Population balance modeling of particle size distribution in monomer‐starved semibatch emulsion polymerization

The evolution of particle size distribution (PSD) in the monomer‐starved semibatch emulsion polymerization of styrene with a neat monomer feed is investigated using a population balance model. The system under study ranges from conventional batch emulsion to semicontinuous (micro)emulsion polymerization depending on the rate of monomer addition. It is shown that, contrary to what is often believed, the broadness of PSD is not necessarily associated with the length of nucleation period. The PSDs at the end of nucleation are found to be independent of surfactant concentration. Simulation results indicate that at the completion of nucleation the particle size is reduced and the PSD narrows with decreasing rate of monomer addition despite nucleation time increasing. The broad distribution of particles frequently encountered in semibatch emulsion polymerizations is therefore attributed to stochastic broadening during the growth stage. The zero‐one‐two‐three model developed in this article allows perceiving that the dominant kinetic mechanism may be different for particles with different sizes. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Semibatch emulsion polymerization of butyl acrylate. II. Effects of emulsifier distribution

The effects of emulsifier distribution ratio between the initial charge and the feed on particle formation and kinetics of butyl acrylate emulsion polymerization, using sodium lauryl sulfate as emulsifier and potassium persulfate as initiator, were investigated. The number of particles increased with initial emulsifier concentration in the reactor charge. It was shown that traditional ranking, in terms of number of particles produced, of semibatch emulsion polymerization with monomer emulsion feed is not always justified and a semibatch emulsion polymerization can produce far more particles than a conventional batch emulsion polymerization. The number of polymer particles was found to be practically independent of the emulsifier distribution ratio between the charge and the feed for a high overall emulsifier concentration, while for a low overall emulsifier concentration, the number of particles increased with initial loading of the emulsifier. The polydispersity index (PDI) of the final latexes showed a minimum with emulsifier distribution. A bimodal particle size distribution, and a latex with a large PDI, was obtained when there was no emulsifier in the charge. As the initial emulsifier charge increased, a unimodal PSD with a smaller PDI was obtained. With higher proportions of emulsifier in the initial charge, the PDI rose again due to particle nucleation at monomer‐starved conditions, and a skewed unimodal PSD was obtained. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 79: 582–597, 2001     

Semibatch emulsion polymerization of butyl acrylate. I. Effect of monomer distribution

The effects of initial monomer charge on the particle formation and on the rate of polymerization were investigated for semibatch emulsion polymerization of butyl acrylate using sodium lauryl sulfate (SLS) as a surfactant and potassium persulfate (KPS) as an initiator. For the semibatch process with monomer (M) feed, it was found that by varying the monomer distribution ratio between the initial reactor charge and the feed it is possible to alter the contribution of monomer‐flooded and monomer‐starved nucleation mechanisms to the whole nucleation process. The number of particles increases as the initial monomer charge decreases, if the monomer concentration is below a critical value for any fixed system. The increase in number of particles is associated with a broad particle‐size distribution which might depict an emerging second peak on the particle‐size distribution curve. For low emulsifier concentration systems, a larger number of particles was obtained for a lower amount of monomer charge. Particle coagulation and emulsifier adsorption on the monomer droplets were counted as the main reasons for such behavior. For a semibatch process with monomer emulsion (ME) feed, the larger number of particles was formed at a lower initial monomer charge, similar to an M‐add semibatch process. However, the application of monomer charge to an ME‐add process was found to increase the possibility of secondary nucleation and led to the occurrence of a bimodal particle‐size distribution. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 3094–3110, 1999     

Polymer chain extension in semibatch emulsion polymerization with RAFT‐based transfer agent: The influence of reaction conditions on polymerization rate and product properties

A mathematical model was developed for batch and semiemulsion polymerizations of styrene in the presence of a xanthate‐based RAFT agent. Zero–one kinetics was employed along with population balance equations to predict monomer conversion, molecular weight (MWD), and particle size (PSD) distributions in the presence of xanthate‐based RAFT agents. The effects of the transfer agent (AR), surfactant, initiator, and temperature were investigated. Monomer conversion, MWD, and PSD were found to be strongly affected by monomer feed rate. The polymerization rate (Rp), number average molecular weight (Mn) and particle size (r) decreased with increasing AR. With increases in surfactant and initiator concentrations Rp increased, whereas with increase in temperature Mn decreased, Rp increased and r increased. In semibatch mode, Mn and r increased with increase in monomer flow rate. By feeding the RAFT agent along with the monomer (F_M/F_AR = N_Mo/N_ARo = 100), Mn attained a constant value proportional to monomer/RAFT molar ratio. The observed retardation in polymerization and growth rates is due to the exit and re‐entry of small radicals. Thus, chain extension was successfully achieved in semibatch mode. The simulations compared well with our experimental data, and the model was able to accurately predict monomer conversion, Mn, MWD, and PSD of polymer products. Our simulations and experimental results show that monomer feed rate is suitable for controlling the PSD, and the initial concentration and the feed rate of AR for controlling the MWD and PSD. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

