Field Dependence Of Relaxation Rate Research Articles

Single-shot spatially-localized NQR using field-dependent relaxation rates

Nuclear quadrupole resonance (NQR) is commonly used to characterize solid materials containing quadrupolar nuclei. For example, NQR is a promising technique for detecting plastic explosives and other forbidden substances as well as for authenticating pharmaceutical products. Spatially-resolved NQR measurements are of particular interest for enabling automated sample positioning, evaluation of sample heterogeneity, and chemometric authentication of objects. This paper proposes a rapid “single-shot” method for spatially-resolved NQR with the potential to benefit such applications. The proposed method takes advantage of the fact that certain NQR relaxation rates are field-dependent: the observed field dependence is used to convert relaxation time distributions measured in a static field gradient (estimated via Laplace inversion of time-domain data) into spatial distributions. The method was validated using 35Cl and 37Cl NQR of sodium chlorate and other compounds. Effective spatial resolution was also improved by using machine learning (ML) to classify the measured spatial distributions. In particular, experimental results demonstrate accurate ML-based classification of 3D-printed objects containing arbitrary binary distributions of sodium chlorate. Such distributions can thus be used as NQR-based “embedded barcodes” for authenticating high-value objects.

Magnetization relaxation in the single-ion magnet DySc2N@C80: quantum tunneling, magnetic dilution, and unconventional temperature dependence.

Relaxation of magnetization in endohedral metallofullerenes DySc2N@C80 is studied at different temperatures, in different magnetic fields, and in different molecular arrangements. Magnetization behavior and relaxation are analyzed for powder sample, and for DySc2N@C80 diluted in non-magnetic fullerene Lu3N@C80, adsorbed in voids of a metal-organic framework, and dispersed in a polymer. The magnetic field dependence and zero-field relaxation are also studied for single-crystals of DySc2N@C80 co-crystallized with Ni(ii) octaethylporphyrin, as well as for the single crystal diluted with Lu3N@C80. Landau-Zener theory is applied to analyze quantum tunneling of magnetization in the crystals. The field dependence of relaxation rates revealed a dramatic dependence of the zero-field tunneling resonance width on the dilution and is explained with the help of an analysis of dipolar field distributions. AC magnetometry is used then to get access to the relaxation of magnetization in a broader temperature range, from 2 to 87 K. Finally, a theoretical framework describing the spin dynamics with dissipation is proposed to study magnetization relaxation phenomena in single molecule magnets.

Study of the second magnetization peak and the pinning behaviour in Ba(Fe0.935Co0.065)2As2 pnictide superconductor

Isothermal magnetic field dependence of magnetization and magnetic relaxation measurements were performed for the axis on a single crystal of Ba(Fe0.935 Co0.065)2As2 pnictide superconductor having Tc = 21.7 K. The second magnetization peak (SMP) for each isothermal M(H) was observed in a wide temperature range from Tc to the lowest temperature of measurement (2 K). The magnetic field dependence of relaxation rate R(H), showed a peak (Hspt) between Hon (onset of SMP in M(H)) and Hp (peak field of SMP in M(H)), which is likely to be related to a vortex-lattice structural phase transition, as suggested in the literature for a similar sample. In addition, the magnetic relaxation measured for magnetic fields near Hspt showed some noise, which might be the signature of the structural phase transition of the vortex lattice. Analysis of the magnetic relaxation data using Maley’s criterion and the collective pinning theory suggested that the SMP in the sample was due to the collective (elastic) to plastic creep crossover, which was also accompanied by a rhombic to square vortex lattice phase transition. Analysis of the pinning force density suggested a single dominating pinning mechanism in the sample, which did not showing the usual and nature of pinning. The critical current density (Jc), estimated using the Bean critical state model, was found to be 5 × 105 A cm−2 at 2 K in the zero magnetic field limit. Surprisingly, the maximum of the pinning force density was not responsible for the maximum value of the critical current density in the sample.

