Other solid state processes

In this and the other solid-state processes described in this section, we see that the factors determining the products are as follows ... 

Photodimerization of cinnamic acids and its derivatives generally proceeds with high efficiency in the crystal (176), but very inefficiently in fluid phases (177). This low efficiency in the latter phases is apparently due to the rapid deactivation of excited monomers in such phases. However, in systems in which pairs of molecules are constrained so that potentially reactive double bonds are close to one another, the reaction may proceed in reasonable yield even in fluid and disordered states. The major practical application has been for production of photoresists, that is, insoluble photoformed polymers used for image-transfer systems (printed circuits, lithography, etc.) (178). Another application, of more interest here, is the use that has been made of mono- and dicinnamates for asymmetric synthesis (179), in studies of molecular association (180), and in the mapping of the geometry of complex molecules in fluid phases (181). In all of these it is tacitly assumed that there is quasi-topochemical control in other words, that the stereochemistry of the cyclobutane dimer is related to the prereaction geometry of the monomers in the same way as for the solid-state processes. 

Consider now a one-dimensional lattice of parameter /. The distance of each atomic jump depends on the rate of de-excitation once the adatom is excited and is translating along the lattice. This de-excitation process can be described by a characteristic life time r in the symmetric random walk, as in many other solid state excitation phenomena. The initial position of the adatom is taken to be the origin, denoted by an index 0. The adatom accomplishes a jump of distance il if it is de-excited within (i — i)l and (i + i)l, where / is the lattice parameter, or the nearest neighbor distance of the one-dimensional lattice, and i is an integer. The probability of reaching a distance il in one jump is given by... 

Chemical solid state processes are dependent upon the mobility of the individual atomic structure elements. In a solid which is in thermal equilibrium, this mobility is normally attained by the exchange of atoms (ions) with vacant lattice sites (i.e., vacancies). Vacancies are point defects which exist in well defined concentrations in thermal equilibrium, as do other kinds of point defects such as interstitial atoms. We refer to them as irregular structure elements. Kinetic parameters such as rate constants and transport coefficients are thus directly related to the number and kind of irregular structure elements (point defects) or, in more general terms, to atomic disorder. A quantitative kinetic theory therefore requires a quantitative understanding of the behavior of point defects as a function of the (local) thermodynamic parameters of the system (such as T, P, and composition, i.e., the fraction of chemical components). This understanding is provided by statistical thermodynamics and has been cast in a useful form for application to solid state chemical kinetics as the so-called point defect thermodynamics. 

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 aim of this chapter is to clarify the conditions for which chemical kinetics can be correctly applied to the description of solid state processes. Kinetics describes the evolution in time of a non-equilibrium many-particle system towards equilibrium (or steady state) in terms of macroscopic parameters. Dynamics, on the other hand, describes the local motion of the individual particles of this ensemble. This motion can be uncorrelated (single particle vibration, jump) or it can be correlated (e.g., through non-localized phonons). Local motions, as described by dynamics, are necessary prerequisites for the thermally activated jumps responsible for the movements over macroscopic distances which we ultimately categorize as transport and solid state reaction.. 

The methods most commonly used for preparing catalysts are precipitation (Section A 2 1 3) and impregnation (Section A 2 2 1 1) In both of them, the catalyti cally active material is transferred from a liquid phase, usually an aqueous solution, to a solid By contrast, other catalysts are obtained from solid precursors Solid state reactions, namely solid-to-solid reactions in which both the starting material (the catalyst precursor) and the catalyst are solids, offer convenient methods to prepare several industrial catalysts, especially those con taming two or more metallic elements or their oxides The reason of the conspicuous efficiency of these methods to prepare phases containing two or several metallic elements is due to special features of solid-state reactions, compared to liquid-to-solid or gas-to-solid reactions This section briefly outlines these peculiarities and presents the most frequent types of solid-state processes used in preparing catalysts... 

This article will address key questions concerning pharmaceutical cocrystals (i) Do cocrystals offer any advantages over other solid-state forms (ii) What are the criteria for cocrystal former selection (iii) Can cocrystal screening and crystallization methods be theoretically based and (iv) Can cocrystals form as a result of stresses encountered during pharmaceutical processes and storage ... 

The cooperative movement of large numbers of atoms represents an alternative, and in some ways more precise [83], mechanism of reaction in addition to the well-established interface advance and diffusion-controlled processes which are considered throughout this book. Examination of the possible participation of crystallographic shear in the reactions of solids has been largely restricted to refractory oxides, but comparable or related behaviour could, in principle, operate in a variety of other solid state rate processes. 

We shall use the term "Log Normal" for reasons which will clear later. It should be now apparent that we use terms borrowed from statistics and a statistical approach to describe a distribution of particles. The two disciplines are well suited to each other since statistics is easily capable of handling large assemblages, and the solid state processes with which we deal are random growth processes which produce large numbers of particles. 

The mechanochemical treatment by ball milling is a very complex process, wherein a number of phenomena (such as plastic deformation, fracture and coalescence of particles, local heating, phase transformation, and chemical reaction) arise simultaneously influencing each other. The mechanochemical treatment is a non-equilibrium solid-state process whereby, the final product retains a very fine, typically nanocrystalline or amorphous structure. At the moment of ball impact, dissipation of mechanical energy is almost instant. Highly excited state of the short lifetime decays rapidly, hence a frozen disordered, metastable strucmre remains. Quantitative description of the mechanochemical processes is extremely difficult, herewith a mechanochemical reaction still lacks clear interpretations and adequate paradigm. 

Other properties are also significantly affected by solid-state processing, compared to the melt counterpart, viz. dynamic mechanical properties, as well as relaxation behaviour, for example creep [193]. 

Essentially all of the quirks and imperfections that make solid-state systems interesting— point defects, dislocations, grain boundaries, inclusions, voids, surfaces—fall within the scope of materials kinetics. This focus on solid-state processes and heterogeneity—what many would call microstructural development—is what makes materials kinetics unique. In order to tackle this topic, we will need to borrow a lot of concepts from chemical reaction kinetics, which we will cover in Chapter 3 of this textbook, but we will also learn many other concepts that are not usually covered in traditional chemical-based treatments of kinetics. In particular, we will spend a lot of time on solid-state diffusion and transport (Chapter 4). Compared to the gas and liquid phases, transport of matter in the solid phase tends to be slower and more difficult thus, atomic transport processes such as diffusion become much more important in determining kinetic behavior in solid-state systems. 

A quasiracemate is the crystalline product of a 1 1 association between quasienantiomersQuasienantiomers are pairs of compounds, one of which has a molecular structure that is closely related to the enantiomer of the other. Quasiracemates tend to crystallize with pseudoinversion symmetry with packing preferences very similar to their racemate relatives (see Figure 16). Since quasiracemates generally involve heteromeric pairs of enantiopure compounds, quasiracemate formation provides an entry point for controlling the chirality of solid-state processes. ... 

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