The kinetics of hydrolytic polymerization of ε-caprolactam. II. Determination of the kinetic and thermodynamic constants by least-squares curve fitting

The kinetic and thermodynamic constants of the hydrolytic polymerization of ?-caprolactam were determined by least-squares curve fitting. The calculations were carried out using observed kinetic data such as concentration of ?-caprolactam ([CL]), endgroup ([EG]), and ?-aminocaproic acid ([ACA]) and time derivatives of each concentration (rates) ?[CL]/?t, ?[EG]/?t, and ?[ACA]/?t. The sets of the converged constants are obtained for the initial water concentrations of 0.42, 0.82, and 1.18 mole/kg. An averaged set of the constants applicable for this range of the initial composition was also evaluated. The compatibility between observed and calculated concentration and rate curves was improved by the use of the newly developed sets of the constants. The mechanism of the polycondensation reaction is also discussed, based on the rate and kinetic constants obtained by this work.     

The kinetics of hydrolytic polymerization of ε-caprolactam. V. Equilibrium data on cyclic oligomers

The concentrations of the cyclic oligomers (C_i; i = 3, 4, 5, and 6) in the polymeric products of ε-caprolactam were determined by high-performance liquid chromatography. The equilibrium data on the oligomers were obtained as a function of the polymerization temperature and initial water concentration. The concentration of each oligomer in the equilibrated polymer was found to increase with the temperature and/or initial water concentration. A set of the kinetic equations to express the oligomer formation during the polymerization was also proposed.     

The simulation of hydrolytic polymerization of ϵ-caprolactam in various reactors

The concrete simulation models dealing with the kinetic behavior of the hydrolytic polymerization of ?-caprolactam (CL) in various polymerization reactors used in the industry were described, and the method for their numerical solutions was presented. The characteristic data of the polymerization such as the concentrations of CL, end group, water, ?-aminocaproic acid, cyclic dimer, and the hot-water-soluble component, conversion, number average, and weight average molecular weights, and solution and melt viscosities can be calculated at every stage of the polymerization reaction, at every part of the reactors, and/or at the outlet of the reactors. The calculated values based upon the models were found to be quite compatible with the observed values for the reactors. The applicability of the technique was well confirmed for the quality control, process control, modification of existing plants, and development of new chemical process plants.     

Adiabatic anionic polymerization of caprolactam in the presence of N-acylated caprolactam macroactivator: Kinetic study

In this study, bis ?-caprolactam bis-diphenyl methane diisocyanate polypropylene glycol 1000 used as the macroactivator was prepared and well characterized prior to use. The anionic polymerization of ?-caprolactam with the macroactivator as a function of the macroactivator concentration was adiabatically carried out. The adiabatic temperature rise method as well as the macrokinetics were used for elucidation of the kinetics of the polymerization. A nonlinear regression technique was used for determining the parameters of the macrokinetic equation. The equilibrium conversion and equilibrium time obtained were 94–96% and 2–9 min depending on the macroactivator concentration. The effects of the concentrations of macroactivator and ?-caprolactam on the initial rate, apparent overall reaction rate, and the empirical parameters were studied. A side reaction induced by the transfer of the proton in the isocyanurate group of the macroactivator to caprolactam anion was found. According to this finding, a new reaction kinetic model was proposed by properly modifying the macrokinetic equation. © 1993 John Wiley & Sons, Inc.     

Mechanism and kinetics of esterification of adipic acid and ethylene glycol by tetrabutyl titanate catalyst

An eight-step mechanism of esterification reaction between adipic acid (AA) and ethylene glycol (EG) catalyzed by tetrabutyl titanate [Ti(OBu)₄] was studied in detail. The kinetic data for the esterification reaction between AA and EG catalyzed by tetrabutyl titanate [Ti(OBu)₄] were measured in the temperature range of 403 K-433 K. A second-order kinetic model was established, and the model parameters were obtained through an optimization procedure by minimizing the value differences between the simulated component concentrations in the reaction system with the experimental ones. The results demonstrate that the model is suitable for the esterification reaction between AA and EG catalyzed by tetrabutyl titanate [Ti(OBu)₄]. Furthermore, the esterification reaction rate increases with the increase of reaction temperature, concentration of catalyst and the initial reactant ratio of EG to AA.     

