Lamella, bended

According to Hosemann-Bonart s model8), an oriented polymeric material consists of plate-like more or less curved folded lamellae extended mostly in the direction normal to that of the sample orientation so that the chain orientation in these crystalline formations coincides with the stretching direction. These lamellae are connected with each other by some amount of tie chains, but most chains emerge from the crystal bend and return to the same crystal-forming folds. If this model adequately describes the structure of oriented systems, the mechanical properties in the longitudinal direction are expected to be mainly determined by the number and properties of tie chains in the amorphous regions that are the weak spots of the oriented system (as compared to the crystallite)9). 

Note Space filling is achieved by branching, bending or both, of the constituent fibres or lamellae. 

Drilling and bending mechanisms regenerate the original channel geometry before reunification so that a multiple repetition of the separation step can be performed. Thereby, the widths of the lamellae are halved in each consecutive step. In the case of direct subdivision the width of the lamella depends on that of the channel, although repeating steps may be included, too. 

Fig. 22 Phase image showing the joining (J) and bending (B) of lamellae of BA-C8 during their growth and propagation [60]...

To avoid contact of two lamellae propagating in opposite directions, the growth directions of the lamellae can change, resulting in bending of the lamellae. 

Two nonparallel lamellae propagating in a similar direction can join at a certain point. Then, they can propagate along different directions after joining. The join of these two lamellae can cause bending of the lamellae. 

Bend all in 1960 takes into consideration the results of many investigators and has become generally accepted as an overall description of electron flow in chloroplast lamellae. After introducing the concept of redox potential in Chapter 6 (Section 6.1 C), we will portray the energetics of the series representation (see Fig. 6-4, which includes many of the components that we will discuss next). 

A model explaining this behavior is shown in Fig. 42. One has to assume bended lamella which flatten during annealing while the chain orientation does not change. The decrease of the long period is caused probably by this flattening. 

Fig. 31 a. Shear bands (S) and "bright lines" (BL) in the compressive region of a HDPE-bend specimen. The axis of the compressive stress is perpendicular to the direction of the lamellae b Intersections of shear bands with "bright lines acting as sites for crack initiation (Courtesy W. Rose, Erlangen)... 

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. 

Davis summarized the concepts about HLB, PIT, and Windsor s ternary phase diagrams for the case of microemulsions and reported topologically ordered models connected with the Helfrich membrane bending energy. Because the curvature of surfactant lamellas plays a major role in determining the patterns of phase behavior in microemulsions, it is important to reveal how the optimal microemulsion state is affected by the surface forces determining the curvature... 

By considering the paving-stone-like PS domains as spheres (ST-6), the bending rods as cylindrical rods (ST-7), and the lamellae as plane parallel layers (ST-8), the volume fraction, , of each domain was calculated from the diameter, D, and the distance, A, measured on the electron micrographs using the following equations (8) ... 

Lyotropic liquid crystals are principally systems that are made up of amphiphiles and suitable solvents or liquids. In essence an amphiphilic molecule has a dichotomous structure which has two halves that have vastly different physical properties, in particular their ability to mix with various liquids. For example, a dichotomous material may be made up of a fluorinated part and a hydrocarbon part. In a fluorinated solvent environment the fluorinated part of the material will mix with the solvent whereas the hydrocarbon part will be rejected. This leads to microphase separation of the two systems, i.e., the hydrocarbon parts of the amphiphile stick together and the fluorinated parts and the fluorinated liquid stick together. The reverse is the case when mixing with a hydrocarbon solvent. When such systems have no bend or splay curvature, i.e., they have zero curvature, lamellar sheets can be formed. In the case of hydrocarbon/fluorocarbon systems, a mesophase is formed where there are sheets of fluorocarbon species separated from other such sheets by sheets of hydrocarbon. This phase is called the La phase. In the La phase the molecules are orientationally ordered but positionally disordered, and as a consequence the amphiphiles are arranged perpendicular to the lamellae. The La phase of lyotropics is therefore equivalent to the smectic A phase of thermotropic liquid crystals. 

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