Mathematical Modeling of Nylon 6/6,6 Copolymerization: Beneficial Influence of Comonomers on Degree of Polymerization in Batch Reactor

Abstract

A model is developed for hydrolytic copolymerization of caprolactam with hexamethylene diamine (HMD) and adipic acid (ADA) in a batch reactor to produce nylon 6/6,6 copolymer. The reaction mechanism includes hydrolysis of caprolactam and cyclic dimer, polycondensation, polyaddition, transamidation, and ring formation via end biting and back biting. The catalyzing effect of carboxyl groups is accounted for using kinetic parameters from the literature. Model predictions are compared with low‐temperature literature data before simulating reactor conditions of industrial interest. The model predicts a higher degree of polymerization (DP) for nylon 6/6,6 copolymer compared to nylon 6 and 6,6 homopolymers produced using the same reactor conditions. Dynamic changes in concentrations of water, caprolactam, HMD, ADA, and end groups are tracked and used to explain the positive influence of comonomers on reaction rates and DP. Insights gained from this model will form a useful basis to build future models of continuous industrial reactors.

Mathematical Modeling of Nylon 6/6,6 Copolymerization in Batch Reactor: Investigating Recipes without Water and with Cyclic Dimer

“…A vent on the overhead vapor line remained closed during the first hour of operation and was then opened to permit mass transfer of water (along with small amounts of caprolactam and HMD) from the liquid phase to encourage growth in degree of polymerization (DP) via reaction (1.2). The resulting simulations revealed interesting synergies that arise during copolymerization compared to nylon 6 homopolymerization and to nylon 6,6 homopolymerization . For example, a higher DP was predicted in copolymerization simulations compared with the corresponding homopolymerizations because DP builds up quickly at the start of the batch copolymerization due to fast ring opening of caprolactam by amine ends from HMD (i.e., via reaction (1.3)).…”

“…Table 3 shows dynamic model equations, which are material balances on the mass m of the liquid in the reactor, the caprolactam monomer ( M ), the linear monomer (aminocaproic acid) (LM), unreacted HMD and ADA, the linear dimer (LD), CD, water ( W ), amide links ( L ), carboxyl ends ( C ), amine ends ( A ), and the number of moles of water, monomer, and HMD ( W v , M v , and HMD v ) that have evaporated from the liquid into the vapor . Evaporation of CD is neglected in this modeling work due to the low volatility of CD (assumption 2 in Table ) .…”

“…Only these ends can backbite (via reaction (1.5)) to produce CD. Expressions for these probability factors and their derivations are provided in our previous modeling work . ODEs (3.1), (3.2), (3.4), (3.8), and (3.11) also contain lumped mass‐transfer coefficients for water, caprolactam monomer, and HMD (i.e., k w A s , k M A s , and k HMD A s ).…”

“…To the best of our knowledge, the model in Table is the only nylon copolymerization model in the academic literature. To test the validity of its predictions, batch reactor data generated by Heikens et al at a relatively low temperature of 221 °C were used . Heikens et al had performed their experiments in sealed tubes containing mixtures of caprolactam and water to which either HMD or ADA was added to perturb the balance of end groups.…”

“…For example, a higher DP was predicted in copolymerization simulations compared with the corresponding homopolymerizations because DP builds up quickly at the start of the batch copolymerization due to fast ring opening of caprolactam by amine ends from HMD (i.e., via reaction (1.3)). Unlike nylon 6 homopolymerization where water is important for ring opening of caprolactam, in the copolymerization system nearly all of the initial ring opening is caused by amine ends (reaction (1.3)) rather than by water (reaction (1.1)) because of the much higher concentration of amine ends …”