Polarization cross

Cross polarization (CP) pulse sequences are designed to transfer magnetic polarization from abundant nuclei, e.g., protons, to rare nuclei, e.g., 13C nuclei at 1.1% natural isotopic abundance. The result is an enhancement of the NMR signal from the rare nucleus. The principle is sketched here more detailed explanations may be found in books by Mehring (1983) and by Gerstein and Dybowski (1985). 

Springer Series in Wood Science Methods in Lignin Chemistry (Edited by S.Y. Lin and C.W. Dence) 

A generalized CP pulse sequence is shown in Fig. 4.5.2, with vertical displacements indicating transmitter power and the horizontal axis indicating elapsed time. A CP pulse sequence begins with a pulse delay, td, to allow recovery of proton polarization along the static field of the NMR magnet. This can be achieved if td greatly exceeds T,(H), the time constant for recovery of equilibrium polarization. 

The first radiofrequency (RF) pulse is at the proton NMR frequency and is of a duration tp chosen for a 90° displacement of the magnetization vector away from the static field. At the end of tp, the proton transmitter is left on but the oscillation is phase-shifted through 90°. The RF field now oscillates in synchronization with precession of the proton magnetization vector instead of displacing the vector further from the static field, it counteracts any tendency for the vector to drift away from synchronized precession. The magnetization is then said to be spin locked . 

While the proton magnetization remains spin locked, a second RF transmitter is switched on at the l3C NMR frequency for a contact time tc. Any l3C magnetization that builds up during the contact time is conserved through spin locking to the second RF field. Once this is switched off, the receiver is switched on to acquire data over a period of ta. 

3 Selectivity of cross-polarization demonstrated for polyethylene terephthalate at room temperature and a spinning frequency of = 4090 Hz. (a) Polarization of protonated and unprotonated C nuclei with tcp = 5 ms. (b) Polarization of protonated C nuclei for cp = 50 xs. (c) Polarization of unprotonated nuclei for fcp = 5 ms and subsequent dephasing for fa = 100 p.s under the influence of the dipole-dipole coupling. Adapted 

While TipH is about the same for all protons throughout the sample as a result of spin diffusion from multiple homonuclear dipole-dipole couplings, 7 ipc and Tch are different for different parts of the molecule. They need to be known for a quantitative analysis of CP signals [Voel]. 

The cross-polarization technique described above is the basic one most often used in practice [Mid]. Several variations of it exist [Levi, Tegl, Tekl], and other techniques 

This technique involves transfer of polarization from one NMR active nucleus to another [166-168]. Traditionally cross polarization (CP) was employed to transfer polarization from a more abundant nucleus (1) to a less abundant nucleus (S) for two reasons to enhance the signal intensity and to reduce the time needed to acquire spectrum of the less abundant nuclei [168]. Thus CP relies on the magnetization of I nuclei which is large compared to S nuclei. The short spin-lattice relaxation time of the most abundant nuclei (usually proton) compared to the long spin-lattice relaxation time of the less abundant nuclei, allows faster signal averaging (e.g., Si or C). CP is not quantitative as the intensity of S nuclei closer to 1 nuclei are selectively enhanced. Nowadays CP has been extended to other pairs of 

3 Chemical Shift Anisotropy and Magic Angle Spinning 

While the combination of the heteronuclear dipolar decoupling and MAS provides a mean to obtain high-resolution isotropic spectra in solids, the serious problem still remains in addition to the relatively small magnetic moment and low natural 

The transfer of magnetization from the proton spins to the carbon spins occurs now when the Hartmann-Hahn condition, Eq. (2), is fulfilled. 

We now have an additional degree of freedom—the relative values of By 

FIGURE 7.5 Pulse sequence for cross polarization. After a 90° pulse, the I spins transfer polarization to S spins during the contact time as described in the text. The S signal is then detected while the I spins are decoupled. 

Overall, the combination of cross polarization and dipolar decoupling has made feasible the solid-state study of 13C, 15N, 29Si, and many other nuclides of low abundance. Cross polarization can also be applied in situations in which abundant spins can be diluted by isotopic substitution or by dispersing molecules in an inert solid state matrix. 

