Nuclear magnetic relaxation by spin-rotation interaction.

Spin-rotation interaction constants, c, are calculated from the paramagnetic term of the nuclear magnetic shielding constant, σ _p, using a relationship originally due to Ramsey. Calculated values show excellent agreement with experimental determinations from molecular beam measurements. Since σ _p can be easily estimated from the chemical shift of the nuclear resonance this provides a general method for estimating spin-rotation interaction constants.

Chemical shift anisotropies allow the components c _⊥ and c _‖ of the spin-rotation interaction tensor to be determined. Generally both components have the same sign and are of similar magnitude. The r.m.s. value of the spin-rotation interaction constant, required to calculate nuclear spin-lattice relaxation times, is not expected to differ appreciably from average values obtained from molecular beam measurements or magnetic shielding.

Values for the molecular angular velocity correlation time, τ _sr, calculated directly from nuclear spin-lattice relaxation times are about a factor of four longer than those predicted by the relationship between τ _sr and the re-orientation correlation time, τ _d, as given by Hubbard.     

Dynamic polarization of 7Li nuclei in solutions containing radical ions

Dynamic nuclear polarization parameters, obtained at 75 G, are reported for ⁷Li ions in collision with several radical anions and with one radical cation. All systems show large negative ⁷Li N.M.R. enhancements indicative of weak scalar relaxation. However, radical induced relaxation rates derived from ⁷Li T ₁ measurements suggest stronger complexing of lithium ions with radical anions than with the radical cation as would be expected from simple coulombic considerations. Translational modulation of the dipolar interaction best accounts for proton and radical cation dipolar relaxation rates while rotational modulation best accounts for the corresponding radical anion rates; this supports the interpretation above. A model for the lithium radical collision is proposed which implies that, for radical anions, scalar coupling is only apparently weak and that the low ⁷Li scalar relaxation rates observed result from scalar correlation times (τ_c = 10^-8-10^-9 s) longer than any yet observed by this technique. The model predicts that, for certain ranges of τ_c, increasing strength of complex formation should lead to smaller scalar relaxation rates and more negative enhancements, in contrast with the behaviour of fluorocarbons where the reverse was true. The predicted dependence of enhancement upon τ_c also suggests that ⁷Li enhancements should be extremely sensitive to variations in the chemical properties of the system.     

Manifestation of liquid-state and solid-state properties in electron relaxation of paramagnetic ions in solutions: Non-Markovian processes

The linewidth δH and the spin-spin relaxation time T ₂ for Gd³⁺, Mn²⁺, and Cr³⁺ ions in aqueous, water-glycerol, and water-poly(ethylene glycol) solutions at paramagnetic ion concentrations providing the dipole-dipole mechanism of spin relaxation are measured using two independent methods, namely, electron paramagnetic resonance (EPR) and nonresonance paramagnetic absorption in parallel fields. Analysis of the experimental results indicates a gradual crossover from pure liquid-state (diffusion) to quasi-solid-state (rigid lattice) spin relaxation. It is demonstrated that the limiting cases are adequately described by standard, universally accepted formulas for dipole-dipole interactions in the liquid-state (the correlation time of translational motion satisfies the condition τ _c ?τ₂) and solid-state (τ _c ?τ₂) approximations. A complete theoretical treatment of the experimental dependences (including the observed gradual crossover of spin relaxation) is performed in the framework of the non-Markovian theory of spin relaxation in disordered media, which is proposed by one of the authors. Within this approach, the collective memory effects for spin and molecular (lattice) variables are taken into account using the first-order and second-order memory functions for spin-spin and spin-lattice interactions. A correlation between the spin magnitude and the temperature-viscosity conditions corresponding to the crossover to non-Markovian relaxation is revealed, and the situations in which structural transformations occurring in the solutions favor the crossover to solid-state spin relaxation are analyzed.     

On the dynamical coupling between the dipolar and tunneling system of CH3-groups in solids at high temperatures

For methyl groups a dynamical coupling has been predicted between the dipolar and tunnelling systems, also at high temperatures where the observable tunnelling frequency at thermal equilibrium ω_t is zero. This is experimentally confirmed by observed non-exponential dipolar relaxation for ω₀²τ_c² ? 1.     

