Water spin-lattice relaxation time

J. C. Hindman, A. Svirmickas, M. Wood 1973, (Relaxation processes in water. A study of the proton spin-lattice relaxation time),/. Chem. Phys. 59 (3), 1517— 1522. 

Activation volumes were derived from pressure dependent NMR experiments using the equation A E = —kT d In T dp]T, where 7) is the spin—lattice relaxation time. A Evalues for the H and NMR experiments were close to each other as well as to the values based on conductivity. These results imply that the electrical transport is correlated with water molecule rotation. There is a trend of increasing A E with decreasing water content. 

The second role of the chemical exchange phenomena can be seen in Eq. (2) the exchange lifetime competes with the in-complex nuclear spin-lattice relaxation time and can become a limiting factor in the attainable PRE. This aspect of the problem is highly relevant in practical consideration in the case of Gd(III) complexes as a potential contrast agent, because the water exchange in these systems is not too fast. This issue is considered to be outside of the scope of this article and we refer to recent literature on the subject 5,160) and to other contributions in this volume. 

Fig. 1. Magnetic field dependences of the proton spin-lattice relaxation time of water in Bioran B30 and Vycor glasses at temperatures above 27°C and below the temperature where the non-surface water freezes ( —25°C and —35°C). The solid lines represent the power law in the Larmor frequency with an exponent of 0.67 (34).

Fig. 14. Measured water spin-lattice relaxation rates of a hydrated mortar at w/c = 0.38 as a function of the proton Larmor frequency, for different duration of hydration Oh 34 min ( ), 7h 27 min (O), 8h 45 min ( ), and 9h 40 min ( x ), upwards. The insert represents the data obtained after a hydration time of lOh 32 (+), the labels for the two axis are equivalent to those of the main figure. The continuous lines correspond to the best fits to the theory.

Adsorbed water was observed to have a large effect on the F spin-lattice relaxation time for fluorine-doped aluminas in the dilute and intermediate concentration range of fluorine (0.3-8 wt. % F). An increase in Ti by a factor of 2 to 3 was observed in these samples when adsorbed water was removed from the solid by heating between 200-300°. The effect was completely reversible addition of oxygen-free water back to the solid resulted in recovery of the original (shorter) relaxation time. This effect was observed by the measurement of the in phase and ir/2 out of phase components of the dispersion derivative at resonance dx /6Ho at high rf power, from which effective values of Ti may be calculated 46). Values of Ti were also obtained by saturation of the resonance absorption derivative. 

Clearly by working with typical spatial resolutions of approximately 30-50 pm, individual pores within the material are not resolved. However, a wealth of information can be obtained even at this lower resolution (53,54,55). Typical data are shown in Fig. 20, which includes images or maps of spin density, nuclear spin-lattice relaxation time (Ti), and self-diffusivity of water within a porous catalyst support pellet. In-plane spatial resolution is 45 pm x 45 pm, and the image slice thickness is 0.3 mm. The spin-density map is a quantitative measure of the amount of water present within the porous pellet (i.e., it is a spatially resolved map of void volume). Estimates of overall pellet void volume obtained from the MR data agree to within 5% with those obtained by gravimetric analysis. 

There have been two additional experiments which verified this basic picture of the nuclear hyperfine interaction in hemins. Johnson (78) increased the spin-lattice relaxation time by performing the Mossbauer experiment under field and temperature conditions which provide a large value of H/T. At 1.6 °K and in an applied field of 30 kG, a magnetic hyperfine interaction corresponding to that expected for high spin Fe(III) and for the g-values is measured experimentally. Recently, Lang et al. have found that a portion of hemin chloride dissolved in tetrahydro-furan at 1 mM concentration displays a hyperfine interaction at 4 °K in zero applied magnetic field. Their conclusion is that a portion of the hemin is present in a monomeric form in this solvent, a situation which is not apparent to any extent in water, acetic acid, chloroform, or dimethyl sulfoxide (77) at any concentrations used. 

In these equations, the symbols have their customary meanings (see Toth et al. in this volume for an excellent review of the topic), and the correlation times given in Eq. (3) have the following typical values at 50 MHz in water Tle (electron spin-lattice relaxation time) =10 ns, T2e (electron spin-spin relaxation time) = 1 ns, rm (inner sphere water exchange correlation time) = 130 ns [3], and rR = 60 ps. These values, in the context of Eq. (1 - 3), show why rotational dynamics control relaxivity for such chelates. 

