Chain-connected network

The purpose of the following treatment is to define the conditions under which indefinitely large chemical structures, or infinite networks, will occur. To this end we seek the answer to the question Under what conditions is there a finite probability that an element of the structure selected at random occurs as part of an infinite network In order to simplify the problem, any given molecule such as the one shown in Fig. 61 may be regarded as an assemblage of chains connected together through polyfunctional, or branch, units (trifunctional in... 

PSDVB copolymers and their ion exchange derivatives consist of a three dimensional four-connected network structure. Such networks may have a statistically isotropic structure that includes tetrahedral cells, such as the X" unit structure described by Flory (6). The four-connectedness results from the expected pairwise chain connecting function of... 

Figure 8. View showing the details of a hexagon A along with the copper atom belonging to a hexagon B, located near the center of the hexagon A. This view emphasizes the presence of Cu2A-Etrad+-Cu3B-Etrad+ chains connecting the networks A and B.

Fig. 24a and b. Schematic simplified representation of the basic difference between a regular a and irregular b network knots (1), chains connecting nearest-neighbor knots (2), pendant chains (3)... 

This means that the connectivity factor x2 — which was not taken into account — should be close to unity the vast majority of the elastic chains connect first neighbor crosslinks, as long as the average functionality does not exceed S or 6. For PDMS networks the fit is only good up to / = 4. For polystyrene networks the limiting functionality is attained for a proportion of DVB per living end of the order of 5. (Table 3). 

For networks in which the average crosslink functionality exceeds the above-mentioned values, the ratios of the slopes lead to functionalities which are obviously too high. The assumption according to which the connectivity factor x2 is equal to unity cannot hold any more. This means that a fraction of the network chains connect nodules which are not first neighbors. The probability for permanent entanglements to occur is increased. No quantitative treatment of the experimental data is possible in that case, because of the number of parameters to consider, none of them being accessible by independent experiments. 

LADDER POLYMER. An ordered molecular network of double-stranded chains connected by hydrogen or chemical honds located at regular inicrvals along the chains. Many complex proteins, including DNA. arc of this nature. 

Each a chain contains potential glutamine acceptor sites at 221, 237, 328, and 366, and donor sites at lysine 508, 539, 556, 580, and 601 (Greenberg et al., 2003 Matsuka et al., 1996). Since the aC domains associate even in the absence of crosslinking, these interactions probably bring acceptor and donor sites in proximity, facilitating the formation of the isopeptide bonds. These bonds create a covalendy connected network of aC domains, although litde is known of its structure. In addition, there are lesser amounts of 7 trimers, tetramers, and 07 complexes. Factor XIII polymorphisms can have effects on the structure and properties of the fibrin clot (Ariens et al., 2002). 

Schieber JD, Neergaard J, Gupta S (2003) A full-chain temporary network model with sliplinks, chain-length fluctuations, chain connectivity and chain stretching. J Rheol 47(l) 213-233... 

The stress in the network can then be expressed by the virial theorem, Eq. (6), where in the molecular theory, the set of particles considered is not all the atoms of the system but only the end atoms of each chain, and they are regarded as subject to the force in the chain connecting them. That is, the stress ty is then given by... 

The topological state of the system of rings or uncrossable chains connected into a network coincides with that of the initial state and remains without any... 

This means that each of the original /- 1 chains, connecting any network strand to the macroscopic network through a very long tree-like... 

An important network property is the cross-link density or concentration of effective junction points in the infinite network. An A/ unit chosen at random will act as an effective junction point if three or more of its arms lead out to the infinite network, or to the container walls. (If only one arm is infinite, this A/ unit will be just hanging firom the network if, on the other hand, two arms are infinite. A/ forms part of a chain connecting two effective junction points, but it itself is not an effective junction point Consider tetrafunctional At as an example of Ay. TTie probability that A4 is an effective crosslink of degree 4 is just... 

A network is formed by network chains (N number of net chains) which are connected in the cross-links (junction points). The functionality / of cross-links (number of chains connected in a junction point) depends on their chemical nature, e.g., on the cross-linker. In a perfect network each network chain starts in one junction point and ends in another one. A real network is imperfect, but it can be described by two quantities, the network cycle rank and the number of junction points p/. 

If the gel contains a large number of dangling chains connected at one end to the network, represents the average size of... 

Thus for times of or shorter, and only for these times, an assembly of mutually overlapping chains can act as a mechanically connected network. 

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