Numerical and experimental studies of long-range magnetic dipolar interactions

We describe several numerical methods developed to analyze the behavior of spin polarized liquids in the presence of long-range magnetic dipolar interactions and external field gradients. Two of the methods use a discrete lattice of spins. In the first we calculate the magnetic field from the lattice of spins directly, either in the rotating frame, or in the lab frame. In the second method we include the dipolar fields from linear magnetization gradients analytically and calculate the dipolar fields from higher order gradients in Fourier space, where they are a local function of the magnetization. In the third method the magnetization is expanded in a Taylor series and the dipolar fields are calculated analytically for each term. The results of these calculations are compared to experimental data, in which we use two superconducting quantum interference device magnetometers adjacent to a spherical sample of hyperpolarized liquid 129Xe to detect the evolution of magnetization gradients. In particular, we observe an increase by a factor of 100 of the spin dephasing time in a longitudinal magnetic field gradient due to dipolar interactions of the spins. While each of the numerical techniques has certain limitations, they are generally in agreement with each other and with experimental data.     

Revisiting the mean-field picture of dipolar effects in solution NMR

For more than three decades, the classical or mean-field picture describing the distant dipolar field has been almost always simplified to an effective field proportional to the local longitudinal magnetization, differing only by a scale factor of 1.5 for homomolecular (identical resonance frequency) and heteromolecular interactions. We re-examine the underlying assumptions, and show both theoretically and experimentally that the mathematical framework needs to be modified for modern applications such as imaging. We demonstrate new pulse sequences which produce unexpected effects; for example, modulating an arbitrarily small fraction of the magnetization can substantially alter the frequency evolution. Thus, matched gradient pulse pairs (a seemingly innocuous module in thousands of existing pulse sequences) can alter the time evolution in highly unexpected ways, particularly with small flip angle pulses such as those used in hyperpolarized experiments. We also show that specific gradient pulse combinations can retain only dipolar interactions between unlike spins, and the dipolar field can generate a secular Hamiltonian proportional to I(x).     

Off-resonance R(1rho) NMR studies of exchange dynamics in proteins with low spin-lock fields: an application to a Fyn SH3 domain

An (15)N NMR R(1rho) relaxation experiment is presented for the measurement of millisecond time scale exchange processes in proteins. On- and off-resonance R(1rho) relaxation profiles are recorded one residue at a time using a series of one-dimensional experiments in concert with selective Hartmann-Hahn polarization transfers. The experiment can be performed using low spin-lock field strengths (values as low as 25 Hz have been tested), with excellent alignment of magnetization along the effective field achieved. Additionally, suppression of the effects of cross-correlated relaxation between dipolar and chemical shift anisotropy interactions and (1)H-(15)N scalar coupled evolution is straightforward to implement, independent of the strength of the (15)N spin-locking field. The methodology is applied to study the folding of a G48M mutant of the Fyn SH3 domain that has been characterized previously by CPMG dispersion experiments. It is demonstrated through experiment that off-resonance R(1rho) data measured at a single magnetic field and one or more spin-lock field strengths, with amplitudes on the order of the rate of exchange, allow a complete characterization of a two-site exchange process. This is possible even in the case of slow exchange on the NMR time scale, where complementary approaches involving CPMG-based experiments fail. Advantages of this methodology in relation to other approaches are described.     

Enhanced nonlinear magnetic resonance signals via square wave dipolar fields

This report introduces a new approach that enhances nonlinear solution magnetic resonance signals from intermolecular dipolar interactions. The resulting signals can theoretically be as large as the full equilibrium magnetization. Simple, readily implemented pulse sequences using square-wave magnetization modulation simultaneously refocus all even order intermolecular multiple quantum coherences, leading to a substantial net signal enhancement, complex nonlinear dynamics, and improved structural sensitivity under realistic conditions.     

