Network structure randomly crosslinked

If we accept the model proposed for these mixed monofunctional/ difunctional systems, we can draw some conclusions about the network structure in polymers based on I alone. For example, Fig. 7 shows how the Tg varied with the relative crosslink density in the mixed systems. The abcissa represents the probability that a monomer chosen at random is linked to the network at both ends. At moderate degrees of crosslinking, the expected relationship between Tg and crosslink density is linear, so the data were approximated by a straight line (10). From the extrapolation in Fig. 7, one concludes that a typical bis-phthalonitrile cured to a Tg of 280 0 has a relative crosslink density of 0.5, or about 70% reaction of nitrile groups. 

Network structures are still determined by nodes and strands when long chains are crosslinked at random, but the segmental spacing between two consecutive crosslinks, along one chain, is not uniform in these systems which are currently described within the framework of bond percolation, considered within the mean field approximation. The percolation process is supposed to be developed on a Cayley tree [15, 16]. Polymer chains are considered as percolation units that will be linked to one another to form a gel. Chains bear chemical functions that can react with functions located on crosslinkers. The functionality of percolation units is determined by the mean number f of chemical functions per chain and the gelation (percolation) threshold is given by pc = (f-1)"1. The... 

It should be mentioned that recently Dossin and Graessley used equations developed by Pearson and Graessley to derive asymptotic expressions for v, and in randomly crosslinked networks where the sol fraction is negligible. In this case, nearly all crosslinks will have two or more paths leading to the network. Under these conditions the expressions for structural parameters become relatively simple Values for v, and of end-linked PDMS networks have often been calculated... 

Problem 3.20 The structure of a three-dimensional random network may be described quantitatively by two quantities the density of crosslinking designated by the fraction e of the total structural units engaged in crosslinkages and the fraction / of the total units which occurs as terminal units or free chain ends (i.e., which are coimected to the structure by only one bond). Alternative quantities, such as the number (mole) N of primary molecules and the number (mole) v of crosslinked units, in addition to M and Me, de ned above, are also used to characterize a random network structure. Relate N and v to these other quantities. 

For the q range studied, the values for the bimodal networks are found to be similar to unimodal networks. The fact that the correlation size in a swollen network is much lager than in the corresponding semi-dilute solution is usually taken to be an indication of inhomogeneities in the network structure. However, the similarity of the results from the unimodal and bimodal networks seems to suggest that in the absence of non-random crosslinking, the distribution of crosslink densities is not the dominant factor in determining spatial correlations in a swollen network at the level of the network mesh size. 

There are many equivalent definitions of a convenient one is in terms of the average resistance ft(m) between two randomly chosen points on a cluster of mass m. [The resistance of the network is obtained by placing a unit conductor along each bond, with connections at the cross-links. Accidental contacts, other than crosslinks, are not conducting hence ft only depends on the network structure of a cluster and not on its... 

Electron microscopy and X-ray diffraction experiments conducted on resilin-containing insect cuticle provided further support for resilin existing in the rubbery state as a crosslinked random network of protein chains. No fine structure was revealed by the electron microscopy experiments and zero crystallinity could be detected from the X-ray diffraction experiments. Furthermore, the diffraction... 

If we exclude the case of pre-existing order, we have so far considered a network as a random, but completely homogeneous structure. It should now be mentioned that the crosslinking process itself may give rise to "aggregation of network elements and therefore, in the swollen state, to significant fluctuations in segment density. 

When elastomer networks are formed, the segments of chains that are close to each other in space may be crosslinked, independently of their locations along the chain. Therefore, the network has a totally random structure in which the number of cross-linking points and their locations... 

Another important feature controlling the properties of polymeric systems is polymer architecture. Types of polymer architectures include linear, ring, star-branched, H-branched, comb, ladder, dendrimer, or randomly branched as sketched in Fig. 1.5. Random branching that leads to structures like Fig. 1.5(h) has particular industrial importance, for example in bottles and film for packaging. A high degree of crosslinking can lead to a macroscopic molecule, called a polymer network, sketched in Fig. 1.6. Randomly branched polymers and th formation of network polymers will be discussed in Chapter 6. The properties of networks that make them useful as soft solids (erasers, tires) will be discussed in Chapter 7. 

---