Crosslinking randomly crosslinked chains

Small deformations of the polymers will not cause undue stretching of the randomly coiled chains between crosslinks. Therefore, the established theory of rubber elasticity [8, 23, 24, 25] is applicable if the strands are freely fluctuating. At temperatures well above their glass transition, the molecular strands are usually quite mobile. Under these premises the Young s modulus of the rubberlike polymer in thermal equilibrium is given by ... 

More definitive evidence of enzymatic attack was obtained with 1 1 copolymers of e-caprolactone and 6-valerolactone crosslinked with varying amounts of a dilactone (98,99). The use of a 1 1 mixture of comonomers suppressed crystallization and, together with the crosslinks, resulted in a low-modulus elastomer. Under in vitro conditions, random hydrolytic chain cleavage, measured by the change in tensile properties, occurred throughout the bulk of the samples at a rate comparable to that experienced by the other polyesters no weight loss was observed. However, when these elastomers were implanted in rabbits, the bulk hydrolytic process was accompanied by very rapid surface erosion. Weight loss was continuous, confined to the... 

Elastomers exhibit this behavior due to their unique, crosslinked structure (cf. Section 1.3.2.2). It has been found that as the temperatme of an elastomer increases, so does the elastic modulus. The elastic modulus is simply a measme of the resistance to the uncoiling of randomly oriented chains in an elastomer sample under stress. Application of a stress eventually tends to untangle the chains and align them in the direction of the stress, but an increase in temperatme will increase the thermal motion of the chains and make it harder to induce orientation. This leads to a higher elastic modulus. Under a constant force, some chain orientation will take place, but an increase in temperatme will stimulate a reversion to a randomly coiled conformation and the elastomer will contract. 

In the following, we will briefly outline the use of the link p.g.f. (l.p.g.f.) for the calculation of the gel point in /-functional polycondensation without and with cyclization including the f.s.s.e. In Chapter II, section 2.2 we will consider an application in connection with the number of elastically active network chains in random polycondensates or in a collection of randomly crosslinked chains. 

Since the crosslinking density a is the probability of any unit to be cross-linked, the number of additional crosslinked units on an, v-mcric chain, crosslinked to the first chain, is expected to be equal to a. multiplied by the number of remaining crosslinkable groups (.v— 1). Thus, the expected number of additional chains crosslinked to the. v-meric chain, which is crosslinked to the first randomly chosen chain, is a(s— 1). Averaging over all chain sizes will give the average expectance of additional chains v. 

An average expectance of additional chains v, which is greater than unity allows for a non-zero probability of the randomly selected crosslinked chain belonging to an infinitely large system [79,83]. This gives the critical value of crosslinking density ac corresponding to the gel point. 

One important feature of randomly crosslinked chains is that they can be highly strained and/or swollen they recover their initial shape when the stress is interrupted and/or after deswelling. Neither the dependence of the modulus of elasticity, E, upon the variable e nor that of the swelling ratio, Qm, have been exactly predicted, until now. Nevertheless, these two physical quantities as well as the rate %c are functions of the variable, e. 

Considering calibrated gels or randomly crosslinked chains, the effect of linkage of monomeric units on NMR is well detected in spite of the purely statistical definition of the segmental spacing between crosslinks in vulcanised chains. 

The results in Fig. 7 confirmed that the helical poly-L-glutamic acid is significantly stiffer than randomly coiled chain at all range of extension. In both cases, the F-E curves were finally ruptured at a high force of >1.8 nN due to the breakdown of the crosslinking system. 

The concentration of crosslink junctions in the network is also important if too low, flow will be possible if too high, the maximum attainable elongation will be decreased. From the point of view of theoretical analysis, the length of chain between crosslink points must be long enough to be described by random flight statistics. 

It must be crosslinkedor vulcanized. Crosslinking is the chemical joining together of polymer chains, usually by sulfur bonds at random positions, to make a three-dimensional network (see Figure A). 

Schematic of polymer chains randomly placed in space, with crosslinks also placed randomly, but frequently averaging every 5,000-10,000 g/mol along the chains.

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... 

The most investigated examples are to be formd in the precipitation of polyelectrolytes by metal ions. Here, networks are formed by the random crosslinking of linear polymer chains, and the theory requires some modification. The condition for the formation of an infinite network is that, on average, there must be more than two crosslinks per chain. Thus, the greater the length of a polymer chain the fewer crossUnks in the system as a whole are required. 

The theory of gelation (Flory, 1953,1974) has been summarized in Section 2.2.3. This theory regards gelation as the consequence of the random crosslinking of linear polymer chains to form an infinite three-dimensional network. The phenomenon is, of course, well illustrated by examples drawn from the gelation of polycarboxylic acids by metal ions. 

Theoretically, if each molecule in a polymer sample were to be linked to two of its neighbors, a single highly branched molecule would form that would encompass the whole sample. In practice, due to the statistical distribution of chain lengths and the random incorporation of crosslinks, the situation is far more complex. 

If we assume a random distribution of crosslinking events, the average number of crosslinks along the length of a chain is proportional to its length. Thus, we would expect a chain with... 

Crosslinked polyethylene consists of molecular chains that are linked at random points to form a network, as shown schematically in Fig. 18.2 f). The crosslinks can consist of carbon-carbon bonds, which directly link adjacent chains, or short bridging species, such as siloxanes, which may link two, three, or four chains. We often refer to these materials as XLPE. 

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