NMR of Quadrupolar Nuclei in Solid Materials

Roderick E. Wasylishen, Sharon E. Ashbrook, Stephen Wimperis

• Publisher: Wiley
• Year: 2012
• ISBN:
  9781118588840
• Edition: 1
• Topic: Naturwissenschaften
• Subtopic: Spektroskopie & Spektralanalyse

NMR OF QUADRUPOLAR NUCLEI IN SOLID MATERIALS

Over the past 20 years technical developments in superconducting magnet technology and instrumentation have increased the potential of NMR spectroscopy so that it is now possible to study a wide range of solid materials. In addition, one can probe the nuclear environments of many other additional atoms that possess the property of spin. In particular, it is possible to carry out NMR experiments on isotopes that have nuclear spin greater that ½ (i.e. quadrupolar nuclei). Since more that two-thirds of all NMR active isotopes are quadrupolar nuclei, applications of NMR spectroscopy with quadrupolar nuclei are increasing rapidly.

The purpose of this handbook is to provide under a single cover the fundamental principles, techniques and applications of quadrupolar NMR as it pertains to solid materials. Each chapter has been prepared by an expert who has made significant contributions to out understanding and appreciation of the importance of NMR studies of quadrupolar nuclei in solids. The text is divided into three sections: The first provides the reader with the background necessary to appreciate the challenges in acquiring and interpreting NMR spectra of quadrupolar neclei in solids. The second presents cutting-edge techniques and methodology for employing these techniques to investigate quadrupolar nuclei in solids. The final section explores applications of solid-state NMR studies of solids ranging from investigations of dynamics, characterizations of biological samples, organic and inorganic materials, porous materials, glasses, catalysts, semiconductors and high-temperature superconductors.

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PART C

Applications

Chapter 14

Quadrupolar NMR to Investigate Dynamics in Solid Materials

Luke A. O’Dell and Christopher I. Ratcliffe

Steacie Institute for Molecular Sciences, National Research Council of Canada, 100 Sussex Drive, Ottawa, ON K1A 0R6, Canada

14.1 INTRODUCTION

Dynamics, be they vibrational, rotational, or translational, are an important aspect of any solid, as they can play a major role in the overall properties of the material. NMR is perhaps the foremost technique for the study of rotational and translational motions in solid materials, and quadrupolar nuclei have a prominent role in such studies. ²H NMR in particular has been, and will continue to be, a very important tool for the study of molecular dynamics, since the isotope can replace ¹H in countless inorganic and organic systems. ⁷Li has also received a lot of attention, largely for studying motion in ion-conducting materials. With the increased interest in the last decade in quadrupolar nuclei with larger coupling constants (brought about by access to higher magnetic fields and constantly improving experimental techniques and probe technology), there are increasing numbers of reports of dynamics observed using other quadrupolar nuclei, especially ¹⁷O, as well as ¹¹B, ¹⁴N, ²³Na, ²⁷Al, and ¹³³Cs, and also some transition metals involved in tetrahedral oxide ions, such as ^185,187Re and ⁵⁵Mn.

Quadrupolar NMR studies of dynamics can yield structural information such as molecular orientation with respect to a crystallographic axis, or local symmetry, and this can sometimes be used to improve or direct structural refinements. It can distinguish between static and dynamic disorder among partially occupied sites and can indicate phase transitions and perhaps give insight into possible mechanisms for these. More directly, the NMR studies can provide rotational rate constants or correlation times, which, if studied as a function of temperature, yield activation energies for the motions.

The underlying behavior which makes the observation of dynamic effects possible in NMR is the modulation of the resonance frequency, brought about by any motion that causes the electric field gradient (EFG) tensor, and hence the quadrupolar interaction tensor, to undergo changes in magnitude and/or orientation.^1–4 These changes can be affected by either motion of the nucleus itself or motion of neighboring nuclei. Since most motions are stochastic processes, they are usually described in terms of an autocorrelation function G(τ):

(14.1)

where f (t) is a function of the position and orientation of a molecule at time t and the bar represents an ensemble average. In essence, G(τ) is a measure of the fraction of molecules whose position and orientation are unchanged after a time τ. If there is motion occurring, G(τ) will decrease over time and, in most cases, this decay can be modeled as an exponential function with a correlation time τ_c that is inversely related to the rate of motion:

(14.2)

For thermally activated processes, where the molecule must surmount an energy barrier to move between potential wells, τ_c is assumed to have an Arrhenius dependence on the activation energy (E_a) and on temperature (T ):

(14.3)

from which it is seen that as T increases, τ_c decreases (and the rate of a motion increases).

As well as the rate of the motion, the geometry of the dynamic process will also determine how the motion will manifest itself in the NMR response of the quadrupolar nucleus under study, since this affects the change in orientation of the quadrupolar interaction tensor. For example, a 180° rotation about any of the principal axes of the EFG tensor will leave it unchanged and will therefore have no effect, a situation that often arises for twofold molecular reorientations.

Different experimental approaches are generally used to probe motions on different timescales, e.g., 2D exchange experiments for slow rates of motion, lineshape measurements for intermediate rates, and relaxation measurements for fast rates. In this chapter, we provide qualitative descriptions of the underlying mechanisms by which the NMR spectra of various quadrupolar nuclei can be affected by dynamics over an extremely wide range of timescales, as well as discuss the basic principles behind various experimental methods. In Sections 14.2–14.5, we focus on the quadrupolar nuclei ²H, ¹⁴N, ¹⁷O and ^6/7Li respectively, each of which exhibits different NMR properties and are therefore used in distinct ways to study dynamic processes. In Section 14.6, we consider the effects that dynamics can have on high-resolution, multiple-quantum experiments.

14.2 DEUTERIUM

14.2.1 T₂ Anisotropy and ²H Spin-echo Experiments

Deuterium is perhaps the most commonly exploited quadrupolar nucleus for studying molecular dynamics.⁵ It is a nucleus with spin I = 1; thus, the first-order quadrupolar interaction is typically the dominant perturbation and smaller interactions may often be ignored. Fortunately, the nucleus has a relatively small quadrupole moment (Q = 2.86 mbarn), and the quadrupolar splittings typically only range up to around 250 kHz. Such pattern widths can be uniformly excited and observed relatively easily on modern spectrometers, most commonly by using the quadrupolar-echo pulse sequence (π/2_x –τ_d –π/2_y –τ_d –acquire), which allows the signal acquisition to begin at the echo top and thus avoids the spectral distortions due to equipment dead time that are associated with single-pulse experiments. Furthermore, the EFG at the deuterium site and, therefore, the quadrupolar interaction tensor itself are often axially symmetric (η_Q = 0) with the unique axis aligned along a covalent bond (e.g., a C–H bond in an organic molecule). This can greatly simplify the interpretation of results, since the interaction is then described by only two parameters (C_Q, and the angle θ between the unique axis and B₀). Less fortunately, the ²H isotope has a very low natural abundance (0.012%), making isotopic enrichment necessary. This can, however, be considered an advantage, in some cases, in that it allows the possibility of selective labeling, which, as well as aiding spectral resolution, can be used to probe specific sites in complex systems.

The most common method for extracting dynamic information using ²H NMR is to record the powder pattern from a stationary sample using a spin-echo experiment and then to compare the resultant spectral lineshape to simulations which model a Markovian jump process with a specific geometry and jump rate k.^6,7 Powder lineshapes are generally sensitive to motional rates comparable to their linewidth. At slower rates (or in the absence of motion), the ...