Carr-Purcell Sequence Research Articles

New, compensated Carr-Purcell sequences

New, compensated Carr-Purcell pulse sequences are reported, all based on x and y phase alternation of the π pulses. The sequences compensate cumulative pulse errors for all three components of magnetization. Applications include the measurement of homonuclear dipole coupling in the presence of chemical shifts and the measurement of heteronuclear dipole coupling in magic-angle spinning experiments (REDOR). The performance of the new pulse sequences is compared experimentally to previously reported schemes.

The determination of bond lengths in solids using the Carr-Purcell sequence

Nutation NMR spectroscopy has been used to measure bond lengths in orientationally disordered solids by suppression of the chemical-shift anisotropy broadening (I ). In this technique, removal of this unwanted broadening is accompanied by a reduction of the splitting in the Pake doublet (2) by a factor of two. In many cases of special interest, however, the isolated pairs of spins involved in the Pake doublet may belong to more than one class. For example, two different bond lengths (3) may be present leading to a superposition of two Pake doublet patterns. A similar situation may occur even if all pairs are characterized by a single bond length but are associated, for example, with two classes of molecules in quite different motional states. If one of these situations prevails, it is highly desirable to take advantage of the best possible resolution to permit correct assignments in increasingly complex spectra. The Carr-Purcell sequence (4) is another method for suppressing the chemical-shift anisotropy broadening; in principle, it should not scale down the dipolar interaction. Although a reduction of the homonuclear dipolar splitting does take place in practice, as shown below, it is not as severe as in the nutation experiment. For the determination of internuclear distances using the Carr-Purcell sequence it is essential to know the scaling behavior of the Pake doublet splitting as the pulse separation and pulse width are varied. We show that under ideal conditions this scaling should be a linear function of the duty factor. Our measurements in two different systems employing a modified Carr-Purcell sequence confirm this prediction over a wide range of duty factors. 13C pulsed NMR experiments were performed at a magnetic field strength of 1.4 1 T ( 15 MHz). Although the suppression of dipolar broadening by protons is partly

Nuclear magnetic resonance: Free-induction decay and spin echoes in a 0.05-T magnetic field

NMR-absorption signals in a 2-cm3 sample of glycerol can be observed in a small permanent magnet producing a field of 50 mT. Observing the beat frequency between the marginal oscillator used as spin detector and the Larmor frequency of the spin system after excitation with 10- to 20- μs high-frequency pulses, the free-induction decay and spin echoes can be detected. The experiment is capable of demonstrating the principles of NMR tomography, e.g., the Carr–Purcell sequence, inversion recovery, and image formation in a field gradient.

An NMR study of the geometry of a CO layer chemisorbed on Pt particles

The authors have analyzed the shape of the 13C spin echo envelope of a 13CO layer chemisorbed on supported Pt particles. They show that it contains information about the geometry of the array of molecules on the surface. They find that two mechanisms are responsible for the shape. The coupling of the C spins with the surface Pt spins gives rise to a T2 of 2.9 ms at 77 K. By applying a Carr–Purcell sequence to the 13C spins, the effects of the coupling to the Pt can be eliminated. The dipolar coupling between 13C molecules then remains, producing a ‘‘slow beat’’ in the spin echo envelope. It can be analyzed exactly since mutual spins flips among C spins are not allowed, owing to large field inhomogeneities at the surface of the Pt particles. Analysis of the slow beat yields information about the structure of the array. The authors report evidence for the coalescence of islands of CO at low coverage and demonstrate that the coverage is uneven among the Pt particles if the sample powder is exposed to less than a monolayer of CO.

A programmable digital pulse generator for pulsednmr spectroscopy

The pulse programmer generates highly stable pulses and is capable of producing various scheme of pulses (i.e. a given specific number of pulses with independently variable widths and separations) employed in pulsednmr spectroscopy. The construction and working of the programmer is described with reference to the two most commonly used schemes, namely, a two-pulse sequence and the Carr-Purcell sequence.

The time evolution of the transverse magnetization in Carr-Purcell sequences in the presence of chemical exchange

The time evolution of the transverse magnetization in Carr-Purcell sequences in the presence of fast chemical exchange is calculated using perturbation theory in an interaction representation that removes external parts from the Hamiltonian. The method is more general than the use of the extended Bloch equations, as it in principle allows incorporation of other relaxation mechanisms apart from exchange into the fluctuating Hamiltonian. The Luz-Meiboom equation is shown to be valid in a wider range of exchange times and pulse spacings than proposed formerly. The case of a spin I having a heteronuclear scalar coupling to a spin S is treated. It is shown how the influence of S relaxation can be taken into account.

