Crosslink junction elastically active

Assumptions made in the derivation of these relationships are as follows, a) The fraction of the total number of junctions in the gel that contribute to the elasticity, i.e. the fraction of the number of elastically active crosslinks, is a function of concentration and not of temperature. This assumption is questionable, since the degree of intramolecular crosslinking will depend on the concentration, becoming smaller with increasing concentration. However, the variation in T with concentration is relatively small, so that the question of the strict validity of this assumption is rather irrelevant. 

The most important molecular parameter characteristic of a polymer network is the concentration of the elastic chains or that of the crosslinks connecting the macromolecules. An active junction is joined by at least three paths to the polymer network and an active chain is defined as one terminated by active junctions at both ends. There are several ways to express the extent of crosslinking (1) the concentration of the elastically active chains, r ei/Po, where v is the number of chains connecting two elastically active junctions and To is the volume of the dry network, (2) the molecular weight of the polymer chains between the junctions... 

Another important parameter is the crosslink functionality, /, which is the number of chains emanating from a network junction. Only junctions with functionality higher than 2 are elastically active. For perfect networks, i.e., cross-... 

The ideal network structure can be envisaged as a three-dimensional array of crosslink points, each crosslink point being connected to at least three other crosslink points via linear polymer segments, which are called elastically active network chains. In practice non-ideal network elements are also present, such as loops or dangling ends (Figure 16.1). Network density, or crosslink density, is expressed as the concentration of either the crosslink joints or the elastically active network chains (those chains that are part of the infinite structure and attached to crosslink junctions at both ends) per unity of volume of the unswollen material. 

Scanlan has suggested another criterion (282). An effective network junction point is a crosslink in which at least three of the four strands radiating from it lead independently to the network. A crosslink with only two strands anchored to the network simply continues an active strand a crosslink with only one anchored strand is part of a dangling end and can make no elastic contribution at equilibrium. An elastically effective strand is therefore one which joins two effective network junction points. Accordingly, the total number of active strands is simply one half the number of gel-anchored strands radiating from effective junction points ... 

The plateau value of the storage modulus G increases with crosslinker concentration, and the timescale for onset of gelation decreases with crosslinker concentration over the entire range of formulations studied (Figure 4). This is expected based on the enhanced capability to form active elastic junctions when additional crosslinker molecules are available for incorporation into growing polymer chains. This effect. 

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