What is the difference between single-quantum coherence and zero- 

Can the simple vector presentation be used to display the effects of a 90° pulse on zero- or multiple-quantum magnetizations  

Clearly the extent to which the H nuclei line up along the x -axis (lid) will depend on the duration of 1, which in turn will determine the extent of the antiphase z-magnetization created by the second 90° H pulse. The 

The experiment just discussed represents a heteronuclear spin system. In a homonuclear case, the separate 90° C pulse necessary in the heteronuclear system is not required, since the second 90° H pulse affects the coupled partner H nucleus as well. The nucleus detected therefore has its two transitions antiphase with respect to each other, corresponding to the states represented in Fig. 2.7, Ilg, Ilh, etc. at detection. 

Suppose, for clarity, we add a common factor [ V2)yn + (V2)yc] to all four energy levels so the energy difference between them does not change. The values of these energy levels will then become y, yc, Vh. and Xh + yc-Since yH is about four times yc, let us also assume that yn = 4 and yc = 1-The populations of the four energy levels will then be 0, 1, 4, and 5. The population difference between the two C spin states before the application of the H polarization transfer pulse corresponds to the lower energy state minus the upper energy state, i.e. 1—0 = 1 or 5 — 4=1. 

In addition to dipolar coupling and chemical shift anisotropy, one 

How can we circumvent the long signal accumulation times required by the low repetition rate for nuclei with long values in solid samples The answer lies in the ability to transfer the polarization of abundant H nuclear spins with short Tj values to the rare nuclei. The repetition rate for signal averaging is now determined by the short H values, because energy is being transferred from the protons to the carbons. This process of polarization transfer from abundant to rare spins is termed cross-polarization (CP) and was introduced by Pines et al [11]. 

Although H and nuclei have Larmor frequencies different by a factor of four, Hartmann and Hahn [12] showed that energy may be transferred between them in the rotating reference frame when 

The proton and carbon spin systems are equilibrated in the magnetic field 

Polarization is transferred between the proton and carbon nuclei as they both precess about the y -axis by adjusting the power levels of the applied fields B fj and B until the Hartmann-Hahn condition is matched (7h ih = 7c ic) The transfer of polarization is made possible because the z -com-ponents of both and magnetizations have the same time dependence 

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A RIKES experunent is essentially identical to that of CW CARS, except the probe laser need not be tunable. The probe beam is linearly polarized at 0° (—>), while the polarization of the tunable pump beam is controlled by a linear polarizer and a quarter waveplate. The pump and probe beams, whose frequency difference must match the Raman frequency, are overlapped in the sample (just as in CARS). The strong pump beam propagating tlirough a nonlinear medium induces an anisotropic change in the refractive mdices seen by tlie weaker probe wave, which alters the polarization of a probe beam [96]. The signal field is polarized orthogonally to the probe laser and any altered polarization may be detected as an increase in intensity transmitted tlirough a crossed polarizer. When the pump beam is Imearly polarized at 45° y), contributions... 

Called CYCLCROP (cyclic cross polarization) [24], the method works by first exciting all magnetization. Cross polarization pulses are then applied at the specific Lannor frequencies of the H- C pair of interest so as to transfer coherence from to C. The transfer pulses must satisfy the Hartmaim-Halm condition... 

Figure Bl.14.8. Time course study of the arrival and accumulation of labelled sucrose in the stem of a castor bean seedling. The labelled tracer was chemically, selectively edited using CYCLCROP (cyclic cross polarization). The first image in the upper left comer was taken before the incubation of the seedlmg with enriched hexoses. The time given in each image represents the time elapsed between tire start of the incubation and the acquisition. The spectmm in the lower right comer of each image shows the total intensity...

Kunze C and Kimmich R 1994 Proton-detected C imaging using cyclic-J cross polarization Magn. Reson. Imaging 12 805-10... 

Disclinations in tire nematic phase produce tire characteristic Schlieren texture, observed under tire microscope using crossed polars for samples between glass plates when tire director takes nonunifonn orientations parallel to tire plates. In thicker films of nematics, textures of dark flexible filaments are observed, whetlier in polarized light or not. This texture, in fact, gave rise to tire tenn nematic (from tire Greek for tliread ) [40]. The director fields... 

