Degree of interpenetration

Since the power 7 is easier to detect in two than in three dimensions, the first MC study [62] sampled a two-dimensional MWD in a range of temperatures (that is, of (L)), so that a change in the degree of interpenetration should trigger a crossover from dilute to semi-dilute regime at some density 0. Evidently, indeed, from Fig. 4, the MWD follows the form of Eq. (16). At 0 one observes a power 7eff 1.300 0.005 which comes closely to the expected one. Above 0 one finds 7eff —> 1, and the distribution (11) becomes relevant. 

It may be noted that the statement made above—that the surface potential in the electrolyte phase does not depend on the orientation of the crystal face—is necessarily an assumption, as is the neglect of S s1- It is another example of separation of metal and electrolyte contributions to a property of the interface, which can only be done theoretically. In fact, a recent article29 has discussed the influence of the atomic structure of the metal surface for solid metals on the water dipoles of the compact layer. Different crystal faces can allow different degrees of interpenetration of species of the electrolyte and the metal surface layer. Nonuniformities in the directions parallel to the surface may be reflected in the results of capacitance measurements, as well as optical measurements. 

Most network structures are effective host structures for small guest molecules, often the solvent. Exceptions arise when there is a high degree of interpenetration, i.e. where two or more networks are entangled [7]. This type of host-guest behaviour is not intrinsic to the molecular components themselves, but occurs in cavities or clefts created by the assembly of the network structure. Mol-... 

Pseudo or semi-IPNs are combinations of linear with crosslinked polymers resulting in various degrees of interpenetration. (28-34)... 

From nickel onward, however, no boundary can be detected for iV = 28 e—an observation that is con-sistent with a relatively significant degree of interpenetration, for third-row atoms, between the 3d, 4, or Ap electrons and the 3 or 3p electrons, as shown by Politzer and Darker [71]. 

By far the largest class of interpenetrating structures involves diamond-related nets. 2-Fold interpenetration in the case of Zn(CN)2 has already been considered and many examples varying in the degree of interpenetration from 2-fold to 9-fold are referred to in the comprehensive review [1]. The mode of 9-fold interpe-... 

As a first approximation we postulate the existence of an equally sized hard core volume located in the center of each cylinder that defines the excluded volume per segment, according to the degree of interpenetration of neighboring cylinders. This simple construction includes complicated local intersegmental configurations, but it imposes a unique local orientation correlation of segments within the domains of a PE melt The shape of those impenetrable correlation cylinders is assumed also to be cylindrical. 

If the elastic chains solely connect first neighbor nodules, x2 = 1. If the proportion of chains linking crosslinks which are not first neighbors increases, the value of x2 also increases. The parameter x2 therefore characterizes the degree of interpenetration of the network chains, and it should be related to the proportion of entanglements present in the network. In practice, it can be expected that for networks in which the functionality of the crosslinks is low, entanglements are quite unlikely, and the value of x2 should stay close to unity. 

As we progress from 0D to networks the compounds become insoluble, but all are potentially capable of including guests depending on the lengths of the spacers, size of the nodes and degree of interpenetration. 

Figure 9.39 Schematic representations of metal 4,4 -bipyridyl porous networks. Lines represent the bipyridyl ligand except for vertical lines in (c), which represent Ag - Ag bonds (2.977 A long), and horizontal lines in (d) which represent Cu---Cu. The chemical formula, framework dimensionality, structure type, degree of interpenetration and pore aperture are listed under each representation. (Reproduced with permission from Reference 38).

The way in which SBU size affects interpenetration has been investigated systematically and theoretically for the terbium (III) SBU 9.21 with the extended dicarboxylate 9.20. These components crystallise from DMSO to give MOF-9, a doubly interpenetrated cubic network with significant void space filled by DMSO molecules. The question arose as to whether the observed doubly interpenetrated network is the maximum degree of interpenetration possible given the size of the SBU. The compound can be described... 

