Modified Bloch equations chemical

A chemical system related to that just discussed is the aqueous Cl + CI2 system. Also this system has been the subject of two independent, and partly contradictory, NMR studies. The earliest is that by Hall, Kydon, Richards and Sharp [135] who used the system as a model for multi-site exchange processes. The authors present a comprehensive discussion of the analytical and numerical features of the modified Bloch equations as applied to chemical exchange in a general n-site system. Hall et al, then apply their treatment to the exchange equilibrium... 

The modified Bloch equations for chemical exchange in a system of two sites, A and B, may in a matrix representation be written as... 

Various theoretical formalisms have been used to describe chemical exchange lineshapes. The earliest descriptions involved an extension of the Bloch equations to include the effects of exchange [1, 2, 12]. The Bloch equations formalism can be modified to include multi-site cases, and the effects of first-order scalar coupling [3, 13, 24]. As chemical exchange is merely a special case of general relaxation theories, it may be compre-... 

Expressions for determining rate constants from exchange contributions to observed linewidth for unequally populated systems in the fast exchange limit have been derived from the formal solutions to the Bloch equations modified for chemical exchange [3, 127-129]. These equations relate each rate constant to the site populations, chemical shift difference between sites, and spin relaxation times T and T2. For example, the forward rate A i 2 is given by [3, 127] ... 

Using the chemical shifts and the half-widths of signals for various protons in the low-temperature spectrum corresponding to the 1-H-1,2,3,4,5,6-hexamethylben-zenium ion one can, by the Bloch equations modified for exchange processes by... 

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