Modeling evidence in support of coagulative nucleation theory

An extensive lumped model was developed for emulsion polymerization. It incorporated all of the complex processes: aqueous‐phase radical balances for all radical species arising from initiator decomposition and from exit; determination of radical number inside the particles by balance among rates of radical entry into, exit from, and termination inside the particles; determination of the monomer concentration inside the particles and in the aqueous phase by a thermodynamic equation; and particle formation by micellar, homogeneous, and coagulative nucleation. Model validation was done for the system with styrene (monomer), potassium persulfate (initiator), and sodium dodeceyl sulfate (emulsifier) and for the variables, which included the duration of nucleation, conversion at the end of nucleation, and total number of particles formed. The validation process revealed that coagulation during nucleation needed to be included in the model, even for emulsifier concentrations above the critical micelle concentration. The model predictions were in good quantitative agreement with the experimental data. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011.     

An analysis of various nucleation mechanisms for sulfate particles in the stratosphere

A theoretical analysis of particle formation mechanisms under stratospheric conditions was carried out using a fully interactive one-dimensional model of aerosol formation and evolution. The formation mechanisms considered are homogeneous, ion and heterogeneous heteromolecular nucleation of H₂SO₄---H₂O systems, the clustering of sulfate radicals, and heterogeneous nucleation onto stable neutral ion—ion recombination complexes. We develop theoretical expressions for the nucleation rates, describe the manner in which the nucleation mechanisms are incorporated into the model, and present the results of model calculations. We find that although the different nucleation processes lead to greatly different rates of particle formation, the observed characteristics of the aerosol are hardly affected by the assumed particle formation mechanism. Consequently, it will be difficult to devise measurements to evaluate the relative importance of the various formation mechanisms. Our results show that the homogeneous and ion nucleation rates in the stratosphere are negligible. Heterogeneous nucleation onto stable ion—ion recombination products and the clustering of sulfate radicals are two processes which could lead to the generation of large numbers of particles in the stratosphere. Using presently available experimental techniques it is not possible to determine unambiguously which formation mechanism is responsible for the production of the stratospheric particles.     

Modelling particle size distributions and secondary particle formation in emulsion polymerisation

An extensive model is given for the particle size distribution (PSD), particle number, particle size and amount of secondary nucleation in emulsion polymerisations. This incorporates what are thought to be all of the complex competing processes: aqueous phase kinetics for all radical species arising from both initiator and from exit (desorption), radical balance inside the particles, particle formation by both micellar and homogeneous nucleation mechanisms, and coagulation (the rate of which is obtained using the Healy–Hogg extension of DLVO theory). The predictions of the model are compared to extensive experimental results on rates, time evolution of the particle size distribution, and relative amounts of secondary nucleation, for styrene initiated by persulfate with sodium dodecyl sulfate and with sodium dihexyl sulfosuccinate as surfactants. For this system values of almost all of the many parameters needed for the model are available from independent measurements, and thus no significant parameter adjustment is plausible. Accord with experiment is imperfect but quite acceptable, supporting the validity of the various mechanisms in the model. Effects such as the experimental variation of particle number with ionic strength, as well as calculated coagulation rate coefficients as functions of particle size, suggest that coagulation of precursor (i.e., newly-formed) particles is a significant effect, even above the cmc. The modelling also suggests why secondary nucleation occurs readily in systems stabilised with polymeric surfactant.     

Synthesis of Fe3O4/PMMA composite latex particles: Kinetic modeling

In this work, a generalized mathematical model was developed to estimate the variation of particle concentration during the entire course of soapless emulsion polymerization of methyl methacrylate with ferrofluid. Two mechanisms for the nucleation and growth of particles throughout the polymerization reaction were discussed: Mechanism I – seeded polymerization; and Mechanism II – self‐nucleation polymerization. Here, the self‐nucleation included homogeneous nucleation and micelle nucleation. Coagulation between particles, which came from different nucleation mechanisms during the course of polymerization, was considered and included in this model. When appropriate parameters were selected, this model could be successfully used to interpret the variation of particle concentration during the entire reaction. Under different conditions, rate of polymerization, number of radicals in each particle, average molecular weight of polymers, and rate constant of termination were also calculated. All of them explained the experimental results quite well. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 4925–4934, 2006     

Emulsion polymerization of styrene in a continuous stirred reactor

The emulsion polymerization of styrene has been carried out in a continuous stirred reactor at 50°C. Polymerization rates were initially very high but declined subsequently. These rates did not always attain a steady value, but sometimes oscillated with time. Size analysis of the polymer particles showed that particle nucleation almost stopped soon after start-up. A new generation of particles appeared later in the process. The average number of radicals per particle was usually, but not always, >0.5. The time-average polymerization rate was only weakly dependent on the initiator concentration but varied with the first power of the emulsifier concentration.     