Plastic pinning replaces collective pinning as the second magnetization peak disappears in the pnictide superconductor Ba0.75K0.25Fe2As2

We report a detailed study of isofield magnetic relaxation and isothermal magnetization measurements with $H$$\parallel$c on an underdoped Ba$_{0.75}$K$_{0.25}$Fe$_2$As$_2$ pnictide single crystal, with superconducting transition temperature $T_c$ = 28 K. The second magnetization peak (SMP) has been observed at temperatures below $T_c$/2 and vanished at higher temperatures. The observed behaviour of the SMP has been studied by measuring the magnetic field dependence of relaxation rate, $R(H)$ and by performing the Maley's analysis. The results suggest that the crossover from collective to plastic pinning observed in the SMP disappears above 12 K with plastic pinning replacing collective pinning. An interesting $H$-$T$ phase diagram is obtained. The critical current density ($J_c$) was estimated using Bean's model and found to be $\sim$ $3.4 \times 10^9$ A/m$^2$ at 10 K in the SMP region, which is comparable to an optimally doped Ba-KFe$_2$As$_2$ superconductor and may be exploited for potential technological applications. The pinning mechanism is found to be unconventional and does not follow the usual $\delta l$ and $\delta T_c$ pinning models, which suggest the intrinsic nature of pinning in the compound.

Influence of size distribution and field amplitude on specific loss power

Herein we present the results of specific loss power (SLP) analysis of polydisperse water based ferrofluids, Fe3O4/PEG200 and Fe3O4/PEG6000, with average Fe3O4 particle size of 9 nm and 11 nm, respectively. Specific loss power was measured in alternating magnetic field of various amplitudes and at fixed frequency of 580.5 kHz. Maximum SLP values acquired were 195 W/g for Fe3O4/PEG200 and 60 W/g for Fe3O4/PEG6000 samples. The samples were labeled as superparamagnetic by magnetization measurements, but SLP field dependence showed deviation from the behavior predicted by the commonly employed linear response theory. The scope of this theory for both samples with wide particle size distribution is discussed. Deviation from the expected behavior is explained by referring to polydisperse nature of the samples and field dependent relaxation rates.

Quantitative Susceptibility Mapping by Inversion of a Perturbation Field Model: Correlation With Brain Iron in Normal Aging

There is increasing evidence that iron deposition occurs in specific regions of the brain in normal aging and neurodegenerative disorders such as Parkinson's, Huntington's, and Alzheimer's disease. Iron deposition changes the magnetic susceptibility of tissue, which alters the MR signal phase, and allows estimation of susceptibility differences using quantitative susceptibility mapping (QSM). We present a method for quantifying susceptibility by inversion of a perturbation model, or "QSIP." The perturbation model relates phase to susceptibility using a kernel calculated in the spatial domain, in contrast to previous Fourier-based techniques. A tissue/air susceptibility atlas is used to estimate B0 inhomogeneity. QSIP estimates in young and elderly subjects are compared to postmortem iron estimates, maps of the Field-Dependent Relaxation Rate Increase, and the L1-QSM method. Results for both groups showed excellent agreement with published postmortem data and in vivo FDRI: statistically significant Spearman correlations ranging from Rho=0.905 to Rho=1.00 were obtained. QSIP also showed improvement over FDRI and L1-QSM: reduced variance in susceptibility estimates and statistically significant group differences were detected in striatal and brainstem nuclei, consistent with age-dependent iron accumulation in these regions.

Magnetic Bistability of Isolated Giant‐Spin Centers in a Diamagnetic Crystalline Matrix

Polynuclear single-molecule magnets (SMMs) were diluted in a diamagnetic crystal lattice to afford arrays of independent and iso-oriented magnetic units. Crystalline solid solutions of an Fe(4) SMM and its Ga(4) analogue were prepared with no metal scrambling for Fe(4) molar fractions x down to 0.01. According to high-frequency EPR and magnetic measurements, the guest SMM species have the same total spin (S=5), anisotropy, and high-temperature spin dynamics found in the pure Fe(4) phase. However, suppression of intermolecular magnetic interactions affects magnetic relaxation at low temperature (40 mK), where quantum tunneling (QT) of the magnetization dominates. When a magnetic field is applied along the easy magnetic axis, both pure and diluted (x=0.01) phases display pronounced steps at evenly spaced field values in their hysteresis loops due to resonant QT. The pure Fe(4) phase exhibits additional steps which are firmly ascribed to two-molecule QT transitions. Studies on the field-dependent relaxation rate showed that the zero-field resonance sharpens by a factor of five and shifts from about 8 mT to exactly zero field on dilution, in agreement with the calculated variation of dipolar interactions. The tunneling efficiency also changes significantly as a function of Fe(4) concentration: the zero-field resonance is significantly enhanced on dilution, while tunneling at ±0.45 T becomes less efficient. These changes were rationalized on the basis of a dipolar shuffling mechanism and transverse dipolar fields, whose effect was analyzed by using a multispin model. Our findings directly prove the impact of intermolecular magnetic couplings on SMM behavior and disclose the magnetic response of truly isolated giant spins in a diamagnetic crystalline environment.

