Modeling and Multiobjective Optimization of A Fed-Batch Emulsion Copolymerization Process to Control the Resulting Particles Core-Shell Morphology

Summary: This paper deals with the design and control of the morphology of core-shell nanoparticles elaborated by fed-batch emulsion copolymerization of styrene and butyl-acrylate in the presence of a chain transfer agent (n-dodecyl mercaptan). A mathematical model was elaborated and validated. It consists of a system of differential algebraic equations involving 49 unknown kinetic and thermodynamic parameters, many of them being impossible to be accurately estimated, due to the lack of experimental data. A method based on the sensitivity analysis allowed us to determine a subset of the 21 most influential parameters. The 28 non estimable parameters were taken from the literature. The validated model was then used in a dynamic multiobjective optimization to optimize the best profile of the pre-emulsion feed rate to control (i) the composition and average molar masses of the copolymer, (ii) the instantaneous glass transition temperature, corresponding to a core-shell morphology suited for special end-use properties.     

Modeling and Sensitivity Analysis of Particle Size Distribution and Chain Length Distribution in a Semibatch Emulsion Copolymerization Reactor

Summary: A comprehensive model is developed to predict the relationship between the particle size distribution and molecular weights of particles in an emulsion copolymerization reactor. A full population balance equation is used for the particle size distribution and extended to the model for the molecular properties using a continuous reactor approach. The numerical prediction clearly distinguishes the characteristics of molecular properties of particles by homogeneous nucleation from those by micellar nucleation with the dependence on the particle size. Sensitivity analysis of the proposed model under a variety of conditions shows that the compartmentalized feature of the emulsion system should be considered for better prediction of molecular properties, and provides information on the manipulated variables and lumped parameters which effectively decompose the correlation of both properties. Finally, a control strategy utilizing a lumped parameters tracking method is suggested for the regulation of both the particle size distribution and molecular properties.

Time evolution of number‐averaged molecular weights in the element under base conditions.     

丙烯酰胺-N-羟甲基丙烯酰胺反相乳液共聚合

：以Ｓｐａｎ ４０ 为乳化剂,过硫酸铵为引发剂,进行了丙烯酰胺 Ｎ 羟甲基丙烯酰胺反相乳液共聚反应,研究了反应温度、单体浓度、引发剂浓度、乳化剂浓度等因素对聚合动力学的影响,并讨论了其聚合机理。     

Emulsion polymerization of vinyl acetate using a polymerizable surfactant. III. Mathematical model

A mathematical model was developed to aid in the further understanding of the growth of latex particles in the emulsion polymerization of vinyl acctate using a polymerizable surfactant, sodium dodecyl allyl sulfosuccinate (TREM LF-40). The model incorporates the main features of the system observed experimentally: copolymerization in the aqueous phase, at the particle surface, and chain transfer to TREM LF-40. The reactions at the particle/water interface and, more specifically, the chain transfer to TREM LF-40 leading to a decrease in the average number of radicals per particle, was found to be the most significant mechanism for explaining the difference in kinetic results found for TREM LF-40 and its nonpolymerizable counterpart. The copolymerization of vinyl acetate with TREM LF-40 was also shown to slow the overall polymerization rate. However, the copolymerization alone was not sufficient to account for the decreased polymerization rates observed experimentally. A combination of copolymerization and chain transfer to TREM LF-40 was found to provide a good fit of the experimental results. © 1993 John Wiley & Sons, Inc.     

The Influence of Xanthate‐Based Transfer Agents on Styrene Emulsion Polymerization: Mathematical Modeling and Model Validation

A mathematical model was developed to account for the evolution of polymer product attributes in the emulsion polymerization of styrene. The effects of transfer agent, surfactant, initiator and temperature were investigated. Polymerization rate, and particle size decreased with increasing concentration of the transfer agent. The polymerization rate increased with increasing surfactant and initiator concentrations, while an increase in temperature led to a decrease of molecular weight but an increase of polymerization rate and particle size. Chain extension was successfully achieved in the presence of our RAFT agent. The model predictions compared well with our experimental results.