High solids content emulsions. III. Synthesis of concentrated latices by classic emulsion polymerization

Two different methods of producing bi‐ and trimodal latices of a mixture of methyl methacrylate, butyl acrylate, and small amounts of acrylic acid were tested. It is shown that a combination of concentrating blends of seed particles by semibatch reaction, followed by a nucleation of small particles plus a second semibatch phase allowed us to obtain stable latices with solids contents over 65% and viscosities of below 2500 mPa s^?1 with little coagulum formation. The key parameter in determining latex stability, coagulum formation, and viscosity appears to be the the particle size distribution, and especially its modification attributed to secondary nucleation. Because it is not possible to eliminate water‐soluble monomers from the polymerization recipe, secondary (homogeneous) nucleation must be minimized by careful addition of the free‐radical initiator and choice of monomer feed flow rates. The nucleation of the third population in the trimodal latices is best accomplished with a mixed surfactant system because renucleation by anionic surfactant alone leads to detrimental changes in the particle size distribution (PSD) resulting from excessive flocculation of particles. In addition, it was found that the viscosity of the final products was not sensitive to small changes in the ionic strength of the latex, although neutralization to a pH of 6 effectively doubles the final latex viscosity. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 84: 1916–1934, 2002; DOI 10.1002/app.10513     

乳液聚合成核阶段的模拟与分析

建立了乳液聚合成核阶段的Monte Carlo模型，并用计算机对一个体积为10^-17m^3的微型反应器中苯乙烯的乳液聚合进行了模拟。以计算机生成随机数作为自由基被胶束和乳胶粒捕获的几率，模拟了在微型反应器中每一个自由基的生成、被胶束或乳胶粒捕获的过程以及每一个乳胶粒的生成及增长过程。通过对每一个乳胶粒在增长过程中各参数的统计计算，研究了乳液聚合成核阶段诸参数(乳胶粒数目、乳胶粒直径与粒径分布、单体转化率、聚合反应速率等)与乳化剂浓度[S]及引发剂浓度[I]的关系。结果表明，苯乙烯的乳液聚合体系中乳胶粒数目与[S]^0.5996[I]^0.4016成正比：在成核阶段乳胶粒直径分布先变宽后变窄，乳液聚合过程中乳胶粒直径分布有自动变窄的趋势；成核阶段持续时间t12与[S]^0.60[I]^0.60成正比，成核阶段结束时的单体转化率X12与[S]^1.20[I]^0.20成正比。     

Thiol-ene emulsion polymerization using a semi-continuous approach

The thermally initiated thiol-ene emulsion polymerization of diallyl phthalate (DAP) diene and ethylenedioxy diethanthiol (EDDT) dithiol monomers in batch and semibatch emulsion polymerization is investigated. The batch process leads to larger and broader particle sizes than when the polymerization is carried out in semibatch. The evolution of the particle size and the final particle size distribution indicate that the stability of the latexes is limited and, hence, aggregation phenomena occurred in both processes. In particular, the evolution of the particle size distribution (PSD) in the semibatch process indicates nucleation, growth, and aggregation occurring simultaneously that produced a bimodal particle size. When the diene monomer was changed to diallyl terephthalate (DATP), the semibatch polymerization yielded smaller particles and narrow distribution without any indication of aggregation. The partial substitution of the dithiol by a trithiol monomer that is substantially more water insoluble affected nucleation of the particles, yielding for both systems smaller particles. The polythioether polymers synthesized present low glass transition temperatures (~ −30/−40°C) and those containing the therephthalate yield crystalline films. The potential application of the polymers as pressure sensitive adhesives (PSAs) was preliminarily assessed.     

