Лако-красочные материалы — производство

These methods generate structures by random combinations of reacting functional groups. This approach is thorough and the results are good when dealing with equilibrium — controlled reactions. The results are often a good approximation in kinetic-controlled reactions. Most of the formaldehyde-based polycondensations are equilibrium-controlled reactions, this being particularly true for urea-formaldehyde, melamine-urea — formaldehyde, phenol-formaldehyde and phenol-resorcinol-formaldehyde adhesive resins. Statistical methods are then ideal to describe these adhesive systems at the moment of gel formation and during formation of the hardened network.

Among the statistical method dealing with polymer networking and gelation in the field of polycondensation must be considered:

(1) The gel theory of Carothers [4] in which the critical degree of conversion at the gel point (pgel) is defined as pgel = 2/f, with f being the average functionality of the monomers in the system.

(2) The probabilistic gel theory of Flory [5]-Stockmayer [6,7] in which pgel is defined through the coefficient of branching a = 1/(f — 1). In this theory f is taken as the functionality of the monomer of greater functionality. The main expression of this theory is the equation a = rp2p/[1 — rp2(1 — p)] where p is both the degree of conversion and the probability that a certain reactive group type has in fact reacted, p is the proportion of such a reactive group type belonging to branching units, and r is the ratio of the types of reactive groups of the two monomers participating in the polycondensation.

(3) The cascade process theory of Gordon [8,9] based on more complex functions than the two preceding ones but also offering some further advantages over them.

(4) The Miller-Macosko [10] recursive method.

(5) The stochastic graphes theory of Bruneau [11] which is a more complete theory but very complex and complicated to use.

Even more complex theories can be found in the review literature [2,3]. Of the above theories the first two are of such a simplicity to be constantly used and the third and fourth
ones are also used sometimes. They all suffer from some drawback: the Carothers theory, for instance, overestimates the numerical value of pgel while Flory’s theory underestimates it, but they are nonetheless extremely useful in solving applied problems. Furthermore, they do not describe what happens in the system between reaching the gel point and complete hardening of the network.

Percolation is another technique that is also used for structure growth simulation. Percolation techniques are only statistical methods of a slightly differently nuanced approach, and they appear not to be very suitable general methods to correlate structure and structure growth parameters but seem to be useful in examining structure growth near the gel point.