In the case of the formulation of mixed resins for adhesives for which extensive formulation experience does not exist, the gel theory approach is also particularly useful. Le us examine, as an example, what would be the degree of conversion at the gel point of a resin based on the reaction of resorcinol (R) with acetaldehyde (A) and formaldehyde (F) in relative molar proportions of, respectively, R:A:F = 1:1:0.5. The two aldehydes can react and do react with resorcinol; while under the conditions used they are considered as not being able to react with each other (aldol condensation is indeed minimal under the conditions used to prepare adhesive resins). In short to avoid any gelling of our prereacted resin in the reactor, during manufacture, we want to know at what degree of conversion we can advance reaction of the resin without gelling it.
As the system is relatively complex and presents more than two reagents the simpler approach is to use the formula of Durand and Bruneau (Eq. (10)). This will tell us then that the functionality of resorcinol is 3; the functionality of the two aldehydes in the proportions given is 2 (they are both bifunctional, which simplifies matters), and thus fA = 3 and fB = 2, while r = (1 x 3)/(1 x 2 + 0.5 x 2) = 1, to yield according to Eq. (10) Pgel — 1/[1(3 — 1)(2 — 1)]1/2 = 0.707 so according to Flory, gel intervenes at 70.7% of the reagent having in fact reacted.
As we know that Flory’s and derived formulas such as Eq. (10) underestimate by approximately 10% the degree of conversion at the gel point one could also use the more exact but more complex Eqs. (18) and (19). In this case Eq. (19) is the one suitable to use. We will then have that pgel = [(1 + 1 + 0.5)/(1 x 3 + 1 x 2 + 0.5 x 2)] + 1/2(0.5/1)1/2 = 0.770. This indicates that the gel of the system intervenes when 77.0% of the reagents have in fact participated in the reaction, the latter formula yielding a precision of 99.5% while the previous one yields a precision of 91% only.
In conclusion, the use of the simpler polymer networking and gel theories constitutes a very useful approach to focus more rapidly and within narrower limits applied formulation research for any polycondensation adhesive resin. This allows much faster adhesive formulation than just the empirical scan