注乙二醇溶液分解甲烷水合物的实验研究

在甲烷水合物一维分解模拟系统上,进行了模拟注乙二醇溶液分解甲烷水合物的实验研究。使用甲烷气体与纯水在一定温度、压力条件下,在沉积物中合成水合物。通过以不同速率注入不同浓度的乙二醇溶液,研究了化学法分解水合物过程中甲烷气体和水生产规律。实验结果表明,水合物分解产出甲烷气体的过程主要分为4个阶段：初始注入段、化学剂稀释段、水合物分解段和残余气体产出段。整个分解过程中,水的生产速率几乎保持恒定。通过对实验结果的能量分析表明,本实验条件下分解综合效率在0.20～0.88之间,并且受注入速率和化学剂浓度影响。在恒定注入速率条件下,分解效率在化学剂质量分数为60%时达到最大值。     

甲烷水合物在纯水和抑制剂体系中的生成动力学

Kinetic data of methane hydrate formation in the presence of pure water,brines with single salt and mixed salts,and aqueous solutions of ethylene glycol(EG) and salt EG were measured.A new kinetic model of hydrate formation for the methane water systems was developed based on a four-step formation mechanism and reaction kinetic approach.The proposed kinetic model predicts the kinetic behavior of methane hydrate formation in pure water with good accuracy.The feasibility of extending the kenetic model of salt(s) and EG containing systems was explored.     

Controlled synthesis of crosslinked polyamide 6 using a bis-monomer derived from cyclized lysine

The controlled synthesis of polyamide 6 chemical networks by anionic ring-opening copolymerization of ε-caprolactam (CL) with synthesized bis-ε-caprolactam derived from α-amino-ε-caprolactam, i.e. N-functionalized α-amino-ε-caprolactam bis-monomers, using sodium ε-caprolactamate as an initiator and hexamethylene-1,6-dicarbamoylcaprolactam as di-functional fast activator was examined in bulk at 140 °C. An urea-based bis-monomer and CL were first shown to copolymerize with a decreasing polymerization rate due to side reactions. On the contrary, quantitative copolymerization of CL with various amounts of bis-N(2-oxo-3-azepanyl)-1,6-tetramethylenediamide, an amide-based bis-monomer, leads to fast kinetics similar to the homopolymerization of CL. Crosslinked PA6 with network exhibiting elastic or viscoelastic behaviors, depending on the amount of crosslinker, were observed and characterized by swelling in hexafluoroisopropanol, dynamic mechanical analysis and rheology measurements. Crystallinity and swelling were shown to decrease with the increasing content of the crosslinking agent.     

Solid-state polycondensation of poly(ethylene terephthalate) modified with isophthalic acid: kinetics and simulation

The kinetics for the solid-state polycondensation (SSP) of poly(ethylene terephthalate) modified with isophthalic acid at the protection of nitrogen gas was studied in the paper. A kinetic model controlled by the reversible chemical reactions and the three dimension diffusions of small molecule by-products has been established. The kinetic parameters of the SSP of PET at different temperatures, including the forward rate constants of transesterification reaction (k₁) and esterification reaction (k₂), the diffusion coefficients of EG (D₁) and water (D₂), the concentrations of EG (g_s) and water (w_s) on the surface of PET chips in SSP, and the activation energies of these kinetic parameters were obtained by experiments and solution of the model. Using the model and the kinetic parameters, the SSP of poly(ethylene terephthalate) modified with isophthalic acid can be simulated with good accuracy. In addition, the influences of nitrogen gas flow rate, the chip dimension and the carboxyl end-group concentration of the PET prepolymer on the molecular weight of PET after SSP, and the change of the EG concentration of PET chips with reaction time were also studied by simulation.     

