Solid-state multiphase systems

Interfacial polarizations have been recorded for many multiphase solid-state polymer systems semicrystalline polyamides... 

The foregoing chapters mark a long and not yet finished journey through the special field of the chemical kinetics of solids. It differs from the more common textbooks on kinetics not only because of the immense variety of crystalline phases, but even more in view of the ambiguity in the definition of the correct number of independent thermodynamic state variables. This is the source of many difficulties and particularly with solids containing one or more immobile components or multiphase systems composed of coherent or semicoherent crystals. In coping with this inherent complexity in the foregoing chapters, we chose to restrict ourselves mainly to the fundamental aspects rather than to present many uncorrelated details. 

Let us concentrate a little longer on ceramics. Here micro-analysis only slowly won ground and the application of solid state physics lagged behind. Very slowly the relationship between the properties of a material and its microstructure was being discovered. Metallurgy had already been characterized by a theoretical approach for some time and consequently metals were about 15 times as important as ceramic materials in 1960 (see Ashby s graph). This was of course influenced by the fact that metals have relatively simple structures which, in their turn, simplify theoretical comtemplations. Ceramic structures are very often complex and are characterized by multiphase systems. However, at present ceramic materials are approached much differently than for instance in 1900. 

The idea about the summation of the times of consecutive steps of the examined solid-state process is of primary importance for understanding the peculiarities of multiphase growth of compound layers in binary heterogeneous systems. Moreover, even in the case of formation of a single compound layer, this idea makes it possible to reveal a few aspects of reaction... 

F.J.J. van Loo. Multiphase diffusion in binary and ternary solid-state systems // Prog.Solid St.Chem.- 1990.- V.20.- P.47-99. 

In spite of their seeming variety, theoretical approaches of different authors to the consideration of solid-state heterogeneous kinetics can be divided into two distinct groups. The first group takes account of both the step of diffusional transport of reacting particles (atoms, ions or, in exceptional cases if at all, radicals) across the bulk of a growing layer to the reaction site (a phase interface) and the step of subsequent chemical transformations with the participation of these diffusing particles and the surface atoms (ions) of the other component (or molecules of the other chemical compound of a binary multiphase system). This is the physicochemical approach, the main concepts and consequences of which were presented in the most consistent form in the works by V.I. Arkharov.1,46,47... 

It can be directly derived from the rule of three functions (see below. Section 2.2.7) that three substrates (it might suffice that these are different enantiomers or diastereomers) correspond to three enzymes which can be distinguished in both functional and chemical terms. For each essential element, there thus must be at least four substances (three solid or dispersed/membrane-attached enzymes and the very speciation form of the essential element in dissolved or atmospheric (N, O, C, H, S) states) in the organism or directly linked to it in the enviromnent (soil, water, food, for photoautotrophs also the atmosphere (CO )). Living beings share one more property with traditional multiphase systems the... 

DYNAMICS OF DISTRIBUTION The natural aqueous system is a complex multiphase system which contains dissolved chemicals as well as suspended solids. The metals present in such a system are likely to distribute themselves between the various components of the solid phase and the liquid phase. Such a distribution may attain (a) a true equilibrium or (b) follow a steady state condition. If an element in a system has attained a true equilibrium, the ratio of element concentrations in two phases (solid/liquid), in principle, must remain unchanged at any given temperature. The mathematical relation of metal concentrations in these two phases is governed by the Nernst distribution law (41) commonly called the partition coefficient (1 ) and is defined as = s) /a(l) where a(s) is the activity of metal ions associated with the solid phase and a( ) is the activity of metal ions associated with the liquid phase (dissolved). This behavior of element is a direct consequence of the dynamics of ionic distribution in a multiphase system. For dilute solution, which generally obeys Raoult s law (41) activity (a) of a metal ion can be substituted by its concentration, (c) moles L l or moles Kg i. This ratio (Kd) serves as a comparison for relative affinity of metal ions for various components-exchangeable, carbonate, oxide, organic-of the solid phase. Chemical potential which is a function of several variables controls the numerical values of Kd (41). 

A solid-state fermentation is a multiphase system and the homogeneity in the solid phase is generally imperfect making it more difficult to model the process. 

Our recent work on the bismuth-cerium molybdate catalyst system has shown that it can serve as a tractable model for the study of the solid state mechanism of selective olefin oxidation by multicomponent molybdate catalysts. Although compositionally and structurally quite simple compared to other multiphase molybdate catalyst systems, bismuth-cerium molybdate catalysts are extremely effective for the selective ammoxidation of propylene to acrylonitrile (16). In particular, we have found that the addition of cerium to bismuth molybdate significantly enhances its catalytic activity for the selective ammoxidation of propylene to acrylonitrile. Maximum catalytic activity was observed for specific compositions in the single phase and two phase regions of the phase diagram (17). These characteristics of this catalyst system afford the opportunity to understand the physical basis for synergies in multiphase catalysts. In addition to this previously published work, we also include some of our most recent results on the bismuth-cerium molybdate system. As such, the present account represents a summary of our interpretations of the data on this system. 

