Smectic membranes model

The most successful continuum description of membrane elasticity, dynamics, and thermodynamics is based on the smectic bilayer model (for examples of different versions and applications of this approach see Ref. 76-82 and references therein). We introduce this model in conjunction with the question of membrane undulations. 

There are a number of reasons for the interest in free-standing smectic membranes. First, thin smectic membranes are models of two-dimensional fluids (SmA and SmC) and crystals (SmB). By varying the film thickness, one therefore can study the crossover from three- to two-dimensional behavior as well as the influence of surfaces on the morphology and the phase behavior. 

A final example of the simulation of a complex system is a series of MD simulations of bilayer membranes. Membranes are crucial constituents of living organisms they are the scene for many important biological processes. Experimental data are known for model systems for example for the system sodium decanoate, decanol and water that forms smectic liquid crystalline structures at room temperature, with the lipids organized in bilayers. 

It follows from previous discussion that the destabilizing electrostatic contribution grows in absolute value with x (with increasing A.). But the influence of the nonuniform electrical force is overwhelmed by the stabilizing bending and stretching contributions. As a result, the traditional smectic model cannot explain how a small transmembrane voltage can lead to membrane breakdown. The obvious solution is to abandon this approach and to develop an alternative, such as the pore formation model. However, as we noticed before, this approach postulates rather than proves the appearance of hydrophobic pores. 

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... 

To discuss the models in this section, we should mention two issues. First, the models assume the membrane is sufficiently soft that the tilt direction can vary with an energy cost that scales as (Vc(j)2. This is appropriate if the membrane is in a fluid phase like a smectic-C liquid crystal, with order in the tilt direction but not in the positions of the molecules. It is also appropriate if the membrane is in a tilted hexatic phase, with order in the orientations of the intermolecular bonds as well as the tilt. However, this assumption is not appropriate if the membrane is in a crystalline phase, because the tilt direction would be locked to the crystalline axes, and varying it would cost more energy than (V(f>)2. 

The Singer and Nicholson (13) model for the plasma membrane, which now receives much support, is basically a smectic liquid crystal consisting of one bilayer of phospholipid (Figure 4a). The phospholipid bilayer contains cholesterol at a concentration which depends on cell type. Embedded in the lipid liquid crystal he protein molecules. Some of these protein molecules transverse the entire lipid bilayer and communicate both with the inside and the outside of the cells. Some of these may... 

We note that earlier research focused on the similarities of defect interaction and their motion in block copolymers and thermotropic nematics or smectics [181, 182], Thermotropic liquid crystals, however, are one-component homogeneous systems and are characterized by a non-conserved orientational order parameter. In contrast, in block copolymers the local concentration difference between two components is essentially conserved. In this respect, the microphase-separated structures in block copolymers are anticipated to have close similarities to lyotropic systems, which are composed of a polar medium (water) and a non-polar medium (surfactant structure). The phases of the lyotropic systems (such as lamella, cylinder, or micellar phases) are determined by the surfactant concentration. Similarly to lyotropic phases, the morphology in block copolymers is ascertained by the volume fraction of the components and their interaction. Therefore, in lyotropic systems and in block copolymers, the dynamics and annihilation of structural defects require a change in the local concentration difference between components as well as a change in the orientational order. Consequently, if single defect transformations could be monitored in real time and space, block copolymers could be considered as suitable model systems for studying transport mechanisms and phase transitions in 2D fluid materials such as membranes [183], lyotropic liquid crystals [184], and microemulsions [185],... 

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