<Superscript>1</Superscript>H Spin–Lattice Relaxation Study of Dynamical Inequivalence of Methyl Groups in Solid 1,2-<Emphasis Type="Italic">O</Emphasis>-(1-Ethylpropylidene)-α-<Emphasis Type="SmallCaps">d</Emphasis>-Glucofuranose

We investigated the dynamics of methyl groups in organic polycrystalline 1,2-O-(1-ethylpropylidene)-α-d-glucofuranose by the proton spin–lattice relaxation method. The temperature and nuclear magnetic resonance Larmor frequency dependence of relaxation time is presented and interpreted in terms of simple possible dynamical model for the reorientation of methyl groups: the random hopping for methyl groups, which are in a, b, and c sites in the crystal. The energy E _a of 13.5 kJ mol⁻¹ for the a-type methyl groups is typical for methyl groups in ethyl groups. In contrast, the b- and c-methyl groups characterized by the lower E _a values of 9.5 and 6.5 kJ mol⁻¹ are located in the crystal structure where the intermolecular interactions significantly influence the potential, leading to a decrease in the total energy.     

13C- and 1H-NMR Relaxation Investigation of a Polyciclic Nitrogen Compound: 3,3-Dimethyl-1,5-diphenyl-9-hydroxy-bispidinium Iodide

The rigid polycyclic nitrogen compound was considered as a test for the reliability of internuclear distances calculated by ¹H-NMR spin-lattice relaxation rates. The ‘isotropic’ motional correlation time was calculated from ¹³C relaxation rates (τ_C = 0.11 ns at 298 K). Dipolar cross-relaxation rates were calculated by measuring non-, mono- and double-selective proton spin-lattice relaxation rates. All the experimental relaxation rates were thoroughly accounted for by dipolar pairwise interactions. Only at high temperatures a certain contribution from the spin rotational mechanism was apparent.     

Rare earth paramagnetism,as studied by μSR

Some recent result of muon spin relaxation measurements in rare earth metals and intermetallic compounds are reviewed. Special emphasis is put on measurements that relate to the properties of correlated regions of spins existing relatively far above the ordering temperature in the rare earth ions. As far as comparable data from paramagnetic neutron scattering exist, they will be discussed in the same framework. For each temperature the correlated regions (or short-lived magnetic clusters) are characterized by their size, possible anisotropy with respect to the crystalline axes and their lifetime. The actual form of the interaction between the rare earth spins themselves and with the crystal fields determine the temperature dependence of these properties; a strong dipole interaction can, for instance, be expected to change the critical behaviour nearT _c . Much of the time will be devoted to experiments on Gd-metal where there are experimental indications that several interesting phenomena occur: (1) a strong effect of a cross-over from a non-conserved dynamics (dipolar) regime to a conserved (exchange dominated) regime some 10 K aboveT _c , (2) an anisotropy of the magnetic clusters with respect to the hexagonalc-axis, and (3), a persistence of spin correlations far aboveT _c . Some attempts to correlate the rare earth spin relaxation times measured in this region with cluster lifetimes deduced from neutron scattering will be reviewed, as well as a model for understanding these lifetimes in terms of temperature dependent cluster wall motion, which is determined by exchange and magnetic anisotropy parameters. Effects of possible quantum correlations originating from the “spin system+bath” interaction will be mentioned.     

Microwave dielectric response of binary mixture of N,N-dimethylformamide with propylene glycol using TDR method

Dielectric relaxation study of N,N-dimethylformamide (DMF) has been carried out with propylene glycol (PLG) at different temperatures. Time domain reflectometry (TDR) in reflection mode has been used to measure the reflection coefficient in frequency range of 10 MHz to 20 GHz. The dielectric parameters static dielectric permittivity (? ₀) and relaxation time (τ) have been obtained by Fourier transform and least squares fit methods. The experimental results show nonlinear variation in dielectric permittivity and relaxation time with volume fraction of PLG confirm the structural formation due to the intermolecular interaction between N,N-dimethylformamide and PLG. The variation in excess permittivity (ε ^E), excess inverse relaxation times (1/τ)^E, Kirkwood correlation factors (g ^eff, g ^f), activation enthalpy (ΔH) and entropy (ΔS) are also calculated to study the binary mixture interaction.     

