BPP Theory Research Articles

Molecular Modes Elucidate the Nuclear Magnetic Resonance Relaxation of Viscous Fluids.

The Bloembergen, Purcell, and Pound (BPP) theory of nuclear magnetic resonance (NMR) relaxation in fluids dating back to 1948 continues to be the linchpin in interpreting NMR relaxation data in applications ranging from characterizing fluids in porous media to medical imaging (MRI). The BPP theory is founded on assuming molecules are hard spheres with 1H-1H dipole pairs reorienting randomly; assumptions that are severe in light of modern understanding of liquids. Nevertheless, it is intriguing to this day that the BPP theory was consistent with the original experimental data for glycerol, a hydrogen-bonding molecular fluid for which the hard-sphere-rigid-dipole assumption is inapplicable. To better understand this incongruity, atomistic molecular simulations are used to compute 1H NMR T1 relaxation dispersion (i.e., frequency dependence) in two contrasting cases: glycerol, and a (non hydrogen-bonding) viscosity standard. At high viscosities, simulations predict distinct functional forms of T1 for glycerol compared to the viscosity standard, in agreement with modern measurements, yet both in contrast to BPP theory. The cause of these departures from BPP theory is elucidated, without assuming any relaxation models and without any free parameters, by decomposing the simulated T1 response into dynamic molecular modes for both intramolecular and intermolecular interactions. The decomposition into dynamic molecular modes provides an alternative framework to understand the physics of NMR relaxation for viscous fluids.

Development of low field NMR technique for analyzing segmental mobility of crosslinked polymers

ABSTRACTThis low field NMR study established the correlation between the degree of crosslinking in rigid model systems to the proton spin lattice relaxation time (T1) measured. For three model epoxy samples, our data have shown that as the number of crosslinks increases the T1 minima shift toward higher temperatures. In addition, the magnitude of the T1 minimum is also observed to shift to higher values as a function of crosslinks formed. These trends are consistent with the predictions of the Bloembergen, Purcell, and Pound analysis. For these highly crosslinked systems, it was necessary to incorporate the Fuoss Kirkwood distribution function for describing the coupled dynamics of the connected individual monomer units of each crosslink. By fitting the spin lattice relaxation data at different temperatures to the Fuoss Kirkwood modified BPP theory, the average activation energy for the molecular motion and the breadth of the relaxation spectrum were obtained. For these model systems, the increase in the activation energy to achieve mobility and the broadening of relaxation distribution have also been determined quantitatively. The results of this study provide the foundation for using T1 to analyze the crosslinking process of polymeric systems. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018, 56, 639–642

Anomalous proton spin‐lattice relaxation in organic compounds containing methyl groups

AbstractTemperature measurements of proton spin‐lattice relaxation time performed for acetates ((CH3COO)2Ba, (CH3COO)2Cd, and (CH3COO)2Ca) and acetyl halides ((CH3CO)2O, CH3COBr and CH3COCl) are fitted to a Haupt equation. It is impossible to fit the temperature dependence of T1 protons using the BPP equation. Of importance is the assumption that complex C3 molecular motion of methyl protons takes place. An understanding of the correlation functions of complex C3 reorientation allow for the calculation of the relaxation time, T1, and the second moment of the NMR resonance. The spectral densities are calculated applying Woessner theory of complex motion and assuming a tunneling correlation time implemented from solving the Schrödinger equation. The acceptance of the tunneling correlation time resulting from the Schrödinger equation elucidates the reduction in the second moment at 0 K. The fitting leads to an excellent agreement between the experimental results of T1 temperature dependences and theoretical equations. From this, the tunneling splitting and motional parameters of methyl groups were estimated. The highest value of T1 minimum in the temperature dependence for (CH3COO)2Ba indicates the highest value of tunneling splitting. The smallest value, which is close to the T1 minimum value predicted by the BPP theory for CH3COCl, shows a lack or significantly reduced tunneling splitting. The tunneling jumps disappear at Ttun temperature, which was estimated for all studied compounds. The limitations on the use of Haupt's equation are presented. The presented approach differs from the other theoretical approaches and these differences are evaluated.

