Proton relaxation rate

The second reason is related to the misconception that proton dipolar relaxation-rates for the average molecule are far too complicated for practical use in stereochemical problems. This belief has been encouraged, perhaps, by the formidable, density-matrix calculations " commonly used by physicists and physical chemists for a rigorous interpretation of relaxation phenomena in multispin systems. However, proton-relaxation experiments reported by Freeman, Hill, Hall, and their coworkers " have demonstrated that pessimism regarding the interpretation of proton relaxation-rates may be unjustified. Valuable information of considerable importance for the carbohydrate chemist may be derived for the average molecule of interest from a simple treatment of relaxation rates. 

This simple relaxation theory becomes invalid, however, if motional anisotropy, or internal motions, or both, are involved. Then, the rotational correlation-time in Eq. 30 is an effective correlation-time, containing contributions from reorientation about the principal axes of the rotational-diffusion tensor. In order to separate these contributions, a physical model to describe the manner by which a molecule tumbles is required. Complete expressions for intramolecular, dipolar relaxation-rates for the three classes of spherical, axially symmetric, and asymmetric top molecules have been evaluated by Werbelow and Grant, in order to incorporate into the relaxation theory the appropriate rotational-diffusion model developed by Woess-ner. Methyl internal motion has been treated in a few instances, by using the equations of Woessner and coworkers to describe internal rotation superimposed on the overall, molecular tumbling. Nevertheless, if motional anisotropy is present, it is wiser not to attempt a quantitative determination of interproton distances from measured, proton relaxation-rates, although semiquantitative conclusions are probably justified by neglecting motional anisotropy, as will be seen in the following Section. 

The observed proton relaxation rate, l/rlobs, is the sum of a diamagnetic contribution, 1/Tld, and the paramagnetic relaxation rate enhancement, 1/Tlp, this latter being linearly proportional to the concentration of the paramagnetic species, [Gd], In Equation (1), the concentration is usually given in mmol L 1, thus the unity of proton relaxivity, rh is mM 1 s 1. 

Quantitative solid state 13C CP/MAS NMR has been used to determine the relative amounts of carbamazepine anhydrate and carbamazepine dihydrate in mixtures [59]. The 13C NMR spectra for the two forms did not appear different, although sufficient S/N for the spectrum of the anhydrous form required long accumulation times. This was determined to be due to the slow proton relaxation rate for this form. Utilizing the fact that different proton spin-lattice relaxation times exist for the two different pseudopolymorphic forms, a quantitative method was developed. The dihydrate form displayed a relatively short relaxation time, permitting interpulse delay times of only 10 seconds to obtain full-intensity spectra of the dihydrate form while displaying no signal due to the anhydrous... 

The efficiency of a paramagnetic chelate to act as a contrast agent is expressed by its proton relaxivity, ri or r2, referring to the paramagnetic enhancement of the longitudinal or transverse water proton relaxation rate, 1/T1 and 1/T2, respectively, by a unity concentration of the agent (ImM) ... 

To continue the investigation, carbon detected proton T relaxation data were also collected and were used to calculate proton T relaxation times. Similarly, 19F T measurements were also made. The calculated relaxation values are shown above each peak of interest in Fig. 10.25. A substantial difference is evident in the proton T relaxation times across the API peaks in both carbon spectra. Due to spin diffusion, the protons can exchange their signals with each other even when separated by as much as tens of nanometers. Since a potential API-excipient interaction would act on the molecular scale, spin diffusion occurs between the API and excipient molecules, and the protons therefore show a single, uniform relaxation time regardless of whether they are on the API or the excipients. On the other hand, in the case of a physical mixture, the molecules of API and excipients are well separated spatially, and so no bulk spin diffusion can occur. Two unique proton relaxation rates are then expected, one for the API and another for the excipients. This is evident in the carbon spectrum of the physical mixture shown on the bottom of Fig. 10.25. Comparing this reference to the relaxation data for the formulation, it is readily apparent that the formulation exhibits essentially one proton T1 relaxation time across the carbon spectrum. This therefore demonstrates that there is indeed an interaction between the drug substance and the excipients in the formulation. 

Several other nmr procedures have been used for the determination of fractionation factors. These have advantages in some systems. Instead of determining the effect of the concentration of an exchanging site on the averaged chemical shift, the effect on the averaged relaxation rate of water protons can be used in a very similar way (Silverman, 1981 Kassebaum and Silverman, 1989), For example, addition of the enzyme Co(ii)-carbonic anhydrase to an aqueous solution increases the observed value of XjT because the proton-relaxation rate is the average of that for the bulk solvent (cfl. 0.3 s ) and that for water bound to the cobalt ca. 6x 10 s ). The average is different in an H2O/D2O mixture if the bulk solvent and the Cobound solvent have different deuterium contents, and it has been used to determine a value for the fractionation factor of Co-bound water molecules in the enzyme. 