1H NMR relaxation investigation of herbicides interacting with photosystem II preparations fromSpinacia oleracea L.

The interaction of three common herbicides, paraquat, acifluorfen and alachlor, with spinach chloroplast photosystem II (PS II) was investigated by measuring¹H nuclear magnetic resonance spin-lattice relaxation rates, transient nuclear Overhauser effect (NOE) and NOE spectroscopy (NOESY) spectra. Binding to PS II was detected by (i) the enhancement of single-selective relaxation rates and (ii) the decrease in the optimal mixing time providing maximal cross-peak intensity in NOESY spectra. Titration of relaxation enhancements was used to calculate the dissociation constants (K _d) from the bound state for paraquat (K _d = 292 ± 71 μM⁻¹) and acifluorfen (K _d = 311 ± 58 μM⁻¹). A similarK _d was apparent for alachlor. Double-selective relaxation rates allowed the isolation of dipolar relaxation terms between selected proton pairs wherefrom dynamic features of the bound state were evaluated. In all cases the motional correlation time of bound herbicide (τ_c = 0.1−0.4 ns at 300 K) was found two orders of magnitude slower than in the free-solution state. In the case of alachlor the E and Z isomers were observed to bind differently to PS II and a change in conformation could be hypothesized.     

Proton NMR relaxation in albumin solutions doped with Mn(II)

The aim of this study is to obtain further information about the source of proton relaxation in the Mn(II)-human serum albumin complex. For this purpose, proton relaxation rates in albumin solutions 1/T ₁ and 1/T ₂ were measured versus increasing amounts of manganese [Mn_t]. The fractions of manganese bound to albumin [Mn_b] and free manganese [Mn_f] were then determined from proton relaxation rate enhancement data. Paramagnetic contributions of bound manganese to the observed relaxation rates (1/T _1p^*)_b and (1/T _2p^*)_b were also determined. Finally, the (1/T _2p^*)_b/(1/T _1p^*)_b ratio was used in a derived equation to estimate an effective correlation time τ. Mean τ value of the complex was found to be in the order of 3 ns, while the hydration number of bound manganese q was estimated to be about 4. The 1/τ was found to be the sum of the inverse values of rotational correlation time 1/τ _r, mean residence time of water in hydration spheres of the complex 1/τ _m, and longitudinal electronic relaxation time of manganese 1/τ _s in the complex. In conclusion, the relaxation mechanism in albumin solutions containing Mn(II) can be interpreted through dipolar and scalar interactions modulated by τ _r, τ _m and τ _s. This analysis enables one to get reasonable figures for the τ _r and q of Mn(II) in albumin solution.     

Natural orbitals,diatomic molecules and ERD

The effects of molecular motions on spin-echo signals (2n + 1)90°_y—τ—90°_x:—Acq(t) in nuclear spin systems with dipolar interactions have been investigated. It was found that in the case of a rigid lattice (M₂τ² _c: >> 1) and a motionally narrowed NMR line (M₂τ² _c,<< 1) a maximum of echo signals is observed at t_e = 2τ + t₂—t₁/2, where t₁ and t₂ are the widths of the RF pulses. It also was found that in the slow motion region (M₂τ² _c ? 1) an amplitude of the dipolar echo signal is reduced and the maximum of the echo signal is shifted to the end of the second pulse. The theory developed is confirmed by the experimental results obtained for C₆H₆.     

Äquivalente Operatoren der Wechselwirkung zwischen Atomen und elektromagnetischem Feld

As well-known the dynamical interaction theory of molecules or atoms with the electromagnetic field may be based alternatively on one of two HAMILTON ians, ^IH or ^IIH. where the vector potential appears in the interaction term of ^IH while this of ^IIH is expressed in terms of the electric and the magnetic field strength coupled to atomic multipoles. Using a calculus of transversal functional derivation with respect to a vector function we show that we can go from ^IH to ^IIH by a comperatively simple canonical transformation which may be interpreted within the classical theory as well as within as the quantized theory. The equivalence of both HAMILTON ians is lost if, as customary in quantum optics, only a few atomic levels are taken into account. We give a plausible argument that in this case the multipole HAMILTON ian ^IIH is more suitable.     