Molecular Dynamics of Water in Wood Studied by Fast Field Cycling Nuclear Magnetic Resonance Relaxometry

Water plays a very important role in wood and wood products. The molecular motion of water in wood is susceptible to thermal activation. Thermal energy makes water molecules more active and weakens the force between water and wood; therefore, the water molecules dynamic properties are greatly influenced. Molecular dynamics study is important for wood drying; this paper therefore focuses on water molecular dynamics in wood through fast field cycling nuclear magnetic resonance relaxometry techniques. The results show that the spin-lattice relaxation rate decreases with the Larmor frequency. Nuclear magnetic resonance dispersion profiles at different temperatures could separate the relaxation contribution of water in bigger pores and smaller pores. The T1 distribution from wide to narrow at 10 MHz Larmor frequency reflects the shrinkage of pore size with the higher temperature. The dependence of spin-lattice relaxation rate on correlation time for water molecular motion based on BPP (proposed by Bloembergen, Purcell, and Pound) theory shows that water correlation time increases with higher temperature, and its activation energy, calculated using the Arrhenius transformation equation, is 9.06±0.53 kJ/mol.

The 2003 Nobel Prize for MRI: significance and impact.

The 2003 Nobel Prize for MRI: significance and impact.

7Li and 133Cs spin–lattice relaxation in a nonlinear optical crystal CsLiB 6O 10

Spin–lattice relaxation rates ( T 1 −1) for 7Li and 133Cs nuclear magnetic resonance in the nonlinear optical crystal CsLiB 6O 10 were measured in the temperature range 20–300 K. The dominant relaxation of this crystal in the whole temperature investigated is due to quadrupolar interaction. 7Li spin–lattice relaxation time on the CsLiB 6O 10 yielded a minimum, attributed to the effect of molecular motion. These experiments have been analyzed by BPP theory, and the activation energy for the molecular motion was determined to be 21.19 kJ/mol. T 1 −1 for the 133Cs nucleus is well described with the simple power law of T 1 −1= AT k + B, where T is the temperature. The measured relaxation rate was found to be proportional to the T 2. The temperature dependence of the relaxation rates for the 133Cs nucleus in a CsLiB 6O 10 single crystal is in accordance with a Raman process.

Anomalous Larmour Frequency Dependence of Proton Spin-Lattice Relaxation Time (T1) in the Ferroelectric Glycine Phosphite

We report here the results of our $^{1}H$ NMR spin lattice relaxation time $(T_1)$ studies in glycine phosphite which is ferroelectric below 224 K. The experiments have been carried out in the temperature range from 200 to 419 K and at two Larmour frequencies of 11.40 and 23.56 MHz. We have noticed a Larmour frequency dependence of $T_1$ on the high-temperature side of the $T_1$ minimum. A model is proposed based on the BPP theory to explain the observation.

Anomalous Larmour Frequency Dependence of Proton Spin–Lattice Relaxation Time (T1) in the Ferroelectric Glycine Phosphite

We report here the results of our 1 H NMR spin–lattice relaxation time (T1) studies in glycine phosphite which is ferroelectric below 224 K. The experiments have been carried out in the temperature range from 200 to 419 K and at two Larmour frequencies of 11.40 and 23.56 MHz. We have noticed a Larmour frequency dependence of T1 on the high-temperature side of the T1 minimum. A model is proposed based on the BPP theory to explain the observation.

NMR Relaxation Study of Ion Dynamics in Nanocrystalline and Polycrystalline LiNbO3

Nanocrystalline (n) LiNbO3 was prepared by high-energy ball milling from the polycrystalline (p) material. Grain sizes were determined by XRD measurements and TEM images; thermal stability ranges of the samples were examined by DTA. NMR investigations of the diffusion-induced 7Li spin-lattice relaxation (SLR) rate T1-1 of n-LiNbO3 in the temperature range from T = 140 to 460 K at frequencies between ν = 24 and 78 MHz revealed a reduced activation energy on the low-temperature side of the typical peak in a log T1-1 vs T -1 plot in comparison with results obtained from experiments performed on the p-material between 300 and 1400 K. Corresponding measurements of the SLR rate in the rotating reference frame yielded an asymmetric peak in the case of p-LiNbO3, in contradiction to standard BPP theory, whereas in n-LiNbO3 only a weakly temperature-dependent relaxation rate background was observed. Furthermore, neither in n- nor in p-LiNbO3 BPP-type frequency dependencies of the SLR rate, i.e., T1-1 ∝ ν-β with β =...

