Solid state reactions geometric

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When the course taken by a given solid-state reaction is determined by geometrical details of the crystal lattice, the reaction type falls under the general category of topochemistry. In a topochemical reaction, the reaction takes place in the solid state with a minimum amount of molecular motion. For example, bimolecular reactions are expected to take place between nearest neighbors, which then suggests that the product of the reaction would be a function of the geometric relation in the crystal structure of the reactant molecules. 

This first industrial device has been designed by MES company [65] for drying. It could be used for solid state reactions with powder reactants. Consequently, the reactor cannot be a classical chemical vessel or a classical chemical reactor with stirrer and others associated technical devices but a container able to enclose a reactant powder layer. The geometrical shape of the microwave applicator is parallelepiped box and the reactants are supported by a dielectric conveyor belt with edges as described by the Fig. 1.18. 

These examples illustrate a number of points. Solid-state reactions can, in many cases, be performed very easily. Their courses are frequently interpretable in terms of straightforward geometrical principles concerning conformation and/or packing of the reactant molecules. It is sometimes possible to design the reactant molecule with suitable substituents to ensure a desired crystal structure... 

In the crystal structure of the polymer phase (Fig. 17a), the polymer chains are aligned along the c-axis and the distance (3.71 A) between the centres of adjacent cyclobutane and pyrazine rings corresponds to half the c-axis repeat of the unit cell. For comparison between the monomer and polymer structures, an overlay plot of these structures is shown in Fig. 17b. It is clear that the solid-state reaction is associated with only very small atomic displacements at the site of the [2-1-2] photocyclization reaction (the displacement of the carbon atoms of the C=C double bonds of monomer molecules on forming the cyclobutane ring of the polymer is only ca. 0.8 A for one pair of carbon atoms and ca. 1.6 A for the other pair). Such small displacements are completely in accord with the assignment of this solid-state reaction as a topochemical transformation [124—127] (in which the crystal structure of the reactant monomer phase imposes geometric control on the pathway of the... 

Another solid state reaction problem to be mentioned here is the stability of boundaries and boundary conditions. Except for the case of homogeneous reactions in infinite systems, the course of a reaction will also be determined by the state of the boundaries (surfaces, solid-solid interfaces, and other phase boundaries). In reacting systems, these boundaries are normally moving in space and their geometrical form is often morphologically unstable. This instability (which determines the boundary conditions of the kinetic differential equations) adds appreciably to the complexity of many solid state processes and will be discussed later in a chapter of its own. 

The possibility of covalent interfullerene bond formation in solid and in some of its salts, results in a variety of dimers and polymers. Both the dimerization and the polymerization of Cgo are characteristic solid state reactions, up to now, neither of them were carried out in solution. In the fee lattice of C g the concentration of the reacting molecules is about 3 orders of magnitude higher than that in solution. The free rotation of the molecules allows for the geometrical conditions required by the transition state of the polymerization and the rigid polymer rods or sheets can form by a small rearrangement of the precursor structure. 

The geometric models of solid state reactions are based upon the processes of nucleation and growth of product nuclei by interface advance. These processes are discussed individually in the next section, followed by a description of the ways in which these contributions are combined to give rate equations for the overall progress of reaction. 

The rate equations which have found most widespread application to solid state reactions are summarized in Table 3.3. Other functions can be found in the literature. The expressions are grouped according to the shape of the isothermal a-time curves as acceleratory, sigmoid or deceleratory. The deceleratory group is further subdivided according to the controlling factor assumed in the derivation, as geometrical, diffusion or reaction order. 

The mathematical kinetic models proposed by Korobov. Korobov [96] has discussed the limitations of the traditional geometric-probabilistic approach to describing solid state reaction kinetics. He proposes that some of the more recently developed mathematical techniques (see Section 6.8.5.) should be used to provide improved descriptions of the advance of the reaction fi"ont within the structural symmetry of an individual reactant. 

In general, photoinert auxiliary molecules have been used as templating agents to direct double bonds in parallel orientations of single olefins and with distances smaller than 4.2 A. These geometrical parameters are strictly required as previous steps in order to achieve the photoreaction via topochemical control and then the template must be liberated from the expected product. We envisage that an alternative way to increase the level of sophistication in the design of solid state reactions is the possibility to extend the self-assembly of two or more potentially reactive unsaturated molecules controlled by directional supramolecular synthons. 

Since the traditional kinetic models of solid-state reactions are often based on a formal description of geometrically well defined bodies treated under strictly isothermal conditions, they are evidently not appropriate to describe the real process, which requires accoimt to be taken of irregularity of shape, polydispersity, shielding and overlapping, unequal mixing anisotropy and so on, for sample particles under reaction. One of the measures which has been taken to solve the problem is to introduce an accommodation function a a) [32]. The discrepancy between the idealized /(a) and the actual kinetic model function h a) can be expressed as... 

Koga, N., Tanaka, H. (2002). A physico-geometric approach to the kinetics of solid-state reactions as exemplified by the thermal dehydration and decomposition of inorganic solids. Thermochimica Acta, 388, 41-61. doi 10.1016/S0040-6031(02)00051-5. 

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