Networks with tetrafunctional

Thermodynamic Analysis. As reported previously, the storage modulus G of PDMS networks with tetrafunctional crosslinks is independent of frequency between 10 3 and 1 Hz (21). This behaviour which is entirely different from that of vulcanized natural rubber or synthetic polyisoprene networks, was attributed to the lack of entanglements, both trapped and untrapped, in these PDMS networks. Figure 4 shows that G of a network with comb-like crosslinks is also frequency independent within an error of 0.5%. For comparison, two curves for PDMS having tetrafunctional crosslinks are also shown. The flat curves imply that slower relaxations are highly unlikely. Hence a thermodynamic analysis of the G data below 1 Hz can be made as they equal equilibrium moduli. 

In Figure 6, these data are plotted versus the branching density z of crosslinking molecules. Gy./G is fairly independent of network microstructure. It covers a range of 0.24 to 0.32 as a result of statistical scattering, averaging to 0.28 as in case of the networks with tetrafunctional crosslinks. 

For an ideal network with tetrafunctional crosslink points, it can be shown... 

To form a cross-link network with tetrafunctional branch points, it is necessary to have one branch point and one cross-link bond per primary chain. With trifunctional branching, on the other hand, two branch points are required per primary molecule. 

The previous expression assumes a network with tetrafunctional crosslinking (i.e., no branching). 

To form a cross-link network with tetrafunctional branch points, it is... 

This expression assumes a network with tetrafunctional crosslinking (i.e., no branching). This technique is particularly useful for samples than do not swell isotropically due to residual stress from molding or oriented structure. 

In order to enable these fluctuations to occur, the network chains are assumed to be "phantom" in nature i.e. their material properties are dismissed and they act only to exert forces on the junctions to which they are attached. With common networks having tetrafunctional junctions, the results of the two approaches differ by a factor of two. Identical results are only obtained from both theories, when the functionality is infinite. From a practical viewpoint, however, a value of about 20 for f can already be equated to infinity because crosslink densities can hardly be obtained with an accuracy better than 10%. 

Concluding, we can state that the absolute values of the small-strain moduli, which are greater for networks having comblike crosslinks, than for those with tetrafunctional junctions, are understandable, if we assume that the fluctuations of junctions are restricted by the very short chains. The strain dependent measurements do not agree quantitatively with the recent theory, although the trends are in accordance. An exact correspondence... 

Curves 1 and 2, and 3 to 6 in Figure 1 refer, respectively, to HDI/POP triol and HDI/POP tetrol polymerisations with different values of V. Marked reductions in modulus occur even for bulk reaction systems, which give the points at the lowest values of Pj- q for the different systems. More inelastic chains are formed in trifunctional as compared with tetrafunctional networks for a given value of pp q (cf. curves 1 and 2 with 3 to 6. In addition, for a given functionality, as V decreases the proportion of inelastic loops increases. Similar results have been obtained for polyester-forming systems using POP triols and diacid chlorides(13). 

If entanglements acted like ordinary crosslinks (vN/2) per unit volume) the stored energy function would be given by the usual expression for tetrafunctional phantom networks with the spatial fluctuations of junctions suppressed ... 

The relative posiMons of the lines for the various systems can be related to M(.o(or v), f, and the chain structures of the reactants(1.2.9-12). The slopes of the lines show that the reduction in modulus with pre-gel intramolecular reaction is larger for trifunctional compared with tetrafunctional networks (c.f. systems 1 and 2 with 4 and 5), although higher values of p- Q obtain for tetrafunctional reaction systems (c.f. Figure 2 . 

In order to produce model networks with a more accurately known functionality, three- and tetrafunctional allyloxy derivatives of triazine (I) and (II),... 

Fig. la- . Schematic illustration of network structure a) for a polymer with tetrafunctional C—C bonds (orrom indicate crosslinks). 

Swelling experiments and stress-strain measurements are widely used to estimate the crosslinking density in liquid-crystalline networks [101,106-108], For ideal rubbers with tetrafunctional crosslinks, these techniques allow the evaluation of the number average molecular weight between crosslinks [104, 105]. 

A new, valuable type of experiment are computer simulations of network properties. Computer simulations are well established both in equilibrium and non-equilibrium physics of systems of linear chains and have been used for the study of networks and melts. The effect of the topological constraints on the stress-strain behaviour of tetrafunctional networks with a regular structure has been investigated by Elyashevich and Remeev using Monte Carlo methods to generate Marko-... 

Schematization of a random chain scission in a network with trifunctional (above) and tetrafunctional (below) nodes. 

A new and elegant solvent-free approach to main chain LCEs was found by Yang et al. [39] who, based on the work on linear LC polymers by Lub et al. [40 2], made use of the photo-induced addition of thiols and olefins (click-chemistry) to synthesize nematic polymer networks. Starting from a mixture of the mesogen, a tetrafunctional crosslinker and a photo-initiator networks with a around 170 °C were obtained by UV crossUnking (Scheme 8). 

Fig. 1. Percent gel and distribution of cross-link density between sol and gel versus the log of the total cross-link density for the cross polymerization of primary chains having a most probable distribution. Two curves representing networks with junction functionalities of 4 (solid) and 24 (dashed) are shown with arrows pointing to the left. In each case M 358,000. The other solid lines represent the gelation behavior of a tetrafunctional system and have arrows pointing to the right.

Effects of Junction Functionality. End linking of chains with linkers of a known functionality is used to control the structure in this way. Increasing the junction functionality decreases the fluctuation amplitudes of the junctions in the undeformed state. A network with suppressed junctions behaves close to an affine network under deformation. However, the affineness diminishes under increasing extension. Trifimctional and tetrafunctional PDMS networks prepared in this way have been used to test the molecular theories of rubber... 

In polymer networks, the region of space pervaded by a given chain is shared with many other chains and junctions. A tetrafunctional, statistically cross-linked cis-l,4-polyisoprene network, with a typical average molecular weight between junctions of 5000 g mol" contains of the order of 5 x 10 junctions cm"The characteristic ratio for the a s-l,4-polyisoprene chain is 5.0 and, according to equation (28), the radius of the volume occupied by such a chain will be 56 A. From... 

Table 2. Calculation of the ratio n/f of the total number of first neighbours over the number of topological first neighbours for dry tetrafunctional PS networks with different mesh sizes.

As pointed out in the first part of this work, tetrafunctionally crosslinked PDMS also shows some dependence of the energy part of the modulus on network density and on the measuring method, but the effects observed there, are much smaller than the great variation of /a with branching density in case of networks... 

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