Nuclear Overhauser enhancement factors

The 13C NMR sensitivity can sometimes be a problem, but for the kind of samples studied here the effective concentration of monomer units is several molar which does not place excessive demands on present Fourier transform NMR spectrometers. In addition to the sensitivity of the chemical shift to structure (9), the relaxation of protonated carbons is dominated by dipole-dipole interaction with the attached proton (9). The dependence of the relaxation parameters T, or spin-lattice, and Tor spin-spin, on isotropic motional correlation time for a C-H unit is shown schematically in Figure 1. The T1 can be determined by standard pulse techniques (9), while the linewidth at half-height is often related to the T2. Another parameter which is related to the correlation time is the nuclear Overhauser enhancement factor, q. The value of this factor for 13C coupled to protons, varies from about 2 at short correlation times to 0.1 at long correlation... 

Little difference was noted when peak heights were used. The error in the T data is less than + 10%. Nuclear Overhauser enhancement factors (q) were obtained by measuring the integrated intensity of peaks in a difference spectrum from one with enhancement minus one with no enhancement and dividing that value by the integral from the one with no enhancement i.e. n ( nOe no nOe / (I nOe" Accuracy should be 10% or better. Linewidtns were measured at half heights, and chemical shifts are relative to TMS. 

C Linewidth (Hz), Nuclear Overhauser Enhancement Factor (p), and T- (s), for Linear PS and 1% Cross-Linked PS in Chloroform and Dimethylformamide. 

Figure 3. Chloroform nuclear Overhauser enhancement factor as a function of temperature at the indicated polymer concentrations.

Spin-lattice relaxation times were measured by the fast inversion-recovery method (24) with subsequent data analysis by a non-linear three parameter least squares fitting routine. (25) Nuclear Overhauser enhancement factors were measured using a gated decoupling technique with the period between the end of the data acquisition and the next 90° pulse equal to eibout four times the value. Most of the data used a delay of eibout ten times the Ti value. (26)... 

The terms pc and py correspond to 1/Tic and 1/Tih, respectively, and CTCH is the cross-relaxation rate. It should be stressed that the simplicity of the above equation is a consequence of the rareness of the I spins and of the dominant strength of the dipolar interaction between directly bonded nuclei. The situation for homonuclear proton spin systems is often more complicated, since the protons usually constitute a much larger spin system, and a separation into distinct two-spin systems may be not valid in this case. The broadband irradiation of the protons yields, in a steady state, Mhz = 0 and M z = Mj (1 rj). The factor 1 + 77 is called, as introduced above, the nuclear Overhauser enhancement factor. The NOE factor is related in a simple way to the equilibrium magnetizations of the I- and S-spins (which are proportional to the magnetogyric ratios 71 and 7s), the cross-relaxation rate and the relaxation rate of the I-spin ... 

Table II. Nuclear Overhauser Enhancement Factors for Poly (n-...

Table XIV. Calculated Methylene Spin-Lattice Relaxation Times and Nuclear Overhauser Enhancement Factors for the C-2 Carbon...

FIG. I. Spin-lattice relaxation time of Li in 3-9 M LiClin HiOasafunctionofinverse absolute temperature. Circles experimental relaxation time. 7 ," crosses dipolar contribution, obtained from T,"" and the nuclear Overhauser enhancement factor t). The linear least-squaresfit for the latter yields an activation energy of 3-6kcalmol (16)... 

FIG. 11. Be spin-lattice relaxation time in 1 m aqueous Be(N03)j as a function of temperature. Open circles experimental relaxation time squares dipolar relaxation time. T°°. obtained from 7 " and the nuclear Overhauser enhancement factor, t) filled circles nondipolar relaxation time, (1/T -p- l/ri°°)- -. (102)... 

Nuclear Overhauser enhancement factors q were determined to calculate (Eq. 3 and Eq. 4). 

Tn.Ysi = gyromagnetic ratios of H or Si T = nuclear Overhauser enhancement factor... 

IT was calculated for different temperatures. The nuclear Overhauser enhancement factors T were set as independent of temperature, which was confirmed by our results. Table 2 lists measured and calculated relaxation times and rates for the silane mixture mentioned above. 

Analysis by C-NMR permits quantification of the reaction between phenolic compounds and metfaanal [64,73,232,233,235-237]. In some cases, [tris(l,l,2,2,3,3-heptafluoro-7,7-dimethyl-4,6-octanedione)europium(III)] (Eu(fod)j) is added as shift reagent to shift apart superimposed resonances in the spectra [232]. The C-NMR assignments for phenolic carbons and for carbons in products that are formed during the reaction of the unsubstituted phenol with methanal are summarized in Scheme 39. Similarly, the C-NMR assignments for the starting phenolic compound and several products fiom the reaction between 1,3-benzenediol and methanal are shown in Scheme 40. Nuclear Overhauser enhancement factors must be considered for quantification of any intensity data [232,233]. The nuclear Overhauser enhancement fectors that are used for quantification of the reaction between methanal and phenol or 1,3-benzenediol are given in Scheme 41. 

Nuclear Overhauser Enhancement Factors (NOE) for Phenol, 1,3-Benzenediol, and their Products with Methanal [232,233],... 

The ratio (1 + )/l in equation (4.7) is called the nuclear Overhauser enhancement or NOE. Alternatively, rj is called the nuclear Overhauser enhancement factor, or NOEF. One should not be surprised that rj O, because energy is being continuously supplied to the spins. 

Table 2.1, Longitudinal relaxation times and nuclear Overhauser enhancement factor n of N atoms in compounds containing an amino group. (See also Table 2.2) spectrometer frequency for the resonance of T temperature in Kelvin...

Table 2.2, Longitudinal relaxation times and nuclear Overhauser enhancement factor n of taining a >NH group. 

Figure 3.10 The nuclear Overhauser enhancement factor n for carbons as a function of correlation time at 125 and 50 Mhz. The intensity measured with the NOE is 1 + r. Reprinted with permission...

In the spectrum shown in Figure 7b, most of the carbons at natural abundance are visible. Comparison of peak heights shows a C-enrichment of about S %, assuming a constant nuclear Overhauser enhancement factor. 

If the relaxation of spin I is significantly affected by the motions of a different spin, S, then in general any deviation from Boltzmann equilibrium of the S spins will also render the I spin populations non-Boltzmann. The resulting change in the intensity of resonance I is called a nuclear Overhauser enhancement (NOE) when spins I and S both belong to nuclei. The nuclear Overhauser enhancement factor is conventionally ri, so that 1 -l- tjjs is defined as the intensity of the I resonance when the S spin populations are equalized, divided by the intensity of the I resonance when the... 

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