Emulsion polymerization of styrene: Simulation the effects of mixed ionic and non-ionic surfactant system in the presence of coagulation

A detailed model was developed for emulsion polymerization of styrene in batch reactor to predict the evolution of the product particle size distribution. The effect of binary surfactant systems (ionic/non-ionic surfactants) with different compositions was studied. The zero–one kinetics was employed for the nucleation rate, with the model comprising a set of rigorously developed population balance equations. The modeling incorporated particle formation by both nucleation and coagulation phenomena. The partial differential equations describing the particle population were discretized using finite volume elements. Binary surfactant systems, comprising sodium dodecyl sulfate (SDS) as anionic, and a commercial polyether polyol (Brij35^®) as non-ionic surfactants, were examined with different mass ratios. Increasing non-ionic surfactant mass fraction in binary surfactant system showed the decrease of particle number due to intensifying the coagulation between particles. Broader particle size distributions with greater average particle size were obtained with non-ionic surfactant comparing those obtained with anionic one.     

Numerical study on particle size distribution in the process of preparing ultrafine particles by reactive precipitation

Based on the population balance and mass balance in a reactive precipitation process, a numerical simulation model was developed to predict the particle size distribution (PSD) in the reactive precipitation process. The precipitation system of BaCl₂ with Na₂SO₄ to prepare BaSO₄ in aqueous solution was adopted to obtain ultrafine particles in a stirred precipitation reactor and the particle size distribution and the morphology of the particle were observed under transmission electron microscope. It was illustrated by the experimental observation of the micrographs of BaSO₄ particles obtained that apparent agglomeration occurred between the particles, which phenomenon must be taken into consideration in PSD modeling. The population balance equation was calculated by discretization method to obtain particle number and particle size distribution. By implementing the model, the reactive precipitation process in a batch reactor including reaction, nucleation, growth and agglomeration was simulated. The simulation results were validated by the experimental data of BaSO₄ precipitation. Further analysis was endeavored to explore the effects of some important factors such as the supersaturation degree and agglomeration on the evolution of the volume-based characteristic particle size and the variance of volume-based characteristic size of the particles. It was depicted that particle size and particle size distribution are controlled by the supersaturation degree and agglomeration between the particles. Stemming from the analysis in the context, the disciplinarian of the influences of these factors and the method for controlling particle size distribution were presented for the reactive precipitation process.     

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.     

A basic population balance model for fluid bed spray granulation

A basic population balance approach is developed for a granulation process in a fluid bed spray granulator. The particle size distribution predicted by the model is confirmed by plant data. Hence this model is considered to be useful to describe and optimize an industrial process. The model depends on a limited number of parameters (most of these factors can be measured or are known): the spray volume flux, the nucleation fraction (the fraction of the spray volume flux which leads to new particles formed), the nucleation particle diameter, the product withdrawal threshold diameter, and the product withdrawal rate. Analysis of the model reveals a steady-state constraint; a steady state does not exist if the nucleation fraction is too large. For cases where the steady state does exist, the steady-state particle size distribution is solved analytically. A numerical implementation of the model is used to illustrate the transient evolution of the process. The steady-state solution appears to be stable for a constant nucleation fraction. However, if the nucleation fraction depends on the bed height the steady state can be unstable. Such a situation may occur if the spray inlet is near the height of the bed surface. Instead of convergence towards a steady state, the transient solution displays ongoing oscillatory behavior with an oscillation period of a number of hours. A linear stability analysis is performed to confirm the findings on the stability of the steady state.     

Controlled Nucleation Aerosol Reactors: Production of Bulk Silicon

A new type of aerosol reactor is described. By controlling the rate of gas phase reactions such that vapor diffusion to existing particles is favored over homogeneous nucleation, a small number of seed particles can be grown to supermicron sizes. A model for the influence of growing particles on the rate of homogeneous nucleation has been used to design a reactor for the production of silicon particles by thermal decomposition of silane gas. Particles as large as 9 μm mass median diameter have been grown in this two-stage reactor. Silicon aerosol yields ranging from 70% to 83% have been achieved with this system.     

