Asymmetric interpenetration

Figure 14 Asymmetric interpenetration of two porph3Tin containing 3D PtS networks.

The asymmetric interpenetration in this porphyrin-based material is likely due to favorable interactions between the networks which, as mentioned before, can be important to both the formation of interpenetrating nets, and in the way those nets associate with each other. The structure of [Cu3(tpt)4](C104)3-solv is an excellent illustration of this. The structure contains two interpenetrating 3,4-connected networks with boracite topology that interpenetrate in such a way that pairs of tpt ligands come in close contact and form x -stacked pairs between... 

Figure 14 Asymmetric interpenetration of two PtS networks in the structure of [Cu(tcp)CuBF4].17CgH5N02, Cu(tcp) = 5,10,15,20-tetrakis(4-cyanophenyl)-21H,23H-porphine...

Mean values of the short and long bonds of the four asymmetrically bound ligands. K Mean values of the four angles in the two interpenetrating trapezoids. 

Fig. 5.21 Highest residual electron density maxima in tol-Ol.res forming a disordered toluene molecule on a mirror. Left-hand side asymmetric unit right-hand side with symmetry equivalent atoms, revealing interpenetration toluene orientations.

The PtS network consists of equal numbers of tetrahedral and square-planar centers. Two such networks interpenetrate in the structure of [ Cu (tcp) Cu ]BF4-I7C6H5NO2 [Cu (tcp) = 5,10,15,20-tetrakis(4-cyano-phenyl)-21H,23H-porphine copper(II)]. The networks interpenetrate in an asymmetric fashion, i.e., the second net does not lie in the center of the channels and cavities of the first, but rather lies to one side. Attractive internet porphyrin... porphyrin interactions are the likely cause, and it produces larger channels and cavities, which contain large amounts of essentially liquid solvent, than would normally be expected. 

Y. Chi, S. T. Scroggins, J. M. J. Erechet, J. Am. Chem. Soc. 2008, 130, 6322-6323. One-pot multi-component asymmetric cascade reactions catalyzed by soluble star polymers with highly branched non-interpenetrating catalytic cores. 

Fig. 3 (a) Asymmetric unit representation of [Zn(aptz)2] showing that the Zn center displays a slightly distorted tetrahedron. After [23]. (b) A non-interpenetration diamondoid net of [Zn(aptz)2]. After [23]... 

In very asymmetric systems where the radius ratio o is either very large or very small, the mutual virial coefficient Gab (o equivalently the mutual interpenetration function Was) is very difficult to measure because it gives only a small contribution to the osmotic pressure or scattering intensity. In the symmetric case where the masses of the two different polymers are equal, Waa Was are of the same order of magnitude and their difference has been measured recently by lightscattering using the so-called optical 0-solvent method which gives direct access to the monomer virial coefficient difference... 

Since the introduction of our review article of combined acid catalysis in 2005 [2], this concept has clearly continued to interpenetrate the area of asymmetric catalysis and rapidly evolving, as is apparent from the summary described herein. 

The functions in equations (95) and (96) are monotone, increasing with increasing z, but T(z)fko increases much more rapidly than T(z)cm- These dependences appear to represent extremes in behavior a number of other proposed approximate functions give plots vs, z that lie between these two cases. It will be noted that these two functions also correspond to extremes in symmetry of models for the bimolecular cluster, i.e, the interpenetration of two soft spheres in the FKO model describes inherently asymmetric configurations of segments, while the CM model makes every configuration a spherically symmetrical superposition of the segments of the two participant chains. 

The excluded volume theory is the most commonly used continuum analytical model of percolation. The excluded volume of an object is defined as the volume around the object into which another identical object cannot enter without contacting the first object as illustrated in Figure 2. ° The principal concept in the excluded volume model is that the percolation threshold of a system is determined by the excluded volume of filler particles, rather than their true volume. This is particularly applicable to asymmetrical, unaligned objects for which the excluded volume can differ significantly from their true volume. Therefore, this model has been applied to describe critical percolation phenomena for a wide variety of filler geometries. In addition, excluded volume arguments provide useful theoretical approximations in many computational stu-dies. Excluded volume solutions were first formulated for soft-core (interpenetrable) fillers, and later extended to core-shell (impenetrable hard-core surrounded by a penetrable shell) fillers. ... 

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