In some but not so rare cases, however, reactivity of macromonomers was found to be apparently reduced by the nature of their polymer chains. For example, p-vinylbenzyl- or methacrylate-ended PEO macromonomers, 26 (m=l) or 27b, were found to copolymerize with styrene (as A) in tetrahydrofuran with increasing difficulty (l/rA is reduced to one half) with increasing chain length of the PEO [41]. Since we are concerned with polymer-polymer reactions, as shown in Fig. 3, the results suggest that any thermodynamically repulsive interaction, which is usually observed between different, incompatible polymer chains, in this case PEO and PSt chains, may retard their approach and hence the reaction between their end groups, polystyryl radical and p-vinylbenzyl or methacrylate group. Such an incompatibility effect was discussed in terms of the degree of interpenetration and the interaction parameters between unlike polymers to support the observed reduction in the macromonomers copolymerization reactivity [31,40]. Similar observations of reduction of the copolymerization reactivity of macromonomers have recently been reported for the PEO macromonomers, 27a (m=ll) with styrene in benzene [42], 27b with acrylamide in water [43], and for poly(L-lactide), 28, with dimethyl acrylamide or N-vinylpyr-rolidone in dioxane [44]. 

While adding connecting chains is an effective way to reinforce polymer interfaces, there are situations where that solution may be impractical. An alternative option is to increase the average degree of interpenetration of the two immiscible polymers, effectively broadening the interfacial width. In this case, however, there is no longer a well-defined areal density of chains 2 or a well-defined interpenetration degree of polymerization N,but rather a distribution of ATs. 

Schnell at al. argue that the low degree of interpenetration necessary to activate the plastic deformation mechanisms could be indicative of the formation of a significant number of loops at the interface rather than chain ends, as shown schematically in Fig. 42. This argument would apply even more strongly for the results on PS-r-PVP/PS interfaces recently reported by Benkoski et al. [70] but would not apply to PMMA interfaces where the transition from regimes I and II occurs for much wider interfaces [69]. 

The classification is based on recognizing the dimensionality (ID, 2D, 3D), the connectivity of the nodes and the topology of the individual interpenetrating motifs, the degree of interpenetration and the possible modes of interpenetration. The last point, the less known, is concerned with the relative disposition of the individual motifs in the three-dimensional space and the consequent mutual... 

Class I (Translational) The individual nets are exclusively related by translations. The degree of interpenetration Z corresponds to the translational degree of interpenetration Zt. There are two distinct subclasses (la and lb) depending on the... 

Class II (Non-translational) The individual nets are related by means of space group symmetry elements, mainly inversion centers, but also proper rotational axes, screw axes and glide planes. The degree of interpenetration Z corresponds to the non-translational degree Zn, i.e. the order of the symmetry element that generates the interpenetrated array from the single net. In almost all cases Zn is 2, but a few examples with Zn up to 4 are known. 

It was observed that 57% of the structures fall in class I of translational interpenetration (that favors high degrees of interpenetration), while 40% belong to class II (non-translational) with degree of interpenetration equal to 2 for almost all (there are only 5 known structures with degree 3 or 4). Class III is rather unusual... 

It was recently proposed [65] that interpenetrating networks (called catenated therein) could be differentiated on the basis of the relative displacement of the subnets so we have interpenetration , when the frameworks are maximally displaced from each other, or interweaving when they are minimally displaced and exhibit many close contacts. However, a quantitative criterion to establish when the separation is maximal or minimal is still lacking, and difficult to find, especially with a degree of interpenetration exceeding 2. 

A survey of 301 interpenetrated structures in the CSD and ICSD was undertaken in 2004 which showed the distribution of structure types given in Figure 9.34. The 3D diamondoid net with its large adamantoid cavities proved to be by far the most common interpenetrated solid. For coordination polymers the highest degree of interpenetration is 10-fold and occurs for a silver(l) complex of... 

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