Lamellar bending

Ruland and Smarsly [84] study silica/organic nanocomposite films and elucidate their lamellar nanostructure. Figure 8.47 demonstrates the model fit and the components of the model. The parameters hi and az (inside H ) account for deviations from the ideal two-phase system. Asr is the absorption factor for the experiment carried out in SRSAXS geometry. In the raw data an upturn at. s o is clearly visible. This is no structural feature. Instead, the absorption factor is changing from full to partial illumination of the sample. For materials with much stronger lattice distortions one would mainly observe the Porod law, instead - and observe a sharp bend - which are no structural feature, either. 

Weak preference to block copolymer. Figure 26 shows the MC simulated morphologies of A5B5 diblock copolymers confined in cylindrical nanopores with the different exterior radii Rex and eAS = bs = 0. It is shown that the lamellar structure forms parallel to the pore axis. However, there is a little difference between small and large Rex. The lamellar structure is not bended at small Rex as shown in Figure 26a, while it is bended like the wave-shape at large Rex as... 

Compact bone Circumferential, concentric lamellar Prevents bending of long... 

The elastic bending modulus Kc for lipid bilayers was found to be of the order of 10 x 10-20 J.6 For the lyotropic lamellar liquid crystals, the additional presence of a cosurfactant at the interface shouldleadto smaller values. Various experimental measurements21 provided values ranging between 0.08 and 5 x 10-20 J. 

In the first part of the paper, a thermodynamic formalism developed earlier10 was used to obtain information about the domains of stability of the lamellar phase. It was shown that, for a set of interaction parameters between layers and bending modulus of the interface, only certain thicknesses are allowed for the water and oil layers. 

The XRD patterns of S], S2 are shown in Fig.3. The peak near 2.9° changes to 3.4° for the TEOS-treated sample, which means the interlamellar distance decreases when treated with TEOS. And the strength of the peaks at low angles becomes less sharp than the salt. It is contrast to the increase surface area of the material. We can deduce that the addition of Si leads to the bending of the layers, and at last results in the transformation of the lamellar salt into a porous structured compound through the... 

Alternatively, if one dilates a smectic stack by increasing its thickness by an amount Sh > 27t X, then the sample will prefer to bend the layers in an undulational instability (Rosenblatt et al. 1977 Ostwald and Allain 1985) in order to restore the lamellar spacing to its preferred value (see Fig. 10-29d). Note that the increase in thickness 8h required to produce this instability is independent of the initial thickness h of the stack. Hence for a macroscopic sample of thickness, say, h = 60 p,m, the strain Sh/h required to induce the undulational instability is extremely small, 8h/h IzrXfh 10-4. Thus smectic monodomains are extremely delicate and can easily be disrupted by mechanical deformation. 

When the layers of a lamellar block copolymer are distorted, the free energy density is augmented by a distortional term that can, like the smectic-A phase, be described as the sum of layer compression/dilation and layer-bending energies ... 

The bend and especially the compressive moduli of lamellar block copolymers are therefore typically lower, or at least no higher, than those of small-molecule smectic-A liquid crystals, while the viscosities of the former are usually much larger than the latter. By analogy with nematics, for layered materials one can define characteristic Ericksen numbers as Erj = r]yh /K and Er = where is a characteristic viscosity and... 

Thus, these mesostructures are predominantly lamellar, and identified as conventional (parabolic) lamellar phases, although they may in fact be hyperbolic. Indeed, unless v/al is exactly unity, a planar interface (lamellar mesophase) incurs a bending energy cost hyperbolic sponge monolayers or bilayers or mesh monolayer mesophases are favoured if v/al differs from unity. It is likely then that many "lamellar"" phases in fact adopt a hyperbolic geometry. Careful neutron-scattering studies of a lamellar phase have revealed the presence of a large number of hyperbolic "defects" (pores within the bilayers) in one case [16]. (An example of this mis-identification of hyperbolic phases in block copolymers is discussed in section 4.10.)... 

The elasticity of multilamellar vesicles can be discussed in reference to that of emulsion droplets. The crystalline lamellar phase constituting the vesicles is characterized by two elastic moduli, one accounting for the compression of the smectic layers, B, and the second for the bending of the layers, K [80]. The combination has the dimension of a surface tension and plays the role of an effective surface tension when the lamellae undergo small deformations [80]. This result is valid for multilamellar vesicles of arbitrary shapes [81, 82]. Like for emulsion droplets, the quantity a/S is the energy scale that determines the cost of small deformations. 

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