Metal model, expanded

The monomer species, M, has been described by Kraus (31) as an ion pair. Although he did not elaborate on its possible structure, one may assume that he pictured this species as two ammoniated ions held together by electrostatic forces. Douthit and Dye (12) pointed out that such a picture is consistent with the absorption spectra of sodium-ammonia solutions. Becker, Lindquist, and Alder (2) proposed an expanded metal model in which an electron was assumed to circulate in an expanded orbital on the protons of the coordinated ammonia molecules of an M + ion. The latter model is difficult to reconcile with optical, volumetric, and NMR data (16). 

Attempts to determine how the activity of the catalyst (or the selectivity which is, in a rough approximation, the ratio of reaction rates) depends upon the metal particle size have been undertaken for many decades. In 1962, one of the most important figures in catalysis research, M. Boudart, proposed a definition for structure sensitivity [4,5]. A heterogeneously catalyzed reaction is considered to be structure sensitive if its rate, referred to the number of active sites and, thus, expressed as turnover-frequency (TOF), depends on the particle size of the active component or a specific crystallographic orientation of the exposed catalyst surface. Boudart later expanded this model proposing that structure sensitivity is related to the number of (metal surface) atoms to which a crucial reaction intermediate is bound [6]. 

The dimer species, M2, was described by Huster (21) as a simple dissolved diatomic molecule. Such a species would be very unstable with respect to the ammoniated species, M + and e and may be ruled out by thermochemical data. The expanded metal dimer model of Becker, Lindquist, and Alder, in which two ammoniated metal ions are held together by a pair of electrons in a molecular orbital located principally between the two ions, is just as difficult to reconcile with optical, volumetric, and NMR data as the expanded metal monomer. In order to account for the similar absorption spectra of e, M, M2 (and any other species such as M or M4 that might exist at moderate concentrations of metal), Gold, Jolly, and Pitzer (16) assumed that species such as M and M2 consist of ionic aggregates in which the ammoniated electrons remain essentially unchanged from their state at infinite dilution. 

Danesl and coworkers have developed a model for metal extraction using supported liquid membranes. Danesl et al. (74) included both Interfaclal reaction and boundary layers In their analysis. As they demonstrate, both effects can be Important. Recently, Danesl (75) developed a simplified model of metal extraction In hollow fiber membranes based on the model above. Danesl and Relchley-Ylnger (76) have expanded this model to Include deviations from a first order rate law. 

Analysis of possible structures and reaction pathways in reactions 1-4 led to various model structures for these complexes (9t25). Some of these involved C-H activation of the substituents attached to the unsaturated carbon atoms. To test the validity of these models, two additional types of metal vapor reactions were examined. In one case, reactions with simpler unsubstituted hydrocarbons were examined. In another case, substrates ideally set up for oxidative addition of C-H to the metal center were examined. As described in the following paragraphs, both of these approaches expanded the horizons of organolanthanide chemistry. 

Some theoretical prerequisites for application of modified and expanded graphites, Si- and Sn-based composites and alloys, electroconducting polymers as active materials, catalysts and electro-conductive additives for lithium - ion batteries, metal-air batteries and electrochemical capacitors are considered. The models and the main concepts of battery-related use for such materials are proposed. 

When the random-walk model is expanded to take into account the real structures of solids, it becomes apparent that diffusion in crystals is dependent upon point defect populations. To give a simple example, imagine a crystal such as that of a metal in which all of the atom sites are occupied. Inherently, diffusion from one normally occupied site to another would be impossible in such a crystal and a random walk cannot occur at all. However, diffusion can occur if a population of defects such as vacancies exists. In this case, atoms can jump from a normal site into a neighboring vacancy and so gradually move through the crystal. Movement of a diffusing atom into a vacant site corresponds to movement of the vacancy in the other direction (Fig. 5.7). In practice, it is often very convenient, in problems where vacancy diffusion occurs, to ignore atom movement and to focus attention upon the diffusion of the vacancies as if they were real particles. This process is therefore frequently referred to as vacancy diffusion... 

The sensor covalently joined a bithiophene unit with a crown ether macrocycle as the monomeric unit for polymerization (Scheme 1). The spatial distribution of oxygen coordination sites around a metal ion causes planarization of the backbone in the bithiophene, eliciting a red-shift upon metal coordination. They expanded upon this bithiophene structure by replacing the crown ether macrocycle with a calixarene-based ion receptor, and worked with both a monomeric model and a polymeric version to compare ion-binding specificity and behavior [13]. The monomer exhibited less specificity for Na+ than the polymer. However, with the gradual addition of Na+, the monomer underwent a steady blue shift in fluorescence emission whereas the polymer appeared to reach a critical concentration where the spectra rapidly transitioned to a shorter wavelength. Scheme 2 illustrates the proposed explanation for blue shift with increasing ion concentration. 

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