Kinetics, solid-phase

Freidig, A.P., Garciano, E.A., Busser, F.J.M., and Hermens, J.L.P. (1998) Estimating impact of humic acid on bioavailability and bioaccumulation of hydrophobic chemical in guppies using kinetic solid-phase extraction. Environ. Toxicol. Chem. 17, 998-1004. 

More recently, studies of the hysteresis of these phase transitions have illuminated the importance of kinetic factors in solid-solid phase transitions [224]. The change between crystal stmctures does not occur at the same point when pressure is increasing, as when it is decreasing the difference between this up-stroke and down-stroke pressure... 

Intraparticle Transport Meclianisms Intraparticle transport may be hmited by pore dijfusion, solid dijfusion, reaction kinetics at phase boundaries, or two or more of these mechanisms together. 

FIG. 16-9 General scheme of adsorbent particles in a packed bed showing the locations of mass transfer and dispersive mechanisms. Numerals correspond to mimhered paragraphs in the text 1, pore diffusion 2, solid diffusion 3, reaction kinetics at phase boundary 4, external mass transfer 5, fluid mixing. 

Fig. 6. Kinetic curves of the shift of Amax in the luminescence spectra of PAN samples thermally treated in solid phase. ( ) at 200 °C (o) at 180 °C (A) 150 °C. Dotted lines refer to PAN-r, solid lines refer to PAN-c...

The following section deals with the crystallization and interconversion of polymorphic forms of polymers, presenting some thermodynamic and kinetic considerations together with a description of some experimental conditions for the occurrence of solid-solid phase transitions. 

The concentrations of reactants are of little significance in the theoretical treatment of the kinetics of solid phase reactions, since this parameter does not usually vary in a manner which is readily related to changes in the quantity of undecomposed reactant remaining. The inhomogeneity inherent in solid state rate processes makes it necessary to consider always both numbers and local spatial distributions of the participants in a chemical change, rather than the total numbers present in the volume of reactant studied. This is in sharp contrast with methods used to analyse rate data for homogeneous reactions in the liquid or gas phases. 

Flynn and Dickens [142] have translated the relaxation methods of fluid kinetics into terms applicable to solid phase thermogravimetry. The rate-determining variables such as temperature, pressure, gas flow rate, gas composition, radiant energy, electrical and magnetic fields are incremented in discrete steps or oscillated between extreme values and the effect on reaction rate determined. 

Some limitations of optical microscopy were apparent in applying [247—249] the technique to supplement kinetic investigations of the low temperature decomposition of ammonium perchlorate (AP), a particularly extensively studied solid phase rate process [59]. The porous residue is opaque. Scanning electron microscopy showed that decomposition was initiated at active sites scattered across surfaces and reaction resulted in the formation of square holes on m-faces and rhombic holes on c-faces. These sites of nucleation were identified [211] as points of intersection of line dislocations with an external boundary face and the kinetic implications of the observed mode of nucleation and growth have been discussed [211]. 

Measurements of electrical conductivity permit the identification of the charge-carrying species in the solid phase and also the detection of ionic melts [111,417]. Bradley and Greene [418], for example, could determine the kinetics of reactions between Agl, KI and Rbl because the product (K, Rb)Ag4Is had a considerably higher conductivity than the reactants. The conductivity of the reactant mixture was proportional to the thickness of the product layer. 

The systematic treatment of interface advance reactions given by Jacobs and Tompkins [28] remains a valuable survey of the kinetics of solid phase decompositions. A later account was given by Young [29]. Greater mathematical emphasis is to be found in the books by Delmon [30] and by Barret [31]. 

The several distinct derivations of eqn. (6) originally provided [30] by Avrami [436], by Erofe ev [437,448] and by Mampel [447] and developed by others, is a consequence of the importance to be attached to this expression for the kinetic analysis of solid phase reactions. Written in general form... 