Tuning of the size of Dy2O3 nanoparticles for optimal performance as an MRI contrast agent

The transverse 1H relaxivities of aqueous colloidal solutions of dextran coated Dy2O3 nanoparticles of different sizes were investigated at magnetic field strengths (B) between 7 and 17.6 T. The particle size with the maximum relaxivity (r2) appears to vary between 70 nm at 7 T (r2 approximately = 190 s(-1) mM(-1)) and 60 nm at 17.6 T (r2 approximately = 675 s(-1) mM(-1)). A small difference between r2 and r2* was observed, which was ascribed to the effect of the dextran coating. The value of r2 is proportional to B2 up to 12 T after which it saturates. Independent magnetization measurements on these particles at room temperature at magnetic field strengths up to 30 T, however, show a typical paramagnetic behavior with a magnetization of the particle that is proportional to the field strength. The saturation in the curve of r2 as a function of B2 was tentatively explained by the presence of an extremely fast relaxing component of the signal at high field strengths, which is not observable on the NMR time scale. The results of this study can be exploited for the rational design of MRI contrast agents, based on lanthanide oxide particles, with high efficiencies at magnetic field strengths of more than 1.5 T.     

Anomalous nonlinear dielectric and Kerr effect relaxation steady state responses in superimposed ac and dc electric fields

It is shown how the rotational diffusion model of polar molecules (which may be described in microscopic fashion as the diffusion limit of a discrete time random walk on the surface of the unit sphere) may be extended to anomalous nonlinear dielectric relaxation and the dynamic Kerr effect by using a fractional kinetic equation. This fractional kinetic equation (obtained via a generalization of the noninertial kinetic equation of conventional rotational diffusion to fractional kinetics to include anomalous relaxation) is solved using matrix continued fractions yielding the complex nonlinear dielectric susceptibility and the Kerr function of an assembly of rigid dipolar particles acted on by external superimposed dc E0 and ac E1(t)=E1 cos omegat electric fields of arbitrary strengths. In the weak field limit, analytic equations for nonlinear response functions are also derived.     

Signal irreproducibility in high-field solution magnetic resonance experiments caused by spin turbulence

Turbulent spin dynamics arising from the joint action of radiation damping and the distant dipolar field are shown to generate irreproducible measurements in popular high-field, gradient-based magnetic resonance (MR) experiments, undermining the prevailing assumption of essentially predictable observables in MR. Sizeable fluctuations in echo amplitudes are reported and numerically simulated for pulsed gradient spin echo and stimulated echo diffusion measurements. The underlying microscopic dynamical instability is characterized by analysis of the finite-time Lyapunov exponents. Perturbations to the modulated magnetization are shown to render magic-angle gradients ineffective in suppressing signal fluctuations. Alternative approaches are suggested for cancelling out the feedback interactions leading to spin turbulence.     

Precision 1H-1H distance measurement via 13C NMR signals: utilization of 1H-1H double-quantum dipolar interactions recoupled under magic angle spinning conditions

We applied the POST-C7 DQ-dipolar recoupling pulse sequence to the measurement of (1)H-(1)H distances with high precision. The spectral resolution is enhanced by detecting the (1)H magnetization via (13)C signals. A least-squares fitting of the build-up curve of the transferred magnetization to the exact numerical simulations yielded a (1)H(alpha)-(1)H(beta) distance of 248 +/- 4 pm for fully (13)C-labeled L-valine. This distance agrees with the neutron diffraction study. The negative transferred magnetization clearly indicates that the direct DQ (1)H-(1)H dipolar couplings have the largest effect. The signal for the magnetization transfer builds up rapidly by the direct (1)H-(1)H dipolar coupling, and decreases to zero at longer mixing time when the relayed magnetization transfer becomes significant. This large intensity change of the signal leads to the high precision in the distance measurement. We inspected factors that limit the effective bandwidth of the POST-C7 recoupling for the (1)H and (13)C homonuclear spin systems. The spin interactions at times shorter than the cycle time of the C7 sequence were also evaluated to measure the distances. The carbon-detected 2D (1)H DQ mixing experiment was demonstrated for the measurement of multiple (1)H-(1)H distances.     

