Interaction between layers

The interest in vesicles as models for cell biomembranes has led to much work on the interactions within and between lipid layers. The primary contributions to vesicle stability and curvature include those familiar to us already, the electrostatic interactions between charged head groups (Chapter V) and the van der Waals interaction between layers (Chapter VI). An additional force due to thermal fluctuations in membranes produces a steric repulsion between membranes known as the Helfrich or undulation interaction. This force has been quantified by Sackmann and co-workers using reflection interference contrast microscopy to monitor vesicles weakly adhering to a solid substrate [78]. Membrane fluctuation forces may influence the interactions between proteins embedded in them [79]. Finally, in balance with these forces, bending elasticity helps determine shape transitions [80], interactions between inclusions [81], aggregation of membrane junctions [82], and unbinding of pinched membranes [83]. Specific interactions between membrane embedded receptors add an additional complication to biomembrane behavior. These have been stud-... 

After a layer fails, the behavior of the laminate depends on how the mechanical and thermal interactions between layers uncouple. Actually, failure of a layer might not mean that it can no longer carry load. In the present example of a cross-ply laminate, the inner layer with fibers at 90° to the x-axis has failed, but, because of the orientation of the fibers (perpendicular to the main failure-causing stress), the failure should be only a series of cracks parallel to the fibers. Thus, stress can still be carried by the inner layer in the fiber direction (y-direction). 

For cross-ply laminates, a knee in the load-deformation cun/e occurs after the mechanical and thermal interactions between layers uncouple because of failure (which might be only degradation, not necessarily fracture) of a lamina. The mechanical interactions are caused by Poisson effects and/or shear-extension coupling. The thermal interactions are caused by different coefficients of thermal expansion in different layers because of different angular orientations of the layers (even though the orthotropic materials in each lamina are the same). The interactions are disrupted if the layers in a laminate separate. 

Now, what can we say about the phosphorus-phosphorus interaction between layers Comparing the layer structure of MruPl- with the unit cell in Fig. 7.28, we see that the 3-D structure of BaMn2P2 consists of alternating and Bai+ layers. 

The structures of M0O3 and V205 are similar. Both are made up of chains of MOe octahedra that are linked to form a layered structure. Interaction between layers is relatively weak. The surface of these two-dimensional layers forms the basal (010) plane on which isolated terminal V=0 or Mo=0 groups are found. These terminal groups show characteristic IR absorption frequencies that are easy to follow. In many cases, these groups form the active centers. 

In crystalline 7 there is only poor interaction between the parallel chains, and it is this property that results in its special inclusion behaviour. The only guests included are small aromatic hydrocarbons, and these usually give a host guest ratio of 1 1. Incorporation of the guests between the parallel chains increases the OFF and EF attractions within the layers, with concomitant reduction of the Br Br interactions between layers. 

In summary, information about the interactions between layers allowed one to identify the domains where the lamellar phase is unstable. A positive derivative off with respect to di or d2 implies that the region is inaccessible to a lamellar phase. In this case, a water or oil phase will separate until the allowed values for dj and 82 will be reached. In addition, a negative surface tension indicates that another phase (cubic,hexagonal, microemulsion, etc.) is stable. It should be, however, emphasized that when y > 0, a phase other than the lamellar one may be the thermodynamically stable one. 

Due to this largely graphitic character, the faceted carbon nanoparticles are more stable than their spherical analogs. In the latter, the graphitic interaction between layers is much less pronounced due to the multitude of defects and the random arrangement of shells. In the parallel domains of the nanoparticles, on the other... 

Now what can we say about the phosphorus-phosphorus interaction between layers Comparing the layer structure of Mi Pj" with the unil cell In Fig. 7.28, we see that the 3 D structure of BaMn2P2 consists of alternating Mn2P and Ba2+ layers. This brings the apical phosphorus atoms of one layer close to those of the next layer, and they interact along the z axis. If we look at the DOS for a single Mn - layer (Fig. 7.30) but now inquire as to the contribution of the phosphorus 3pz orbital, we see that... 

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