DEM study on the discharge characteristics of lognormal particle size distributions from a conical hopper

This study employs the discrete element method (DEM) to investigate the impact of the widths of lognormal particle size distributions (PSDs) with the same mean particle diameter on hopper discharge behaviors, namely, discharge rate, particle velocities, and size‐segregation. Results reveal that (i) the hopper discharge rate decreases as PSD width increases; (ii) the mean discharge rates are constant with time, but the fluctuations increase as the PSD width increases; (iii) the overall size‐segregation increases with PSD width; (iv) the overall mean particle diameters of the narrower PSDs do not exceed the initial mean of 5 mm, whereas that of wider ones do; (v) the relationship between PSD width and particle velocities is non‐monotonic with no consistent trends; and (vi) no direct correlation exists between particle velocity and size‐segregation. The results here provide valuable insights on the behavior of the prevalent polydisperse mixtures in hoppers. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1174–1190, 2018     

Morphology of poly(butyl acrylate)/poly(styrene‐co‐methyl methacrylate) latex prepared by starved emulsion polymerization: II. Development of particle morphology

Heterogeneous latexes were prepared by a two‐stage seeded emulsion polymerization process under monomer starved conditions at 80 °C using potassium persulfate as the initiator and sodium dodecyl sulfate as the emulsifier. Poly(butyl acrylate) latexes were used as seeds. The second‐stage polymer was poly(styrene‐co‐methyl methacrylate). By varying the amount of methyl methacrylate (MMA) in the second‐stage copolymer, the polarity of the copolymer phase could be controlled. It was found that the latex particles displayed different morphologies depending on the monomer ratio. The amount of MMA had a significant effect on the evolution of morphology. The morphologies were observed by transmission electron microscopy. In addition, the evolution of the particle morphology was predicted by the mathmatical model for cluster migration. The model gave the same trends as the experimental results. © 2002 Society of Chemical Industry     

Batch emulsion polymerization of vinyl chloride: Application of experimental design to investigate the effects of operating variables on particle size and particle size distribution

In this article, the influences of operating variables on the particle size (PS) and particle size distribution (PSD) of emulsion poly(vinyl chloride) in batch reactor were investigated using Taguchi experimental design approach. The variables were temperature (T), water to monomer weight ratio (R), concentrations of initiator ([I]) and emulsifier ([E]), and agitation speed (S). Scanning electron microscope was used together with image analysis software to determine the PS and PSD. Statistical analysis of results revealed that the PS of emulsion poly(vinyl chloride) strongly depends on emulsifier and initiator concentrations, respectively, whereas the other factors have no significant effects in the range of levels investigated in this study. Except initiator concentration, all factors have important influence on the PSD (significance sequence: S > R > T > [E]). It is implied from the greater influence of agitation speed relative to temperature on PSD that the shear coagulation predominates the Brownian coagulation in this system. The relative optimum condition for a typical paste application was also determined using overall evaluation criteria. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

用阴离子Gemini 9 B-6-9 B乳化剂合成苯乙烯-丙烯酸丁酯共聚物纳米乳液

以壬基酚、1,6-二溴己烷、氯磺酸为主要原料合成的阴离子Gemini磺酸盐表面活性剂9 B-6-9 B为乳化剂,苯乙烯(St)、丙烯酸丁酯(BA)为单体,合成了乳胶粒径小于100 nm且分布均匀的苯乙烯-丙烯酸丁酯共聚物纳米乳液,考察了聚合温度、乳化剂用量、引发剂用量、单体配比、单体含量对乳液的影响,探讨了乳胶粒子成核机理。结果表明,随着温度的升高,乳胶粒子的平均粒径减小,转化率与凝胶率增大;随着乳化剂或引发剂用量的增加,乳胶粒子的平均粒径和凝胶率减小,转化率增大;随着软单体比例的增加,乳胶粒子的平均粒径与转化率增大,粒径分布变宽,凝胶率减小;单体用量增大,乳胶粒子的平均粒径与凝胶率增大,转化率降低;乳胶粒子的粒径呈单峰分布,可能是按胶束成核机理形成的。     

Semibatch emulsion copolymerization of butyl acrylate and glycidyl methacrylate: Effect of operating variables

Semibatch emulsion copolymerization was carried out to prepare poly(butyl acrylate‐co‐glycidyl methacrylate) latexes at 75°C, using potassium persulfate as an initiator, sodium dodecylbenzene sulfonate as an emulsifier and sodium bicarbonate as a buffer. The reaction was conducted in three stages; a further stage (called the steady stage, 2 h) was added to the traditionally stages (i.e., feed and seed stages) to improve considerably the monomer conversion. The monomer conversion and particle size distribution were studied by gravimetric and laser light scattering methods, respectively. The effects of variables such as agitation speed, emulsifier concentration, initiator concentration, feeding rate and comonomers ratio were fully investigated based on the monomer conversion‐time profiles and the particle size distribution to find the optimized copolymerization conditions. Increasing the agitation speed had a negative effect on the monomer conversion, but reduced coagulation of polymer particles. Monomer conversion could be improved by increasing the initiator or emulsifier contents. Feeding rate increased the polymer particle size sharply; however, it showed no significant effect on conversion. The final conversions were as high as 97–99% and they were recognized to be independent of the comonomers ratios employed. Morphological studies by scanning electron microscopy showed nano‐sized isolated particles which were partially aggregated. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