Investigation of dipolar-mediated water-protein interactions in microcrystalline Crh by solid-state NMR spectroscopy

Water-protein interactions play a major role in protein folding, structure, and function, and solid-state NMR has recently been shown to be a powerful tool for the site-resolved observation of these interactions in solid proteins. In this article we report investigations on possible water-protein dipolar transfer mechanisms in the microcrystalline deuterated protein Crh by a set of solid-state NMR techniques. Double-quantum (DQ) filtered and edited heteronuclear correlation experiments are used to follow direct dipolar water-protein magnetization transfers. Experimental data reveal no evidence for "solid-like" water molecules, indicating that residence times of solvent molecules are shorter than required for DQ creation, typically a few hundred microseconds. An alternative magnetization pathway, intermolecular cross-relaxation via heteronuclear nuclear Overhauser effects (NOEs), is probed by saturation transfer experiments. The significant additional enhancements observed when irradiating at the water frequency can possibly be attributed to direct heteronuclear water-protein NOEs; however, a contribution from relayed magnetization transfer via chemical exchange or proton-proton dipolar mechanisms cannot be excluded.     

Low density mesostructures of confined dipolar particles in an external field

Mesostructures formed by dipolar particles confined between two parallel walls and subjected to an external field are studied by Monte Carlo simulations. The main focus of the work is the structural behavior of the Stockmayer fluid in the low density regime. The dependence of cluster thickness and ordering is estimated as a function of density and wall separation, the two most influential parameters, for large dipole moments and high field strengths. The great sensitivity of the structure to details of the short-range part of the interactions is pointed out. In particular, the attractive part of the Lennard-Jones potential is shown to play a major role in driving chain aggregation. The effect of confinement, evaluated by comparison with results for a bulk system, is most pronounced for a short range hard sphere potential. No evidence is found for a novel "gel-like" phase recently uncovered in low density dipolar colloidal suspensions [A. K. Agarwal and A. Yethiraj, Phys. Rev. Lett. 102, 198301 (2009)].     

Molecular diffusion on a time scale between nano- and milliseconds probed by field-cycling NMR relaxometry of intermolecular dipolar interactions: application to polymer melts

A formalism is presented permitting the evaluation of the relative mean-squared displacement of molecules from the intermolecular contribution to spin-lattice relaxation dispersion of dipolar coupled spins. The only condition for the applicability is the subdiffusive power law character of the time dependence of the mean-squared displacement as it is typical for the chain mode regime in polymer liquids. Using field-cycling NMR relaxometry, an effective diffusion time range from nano- to almost milliseconds can be probed. The intermolecular spin-lattice relaxation contribution can be determined with the aid of isotopic dilution, that is, mixtures of undeuterated and deuterated molecules. Experiments have been performed with melts of polyethyleneoxide and polybutadiene. The mean-squared segment displacements have been evaluated as a function of time over five decades. The data can be described by a power law. The extrapolation to the much longer time scale of ordinary field-gradient NMR diffusometry gives good coincidence with literature data. The total time range thus covers nine decades.     

Magnetic field induced dipolar couplings in the pretransitional region of a nematic liquid crystal

13C and 1H NMR spectroscopy have been used to study the orientational order which develops when a nematogenic compound, 4-pentyl-4'-cyanobiphenyl (5CB), approaches the transition from the isotropic to the nematic phase at T(NI). The experiments yield values of field induced dipolar couplings, (1), between all of the directly bonded carbon and hydrogen nuclei in the molecule, and 2D(HH)B, the geminal dipolar coupling between protons in the first methylene group in the alkyl chain. The temperature dependence of these couplings shows that in each case they follow a divergence behavior governed by (T - T*)(-1),where T* is a temperature determined from the experimental data and which is close to but less than T(NI). Experiments performed at spectrometer field strengths of 11.75 and 18.79 T confirm the prediction that the induced couplings should depend on the square of the applied field strength. It was found that, within experimental error, T* is the same for each field-induced coupling, and that T(NI) - T* is the same at 11.75 and 18.79 T. It is shown that the set of field-induced couplings 1D(CHi)B obtained at a temperature close to T(NI) can be used to derive a conformer distribution for 5CB in the isotropic phase.     