Analysis of electron spin echoes by spectral representation of the stochastic Liouville equation

Motional effects can easily be incorporated into calculated spin echo decay envelopes by idealizing the effects of the pulses and by using the stochastic Liouville equation (SLE) to govern the time dependence of the density matrix between pulses. The spectral representation of the 90°-τ-180°-τ envelope is: Σl,mal,mexp[−(Λl+Λ*m)τ], where Λl is the lth eigenvalue of the SLE matrix, and al,m are products of relevant components of eigenvectors. The long time (large τ) phase memory time T∞m is equal to (Re Λ1)−1, where Λ1 is the smallest eigenvalue. For an axially symmetric g-tensor case in the slow motional region, T∞m/τR≂ 3‖ℱτR‖−1/2, 2‖ℱτR‖−1/3, and 1, for Brownian, free, and jump diffusion models, respectively, with ℱ≡2βeH0(g∥−g⊥)/3ℏ and τR the rotational correlation time. Analogous results hold for nitroxides having nuclear hyperfine tensors. The echo results are compared with simple methods of measuring τR from cw spectra. The overall shape of the echo envelopes in the slow motional region is exp(−bℱ2τ3/τR) for very short times and exp(−2τ/T∞m) for the longer times. Carr–Purcell (CP) sequences suppress the initial exponential in τ3 and increase the phase memory times as a function of decreasing τ. Detailed analysis of CP sequences can provide information on motional model. The analysis of motional averaging of nuclear modulation effects by our method is also given and it is pointed out that this approach may be useful in studying very slow motions. Despite the simplicity of the methods, we are able to approximately fit experimental data from the Tempone/glycerol–water system in both fast and slow motional regions.

A solid state pulsed NMR spectrometer

A 10 MHz pulsed NMR spectrometer, built using mostly solid state devices, is described. The pulse programmer provides 2-pulse, 3-pulse, saturation burst and Carr-Purcell sequences both in repetitive and manual modes of operation. The transmitter has a maximum power output of ∼ 2 kW with a 75 Ω output impedance termination. The total gain of the receiver system is around 120 dB with a minimum band width of 2 MHz. The recovery time of the receiver is ∼ 7 µsec. A two-channel boxcar integrator capable of working in the single channel, differential and double boxcar modes provides signal to noise ratio improvement. The sensitivity and the linearity of the boxcar integrator are ∼ 2 mV and ∼ 0.1% respectively.

A physico-chemical study of heparin: Evidence for a calcium-induced co-operative conformational transition

The conformations of heparin in aqueous solution in the presence of sodium, potassium, magnesium and calcium cations were studied using circular dichroism, optical rotation, nuclear magnetic resonance and equilibrium dialysis. Potassium and magnesium cations, when added to sodium heparinate solutions, cause small chiroptical changes. Binding of calcium ions gives rise to large changes in both optical rotation and circular dichroism. This is indicative of a major change in chain conformation, which is also manifest in 13C and 1H n.m.r. § § Abbreviations used: n.m.r., nuclear magnetic resonance; p.p.m., parts per million. Equilibrium dialysis suggests one mole of calcium bound per mole of tetrasaccharide, which n.m.r. indicates to be appropriately sulphated iduronateglucosamine-iduronate-glucosamine. The calcium is chelated by two iduronate carboxyl groups. Proton-proton coupling constants, determined by convolution difference spectroscopy and Carr-Purcell sequences, indicate that, over the temperature range 285 to 353 K, the iduronate ring is best described as 1C 4( l) and the glucosamine residue as 4C 1( d) for both sodium and calcium forms. The conformational change induced by calcium is ascribed to rotation around the glycosidic linkages. The binding process is co-operative and the binding constant of 10 3 to 10 4 m −1 is biologically significant. The findings are consistent with intramolecular binding. Hence, this study represents the first report of a polysaccharide undergoing a cation-induced intramolecular disorder-order process. The authors postulate that a function of the post-polymerization epimerization of d-glucuronate to l-iduronate is the attainment of the precise geometry required for co-operative calcium binding with consequent modulation of the flexibility of the tetrasaccharide units.