Polar relaxation mode in PbZrO3 crystals

Abstract

In antiferroelectric lead zirconate crystal with one phase transition a nearly monodispersive dipolar relaxation has been found in the paraelectric phase and temperature range 20 K below T _c in the frequency region 20—3 ′ 10⁵ Hz. This relaxation has a dominating influence on the temperature dependence of dielectric susceptibility. Relaxation time obeys the Arrhenius law increasing up to 1.5 ′ 10^?2s (11 Hz) at T _c and then exhibiting a distinct jump.     

Proton spin-lattice relaxation in liquid water and liquid ammonia

The proton spin-lattice relaxation time has been measured at 20·8 Mc/s for a series of solutions of water in heavy water and solutions of ammonia in heavy ammonia for the temperature range from the melting point to the liquid-vapour critical temperature. Measurements have also been made for water over limited temperature ranges at several fixed densities.

The contributions to the spin-lattice relaxation time from direct dipolar and spin-rotation interactions have been separated. The spin-rotation interaction contribution appears to be the same for H₂O as for HDO and also as between NH₃, NH₂D and NHD₂ and this result is justified. The correlation times for molecular re-orientation, τ_d, and for molecular angular velocity, τ_sr, are derived from the results and in so doing some support for the Hubbard [12] relation betweent τ_sr and τ_d is adduced. It is found that at the critical temperature τ_sr?τ_d which contrasts with other liquids for which it is usually found that τ_sr??τ_d. The spin-rotation interaction constants in the water and ammonia molecules are found to be approximately 120 kc/s and 80 kc/s, respectively.

An attempt to separate the inter- and intra-molecular contributions to the dipolar spin-lattice relaxation time is possible in principle, in spite of the rapid proton exchange, but is frustrated by the fact that the equilibrium constants are little different from their statistical values. Nevertheless there is evidence that the two interactions vary in much the same way with temperature.

The correlation times deduced from the dipolar relaxation time show close relationship with dielectric, self diffusion and deuteron relaxation time data.

It is suggested that the re-orientation of both water and ammonia molecules may be by a small angle Brownian diffusion even near the critical temperature.     

Bestimmung der Atomspinkorrelationszeiten der Fe3+-Ionen in FeNH4(SO4)2·12 H2O mit Hilfe des Mössbauereffektes

The Mössbauer effect studies of⁵⁷Fe in the paramagnetic salt FeNH₄(SO₄)₂·12 H₂O reported byObenshain et al. were extended to higher values of the applied external magnetic fieldH _a. The results are discussed in terms of the theoretical calculations given byWegener. The data can be fitted using a maximum internal fieldH _max=(598±10) kOe and two atomic spin correlation times τ_c=2,4 · 10^?9 sec andτ′ _c=2,1 · 10^?9 sec.τ _c andτ′ _c are independent ofH _a and the temperatureT. It is assumed in the analysis that the distribution w(H) of the internal fields can be described by a continuous function of the Boltzmann factor type with two parameters. These two parameters are determined by the normalization and the macroscopic magnetization.     

Oxygen effect on spin relaxation of the surface paramagnetic centers in carbon chars

The original technique with the use of longitudinal electron paramagnetic resonance detection was applied to measure longitudinal and transversal electron relaxation times (T ₁ andT ₂) in specially prepared carbon chars containing paramagnetic centers (PCs) on the surface. The results not only confirmed the conclusions of our previous studies but enabled us to determine the exchange integral and clarify the mechanism of interaction between the PCs and adsorbed molecular oxygen O₂. A spin relaxation mechanism was also suggested which takes into account both the exchange and dipolar interactions in the systems combining PC and O₂. The value of the exchange integral between PCs as well as its functional dependence on the oxygen content were estimated.     