The heterogeneous nucleation of microcellular foams assisted by the survival of microvoids in polymers containing low glass transition particles. Part I: Mathematical modeling and numerical simulation

The existing models based on classical nucleation theory are not able to explain satisfactorily the nucleation phenomenon of microcellular foams in thermoplastics. Here, we extend the analysis of Kweeder (24), who developed a new model that considers the presence of microvoids, resulting from the thermal processing history of the polymer, as potential nucleation sites. The nucleation model “concentrates” on the stresses and thus void formations in the rubber particles. Since these are pre-existing microvoids, bubble nucleation depends on the survival of these voids to grow rather than the formation of a new phase as modeled by classical nucleation theory. The population of viable microvoids with a sufficiently large radius to survive and overcome surface and elastic forces has been modeled to yield the cell density. A log-normal distribution, which relates to the rubber particle size, has been used to model the distribution of microvoids in the polymer composite material. The model depends on various process parameters such as saturation pressure, foaming temperature, concentration of nucleating agents, solubility of the blowing agent in the polymer, and the modulus. High impact polystyrene (HIPS) was added to polystyrene to obtain polymers with different concentrations of rubber gel particles, the nucleating agent, and used here for this study.     

Fluidized‐bed reactor modeling for polyethylene production

Gas‐phase technology for polyethylene production has been widely used by industries around the world. A good model for the reactor fluid dynamics is essential to properly set the operating conditions of the fluidized‐bed reactor. The fluidized‐bed model developed in this work is based on a steady‐state model, incorporating interactions between separate bubble, emulsion gas phase, and emulsion solid polymer particles. The model is capable not only of computing temperature and concentration gradients for bubble and emulsion phases, calculating polymer particle mean diameter throughout the bed and polyethylene production rate, but also of pinpointing the appearance of hot spots and polymer meltdown. The model differs from conventional well‐mixed fluidized‐bed models by assuming that the particles segregate within the bed according to size and weight differences. The model was validated using literature and patent data, presenting good representation of the behavior of the fluidized‐bed reactor used in ethylene polymerization. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 321–332, 2001     

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.     

Analysis of non-spherical polydisperse particle growth in a two-dimensional tubular reactor

Polydisperse aggregate particle growth considering coalescence, coagulation, generation and spatial transport processes is studied in a two-dimensional reactor for the first time. Effects of two-dimensional spatial transport processes, such as convection, diffusion, deposition and thermophoresis as well as nucleation, coagulation and coalescence are of primary interests. An efficient particle dynamics model based on two sets of coupled sectional equations (J. Aerosol Sci. 32 (2001) 565) is used to facilitate the severe computation loads for analyzing the growth of non-spherical polydisperse particles in an axi-symmetric two-dimensional geometry. Fluid dynamics calculations indicate the existence of non-uniform distributions of temperature and flow fields in the radial direction as well as in the axial direction inside the reactor. Particle dynamics simulations also demonstrate the significant inhomogeneous spatial distributions of the characteristics of aggregate particles. The present two dimensional calculations for reactor temperatures and particle size distributions are in agreement with the previous experimental data. The validity of simplified one-dimensional analysis is also evaluated against the present two-dimensional analysis. While the one-dimensional analysis agreed well with the spatially two-dimensional one for the cases of low flow rates, it resulted in significant errors for high flow rates.     

