Beat H. Meier

Adiabatic passage Hartmann-Hahn cross polarization in NMR under magic angle sample spinning

Abstract We have recently demonstrated that polarization transfer using an adiabatic passage through the Hartmann-Hahn condition (APHH-CP) by a variation of the radio-frequency amplitude can substantially improve the transfer efficiency over Hartmann-Hahn cross polarization. Here we show that APHH-CP can be combined with fast magic angle sample spinning (MAS). The heteronuclear dipolar order, established in the course of the transfer, can indeed be created and preserved.

A homonuclear spin-pair filter for solid-state NMR based on adiabatic-passage techniques

Abstract A filtering scheme for the selection of spin pairs (and larger spin clusters) under fast magic-angle spinning is proposed. The scheme exploits the avoided level crossing in spin pairs during an adiabatic amplitude sweep through the so-called HORROR recoupling condition. The advantages over presently used double-quantum filters are twofold. (i) The maximum theoretical filter efficiency is, due to the adiabatic variation, 100% instead of 73% as for transient methods. (ii) Since the filter does not rely on the phase-cycling properties of the double-quantum coherence, there is no need to obtain the full double-quantum intensity for all spins in the sample at one single point in time. The only important requirement is that all coupled spins pass through a two-spin state during the amplitude sweep. This makes the pulse scheme robust with respect to rf-amplitude missetting, rf-field inhomogeneity and chemical-shift offset.

Formalized quantum mechanical Floquet theory and its application to sample spinning in nuclear magnetic resonance

Quantum mechanical Floquet theory, a powerful tool for the solution of Schrodinger equations with a periodically time-dependent Hamiltonian is formalized by the systematic usage of the Floquet Hilbert space, the Floquet density operator, Floquet detection operators, and of the Floquet Liouville space. A concise description is obtained that is useful in analytical calculations and for computer simulations. It is implemented in the context of the general computational environment ‘GAMMA’. Simplified expressions are derived for single-axis and double-axis sample-spinning experiments in NMR.

Adiabatic homonuclear polarization transfer in magic-angle-spinning solid-state NMR

Abstract An adiabatic homonuclear polarization-transfer scheme is introduced. It involves an adiabatic passage through the rotational-resonance condition (APRR) experimentally realized by a ramp of the MAS speed. The APRR experiment is demonstrated to lead to a more complete transfer and to be more broadbanded than the rotational-resonance experiment. APRR can be looked at as a prototype for a whole class of homonuclear adiabatic polarization-transfer schemes.

RF-driven and Proton-Driven NMR Polarization Transfer for Investigating Local Order : an Application to Solid Polymers

A comparative study of proton-driven and radio-frequency-driven polarization-transfer processes in NMR of rare spins is presented in view of investigating order in partially disordered solids. The results exemplify the complementary use of the two techniques: proton-driven polarization transfer for recording quasi-equilibrium spectra that characterize long-range order, and radio-frequency-driven transfer for the measurement of geometrical rate factors from which information about local order is obtained. Procedures are described for the evaluation of polarization-transfer data. The techniques are applied to the study of order in amorphous samples of atactic polystyrene and syndiotactic poly(methyl methacrylate). In polystyrene, orientational correlation among the phenyl groups is found within a range of 5 A. In poly(methyl methacrylate), local order is below the detection limit.

Chapter 4 – Spin Diffusion in Solids

The term “spin diffusion” is used to describe multispin polarization-transfer processes, whether or not the process can actually be described by a diffusion equation. Spin diffusion has found two important classes of applications in solid-state nuclear magnetic resonance (NMR). The first application is to measure distances between spins and the other is to be used as a transport mechanism to transfer magnetization in a two-dimensional correlation experiment that establishes the relative orientation of tensorial interactions. There are two requirements for the use of multiple-pulse sequences to speed up the spin-diffusion process; the scaling factor of the homonuclear dipolar coupling should be as large as possible and the effective spin lock has to be larger than the homonuclear dipolar interactions between the S-spins to prevent loss of sum magnetization into dipolar order. This requires the use of a multiple-pulse scheme with a nonvanishing effective rotating-frame (r.f.) field. Such a nonvanishing effective field can be added to a sequence without an effective field by either adding an additional small-angle pulse after a full cycle of the sequence or by increasing the power of one of the pulse phases by a small amount.

J cross polarization in magic-angle-spinning NMR

Abstract J cross polarization in magic-angle-spinning (MAS) solid-state NMR spectroscopy is demonstrated. In the fast spinning limit, pure J cross polarization can be obtained at the centerband of the Hartmann-Hahn matching profile while dipolar cross polarization takes place at the sideband. Transient oscillations with the phase- and intensity patterns characteristic for the J-cross-polarization process are observed.

TIME-REVERSAL OF CROSS-POLARIZATION IN NUCLEAR MAGNETIC RESONANCE

It is demonstrated that the time evolution of the heteronuclear polarization-transfer process in a dipolar-coupled nuclear spin system can be reversed, leading to the observation of cross-polarization echoes. The cross-polarization echoes are induced by consecutive application of two pulse trains that produce effective Hamiltonians that differ only in sign. Cross-polarization echoes have been recorded for a powder sample of alanine. The time evolution of the spin system is consistent with both unitary quantum dynamics and with spin thermodynamics of two systems approaching a common spin temperature.

Reversal of radio-frequency-driven spin diffusion by reorientation of the sample spinning axis

The dipolar Hamiltonian in a rapidly rotating sample is scaled by the second Legendre polynomial of the cosine of the angle between the rotation axis and the static magnetic field. It is, therefore, possible to refocus the spatial polarization-transfer process, often termed spin diffusion, in extended spin systems by reorienting the rotor axis such that the dipolar interaction Hamiltonian changes sign. We present experimental results which demonstrate that a rapid mechanical sample reorientation leads to a time reversal of the “radio-frequency-driven” spin diffusion among 13C spins.

Investigation of the feasibility of amplitude-modulated dipolar decoupling in magic-angle spinning solid-state nuclear magnetic resonance

The feasibility of using periodic amplitude-modulated radio-frequency (RF) irradiation under `magic-angle spinning for heteronuclear dipolar decoupling in solid-state nuclear magnetic resonance is addressed. The RF waveforms used are tailored to satisfy the theoretical criterion for decoupling which calls for an irradiated spin propagator which is cyclic in the sense that it equals the identity matrix irrespective of the strength and orientation of the chemical shift and dipolar coupling tensors. This requirement is met by using the Floquet formalism to provide insight into the influence of an arbitrary waveform on the dynamics of the irradiated spin-½ nuclei and invoking perturbation methods to design particular modulation functions which impose the required cyclicity on the propagator. Simple RF modulations which are synchronized with the sample spinning are thus derived analytically. Finally, the validity of the scheme is explored in simple test experiments and the decoupling performance is compared with the traditional `continuous-wave method and the recently developed technique of `two-pulse phase modulation.