Smith equation Selective

The equations derived in Sec. 6.7 are based on the assumption that termination occurs exclusively by either disproportionation or combination. This is usually not the case Some proportion of each is the more common case. If A equals the fraction of termination occurring by disproportionation, we can write n = A[ 1/1 - p] + (1 - A)[2/(l - p)] and n /n = A(1 + p) + (1 - A)[(2 + p)/2]. From measurements of n and n /n it is possible in principle to evaluate A and p. May and Smith have done this for a number of polystyrene samples. A selection of their data for which this approach seems feasible is presented ... 

When one of the reacting partners in the Wittig-Horner reaction, either the phosphine oxide or the carbonyl compound, has a double bond, the product is a diene. The Wittig-Horner reaction was utilized by Smith and coworkers in the total synthesis of milbemycin (equation 98)170. They found that when sodium hexamethyldisilazide was employed as a base, the desired E-diene selectivity is high (85%). Some examples from the literature where the Wittig-Horner reaction has been utilized for the construction of E-double bonds present in dienes and polyenes are given in Table 19171. 

The implementation is different from the standard polyphase filters of Crochiere and Rabiner et al. In the polyphase filter approach, each sub-filter is composed of coefficients which are reordered from a prototype filter. In the Smith and Gosset approach, the coefficients of the prototype filter are stored non- reordered, and each output sample is formed from an inner product of input samples and coefficients which are selected from the filter table at run time. The indexing equation is very similar to the equation that Crochiere and Rabiner give for re-ordering the prototype filter to generate their polyphase filter designs. 

Application of the Hammett pa equation to the related reaction of ethoxycarbonylmethylene with substituted benzenes indicates that here too the carbene behaves as an electrophile of low selectivity (Baldwin and Smith, 1967). 

In addition reactions of bromine to alkenes, Risbood and Ruthven154 have shown that 5A zeolite preadsorbed with bromine can selectively brominate styrene in presence of cyclohexene. By simple alteration of the order of adsorption of reactants to Pentasil zeolites, Smith and Fry155 have been able to add selectively bromine to the double bond of linear alkenes in presence of cyclic and branched alkenes, or to brominate cyclic or branched alkenes in presence of linear ones. An example is shown in equation 9. 

Low temperature heat capacity measurements by Anderson 10) y Bronson and MacHattie 42) y Keesom and van den Ende 176) y and Armstrong and Grayson-Smith 16) were used to calculate an entropy and enthalpy at 298 K. of 13.58 e. u. and 1536 cal./gram atom, respectively. From many sources, Kelley 186) derives an equation for the solid heat capacity above 298 K. Kubaschewski and coworkers 206) select 544.5 K. as the melting point and 2600 50 cal./gram atom for the heat of melting. Data on... 

Garden [81,84 Appendix 4.3] thoroughly reviewed and confirmed the assumptions of the Smith-Ewart theory, and (assuming collisional entry of radicals into particles) cast the equations into convenient forms for numerical calculations. Suitable values of the parameters were selected for several monomers (styrene, methyl methacrylate, butyl acrylate) to which the theory could be e iq)ectBd to be applicable. Although these values fit the experimental results well, some of them difier significantly from what now seen to be the best values there may be a compensauon of errors. 

Smith, Fainberg, and Winsteih s (46) classical study of solvent effects on the solvolysis of/ -mcthoxyneophyl tosylate at 75°C. It provides data for nine select solvents ranging from Et20 to DMSO. The free energy of activation (in kcal mole" in the mole 1" scale) is related to 0( a) by Equation 23 ... 

Smith et al [Sm 61] utilized kinetic data to characterize the solvent effect. Selecting the rate constant (kion) (and its logarithm) of the ionization of 2-(p-methoxyphenyl)-2-methylpropyl p-toluenesulphonate, as described by the following equation ... 

Dymond and Smith (1980) present an extensive collection of both second and third coefficients for many componnds at many temperatures from various investigators. For water at 400 °C, we select the data of Kell, McLaurin and Whalley, (1968), who give B = —73.47cm mol", C = lllOcm mol . Converting these to the pressure form of the equation ( 13.5),... 

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