Lewis parameter

Desimoni et al. initially advocated the Acceptor Number (AN) as the dominant solvent parameter" The AN describes the ease with which a solvent can act as an electron pair acceptor (Lewis acid) and... 

Several alternative attempts have been made to quantify Lewis-acid Lewis-base interaction. In view of the HSAB theory, the applicability of a scale which describes Lewis acidity with only one parameter will be unavoidably restricted to a narrow range of struchirally related Lewis bases. The use of more than one parameter results in relationships with a more general validity ". However, a quantitative prediction of the gas-phase stabilities of Lewis-acid Lewis-base complexes is still difficult. Hence the interpretation, not to mention the prediction, of solvent effects on Lewis-add Lewis-base interactions remains largely speculative. 

The second important influence of the solvent on Lewis acid - Lewis base equilibria concerns the interactions with the Lewis base. Consequently the Lewis addity and, for hard Lewis bases, especially the hydrogen bond donor capacity of tire solvent are important parameters. The electron pair acceptor capacities, quantified by the acceptor number AN, together with the hydrogen bond donor addities. O, of some selected solvents are listed in Table 1.5. Water is among the solvents with the highest AN and, accordingly, interacts strongly witli Lewis bases. This seriously hampers die efficiency of Lewis-acid catalysis in water. 

So far the four metal ions have been compared with respect to their effect on (1) the equilibrium constant for complexation to 2.4c, (2) the rate constant of the Diels-Alder reaction of the complexes with 2.5 and (3) the substituent effect on processes (1) and (2). We have tried to correlate these data with some physical parameters of the respective metal-ions. The second ionisation potential of the metal should, in principle, reflect its Lewis acidity. Furthermore the values for Iq i might be strongly influenced by the Lewis-acidity of the metal. A quantitative correlation between these two parameters... 

In summary, the effects of a number of important parameters on the catalysed reaction between 2.4 and 2.5 have been examined, representing the first detailed study of Lewis-acid catalysis of a Diels-Alder reaction in water. Crucial for the success of Lewis-acid catalysis of this reaction is the bidentate character of 2.4. In Chapter 4 attempts to extend the scope of Lewis-acid catalysis of Diels-Alder reactions in water beyond the restriction to bidentate substrates will be presented. 

Limiting L ws. Simple laws that tend to describe a narrow range of behavior of real fluids and substances, and which contain few, if any, adjustable parameters are called limiting laws. Models of this type include the ideal gas law equation of state and the Lewis-RandaH fugacity rule (10). 

Figure 23-19 is one of several by Weisz and Hicks Chem. Eng. ScL, 17, 263 [1962]). Although this predic ts some very large values of T in some ranges of the parameters, these values are mostly not reahzed in practice, as Table 23-5 shows. The modified Lewis number is Lw =... 

The other class of acrylic compatible tackifiers includes those based on ter-penes. Terpenes are monomers obtained by wood extraction or directly from pine tree sap. To make the polyterpene tackifiers, the monomers have to be polymerized under cationic conditions, typically with Lewis acid catalysis. To adjust properties such as solubility parameter and softening point, other materials such as styrene, phenol, limonene (derived from citrus peels), and others may be copolymerized with the terpenes. 

Whereas Freeman and Lewis reported the first comprehensive analysis of hydroxymethylation of phenol, they were not the last to study this system. A number of reports issued since their work have confirmed the general trends that they discovered while differing in some of the relative rates observed [80,84-99], Gardziella et al. have summarized a number of these reports ([18], pp. 29-35). In addition to providing new data under a variety of conditions, the other studies have improved on the accuracy of Freeman and Lewis, provided activation parameters, and added new methodologies for measuring product development [97-99],... 

Drago and co-workers have correlated a large body of enthalpies of adduct formation in Lewis acid-base systems, including some solvents as reactants, with this four-parameter equation ... 

The parameters and Ca are associated with the Lewis acid, and Eg and Cb with the base. a and b are interpreted as measures of electrostatic interaction, and Ca and Cb as measures of covalent interaction. Drago has criticized the DN approach as being based upon a single model process, and this objection applies also to the — A/y fBFs) model. Drago s criticism is correct, yet we should be careful not to reject a simple concept provided its limits are appreciated. Indeed, many very useful chemical quantities are subject to this criticism for example, p o values are measures of acid strength with reference to the base water. 

As one would expect, in those cases in which the ionic liquid acts as a co-catalyst, the nature of the ionic liquid becomes very important for the reactivity of the transition metal complex. The opportunity to optimize the ionic medium used, by variation of the halide salt, the Lewis acid, and the ratio of the two components forming the ionic liquid, opens up enormous potential for optimization. However, the choice of these parameters may be restricted by some possible incompatibilities with the feedstock used. Undesired side reactions caused by the Lewis acidity of the ionic liquid or by strong interaction between the Lewis acidic ionic liquid and, for example, some oxygen functionalities in the substrate have to be considered. 