Control of nitrification rate by increasing ammonium concentration

Lysimeter experiments with maize and incubation experiments showed that increased ammonium concentrations in soil reduced nitrification rates. A modified Lees and Quastel kinetic model was proposed for predicting the relation between initial ammonium concentration in soil and nitrification rate. A term Mi strongly dependent on initial ammonium concentration ([NH4₀]) was introduced into the model which took the form: dy/dt = R(A – y)(Mi + y), where R is a rate constant, y represents the concentration of formed nitrate and A is an asymptotic value of initial ammonium concentration. Mi was obtained by a curve fitting procedure applied to experimental data. An exponential decay of Mi with [NH4]₀ was formulated. The modified model thus obtained provides an effective tool for predicting nitrification rates related to a wide range of ammonium concentrations.     

Kinetics of anionic polymerization of lactams. (Solution of non-isothermal kinetic problems by the inverse method)

Wide use has been made of non-isothermic studies for obtaining kinetic data on the anionic polymerization of ?-caprolactam and ω-dodecalactam. Data are obtained by measuring changes in reaction temperature, under conditions of heat exchange with the surroundings and by solving the inverse thermophysical problem. This solution yields kinetic constants, which when substituted into heat conduction and kinetic equations minimize the deviations of calculated temperature dependences on time and the deviations in experimental data. Thus, we have studied qualitatively the polymerization of lactams. Numerical values of the basic kinetic constants in the macrokinetic scheme have been determined. Some new effects, such as self-acceleration in the polymerization of caprolactam and the increase of the apparent activation energy at high degrees of conversion in the polymerization of dodecalactam were detected. The approach may be useful in studying other polymerizations.     

Synthesis and characteristics of the composites based on poly(caproamide) and multiwalled carbon nanotubes

Polycaproamide composites are synthesized by the anionic activated bulk polymerization of ?-caprolactam in the presence of 0.1–5.0 wt % of multiwalled carbon nanotubes and using low-molecularmass monofunctional (N-acetyl-?-caprolactam) and macromolecular polyfunctional (aromatic polyimides) activating agents. The effect of nanotubes on the polymerization of ?-caprolactam is studied, and this effect is shown to become more pronounced as the concentration of nanotubes is increased. The effect of nanotubes on the microstructure, phase composition, water sorption, thermophysical, mechanical, and friction characteristics of poly(caproamide) is analyzed.     

Optimization of nylon 6 reactors with end-point constraints

Optimal temperature profiles for nylon 6 polymerization in plug–flow reactors have been obtained with end-point constraints involving the degree of polymerization and the cyclic dimer concentration, using the most recent kinetic information. Computations suggest that the temperature at the feed end of the reactor must be maintained close to the highest permissible level (determined by the boiling point of the ?-caprolactam). The temperatures in this region control the degree of polymerization more than other variables. Thereafter, the temperature should be reduced. This second zone controls the undesirable cyclic dimer concentration. The effect of a systematic change of values of the various design variables is studied. The profiles obtained herein are qualitatively similar to those obtained by earlier workers using similar formulations. However, they differ significantly from the profiles obtained by us earlier, using different objective functions which are more relevant to the design of new reactors. Attempts have also been made to obtain a global optimal scheme to produce polymer of a desired degree of polymerization and cyclic dimer content, using as short a reactor as possible, and using the water content and the modifier concentration in the feed as the independent variables.     