Quantitative time- and frequency-domain analysis of the two-pulse COSY revamped by asymmetric Z-gradient echo detection NMR experiment: Theoretical and experimental aspects, time-zero data truncation artifacts, and radiation damping

The two-pulse COSY revamped by asymmetric Z-gradient echo detection (CRAZED) NMR experiment has the basic form 90 degrees -Gdelta-t(rec)-beta-nGdelta-t(rec)-FID, with a phase-encoding gradient pulse G of length delta applied during the evolution time tau for transverse magnetization, readout pulse beta, rephasing gradient nGdelta, and recovery time t(rec) prior to acquisition of the free-induction decay. Based on the classical treatment of the spatially modulated dipolar demagnetizing field and without invoking intermolecular multiple-quantum coherence, a new formulation of the first-order approximation for the theoretical solution of the nonlinear Bloch equations has been developed. The nth-order CRAZED signal can be expressed as a simple product of a scaling function C(n)(beta,tau) and a signal amplitude function A(n)(t), where the domain t begins immediately after the beta pulse. Using a single-quantum coherence model, a generalized rf phase shift function has also been developed, which explains all known phase behavior, including nth-order echo selection by phase cycling. Details of the derivations are provided in two appendices as supplementary material. For n>1, A(n)(t) increases from zero to a maximum value at t=t(max) before decaying and can be expressed as a series of n exponential decays with antisymmetric binomial coefficients. Fourier transform gives an antisymmetric binomial series of Lorentzians, where the composite lineshape exhibits negative wings, zero integral, and a linewidth that decreases with n. Analytical functions are presented for t(max) and A(n)(t(max)) and for estimating the maximal percent error incurred for A(n)(t(max)) when using the first-order model. The preacquisition delay Delta=delta+t(rec) results in the loss of the data points for t=0 to Delta. Conventional Fourier transformation produces time-zero truncation artifacts (reduced negative wing amplitude, nonzero integral, and reduced effective T(2) ( *)), which can be avoided by time-domain fitting after right shifting the data by Delta. A doped water sample (9.93 mM NiSO(4), 10 mm sample tube) was used to study the behavior of the CRAZED signal for n=1-4 with beta=90 degrees at 7 T (300 MHz (1)H frequency) as a function of Delta, with and without radiation damping. Pulse-acquire experiments were used to determine the relaxation times (T(1)=61.8 ms and T(2) ( *)=29.7 ms), and the radiation damping time constant T(rd)=18.5 ms. When experimental CRAZED data sets were right shifted by Delta, excellent least-squares fits to the first-order model function were obtained for all n using a minimal set of free variables. Without radiation damping the fitted T(2) ( *)values (29.7-30.2 ms) agreed with the reference value. With radiation damping the fitted effective T(2) ( *) values were 16.2 ms for a 90 degrees pulse-acquire experiment and 18.8-20.2 ms for the CRAZED experiment with n=1-4 and signal amplitudes spanning a range of 10(5).     

Analytical solution for restricted diffusion in circular and spherical layers under inhomogeneous magnetic fields

We propose an analytical solution for restricted diffusion of spin-bearing particles in circular and spherical layers in inhomogeneous magnetic fields. More precisely, we derive exact and explicit formulas for the matrix representing an applied magnetic field in the Laplacian eigenbasis and governing the magnetization evolution. For thin layers, a significant difference between two geometrical length scales (thickness and overall size) allows for accurate perturbative calculations. In these two-scale geometries, apparent diffusion coefficient (ADC) as a function of diffusion time exhibits a new region with a reduced but constant value. The emergence of this intermediate diffusion regime, which is analogous to the tortuosity regime in porous media, is explained in terms of the underlying Laplace operator eigenvalues. In general, regions with constant ADCs would be reminiscent of multiscale geometries, and their observation can potentially be used in experiments to detect the length scales by varying diffusion time.     

Brownian dynamics investigation of magnetization and birefringence relaxations in ferrofluids

Brownian dynamics simulations are used to investigate the dynamics of orientational properties of real charge-stabilized ferrofluids, i.e. stable colloidal dispersions of magnetic nanoparticles. The relaxation times of the magnetization and of the birefringence, data accessible by experimental techniques, have been computed at several volume fractions. Besides, the effect of hydrodynamic interactions has been investigated. Equilibrium simulations without field are found to be inadequate to determine the aforementioned relaxation times for the systems under study, the dipolar interaction being too weak. Thus a nonequilibrium simulation procedure that mimics the experimental operating mode has been developed. After equilibrium simulations under a magnetic field, both birefringence and magnetization decays are recorded once the field is suppressed. Birefringence and magnetization decays are markedly impeded as the volume fraction increases, whereas they are barely enhanced when the intensity of the initial magnetic field is increased at a fixed volume fraction. Eventually, hydrodynamic interactions exhibit a slight but systematic lengthening of the relaxation times.     