The performance of the emulsion polymerization of styrene in a continuous loop tubular reactor

The emulsion polymerization of styrene in a continuous loop tubular reactor (CLTR) has been used to study the process kinetics under eigth levels of sodium lauryl sulfate (SLS) concentration, eight levels of potassium persulfate (KPS) concentration, and three levels of styrene monomer (St) concentration. A critical surfactant concentration for the overshoot phenomenon in the monomer conversion exists between 8.02 and 12.40 g-SLS/1-water. Overshoot was not eliminated by changing concentrations of the initiator and monomer. The overshoot in the number concentration of polymer particles was observed in all the polymerizations studied. The dependences of the rate of polymerization and the number concentration of particles in the steady state on the SLS and KPS concentrations are presented. The growth of the average cumulant diameter of particles shows a transient period followed by a steady state. The dependences of the volumetric growth rate of polymer particles on diameter are of the order of 1 for the lower SLS concentration and 0.5 for the higher SLS concentration, respectively. The steady state cumulant diameter depends on an order of ?0.24 for the SLS concentration.     

A Mathematical Model for Ultrafine Iron Powder Growth in a Thermal Plasma

ABSTRACT

A two-dimensional model is developed for the growth of ultrafine metal powders in a thermal plasma reactor. The model accounts for particle formation by nucleation, and growth by condensation and Brownian coagulation. Transport of particles occurs by convection, thermophoresis, and Brownian diffusion. The conservation equations for the moments of the particle size distribution are solved, coupled to the equation for the conservation of metal vapor. Elliptic conservation equations result from the consideration of both axial and radial diffusion of the particles. This allows for simulations in complex, recirculating flows, which are likely to occur for numerous reactor configurations and parameters. A progressive grid refining technique is used to accelerate convergence. The model is applied to the case of a typical thermal plasma reactor for the production of ultrafine iron powders. The fields of the macroscopic properties of the aerosol population and the contribution of the different mechanisms are analyzed in various conditions, some of which involve important recirculations. The effect of operating parameters on the properties of the powder generated is studied. The results are compared for some of the conditions to those obtained numerically and experimentally by Girshick et al. (1993).     

Computational Modeling of Silicon Nanoparticle Synthesis: II. A Two-Dimensional Bivariate Model for Silicon Nanoparticle Synthesis in a Laser-Driven Reactor Including Finite-Rate Coalescence

In this work, a two-dimensional model was developed for silicon nanoparticle synthesis by silane thermal decomposition in a six-way cross laser-driven aerosol reactor. This two-dimensional model incorporates fluid dynamics, laser heating, gas phase and surface phase chemical reactions, and aerosol dynamics, with particle transport and evolution by convection, diffusion, thermophoresis, nucleation, surface growth, coagulation, and coalescence processes. Because of the complexity of the problem at hand, the simulation was carried out via several sub-models. First, the chemically reacting flow inside the reactor was simulated in three dimensions in full geometric detail, but with no aerosol dynamics and with highly simplified chemistry. Second, the reaction zone was simulated using an axisymmetric two-dimensional CFD model, whose boundary conditions were obtained from the first step. Last, a two-dimensional aerosol dynamics model was used to study the silicon nanoparticle formation using more complete silane decomposition chemistry, together with the temperature and velocities extracted from the reaction zone CFD simulation. A bivariate model was used to describe the evolution of particle size and morphology. The aggregates were modeled by a moment method, assuming a lognormal distribution in particle volume. This was augmented by a single balance equation for primary particles that assumed locally equal number of primary particles per aggregate and fractal dimension. The model predicted the position and size at which the primary particle size is frozen in, and showed that increasing the peak temperature was a more effective means of improving particle yield than increasing silane concentration or flowrate.     

Semibatch styrene suspension polymerization processes

Emulsion and suspension polymerization processes have widely been studied for more than 40 years. Although both polymerization processes are performed in heterogeneous media, each one presents its own typical characteristics, such as the particle size distribution, molecular weight distribution, polymer particle nucleation rate, and polymerization rate. In this study, semibatch styrene suspension polymerizations were carried out with feed compositions typical of emulsion processes. The initial reactor charge resembled the recipe of standard styrene suspension polymerizations, and the emulsion polymerization constituents were added during the batch. The influence of the moment at which the emulsion feed was started on the course of the polymerization and the effects of the feed on the polymer properties were analyzed. The polymer particle morphology and the average molecular weights changed very significantly with the emulsion feed time, and the changes could lead to the production of broad molecular weight distributions. Core–shell polymer particles could also be obtained, with the core being formed of polymer particles originating from the suspension polymerization process and the shell being formed of polymer particles originating from the emulsion polymerization. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 3021–3038, 2003     

