Molecular tilt

Thus the formation of tilted analogues of the smectic A phases, i.e. monolayer Cl and bilayer C2, is possible for mesogens with relatively large electric quadrupoles. In the case of strongly sterically asymmetric molecules (e.g., zigzag shaped or dumbell shaped molecules, Fig. 3b) these quadrupolar interactions may be steric in origin. From this point of view observation of molecular tilt in the molecular dynamics simulations for a one-layer film of DOBAMBC in the absence of electrostatic interactions is not so surprising [106]. 

Fig. 17a-c. Sketches of the molecular arrangements for the smectic structure with alternating layer-to-layer tilt a conventional and chevron smectic C layering in low molecular mass mesogens b ferroelectric hilayer chevron structures for achiral side-chain polymers c antiferroelectric hilayer chevron structures for achiral side-chain polymers. Arrows indicate the macroscopic polarization in the direction of the molecular tilt... 

The earliest approach to explain tubule formation was developed by de Gen-nes.168 He pointed out that, in a bilayer membrane of chiral molecules in the Lp/ phase, symmetry allows the material to have a net electric dipole moment in the bilayer plane, like a chiral smectic-C liquid crystal.169 In other words, the material is ferroelectric, with a spontaneous electrostatic polarization P per unit area in the bilayer plane, perpendicular to the axis of molecular tilt. (Note that this argument depends on the chirality of the molecules, but it does not depend on the chiral elastic properties of the membrane. For that reason, we discuss it in this section, rather than with the chiral elastic models in the following sections.)... 

The second issue concerns the anisotropy of the membrane. The models presented in this section all assume that the membrane has the symmetry of a chiral smectic-C liquid crystal, so that the only anisotropy in the membrane plane comes from the direction of the molecular tilt. With this assumption, the membrane has a twofold rotational symmetry about an axis in the membrane plane, perpendicular to the tilt direction. It is possible that a membrane... 

It is also possible that a membrane might have an even lower symmetry than a chiral smectic-C liquid crystal in particular, it might lose the twofold rotational symmetry. This would occur if the molecular tilt defines one orientation in the membrane plane and the direction of one-dimensional chains defines another orientation. In that case, the free energy would take a form similar to Eq. (5) but with additional elastic constants favoring curvature. The argument for tubule formation presented above would still apply, but it would become more mathematically complex because of the extra elastic constants. As an approximation, we can suppose that there is one principal direction of elastic anisotropy, with some slight perturbations about the ideal twofold symmetry. In that approximation, we can use the results presented above, with 4) representing the orientation of the principal elastic anisotropy. 

A very different model of tubules with tilt variations was developed by Selinger et al.132,186 Instead of thermal fluctuations, these authors consider the possibility of systematic modulations in the molecular tilt direction. The concept of systematic modulations in tubules is motivated by modulated structures in chiral liquid crystals. Bulk chiral liquid crystals form cholesteric phases, with a helical twist in the molecular director, and thin films of chiral smectic-C liquid crystals form striped phases, with periodic arrays of defect lines.176 To determine whether tubules can form analogous structures, these authors generalize the free-energy of Eq. (5) to consider the expression... 

This calculation shows that molecular chirality has two effects It favors formation of cylinders with a radius scaling as r oc (kHp) 1, and it favors the formation of a striped modulation in the molecular tilt direction. The... 

Figure 5.50 Schematic view of modulated state of tubule. Left Modulation in direction of molecular tilt, as indicated by arrows. Right Ripples in tubule curvature (greatly exaggerated for clarity). Adapted from Ref. 132 with permission of the author. Copyright 1996 by the American Physical Society.

S = (3 is molecular tilt angle to film normal. 

Fig. 11. The dependence of SH intensity (open circle) and molecular tilt angle < > to film normal of the mixed monolayer on the fraction of C18OAZ0NO2.

The values of the envelopes of SH intensity at 45 ° incidence in the mixed monolayers are plotted against the fraction of C180AZ0N02 in Fig.ll. The molecular tilt angle <(> evaluated by the above-mentioned procedure is also shown in this figure. The SH intensity of the single-component monolayer of C180AZ0N02 is very small. This result means that the orientation of amphiphile... 

The MAMs were found to be closely packed. NEXAFS and FTIR spectroscopy studies revealed that the molecular tilting angles relative to the surface normal varied from 4° to 21° as a function of Ax. In wetting studies it was found that the highest water contact angles ( 131°) with the lowest contact angle hysteresis... 

For phases made of tilted molecules, measurements show that the inclination of the unit cell can be higher or smaller than the molecular tilt. This is not surprising since the crystallographic unit cell is defined by complex interactions between the deformed layers. 

In this section we present a model [32, 33] which predicts that regions of favorable splay are connected by regions of unfavorable splay in which layers are inclined to reduce the molecular tilt. Unfavorable splay occurs on a smaller tilt cone and as a result the energy penalty in the unfavorable splay regions is reduced. The local increase of the layer thickness due to the smaller tilt angle leads to the bending of layers and as a result to the formation of undulated layers or fragmented layer structure. 

The stability analysis [32] of the lamellar (one-dimensional) structure shows that it is stable only for weak coupling between the splay of polarization and molecular tilt. When Kv is larger than some critical value, layers start to undulate. 

Fig. 24. Molecular tilts calculated from observed apex angles for specimen M43 indicating transition from roof shaped to curved morphology...

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