Wagner expansions

The Wagner expansion is another form of limited expansion, this time used to represent the logarithms of the activity coefficients for the solutes in a solvent, as reference (II) - an infinitely-dilute solution. 

Wagner (45) also has derived the relationship given by Equation 14, where a is the coefficient of expansion of the metal the first term on the left is —Sff.p, i.e., the partial excess entropy at constant pressure (free surface conditions) and the first term on the right is the corresponding partial excess entropy under constant volume. By combining Equation 9 with Equation 14 and integrating, Oates and Flanagan (47) have obtained Equation 15, where the reference con-... 

An asymmetric [1,2]-Wagner-Meerwein shift has been achieved under Pd catalysis, allowing ring expansion of l-(alkyloxyallenyl)cyclobutanol and simple derivatives to ... 

An interesting double ring expansion sequence developed by Vogel involves the initial pinacol coupling of cyclobutanone, isomerization to ketone 79 in acid, followed by reduction and Lewis acid-promoted Wagner-Meerwein rearrangement with dehydration (Scheme 19).129) For preparative purposes, 80 can be more... 

Aryl nitrenes show ring expansion to seven-membered ring. The mechanism of ring expansion involves the Wagner-Meerwein rearrangement (Scheme 2.62). 

The low-temperature stability of bicyclo[2.2.1]heptane derivatives is well documented by the huge literature on liquid-phase norbornyl carbonium chemistry under such conditions, no ring expansion is observed, but instead, multiple Wagner-Meerwein rearrangements take place, preserving the bicyclo[2.2.1]heptane structure in the course of nucleophilic substitution or elimination reactions. This remarkable behavior is at the origin of the nonclassic carbonium ion concept (28). 

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