In-plane ordering

Figure C2.2.4. Types of smectic phase. Here tire layer stacking (left) and in-plane ordering (right) are shown for each phase. Bond orientational order is indicated for tire hexB, SmI and SmF phases, i.e. long-range order of lattice vectors. However, tliere is no long-range translational order in tliese phases.

In this section we will discuss in some detail the application of X-ray diffraction and IR dichroism for the structure determination and identification of diverse LC phases. The general feature, revealed by X-ray diffraction (XRD), of all smectic phases is the set of sharp (OOn) Bragg peaks due to the periodicity of the layers [43]. The in-plane order is determined from the half-width of the inplane (hkO) peaks and varies from 2 to 3 intermolecular distances in smectics A and C to 6-30 intermolecular distances in the hexatic phase, which is characterized by six-fold symmetry in location of the in-plane diffuse maxima. The lamellar crystalline phases (smectics B, E, G, I) possess sharp in-plane diffraction peaks, indicating long-range periodicity within the layers. 

The confinement may also induce another sort of structure known as the in-plane order, i.e., an ordering structure formed in the plane parallel to the wall. This can be demon-... 

Fig. 20 Pictures of atoms that belong to a the first, b the second, c the third, and d the fourth e layers, which show the in-plane ordering of the chains in each layer at 300 K after 1.28 ns. Especially marked is an ordering in the first layer nearest to the substrate...

In crystalline smectic phases the arrangement of the molecules within the layer is ordered in a hexagonal, orthorhombic or monoclinic fashion and the layers are correlated to each other. The in-plane order of the mesophase is indicated by the existence of sharp wide-angle reflection. The in-plane correlation is recorded by a small value of Full Width of Half Maximum (FWHM) and, in principle, by more than one wide-angle reflex. 

In our experiments, the quench from a swollen to a glassy state has been achieved within tens of seconds, and has been shown not to alter the phase separation in a swollen state[49]. Figure 17 compares surface structures in SB41 films that have been exposed to a relative vapor pressure p/po of 72% and of 80%. With an increase of the solvent concentration, the in-plane order of the microdomains... 

Figure 7. In-plane ordering of graphene layers. The turbostratic case gives rise to Moire and pseudosymmetric supcrlattice structures, detectable in STM images. In many cases, however, no correlation exists between the individual layers. The turbostratic ordering has very little effect on the interplanar spacing. Enlarged cj2 parameters arise from defects such as sp1 centers which accompany the turbostratic graphene layers.

X-ray diffraction is the most common and most accurate method used to determine the polymorphic form of a sample. A change in the diffraction profile (e.g., a change in peak shape or position) indicates a change in polymorphism. The wide-angle reflections, (also called short-spacings ) are used to characterize the polymorphism of a lipid. These reflections correspond to in-plane ordering of the fatty acyl chains on the TAG molecule. Common polymorphic forms include the hexagonal, a form (d = 4.15A), the orthorhombic perpendicular P form (J = 3.8 and 4.2A) and the triclinic P form (d=4.6A) (Larsson 1966). 

Three properties of fluids under shear are discussed in detail flow boundary condition, friction, and shear viscosity. It has been shown that the no-slip boundary condition assumed in fluid mechanical formulations of Newtonian flow past solids can fail at the molecular level. The velocity profiles deviate most from the continuum linear form at small pore separations, low temperatures, high pressures, and high shear rates. Friction is controlled by two factors - interfacial strength and in-plane ordering. 

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