Kinetics measurement of ethylene-carbonate synthesis via a fast transesterification by microreactors

High-purity ethylene carbonate (EC) is widely used as battery electrolyte, polycarbonate monomer, organic intermediate, and so on. An economical and sustainable route to synthesize high-purity ethylene carbonate (EC) via the transesterification of dimethyl carbonate (DMC) with ethylene glycol (EG) is provided in this work. However, this reaction is so fast that the reaction kinetics, which is essential for the industrial design, is hard to get by the traditional measuring method. In this work, an easy-to-assemble microreactor was used to precisely determine the reaction kinetics for the fast transesterification of DMC with EG using sodium methoxide as catalyst. The effects of flow rate, microreactor diameter, catalyst concentration, reaction temperature, and reactant molar ratio were investigated. An activity-based pseudo-homogeneous kinetic model, which considered the non-ideal properties of reaction system, was established to describe the transesterification of DMC with EG. Detailed kinetics data were collected in the first 5 min. Using these data, the parameters of the kinetic model were correlated with the maximum average error of 11.19%. Using this kinetic model, the kinetic data at different catalyst concentrations and reactant molar ratios were predicted with the maximum average error of 13.68%, suggesting its satisfactory prediction performance.     

The photocatalytic activity and kinetics of the degradation of an anionic azo-dye in a UV irradiated porous titania foam

A porous organic–inorganic hybrid titania foam, prepared from a long chain organic surfactant, hexadecylamine (HDA) and a semiconductor powder was characterized by microscopic and spectroscopic techniques and photocatalytically evaluated for the solution phase decomposition of methyl orange under alkaline conditions. Kinetic data obtained indicate conformity with Langmuir–Hinshelwood kinetic model at the initial stages of the degradation reaction. An attempt was made to study the effect of experimental parameters including catalyst loading and dye concentration on photocatalytic degradation of MO. Results indicate that the rate of reaction is governed by adsorption of azo-dye into the surface of the photocatalyst materials and suggests an optimum catalyst load and dye concentration for the degradation reaction. Light absorption and scattering within the substrate reaction zone and arising from differences in optical properties of catalyst material, made it impossible to interpret entire kinetic data on the basis of a simple Langmuir–Hinshelwood kinetics. However, kinetic data obtained at the initial stages of the reaction suggest conformity with first-order kinetics. The foam promises to be a versatile material in that it can be used for the treatment of low concentrations of pollutants of biological, organic and inorganic origins in water and air.     

Kinetics of adiabatic anionic copolymerization of ϵ-caprolactam in the presence of various activators

Adiabatic temperature rise has been recorded as a function of polymerization time to investigate an adiabatic copolymerization kinetics of ϵ-caprolactam (CL) in the presence of several activators, considering different initial copolymerization temperatures ranging from 130 to 160°C. The copolymerization of CL and PEG-diamine has been performed using activators such as tolylene dicarbamoyl dicaprolactam (TDC), hexamethylene dicarbamoyl dicaprolactam (HDC), and cyclohexyl carbamoyl caprolactam (CCC), and sodium caprolactamate as a catalyst. The effect of PEG-diamine on the overall rate of polymerization of CL has been studied by fitting the experimental temperature rise with a new polymerization kinetic equation involving the polymerization exotherm, polymerization-induced crystallization exotherm, and the heat loss due to nonideal adiabatic condition in the experimental situation. Like homopolymerization, the net copolymerization rate is influenced by the variation of activator types in the initiation step. The temperature rise due to polymerization-induced crystallization in copolymerization is drastically decreased with the increasing initial polymerization temperature in the course of polymerization. The high molecular weight and large polydispersity index of copolymers using bifunctional activators indicate that the Claisen type condensation can occur in the course of polymerization processes. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 66: 1195–1207, 1997     

Powdered poly(ethylene terephthalate)

The influence of the conditions of preparation on the properties of powdered poly(ethylene terephthalate) was followed from the point of view of its specific surface. The powdered poly(ethylene terephthalate) prepared by reprecipitation from the melt of 6-caprolactam has a porous and structured surface, and consequently, also a large specific surface in comparison with the powedered poly(ethylene terephthalate) prepared by mechanical milling. The specific surface value is influenced by the cooling rate of the initial homogeneous melt of poly(ethylene terephthalate)-6-caprolactam, by the concentration of poly(ethylene terephthalate) in this melt and by its molecular weight, by the water temperature at the extraction of 6-caprolactam from the tough mixed melt, by the drying temperature of the powdered poly(ethylene terephthalate), and by the content of residual 6-caprolactam in the powdered product. In the examined area, the specific surface value of the powdered poly(ethylene terephthalate) prepared by reprecipitation from the melt of 6-caprolactam ranged from 10 to 110 m²·g^?1.     