The Avrami—Erofe ev equation, eqn. (6), has been successfully used in kinetic analyses of many solid phase decomposition reactions examples are given in Chaps. 4 and 5. For no substance, however, has this expression been more comprehensively applied than in the decomposition of ammonium perchlorate. The value of n for the low temperature reaction of large crystals [268] is reduced at a 0.2 from 4 to 3, corresponding to the completion of nucleation. More recently, the same rate process has been the subject of a particularly detailed and rigorous re-analysis by Jacobs and Ng [452] who used a computer to optimize curve fitting. The main reaction (0.01 < a < 1.0) was well described by the exact Avrami equation, eqn. (4), and kinetic interpretation also included an examination of the rates of development and of multiplication of nuclei during the induction period (a < 0.01). The complete kinetic expressions required to describe quantitatively the overall reaction required a total of ten parameters. 

Rate equations which have found application in kinetic studies of solid phase reactions a... 

Green [491] has given a general account of the applications of statistical methods to kinetic analyses and, without mentioning specific examples, suggests the approach could be of value in rate studies of solid phase reactions. The steps in his treatment are given below [492,493],... 

No single criterion has been recognized as constituting a satisfactory basis for the systematic classification of the kinetics of solid-phase reactions (Chapt. 1, Sect. 3). A classification based on the anion is preferred here since it is this constituent which undergoes breakdown in most reactions of interest and proposed reaction mechanisms for substances containing a common anion often include similar features. 

Reports of kinetic studies do not always include an explicit statement as to whether or not the reactant melted during reaction or, indeed, if this possibility was investigated or even considered (cf. p. 1). This aspect of behaviour is important in assessing the mechanistic implications of any data since reactions in a homogeneous melt, perhaps a eutectic, usually proceed more rapidly than in a crystalline solid. It is accepted that the detection of partial or localized melting can be experimentally difficult, but, in the absence of relevant information, it is frequently impossible to decide whether a reported reaction proceeds in the solid phase. 

The grouping of ammonium salts in a separate section serves to emphasize the similarities of behaviour which are apparent in reactions yielding the volatile NH3 molecule, following removal of a proton from the NH4 cation. This property is not unique indeed, many cations are volatile and numerous salts leave no residue on completion of decomposition. Few kinetic investigations have, however, been reported for other compounds, in contrast to the extensive and detailed rate measurements which have been published for solid phase decompositions of many ammonium salts. Comparisons with the metal salts containing the same anion are sometimes productive, so that no single method of classification is altogether satisfactory. 

Hajek et al. [173] have reported a detailed kinetic study of the solid phase decomposition of the ammonium salts of terephthalic and iso-phthalic acids in an inert-gas fluidized bed (373—473 K). Simultaneous release of both NH3 molecules occurred in the diammonium salts, without dehydration or amide formation. Reactant crystallites maintained their external shape and size during decomposition, the rate obeying the contracting volume equation [eqn. (7), n = 3]. For reaction at 423 K of material having particle sizes 0.25—0.40 mm, the rate coefficients for decompositions of diammonium terephthalate, monoammonium tere-phthalate and diammonium isophthalate were in the ratio 7.4 1.0 134 and values of E (in the same sequence) were 87,108 and 99 kJ mole-1. 

This section is almost entirely concerned with the kinetics of solid phase decompositions of classical coordination compounds, since most of the information available refers to these substances. The hydrates, in which the ligands are water only, are correctly classified under the present heading, but as their dehydrations have been so intensively studied, a separate section (Sect. 1) has been devoted to the removal of water from crystalline hydrates. A separate water elimination step also preceeds many decomposition reactions. 

As with solid phase decompositions (Sect. 1), the kinetic characteristics of solid—solid interactions are controlled by the properties of lattice imperfections, though here many systems of interest involve the migration, in a crystal bulk of a mobile participant, from one interface to another. Kinetic measurements have been determined for reactions in a number of favourable systems, but there remain many possibilities for development in a field that is at present so largely unexplored. 

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