Exchange chemical

There is arbitr iriness in describing phenomena as either physical or chemical, but in some sense the nuclear relaxation mechanisms we have discussed to this point are physical mechanisms, based as they are on rotational motions of molecules, magnetic dipole-dipole interactions, quadrupolar interactions, and so on. Now we discuss a nuclear relaxation mechanism that is chemical in origin. 

Consider a nucleus that can partition between two magnetically nonequivalent sites. Examples would be protons or carbon atoms involved in cis-trans isomerization, rotation about the carbon—nitrogen atom in amides, proton exchange between solute and solvent or between two conjugate acid-base pairs, or molecular complex formation. In the NMR context the nucleus is said to undergo chemical exchange between the sites. Chemical exchange is a relaxation mechanism, because it is a means by which the nucleus in one site (state) is enabled to leave that state. 

To make this more specific let us consider the proton transfer from conjugate base A (site A) to base B (site B), 

From Eqs. (4-65) and (4-66), t = jtaTb = J bTa- For the special case in which Ta = Tb, we have 2t = Ta = tb. The total exchange frequency is 1/t the net exchange frequency is jt, because at equilibrium each time a nucleus passes from A to B, one also passes from B to A. 

We are interested in the effect of chemical exchange on line width, its usual manifestation. The total relaxation frequency contributing to line width is 

In a solntion of methanol and water, or ethanol and water, the hydrogen of the alcohol OH group physically exchanges with hydrogen in the water. Such a proton is said to be labile. If this physical exchange rate is greater than the change in resonance frequency for the nuclei involved, the nearby 

If the chemical exchange frequency is lower than the spectral frequency for the nuclei of interest, there will be a discrete set of resonances for each state. Processes with intermediate rates are studied by physical, organic, and inorganic chemists using NMR because the positions and shapes of the peaks can be used to estimate reaction kinetics and the lifetimes of reactants and products in a reaction. 

In the earlier discussion of the effects of dynamic processes on NMR spectra of small molecules (Chapter 10), the NMR time scale for the exchange process was determined by the relationship between the preexchange lifetimes (or the inverse rate constants) and the chemical shift difference between the two states (or sites). This is also true for many systems of biological importance when the line widths of the resonances 

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Woessner D E 1996 Relaxation effects of chemical exchange Encyclopedia of Nuclear Magnetic Resonance ed D M Grant and R K Harris (Chichester Wiley) pp 4018-28... 

These exchanges often occur while the system is in macroscopic equilibrium—the sample itself remains the same and the dynamics may be invisible to other teclmiques. It is merely the enviromnent of a given nucleus that changes. Since NMR follows an individual nucleus, it can easily follow these dynamic processes. This is just one of several reasons that the study of chemical exchange by NMR is important. 

The timescale is just one sub-classification of chemical exchange. It can be further divided into coupled versus uncoupled systems, mutual or non-mutual exchange, inter- or intra-molecular processes and solids versus liquids. However, all of these can be treated in a consistent and clear fashion. 

The NMR experimental methods for studying chemical exchange are all fairly routine experiments, used in many other NMR contexts. To interpret these results, a numerical model of the exchange, as a frmction of rate, is fitted to the experimental data. It is therefore necessary to look at the theory behind the effects of chemical exchange. Much of the theory is developed for intennediate exchange, and this is the most complex case. However, with this theory, all of the rest of chemical exchange can be understood. 

Figure B2.4.1 shows the lineshape for intennediate chemical exchange between two equally populated sites without scalar coupling. For more complicated spin systems, the lineshapes are more complicated as well, since a spin may retain its coupling infonnation even though its chemical shift changes in the exchange.

In chemical exchange, tire two exchanging sites, A and B, will have different Lannor frequencies, and cOg. Assuming equal populations in the two sites, and the rate of exchange to be k, the two coupled Bloch equations for the two sites are given by equation (B2.4.5)). 

This is the description of NMR chemical exchange in the time domain. Note that this equation and equation (B2.4.11)) are Fourier transfomis of each other. The time-domain and frequency-domain pictures are always related in this way. 

Relaxation or chemical exchange can be easily added in Liouville space, by including a Redfield matrix, R, for relaxation, or a kinetic matrix, K, to describe exchange. The equation of motion for a general spin system becomes equation (B2.4.28). 

In classical kinetics, intemiolecular exchange processes are quite different from the uniniolecular, first-order kinetics associated with intramolecular exchange. However, the NMR of chemical exchange can still be treated as pseudo-first-order kinetics, and all the previous results apply. One way of rationalizing this is as... 

In a coupled spin system, the number of observed lines in a spectrum does not match the number of independent z magnetizations and, fiirthennore, the spectra depend on the flip angle of the pulse used to observe them. Because of the complicated spectroscopy of homonuclear coupled spins, it is only recently that selective inversions in simple coupled spin systems [23] have been studied. This means that slow chemical exchange can be studied using proton spectra without the requirement of single characteristic peaks, such as methyl groups. 

Reeves L W and Shaw K N 1970 Nuclear magnetic resonance studies of multi-site chemical exchange. I. Matrix formulation of the Bloch equations Can. J. Chem. 48 3641-53... 

British Columbia, and three at the U.S. Army Ordinance Works operated by the DuPont Company at Morgantown, West Virginia Cluldersburg, Alabama and Dana, Indiana. The plant at Trail used chemical exchange between hydrogen gas and steam for the initial isotope separation followed by electrolysis for final concentration. The three plants in the United States used vacuum distillation of water for the initial separation followed by electrolysis. Details of these plants and their operations may be found in the Hterature (10). 

A variant of the H2/NH2 chemical exchange process uses alkyl amines in place of ammonia. Hydrogen exchange catalyzed by NH2 is generaHy faster using alkyl amines than ammonia, and a dual-temperature flow sheet for a H2/CH2NH2 process has been developed (69). 

Chemical exchange between hydrogen and steam (catalyzed by nickel—chromia, platinum, or supported nickel catalysts) has served as a pre-enrichment step in an electrolytic separation plant (10,70). If the exchange could be operated as a dual-temperature process, it very likely... 

Partially Reversible Processes. In a partially reversible type of process, exemplified by chemical exchange, the reflux system is generally derived from a chemical process and involves the consumption of chemicals needed to transfer the components from the upflow into the downflow at the top of the cascade, and to accomplish the reverse at the bottom. Therefore, although the separation process itself may be reversible, the entire process is not, if the reflux is not accompHshed reversibly. 

Irreversible processes are mainly appHed for the separation of heavy stable isotopes, where the separation factors of the more reversible methods, eg, distillation, absorption, or chemical exchange, are so low that the diffusion separation methods become economically more attractive. Although appHcation of these processes is presented in terms of isotope separation, the results are equally vaUd for the description of separation processes for any ideal mixture of very similar constituents such as close-cut petroleum fractions, members of a homologous series of organic compounds, isomeric chemical compounds, or biological materials. 

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