Trifunctional gel

These three assumptions were used to calculate the expected neutron scattering from trifunctional gels labeled around the crosslinks by assuming that the gels were made up of trifunctionally connected triblock copolymers. For comparison, the expected scattering from the following infinite branched polymers, all made up of identical triblock copolymers, was also calculated. Each triblock copolymer was assumed to have deuterated ends of equal length. 

The six approximations for the trifunctional gel given below are for gels in which the loops essentially become larger and larger. In spite of the differences in the structure factors for the different approximations, calculations show that the final /(Q) versus Q plots obtained for all the approximations are virtually identical. 

Fig. 1. The right-hand side of equation 1 versus (Q Rgn for two 10% deuterium-labeled infinite branched copolymers and the trifunctional gel compared with their constituent triblock copolymer.

Based on results of NMR and of gel permeation chromatography studies, a simplified composition for the PGCBA that yielded the epoxide equivalent of 0.137 kg/mol was assumed. The molar fraction of tetra functional molecules was taken as v4 = 0.45 and of trifunctional molecules was taken as v3 = 0.55. 

An unusual method has been used to prepare a hyperbranched polyimide starting from two monomers a difunctional A2 and a trifunctional B3. The gel formation can be avoided with careful control of the polycondensation conditions (molar ratio, order of the monomer addition, and low concentration). The A2 and B3 monomers were respectively 6FDA and tris(4-aminophenyl)... 

First of all it is necessary to determine the branching coefficient a, w hich is defined as the probability that a given functional group of a branch unit leads via a chain of bifunctional units to another branch unit. In a polymer of the type shown in Fig. 61, a is the probability that an A group selected at random from one of the trifunctional units is connected to a chain the far end of which connects to another trifunctional unit. As will be shown later, both the location of the gel point and the course of the subsequent conversion of sol to gel are directly related to a. 

Fig. 70.—Weight fractions of various finite species and of gel in a simple trifunctional condensation as a function of a, which in this case equals the extent of reaction p. Curves have been calculated from Eqs. (36) and (45). ...

Gel Point and Shear Modulus. Trifunctional and tetrafunc-tional polyurethane(25,26,28) and trifunctional polyester net-works (32) have been studied. The gelation data for the reaction systems forming the polyurethane networks were those discussed with reference to Figure 6 and Table II. 

The broken curves in Figure 9 are the expected values of Mc/Mc for trifunctional and tetrafunctional networks, assuming that all the ring structures formed are of the smallest size (v bonds), and that only the ring structures formed pre-gel give elastically ineffective loops(29,32). They show that intramolecular... 

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. 

The reactants used to form the networks studied are generally of lower molar mass than those used by other workers to form perfect networks (e.g. (35)). However, the present results do indicate that very little pre-gel intramolecular reaction can have a marked effect on modulus. For example, for pr,c = 0.05, or ac = 0.58, with a trifunctional polyurethane-forming system of Me = 635g mol l, the modulus is reduced by a factor of five below that calculated on the basis of the small-strain(affine) behaviour of the perfect network. As a result, it is recommended that the effective absence of pre-gel intramolecular reaction in endlinking reactions to form perfect networks be confirmed by experiment rather than be assumed. 

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 sol-gel synthesis of siloxane-based hybrid organic-inorganic implants usually involves di- or trifunctional organosilanes co-condensed with metal alkoxides, mainly Si(OR)4 and Ti(OR)4. As we will see in this section, the incorporation of Ca salts is a common strategy to provide bioactivity at the systems. Each of these components has specific roles that will be reviewed and discussed. 

Fig. 12.12 29Si CP-MAS NMR spectra of star gels obtained from Star A and Star B precursors. Trifunctional silicon centers were named with the conventional T notation, where T refers to (SiO) R Si(OR)3 units and n to the number of bridging oxygen atoms surrounding the central silicon atom. In both BSC materials, the T2, T1 and T° relative contribution was...

Thus, a semilogarithmic plot of the gel time as a function of 1/T should be linear, with the slope corresponding to the apparent activation energy. We have determined the gel times for a temperature range of 25°-50° C for a thiol-ene system consisting of stoichiometrically equivalent amounts of a trifunctional thiol, trimethylolpropane tris(2-mercaptoacetate), and a trifiinctional allyl monomer, triallyl isocyanurate. In this system, we also added 0.31% by weight of hydroquinone, to prevent premature polymerization, and 1.0% by weight of a commercial photoinitiator, Esacure TZT. 

Telechelic polymers usually bear monofunctional groups at each of their extremities. However, sometimes each end-group is bifunctional, such as in a, co-bis-unsaturated telechelics, or trifunctional as in a, co-bis(trialkoxysilyl) telechelics wherein they participate in crosslinking by the sol-gel reactions (hydrolysis and condensation of alkoxysilane groups). 

In a wider sense, functionality distribution also means combination of reactive groups of one kind (for instance, hydroxy, or carboxyl, or isocyanate groups) of higher and lower reactivity in one precursor molecule. By this combination, the network build-up can be effectively controlled. For instance, one less reactive A group out of three in a trifunctional monomer in a RA3 + R B2 system promotes chain extension in contrast to branching and shifts the gel point to higher values [30],... 

Wirth, M.J. and Fatunmbi, H.O., Horizontal polymerization of mixed trifunctional silanes on silica. 2. Application to chromatographic silica-gel. Anal. Chem., 65, 822, 1993. 

It is shown that model, end-linked networks cannot be perfect networks. Simply from the mechanism of formation, post-gel intramolecular reaction must occur and some of this leads to the formation of inelastic loops. Data on the small-strain, shear moduli of trifunctional and tetrafunctional polyurethane networks from polyols of various molar masses, and the extents of reaction at gelation occurring during their formation are considered in more detail than hitherto. The networks, prepared in bulk and at various dilutions in solvent, show extents of reaction at gelation which indicate pre-gel intramolecular reaction and small-strain moduli which are lower than those expected for perfect network structures. From the systematic variations of moduli and gel points with dilution of preparation, it is deduced that the networks follow affine behaviour at small strains and that even in the limit of no pre-gel intramolecular reaction, the occurrence of post-gel intramolecular reaction means that network defects still occur. In addition, from the variation of defects with polyol molar mass it is demonstrated that defects will still persist in the limit of infinite molar mass. In this limit, theoretical arguments are used to define the minimal significant structures which must be considered for the definition of the properties and structures of real networks. 

Fig. 2-18 Weight fractions of various finite species and of gel in a trifunctional polymerization where a = p. After Flory [1946] (by permission of American Chemical Society, Washington, DC).

Fig. 5. Interrelation between critical concentrations of crosslink forming (a) and ring forming (a) functionalities at the gel point calculated on the basis of random flight statistics for trifunctional polycondensation (/ = 3) and different values of parameters A and 91 [Gordon and Scantleburry (72)]...

Adequate mixing has also to be provided for. Upon reaction, the polymer solution gels, and it can be expected that the precursor chains are converted into elastic chains, whereas the crosslinks should exhibit the functionality of the electrophilic reagent15,16. Suitable electrophilic reagents are tris(allyloxy)s-triazine(trifunctional) and a similar tetrafunctional compound. Plurifunctional isocyanates have also been used successfully for such syntheses17. ... 

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