Transverse NMR relaxation of water in wood

The transverse NMR relaxation times of hydrogen nuclei of water absorbed in white spruce sapwood [Picea glauca (Meunch) Voss] were measured for moisture contents in the range from 5 to 176%. The spin echo amplitudes resulting from the Carr–Purcell sequence decay nonexponentially suggesting the possibility of at least two different relaxation times for water in wood. A simplified structural model of the wood–water mixture is used to estimate the rates of chemical exchange at room temperature of hydrogen nuclei between various sites in the system. The high-resolution NMR line shape is discussed briefly in terms of this proposed model.

Dipolar narrowed Carr–Purcell measurement of rotating frame spin–lattice parameters in polymers

The use of the dipolar-narrowed Carr–Purcell sequence for measuring the spin–lattice contribution to the linewidth under multiple pulse sequences is demonstrated. The relaxation in polyisoprene is exponential with a time constant, T1y, of the order of T1ρ for the sample. The relaxation rate depends on pulse spacing in a manner not predicted by assuming an exponential correlation function for the reorientation.

Nuclear spin–lattice relaxation in periodically irradiated systems

A master equation for nuclear magnetic relaxation under conditions of periodic and cyclic rf irradiation is derived based on the stochastic Liouville equation. Conditions for the validity of the equation, involving both use of the motional narrowing approximation and the Magnus expansion, are discussed with particular attention given to the simultaneous presence of fluctuating and nonfluctuating interactions. The expressions derived are applied to several irradiation schemes: the Carr–Purcell sequence, where the echo decay time under translational diffusion is calculated; the cw and pulsed versions of spin locking in solids, with special emphasis on the origin and role of spin diffusion and on the exact relationship between the second moment and the prefactor in the T1ρ expression; and, finally, the four- and eight-pulse sequences used for suppression of homonuclear dipolar interactions, where it is shown that the x, y, and z axes of the interaction frame are ’’principal axes’’ of relaxation. Physical interpretation of the calculated results is presented. The relaxation times of cyclohexane under the eight-pulse cycle are experimentally determined and shown to confirm the theory.

Pulse NMR studies of water permeability in phosphatidylcholine vesicles containing general anesthetics

Phosphatidylcholine was extracted from egg yolks and sonicated withn-alkyl alcohols to give vesicles. The magnetic environment of the external compartment was then modified by the addition of shift reagent (Co2+). This allowed determination of the average lifetime for exchange of water molecule protons by observing the relaxation rate dependence on the interval between pulses in a Carr-Purcell sequence. For vesicles containingn-hexanol as 33% of lipid, the average water molecule lifetime in the internal compartment was found to be substantially less than that for a vesicle without hexanol. The lifetime, 11.3±4 msec, is equivalent to a permeability coefficient of 60 μ/sec at 34°C.

Homogeneous and inhomogeneous nuclear spin echoes in organic solids: Adamantane

Under conditions of proton dipolar decoupling, the 13C magnetization in adamantane has been further subjected to the following separate coherent averaging procedures: magic angle mechanical spinning, Carr-Purcell, Carr-Purcell-Meiboom-Gill, and multiple-pulse (solid echo) sequences. A comparison of the respective widths of the 13C NMR response demonstrates that in adamantane the 13C 13C intermolecular dipolar coupling is approximately 40 Hz; all but the Carr-Purcell sequence reduced this, albeit with varying efficiencies. It is suggested that in an organic solid with substantial molecular motion in the kilohertz range, the 13C 13C dipolar coupling can limit spectral resolution even under magic angle sample spinning.

A versatile and flexible digital pulse programmer for pulsed nuclear magnetic resonance

A versatile and flexible digital pulse programmer for two-pulse, three-pulse, saturation burst and Carr-Purcell sequences is described. Independently variable controls for pulse widths (0.2 mu s to 100 mu s), delay between pulses (0.2 mu s to 100 s) and for number of pulses (1 to 99) for the saturation burst and for the Carr-Purcell sequence, are brought to the front panel. The programmer can be used for one-shot experiments as well as for repetitive experiments.

