Slow exchange

The spectrum consists of well-separated lines at Va and vj, for the limiting case of slow exchange, i.e. for  

Determination of the frequencies vj and relative concentrations pj from the spectra is complicated in the case of intermediate exchange rates, i.e. for  

Therefore, we shall discuss only experiments where the exchange of the probe molecules among the adsorption sites can be assumed to be slow (Eq. 27) or rapid (Eq. 28). 

The complete suppression of the influence of rapid exchange processes upon the spectra may require measurements at very low temperatures, especially for small probe molecules of high mobility (see Sect. 2.4). In the experiments to be described in this section, the NMR spectra exhibit various lines so that the Umiting case of slow exchange can be assumed, at least approximately for the analysis of the spectra. 

Trimethylphosphine on a second type of Lewis acid site in H - Y 30 

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For slow exchange, a convenient matrix of eigenvectors is given by equation (B2.4.23). 

Figure B2.4.5. Simulated lineshapes for an intennolecular exchange reaction in which the bond joining two strongly coupled nuclei breaks and re-fomis at a series of rates, given beside tlie lineshape. In slow exchange, the typical spectrum of an AB spin system is shown. In the limit of fast exchange, the spectrum consists of two lines at tlie two chemical shifts and all the coupling has disappeared.

For substituted cyclohexanes, the slow-exchange condition is met at temperatures below about —50 C. Table 3.5 presents data for the half-life for conformational equilibration of cyclohexyl chloride as a function of temperature. From these data, it can be seen that conformationally pure solutions of equatorial cyclohexyl chloride could be maintained at low temperature. This has been accomplished experimentally. Crystallization of cyclohexyl chloride at low temperature affords crystals containing only the... 

Very slow exchange. Slow exchange means that the lifetime ta = tb in each site is very long. Thus, a nucleus in site A precesses many times, at frequency (vq i a) in the rotating frame, before it leaves site A, and similarly for a nucleus in site B. Thus, there is time for absorption of energy from the radio-frequency field ffi, and resonance peaks appear at Va nd Vb in the laboratory frame. 

Moderately slow exchange. The state lifetime is 2t we ask how the absorption band is affected as this becomes smaller. The uncertainty principle argument given earlier is applicable here lifetime broadening will occur as the state lifetime decreases. Thus, we expect resonance absorption at (or near) frequencies Va nnd Vb but the bands will be broader than in the very slow exchange limit. Equation (4-68) is applicable in this regime. 

Figure 4-8. NMR absorption by a hypothetical two-identical site system with chemical exchange (/I) Slow exchange limit. (B) Moderately slow exchange. (D) Coalescence. (F) Fast exchange limit.

This is most readily studied with cyclohexane- /n in which 11 of the 12 protons are replaced with deuterium. The spectrum of cyclohexane- /n resembles the behavior shown in Fig. 4-8 at about — 100°C (the slow exchange regime) two sharp lines are seen these broaden as the temperature is increased, reaching coalescence at — 61.4°C, and becoming a single sharp line at higher temperatures. (The deuterium nuclei must be decoupled by rf irradiation.) Rate constants t for the conversion were measured over the temperature range — 116.7°C to — 24.0°C by Anet and Bourne. It is probable that the chair-chair inversion takes place via a boat intermediate. 

This exchangeability of adsorbed layers should be considered for better understanding of the irreversible adsorption of polymers. Apparently, penetration by the macromolecules adsorbed later through the layer of the initially adsorbed ones will include a slow exchange between the positions of segments and take a longer time. 

To see how this method works, let us construct the NMR spectra according to Eq. (11-37). We shall consider the case where a = p = 0.5. That is, this reaction will represent an exchange process such as that in dimethylformamide. We shall use the values (8 v) = 30.0 Hz and A = 1.00 Hz and assume that they are independent of temperature. The results are displayed in Fig. 11-5 over a range of lifetimes, 10-4 = r< 1 s. The extremes of this range provide the limits of fast and slow exchange in which one or two sharp singlets are seen. 

In the slow exchange limit, where 22 > A2, two Lorentzians, centered at cb + A and bb — A, respectively, are observed with width 2/Tf + 20. The exchange imposed by the molecular motion thus causes an extra broadening of the lines observed in absence of motion. 

Fig. 1. 13C-NMR fast exchange-slow exchange transition for the conformational interconversion of cyclododecane in solution of propane-d, (left side) and in the solid by CP-MAS techniques (right side) at 75.47 MHz. The temperature decreases from top to bottom as indicated at the spectra. Chemical shifts are given at the signals and refer to TMS = 0 ppm. (Ref.7))...

Fig. 3a and b. Fast exchange-slow exchange NMR transition for the conformational interconversion of octamethyltetrasiloxane. a, MAS 13C-NMR solid state spectra on the left side in comparison to solution spectra in propane-di on the right side (at 75.47 MHz), b. MAS 29Si-NMR spectra at 59.63 MHz. Temperatures are indicated in K, shift positions refer to TMS = 0 ppm and correspond to the scale at the bottom. (Ref. I0))... 

The influence of the a-bond isomerism is in agreement with the slow exchange spectra of 2,3-dimethylbutane and 1,2-dimethycylohexane in solution 16,17). Taking into account the different isomeric states of the bonds in a- and P-position on both sides of the observed carbons the slow exchange spectra of CH2-chain molecules have to be explained by conformational variations in chain segments of five carbon atoms. 

Fig. 15. Splitting pattern with the assignment of the 13C-NMR shifts of meso-4,5-dimethyloctane at 100.6 MHz within the slow exchange regime of the CH—CH bond rotation. Chemical shifts refer to TMS = 0 ppm. (Ref. 30>)...

Fig. 14-6 Profiles of potential temperature and phosphate at 21 29 N, 122 15 W in the Pacific Ocean and a schematic representation of the oceanic processes controlling the P distribution. The dominant processes shown are (1) upwelling of nutrient-rich waters, (2) biological productivity and the sinking of biogenic particles, (3) regeneration of P by the decomposition of organic matter within the water column and surface sediments, (4) decomposition of particles below the main thermocline, (5) slow exchange between surface and deep waters, and (6) incorporation of P into the bottom sediments.

Time-resolved luminescence quenching measurements using the probe Tb(pyridine-2,6-dicarboxylic acid)i and the quencher bromophenol blue show the existence of micellar clusters in AOT-based w/o microemulsions. The fast exchange appearing over several microseconds was attributed to intracluster quenching, whereas the slow exchange on the millisecond time scale was attributed to intercluster exchange [243]. 

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