An Introduction to NMR Titration for Studying Rapid Reversible Complexation Roger S. Macomber University of Cincinnati, Cincinnati, OH 45221-0172
Nuclear magnetic resonance (NMR) spectroscopy is one of the most useful techniques available to chemists for the investieation of dvnamic molecular Drocesses. Most basic treatments of NMR include at least a qualitative description of the effect of "exchanre". - . that is. rcvcrsiblc dvnamlc processes, on the appearance of NMR spectra (I).
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Fast and Slow Exchange The topic is often introduced with a discussion of a simple two-site exchanging system, for example, the methyl groups in dimethylformamide.
the equilibrium constant K can be calculated from the signal integrals of the two signals.
(n
As the rate. of exchange is allowed to increase (e.g., by raising the temperature), a rather involved technique known as complete lineshape analysis (I)is required to extract values for kl and k_l.Fortunately, it is somewhat simpler to determine the value of K in the fast-exchange region, provided that 6, and 6b are known. Since nb = 1- n., eq 1 can be written 6 = n,S,
+ (1- n,)Sb = n,(A6) + 6b
(2)
Thus, I t is stated that under "slow-exchange" conditions the spectrum consists of two signals: one for species A a t chemical shift 6. and one for species B a t 66. By contrast, under "fast-exchange" conditions there is just one signal at the population-averaged chemical shift. S = n,6, + nb& (fast exchange) (1) where n represents the mole fraction. In this context, "slow exchange" means that the difference in chemical shift between A and B, AS = 8, - fib, expressed in Hz, is much larger than the rate constant for interconversion k = kl + k-, in Hz. Conversely, fast exchange means thatk >> A6 (1). By measuring the spectrum under slow-exchange conditions (e.g., at sufficiently low temperature), it is usually possible to determine both 8, and tibdirectly. Furthermore,
and nb
So-6
K=-=n. S - Sb
(fmt exchange) (5)
Complexation One of the most active areas in modern chemical research involves "molecular recognition", the formation of so-called host-guest (or H-G) complexes (C).
Volume 69 Number 5 May 1992
375
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K = 0.1/0.5/1/5/10/50/100
AND CHI0 = 0 . 1
a
=r
1-18
DILUTION CURVE V/
& INITIAL
[GI0 = [HI0 = 1 .0
I YI
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