Silica, alumina, and silica-alumina samples are often complex materials, sometimes multiphase systems, almost always having a distribution of structures at the surface. From the point of view of catalysis, structures at both the surface and in the interior (bulk properties) are important. In this chapter we focus on surfaces. Because of NMR s sensitivity to local structure and its forgiveness of long-range disorder, solid-state NMR is one of the methods of choice for studying the structures of these materials. NMR is, of course, also a powerful tool for studying dynamics. 

Lorcher, R., Strecker, K., Riedel, R., Telle, R., and Petzow, G. in Solid State Phenomena 8 9, Proc. Int. Conf. Sintering of Multiphase Metal and Ceramic Systems, Upadhyaya, G. S. (Ed.), Sci-Tech Publications, Vaduz, Gower Publ. Co., Brookfield, VT, 1990, pp. 479-492. 

In a multicomponent, multiphase system at equilibrium, ji, is the same in every phase, but in most cases /i° and therefore fi, — fi° is different for solids, liquids, gases, and solutes (we know this without knowing the numerical value of either term). Thermodynamic properties are determined and tabulated for substances in these various standard states, and how they relate to one another in chemical reactions can be seen when we consider the equilibrium constant (Chapter 9). 

R198 A. Martinez-Richa and R. L. Silvestri, Solid-State NMR Spectroscopy of Multiphase Polymer Systems , in Handbook of Multiphase Polymer Systems, eds. A. Boudenne, L. Ibos, Y. Candau and S. Thomas, John Wiley Sons Ltd., Chichester, UK, 2011, Vol. 2, p. 519. 

As we have seen, the highest dielectric permittivity is found in such solids which are heterogeneous on microscopic level. The effect can be even more drastic in multiphase systems, especially if one of the phases is water. In 1934 Smith-Rose [91] discovered that soils, which in dry state have s of 2-10, increase it by several orders of magnitude if impregnated with water (which has 80). Later, similar... 

Santhosh P, Manesh KM, Gopalan A, Lee K-P (2007) Novel amperometric carbon monoxide sensor based on multi-wedl carbon nanotubes grafted with polydiphenylamine-fabrication and performance. Sens Actuators B 125 92-99 Shai K, Wagner J (1982) Enhanced ionic conduction in dispersed solid electrolyte systems (DSES) and/or multiphase systems Agl-Al Oj, Agl-SiO, Agl-Ely ash, and Agl-AgBr. J Sohd State Chem 42 107-119 Shimizu Y, Yamashita N (2000) Solid electrolyte CO sensor using NASICON and perovskite-type oxide electrode. Sens Actuators B 64 102-106... 

Fu W, Sun P (2011) Solid state NMR study of hydrogen bonding, miscibility, and dyntimics in multiphase polymer systems. Front Chem China 6173-189 Gaisford S (2005) Stability assessment of pharmaceuticals and biopharmaceuticals by isothermtd calorimetry. Curr Pharm Biotechnol 6 181-191... 

Pure substances may occur in a variety of phases, depending on the boundary conditions. Thus, increasing the temperature of a solid at constant pressure causes its fusion and finally its vaporization to a gas. In pure substances, phases correspond to the states of aggregation. In a heterogeneous system, on the other hand, a number of phases in the same state of a regation may coexist (see earlier examples). Here, we shall describe the conditions under which a multiphase system is in equilibrium in other words, when does a homogeneous system dissociate into different phases. ... 

Dynamic mechanical analysis in polymeric multiphase systems in solid state, as part of rheology, is associated with oscillatory tests that are employed to investigate all kinds of viscoelastic material from the point of view of flow and deformation behavior. In particular, it evaluates the molecular mobility in polymers, the pattern of which may be an indication of phase-separated systems. Although there are certain preferred tools for visual examination of phenomena for these kinds of systems, dynamic mechanical analysis has the advantage of examination in dynamic conditions and of the prediction of properties. 

It has been reported (Akinay et al. 2001,2002) that the Hartman equation works well for both polymeric solids and melts, including amorphous and crystalline polymers and their blends. Moreover, it also works well in more complicated multiphase systems, such as liquid crystalline polymers (LCPs). Use of the Hartman equation is relatively simple, and its variables can be measured experimentally. Several other equations of state are cited in the Polymer Handbook (Brandrup 1999). Some of these do not permit direct measurement of parameters or contain universal constants that complicate determination of the required parameters. Another advantage of the Hartman... 

The improvements in technology in the last decade allowed NMR spectroscopy to emerge as one of the most important methods for polymer characterization. High resolution solution NMR, solid-state NMR, and the introduction of multidimensional NMR offer more detailed information, at higher resolution and in diverse conditions, on the polymer structure and polymerization mechanisms, chain conformation, and molecular dynamics of the polymers, blends, and multiphase polymer systems. 

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