Aso et al. (40) examined the molecular mobility of sucrose and polyvinylpyrrolidone in 1 1 lyophilized mixtures by measuring the spin-lattice relaxation times (7)) of individual carbon atoms by NMR for systems containing residual moisture at varying levels. 7) of the pyrrolidone ring carbon increased with residual moisture for lyophilized PVP alone. However, the mobility of these carbons did not increase with residual moisture when PYP was colyophilized with sucrose. Similarly, the mobility of sucrose did not increase with water activity as much in sucrose/PVP mixtures as much as in sucrose alone. Inhibition of sucrose crystallization by PVP in the presence of water appears to be linked to the effect of PVP on the molecular mobility of sucrose. 

The effect of halo thane (CF3CHBrCl) on the lateral surface conductance and membrane hydration has been studied by Yoshida and coworkers [41]. Below the pretransition temperature, the activation energy of the ion movement (H30++0FT) was 18.1 kj/mol, which corresponds to that of the spin-lattice relaxation time of water (18kJ/mol) above pretransition the activation energy increased to 51.3 kj/mol. Halothane did not show any effect on the ion movement when the temperature was below the pretransition temperature. When the temperature exceeded the pretransition temperature, the authors observed at 0.35 mM halothane (equilibrium concen-... 

Cu isotopes both with nuclear spin I-3/2. The nucle r g-factors of these two isotopes are sufficiently close that no resolution of the two isotopes is typically seen in zeolite matrices. No Jahn-Teller effects have been observed for Cu2+ in zeolites. The spin-lattice relaxation time of cupric ion is sufficiently long that it can be easily observed by GSR at room temperature and below. Thus cupric ion exchanged zeolites have been extensively studied (5,17-26) by ESR, but ESR alone has not typically given unambiguous information about the water coordination of cupric ion or the specific location of cupric ion in the zeolite lattice. This situation can be substantially improved by using electron spin echo modulation spectrometry. The modulation analysis is carried out as described in the previous sections. The number of coordinated deuterated water molecules is determined from deuterium modulation in three pulse electron spin echo spectra. The location in the zeolite lattice is determined partly from aluminum modulation and more quantitatively from cesium modulation. The symmetry of the various copper species is determined from the water coordination number and the characteristics of the ESR spectra. 

In order to characterize the hydration phenomena in more detail, it is worthwhile to obtain information on the dynamics of water molecules involved in the hydration shell. One of the useful techniques for such a purpose is 170-NMR spectroscopy. In the so-called two-state model, 170 nuclei in the aqueous solution are assumed to be distributed between the following two motional states the water in the hydration shell and the bulk water. Under this assumption, the analysis of concentration-dependent changes of the spin-lattice relaxation time of 170 nucleus gives the following important parameter known as the dynamic hydration number [17] ... 

Early studies involving NMR include the work by Hanus and Gill is [6] in which spin-lattice relaxation decay constants were studied as a function of available surface area of colloidal silica suspended in water. Senturia and Robinson [7] and Loren and Robinson [8] used NMR to qualitatively correlate mean pore sizes and observed spin-lattice relaxation times. Schmidt, et. al. [9] have qualitatively measured pore size distributions in sandstones by assuming the value of the surface relaxation time. Brown, et. al. [10] obtained pore size distributions for silica, alumina, and sandstone samples by shifting the T, distribution until the best match was obtained between distributions obtained from porosimetry and NMR. More recently, low field (20 MHz) NMR spin-lattice relaxation measurements were successfully demonstrated by Gallegos and coworkers [11] as a method for quantitatively determining pore size distributions using porous media for which the "actual" pore size distribution is known apriori. Davis and co-workers have modified this approach to rapidly determine specific surface areas [12] of powders and porous solids. 

The proton spin-lattice relaxation times for solvent water are strongly perturbed if the water is in rapid exchange with a paramagnet. In particular, Mn is a strong relaxer for water protons and thus nuclear magnetic resonance (NMR) spectroscopy provides a sensitive probe for the presence of exchangeable water molecules bound to Mn in Mn proteins. 

The spin-lattice rehucation times Ti are measured by the inversion-recovery method By the capillary method, we have measured the spin-lattice relaxation times Tj for heavy water (D2Q) over a wide range of temperature. The results are in good agreement with those given by Hindman and co-workers - within the expe ental uncertainties our and their uncertainties ate 1% and 12%, respectively. The uncertainty of tempm ture is 0.1 C in the present work. 

The large decreases in spin-lattice relaxation times of nuclei surrounding Mn (3d , five unpaired electrons) can be interpreted to give structural information. The ion is widely used in all three of the above categories. Table 3.1 illustrates some recent experiments. Many are concerned with relaxation-enhancement studies. The spin-lattice relaxation times of water ( H or O) are usually enhanced when water is bound to a Mn -macromolecule, compared with an identical solution without the macromolecule. It is often possible to calculate Mn hydration numbers, Mn -water bond lengths, and solvent accessibilities [11]. 

---