Rates of Polycondensation Reactions

Since the reactivity of two functional groups (or rate constant) is independent of the size of the molecule to which they are attached, it is possible to measure the polycondensation reaction rate simply by determining the concentration of functional groups as a function of time. For example, in a polyesterification reaction, the general reaction at any time t is as shown by Eq. (5.13) and, as the reaction proceeds, the functional groups -COOH and -OH disappear at the same rate. The rate of the polyesterification reaction can then be defined simply as 

Let us consider the polyesterification of a diacid and a diol to illustrate the general form of kinetics of a typical step polymerization. Like simple esterification, polyesterification is an acid-catalyzed reaction [2] 

In the above equations, the wavy lines (vww) are used to indicate that these equations apply to all acid or alcohol species in the reaction mixture, i.e., monomer, dimer, trimer, n-mer. 

The rate of a step polymerization is usually most conveniently expressed in terms of the rate of disappearance of the reacting functional groups. Thus, the rate of polyesterification, Rp, can be expressed as the rate of disappearance of carboxyl groups  

Polyesterification reactions, like many other step polymerizations, are equilibrium reactions. However, for obtaining high yields of high-molecular-weight product such polymerizations are usually run in a manner so as to continuously shift the equilibrium in the direction of the polymer. In the case of a polyesterification this is usually accomplished by removal of the water, which is a product of the reaction of species II (Eq. 5.19). Under the 

Since the reactivity of two fimbtional groups (or rate constant) is independent of the size of the molecule to which they are attached, it is possible to measure the polycondensation reaction rate simply by determining the concentration of functional groups as a function of time. 

Let us consider the polyesterification of a diacid and a diol to illustrate the kinetic behavior of a typical step polymerization. Like simple esterification (Sykes, 1986), polyesterification is an acid-catalyzed reaction that can be represented by a sequence of reactions as shown by Eqs. (5.4)-(5.6). In these equations, the wavy lines (www) are used to signify that these equations apply, irrespective of the size of the molecular species. Equation (5.4) represents pfotohation of oxygen in carbon-oxygen double bond which leads to a more positive carbon atom for subsequent addition of a nucleophile, in this case www-OH [Eq. (5.5)], followed 

Step-growth/condensation polymerization Chain-growth/addition polymerization 

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). 

---

The properties and usefulness of the final polymer depend on its structure and can be directed by appropriate control of process variables during polymerization. Temperature control and the choice of catalyst are critical in minimizing the side reactions, such as formation of carboxyl end groups by elimination of tetrahydrofuran (THE) from 4-hydroxybutyl ester end groups. The proper choice of co-catalyst could promote direct polycondensation reaction with less extent of side reactions. For example, tetrapropyl zirconate is known as an efficient co-catalyst [23]. The temperature and pressure are also significantly important in controlling the rate of polycondensation reaction and degradation. 

The kinetics of polycondensation reactions might be expected to be similar to those found in condensation reactions of small molecules (evidence suggests that rate coefficients are independent of polymer size). Polyesterification reactions between dibasic carboxylic acids and glycols can be catalysed by strong acids. In the absence of added catalyst, it has been suggested that the acidic monomer should act as a catalyst, whereupon the rate of reaction should be given by... 

Fully aromatic polyamides are synthesized by interfacial polycondensation of diamines and dicarboxylic acid dichlorides or by solution condensation at low temperature. For the synthesis of poly(p-benzamide)s the low-temperature polycondensation of 4-aminobenzoyl chloride hydrochloride is applicable in a mixture of N-methylpyrrolidone and calcium chloride as solvent. The rate of the reaction and molecular weight are influenced by many factors, like the purity of monomers and solvents, the mode of monomer addition, temperature, stirring velocity, and chain terminators. Also, the type and amount of the neutralization agents which react with the hydrochloric acid from the condensation reaction, play an important role. Suitable are, e.g., calcium hydroxide or calcium oxide. 

Figure 2. Dependence of hydrogen chloride liberation rate in polycondensation reaction of dichlorohexaphenylcyclotetrasiloxane with a,co-dihydroxydimethylsiloxanes curves 1 and 2 - with 1,5-disposition of chlorine atoms and at n = 25,70, respectively curves 1 and 2 - with 1,3-disposition of chlorine atoms and at n = 25,70, respectively.