Experimental study of emulsion polymerization with crosslinking

Herein is reported the results of an extensive experimental investigation of the kinetics of emulsion polymerization as affected by crosslinking in the polymer particles. The model monomer system, methyl methacrylate (MMA) and ethylene glycol dimethacrylate (EGDMA), was chosen for this study due to its earlier comprehensive investigation in bulk polymerization. Standard recipes with sodium dodecylsulfate (SDS) as anionic emulsifier and potassium persulfate (KPS) as initiator were used for the batch emulsion polymerizations. Results, which clearly show the effect of crosslinking on the kinetics, are discussed in detail. These include swellability of polymer particles by monomer; polymer particle nucleation rates, below and above the critical micelle concentration (CMC); average number of radicals per particle; and gel-sol levels. It was found advantageous to use electron spin resonance (ESR) to follow radical concentrations during crosslinking in polymer particles. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 66: 935–957, 1997     

Nitroxide mediated living radical polymerization of styrene in miniemulsion—modelling persulfate-initiated systems

Recently we have constructed a mechanistic model describing the nitroxide mediated miniemulsion polymerization (NMMP) of styrene at 135°C, using alkoxyamine initiators to control polymer growth (Nitroxide-Mediated Polymerization of Styrene in Miniemulsion. Modeling Studies of Alkoxyamine-Initiated Systems, 2001b). The model has since been expanded to describe styrene NMMP at 135°C using TEMPO and the free radical initiator, potassium persulfate (KPS). The model includes mechanisms describing reactions in the aqueous and organic phases, particle nucleation, the entry and exit of oligomeric radicals, and the partitioning of nitroxide and styrene between the aqueous and organic phases. Predicted monomer conversions, number average molecular weights and polydispersities were in agreement with experimentally measured values. Model simulations revealed that for systems employing high ratios of TEMPO:KPS, the consumption of TEMPO by polymer radicals derived from KPS decomposition and styrene thermal initiation (using the accepted literature kinetic rates) is not sufficient to lower TEMPO concentrations to levels where polymer growth can occur. By accounting for the consumption of TEMPO by acid-catalyzed disproportionation, TEMPO concentrations are significantly reduced, allowing for accurate model predictions of monomer conversion, number average molecular weight and polydispersity at every experimental condition considered.     

Numerical simulation of particle formation in the rapid expansion of supercritical solution process

In this paper, we numerically study particle formation in the rapid expansion of supercritical solution (RESS) process in a two dimensional, axisymmetric geometry, for a benzoic acid + CO₂ system. The fluid is described by the classical Navier–Stokes equation, with the thermodynamic pressure being replaced by a generalized pressure tensor. Homogenous particle nucleation, transport, condensation and coagulation are described by a general dynamic equation, which is solved using the method of moments. The results show that the maximal nucleation rate and number density occurs near the nozzle exit, and particle precipitation inside the nozzle might not be ignored. Particles grow mainly across the shocks. Fluid in the shear layer of the jet shows a relatively low temperature, high nucleation rate, and carries particles with small sizes. On the plate, particles within the jet have smaller average size and higher geometric mean, while particles outside the jet shows a larger average size and a lower geometric mean. Increasing the preexpansion temperature will increase both the average particle size and standard deviation. The preexpansion pressure does not show a monotonic dependency with the average particle size. Increasing the distance between the plate and the nozzle exit might decrease the particle size. For all the cases in this paper, the average particle size on the plate is on the order of tens of nanometers.     

The role of aqueous-phase kinetics in emulsion polymerizations

The kinetics of species in the aqueous phase control many events in emulsion polymerization: the rate of entry of free radicals into particles (equivalent to initiator efficiency), the rate of exit (desorption) of free radicals from particles, the fate of desorbed free radicals and of free-radical species derived directly from aqueous-phase initiator. Aqueous-phase kinetics also dominate particle nucleation and re-seeding (secondary nucleation), and the in situ formation of surfactant. The mechanisms of each of these events are discussed, and it is shown how general methods can be constructed to deduce the ratedetermining events for each of these. The methodology is then applied extensively to styrene, which leads to the following conclusions. (a) The aqueous-phase events which govern entry (initiator efficiency) are propagation and termination, with entry occurring irreversibly when a critical degree of propagation z is reached so that the resulting species (a di- or tri-styrenesulfonate species in the case of styrene with persulfate initiator) is sufficiently surface-active that, once adsorbed onto the particle it does not desorb before it propagates; the actual adsorption event is sufficiently rapid so as not to be rate-determining except during nucleation. (b) Exit of free radicals is governed by transfer inside the particle to form a monomeric radical which may desorb and diffuse irreversibly away from the parent particle before it propagates therein. (c) The fate of desorbed free radicals in the wide range of styrene systems examined is to re-enter another particle and remain therein, rather than the other possible fates (aqueous-phase termination or re-exit until intra-particle termination eventually occurs). (d) Below the cmc, nucleation is by the homogeneous-coagulative mechanism, while above the cmc, nucleation is through a process which combines the essential features of both homogeneous-coagulative and micellar-entry models. (e) Analysis of the aqueous-phase products produced in an emulsion polymerization shows that the species involved in termination, entry and exit also undergo subsequent reactions: hydrolysis and reaction with persulfate.     

