Irreversible Polycondensation Kinetics

Monomers bearing functional groups such as -OH, -COOH, -NH2, -NCO, etc., undergo step polymerization. 

Monomers with carbon-carbon unsaturation undergo polymerization when an active center is formed. 

The growth of polymer molecules proceeds by a stepwise intermolecular reaction (at a relatively slow rate), normally with the elimination of small molecules as by-products of condensation, such as H2O, HCl, NH3, etc., in each step. The molecule never stops growing during polymerization. 

Each polymer molecule/chain increases in size at a rapid rate once its growth has been started by formation of an active center. When the macromolecule stops growing (due to termination reaction) it can generally not react with more monomers (barring side reactions). 

Monomer units can react with each other or with polymers of any size. Growth occurs in a series of fits and starts as the reactive species of a monomer or polymer encounters other species with which it can form a link. This can occur even in the absence of an added catalyst 

For the usual polyesteri cation, i, i, and 3 are large compared to ki. So when the reaction is run under nonequilibrium conditions by continuous removal of the by-product water, the polymerization rate can be considered to be synonymous with the rate of the forward reaction in Eq. (5.5) (Moore and Pearson, 1981)  

Equation (5.10) leads to two distinct kinetic situations depending on the source of H, that is, on whether or not a strong acid such as sulfuric acid or p-toluene sulfonic acid is externally added as a catalyst. The former is known as catalyzed polyesteri cation and the latter as uncatalyzed or self-catalyzed polyesteri cation (Odian, 1991). 

In uncatalyzed or self-catalyzed polyesteri cation, the diaeid monomer acts as its own catalyst for the esteri cation reaction. Assuming then that [H ] is proportional to [COOH], Eq. (5.10) can be written (Hory, 1953) as 

Eor equimolar initial concentrations of the diacid and diol, [COOH] = [OH] = C and Eq. (5.11) may then be simpli ed (Ghosh, 1990 Odian, 1991) to 

It is convenient here and for many other purposes as well to introduce a parameter p, called the extent of reaction (Ghosh, 1990 Odian, 1991), which represents the fraction of functional groups initially present that have undergone reaction at time t, that is. 

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Fig. 1. The dependence of weight fraction of gel on conversion of functional groups A under irreversible polycondensation of monomer SA3 described by the simplified FSSE model with kinetic parameters K k k0 and K2=k2/k0. The curves are depicted proceeding from the results of calculations at values of these parameters equal to kx=1, k2=0.1 (a), and kx=1, 2=10 (b)...

THE DESCRIPTION OE POLYCONDENSATION KINETICS WITHIN THE FRAMEWORKS OF IRREVERSIBLE AGGREGATION MODELS... 

Kozlov, G. V Burya, A. I. Temiraev, K. B. Mikitaev, A. K. Chigvintseva, O. P. The description of low-temperature polycondensation kinetics within the frameworks of irreversible aggregation models and fractal analysis. Problems of Chemistry and Chemical Technology, 1998, (3), 26-29. 

For irreversible polycondensations, recent studies by Kricheldorf [24, 25] using MALDI mass spectroscopy have in several circumstances detected quite an appreciable concentration of ring molecules. Unfortunately, dependence of ionization and thus of instrumental response factor of polymer molecules on the nature of the end groups [26] prevents a quantitative exploration of those findings. But it can be concluded that extension of kinetic modeling in order to take into account the presence of rings is more important than was previously acknowledged. 

The kinetics has been studied by Enikolopyan et al. [242] and Gao [243], among others. Branching formation occurs to a low extent and can usually be neglected the reaction can be described as a linear irreversible polycondensation AXA + BYC, with A = -OH, B = -Cl, and C = epoxide (ECH and oligomers have different reactivities). 

Hence, the performed above analysis has shown that different solvents using in low-temperature nonequilibriiun polycondensation process can result not only in symthesized polymer quantitative characteristics change, but also in reaction mechanism and polymer chain structure change. This effect is comparable with the observed one at the same polymer receiving by methods of equilibrium and nonequilibrium polycondensation. Let us note, that the fractal analysis and irreversible aggregation models allow in principle to predict symthesized polymer properties as a function of a solvent, used in synthesis process. The stated above results confirm Al-exandrowicz s conclusion [134] about the fact that kinetics of branched polymers formation effects on their topological structures distribution and macromolecules mean shape. 

With regard to structural evolution, perhaps the most important feature of the acid-catalyzed growth mechanism is that for most oligomeric species condensation is virtually irreversible. Tenuous, fractal structures are therefore kinetically stabilized, because there is no mechanism for restructuring and there is little monomer available to fill in voids. Unlike basic conditions in which dissolution-reprecipitation and the condensation process (monomer-cluster growth) naturally result in an inverted Q distribution (primarily Q and Q" species), acidic conditions produce a distribution of Q -Q" species as expected for classic polycondensation of tetrafunctional monomers. (See Fig. 33.) The importance of irreversible condensation to the evolving silicate structures was predicted by Her [1]. 

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