Fig. 5. Nematic schlieren texture observed between crossed polarizers. Courtesy of G. H. Brown, Liquid Crystal Institute, Kent State University.

Fig. 7. Nmr spectra of quinine [103-95-0] C2QH24N2O2, acquired on a Bruker 300AMX spectrometer using a Bmker broadband CP/MAS probe, (a) Proton-decoupled spectmm of quinine in CDCl (b) the corresponding spectmm of solid quinine under CP/MAS conditions using high power dipolar decoupling (c) soHd-state spectmm using only MAS and dipolar decoupling, but without cross-polarization and (d) soHd quinine mn using the...

Polypropylene molecules repeatedly fold upon themselves to form lamellae, the sizes of which ate a function of the crystallisa tion conditions. Higher degrees of order are obtained upon formation of crystalline aggregates, or spheruHtes. The presence of a central crystallisation nucleus from which the lamellae radiate is clearly evident in these stmctures. Observations using cross-polarized light illustrates the characteristic Maltese cross model (Fig. 2b). The optical and mechanical properties ate a function of the size and number of spheruHtes and can be modified by nucleating agents. Crystallinity can also be inferred from thermal analysis (28) and density measurements (29). 

The detection of Hquid crystal is based primarily on anisotropic optical properties. This means that a sample of this phase looks radiant when viewed against a light source placed between crossed polarizers. An isotropic solution is black under such conditions (Fig. 12). Optical microscopy may also detect the Hquid crystal in an emulsion. The Hquid crystal is conspicuous from its radiance in polarized light (Fig. 13). The stmcture of the Hquid crystalline phase is also most easily identified by optical microscopy. Lamellar Hquid crystals have a pattern of oil streaks and Maltese crosses (Fig. 14a), whereas ones with hexagonal arrays of cylinders give a different optical pattern (Fig. 14b). 

Fig. 12. A liquid crystal layer is radiant (middle) when placed between crossed polarizers and viewed against a light source.

Fig. 14. A sample of a lamellar liquid crystal between crosses polarized in an optical microscope gives a pattern of "oily streaks" and Maltese crosses (a) while the Hquid crystal consisting of an array of cylinders shows the characteristic sectional pattern (b).

The Bertrand lens, an auxiliary lens that is focused on the objective back focal plane, is inserted with the sample between fully crossed polarizers, and the sample is oriented to show the lowest retardation colors. This will yield interference figures, which immediately reveal whether the sample is uniaxial (hexagonal or tetragonal) or biaxial (orthorhombic, monoclinic, or triclinic). Addition of the compensator and proper orientation of the rotating stage will further reveal whether the sample is optically positive or negative. 

Figure 8.1. (a) Spherulites growing in a thin film of isotactic polystyrene, seen by optical microscopy with crossed polars (from Bassett 1981, after Keith 196.3). (b) A common sequence of forms leading to sphertililic growth (after Bassett 1981). The fibres consist of zigzag polymer chains. 

Wu [79] has suggested that the cross-dispersion as well as the cross-polar interactions are more appropriately expressed using harmonic rather than geometric means, so that... 

Under an optical microscope with crossed polarizers, the LC-forming OPV5s show isolated droplets and extended domains having the typical Schlicren texture... 

Lindberg, J. J. and Hortling, B. Cross Polarization — Magic Angle Spinning NMR Studies of Carbohydrates and Aromatic Polymers. Vol. 66, pp. 1—22. 

Moller,M. Cross Polarization — Magie Angle Sample Spinning NMR Studies. With Respect to the Rotational Isomeric States of Saturated Chain Molecules. Vol. 66, pp. 59 — 80. 

Two crossed polarizers are frequently used to inspect transparent materials placed between them for optical activity, either for birefringence or for optical rotary effects. Birefringence effects are produced by materials with a regular ordered structure that allows light to pass through at one orientation at a higher velocity than at another orientation. As a result of this, the two wave trains generated by the different velocities... 

The crossed polarizer effects of both types are used in analysis work. The concentration of optically active organic materials is determined by the degree of rotation. In plastic processing the residual strains in molded materials as well as the degree of orientation of polymers is determined by the effect on polarized light. Crossed polarizers are used with special wave plates to control the amount of light that passes through an optical system. 

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