Batch polymerization of methyl methacrylate in mini/macroemulsions

The kinetics of the isothermal batch macroemulsion and miniemulsion polymerizations of methyl methacrylate (MMA) at 50°C have been studied. Hexadecane was used as the cosurfactant or swelling agent. The nucleation mechanisms were observed to be different between macroemulsions and miniemulsions. The effect of surfactant, cosurfactant, initiator, shear, and hold time on droplet nucleation was studied. The miniemulsion particles were found to contain more radicals on average than the macroemulsion particles using certain recipes. This resulted in higher polymerization rates for the miniemulsions at identical particle numbers. The latex-particle-size distributions were similar even though the mini-emulsion droplets start out with a high polydispersity of around 1.5. Miniemulsion latexes were found to be more stable under shear. Conductance of emulsions during polymerization was found to be a valuable on-line tool for investigating particle nucleation and growth. © 1993 John Wiley & Sons, Inc.     

Monomer Effects on Emulsion Polymerization with ASR as the Surfactant

In this paper, alkali soluble resin (ASR) was evaluated as a surfactant in the emulsion polymerizations of methyl methacrylate (MMA), ethyl methacrylate (EMA), and butyl methacrylate (BMA). It was found that the number of particles formed was proportional to the hydrophilicity of monomer and the concentration of initiator. Kinetic analysis indicated that the monomer concentration within the latex particle influences the average number of radicals per latex particle. The increase of monomer concentration within the particle enhances radical desorption from the particle and reduces the average number of radicals per particle. Experimental results show that the grafting reaction of ASR is proportional to the concentration of initiator or ASR. But the hydrophilicity of monomer is the major factor which influences the grafting reaction. This phenomenon is due to the fact that particle nucleation is different between the hydrophilic and hydrophobic monomer.     

Main events occurring in styrene microemulsion polymerization

A previously presented model with four states (conversion, active and inactive particles and micelles) is further tested with conversion versus time experimental data at 50, 60, and 70°C, to recognize the main events occurring in styrene microemulsion polymerization. The S‐shaped conversion–with no overprediction‐ and the bell‐shaped active particles number concentration–evidencing diffusive effects at late stages–versus time data, are well described by the proposed model. It was found that: (i) transfer of monomer and surfactant from micelles to particles occurs, (ii) the capture of radicals by micelles is the only cause of particle nucleation, (iii) the rate coefficient of radical‐entry‐to‐micelles is much smaller than that of exit‐from‐particles, and (iv) no coagulation between particles was detected. The Arrhenius dependency on temperature of the kinetic rate parameters is also reported. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 41720.     

Secondary particle formation in suspension polymerization using a particulate surfactant

ABSTRACT

Suspension polymerization is widely used for the preparation of microsphere and microcapsules for many applications. However, the formation of secondary particle byproducts decreases drastically the obtained microsphere yield and microcapsule shell strength. It is surprisingly finding that the secondary particles were not observed in the preparation of polymethyl methacrylate particles by suspension polymerization using particulate surfactant called Pickering emulsion. Therefore, in this work, the mechanism of secondary particle formation during suspension polymerization was investigated using various surfactants (zinc oxide, titanium dioxide, and silica nanoparticles compared to polyvinyl alcohol) and monomers (styrene, methyl methacrylate, and methyl acrylate) with different water solubilities. Results showed that submicrometer-sized secondary particles were still formed by homogeneous nucleation mainly due to radical exit from the monomer droplets. However, the formed secondary particles were unstable and then adsorbed on the main microsphere surface. The number of secondary particles increased when monomers with higher water solubility were used.     

Modeling and experimental evaluation of an aerosol generator for very high number currents based on a free turbulent jet

In this paper we report on theoretical and experimental work on aerosol formation in a free turbulent jet. A hot DEHS vapor issues through a circular nozzle into slowly moving cold air. Vapor concentration and temperatures are such that particles are formed via homogeneous nucleation close to the nozzle upon mixing with the surrounding air. The vapor is completely quenched in the nucleation regime so that further particle growth is controlled by coagulation. A simple growth dynamics model is presented and the theory is used to design a generation system that produces liquid aerosols at a very high number current [up to 10¹² particles (s)]. The aerosol properties can be controlled by two easily adjustable parameters. The aerosol properties are related to these parameters by simple scaling laws. The results of measurements of the number current and the average particle size support these scaling laws.     