The spin-dynamics method was applied to the intramolecular PRE in the case of aqueous and methyl protons in the Ni(II)(acac)2(H20)2 complex (acac = 2,4-pentanedione) (131,132). The two kinds of protons are characterized by a different angle between the principal axis of the static ZFS and the dipole-dipole axis. The ratio, p, of the proton relaxation rates in the axial (the DD principal axis coinciding with the ZFS principal axis) and the equatorial (the DD principal axis perpendicular to the ZFS principal axis) positions takes on the value of unity in the Zeeman limit and up to four in the ZFS limit. A similar spin-dynamics analysis of the NMRD data for a Mn(II) complex has also been reported (133). 

As stated in Section II.B of Chapter 2, the actual correlation time for electron-nuclear dipole-dipole relaxation, is dominated by the fastest process among proton exchange, rotation, and electron spin relaxation. It follows that if electron relaxation is the fastest process, the proton correlation time Xc is given by electron-spin relaxation times Tie, and the field dependence of proton relaxation rates allows us to obtain the electron relaxation times and their field dependence, thus providing information on electron relaxation mechanisms. If motions faster than electron relaxation dominate Xc, it is only possible to set lower limits for the electron relaxation time, but we learn about some aspects on the dynamics of the system. In the remainder of this section we will deal with systems where electron relaxation determines the correlation time. 

Ti, = 2-3 X 10 s (providing Xso = 3.5 x 10 s). The measurement of the transverse proton relaxation rate at high fields, in fact, permits to obtain the field dependence of the electron relaxation time from the contact contribution to relaxation. The constant of the contact interaction is calculated to be equal to 0.65 MHz. 

The water proton NMRD of the pseudooctahedral Co(H20)g (reported in Fig. 13) shows almost field-independent water proton relaxation rate values in the 0.01-60 MHz region (47). Therefore, the (Os c = 1 a nd of course the co/Cc = l dispersions must occur at fields higher than 60 MHz. This provides an upper limit value for Tig equal to 4 x 10 s. Such a low Tig value is consistent with the low water proton relaxation rate values. By using the SBM theory, Tie at 298 K can be estimated to be about 10 s. It can be larger, if the presence of a probable static ZFS is taken into account (47). When measurements are performed in highly viscous ethyleneglycol the observed rates are similar to those obtained in water. This suggests that Tig is also similar and, therefore, it is rotation-independent (47). 

Fig. 25. Outer-sphere contribution to the water proton relaxation rate, calculated for a distance of closest approach, d, of 3 A and different values of S (1/2,1, 3/2, 2, 5/2).

Fig. 17. Plot of the pOi dependence of the longitudinal water proton relaxation rate of a 0.125 mM solution of MnTPPS (Chart 13) (20 MHz, 25°C and pH 7).

Figure 8. Temperature and concentration dependence of the solvent proton-solvent proton relaxation rate (%),20% (O), 10% (X), 0%.

C.S. Lai, S. Stair, H. Miziorko, J.S. Hyde, Effect of oxygen and the spin label TEMPO-Laurate on F and proton relaxation rates of the perfluorochemical blood substitute FC-43 emulsion, J. Magn. Reson. 57 (1984) 447-452. 

The enhancement of the proton relaxation rate on copper binding, as studied by Joyce and Cohn (481), can be used to infer details of the protein environment at the binding site. The value of the enhancement for the strong site in RNase-S was less than in RNase-A indicating a... 

ESR spectra of type 2 Cu suggest the presence of three to four nitrogen ligands, while bound water has also been implicated by proton relaxation rate measurements. A number of anionic inhibitors bind to type 2 Cu. These results suggest that substrates may bind to the type 2 copper centres in oxidases. 

Figure 4. Schematic representation of proton relaxation rates as function of frequencies. No measurements were made in the 0.1 MHz range which is between the domain of the Tlp and Tt techniques.

The central metal ion has nine coordination sites. It is attached to the three nitrogen atoms and to five carboxylate moieties (oxygen atoms). A single water molecule is able to coordinate at the vacant ninth site resulting in a strong enhancement of the water proton relaxation rate. The chelate can be described as a distorted capped square antiprism according to X-ray analysis [6]. 

The four examples given above illustrate the effect of water exchange or more exactly proton exchange rate and of the number of water molecules in the first coordination sphere of the paramagnetic metal ion on the water proton relaxation rate. Nonetheless, the relaxivity of a contrast agent can also be strongly... 

There are other variations of these imbibition methods, plus somewhat more direct methods such as cryomicroscopy (to visualize the distribution of liquids within the pores), and NMR (which is based on the different proton relaxation rates that occur for water near oil-wet versus water-wet surfaces). 

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