The purity of ionic liquids is a key parameter, especially when they are used as solvents for transition metal complexes (see Section 5.2). The presence of impurities arising from their mode of preparation can change their physical and chemical properties. Even trace amounts of impurities (e.g., Lewis bases, water, chloride anion) can poison the active catalyst, due to its generally low concentration in the solvent. The control of ionic liquid quality is thus of utmost importance. 

Catalyst acid properties depend on several parameters, including method of preparation, dehydration temperature, silica-to-alumina ratio, and the ratio of Bronsted to Lewis acid sites. 

Green, L. C., Mulder, M. M., Milner, P. C., Lewis, M. N., Woll, J. W., Jr., Kolchin, E. K., and Mace, D., Phys. Rev. 96, 319, (iii) Analysis of the three parameter wave function of Hylleraas for the He I ground state in terms of central field wave-functions/ Configurational interaction. 

The dimensionless parameter Dpc / is called the Lewis number, which is the ratio of the diffusion coefficient of a gas through the mixture divided by the thermal diffusion coefficient of the gas mixture. 

A fundament of the quantum chemical standpoint is that structure and reactivity are correlated. When using quantum chemical reactivity parameters for quantifying relationships between structure and reactivity one has the advantage of being able to describe the nature of the structural influences in a direct manner, without empirical assumptions. This is especially valid for the so-called Salem-Klopman equation. It allows the differentiation between the charge and the orbital controlled portions of the interaction between reactants. This was shown by the investigation of the interaction between the Lewis acid with complex counterions 18> (see part 4.4). 

A major goal was to investigate the solid state structures of such compounds by single crystal X-ray diffraction. It was found that Lewis acid-base adducts R3M—ER3 show general structural trends, which allow estimations on the relative stability of the adducts. The experimental results were confirmed by computational calculations, giving even deeper insights into the structural parameters and the thermodynamic stability of simple Lewis acid-base adducts. In addition, their thermodynamic stability in solution was investigated by temperature-dependent NMR spectroscopy. 

Fitting Results for Lewis Acid Complex Formation (a) Best fit parameter... 

A general method has been developed for the estimation of model parameters from experimental observations when the model relating the parameters and input variables to the output responses is a Monte Carlo simulation. The method provides point estimates as well as joint probability regions of the parameters. In comparison to methods based on analytical models, this approach can prove to be more flexible and gives the investigator a more quantitative insight into the effects of parameter values on the model. The parameter estimation technique has been applied to three examples in polymer science, all of which concern sequence distributions in polymer chains. The first is the estimation of binary reactivity ratios for the terminal or Mayo-Lewis copolymerization model from both composition and sequence distribution data. Next a procedure for discriminating between the penultimate and the terminal copolymerization models on the basis of sequence distribution data is described. Finally, the estimation of a parameter required to model the epimerization of isotactic polystyrene is discussed. 

Mayo-Lewis Binary Copolymeriration Model. In this exeimple we consider the Mayo-Lewis model for describing binary copolymerization. The procedure for estimating the kinetic parameters expressed as reactivity ratios from composition data is discussed in detail in our earlier paper (1 ). Here diad fractions, which are the relative numbers of MjMj, MiMj, M Mj and MjMj sequences as measured by NMR are used. NMR, while extremely useful, cannot distinguish between MiM and M Mi sequences and... 

The diad fractions for the low conversion experiments only are reproduced in Table II. The high conversion data cannot be used since the Mayo-Lewis model does not apply. Again diad fractions have been standardized such that only two independent measurements are available. When the error structure is unknown, as in this case, Duever and Reilly (in preparation) show how the parameter distribution can be evaluated. Several attempts were made to use this solution. However with only five data points there is insufficient information present to allow this approach to be used. 

One significant result from the studies of stretched premixed flames is that the flame temperature and the consequent burning intensity are critically affected by the combined effects of nonequidiffusion and aerodynamic stretch of the mixture (e.g.. Refs. [1-7]). These influences can be collectively quantified by a lumped parameter S (Le i-l)x, where Le is the mixture Lewis number and K the stretch rate experienced by the flame. Specifically, the flame temperature is increased if S > 0, and decreased otherwise. Since Le can be greater or smaller than unity, while K can be positive or negative, the flame response can reverse its trend when either Le or v crosses its respective critical value. For instance, in the case of the positively stretched, counterflow flame, with k>0, the burning intensity is increased over the corresponding unstretched, planar, one-dimensional flame for Le < 1 mixtures, but is decreased for Le > 1 mixtures. 

Gilbert N. Lewis (1907) suggested employing another parameter, the thertnodynamic activity which has the dimensions of concentration and is defined by the equation... 

The beginning of the twentieth century also marked a continuation of studies of the structure and properties of electrolyte solution and of the electrode-electrolyte interface. In 1907, Gilbert Newton Lewis (1875-1946) introduced the notion of thermodynamic activity, which proved to be extremally valuable for the description of properties of solutions of strong electrolytes. In 1923, Peter Debye (1884-1966 Nobel prize, 1936) and Erich Hiickel (1896-1981) developed their theory of strong electrolyte solutions, which for the first time allowed calculation of a hitherto purely empiric parameter—the mean activity coefficients of ions in solutions. 

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