MRI estimates of brain iron concentration in normal aging using quantitative susceptibility mapping

Quantifying tissue iron concentration in vivo is instrumental for understanding the role of iron in physiology and in neurological diseases associated with abnormal iron distribution. Herein, we use recently-developed Quantitative Susceptibility Mapping (QSM) methodology to estimate the tissue magnetic susceptibility based on MRI signal phase. To investigate the effect of different regularization choices, we implement and compare ℓ1 and ℓ2 norm regularized QSM algorithms. These regularized approaches solve for the underlying magnetic susceptibility distribution, a sensitive measure of the tissue iron concentration, that gives rise to the observed signal phase. Regularized QSM methodology also involves a pre-processing step that removes, by dipole fitting, unwanted background phase effects due to bulk susceptibility variations between air and tissue and requires data acquisition only at a single field strength. For validation, performances of the two QSM methods were measured against published estimates of regional brain iron from postmortem and in vivo data. The in vivo comparison was based on data previously acquired using Field-Dependent Relaxation Rate Increase (FDRI), an estimate of MRI relaxivity enhancement due to increased main magnetic field strength, requiring data acquired at two different field strengths. The QSM analysis was based on susceptibility-weighted images acquired at 1.5 T, whereas FDRI analysis used Multi-Shot Echo-Planar Spin Echo images collected at 1.5 T and 3.0 T. Both datasets were collected in the same healthy young and elderly adults. The in vivo estimates of regional iron concentration comported well with published postmortem measurements; both QSM approaches yielded the same rank ordering of iron concentration by brain structure, with the lowest in white matter and the highest in globus pallidus. Further validation was provided by comparison of the in vivo measurements, ℓ1-regularized QSM versus FDRI and ℓ2-regularized QSM versus FDRI, which again yielded perfect rank ordering of iron by brain structure. The final means of validation was to assess how well each in vivo method detected known age-related differences in regional iron concentrations measured in the same young and elderly healthy adults. Both QSM methods and FDRI were consistent in identifying higher iron concentrations in striatal and brain stem ROIs (i.e., caudate nucleus, putamen, globus pallidus, red nucleus, and substantia nigra) in the older than in the young group. The two QSM methods appeared more sensitive in detecting age differences in brain stem structures as they revealed differences of much higher statistical significance between the young and elderly groups than did FDRI. However, QSM values are influenced by factors such as the myelin content, whereas FDRI is a more specific indicator of iron content. Hence, FDRI demonstrated higher specificity to iron yet yielded noisier data despite longer scan times and lower spatial resolution than QSM. The robustness, practicality, and demonstrated ability of predicting the change in iron deposition in adult aging suggest that regularized QSM algorithms using single-field-strength data are possible alternatives to tissue iron estimation requiring two field strengths.

Gender and Iron Genes May Modify Associations Between Brain Iron and Memory in Healthy Aging

