Anisotropic Spin Interactions

The information that can be extracted from solid-state NMR spectra is encoded via spin interactions such as the chemical shielding, the quadrupolar interaction and the homo-and hetero-nuclear dipolar interactions [1,9-10]. Some knowledge of the spin interactions that determine the features of the spectra are thus of prime importance. 

A common characteristic of the relevant spin interactions is that they are anisotropic and can be described by second-rank tensors. The resulting orientation-dependent NMR frequency is of the following form [1,9]  

For abundant nuclei with spin V2, the spectrum is often dominated by heteronuclear or homonuclear dipolar interactions, i.e., the interactions between the magnetic moments of two neighbouring spins. In this case there is no isotropic contribution and q is zero, so that Equation 14.1 simplifies correspondingly. For a two-spin system one obtains a spin Hamiltonian of the form  

In case of a deuterated sample (spin 1 case), the spectra are usually dominated by the quadrupolar interaction, that is, the coupling of the nuclear quadrupole moment with the electric field gradient of the C-2H bond. For deuterons in C-2H bonds this can lead to a splitting of about 250 kHz. As in the case of dipolar interaction, a Pake spectrum is obtained for a powder sample. The z-principal axis of the quadrupolar interaction is oriented along the bond axis which makes deuteron NMR particularly useful for studies of segmental orientations and molecular dynamics (reorientation) [1], 

In sufficiently mobile, (i.e., liquid-like), systems, the anisotropy is averaged out by the isotropic thermal motions leaving only the isotropic contributions. As already stated, viscoelastic polymers represent an intermediate between the two extremes of rigid or mobile materials and the implications of this will be discussed in 14.2.3 in more detail. 

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Molecules in ordinary liquids average out all anisotropic spin interactions due to isotropic Brownian motions, and their NMR spectra are governed by the Hamiltonian in units of Hz due to the Zeeman interaction, the isotropic chemical shift (a) and the isotropic indirect spin-spin coupling (7)... 

Among spatial reorientation techniques, one can find MAS, OMAS, variable angle spinning (VAS) and switched angle spinning (SAS) techniques. Mechanical spinning of LC materials, which has dated back to the early seventies,63,64 can control the averaging of anisotropic spin interactions... 

Figure 14.1 ID spectra of a typical rubber, styrene-butadiene-rubber (SBR). a) Static spectrum acquired at a Larmor frequency of 500 MHz. The dipolar coupling is motionally averaged and different lines can be distinguished although they are still broadened by the residual dipolar couplings, b) MAS spectrum of the same sample at a MAS spinning frequency of 15 kHz. The line-broadening due to anisotropic spin interactions, e.g., residual dipolar couplings, is removed...

Nuclear magnetic resonance (NMR) has been used to determine electrical properties in a conventional setup [23], but recently, applied electric fields have been incorporated for the determination of properties [24, 25]. Polar liquids and solutions of polar molecules align when a strong electric field (about 300 kV/cm) is applied. The anisotropic spin interactions essentially modify the NMR spectrum, and determinations of the lowest order dipole polarizability can be made. To low order, the interaction energy may be taken to be... 

In general, 2D correlations of any two distinct, non-collinear, anisotropic spin interactions provide molecular images, like PISA wheels in the PISEMA spectrum. For proteins, spectra obtained from suitable combinations... 

The ability to retain anisotropic spin interactions and the power to selectively suppress unwanted interactions using pulse sequences such as PISEMA in aligned solids have played a significant role in the applications of solid-state NMR spectroscopy. In addition, the excellent control over the order parameter (ranging from isotropic to rigid solids) of a system and creation of model biological systems obviously invited, simplified, created, and amplified the applications of solid-state NMR techniques. Although solid-state NMR... 

In liquid-state NMR, spin relaxation due to cross-correlation of two anisotropic spin interactions can provide useful information about molecular structure and dynamics. These effects are manifest as differential line widths or line intensities in the NMR spectra. Recently, new experiments were developed for the accurate measurement of numerous cross-correlated relaxation rates in scalar coupled multi-spin systems. The recently introduced concept of transverse relaxation optimized spectroscopy (TROSY) is also based on cross-correlated relaxation. Brutscher outlined the basic concepts and experimental techniques necessary for understanding and exploiting cross-correlated relaxation effects in macromolecules. In addition, he presented some examples showing the potential of cross-correlated relaxation for high-resolution NMR studies of proteins and nucleic acids. 

Fig. 3.1.1 Anisotropic spin interactions, (a) Quadrupole coupling of nucleus to the electric field gradient of a C- H bond, (b) Dipole-dipole coupling between C and H. (c) Anisotropic magnetic shielding of C nuclei. Left Geometry of the interaction and principal axes of the coupling tensor. Middle NMR spectrum for a single molecular orientation. Right The average over all orientations is the powder spectrum. The parameters A>, denote the anisotropy of the interaction k. S is the chemical shift. Adapted from [Blii3] with permission from Wiley-VCH.

