Structure of a Typical Network

A network is obtained by linking polymer chains together, and this linkage may be either physical or chemical. Physical linking can be obtained by (1) absorption of chains onto the surface of finely divided particulate fillers, (2) formation of small crystallites, (3) coalescence of ionic groups, or (4) coalescence 

The structure of a perfect network may be defined by two variables, the cycle rank and the average junction functionality 0. Cycle rank is defined as the number of chains that must be cut to reduce the network to a tree. The three other parameters used often in defining a network are (1) the number of network chains (chains between junctions) v, (2) the number of junctions jx, and (3) the molecular weight Me of chains between two junctions. They may be obtained from and 0 using the relations 

The cycle rank completely defines the connectivity of a network and is the only parameter that contributes to the elasticity of a network, as will be 

These physical cross-links are, in general, not permanent and may disappear on swelling or increase in temperature. The corresponding networks are referred to as physical or thermoreversible and are not considered in this chapter. The reader may refer to Burchard and Ross-Murphy [17-19] for further information on such materials. 

The cycle rank completely defines the connectivity of a network and is the only parameter that contributes to the elasticity of a network, as will be discussed further in the following section on elementary molecular theories. In several other studies, contributions from entanglements that are trapped during cross-linking are considered in addition to the chemical cross-links [23,24]. The trapped entanglement model is also discussed below. 

In a typical elastomer, the number of skeletal bonds in a network chain range from about 100 to 700 [25]. Networks with chains shorter than 100 bonds have 

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The structure of a typical feed-forward neural network. 

The various structural features of a typical network formed by peroxide vulcanization may be represented schematically as follows [2] ... 

Lack of steady flow of a liquid-bearing colloidal solution requires the existence of a space-filling, three-dimensional structure. As we might select a perfect crystal as a csuionical solid, or liquid argon as a prototypical liquid, we csui choose the covalently crosslinked network, without any entanglements, to represent the ideal gel state. Then an appropriate time scale for reversible gels would be the lifetime of a typical crosslink bond if subjected to conditions that would cause flow in a pure... 

Extensive studies on different rubber compounds (see, for example, Table 1 in [105]) yield Ec 0.05 to 0.15 eV per filler-filler bond [105,106], i.e., typical values for physical (van der Waals like) bonds. Similar values were obtained within an approach which assumes a hypothetical analogy between the structure of a statistical carbon black network and that of a Gaussian elastomeric (unfilled) polymer network [107]. As in the Kraus approach, the carbon black network scission process is assumed to be thermally activated. 

The formation of a polymer networks starts with an increase in molecular weight and formation of branched structures. At a typical extent of reaction, the gelation point is that point at which a network is first formed. The extent of reaction as well as the cross-linking density in radiation-induced cross-linking processes is determined by the radiation dose. The term dose means the quantity of radiation applied to or absorbed accidentally by a given volume or mass of sample. The absorbed dose is measured in Gray (Gy), 1 Gy = 1J kg-1. Therefore, the formation of a polymeric network needs a certain dose, the gelation dose Dg, which can be determined by sol-gel analysis. ... 

Precrosslinked" or "intramolecularly crosslinked" particles are micronetworks [1]. They represent structures intermediate between branched and macroscopically crosslinked systems. Their overall dimensions are still comparable with those of high molecular weight linear polymers, the internal structure of micronetworks (p-gels), however, resembles a typical network [2]. Synthesis is performed either in dilute solution or in a restricted reaction volume, e.g., in the micelles of an emulsion. Particle size and particle size distribution can be controlled by reaction conditions. Functional groups can be... 

On the other hand, if the cross-link density is low (the length of the chains between cross-links is large) and the mobility of the chains is high, the cross-linked material is called an elastomer. An example of a typical elastomer is cw-l,4-polyisoprene (natural rubber), which, by means of a cross-linking reaction with sulfur (vulcanization), gives rise to a network structure (see Fig. 1.4). 

TOCSY (Total Correlation Spectroscopy) is another important homonuclear 2D correlation experiment where correlations arise due to the presence of homonuclear scalar coupling.In the standard COSY experiment, crosspeaks appear for spins in which the scalar coupling occurs over typically two to four bonds. In the TOCSY experiment crosspeaks can appear for spins separated by many more bonds as long as they are part of a contiguous network of coupled spins. The correlations are effected by the application of a series of low-power rf pulses termed the spin-lock. The duration of the spin-lock period determines the extent to which the correlations are propagated through the spin system. The TOCSY experiment is a useful complement to the COSY methods for the elucidation of complex structures. 

Spectrum Simulation is a method for creating spectra from information about the chemical structure of a molecule, for which none exist this is typically supported by prediction technologies, such as artificial neural networks. 

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