中空聚合物微球的制备——种子及核乳胶粒的制备

为了制得具有中空结构的聚合物微球,首先以十二烷基苯磺酸钠(SDBS)为乳化剂,在其用量低于CMC的条件下,进行甲基丙烯酸甲酯(MMA)、甲基丙烯酸(MAA)和丙烯酸丁酯(BA)的乳液聚合,制备了带羧基的种子乳胶粒.然后采用MMA、MAA和二乙烯基苯为单体进行种子乳液聚合,制备了轻度交联的带羧基的核乳胶粒.该核乳胶粒经过核-壳乳液聚合和适当的碱处理工艺就可成为具有中空结构的聚合物微球.采用粒度仪测定了乳胶粒的直径及其分布,采用TEM对乳胶粒结构形态进行了表征.研究了种子及核乳胶粒制备过程中单体加料方式、乳化剂用量及羧基单体种类等因素对聚合稳定性、乳胶粒直径及其分布以及最终的中空聚合物微球结构形态的影响,确定了制备种子及核乳胶粒的最佳工艺条件.在制备种子阶段,SDBS用量为单体总量的0.5%,采用一次性加入单体的进料工艺;在核乳胶粒制备阶段,以MAA为羧基单体,所有单体采用"饥饿式"加料,半连续补加乳化剂并使乳化剂用量为核单体总量的0.15%时可保持聚合稳定性并保证无新乳胶粒生成.     

Reduced-order methodologies for feedback control of particle size distribution in semi-batch emulsion copolymerization

Within-batch feedback control strategies are developed for the regulation of the particle size distribution (PSD) in a semibatch vinyl acetate (VAc)/butyl acrylate (BuA) emulsion copolymerization system. These strategies are also applicable for regulation of distributions in other particulate systems governed by population balances. In the first strategy, PID controllers are employed for regulating nucleation and growth events through tracking the nominal trajectories of total number of particles and the solids content by manipulating the feed-rates of the more reactive monomer, BuA, and the surfactant. The second control strategy is based on tracking nominal trajectories of the moments of the distribution with a quadratic dynamic matrix controller (QDMC). To determine the appropriate number of moments to describe the PSD during various stages of a nominal batch, a maximum-entropy approach is utilized. In the final and most complex approach, a nonlinear model predictive controller is designed utilizing the detailed population balance model of the system. The ill-conditioning resulting from the high-dimensionality of the resulting dynamical system is removed by principal component analysis (PCA)-based model order reduction and a multi-rate estimator is designed to compensate for the measurement delay associated with the PSD measurements.     

Kinetic investigations of acrylic–polyurethane composite latex

The effect of various reaction parameters on the rate of polymerization, R_p, and on the particle size and morphology of aqueous acrylic–polyurethane hybrid dispersions, prepared by semibatch emulsion polymerization, was investigated. The particles of polyurethane dispersion were used as seeds during the polymerization of acrylic component: methyl methacrylate (MMA), butyl acrylate (BA), and a mixture of MMA and BA with the ratio of 1:1. These emulsions were found to form structured polymer particles in aqueous media using scanning electron microscopy. The kinetics of the emulsion polymerization was studied on the basis of Wessling's model. The influence of emulsifier and initiator concentrations, including the monomer feed rates, R_m, on the rates of polymerization and on the properties of the resulting dispersions were studied. The number of particles and the particle size were also measured during the polymerization process. The final values were found to be independent of the concentration of the emulsifier, initiator and the monomer feed rate in monomer starved conditions. In the steady‐state conditions, during the seeded semibatch hybrid emulsion polymerization, the rate of polymerization and the monomer feed rate followed the Wessling relationship 1/R_p = 1/K + 1/R_m. The dispersions MMA/PU, BA/PU, and MMA/BA/PU have K values of 0.0441, 0.0419 and 0.0436 mol/min, respectively. The seeded BA/PU hybrid polymerization proceeded according to Smith‐Ewart Case I kinetics, while the MMA/PU hybrid emulsions demonstrate Case II of the Smith‐Ewart kinetic model. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 84: 2639–2649, 2002     

Particle nucleation and growth in seeded semibatch miniemulsion polymerization of hybrid CeO2/acrylic latexes