Brain iron increases with age and is abnormally elevated early in the disease process in several neurodegenerative disorders that impact memory including Alzheimer's disease (AD). Higher brain iron levels are associated with male gender and presence of highly prevalent allelic variants in genes encoding for iron metabolism proteins (hemochromatosis H63D (HFE H63D) and transferrin C2 (TfC2)). In this study, we examined whether in healthy older individuals memory performance is associated with increased brain iron, and whether gender and gene variant carrier (IRON+) vs noncarrier (IRON-) status (for HFE H63D/TfC2) modify the associations. Tissue iron deposited in ferritin molecules can be measured in vivo with magnetic resonance imaging utilizing the field-dependent relaxation rate increase (FDRI) method. FDRI was assessed in hippocampus, basal ganglia, and white matter, and IRON+ vs IRON- status was determined in a cohort of 63 healthy older individuals. Three cognitive domains were assessed: verbal memory (delayed recall), working memory/attention, and processing speed. Independent of gene status, worse verbal-memory performance was associated with higher hippocampal iron in men (r=-0.50, p=0.003) but not in women. Independent of gender, worse verbal working memory performance was associated with higher basal ganglia iron in IRON- group (r=-0.49, p=0.005) but not in the IRON+ group. Between-group interactions (p=0.006) were noted for both of these associations. No significant associations with white matter or processing speed were observed. The results suggest that in specific subgroups of healthy older individuals, higher accumulations of iron in vulnerable gray matter regions may adversely impact memory functions and could represent a risk factor for accelerated cognitive decline. Combining genetic and MRI biomarkers may provide opportunities to design primary prevention clinical trials that target high-risk groups.

Prevalent Iron Metabolism Gene Variants Associated with Increased Brain Ferritin Iron in Healthy Older Men

Prevalent gene variants involved in iron metabolism [hemochromatosis (HFE) H63D and transferrin C2 (TfC2)] have been associated with higher risk and earlier age at onset of Alzheimer's disease (AD), especially in men. Brain iron increases with age, is higher in men, and is abnormally elevated in several neurodegenerative diseases, including AD and Parkinson's disease, where it has been reported to contribute to younger age at onset in men. The effects of the common genetic variants (HFE H63D and/or TfC2) on brain iron were studied across eight brain regions (caudate, putamen, globus pallidus, thalamus, hippocampus, white matter of frontal lobe, genu, and splenium of corpus callosum) in 66 healthy adults (35 men, 31 women) aged 55 to 76. The iron content of ferritin molecules (ferritin iron) in the brain was measured with MRI utilizing the Field Dependent Relaxation Rate Increase (FDRI) method. 47% of the sample carried neither genetic variant (IRON-) and 53% carried one and/or the other (IRON+). IRON+ men had significantly higher FDRI compared to IRON- men (p=0.013). This genotype effect was not observed in women who, as expected, had lower FDRI than men. This is the first published evidence that these highly prevalent genetic variants in iron metabolism genes can influence brain iron levels in men. Clinical phenomena such as differential gender-associated risks of developing neurodegenerative diseases and age at onset may be associated with interactions between iron genes and brain iron accumulation. Clarifying mechanisms of brain iron accumulation may help identify novel interventions for age-related neurodegenerative diseases.

MRI estimates of brain iron concentration in normal aging: Comparison of field-dependent (FDRI) and phase (SWI) methods

Different brain structures accumulate iron at different rates throughout the adult life span. Typically, striatal and brain stem structures are higher in iron concentrations in older than younger adults, whereas cortical white matter and thalamus have lower concentrations in the elderly than young adults. Brain iron can be measured in vivo with MRI by estimating the relaxivity increase across magnetic field strengths, which yields the Field-Dependent Relaxation Rate Increase (FDRI) metric. The influence of local iron deposition on susceptibility, manifests as MR phase effects, forms the basis for another approach for iron measurement, Susceptibility-Weighted Imaging (SWI), for which imaging at only one field strength is sufficient. Here, we compared the ability of these two methods to detect and quantify brain iron in 11 young (5 men, 6 women; 21 to 29 years) and 12 elderly (6 men, 6 women; 64 to 86 years) healthy adults. FDRI was acquired at 1.5 T and 3.0 T, and SWI was acquired at 1.5 T. The results showed that both methods detected high globus pallidus iron concentration regardless of age and significantly greater iron in putamen with advancing age. The SWI measures were more sensitive when the phase signal intensities themselves were used to define regions of interest, whereas FDRI measures were robust to the method of region of interest selection. Further, FDRI measures were more highly correlated than SWI iron estimates with published postmortem values and were more sensitive than SWI to iron concentration differences across basal ganglia structures. Whereas FDRI requires more imaging time than SWI, two field strengths, and across-study image registration for iron concentration calculation, FDRI appears more specific to age-dependent accumulation of non-heme brain iron than SWI, which is affected by heme iron and non-iron source effects on phase.

