Modeling of melamine formaldehyde polymerization. II. Development of a simpler model

Abstract

SynopsisThe kinetic modeling of melamine-formaldehyde polymerization presents a relatively formidable mathematical challenge because of the simultaneous presence of several types of deviations from Flory's equal reactivity hypothesis. A molecule of melamine has six reactive amide hydrogens, which can react with the -CH,OH groups of formaldehyde in solution. The reactivity of the secondary hydrogens on the melamine is about 61% of that of the primary hydrogens (induced asymmetry). There is a shielding effect present, i.e., the reactivity of the hydrogens near the outside of a multiringed polymer molecule is higher than that of the hydrogens inside the coiled molecules. Two bound -CH,OH groups on the polymer molecules can selfcondense to give methylene linkages, the reactivity depending upon the location of the two groups. And, to confound modeling efforts still further, all these reactions are reversible. An earlier attempt at modeling this system considered the reactions between 36 "basic" species. This model was far too detailed and failed to account for the reverse reactions.In the present study, a simpler model has been proposed which involves fewer "basic" species. An improved model for intramolecular reactions is also developed. Several important characteristics of the polymerization have been obtained as a function of time. F&sults from this model have been compared with those obtained from the earlier model, and also compared with the short-time experimental results. The present model can be extended to account for the reverse reactions quite easily.

Methylolation of melamine with incipient condensation. II. Mathematical modeling

“…Consider the detailed kinetics of Table IV. Equations (9)(10)(11)(12)(13)(14) are equivalent to eqs. (1)(2)(3)(4)(5)(6), except for the fact that any M-based molecule is characterized by P A 0 ;A 1 ;A 2 ;M 0 ;E 0 ; where A 0 , A 1 , and A 2 are the number of primary, secondary, and tertiary amines [ANH 2 , ANHCH 2 OH, and AN(CH 2 OH) 2 , respectively]; and M 0 and E 0 are the number of unsubstituted methylene and ether bridges (ANHCH 2 NHA and ANHCH 2 OCH 2 NHA, respectively).…”

“…In the first part of this series,10 five reactions between F and M were carried out, and the main results are presented further below. Gupta11 employed 10 “chemical entities” for modeling a batch reaction between M and F. The models assume 12 irreversible methylolations, 13 irreversible methylene bridge formations, and only five kinetic constants. The model produces a gross estimate of the average number of rings per molecule 11.…”

“…Gupta11 employed 10 “chemical entities” for modeling a batch reaction between M and F. The models assume 12 irreversible methylolations, 13 irreversible methylene bridge formations, and only five kinetic constants. The model produces a gross estimate of the average number of rings per molecule 11. Kumar and Chandra12 extended the model by Gupta,11 by assuming either irreversible methylolations with reversible condensations or reversible methylolations with irreversible condensations; and adjusted the five associated kinetic constants on the basis of the mentioned measurements by Tomita 8.…”

“…The model produces a gross estimate of the average number of rings per molecule 11. Kumar and Chandra12 extended the model by Gupta,11 by assuming either irreversible methylolations with reversible condensations or reversible methylolations with irreversible condensations; and adjusted the five associated kinetic constants on the basis of the mentioned measurements by Tomita 8. Kumar and Katiyar13 readjusted the models by Kumar and Chandra12 on the basis of new measurements from a single variable, the total formaldehyde concentration.…”