Intermolecular interaction effect on the line-shape of hyper-Rayleigh light scattering by molecular liquids

Scattering on molecules, correlated in regions of short-range quasi-ordering, is analysed with regard to its effect on the spectrum of hyper-Rayleigh light-scattering by molecular liquids. The general form of S ^2ω _c(?, Δω) derived using spherical tensors and expanding the orientational-positional-time pair correlation function in Wigner functions, is discussed on the assumption that Vineyard's [22] approximation can be applied to calculate G _c[τ₁(t), τ₂(0)]. Successive terms of the expansion are calculated assuming dipole-dipole interaction energy as predominant in the total molecular electric multipole interaction energy. In the present approximation the contribution from scattering on correlated molecules is shown to be given by the difference of two Lorentz lines, whose maxima depend on the magnitude of the interactions. The integral intensities, calculated from the formulae derived here, are in agreement with those of the literature.     

Proton magnetic relaxation in solutions of E. coli ribosomal RNA containing Mn2+ ions

A study has been made over a range of temperatures and magnetic field strengths of the spin relaxation of water protons in aqueous solutions of E. coli ribosomal RNA containing Mn²⁺ ions. The effects of the paramagnetic ions are enhanced in the presence of the RNA. As the temperature falls T ₁ passes through a minimum value, the magnitude of which is field dependent, and this is attributed to a change in dipolar relaxation mechanism from rotation of the aquocomplex to electron spin relaxation. The relevance of this work is assessed in relation to other work on proton relaxation enhancement in Mn²⁺-containing solutions of biopolymers.     

Nuclear magnetic spin-lattice relaxation and molecular motion in solid white phosphorus and in liquid phosphorus

The ³¹P spin-lattice relaxation rates have been measured in solid white phosphorus and in liquid phosphorus over the temperature range 110 K to 400 K and at Larmor frequencies of 10 MHz and 30 MHz. The contributions to the measured relaxation rate from the different interactions have been separated. In the low-temperature, crystalline phase there are important contributions to the relaxation rate from the anisotropic chemical shielding and the intramolecular dipole-dipole interactions which are modulated by the reorientational motion of the molecule. Interference effects between these two interactions, which are important in liquids, are demonstrated to be quenched by the strong dipolar interactions in the solid. The reorientational correlation time is given by

and the chemical shielding anisotropy by

In the high-temperature, plastic-crystalline phase the reorientational correlation time is

as obtained from the anisotropic chemical shielding relaxation rate which is separated from the other contributions by its quadratic dependence on the Larmor frequency. Using this τ _R the intramolecular dipole-dipole relaxation rate is calculated. The contribution from the translational diffusion modulated intermolecular dipole-dipole interaction is calculated from the self-diffusion coefficient. When these contributions are subtracted from the observed relaxation rate, there remains a frequency-independent relaxation rate, proportional to 1/δ _R , which is attributed to the spin-rotational interaction. The latter is shown to be quantitatively consistent with large-angle reorientational jumps of the P₄ molecules by 120° about their C _3v axes. The relaxation in the liquid phase is dominated by the spin-rotational interaction and the expression representing the spin-rotational relaxation rate is the same as the one derived in the plastic-crystalline phase. The mechanism of molecular reorientation in the liquid is therefore the same as in the plastic-crystalline phase.     

The effect of a surface on the dynamic and thermodynamic properties of S=1 Heisenberg ferromagnet with biquadratic exchange

Properties of semi-infinite (S=1) Heisenberg ferromagnet with biquadratic exchange were studied in terms of surface exchange (=I_S/I) and biquadratic coupling (a). It was shown that a strict correlation exists, depending on , between the type of surface spin waves (acoustic or optical) and the mean-field (MF) critical temperature, bulk (T_c) and surface T_c^S>T_c (for ). Within the framework of the Landau–Ginsburg theory for semi-infinite simple cubic ferromagnet, a detailed study is presented of the critical behaviour of the system, in particular in the vicinity of the tricritical point which is the consequence of the biquadratic interaction. It is shown that tricritical exponents satisfy exactly the scaling relations for d=3. The analysis of the spin–spin correlation function within the framework of the same theory, shows that there occurs the critical magnetic scattering of low-energy electrons (LEED) from the surface in the case , when the ordering temperature T_c^S is approached from above (from paramagnetic phase). In the opposite case, , there occurs no surface critical scattering. It was also shown that in the vicinity of the tricritical point, the biquadratic interaction increases the range of validity of the MF approximation.