Trifunctional junctions

This estimated value of is twofold or more larger than the computed values of Gj ax in Table m. This difference could result if the sol fractions (Table I) are actually less than the true values, for reasons mentioned earlier, and if h is greater than zero. For PDMS elastomers containing trifunctional junctions, h has been reported (19) to be 0.95. 

FIGURE 2.2 Monomers can form different shapes of polymer, (a) Randomly coiled linear thermoplastics, e.g. PMMA. (b) Shghdy branched thermoplastics, e.g. PVAC. (c) Highly branched thermoplastics, e.g. polyurethane foam pre-polymer, (d) Cross-hnked polymers with trifunctional junctions, perhaps formed by reaction of (c), e.g. epoxy resin, (e) Cross-linked polymer with tetra-functional junctions, e.g. polyester casting resin. Source Brydson (1982). 

C. C. Han, H. Yu and their colleagues (23) have presented some new SANS data on end-linked trifunctional isoprene networks. These are shown in Figure 10. Those materials of low molecular weight between crosslinks exhibit greater chain deformation consistent with the thesis that the junction points are fixed. This is the reverse of that found by Beltzung et al. for siloxane networks. 

On the other hand, the parts of each crosslinking molecule between two adjacent branch points can be taken as short network chains. In this case the junctions are trifunctional (f = 3) and the chains have a bimodal distribution. The total number of network chains,, is threefold the number of former a,u-divinyl chains, because two short chains and one long chain proceed from each crosslink. Vj is also tabulated in Table II. 

Studies have been made of the elastic (time-independent) properties of single-phase polyurethane elastomers, including those prepared from a diisocyanate, a triol, and a diol, such as dihydroxy-terminated poly (propylene oxide) (1,2), and also from dihydroxy-terminated polymers and a triisocyanate (3,4,5). In this paper, equilibrium stress-strain data for three polyurethane elastomers, carefully prepared and studied some years ago (6), are presented along with their shear moduli. For two of these elastomers, primarily, consideration is given to the contributions to the modulus of elastically active chains and topological interactions between such chains. Toward this end, the concentration of active chains, vc, is calculated from the sol fraction and the initial formulation which consisted of a diisocyanate, a triol, a dihydroxy-terminated polyether, and a small amount of monohydroxy polyether. As all active junctions are trifunctional, their concentration always... 

Background. Consider that pairwise interactions between active network chains (13), commonly termed trapped entanglements, do not significantly affect the stress in a specimen deformed in simple tension or compression. Then, according to recent theory (16,17), the shear modulus for a network in which all junctions are trifunctional is given by an equation which can be written in the form (13) ... 

Data obtained by various investigators (13,14,18,19) indicate that trapped entanglements commonly contribute to the modulus. To represent the modulus, an equation has been used which, if all junctions are trifunctional, becomes ... 

Let Pxi be the probability that a chain originating in a trifunctional moiety terminates in the gel. For a trifunctional moiety to be an active junction, all three emanating chains must terminate in the gel, the probability of which is P3j. Thus, the concentration of active junctions is CtriolD Pxi and the concentration of active chains is (3/2)CtriolDP3j, where CtriolD denotes the mole/cm3 of trifunctional moieties in the network. 

The functionality of alkoxy groups at the silicon allows us to localize the probe in the polymer. Trifunctional compounds are located at the network junction of a crosslinked poly-dimethylsiloxane while bifunctional probe molecules are placed on the main chain during polymer formation. 

Experimental results on reactions forming tri- and tetrafunctional polyurethane and trifunctional polyester networks are discussed with particular consideration of intramolecular reaction and its effect on shear modulus of the networks formed at complete reaction. The amount of pre-gel intramolecular reaction is shown to be significant for non-linear polymerisations, even for reactions in bulk. Gel-points are delayed by an amount which depends on the dilution of a reaction system and the functionalities and chain structures of the reactants. Shear moduli are generally markedly lower than those expected for the perfect networks corresponding to the various reaction systems, and are shown empirically to be closely related to amounts of pre-gel intramolecular reaction. Deviations from Gaussian stress-strain behaviour are reported which relate to the low molar-mass of chains between junction points. 

Fig. 3.3 Multiplicity of the cross-link junctions in the polycondensation of trifunctional molecules.

Figures 10.21(a)-(c) shows how the phase behavior changes depending upon the relative strength of the association constant X and the excitation constant tj. All phase diagrams are calculated for trifunctional (/=3) low-molecular weight molecules (w = 1) with triple junctions k = 3). All-or-none excitation of the functional groups is assumed. In all three diagrams, solid lines show the binodal, broken lines the sol-gel transition, and the shaded areas are unstable regions.

For imperfect networks, the comparison of the ratio 2Ci/vRT with 1 — 2/q> is no longer possible because the number of effective chains v is not known, and became not all of the junctions have the same functionality. Nevertheless, 2Ci can be compared with the value of the phantom modulus, which is (v, — pj RT [see Eq. (4)], and also with (v — p) RT. The variation of the ratio 2Ci/(v, — p ) RT with M is reported in Fig. 8 and 9 for trifunctional and tetrafunctional PDMS networks, resp Aively. Here M is different from because an active chain can be formed by two or more chains bound with difunctional junctions. The constant 2Ci is always hi er than the phantom modulus and the conclusions are similar to those readied in Section 4.2. 

The usual one is to take into account only tte active chains and jum tions. The difunctional junctions are thus not iiKluded. Therefore the molecular wdght between crosslinks can be different from M and its distribution is unknown. Nevertheless one gains more knowledge about the functionality of the considered juiKtims, three in an imperfect trifunctional network, a mixture of three and four in a tetrafunctional one. The Flory parameter v. and the Graessley parameter h are not defined. One can take an average over the distribution of molecular weights between crosslinks and the different functionalities. 

Some authors consider four chains (as opposed to three chains) to emanate from a crosslink, regarding a trifunctional crosslink as merely a junction point. 

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