Diffusion tensor imaging of deep gray matter brain structures: Effects of age and iron concentration

Diffusion tensor imaging (DTI) of the brain has become a mainstay in the study of normal aging of white matter, and only recently has attention turned to the use of DTI to examine aging effects in gray matter structures. Of the many changes in the brain that occur with advancing age is increased presence of iron, notable in selective deep gray matter structures. In vivo detection and measurement of iron deposition is possible with magnetic resonance imaging (MRI) because of iron's effect on signal intensity. In the process of a DTI study, a series of diffusion-weighted images (DWI) is collected, and while not normally considered as a major dependent variable in research studies, they are used clinically and they reveal striking conspicuity of the globus pallidus and putamen caused by signal loss in these structures, presumably due to iron accumulation with age. These iron deposits may in turn influence DTI metrics, especially of deep gray matter structures. The combined imaging modality approach has not been previously used in the study of normal aging. The present study used legacy DTI data collected in 10 younger (22–37 years) and 10 older (65–79 years) men and women at 3.0 T and fast spin-echo (FSE) data collected at 1.5 T and 3.0 T to derive an estimate of the field-dependent relaxation rate increase (the “FDRI estimate”) in the putamen, caudate nucleus, globus pallidus, thalamus, and a frontal white matter sample comparison region. The effect of age on the diffusion measures in the deep gray matter structures was distinctly different from that reported in white matter. In contrast to lower anisotropy and higher diffusivity typical in white matter of older relative to younger adults observed with DTI, both anisotropy and diffusivity were higher in the older than younger group in the caudate nucleus and putamen; the thalamus showed little effect of age on anisotropy or diffusivity. Signal intensity measured with DWI was lower in the putamen of elderly than young adults, whereas the opposite was observed for the white matter region and thalamus. As a retrospective study based on legacy data, the FDRI estimates were based on FSE sequences, which underestimated the classical FDRI index of brain iron. Nonetheless, the differential effects of age on DTI metrics in subcortical gray matter structures compared with white matter tracts appears to be related, at least in part, to local iron content, which in the elderly of the present study was prominent in the FDRI estimate of the putamen and visibly striking in the diffusion-weighted image of the basal ganglia structures.

Brain ferritin iron may influence age- and gender-related risks of neurodegeneration

Background Brain iron promotes oxidative damage and protein oligomerization that result in highly prevalent age-related proteinopathies such as Alzheimer's disease (AD), Parkinson's disease (PD), and Dementia with Lewy Bodies (DLB). Men are more likely to develop such diseases at earlier ages than women but brain iron levels increase with age in both genders. We hypothesized that brain iron may influence both the age- and gender-related risks of developing these diseases. Methods The amount of iron in ferritin molecules (ferritin iron) was measured in vivo with MRI by utilizing the field dependent relaxation rate increase (FDRI) method. Ferritin iron was measured in four subcortical nuclei [caudate (C), putamen (P), globus pallidus (G), thalamus (T)], three white matter regions [frontal lobe (Fwm), genu and splenium of the corpus callosum (Gwm, Swm)] and hippocampus (Hipp) in 165 healthy adults aged 19–82. Results There was a high correlation ( r > 0.99) between published post-mortem brain iron levels and FDRI. There were significant age-related changes in ferritin iron (increases in Hipp, C, P, G, and decreases in Fwm). Women had significantly lower ferritin iron than men in five regions (C, T, Fwm, Gwm, Swm). Conclusions This is the first demonstration of gender differences in brain ferritin iron levels. It is possible that brain iron accumulation is a risk factor that can be modified. MRI provides the opportunity to assess brain iron levels in vivo and may be useful in targeting individuals or groups for preventive therapeutic interventions.