In the following, MAS imaging is treated. The technique has been proposed by Wind and Yannoni [Winl] and implemented first by Cory, de Boer, and Veeman [Cor5, Cor6]. Conceptually, it is one of the simplest methods to eliminate the anisotropic spin interactions, but in most cases it is necessary that the coupling strength measured by the linewidth of the static NMR spectrum does not exceed the MAS firequency. Therefore, the... 

The previous discussion is a clear example of the separation of dynamic and structural influences on NMR spectra. Before a detailed analysis of anisotropic spin interaction data can be realized, the dynamic averaging of the tensors must be appreciated. In fact, a detailed description of local dynamics can be achieved in which models of the motions are characterized by an axis fixed in the molecular frame, an amplitude for the motion and a motional model, such as diffusion within an arc or three site jumps, etc. [21]. The data in Fig. 6.4.6 shows that the averaging of the tensor above 200 K for this labeled indole site is anisotropic [22]. 

Fast MAS leads to high resolution and sensitivity, the basic requirement for sequential assignment of protein stmctures in SSNMR. However, all anisotropic spin interactions which can be used to extract molecular geometry information are averaged out by MAS. In order to get back the anisotropic spin interactions in the presence of MAS, recoupling techniques were developed to retrieve selectively the anisotropic spin interactions for rotating solids [189-190]. Generally, there are two approaches to reintroduce anisotropic dipolar interactions, either mechanically,... 

Solid-state NMR spectroscopy is well suited for studies of intramolecular dynamics because side chain motions can be analyzed Independent of overall molecular reorientation in crystalline samples. It is an alternative spectroscopic strategy to solution NMR because partial motional averaging of the anisotropic spin interactions occurs. Dipolar, chemical shift, and quadrupolar interactions can be used to describe the dynamics of aromatic rings of proteins and peptides. 

So far, we were concerned with site-directed solid-state NMR studies on fully hydrated integral membrane proteins in which anisotropic spin interactions leading to broadened line widths are not averaged as they are in solution NMR but a variety of motions with various timescale from millisecond to microsecond are persistent because of integration into the lipid bilayer. It is still difficult to obtain structural information for peripheral membrane proteins which are not integrated but bound to a membrane surface, because the persistent anisotropic interaction with the membrane surface still hampers the utilization of the solution NMR approach. 

R 226 M. Marjanska, R.H. Havlin and D. Sakellariou, Coherent Averaging and Correlation of Anisotropic Spin Interactions in Oriented Molecules , p. 45... 

Information about the molecular order can be derived from any of the anisotropic spin interactions introduced in the previous section. Most commonly the quadrupole... 

A qualitative discussion is given of the main anisotropic spin interactions which are important in the NMR of solids. The effects of time dependence, whether thermally produced or imposed by the experimenter, are discussed. The techniques whereby high resolution may be achieved in NMR in solids are outlined as are some features of spin relaxation specific to solids. 

Before leaving this section we should broaden our view of what effects can produce time dependence and, hence, averaging of anisotropic spin couplings. Clearly, movement of the spins due to thermal motion of the molecules containing them causes the angles and distances, etc., defining the anisotropic spin interactions to be time dependent. There are, however, two approaches available to the NMR spectroscopist to Impose time dependence on the spins. The first is just irradiation of spins with radiation at or close to their resonance frequency. In simple, pictorial terms, such irradiation drives transitions of... 

The first point to be noted is that motion in solids is generally restricted and highly anisotropic. As noted earlier, this means that the anisotropic spin interactions are only partly... 

Carbon-13 NMR spectroscopy has several advantages for studying columnar mesophases. Spectra with good signal-to-noise ratios may be obtained in samples with the natural isotopic abundance. Resonances from chemically non-equivalent sites are typically well resolved and can often be readily assigned. Anisotropic spin interaction, such as dipolar couplings, provide rich information on ordering, conformational structure, and phase transitions. In this chapter, the application to columnar mesophases of recently developed and advanced NMR methods for measurements of heteronuclear spin interactions are described. 

For liquids, a pulsed-gradient NMR technique is the most direct method of measuring the diffusion coefficients. It monitors spatial displacement of molecules in the direction of the applied magnetic field gradients and does not require any assumptions about the long-time behavior of the velocity autocorrelation function, as QENS, or chemical modification of molecules, as FRS. The method is routinely used for liquids, where anisotropic spin interactions are averaged by molecular motions and NMR peaks are sharp, usually on the order of few Hz. 

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