Tetrafunctional systems

Typical molecular weight distributions for the tetrafunctional system are depicted in Figure 5. In contrast to the monotonic w function predicted by the acyclic model ( ), our findings ihow that the weight fractions have a maximum at the trimer. The high proportion of cyclic trimer. 

Figure 5. Histogram of the weight fractions of x-mer versus x for the tetrafunctional system with n-50 and P -0.886 (symbols same as in Figure 3).

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.

The improved flame retardancy of TGEP-1, TGEP-2 may be due to the char-forming abihty of phosphorous present in the backbone of such epoxy matrices resulting in VO rating. The siloxane skeletal modified tetrafunctional systems, on the other hand, have also showed flame retardancy on a par with phosphorous-based epoxy systems due to their char-protecting nature. The lower surface energy of siloxane moiety may be responsible for enhanced flame retardancy compared to the sulphone and neat tetrafunctional epoxies. 

In Figure 6, the larger values of A b for systems 4 and 5 compared with the other systems illustrate the increased opportunities for intramolecular reaction in tetrafunctional compared with trifunctional systems. Further, the smaller values of b for system 5 compared with those for system 1, with the same value of v, probably indicated that equation(3) relatively undercounts the opportunities for intramolecular reaction for tetrafunctional as compared with trifunctional reactants, so that smaller values of b are required in compensation. System 3, based on aromatic diisocyanate, gives the largest values of b, characteristic of its stiffer chain structure. 

Figure 8. Part of a tetrafunctional network formed from an RA t and RBi polymerization corresponding to Mc°, the molar mass between junction points of the perfect network (a). Detail of the chain structure defining Mc° for HDl reacting with an OPPE, n is the number-average degree of polymerization of each arm with respect to oxypropylene units, (b). Part of the chain structure defining v, the number of bonds in the chain forming the smallest ring structure (C), for the reaction system in (b) (29). Reproduced, with permission, from Ref. 21. Copyright 1980, Stein-...

The deviations from Gaussian stress-strain behaviour for the tetrafunctional polyurethane networks of Figure 9 are qualitatively similar to these found for the trifunctional polyester networks (Z5), and the error bars on the data points for systems 4 and 5 in Figure 9 indicate the resulting uncertainties in Mc/Mc. It is clear that such uncetainties do not mask the increases in Mc/Mc with amount of pre-gel intramolecular reaction. 

Figure 5.7 Calculated dependence of the weight-average degree of polymerization of molecules, (P)w, and hard clusters, (Pc)w, on conversion in a stoichiometric Adh) + B2(h) + B2(s) system (h - hard, s - soft). The system corresponds to a mixture of short and hard chains crosslinked with a tetrafunctional crosslinking agent...

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). 

It is difficult to find crosslinking systems that are ideal in that all functional groups are of equal reactivity and intramolecular cyclization is negligible. The crosslinking of vinyl terminated poly(dimethylsiloxane) polymers with tri- and tetrafunctional silanes appears to be an exception. Thus the calculated and experimental pc values were 0.578 and 0.583, respectively, for the tetrafunctional silane and 0.708 and 0.703, respectively, for the trifunctional silane (with r — 0.999) [Valles and Macosko, 1979]. 

The ion couling reaction of bifunctional l c with tri- and tetrafunctional carboxylates was carried out to produce first the ion-exchange, pseudo-network, products crosslinked through the Coulombic interaction, which was found to remain soluble in a good solvent like THF. This unique feature of pseudo-network products allows one to observe the products by solution H NMR spectroscopy. The spectra of the ion-exchange products of l c with tri- and tetrafunctional carboxylates demonstrated the nearly quantitative ion-exchange reaction to occur for both systems. 

Let us consider an A2 + A4 chainwise polymerization e.g., a vinyl - divinyl system with af = 0.01 (a very small concentration of the crosslinker in order to keep ideal conditions), and q = 0.999. Figure 3.22 shows the fraction of tetrafunctional crosslinks, nc 4/[A4o], as a function of conversion, for two limiting values of ,. Termination by combination (E, = 1) increases the crosslink concentration with respect to termination by chain transfer or disproportionation (2, = 0). At full conversion, termination by combination leads... 

For epoxy systems, no exception was found to the rule expressed by the above relationships. There is only one eventual ambiguity, illustrated as follows let us consider the CRU of a system based on a difunctional epoxide (E) and a tetrafunctional amine D (NH2)2 ... 