Nuclear magnetic relaxation study of poly(propylene oxide)complexed with lithium salt

Measurements of 7Li, 1H and 19F nuclear relaxation times and 7Li linewidths are reported for poly(propylene oxide) complexed with lithium salts (LiClO 4, LiBF 4 and LiAsF 6). For PPO 6LiBF 4 and PPO 8LiClO 4 the onset of the 7Li motional line narrowing, occurs at approximately T G . The NMR decoupling methods was used to eliminate heteronuclear contribution to 7Li line shape. It was found that the Li- H interaction accounts for 80–90% of the linewidth. The remarkably similar temperature dependence of the measured 1H and 7Li spin-lattice relaxation rates, which shows rate maxima at 340–350 K in this PPOLi salts complexes, gives additional evidences for correlation between the cationic and the polymeric motions. The nuclear spin-lattice relaxation rates of the PPO complexes always peak at higher temperatures than the POE complexes, suggesting a lower ionic mobility for the former complexes. The frequency dependence of the relaxation rates cannot be described in the framework of the BPP theory.

Temperature dependence of the Spin-Lattice Relaxation Time of the 23Na-NMR Line in NaNO2

Abstract The spin-lattice relaxation time, T1, of the 23Na-NMR line in NaNO2 is measured between 25 K and 160 K at two magnetic field strengths, 1.1 T and 6.9 T. The temperature dependence of T1 for the center line, observed on a polycrystalline sample prepared by precipitation from aqueous solution, is given by a monotonous curve. T1 increases gradually as the temperature decreases. On the other hand for a single crystal, which is made by a modified Bridgman method, the temperature dependence of T1 shows two deep dips below 150 K and a frequency dependence which cannot be explained by ordinary BPP theory. The dominant relaxation mechanism above and below 150 K is also investigated.

Theory of the effect of random rotational jumps on the nuclear spin-lattice relaxation in solids

Starting from the weak collision limit, the BPP theory is applied to develop a theory of nuclear spin-lattice relaxation resulting from random rotational jumps of molecular groups in solids. The molecular motion modeled by an invariant continuous-time random walk on a finite group of rotations is assumed to modulate the dipole-dipole interaction between resonant nuclei. Straightforward group-theoretical techniques are used, yielding analytic expressions for the spin-lattice relaxation times T 1 and T 1 π , The tables included in the text allow our results to be applied to numerous cases of practical interest. The effect of a ( π 2 ) rotational jump of the PF 6 − ion is analyzed to illustrate the theory.

Competitive network modification in non-oxide chalcogenide glasses structural and motional properties of glasses in the system Li2S-P2S5-B2S3 studied by multinuclear NMR techniques

