a (different) solid and rate processes in which one reactant is volatilized, e.g. reaction of carbon (-> C02) with a solid oxidizing agent. 

This account of the kinetics of reactions between (inorganic) solids commences with a consideration of the reactant mixture (Sect. 1), since composition, particle sizes, method of mixing and other pretreatments exert important influences on rate characteristics. Some comments on experimental methods are included here. Section 2 is concerned with reaction mechanisms formulated to account for observed behaviour, including references to rate processes which involve diffusion across a barrier layer. This section also includes a consideration of the application of mechanistic criteria to the classification of the kinetic characteristics of solid-solid reactions. Section 3 surveys rate processes identified as the decomposition of a solid catalyzed by a solid. Section 4 reviews other types of solid + solid reactions, which may be conveniently subdivided further into the classes... 

The kinetic principles operating during the initiation and advance of interface-controlled reactions are identical with the behaviour discussed for the decomposition of a single solid (Chaps. 3 and 4). The condition that overall rate control is determined by an interface process is that a chemical step within this zone is slow compared with the rate of arrival of the second reactant. This condition is not usually satisfied during reaction between solids where the product is formed at the contact of a barrier layer with a reactant. Particular systems that satisfy the specialized requirements can, however, be envisaged for example, rate processes in which all products are volatilized or a solid additive catalyzes the decomposition of a solid yielding no solid residue. Even here, however, the kinetic characteristics are likely to be influenced by changing effectiveness of contact as reaction proceeds, or the deactivation of the catalyst surface. 

If it slow, then nucleation is likely to be due solely to proximity. Model D is an example of volame nucleation idiere decomposition of a solid is involved whereas Model E is that involving gas or liquid nucleation of the solid. Note that if nucleation does not occur, the solid reacts uniformly throughout its whole volume (Model F). However, this mode is rare and the nucleation stages are more likely to occur. We wUl not dwell upon how these nucleation models were derived and will only present the results here. One is referred to Appendix I wherein one can study the mathematics used to obtain the net-result. 

The minimum temperature for a specified test method, test apparatus (including material of construction and test volume) and initial pressure required to initiate self-sustained decomposition of a solid, liquid or gaseous substance without any other apparent source of ignition and without air or other oxidants present. 

The simple solid state reaction may involve either (i) the interfacial reaction or (ii) the diffusion of reactants to each other, as the rate determining step. For example, decomposition of a solid giving rise to another solid... 

How the kinetics of thermal decomposition of a solid can be studied experimentally ... 

Shannon calculated the rate constant for thermal decomposition of a solid from absolute reaction rate theory. The resulting equation is of the same form as Equation 1.27, but v is replaced by a partition function ratio ... 

Precursors of Flexible Composition There are still other ways to avoid segregation of phases during the decomposition of a solid precursor to form an oxide. 

In solid phase reaction s3mthesis, there are three types of chemical reactions oxidation or reduction of a solid, thermal decomposition of a solid, and solid state reaction between two t3 s of solid. With liquid phase ssmthesis of ceramic powders, there are five different methods drying of a liquid, precipitation, sol-gel sjmthesis, hydrothermal S5m-thesis, and reactions of a liquid metal melt with a gas to give a solid ceramic. There are basically three operational principles for precipitation temperature change, evaporation, and chemical reaction. Sol—gel... 

Solid state reactant Thermal decompositions of a solid Oxidation or reduction of a solid Precipitation Solution heating or cooling Evaporative salting-out Chemical reaction with insoluble product Hydrothermal synthesis Forced insolubility Dissolution reprecipitation Evaporative Condensation Gas phase reaction with solid product Thermal decompositions Oxidation or reduction reactions Combination reactions with a solid product Solvent removal Spray drying Freeze drying Spray roasting Sol-gel synthesis Melt solidification... 

The experimental stages in the study of a decomposition of a solid are as follows. Some or all of these stages may be omitted depending on the facilities available and the overall objectives of the work, though such omissions necessarily restrict the value and reliability of the conclusions obtained ... 

Sublimation may be regarded as a form of decomposition of a solid. LVov and Novichikhin [43,44] have interpreted the measured rates of product formation for a munber of decompositions by regarding them as sublimation-type reactions. Decomposition of compound S is regarded as forming the gaseous products A, B,... 

Temperature is, of course, only one of a number of variables which may influence the rates of chemical changes in crystals. Other possible variables include a, pressure of volatile product (most significant in reversible reactions), reactant pressure (in gas-solid reactions), etc. Thus the overall rate equation applicable to the decomposition of a solid may be a function of several variables [5] ... 

