Inclined interpenetration

Two major categories of interpenetrating 2D network can be discerned - one we shall refer to as parallel interpenetration and the other as inclined interpenetration . Inclined interpenetration inevitably leads to a 3D interlocked composite, whereas in all cases but one very recent one, parallel interpenetration yields a 2D composite. 

In the inclined mode of interpenetration any one sheet has an infinite number of inclined ones passing through it to produce an interlocked 3D composite in the manner represented in Figure 16. In contrast to parallel interpenetration, each sheet passes through an inclined one just once along a line of intersection of the two planes. All examples of inclined interpenetration known at present involve either (4,4) or (6,3) nets. 

Figure 17. Inclined interpenetration (actually perpendicular) of two (4,4) nets in [M(4,4 -bipy)2(H20)2](SiF6). 4-Connecting nodes are provided by M which has two pendant trans H20 ligands not shown here and connections between nodes are provided by 4,4 -bipy.

Figure 18. Inclined interpenetration of (6,3) sheets in the structure of Cu2(pyrazine)3(SiF6). Circles represent Cu and connections between Cu atoms are provided by pyrazine. Sheets passing through rings at the top, bottom, front, and back of the collection shown here have been omitted for clarity.

Figure 19. Schematic representation of the 2D inclined interpenetration of (4,4) sheets in the structure of [Cd(py)2 Ag(CN)2 2], py is pyridine. Each window of each sheet, all of which are equivalent, has parts of two other sheets passing through it. Circles represent Cd atoms.

Figure 1.3.14 Three possible topological entanglements of hexagonal 63 layers showing interpenetration versus catenation (parallel and inclined).

The generation of a 3D entanglement from the interpenetration of ID networks is displayed by the structure of CdLi.5(N03)2 [L = l,4-Z7w(4-methylpyridyl)benzene]. Each window of each ID ladder-like net is penetrated by four other ladders at an inclined angle to the first (Fig. Ic), resulting in an overall 3D entanglenlent (ID 3D inclined interpenetration). Another possible topology of interpenetration. ID 3D parallel interpenetration, is yet to be observed. 

Another long-known example of 2D inclined interpenetration is the structure of trimesic acid (1,3,5-benzene-tricarboxylic acid). It contains hydrogen-bonded (6.3) sheets that interpenetrate such that each window of each sheet is penetrated by three other inclined sheets. It is also possible for more than two stacks of parallel sheets to show inclined interpenetration—the remarkable structure of Co2(azpy)3(N03)4-Me2CO-3H20 [a /73 =4,4 -azo/ zT-(pyridine)] contains four separate stacks of parallel (6,3) sheets that all interpenetrate at mutually inclined angles.Combinations of network and interpenetration topologies are also possible. Inclined interpenetration between (4,4) and (6.3) sheets has been reported,and... 

There is an instructive error in this paper which leads to an important safeguarding principle in making balances. Namely, when a sub-region of a process has been assumed to be uniform, balances that involve its properties must be taken over the whole of it. In simple situations there is little inclination to do otherwise, but in complex cases this may be the effect of a differential balance over another interpenetrating phase. See Aris for a full analysis [9]. We assume spherical particles of radius, R, and call the profile of concentration at time, a, c(r,a). If D is the diffusivity of the reactant and k the rate constant per unit volume of catalyst. 

Figure 4.36 1 D 2D inclined interpenetration (it is also possible for 1 D 2D interpenetration to occur when one-dimensional chains are parallel).

Two-dimensional sheets may interpenetrate in one of three ways, i.e. 2D 2D parallel, 2D->3D parallel and 2D 3D inclined. 2D 2D parallel interpenetration can only occur when the mean planes of the intertwined layers are coincidental i.e. the layers are not offset in the direction perpendicular to their... 

Twins occur, especially for lower molecular masses. For example, objects with six arms are common for 110 twinning in low mass polyethylene because (110) and (liO) faces are inclined at 67.5°, close to 60° (18). Moreover, laths are prone to develop with such a twin boundary along its center line (11,19) because of the accelerated growth provided by the notch at its tip, which aids molecular attachment. More exotic, three-dimensional twins are shown by a-polypropylene in quadrites (20) and by interpenetrating layers in polyethylene (21). 

The first aspect is that networks can interpenetrate such that their mean lines of propagation (or mean planes in the case of 2D nets) can either be aU parallel or be inclined at two or more angles to each other. The second aspect is that the interpenetration can lead to overall entanglements that are either of the same dimension as the individual nets or of higher dimensions. The latter case is sometimes referred to as polycatenation (as opposed to interpenetration) however, here we refer to both cases as interpenetration as they both clearly fall under the definition given above. 

Figure 4 Different interpenetration modes for ID nets (a) ID ID parallel interpenetration (b) ID 2D parallel interpenetration (c) ID 3D parallel interpenetration (d) ID 2D inclined interpenetration and (e) ID 3D inclined interpenetration.

Inclined interpenetration of ID nets cannot result in ID entanglement. Figure 4(d) shows ID -> 2D inclined interpenetration as observed for coordination polymers of 1-(l-imidazolyl)-4-(imidazol-l-ylmethyl)benzene. Similarly, ID - 3D inchned interpenetration (Figure 4e) has been observed for coordination polymers of another linear dipyridyl ligand, namely, l,4-bis(4-pyridyhnethyl) benzene. " ... 

Figure 9 Three topologically different ways for (4,4) sheets to interpenetrate in an inclined manner.

The other common way for 2D nets to interpenetrate is in an inclined manner. Since this must always produce a 3D entanglement, this mode can simply be referred to... 

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