Measurement of carbon-proton dipolar couplings in liquid crystals using DAPT

Dipolar couplings provide valuable information on order and dynamics in liquid crystals. For measuring heteronuclear dipolar couplings in oriented systems, a new separated local field experiment is presented here. The method is based on the dipolar assisted polarization transfer (DAPT) pulse sequence proposed recently (Chem. Phys. Lett. 2007, 439, 407) for transfer of polarization between two spins I and S. DAPT utilizes the evolution of magnetization of the I and S spins under two blocks of phase shifted BLEW-12 pulses on the I spin separated by a 90 degree pulse on the S spin. Compared to the rotating frame techniques based on Hartmann-Hahn match, this approach is easy to implement and is independent of any matching conditions. DAPT can be utilized either as a proton encoded local field (PELF) technique or as a separated local field (SLF) technique, which means that the heteronuclear dipolar coupling can be obtained by following either the evolution of the abundant spin like proton (PELF) or that of the rare spin such as carbon (SLF). We have demonstrated the use of DAPT both as a PELF and as a SLF technique on an oriented liquid crystalline sample at room temperature and also have compared its performance with PISEMA. We have also incorporated modifications to the original DAPT pulse sequence for (i) improving its sensitivity and (ii) removing carrier offset dependence.     

Influence of dipolar interactions on radical pair recombination reactions subject to weak magnetic fields

Monte Carlo simulations of the effects of weak magnetic fields on the recombination of interacting radical pairs undergoing free diffusion in solution have been performed, with the aim of determining the influence on the low field effect of the magnetic dipolar coupling between the radicals. The suppression of singlet-triplet interconversion in the radical pair by the dipolar interaction is found to be pronounced at magnetic field strengths comparable to the hyperfine interactions in the radicals, to the extent that the low field effect is completely abolished. The averaging of the dipolar coupling by the translational diffusion of the radicals around one another is relatively efficient in the presence of strong magnetic fields but becomes ineffective in weak applied fields where the strength of the dipolar interaction is independent of the orientation of the inter-radical vector. Low field effects are only likely to be observed if the motion of the radical pair is restricted in some way so as to increase the likelihood that, having separated to the large distance required for the dipolar interaction to have a negligible effect, the radicals subsequently encounter and have the opportunity to recombine.     

Investigation of dipole alignments by swelling in poled thin films of a side-group polymer using second harmonic generation

This paper deals with relations between solvent diffusion and changes in second harmonic generation (SHG) in a side-group polymer with nonlinear optical (NLO) chromophores. The SHG signal of poled polymer thin films was measured as a function of time during the swelling process with methanol. The results indicated that the diffusion process was Fickian. The topographic results obtained by atomic force microscopy, together with the SHG data, also demonstrated the existence of the domain layer formed during poling that gave rise to the principal SHG intensity for this sample. Also, a noncentrosymmetric chromophore ordering was induced by swelling in the absence of a poling electric field. This time-varying SHG signal upon swelling was discussed in terms of dipolar and polar alignments of the side-group NLO chromophores. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3108–3114, 1999     

Determination of the anomeric configuration in carbohydrates by longitudinal cross-correlated relaxation studies: application to mono- and disaccharides

The role of cross-correlated relaxation between the anomeric proton chemical shift anisotropy (CSA) and its dipolar relaxation with nearby proton on the longitudinal relaxation in mono- and disaccharides at two magnetic field strengths has been investigated and shown to directly report the identity of their anomeric configuration.     

Giant enhancement of photodissociation of polar diatomic molecules in electric fields

We explore the photodissociation of polar diatomic molecules in static electric fields in the rotationally cold regime using the example of the LiCs molecule. A giant enhancement of the differential cross section is found for laboratory electric field strengths, and analyzed with varying rovibrational bound states, continuum energies as well as field strengths.