Mechanism and kinetics of adiabatic anionic polymerization of ϵ-caprolactam in the presence of various activators

Nylon 6 was prepared by adiabatic anionic polymerization of ?-caprolactam using hexamethylene dicarbamoyl dicaprolactam (HDC), cyclohexyl carbamoyl caprolactam (CCC), or phenyl carbamoyl caprolactam (PCC) as activators and sodium caprolactamate (NaCL) as a catalyst at various initial reaction temperatures ranging from 130 to 160°C. Adiabatic temperature rise was recorded as a function of polymerization time to investigate polymerization kinetics. Kinetic parameters for polymerization, which are more accurate than data reported to date, could be obtained by fitting the temperature rise data with a new polymerization kinetic equation involving crystallization exotherm and thermal conduction. The polymerization rate highly depended on the chemical structure of the activator used, which indicates that the initiating step where the activator is attacked nucleophilically by NaCL is a very important reaction step, affecting the overall polymerization rate. CCC showed the fastest polymerization rate, whereas HDC and PCC showed the medium and the slowest rate, respectively. The contributions of crystallization exotherm and thermal conduction to the resultant temperature rise during polymerization were significant, when the initial reaction temperature was lower than 140°C. In all cases, the molecular weight obtained from intrinsic viscosity measurement was greater than the expected molecular weight. This may be attributed to the branching and/or crosslinking reaction through Claisen-type condensation reactions. © 1995 John Wiley & Sons, Inc.     

Ethylene glycol production from glucose over W‐Ru catalysts: Maximizing yield by kinetic modeling and simulation

The kinetics of glucose conversion to ethylene glycol (EG) in the presence of ammonium paratungstate and Ru/AC catalysts was studied to model and predict the reaction performance under a range of conditions. A mathematical model was established through the rational simplification of the reaction network on the basis of a continuous stirred‐tank model. The kinetic data of six major reactions in the network were experimentally measured, and the analytical expressions of overall reaction kinetics were obtained by introducing the kinetic data to the model. Yields of EG, hexitols and gas were described as functions of the reaction temperature, the concentration of glucose in the feedstock and the feeding rate. The simulation results matched the experimental data of glucose conversion, demonstrating the validity of the model and method for studying the overall kinetics of glucose conversion to EG over W‐Ru catalysts. © 2016 American Institute of Chemical Engineers AIChE J, 63: 2072–2080, 2017     

Micro-kinetic model of fructo-oligosaccharide synthesis for prebiotic products

A new micro-kinetic model of the enzyme-catalyzed synthesis of fructo-oligosaccharides (FOS) was developed. A commercial enzyme mixture Pectinex® Ultra SP-L derived from Aspergillus aculeatus was used. A variety of initial enzyme concentrations (1–5 vol%) and sucrose concentrations (400–600 g/L) were experimentally investigated and included in kinetic modeling. Several variations of kinetic mechanisms and corresponding models have been examined. A hybrid genetic algorithm was used to predict the kinetic parameters simultaneously for all experimental data. The best fitting model has been adopted, and with an average error of 13.34%, it describes the experimental data very well. The influence of initial concentrations on the conversion of sucrose and production of FOS is being carefully investigated. It was shown that the initial sucrose concentration significantly affects the highest level of FOS concentration, but the enzyme concentration controls the time at which maximum is reached as well as the rate of FOS decomposition.