     

Reactive Surfactant in the Emulsion Copolymerization of Methyl Methacrylate and Octyl Acrylate

The emulsion copolymerization of methyl methacrylate and octyl acrylate was studied using a reactive surfactant ammonium sulfate allyloxy nonylphenoxy poly(ethyleneoxy) (10) ether (DNS‐86), and a conventional surfactant sodium dodecylbenzene sulfonate (DBS) with a similar structure as a comparison sample. A series of latex samples have been prepared with two kinds of surfactants, and their properties have been characterized and compared. ¹H‐NMR proves that the reactive surfactant has been incorporated into the resulting copolymers. The atomic force microscopy (AFM) proves that the reactive surfactant DNS‐86 migrate to the surface of the latex film to a much less degree than the conventional surfactant DBS. Transmission electron microscopy (TEM) demonstrates that there are some differences in the particle morphologies. The stability and water‐resistance of the latex films prepared by reactive surfactant DNS‐86 are better than those prepared by the conventional surfactant DBS.     

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

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 Chemical Reactors—Development and Implementation of Novel Technologies

Mathematical modeling is an important tool for rapid and reliable reactor development and design. The models are built up from basic studies of the reaction mechanism and kinetics, the transfer processes, and the interactions within the system. A detailed understanding of the elementary processes enables the construction of powerful and complex models for dynamic and steady-state simulation. With the aid of experimentally determined parameter values one can develop new processes or improve existing ones. Excellent results obtained in experimental work under idealized laboratory conditions can seldom be fully realized in practice. This is due to factors such as transfer resistances, local gradients, fluctuating conditions, and constructional and other limitations which lead to unsatisfactory parameter values and higher costs to compensate for these shortcomings. Some recommendations are made for circumventing these deficiencies.     

Comparison of Vinyl Acetate - Butyl Acrylate Emulsion Copolymerizations Conducted in a Continuous Pulsed Sieve Plate Column Reactor and in a Batch Stirred Tank Reactor

In this work, vinyl acetate/butyl acrylate emulsion copolymerizations carried out in a continuous tubular reactor (pulsed sieve plate column, PSPC) were compared to those conducted in a semibatch stirred tank reactor under similar operational conditions. In order to minimize the compositional drift along the PSPC, reactions were carried out with different numbers (2, 3 and 4) of lateral feed streams of the more reactive monomer (butyl acrylate). For comparison, fed batch reactions were conducted with the same number of intermittent shot additions of butyl acrylate, at the corresponding batch times. Both systems (tubular and semibatch) with distributed feeding of more reactive monomer are able to reduce composition drift thus providing more uniformity in copolymer composition. In addition, the tubular reactor presents much better control of temperature than the tank reactor, which is important to achieve higher productivity.     

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

A model is used to simulate batch copolymerization of caprolactam with hexamethylene diamine (HMD) and adipic acid (ADA) to produce nylon 6/6,6. Four different recipes are considered: a recipe containing caprolactam and an aqueous solution of HMD and ADA, a recipe containing caprolactam and dry HMD/ADA salt, and two recipes with a portion of the caprolactam replaced by nylon 6 cyclic dimer (CD). Consuming CD would be advantageous because CD is an undesirable side product from nylon 6 production. Simulation results lead to three important findings: (i) operation using dry salt rather than aqueous salt solution leads to higher degree of polymerization, (ii) substantial quantities of CD can be consumed to produce nylon 6/6,6 copolymer, and (iii) including water in the recipe is beneficial for achieving improved consumption of CD. The results of this study will be helpful in designing experiments aimed at improving industrial nylon 6/6,6 copolymerization processes.     

Emulsion Copolymerization of Vinyl Acetate and Vinyl Silanes: Kinetics and Development of Microstructure

The batch emulsion copolymerization of vinyl acetate with different vinyl silane functional monomers (vinyl trimethoxysilane [VTMS], vinyl triethoxysilane [VTES], and vinyl silanetriol [VSTO]) is studied. The nature of the silane strongly affects the development of the microstructure and crosslinking ability of the latexes. A combination of techniques (Soxhlet extraction, centrifugation, assymetric‐flow field flow fractionation AF4/MALS/RI) shows that the factor controlling the molar mass and crosslinking density is the degree of hydrolysis of the alkoxysilane, producing higher molar masses and degrees of crosslinking when the degree of hydrolysis is high. Thus, the copolymer containing VSTO produced a very crosslinked latex, the one with VTMS produced a latex with a low degree of crosslinking in the wet state that can yield high degrees of crosslinking upon drying, and the latex with VTES do not produce significant amounts of crosslinking neither before nor after drying.     