Non-oxide chalcogenide glasses based on more than one network former species have certain advantages for applications as solid electrolytes in batteries. To elucidate the influence of competitive glass-formation on the structural and motional properties of ionically conductive chalcogenide glasses, the system (Li2S)0.67[(B2S3)1−y (P2S5) y ]0.33 has been characterized comprehensively by DSC, electrical conductivity and6Li,7Li,31P, and11B solid state NMR techniques. The data obtained provide the first systematic characterization of the coformer effect in a chalcogenide glass system. Homogeneous glassy samples are formed fory=0.3 and 0.9≦y≦1.0, and microphase separated glasses for 0≦y≦0.2. The presence of a coformer leads to an increase in the electrical conductivity and a decrease of the activation energy, as compared to either binary system (Li2S-B2S3 or Li2S-P2S5), but only if homogeneous glasses are formed. The NMR data, in conjunction with systematic DSC and NMR studies of the binary systems (Li2S)x(B2S3)1−x (0.50≦x≦0.75) and (Li2S) x (P2S5)1−x (0.50≦x≦0.70), lead to the following conclusions: 1)11B MAS-NMR is well-suited to quantitate the amounts of three- and four coordinated boron atoms; in the binary glasses, the fraction of four-fold boron (N4) increases with decreasing Li2S/B2S3 ratio; in the ternary glasses N4 increases with increasingy. 2)31P MAS-NMR spectra of the binary glasses discriminate between three different phosphorus microenvironments, assigned to sulfide-analogs of metaphosphate, pyrophosphate, and orthophosphate species, respectively. These results suggest the applicability of network modification models originally developed for oxide glasses. For the ternary glasses, the DSC and NMR data of glasses with low phosphorus contents are consistent with a phase separation model involving a Li-rich thioborate glass that contains all of the phosphorus component and a glass phase less rich in lithium containing the four-fold boron atoms. In addition to the structural studies, the7Li spin-spin relaxation times (T 2) are used to characterize the mobility of the Li atoms. The activation energy of Li motion, determined from temperature dependentT 2 measurements and analyzed by using BPP theory differs from that determined from conductivity measurements by a factor of 2–3, possibly reflecting the inapplicability of this theory to the lithium diffusion process.

Muon motion in titanium hydride.

Motional narrowing of the transverse-field muon spin rotation signal was observed in gamma-TiH(x) for x = 1.83, 1.97, and 1.99. An analysis of the data for TiH1.99 near room temperature indicates that the mechanism responsible for the motion of the muon out of the octahedral site is thermally activated diffusion with an attempt frequency comparable to the optical vibrations of the lattice. Monte Carlo calculations to simulate the effect of muon and proton motion upon the muon field-correlation time were used to interpret the motional narrowing in TiH1.97 near 500 K. The interpretation is dependent upon whether the Bloembergen, Purcell, and Pound (BPP) theory or an independent spin-pair relaxation model is used to obtain the vacancy jump rate from proton NMR T1 measurements. Use of BPP theory shows that the field-correction time can be obtained if the rate of motion of the muon with respect to the rate of the motion for the protons is decreased. An independent spin-pair relaxation model indicates that the field-correlation time can be obtained if the rate of motion for the nearest-neighbor protons is decreased.

Nuclear spin relaxation by transitional diffusion in solids. XII. An analytical approximation

For pt.XI see J. Less-Common Met., vol.129, p.335 (1987). The theory of nuclear spin relaxation due to dipolar coupling between diffusing spins in crystals requires the calculation of spectral density functions for particular jump models of the diffusion. The results of such calculations have always been presented in a tabular form that is inconvenient to use compared with the simpler, but much less accurate, Bloembergen-Purcell-Pound theory. An approximate analytic function is proposed which, when fitted to the results of detailed calculations, has comparable accuracy to these calculations but has the simplicity of use of the BPP theory.

1H NMR Studies on the Motion of Guanidinium Ions and Dipolar‐Quadrupolar Cross Relaxations in Crystalline Guanidinium Tetrachloro‐ and Tetrabromometallates Including Au(III), Pt(II), or Pd(II) as Central Metal Ions