Magnetic relaxation of four-CuO 2-layer TlBa 2Ca 3Cu 4O 11+ δ single crystals

Flux creep properties were investigated in four-CuO 2-layer TlBa 2Ca 3Cu 4O 11+ δ crystals. The relaxation rates defined as dln M/dln t were studied as functions of temperature and magnetic field. A linear temperature dependence of the relaxation rate between 2 and about 30 K yielded a temperature-independent energy barrier. Above 30 K, a decrease of the relaxation rate with increasing temperature was found and the relaxation rate approached zero at the irreversibility line. Field-dependent relaxation rates indicated a linear field dependence for the sample in a partially-penetrated state and a logarithmic function of field in a fully-penetrated state. The relaxation data were compared with those of Bi 1.7Pb 0.3Sr 2CaCu 2O 8 crystals.

Effect of Dissipation on Quantum Tunneling of Vortices in Tl 2 Ba 2 Ca 2 Cu 3 O 10+δ Superconductors

The temperature and magnetic field dependence of the magnetic relaxation rate has been investigated at low temperatures (1.8 < T < 10 K) on two Tl2Ba2Ca2Cu3O10+δ samples (epitaxial thin film and sintered pellet). The temperature dependence gives evidence of a crossover in the mechanism of vortex motion, from classical thermal activation to quantum tunneling as temperature decreases. The field dependence of the relaxation rate indicates a crossover in the dimensionality of vortices, from three-dimensional flux lines to two-dimensional pancake vortices as field increases. For the thin film, the temperature dependence of the rate has been fitted to the theoretically predicted expressions for finite-temperature enhancement of the quantum rate in different regimes of dissipation. In spite of the similarity of the fits, the estimate of the ratio of Hall to viscous drag terms in the equation of motion indicates that quantum tunneling in this system occurs in an intermediate dissipative regime, where both terms contribute to the motion of vortices.

Magnetic relaxation in a Ag-sheathed high Jc BiPbSrCaCuO superconducting tape

Abstract The magnetic relaxation and magnetization curves were studied on the Ag-sheathed and highly c-axis oriented BiPbSrCaCuO tape with transport J c > 10 4 A/cm 2 at 77 K. Zero-field-cooled (ZFC) in-field relaxation for applied field perpendicular to the sample a-b plane was investigated. It was found that the field-dependent relaxation rate had a maximum in the certain applied field at various temperatures. The applied field at this maximum was greater than H ∗ , the first field for which currents flow through the entire volume of the sample in the Bean's critical state model. Pinning energies were estimated at the maximal relaxation rate in a series of temperatures.

Mössbauer parameters of a highly anisotropic low-spin ferric compound: Bis[tris(N-methylimidazol-2-yl) hydroxymethane] ferrate (III) tetrafluoroborate

We have analyzed the Mossbauer spectra of a highly anisotropic low-spin ferric compound, [Fe(TICOH)2](BF4)3, taken in frozen solution as a function of temperature and field. Unlike other low-spin ferric compounds, [Fe(TICOH)2](BF4)3 shows a sharp six-line pattern with an overall s;litting of 14.2 mm/s in an applied field at 4.2 K. Good simulations are obtained using the model of Oosterhuis and Lang with a crystal field of axial symmetry. At higher temperature spin fluctuations become important, and a dynamic lineshape model with temperature- and field-dependent relaxation rates is used to simulate the data.

Determination of motional spectral densities from measurements of 13C-2H scalar relaxation

where e2qQ/h is the quadrupole coupling constant and the spectral density parameters J,(oO) and J2(2wo) are evaluated at indicated multiples of the Larmor frequency. Measurements of R, as a function of external field strength provide insight into motional processes with correlation times on the order of l/oO, and in fluids with local order (I, 2), such slow processes can give rise to field dependent relaxation rates (3, 4) even when the “effective” correlation time r,-defined as the integral of the correlation function-fulfills the condition wo~c 4 1. In such cases, and in general when composite motions are present, it is advantageous to measure Jr(wo) and J2(200) separately, so as to investigate the motional spectrum at a set of well defined single frequencies. The determination of individual spectral densities of motion in isotropic fluids has been accomplished successfully via analysis of dipolar relaxation pathways in scalar coupled 13C (5-7) and proton (8, 9) spin systems, but when the interesting motional processes occur at frequencies too low to be monitored via proton and i3C relaxation rates (4), nuclei of lower gyromagnetic ratio, such as deuterium and nitrogen, are particularly useful. For solids (IO, II) and liquid crystals (12-16) numerous techniques are available which permit determination of the individual spectral densities for deuterium. However, none of these methods can be used for isotropic liquids, where the quadrupolar nucleus gives only a featureless Lorentzian line. In this note we demonstrate that indirect measurements of quadrupolar relaxation, via lineshape analysis of nuclei of spin-% scalar coupled to the relaxing quadrupolar spin, provide enough information to determine both spectral densities without making any assumptions about their relative magnitudes or functional form. In what follows we consider the specific case of a single 13C coupled to a directly bonded deuteron, but extensions to more complex situations are straightforward. The lineshape for a spin ‘/2 coupled to a relaxing spin 1 has, of course, been the subject of numerous studies (I 7-20), but in all cases the relaxation of the quadrupolar nucleus was described simply by a phenomenological spin-lattice relaxation time