Effect of rf field inhomogeneities on spin-echo measurements

The effect of radio frequency inhomogeneities on nuclear magnetic transverse relaxation time (T2) measurements has been investigated experimentally and numerically. Measurements using the Meiboom-Gill modification to the Carr-Purcell sequence have been emphasized; however, some other methods have been considered. The calculations have been performed assuming that the magnetization obeys (a) the Bloch equations and (b) the modified Bloch equations. In case (a) the errors resulting from rf field inhomogeneities were found to be small to moderate, and a method is presented whereby the upper limits to these errors can be determined experimentally. Furthermore, the errors are decreased considerably in a homogeneous main magnetic field adjusted to resonance and go to zero when T1 = T2. In case (b) the errors were considerably larger than in case (a) and the presence of a homogeneous main magnetic field did not necessarily decrease these errors. Even quite small rf field inhomogeneities were found to produce significant errors in the exchange times, chemical shift differences, and activation parameters derived from the transverse relaxation times.

On the Measurement of Transverse Relaxation Rates in Complex Spin Systems

Selective measurement of transverse relaxation rates of each line in a complex NMR spectrum can be accomplished by subjecting the spin system to a nonselective Carr-Purcell sequence of rf pulses, Fourier transforming the free precession following the last echo maximum, and repeating the experiment for several different durations of the echo train. Effects of homonuclear spin coupling on such measurements are exmined in detail. It is shown that such coupling can produce severe distortion of the apparent time decay of partially relaxed spectral lines. Criteria for avoiding the distortion are established, and a general scheme for interpreting selectively measured transverse relaxation rates in the framework of Redfield theory is proposed.

The proton relaxation of CH3OD in the presence of Co(II) ions, as studied by spin-echo techniques

By measurement of the proton relaxation times T 1 and T 2 of CH3OD containing Co++ ions in dilute solution and the dependence of the observed decay time (T 2 †) on t ep the separation between pulses in a Carr-Purcell sequence the coordination number is shown to be six. Since this result has previously been obtained by an independent method, the use of the dependence of T 2 † on t ep to determine coordination numbers is justified for solutions of paramagnetic ions. The validity of analytical expressions derived previously has been checked by numerical methods, and the analytical expression is shown to be valid even in the presence of H 0 and H 1 inhomogeneity and inaccurate pulses of finite duration, provided that the Meiboom-Gill method is used. In an Appendix insight derived from the results of the numerical solutions is used to give a brief derivation of the dependence of T 2 † on H 0, exchange rate and t ep.

A Digital rf Pulse Burst Generator for NMR Relaxation Experiments

This paper describes a pulse burst generator designed to provide coherent rf pulse sequences with lengths applicable to NMR relaxation experiments. The burst generator is based on a principle which provides an inherently high on/off ratio. The frequency of interest is generated by mixing two higher frequencies. Bursts of arbitrary length are generated by gating these two higher frequencies so that in the off intervals there is no signal at the frequency of interest in the entire generator system. Burst lengths are determined digitally to within one cycle by a preset counter. A number of different burst lengths can be selected by several sets of switches to generate a Carr-Purcell sequence of bursts. Bursts with 90° rf phase shift can be generated in this sequence as is required for the Meiboom-Gill method. Phase and frequency relations in the generator are determined digitally, so that no tuning adjustments are required for operation of the generator over the whole frequency range. The described generator employs MECL II integrated circuits which restrict the highest output frequency of the generator to about 10 MHz.

Multiple Spin Echoes in Dipolar Solids

The decay of transverse nuclear spin magnetization in a homogeneously broadened solid can be prolonged for a time ${{T}_{2}}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\gg}{T}_{2}$ by applying a train of 90\ifmmode^\circ\else\textdegree\fi{} pulses in a modified Carr-Purcell sequence with pulse spacing $\ensuremath{\tau}<{T}_{2}$. A time-expansion theory which treats the problem from the viewpoint of spin echoes is used to explain an observed proportionality between ${{T}_{2}}^{\ifmmode\dagger\else\textdagger\fi{}}$ and ${\ensuremath{\tau}}^{\ensuremath{-}5}$, and predicts that ${{T}_{2}}^{\ifmmode\dagger\else\textdagger\fi{}}$ depends upon a modified sixth moment of the resonance. An alternative viewpoint, in which one considers the long-time development of the spin system in a periodically modulated rf field ${H}_{1}(t)$, shows that the experiment is closely related to spin locking and explains the fact that ${{T}_{2}}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\rightarrow}{T}_{1\ensuremath{\rho}}({\overline{H}}_{1})$, the relaxation time parallel to the average rf field, as $\ensuremath{\tau}\ensuremath{\rightarrow}0$. The experiment offers some possibilities for the study of spin-lattice relaxation in weak fields and for double resonance in the rotating frame.