Phase orthogonal

Fig. 5.5.14 Schematic diagram showing how the double-phase encoded DEPT sequence achieves both spatial and spectral resolution within the reactor, (a) A spin-echo ]H 2D image taken through the column overlayed with a grid showing the spatial location within the column of the two orthogonal phase encoded planes (z and x) used in the modified DEPT sequence. The resulting data set is a zx image with a projection along y. In-plane spatial resol-ution is 156 [Am (z) x 141 [xm (x) for a 3-mm slice thickness. The center of each volume from which the data have been acquired is identified by the intersection of the white lines. The arrow indicates the direction of flow.

Differential scanning calorimetry (DSC) Since lc s form phases in a thermodynamic sense, a transition from one phase to another is accompanied by a phase-transition enthalpy. Nevertheless, there are phase transitions of second-order character which can hardly be detected by DSC since there is no phase-transition enthalpy but just a change in heat capacity. A typical example is the transition from orthogonal phases to tilted phases. 

The MLEV-16 sequence, which contains rf pulses with orthogonal phases, has poor heteronuclear transfer characteristics. The effective coupling tensors are neither planar nor isotropic. For two spins on-resonance, the average coupling tensor has the form... 

Detection and identification of related substances caimot be performed by LC-MS alone. In practice, additional experiments are required using various LC gradients and/or orthogonal phase systems, alternative detection techniques like evaporative light scattering detection or optical rotation detection, and other spectroscopic techniques, like UV-DAD and NMR. Obviously, this discussion focusses primarily on the role of LC-MS in the impurity profiling and identification. Developments in LC-MS and especially mass analysers are important in strengthening the power of LC-MS in stmcture elucidation. 

The value of 0o is arbitrary and defines a particular basis set of (cr + 1) mutually orthogonal phase states. The number state n) can be expanded in terms of the 0m) phase-state basis as... 

As two phases in quadrature will allow Carr-Purcell Meiboom-Gill, T, and or other spin-locking experiments, we recommend this as a minimum. However, providing different rf phases for the transmitter pulses is not difficult and this capability should not increase the cost of the spectrometer very much so you might as well go for four orthogonal phases. As discussed elsewhere, the phase shifts can be performed in the IF stage rather than at the carrier frequency so that one phase shifting network can suffice for all carrier frequencies. 

This structure, when it is present, appears always as the first stable tilted phase below the orthogonal SmA phase. Tilts in all layers are equal and also all phase differences a are equal. From this point of view the phase is equal to the SmC and the SmC phase. The main difference in the macroscopic properties is the magnitude of the angle a, which is neither close to zero nor close to tt (Fig. 5.4c and d). The structure is helicoidally modulated but has a very short pitch, which extends from a few tens of layers to shorter periods than four layers. Due to the short pitch, the structure optically does not differ from the orthogonal phase and does not exhibit other properties like optical rotatory power, typical for other helicoidally modulated structmes. 

When molecular axes (director) are tilted by some angle with respect to the smectic normal we have the remarkable correspondence between the tilted and orthogonal phases SmC SmA (both have liquid layer structure) SmF — SmBhex (hexatic layer structure) SmH — SmBciyst (crystalline layer structure). 

Just as the phase is the tilted analogue of the phase, there are tilted analogues of the higher ordered orthogonal phases just described. The phase has two tilted analogues, the Sj and the Sp phases. Similarly, the crystal B phase has two tilted analogues, the... 

The symmetry arguments for achiral or chiral smectic C phases can also be applied in similar ways to the other smectic and soft crystal smectic phases. For example, all of the tilted phases (smectics I and F, and crystal phases J, G, H, and K ) would have broken symmetries leading to polar noncentrosymmetric structures resulting in ferroelectric properties. Even orthogonal phases, such as the smectic A phase would have different symmetries for the chiral versus the achiral forms. For instance, the smectic A phase has symmetry, where-... 

For systems that have two terminal aliphatic chains that can be independently varied in length, tilted phases tend to occur when the two lengths are similar to one another. At short chain lengths, usually orthogonal phases such as smectic B, crystal B, and crystal E occur. In some cases the upper temperature transitions to the smectic A and smectic B phases can occur so close together that a transition from the nematic phase or the liquid phase to the smectic B phase appears to occur only through a transient smectic A phase. This transition is sometimes called a liquid or nematic to SmAB transition [10] (Fig. 6). 

For systems where there is only one terminal alipahtic chain, typically no tilted smectic phases are observed, and orthogonal phases predominate. The smectic A phase is the commonest modification ob-... 

It is generally understood that smectic liquid crystals are more likely to be formed in systems where the central core region has aromatic or heteroaromatic ring structures. Alicyclic ring systems, conversely, tend to disfavour smectic phase formation, see Fig. 15 for relative ordering, and in particular, they tend to depress tilted phases over orthogonal phases. 

Decreasing ability to form smectic phases Increasirtg preference for orthogonal phases... 

The simple, popular picture of a smectic phase (Sm) consisting of elongated molecules in sharp, distinct layers is rather misleading a more realistic picture is one where the molecules are arranged to provide a single sinusoidal density wave [1] with its wave vector either parallel to the molecular director (orthogonal phases such as SmA, SmB, etc. - see Fig. 1) or at some angle to it (tilted phases such as SmC, SmI, etc.). However, it is often convenient to refer to the layered nature of the smectic phase to help explain phenomena such as conductivity anisotropy. 

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