Nitroxide-mediated radical polymerization of styrene in miniemulsion: model studies of alkoxyamine-initiated systems

A mathematical model has been developed to describe the behavior of the nitroxide-mediated miniemulsion polymerization (NMMP) of styrene initiated by alkoxyamine initiators. The model includes mechanisms describing reactions in the aqueous and organic phases, particle nucleation, the entry and exit of oligomeric radicals, and the partitioning of nitroxide and styrene between the aqueous and organic phases. The influence of nitroxide partitioning on the polymerization kinetics was examined by modeling systems initiated by the alkoxyamines BST and hydroxyl-BST; BST and hydroxyl-BST are benzoylstyryl radicals terminated by the nitroxides TEMPO and 4-hydroxyl-TEMPO, respectively.Predicted monomer conversions, number average molecular weights and polydispersities were in agreement with experimentally measured values. Simulations and mathematical analysis showed that the rate of styrene NMMP is not strongly influenced by the partitioning properties of TEMPO and 4-hydroxyl-TEMPO because of the complex interaction between reaction equilibrium, phase equilibrium, termination and thermal initiation. However, in the absence of styrene thermal initiation, nitroxide partitioning was found to have a significant influence on the polymerization kinetics. The model was also used to make quantitative estimates of: the population of active and dormant polymer radicals derived from both alkoxyamine initiators and thermal initiation; the population of dead polymer chains; and the number molecular weight distributions of living and dead polymer chains.     

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。     

Behavior of free radical transfer between aqueous phase and latex particles in emulsion polymerization

The free radical transfer between aqueous phase and latex particles was investigated in the seeded emulsion polymerization using potassium persulfate (KPS) as an initiator. The effects of seed particle size, initiator concentration and polymerization temperature on the radical entry into and/or exit from the particles were emphatically examined. The results suggest that the aqueous-phase radical entry into the particles should be a competitive process, i.e. the competition between radical diffusion from the bulk aqueous phase to the interface of particles and its reactions in the aqueous phase determines whether it may be adsorbed into the particles or not. This implies that the reactions and properties of radicals in the aqueous phase play an essential role in particle nucleation in the emulsion polymerization.     

Fabrication of Fine Mullite Powders by Heterogeneous Nucleation and Growth Processing

Heterogeneous nucleation and growth was used to prepare composite particles with homogeneous component distribution. Composite particles consisting of α-Al₂O₃ cores with an outer amorphous homogeneous silica layer were prepared by heterogeneous nucleation and growth processing using an ethanol suspension containing ammonia, tetraethylorthosilicate, and α-Al₂O₃. Fine mullite powders of average particle size 0.53 μm were fabricated by calcinating the composite particles at 1500°C for 2 h.     

Role of itaconic acid in latex particle nucleation

Itaconic acid, a carboxylated water-soluble monomer, was examined in terms of its role in latex particle nucleation when copolymerized with acrylate monomers. From emulsion polymerizations in which the particle number concentrations were followed as a function of monomer conversion, it was found that the greater the amount of itaconic acid present, the larger the final latex particle diameter. This was interpreted as the result of the lower number of primary particles being initially nucleated. The above observations can be explained by the incorporation of the hydrophilic itaconic acid into acrylate oligomeric radicals that initially form. This incorporation increases the water-solubility of the radicals such that a lower proportion of these radicals is likely to precipitate to form primary particles.     

Measurement of Electrical Charge on Diesel Particles

Nanoparticles (D _p < 50 nm), which are formed as diesel engine exhaust cools and dilutes, constitute minority of total particle mass but majority of total particle number. There are several different theories to explain the nucleation of nanoparticles from diesel exhaust. The two main theories are homogeneous binary nucleation of sulfuric acid and water, and ion-induced nucleation. This study examined the ion-induced nucleation theory. In order to test the ionic nucleation theory, the charged fraction of the diesel particles were measured as a function of particle size using regular diesel fuel in this study. A very small amount of charge was found for the diesel nanoparticles in the nuclei mode, whereas there was a large charged fraction for the diesel particles in the accumulation mode. If ion-induced nucleation were the dominant mechanism for the nucleation of nanoparticles from diesel exhaust, one would expect a significant charge on the nuclei mode particles. The results from this study suggest that ion-induced binary nucleation is at least not a dominant mechanism for the nucleation of diesel exhaust when using regular diesel fuel.

This study also examined the influence of metal additives on nucleation and particle charging. The metal additives examined are of the type used to enhance particle oxidation in diesel particulate filters. When used, the additives led to a large increase in the concentration of solid particles in the nuclei mode, and significantly raised the level of particle charge for particles of all sizes. When additives were used, some of the solid particles in the nuclei mode carried a charge. We believe that these metal related particles form early enough in the combustion process to be charged by ions present during and shortly after combustion.