Network chains isolated

The above analysis was based upon a consideration of deviations from Gaussian behaviour of isolated chains. In reality we are concerned with network chains. This introduces a restriction on the conformational... 

The orientation of the swelling agent (solvent or free chains) has to be taken into account in the analysis of the stress-optical behaviour of swollen networks. Specifically, the segment polarisability (relative to the network chains or to the diluent chains), as currently derived from stress-optical coefficients [33], may not be representative of intrinsic properties of isolated chains. Short-range orientational interactions between the probe molecules and network chains (and between the chains of the matrix itself) must be considered in the interpretation of opticoelastic properties of swollen (and dry) rubbers [67]. 

Epoxy networks may be expected to differ from typical elastomer networks as a consequence of their much higher crosslink density. However, the same microstructural features which influence the properties of elastomers also exist in epoxy networks. These include the number average molecular weight and distribution of network chains, the extent of chain branching, the concentration of trapped entanglements, and the soluble fraction (i.e., molecular species not attached to the network). These parameters are typically difficult to isolate and control in epoxy systems. Recently, however, the development of accurate network formation theories, and the use of unique systems, have resulted in the synthesis of epoxies with specifically controlled microstructures Structure-property studies on these materials are just starting to provide meaningful quantitative information, and some of these will be discussed in this chapter. 

The parameter rl r, sometimes referred to as the front factor, can be regarded as the average deviation of the network chains from the dimensions they would assume if they were isolated and free from all constraints. For an ideal elastomer network, the front factor is unity. 

One way to specify molecular size is by the length of the end-to-end vector r (Fig. 3.6) that runs from the start to the end of an isolated chain, or between the crosslinks at the end of a network chain. The molecule is assumed to be unstressed, so its equilibrium shape has end-to-end vector tq. The average length of to will be calculated for a polymer with a C—C single bond backbone of a particular molecular weight. The average is over a large number of similar chains, and over a period of time. 

Fig. 5 FTIR left) and NMR right) spectra of HM PAAm network chains (P-12 and P-23) together with spectra of unmodified PAAm. P-12 and P-23 denote the polymers isolated from hydrogels with Ah= 12 and 23, respectively. The inset to the figure shows the structure of HM PAAm. The peaks denoted by A and B in NMR spectra arise due to the protons indicated in the inset. From [34] with permission from Elsevier...

When the dominant interaction between the solvent and network chains is a steric restriction, the movement of the solvent in a homogeneous gel can be explained by the fiee volume model. By focusing on an isolated solvent molecule, its difhision coefhcient is expressed by Eq. (1). The friction coefficient C can be expressed by the change of the volume ratio / as. 

These orientational correlations also play a major role in the orientation process of crosslinked chains. According to the results reported in Fig. 5, it appears clear that most of the orientational anisotropy as manifested by the doublet structure in the H-NMR line is attributed to interchain effects rather than the conventional end-to-end stretching of isolated chains. Indeed, as it seems reasonable to assume that both contributions are operative in elastic network chains we would have anticipated much larger splittings for such chains but this is not borne out by the experiments. From that point of view both kinds of chains, crosslinked and uncrosslinked, appear to be locally indistinguishable. 

Since, in contrast to experiment, the simulation knows in detail what the connectivity looks hke, how long the strands are, and how the network loops are distributed, one can attribute this behavior to the non-crossability of the chains. Actually, one can even go further by allowing the chains to cross each other but still keep the excluded volume. Such a technical trick, which is only possible in simulations, allows one to isolate the effect of entanglement and non-crossability in such a case. As one would expect, if one allows chains to cross through each other one recovers the so-called phantom network result. 

The scaling analysis, mentioned in Sec. IIIB, predicts that one should observe a different kind of distribution in the dilute regime for chains which are smaller than the blob size [32] and thus behave essentially as isolated chains. These chains, which are fully swollen and may slip through the network made up from the chains of average size (L) without being seriously... 

Some metahrich silicides have isolated Si atoms and these occur either in typical metallike structures or in more polar structures. With increasing Si content, there is an increasing tendency to catenate into i.solated Si2 or SU, or into chains, layers or 3D networks of Si atoms. Examples are in Table 9.3 and further structural details are in refs. 24, 26 and 27. 

Figure 1. Scheme of the formation of B — B bonds in binary metal borides B(0), borides with isolated B atoms 1b(2), borides with one-dimensional infinite B chains, each B atom having two nearest-B-neighbor atoms iB(3), borides with infinite two-dimensional B nets (three B neighbors for each B atom) formation of a three-dimensional B network (more than three nearest-neighbor B atoms for each B atom). 

It is helpful in the discussion to describe silicate structures using the Q nomenclature, where Q represents [SiOJ tetrahedra and the superscript n the number of Q units in the second coordination sphere. Thus, isolated [SiO ] " are represented as Q and those fully connected to other Q units as Q. In general, minerals based on Q , Q and units are decomposed by acids. Such minerals are those containing isolated silicate ions, the orthosilicates, SiO (Q ) the pyrosilicates, Si O " (Q ) ring and chain silicates, (SiOg) (Q ). Certain sheet and three-dimensional silicates can also yield gels with acids if they contain sites vulnerable to acid attack. This occurs with aluminosilicates provided the Al/Si ratio is at least 2 3 when attack occurs at A1 sites, with scission of the network (Murata, 1943). 

If we were to have an isolated polymer chain with a single nuclear spin attached to each segment (the marked chain) crosslinked into an unmarked network, the second moment of the NMR line of that spin species would carry information relating to the separation of chain segments, and to their relative orientation with respect to the field direction. If the network were to be subjected to a bulk deformation, these geometrical parameters would be altered, and hence we would expect a corresponding change in the value of the experimentally measured... 

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