CeO₂/acrylic hybrid coatings with high solids content and with nanoparticle percentages up to 5 wt% have been successfully synthesized by seeded semibatch miniemulsion polymerization process. The droplet nucleation efficiency has been assessed by Capillary Hydrodynamic Chromatography and TEM analysis. The effect of the stability of the miniemulsion, the type of initiator and the number of particles of the seed on the efficiency of the nucleation of the nanodroplets fed has been investigated. It was found that the less stable the hybrid miniemulsion, the higher the diffusion of the monomer out of the droplets and hence, the seed latex particles grew in size. However, the CeO₂ nanoparticles did not diffuse out with the monomer and remained in very small droplets that eventually nucleate leading to a bimodal population. When stable miniemulsions were produced by using a polymer as hydrophobe, droplet size increased reducing the number of particles in the seed and monomer diffusion was minimized enhancing nucleation of droplets with larger sizes that produced broad PSDs. Coalescence of droplets was negligible because the size distribution of the nanoceria particles did not change from the seed particles to the final latex. The UV–Vis absorption capacity of the films prepared with increasing the amount of CeO₂ increased, but scattering effects were observed at high loading of CeO₂ due to the large size of the CeO₂ aggregates.     

The use of amylose‐rich starch nanoparticles in emulsion polymerization

Regenerated starch nanoparticles (RSNPs) produced from dent corn, an amylose‐rich source of starch, are added to an emulsion polymerization. To reduce or eliminate the challenges of polymerizing in the presence of amylose‐rich starch, a seeded, semibatch, monomer‐starved approach is used. To prevent the accumulation of water soluble amylose in the aqueous phase, reaction with a hydrophobic compatibilizing monomer, butyl acrylate, is used prior to the primary butyl acrylate/methyl methacrylate/acrylic acid feed. In addition, an elevated initiator concentration is used in the seed stage to reduce the molecular weight of the soluble starch and promote grafting. The procedure yields a 100.0 cp latex with 40 wt % solids, 25 wt % RSNP loading, and 40 wt % incorporation. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018 , 135, 46485.     

Monte Carlo模拟在丁二烯/苯乙烯乳液聚合中的应用研究

以概率论中的大数法则和中心极限定理为基础,通过对成核阶段条件的简化,建立了丁二烯/苯乙烯乳液聚合成核阶段的Monte Carlo模型,模拟考察了乳化剂、引发剂浓度对丁苯乳液聚合反应速率的影响,对丁苯乳聚成核阶段模拟结果进行回归表明,乳胶粒数目N p与乳化剂浓度[S]和引发剂浓度[I]的关系为：N p=k[S]0.606 2[I]0.405 5,与Smith-Ewart经典理论相吻合。改善乳液聚合生成的乳胶粒径分布以及乳胶粒数目是提高乳液聚合中单体转化率最为有效的方法。模拟计算结果表明,将单体转化率从62%提高到70%,引发剂浓度的增加量应在12.90%~34.89%（摩尔分数）之间,乳化剂浓度的增加量应在12.6%~22.16%（摩尔分数）之间。与实验结果进行对比,数据吻合,验证了模拟计算的可靠性和有效性。     

Miniemulsion and macroemulsion copolymerization of vinyl acetate with vinyl versatate

The miniemulsion and macroemulsion polymerization of vinyl acetate with vinyl versatate in batch and semibatch systems was investigated. Vinyl versatate was added either as an emulsion with the vinyl acetate, or as a neat liquid stream. In the batch runs, there is a poor dispersion of vinyl versatate during the nucleation period for the runs in which the vinyl versatate was added neat at the beginning of the polymerization. This led to smaller particles, lower polymerization rate, and different polymer composition evolution when compared with runs in which the vinyl versatate was emulsified with the vinyl acetate. In seeded semibatch runs, residual surfactant in the seed latex, along with the propensity for homogeneous nucleation in vinyl acetate emulsions, resulted in continuing nucleation during the entire semibatch interval. The polymerization rate was primarily affected by monomer feed rate rather than the feeding mode. The effect of monomer feeding mode on copolymer composition was weak when the semibatch feed rate was low, indicating some level of vinyl versatate mass transfer resistance. In all runs, only one glass transition temperature was observed, indicating effective copolymerization. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 2219–2229, 2002     

High solids content emulsions. II. Preparation of seed latices

The preparation of concentrated seed latices for use in bimodal and trimodal formulations is presented in the current work. Various recipes of surfactant and initiator were tested in order to allow us to control the number of particles produced during the nucleation stage. Following this, a semi‐batch feed recipe that combined the use of oil‐soluble initiators and pre‐emulsified monomer was used to produce well‐defined latices having well defined particle size distributions. It was found that the primary concern in maintaining latex stability and favorable viscosity was the reduction of undesirable secondary nucleation. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 84: 1897–1915, 2002; DOI 10.1002/app.10512