Smectic membranes

As early as the 1920s, Georges Friedel recognized that one could prepare free-standing films (just like soap films) from smectic liquid crystals. (That could be the reason for calling them smectic, which means soap in Greek). A simple technique was developed, and systematic studies were started at 

Freely suspended smectic film geometry, (a) Schematic of the film holder based on fixed frame and a wiper, (b) A frame with variable size. 

The number of layers, N, contained in the film can be determined by measuring its optical reflectivity, which, for thin film, is proportional to AP. The thickness of a fresh film usually varies from a few layers in the middle 

Thermotropic smectic membranes are similar to the Newton black soap films in respecf to their structure, thickness, and because both are spanned on frames and can exchange molecules with the meniscus. However, the smectic membranes are more complex in the respect that the number N of monolayers is variable, whereas the Newton black films are usually bilayers. Smectic membranes are also similar to vesicles by means of their layered structures however, the vesicles are rather isolated unframed systems in the sense that the number of molecules is conserved, but the surface is free to evolve.  

Besides the variable thickness Nl (I is the thickness of one monolayer) of a smectic membrane, another obvious characteristic is that the membrane stays nearly flat in spite of its weight. This indicates that the membrane must be subject of tension, just like the membrane of a drum. When this tension is released, the thickness of the membrane increases by the addition of new layers. The tension of the membrane can be measured by different meth-ods. i 3,44 jhe most popular (and perhaps the most precise) method is to measure the eigenmodes of the mechanical vibrations of the membrane induced, for example, by applying a potential difference  

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We can assume that heat, as well as molecules, can be exchanged between the different layers, different fields and between the membrane and the meniscus. Therefore in equilibrium, not only the temperature, but also the chemical potential /i of molecules in all layers, fields and in the meniscus must be identical. Let f(N,a,T) be the average free energy per molecule in the field of thickness N, where a is the average surface area per molecule. Since smectic membranes with any number larger than N = 2 can be stable in the limit of weak constraints, for each N (at constant temperatures T) there should be an equilibrium of the surface per molecule, and f(N,a,T) are well defined near a. Hence we can expand f(N,a) as ... 

When smectic membranes are exposed to external pressure from one side, they bend imtil a balance between pressure difference and surface tension is established. In this way, self-supporting spherical bubbles can be produced. ... 

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. 

Study of free-standing membranes is also extremely important to map the polar nature of ferroelectric, ferrielectric and antiferroelectric liquid crystals of chiral and bent-core achiral molecules. An excellent overview of smectic membranes with detailed results and list of literature has been published recently by de Jeu et al. ... 

Similar to smectic membranes, periodic electric fields (although in this case the field is parallel to the fiber axis) can induce mechanical vibration of the strings. Studying the eigenfrequencies of the vibrations of the strings under... 

The three classes of liquid crystals differ in the arrangement of their molecules. In the nematic phase, the molecules lie together, all in the same direction but staggered, like cars on a busy multilane highway (Fig. 5.49). In the smectic phase, the molecules line up like soldiers on parade and form layers (Fig. 5.50). Cell membranes are composed mainly of smectic liquid crystals. In the cholesteric phase, the molecules form ordered layers, but neighboring layers have molecules at different angles and so the liquid crystal has a helical arrangement of molecules (Fig. 5.51). 

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. 

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. 

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... 

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. 

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. 

Figure 1. Possible structural arrangement of a bimolecular lipid membrane (BLM) separating two aqueous solutions. Open circles and zig-zag lines denote polar groups and hydrocarbon chains, respectively. The structure of BLM is akin to a neat or smectic mesophase found in liquid crystals...

Comparson of the transitions observed by differential scanning calorimetry in membranes of M. laidlawii and in water dispersions of the lipids from the membranes support the concept that most of the lipids exist as a smectic mesophase in the membranes. The evidence for a bilayer structure is straightforward in this case. Lipid transition temperatures are a function of fatty acid composition and correlate well with biological properties. The calorimeter possesses advantages over high resolution NMR for M. laidlawii, and perhaps in many other systems, because the data can be interpreted less ambiguously. In M. laidlawii membranes the bilayer appears to be compatible with the same physical properties observed in other membranes—a red-shifted ORD, lack of ft structure in the infrared, reversible dissociation by detergents, and poorly... 

Liquid crystals, liposomes, and artificial membranes. Phospholipids dissolve in water to form true solutions only at very low concentrations ( 10-10 M for distearoyl phosphatidylcholine). At higher concentrations they exist in liquid crystalline phases in which the molecules are partially oriented. Phosphatidylcholines (lecithins) exist almost exclusively in a lamellar (smectic) phase in which the molecules form bilayers. In a warm phosphatidylcholine-water mixture containing at least 30% water by weight the phospholipid forms multilamellar vesicles, one lipid bilayer surrounding another in an "onion skin" structure. When such vesicles are subjected to ultrasonic vibration they break up, forming some very small vesicles of diameter down to 25 nm which are surrounded by a single bilayer. These unilamellar vesicles are often used for study of the properties of bilayers. Vesicles of both types are often called liposomes.75-77... 

Besides differential scanning calorimetry, electron microscopy can also serve for characterizing the mixing behavior of multicomponent vesicular systems. The ripple structure of phospholipids with saturated alkyl chains (also referred to as smectic Bca phase, Fig. 35) is taken to indicate patch formation (immiscibility) in mixed phos-close enough (1-2 nm) lipid molecules are able to diffuse from one membrane to the between the pre- and main-transition of the corresponding phospholipid, electron... 

In membrane systems, temperature at which the crystalline state is converted to the liquid-crystalline state (smectic phases). 

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... 

Golubovic, L. and Golubovic, M. (1998) Fluctuations of quasi-two-dimensional smectic intercalated between membrane in multilamellar phases of DNA-cationic lipid complexes. Phys. Rev. Lett., 80,4341—4344. 

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],... 

Evans et al. also showed that the 1 1 mixture of BAN and (3, y-distearoyl-phos-photidylcholine (DSPC) gives a smectic A texture in the temperature range of 57.3 to 100°C [21]. This is the first notice of lyotropic lamellar liquid crystals formed in the ionic medium. Additionally, Seddon et al. [28] and Neve et al. [29] have described the long-chained A-alkylpyridinium or l-methyl-3-alkylimidazolium ions to display smectic liquid-crystalline phases above their melting points, when Cl or tetrachloro-metal anions like CoCl " and CuCl " are used as the counter ions. Lin et al. have also noted the liquid crystal behavior of 1-alkylimidazolium salts and the effect on the stereoselectivity of Diels-Alder reactions [30]. However, liquid crystals are classified as ionic liquid crystals (ILCs), and they are distinguished from liquid crystals that are dispersed in ionic liquids. Although the formation of micelles and liquid crystal phases in ionic liquids have been thus reported, there has been no mention of the self-assembly of developed nano-assemblies that are stably dispersed in ionic liquids. In the next section the formation of bilayer membranes and vesicles in ionic liquids is discussed. 

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