The polymerisation of benzene through repeated nucleophilic substitutions on the rings was studied by Kovacic et al. using ferric chloride as catalyst and water as cocatalyst. This system is of course outeide the realm of cationic polymerisation throu the double bcmd of an olefin, but illustrates well the role of water in Friedel-Crafts polycondensations. The authors showed that the rate of this reaction went throu a maximum at a catalyst/cocatalyst ratio of one and attributed this observation to the high activity of ferric chloride monohydrate ... 

Polymerization in the melt is widely used commercially for the production of polyesters, polyamides, polycarbonates and other products. The reactions are controlled by the chemical kinetics, rather than by diffusion. Molecular weights and molecular weight distributions follow closely the statistical calculations indicated in the preceding section, at least for the three types of polymers mentioned above. There has been much speculation as to the effect of increasing viscosity on the rates of the reactions, without completely satisfactory explanations or experimental demonstrations yet available. Flory [7] showed that the rate of reaction between certain dicarboxylic acids and glycols was independent of viscosity for those materials, in the range studied. The viscosity range had a maximum of 0.3 poise, however, far below the hundreds of thousands of poises encountered in some polycondensations. 

Applying the concept of equal reactivity of all functional groups, the rate of polycondensation according to the general Equation 2.4 may be expressed in terms of the extent of reaction by the rate equation 2.8. 

This means a decrease of the diffusion distance of the polycondensate chains to the rubber interface by a factor of 10 and an increase of the interface by a factor of 10 , that is, the rate of interfacial reactions is dramatically enhanced. In the case of PA-6/ EPM-g-MA blends (EPM-g-MA, ethylene and propylene monomer grafted with maleic anhydride) the reaction is so fast that as interfaces are created upon melting they become immediately covered with PA-6 chains, causing a quick reduction of the interfacial tension and preventing coalescence, which induces a further refinement of the dispersed phase. 

However, the maximum molecular weight and the rate of polycondensation are reduced by the occurrence of cycUzation reactions. Although, one might speculate that a moderate degree of cycle formation is desired since this will reduce the molecular weight distribution. 

As in all SSP processes, mass transfer phenomena also affect the PET reactions in the solid state, where the main volatile by-produds are ethylene glycol, diethylene glycol, acetaldehyde, and water. The rate of polycondensation can thus be limited by... 

The kinetics of polycondensation reactions is similar to that of ordinary condensation reactions. Since the average chain length is related to conversion in linear polycondensation by (9.7), and conversion is given as a function of time by the kinetic expression, x is directly related to the reaction time, and can thus be controlled by limiting the reaction time. Similarly, the time to reach a gel point is related by the rate expression, (9.18) and (9.19). 

Irzhak et al. [36, 37] contributed two papers dealing with ring-chain competition in non-ideal KC polymerizations. The consequences for the number and mass distributions of the reaction products were discussed. Furthermore, six publications should be mentioned [38 3] reporting on the diffusion control of the rates of cyclization reactions. Yet, the course of KC polycondensations was not discussed. Furthermore, it should be mentioned that several authors have published... 

The rate constants in the reactions (29) may be conveniently envisaged as elements of symmetric matrix k. In order to calculate the statistical characteristics of a particular polycondensation process along with matrix k parameters should be specified which characterize the functionality of monomers and their stoichiometry. To this end it is necessary to indicate the matrix f whose element fia equals the number of groups A in an a-th type monomer as well as the vector v with components Vj,... va,..., v which are equal to molar fractions of monomers M1,...,Ma,...,M in the initial mixture. The general theory of polycondensation described by the ideal model was developed more than twenty years ago [2]. Below the key results of this theory are presented. 

Fatty acids have also been converted to difunctional monomers for polyanhydride synthesis by dimerizing the unsaturated erucic or oleic acid to form branched monomers. These monomers are collectively referred to as fatty acid dimers and the polymers are referred to as poly(fatty acid dimer) (PFAD). PFAD (erucic acid dimer) was synthesized by Domb and Maniar (1993) via melt polycondensation and was a liquid at room temperature. Desiring to increase the hydrophobicity of aliphatic polyanhydrides such as PSA without adding aromaticity to the monomers (and thereby increasing the melting point), Teomim and Domb (1999) and Krasko et al. (2002) have synthesized fatty acid terminated PSA. Octanoic, lauric, myristic, stearic, ricinoleic, oleic, linoleic, and lithocholic acid acetate anhydrides were added to the melt polycondensation reactions to obtain the desired terminations. As desired, a dramatic reduction in the erosion rate was obtained (Krasko et al., 2002 Teomim and Domb, 1999). 

---