Vyazovkin and Liimert [26] also regard the thermal decomposition of a solid as a multistep process. They report a quantitative analysis of the systematic variations of values of E with a using theoretically calculated data for two model processes (i) a simple reversible reaction and (ii) a reversible reaction followed by an irreversible step. It was shown that the dependence of E on a for measurements of the dehydrations of a number of crystalline hydrates was consistent with the latter model, (ii). 

A kinetic/geometric analysis and a description of the bond redistribution steps, which are consistent with each other, are required to provide a complete description of the decomposition of a solid. 

Kinetic Expressions. In this study, we have analyzed nonisothermal TGA data using the Chen-Nuttall equation, the widely accepted Coats-Redfern equation, and the Anthony-Howard equation. These equations are derived from simple rate expressions. The basic single reaction kinetic equation for the decomposition of a solid has been presented by Blazek (24) as... 

Note The term crystolysis reaction was proposed for use in describing the thermal decomposition of a solid reactant (31,72). This specific label is of value as a keyword and index entry, while also confirming that the reaction of interest proceeded in the crystalline state. This important aspect of behavior is not always explicitly stated in reports of many thermal investigations, where the phase in which the change occurs is not positively identified. 

In this method (96), the kinetic constants are calculated from the TG curve by a differential method. It takes into account also the thermal effects of reactions which result in a deviation of the sample temperature from the programmed values of the linear heating. Starting with the differential equation for the thermal decomposition of a solid,... 

Model D is an example of the decomposition of a solid whereas Model E is that involving gas or liquid nucleation of the solid. Note that if nucleation does not occur (this mechanism is not usualfy the norm), the solid reacts uniformly throughout its whole volume (Model F). 

Foundation Thermal decomposition of a solid reactant, R, is usually described by two types of reaction by congruent dissociative vaporization of a reactant R into gaseous products A(g) and B(g), i.e., according to the scheme ... 

Decomposition of a solid under gas development Such decomposition reactions are, e.g.,... 

Armitt et al. investigated the influence of acid vapors (98% H2SO4,35% H2SO4, and 37% HCl) on the decomposition of a solid sample of TATP placed into a crimped vial, where the TATP was separated from the deposited 100 pL liquid acid sample by a plug of cotton wool [62]. The headspace in the sealed vials was sampled with polydimethylsiloxane/Carboxen/divinylbenzene (PDMS/Carboxen/DVB) SPME fibers of film thickness 30 and 50 pm, at 1, 3, 5, and 8 h, and at 1,3, 7, and 10 days. Analysis of the headspace from the TATP samples exposed to vapor from the two sulfuric acids produced similar results, with the sample exposed to the 98% sulfuric acid vapor decomposing at a more rapid rate. The principle decomposition products were DADP and acetone, with some minor production of acetic acid. After 7 days, acetone was the major species observed in the headspace. The analysis of the headspace of the TATP samples exposed to HCl vapors showed rapid decomposition of TATP, with no detection of TATP or DADP after 1 day. Additionally, various chlorinated acetones were also observed, indicating a different decomposition pathway than that observed for the TATP exposed to sulfuric acid vapors. 

The value of the activation energy calculated for a reversible decomposition of a solid may thus be just a procedural value of no real physical meaning other than a number characterizing the individual thermoanalytical experiment. Many sophisticated kinetic methods neglect the distinction between micro-kinetics (molecular level, true chemical kinetics) and macro-kinetics (overall processes in the whole sample bulk). The conventional process of the type, Asoiid Bsoiid + Cgas, as applied to the entire solid sample, consists of many elementary processes, some of them of purely physical in nature (e.g. heat transfer, diffusion). The experimentally obtained kinetic data may then refer to only one of these processes, which is the slowest one, often difficult to link up with a particular reaction mechanism. 

The kinetics of the thermal decomposition of solids are dominated by topochemical considerations. Thus the traditional concepts of order and mole-cularity, which play an important role in the kinetics of gas phase and liquid phase reactions, have little application in considerations of the kinetics of the thermal decomposition of solids. Experimental observations of the isothermal reaction are conveniently represented in the form of a plot of the fractional decomposition a against time t. The objective of a physicochemical study of the thermal decomposition of a solid is then the devising of a mechanism for the chemical reaction which can be formulated in mathematical terms leading to a theoretical representation of the a(f) curve which is in complete agreement with the experimental observations. Such an idealized procedure is seldom realized completely in practice and one often has to be content instead with an empirical analysis of the kinetics. 

Stoichiometric decomposition of a solid into three gases... 

Sublimation of a solid Decomposition of a solid solution with gas departure Stoichiometric reaction with a gas and two solids Stoichiometric reaction of three solids and a gas... 

Variation in stoichiometry by a foreign gas with the solid Stoichiometric reaction with three gases and two solids Stoichiometric decomposition of a solid in three gases... 

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