Preparation of Syndiotacticity-Rich High Molecular Weight Polyvinyl Alcohol by Low Temperature Emulsifier-Free Emulsion Copolymerization of Vinyl Acetate and Vinyl Pivalate

Low temperature emulsifier-free emulsion copolymerization of vinyl acetate (VAc) and vinyl pivalate (VPi) was carried out using a redox initiation system to prepare syndiotacticity-rich high-molecular weight (HMW) polyvinyl alcohol (PVA) with high yield. The effects of the polymerization conditions on the conversion, the molecular weight, the structure of poly (vinyl acetate-co-vinyl pivalate) (P (VAc-VPi)) and syndiotacticity of PVA were investigated. With the increases of the initiator concentration, the VPi molar ratio in monomer and polymerization temperature, the degree of polymerization (DP) of PVA decreases distinctly, but VPi contents in copolymer and syndiotactic diad (S-diad) contents of PVA increase obviously. PVA with the maximum DP of 11030 can be prepared by complete saponification of P(VAc-VPi) obtained under condition that the molar ratio of KPS to monomer is 1/2000, the molar ratio of VAc to VPi is 7:3 and reaction temperature is 12°C. The highest S-diad content in PVA can be up to 59.31% while the DP of PVA decreases to 5180 under the condition that the feed ratio of VPi is 70 mol%, which means the syndiotacticity-rich HMW PVA can be prepared successfully. And the conversions of all reactions are above 80%. Syndiotacticity-rich HMW PVA is effectively prepared in this study, which is useful for the preparation of high-strength and high-modulus PVA fiber.     

Maximum Achievable Particle Size in Emulsion Polymerization: Modeling of Large Particle Sizes

A simplified model for particle formation in emulsion polymerization (comprising aqueous‐phase propagation to degrees of polymerization which may enter a pre‐existing particle and/or form new particles by homogeneous or micellar nucleation, coupled with the aqueous‐phase and intra‐particle kinetics of oligomeric radicals) is formulated to provide a model suitable for the simulation of systems containing large‐sized particles. The model is particularly useful to explore conditions for growth of large particles while avoiding secondary particle formation. Applied to the Interval II emulsion polymerization of styrene with persulfate initiator at 50°C, it is found that there is an effective maximum particle size that can be achieved if the formation of new particles is to be avoided. The parameter space of initiator concentration, particle number concentration and particle radius is mapped to show a “catastrophe” surface at the onset of new nucleation. Advanced visualization techniques are used to interpret the large number of simulations in the series, showing a maximum achievable particle diameter of around 5 μm.     

Synthesis of Bimodal PVC Latexes by Emulsion Polymerization: An Experimental and Modeling Study

The onset and extent of secondary particle formation in the seeded emulsion polymerization of vinyl chloride were investigated by performing a series of seeded polymerizations at different concentrations of seed latex and surfactant. It was found that, in general, both the onset and the extent of secondary particle formation are determined not only by the rate of homogeneous nucleation, but also by the rates of particle coagulation. A comparison of methods to compute the evolution of the particle size distribution in vinyl chloride emulsion polymerization was also carried out. For growth processes, the widely-used pseudo-bulk model gives correct answers. For processes involving particle formation, on the other hand, this model cannot be used because it neglects, among others, the effects of nucleation and coagulation on the radical number distribution. To surmount this problem, we propose to use the zero-one-two model, for which the full population balance equations are given here.     

Metallocene‐Catalyzed Gas‐Phase Ethylene Copolymerization: Kinetics and Polymer Properties

The influence of 1‐hexene is examined on the kinetics of ethylene copolymerization with a metallocene catalyst in gas phase. A model is derived, which is able to describe a large reaction rate increase due to a small amount of incorporated comonomer. This complexation model describes the measured reaction rates for ethylene and 1‐hexene, and the co‐monomer incorporation. Polymer properties were analyzed, such as comonomer weight fraction. The density, melting point, and molecular weight of the produced polymer decreased with increase in 1‐hexene gas concentration. The in situ 1‐hexene sorption is estimated and follows Henry's law, but seems much higher than reported in the literature.

     

Emulsifier‐Free Emulsion Copolymerization of Vinyl Acetate and 3‐Dimethyl(methacryloyloxyethyl)ammonium Propanesulfonate and Swelling Behavior of their Copolymer Matrices

Stable poly{(vinyl acetate)‐co‐[3‐dimethyl(methacryloyloxyethyl)ammonium propanesulfonate]} latexes with different compositions were synthesized by emulsifier‐free emulsion copolymerization. An unusual “overshooting” behavior of the copolymer tablets is explained based on the formation of specific clusters of oppositely oriented dipoles. The variation of their concentration with the zwitterionic monomer unit fraction, ionic strength and temperature is responsible for the differences in the swelling kinetics established. The results show that these parameters can be used to control swelling degree of copolymer matrices and their sustained drug delivery.