AbstractThe temperature dependences of proton spin‐lattice relaxation times T1 at various Larmor frequencies and of 1H NMR second moments at 40 MHz were determined for (guH)AuCl4, (guH)AuBr4, (guH)2PtCl4, (guH)2PtBr4, (guH)2PdCl4, and (guH)2PdBr4, where guH indicates a guanidinium cation [C(NH2)3]+. A solid‐solid phase transition between stable phases was located for (guH)AuCl4, (guH)AuBr4, and (guH)2PtBr4 at 363, 387, and 359 K, respectively. The high‐temperature phases of the three complexes were easily supercooled. For (guH)AuBr4, another phase transition between substable phases was found at 218 K. From the measurements of 1H T1, the motional parameters for the C3 reorientation of the D3h cation in the all complexes studied were evaluated. Below room temperature, (guH)2PtCl4 and (guH)2PdCl4 yielded unusual temperature dependences of 1H T1 unexplainable by the usual BPP theory. Moreover, the 1H T1 values in this temperature region depended strongly and in an anomalous manner on the 1H Larmor frequency employed. These unusual temperature and frequency dependences of 1H T1 can be explained as that the 1H T1 values are drastically affected by the temperature‐variable quadrupolar relaxation of chlorine nuclei in the complex anions through dipolar‐quadrupolar cross relaxation between 1H and chlorine nuclei. The frequency dependence of 1H T1 of (guH)2PtCl4 and (guH)2PdCl4 determined at various temperatures was analyzed by the Kimmich method and it revealed that the onset of anionic motion, presumably the 90° reorientation of the anion approximately as a whole about its C4 axis occurs near 200 and 250 K, respectively, with a rather small activation energy of ca. 30 kJ mol−1 for both complexes. The correlation time of chlorine nuclei for the C4 reorientation of the anions obtained at various temperatures indicated that the fade‐out phenomenon of 35Cl NQR signals observed for these complexes can be explained by the life‐time broadening. From the frequency dependence of 1H T1, the quadrupole coupling constant of chlorine nuclei for both complexes could be roughly estimated at higher temperatures where no signals could be detected by the usual NQR technique because of the fade‐out phenomenon. For (guH)AuCl4, unusual temperature and frequency dependences of 1H T1 attributable to the cross relaxation between 1H and chlorine nuclei were also observed above ca. 300 K and below ca. 230 K.

Proton Spin-Lattice Relaxation in Solid Würster's Blue Perchlorate

Temperature dependence of the proton spin-lattice relaxation time in powdered Wurster's blue perchlorate was measured between 56 and 300 K by using the 90°–τ–90° pulse NMR method at the frequencies 8.0, 12.0 and 23.4 MHz. In the paramagnetic state above the phase transition temperature of 190 K, the relaxation rate was independent of temperature and of frequency and could be explained by the hyperfine interaction modulated by an exchange interaction. Below T c the relaxation time increased with decreasing temperature and depended on frequency in accordance with BPP theory. The relaxation rate is proportional to the product of the triplet population and the effective exchange frequency both of which vary with temperature. Between 70 and 56 K, the relaxation rate is governed by paramagnetic impurities or monomer radicals.

Tunneling Rotation of Methyl-Groups and Spin-Lattice Relaxation TimeT1 ρin the Rotating Frame

In order to investigate the quantum effect of CH 3 -group rotation on spin-lattice relaxation, T 1 ρ , the spin-lattice relaxation time in the rotating frame, has been measured in some methylbenzenes. The temperature dependence of T 1 ρ showed the frequency independent minima which cannot be explained by the BPP theory. A model of T 1 ρ has been proposed considering the effect of quantum rotation. The frequency independent minima were interpreted as the tunneling assisted minima. The tunneling frequencies of CH 3 -groups are determined to be 1.0 ±0.1 MHz at 74 K in pentamethylbenzene and 2.0 ±0.5 MHz at 60 K in hexamethylbenzene. The measurement of T 1 ρ gives a useful information of the quantum rotation which cannot be obtained by T 1 measurement.

Mixed Alkali Effects in δ-Aluminas

ABSTRACTThis paper presents a NMR study of mixed alkali effects in δ-aluminas. It is shown that the BPP theory of relaxation does not describe the NMR results. However, with an elementary analysis of the data, NMR yields information about the cation dynamics which substantially agrees with the diffusion measurements.

NMR spin-lattice relaxation time in liquid bromoform

Measurements of the spin-lattice relaxation time, T 1, of deuterons and protons in deoxygenated samples of CDBr 3 and CHBr 3 CDBr 3 mixtures have been carried out between 7–149°C using NMR pulse techniques. Spin-rotation, inter-and intra-molecular dipole-dipole contributions have been separated and the results show that all of the three mechanisms contribute to the nuclear spin relaxation. The BPP theory modified to include the translational microviscosity factor of 1/2 provides a reasonable agreement with the experimental values of the intermolecular dipole-dipole contribution. However experimental values of intra-molecular dipole-dipole contribution are in disagreement with the BPP theory modified to include the rotational microviscosity factor of about 1/2.