The reaction of Eq. (151) indicates that the equilibrium in the system PbR4 vs Pb is shifted completely towards the side of the neso molecule, PbR4, and the most-branched building unit, tetrafunctional elemental lead. The existence of equilibria of the type of Eq. (151) is supported by the finding that hexaphenyldilead which has been tagged with radium D (a radioactive lead isotope) exchanges rapidly with tetraphenyllead (239). 

In other chemical systems, such as tetrafunctional epoxies, polyimides, phenolics, and polyesters, there have been few attempts 64,65) to establish quantitative relationships between chemical kinetics and dielectric properties. 

The resin cured with excess DICY (assuming DICY is tetrafunctional) is a single phase system while the resins cured with DICY with epoxy groups in excess are two-phase systems which exhibit two maxima in tan 8. Since the IR analysis shows that all NH and epoxy groups disappear, the main reaction is assumed to be the addition reaction of the epoxy groups to the NH groups. 

These do not, so far, constitute industrially important monomers. Nevertheless, they do have some technical importance which is documented by the number of published studies of their polymerization. Acetylenes yield chains with a conjugated system of double bonds with semiconducting properties. It is probably just this possibility of conjugation in the generated chain that prevents formation of three-dimensional structures. Acetylene as such is a potentially tetrafunctional monomer. 

Fig. 9a and b. TBA spectra for a series of isothermal cures showing changes in (a) the relative rigidity and (b) the logarithmic decrement vs. time. Gelation and vitrification are evident in the 80, 125 and 150 °C scans, but only vitrification is observed in the 200 and 250 °C scans. The system studied was a trifunctional epoxy resin, XD7342 [triglycidyl ether of tris(hydroxyphenyl)-methane, Dow Chemical Co.], cured with a tetrafunctional aromatic amine, DDS (diamin iphenyl sulfone, Aldrich Chemical Co.)... 

A comparison of Figs. 11 and 12 also serves to highlight the effect of functionality on cure and properties. The system of Fig. 11 is a trifunctional epoxy cured with a tetrafunctional aromatic amine, whereas the system of Fig. 12 is a difunctional epoxy cured with the same amine. As expected, the more highly functional system has the higher Tg, and shorter times to gelation the times to vitrification are also shorter. The difference in these transformation times arises from two factors ... 

For the nonlinear step growth case above, eiTg, the crosslink density must be related to p. A relevant model, based on calculating the probabilities of finite chains being formed, has been published For the reaction of A -1- 2B2 (e.g., tetra-functional amine -b difunctional epoxy), A4 is considered to be an effective cross-linking site if three or more of its arms lead out to the infinite network. The probability of finding an effective crosslink is related to one minus the probability of a randomly chosen A leading to the start of a finite chain, which in turn is related to the extent of reaction. Application of this procedure to the system of Fig. 15 has been presented in detail The more complicated reaction of a tetrafunctional amine with a trifunctional epoxy was also considered. ... 

The model was also applied to the reaction of a tetrafunctional amine with a trifunctional epoxy, denoted A4 + 4/3Bj, and was compared with available data (Fig. 18). An approximate value of k was obtained from the times to gelation. This model appears to provide a reasonable framework within which the vitrification process for nonlinear systems can be discussed. 

Because each monomer is potentially tetrafunctional, all sorts of partially hydrolyzed and partially condensed species are possible. For example, 10 distinct dimers may be formed. Many cyclic species can occur. Many of the species in solution are metastable with respect to anhydrous, amorphous Si02, and rearrangements occur with time (2). The complexity of this system means that the structure and growth of these polymers can be described only in a statistical and geometric fashion rather than by a more conventional description in terms of topologies (such as chains and cross-links) and molecular weights. The most useful and intuitive description of the structure of these polymers is in terms of fractal geometry. 

Such TTT diagrams have also been useful in describing the cure of polyimide systems, as shown in Palmese (1987), which shows the TTT diagram of a polyamicacid/polyimide system. The TTT diagram of a polycyanurate system is developed by Simon (1993) on the basis of FT-IR, DSC and torsional braid measurements. Kim et al (1993) developed a TTT diagram for a thermoset-thermoplastic blend, specifically a tetrafunctional epoxy-resin/poly(ether sulfone)/dicyandiamide thermoset-thermoplastic blend (Figure 2.9). 

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