Magnetic cross-relaxation among protons in protein solutions

The magnetic spin-lattice relaxation rates of solvent water nuclei are known to increase upon addition of diamagnetic solute protein. This enhancement of the relaxation rate is a function of magnetic field, and the orientational relaxation time of the protein molecules can be deduced from analysis of the field-dependent relaxation rates. Although the nature of the interactions that convey information about the dynamics of protein motion to the solvent molecules is not established, it is known that there is a contribution to the relaxation rates of solvent protons that plays no role in the relaxation of solvent deuterons and 17O nuclei. We show here that the additional interaction arises from a cross-relaxation process between solvent and solute protons. We introduce a heuristic three-parameter model in which protein protons and solvent protons are considered as two separate thermodynamic systems that interact across the protein-solvent interface. The three parameters are the intrinsic relaxation rates of each system and a cross-relaxation term. The sign of the latter term must always be positive, for all values of magnetic field, in order for magnetization energy to flow from the hotter to the cooler system. We find that the magnetic field-dependence of the cross-relaxation contribution is much like that of the remaining solvent proton relaxation, i.e., about the same as the deuteron relaxation field dependence. This finding is not compatible with the predictions of expressions for the cross-relaxation that have been used by other authors, but not applied to data over a wide range of magnetic field strength. The model predicts that the relaxation behavior of both the protein protons and the solvent protons is the sum of two exponentials, the relative contributions of which would vary with protein concentration and solvent isotopic composition in a fashion suggestive of the presence of two classes of protein protons, when there is in reality only one. This finding has immediate implications for the interpretation of published proton relaxation rates in complex systems such as tissues; these data should be reexamined with cross-relaxation taken into account.

Magnetic Field Dependence of the Relaxation Rate of Optically Oriented Nuclei: An Investigation of the Adsorption of Mercury

The magnetic field dependence of the nuclear relaxation rate ${\ensuremath{\tau}}^{\ensuremath{-}1}$ of an optically oriented $^{199}\mathrm{Hg}$ vapor confined in a quartz cell is investigated both theoretically and experimentally. A theoretical expression is obtained for ${\ensuremath{\tau}}^{\ensuremath{-}1}$ as a function of the static magnetic field, the average time of flight ${\ensuremath{\tau}}_{f}$, the average adsorption time ${\ensuremath{\tau}}_{a}$, and other physical parameters characterizing the atom-surface interaction. When the experimental values of ${\ensuremath{\tau}}^{\ensuremath{-}1}$ in the presence of a field ranging between 0 and 1200 G are fitted by this expression, ${\ensuremath{\tau}}_{a}$, a good approximation for ${\ensuremath{\tau}}_{f}$, and information on the other parameters are easily obtained. The adsorption energy has been evaluated to within 20% using values of ${\ensuremath{\tau}}_{a}$ at various temperatures, for the case of an uncoated quartz cell and of a silicone-coated cell. They are 4 and 1.5 kcal/mole, respectively, while ${\ensuremath{\tau}}_{a}$ ranges from 5 \ensuremath{\mu}sec (at 288 K) to 1.8 \ensuremath{\mu}sec (at 328 K) in the former case, from 2.4 \ensuremath{\mu}sec (at 281 K) to 1 \ensuremath{\mu}sec (at 392 K) in the latter, with a 10% uncertainty.