Crosslinking points

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. 

The next step in the development of a model is to postulate a perfect network. By definition, a perfect network has no free chain ends. An actual network will contain dangling ends, but it is easier to begin with the perfect case and subsequently correct it to a more realistic picture. We define v as the number of subchains contained in this perfect network, a subchain being the portion of chain between the crosslink points. The molecular weight and degree of polymerization of the chain between crosslinks are defined to be Mj, and n, respectively. Note that these same symbols were used in the last chapter with different definitions. 

The degree of polymerization of the subchain is n. If the degree of polymerization of the molecule as a whole is n, then there are n/n subchains per molecule. We symbolize the number of subchains per molecule as N. Other properties of the subchain-which, incidentally, should not be confused with the chains between crosslink points in elastomers-will also have the subscript s as they emerge. 

The terminal groups of a dendrimer are large in number and can have functionalities capable of chemical reactions. If the terminal reactive terminal groups were near the periphery, they would be readily accessible for attachment to surfaces or to reagents. Block copolymers or networks with dendrimers as crosslink points would benefit from having them on the outside. 

This is one of the reasons we decided to prepare oligomers containing styrene-type functional groups. Styrene s thermal initiation mechanism is fairly well understood, and the same is true for the kinetics and thermodynamics of its radical polymerization. In addition, thermal and radical polymerization of styrene is much faster than any of the other previous classes of reactive groups and at the same time, the microstructure of the crosslinking points is known. 

The problem of the relationship between reaction conditions and structure of copolymers obtained from multimethacrylate and styrene as well as from multimethacrylate and acrylic acid has been discussed. The method used was similar to the method described above. A description of the structure of these copolymers could be based on the following consideration. Because of random initiation and termination processes as well as a possibility of partial propagation across the template, we can expect that the product obtained contains unreacted double bonds and crosslinking points. The general structure of such macromolecule can be illustrated by Figure 5.1. 

Using labeled initiator and radiometric analysis, the number of initiator fragments from the number of end-groups, R, can be evaluated and the number of crosslinking points can be calculated. The number of unreacted double bonds can be found by the bromometric method. On the basis of such analysis, we can find the percentage of units in the multimonomer which had reacted according to template mechanism. The results of the calculations for two examined systems are presented in Tables 5.3 and 5.4... 

Fig. 1. Schematic representation of gels in collapsed and swollen states. The solid lines and open circles denote polymer chains and crosslinking points, respectively...

Fig. 23. Plot of the dipolar broadening parameter AG (left scale) and its relation to the square root of rigid lattice second moment, AM2 = 15 kHz (right scale), for polystyrene networks crosslinked with DVB (solid symbols) and EDM (open symbols) swollen to equilibrium, vs l/n, the reciprocal nominal number of C—C bonds between crosslinks points. Solvents CC14 ( ), CDC13 (A),...

An example for the polymer network characterization by the 13C CP MAS NMR is shown in Fig. 35. The chemical structure of the cured polystyrylpyridine resins (PSP), synthesized from terephthalic aldehyde and collidine (2,4,6-trimethylpyridine), is determined from CP-MAS spectra by comparison with the solution state spectra of the model compounds and supported by selective DD observations. The CH and CH2 of the crosslinking points, as deduced from the model BP2, give rise to a composite line at about 45 ppm the assignment of other signals is indicated in the figure 239). 

At the end of the ft peak, the entropies (Table 10) are smaller in the DMH-MDA95 and 60 systems than in the HMDA network, indicating that cooperativity is likely to have a larger spatial extent when it proceeds from the crosslink points. It thus appears that the secondary diamines lead to an enhancement of the mobility and a development of a cooperativity that is more limited than the one observed in densely crosslinked networks. 

As a matter of fact, the onset of mobility, as observed from the t /i and Tip (13C) measurements performed on the CHOH-CH2-O and CH2-N groups, occurs in the upper part of this range. This result is consistent with previous assignment of the p transition to motional processes of the HPE sequence. Moreover, the parallel behaviour of the CHOH - CH2 - O and CH2 - N groups, observed in NMR, shows that the crosslink points are involved in the motional processes. However, the temperature of the NMR onset of mobility indicates that the sensitivity of the NMR experiments probes the cooperative motions rather than the isolated ones. This conclusion is in agreement with results obtained by 2H NMR [67]. 

The ft transition clearly originates from motions of the hydroxypropyl ether sequence, but the crosslink points are also involved. Whereas the motions involved in the low-temperature part of the ft transition are quite isolated motions of HPE units, when temperature increases a cooperativity appears directly with the mobility of the crosslinks and, indirectly, with the jr-flip motions of the DGEBA phenyl rings. 

In order to visualise the antiplasticiser placement within the epoxy network, but not its motion, molecular modelling was performed without including crosslink points. The result, presented in Fig. 104, illustrates one plausible (but not definitive) structure in Fig. 104 only the two chains directly above and below the antiplasticiser are shown. 

The NMR experiments clearly show a different effect of the antiplasticiser on the mobility of either the crosslink points (CH2 - N) or the hydroxypropyl ether sequence. Indeed, whereas these two groups have similar mobility in pure epoxy networks, the mobility of the crosslink points is hindered by the antiplasticiser, whereas only a slight slowing down occurs for the HPE units. Furthermore, there is no difference in mobility between the HPE sequence in the epoxy network and the one in the antiplasticiser molecule. 

In the case of epoxy networks with a secondary diamine, like DMHMDA, the network architecture is such that flexible aliphatic sequences are present as chain extenders between the crosslink points. In such architectures, the motions of the HPE units can develop towards other HPE sequences (either along the chain or spatially neighbouring) without involving the crosslink points in their cooperativity. Thus, with these systems a different nature of cooperativity exists compared to the other network architectures. The introduction of an antiplasticiser in such a local packing does not affect the cooperativity as much as with the densely crosslinked architecture, for the crosslinks are not so much involved. Once more, it is important to point out that the flexible nature of the aliphatic amines does not matter since the same behaviours are observed for fully aromatic systems with identical architecture [68]. 

In the absence of pending groups or antiplasticisers, the motions of the hydroxypropyl ether units in the high-temperature part of the transition force motions of the crosslink points that are spatial neighbours of the moving HPE sequence. A crude estimate leads to an extent of cooperativity at high temperatures reaching more than six crosslink points in densely crosslinked networks. 

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