Bamford equation

TABLE 4.1.1.3.3 Reported Henry s law constants of 1-methylnaphthalene at various temperatures and temperature dependence equations Bamford et al. 1999 ... 

In summary, when a reaction is said to be an elementary reaction, the reaction rate law has been experimentally investigated and found to follow the above rate law. One special case is single-step radioactive decay reactions, which are elementary reactions and do not require further experimental confirmation of the reaction rate law. For other reactions, no matter how simple the reaction may be, without experimental confirmation, one cannot say a priori that it is an elementary reaction and cannot write down the reaction rate law, as shown by the complicated reaction rate law of Reaction 1-34. On the other hand, if the reaction rate law of Reaction 1-36 is found to be Equation 1-37, Reaction 1-36 may or may not be an elementary reaction. For example, Reaction 1-32 is not an elementary reaction even though the simple reaction law is consistent with an elementary reaction (Bamford and Tipper, 1972, p. 206). 

Bamford and Tompa (93) considered the effects of branching on MWD in batch polymerizations, using Laplace Transforms to obtain analytical solutions in terms of modified Bessel functions of the first kind for a reaction scheme restricted to termination by disproportionation and mono-radicals. They also used another procedure which was to set up equations for the moments of the distribution that could be solved numerically the MWD was approximated as a sum of a number of Laguerre functions, the coefficients of which could be obtained from the moments. In some cases as many as 10 moments had to be computed in order to obtain a satisfactory representation of the MWD. The assumption that the distribution function decreases exponentially for large DP is built into this method this would not be true of the Beasley distribution (7.3), for instance. 

According to Bamford, the thermal decomposition and explosion of hydrazine is expressed by equations in which free radicals are present ... 

Graphs have been given [Bamford, Elliott, and Hanby (5)] which relate R and /for different values of R0. This relation does not permit the determination of R0 from R (since/is usually not known a priori), but it has been shown [Fraser (6/)] that from the solution of equation (48) for/, viz.,... 

Aryl diazoalkanes (Bamford Stevens reaction of aryl aldehydes or ketones to form aryl diazoalkanes. The products were generally identified as the corresponding I.S-dinilroben/oalc esters. (equation 1). ... 

The problem of distinguishing between carbenoid and carbonium ion mechanisms of decomposition of diazoalkanes in protic media arises also in interpreting the base-induced decomposition of tosylhydrazones. In the original procedure for this widely-used reaction (W. R. Bamford and Stevens, 1952), the tosylhydrazone of a carbonyl compound is treated with the sodium salt of ethylene glycol in refluxing glycol. A mixture of olefins and alkoxyethanol is produced (equation 6). Many... 

Mathematical solutions of rate equations are compiled in Chap. 1 of C. H. Bamford and C. F. H. Tipper, Comprehensive Chemical Kinetics, Vol. 2, The Theory of Kinetics, Elsevier, Amsterdam, 1969. 

Direction substitution of element notation (Equation 10) representing the grafting of polystyrene side chains onto polybutadiene backbone. An AB-crosslinked copolymer of Bamford and Eastmond (14a)... 

We have given the integrated equations for simple first- and second-order kinetics. For integrated equations for a large number of kinetic types, see Margerison, D., in Bamford, C.H. Tipper C.F.H. Comprehensive Chemical Kinetics, Vol. 1, Elsevier, NY, 1969, p. 361. 

The kinetic scheme employed by Ballard and Bamford [71] in the analysis of their experimental data resembles the Michaelis—Menten mechanism descriptive of enzymic reactions. Equation (56) represents adsorption of the monomer by the polysarcosine chain, S, being a sarcosine residue in position i, counting the residues along the chain from the terminal base group, and E, the adsorbed NCA molecule on this site. 

Interesting stereochemical aspects of the protic Bamford-Stevens reactions of the epimeric 7-oxohexa-hydrocannabinol tosylhydrazone acetates (70) and (72) have been recently demonstrated. When the axial epimer (70) was added to sodium ethylene glycol, the ring expansion product (71) was obtained in 38% yield. On the other hand, reaction of the equatorial epimer (72) under the same conditions yielded (73) in 56% yield (equations 45 and 46). Notably, the aprotic Bamford-Stevens reaction of the axial epimer (70) gave rise to (73) (30-40% yield) after acetylation. 

The protic Bamford-Stevens reaction has been successfully utilized in the asymmetric synthesis of the naturally occurring sesquiterpenes (+)-a-eudesmol and (-)-a-selinene. Here, the more-substituted alkene was formed preferentially (equation 4,1). ... 

A structurally intriguing dimethyl[6]ditriaxane (84) has been synthesized from the polycyclic diketone tosylhydrazone (83) by the aprotic Bamford-Stevens reaction via a carbenic interm iate (equation 49). ... 

The Bamford-Stevens reaction is the key step in a convenient procedure for the conversion of aldehydes and ketones into the corresponding diazoalkanes. Here, the use of 2,4,6-triisopropylbenzenesulfo-nylhydrazone (trisylhydrazone) is far superior to the use of the more common tosylhydrazones (equation 50). This behavior is attributed to the greater release of steric compression in the decomposition of ort/io-substituted arenesulfonylhydrazones. 

Bamford et al. ( 1 ) have presented the basic kinetics for free-radical polymerization of styrene, and Hamielec et al., (2 ) employing Bamford s nomenclature, developed differential equations that are the starting point for the mathematical model. 

On treatment of series of a-tosylhydrazonophosphonates with aqueous sodium carbonate, they underwent facile Bamford-Stevens-type elimination to give the corresponding diazoalkanes (equation 132) with the exception of the tosylhydrazone derived from 4-chlorobutyrylphosphonate, which underwent cyclization (equation 133) . ... 

An alternative route involves end-capping to produce a terminal hydroxyl followed by reaction with trichloroacetyl isocyanate (Equation 5.23). This new, reactive end group can be used to initiate the growth of a second block via the photoreduction method proposed by Bamford in which magnesium or ihenium carbonyls are excited by UV or visible radiation and extract a chloride atom from the terminal unit, thereby creating a radical site. As only one radical is formed, this is a much cleaner reaction compared with (1) however, block lengths are more difficult to control in both these radical reactions, and the exact structure of the product formed can depend on the mechanism of the termination reaction. 

Our earlier discussion showed that moments are a straightforward and valuable means of characterizing a PCLD. Bamford and Tompa [16] suggest the use of moments in the analysis of polymerization kinetics since for some systems the set of equations describing the polymerization can be reduced to a small finite set. Hulburt and Katz [45], following Bamford et al [27], have shown that a distribution can be reconstructed using a finite number of moments. This stems from the observation made by Ray [31] that a distribution is generally characterized by only a finite number of moments. The example discussed in section 3.4.4 showed that a Poisson distribution can be completely characterized by only the first moment of the PCLD. 

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