Two‐dimensional model of methane thermal decomposition reactors with radiative heat transfer and carbon particle growth

A two‐dimensional model of methane thermal decomposition reactors is developed which accounts for coupled radiative heat and polydisperse carbon particle nucleation, growth, and transport. The model uses the Navier–Stokes equations for the fluid dynamics, the radiative transfer equation for methane and particle species radiation absorption, the advection–diffusion equation for gas and particle species transport, and a sectional method for particle species nucleation, heterogenous growth, and coagulation. The model is applied to a tubular laminar flow reactor. The simulation results indicate the development of a reaction boundary layer inside the reactor, which results in significant variation of the local particle size distribution across the reactor. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2545–2556, 2012     

Characterisation of an anticorrosive phosphated surfactant and its use in water-borne coatings

The physicochemical features of a surfactant are quite important in the formulation of polymer water-borne coatings mainly due to the strong influence of the micelles on the nucleation and stability of dispersed polymer particles. In consequence, micellar transitions must be determined in order to obtain aqueous dispersions of spherical shaped particles with high monodispersion in size, which allows to obtain coatings with an improved performance. Besides, depending on its chemical structure, the surfactant could also have anticorrosive properties. In this work, a phosphate-based surfactant was characterised and its electrochemical properties were evaluated in order to use it as a stabiliser agent of a series of monodisperse styrene-acrylic lattices, synthesised by semi-continuous emulsion polymerisation. EIS was used to evaluate the anticorrosive properties of coatings obtained from polymeric dispersions.     

Seeded emulsion polymerization of n-butyl acrylate utilizing miniemulsions

Nucleation of polymer particles in the seeded emulsion polymerization of n-butyl acrylate (BuA) was studied through experiments designed to control the amount of new particles formed. The results show that for the batch and semicontinuous seeded polymerization of BuA, a small amount of new particles was formed in the system in which the monomer was added neat, whereas a singificant amount of new particles was formed when the monomer was added as a miniemulsion. This suggests that new particles formed in the miniemulsion process were from nucleation of the monomer droplets. These experiments also showed that monomer-droplet nucleation decreased with increasing seed concentration in the reactor. For the seeded semicontinuous polymerizations, monomer-droplet nucleation decreases with decreasing BuA miniemulsion feed rate. The results also show that monomerdroplet nucleation takes place whenever miniemulsion droplets exist in the reactor. This study suggests that miniemulsions can be used to control the particle size distribution of a polymer latex system.     

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     

Influence of monomer preemulsification on formation of particles from monomer drops in emulsion polymerization

Evidence was obtained supporting the theory that monomer droplets can become a locus of initiation and propagation in emulsion polymerization. This was done by reducing the size of the monomer droplets prior to initiation of polymerization using different preemulsification techniques for a typical latex recipe containing a common anionic surfactant. Monomer droplet size reduction caused an increase in the total surface area of the monomer droplets and thereby increased the competitiveness of these droplets for capturing active free radicals which are generated in the aqueous phase. As the total surface area of the monomer droplets was increased by preemulsification, a corresponding increase in the number of large particles formed by polymerization of these monomer droplets was experimentally measured. This work shows that monomer droplets are a locus of emulsion polymerization. However, the importance of monomer droplet polymerization is limited by their total surface area because of the competition for free radicals with other surfaces and/or particle nucleation processes. The results offer a basis for explaining why broad, and sometimes bimodal, particle size distributions are obtained in some commercial processes where the reactants are preemulsified prior to being charged into a reaction vessel.     

Simulation of true moving bed adsorptive reactor: Detailed particle model and linear driving force approximations

A new true moving bed (TMB) adsorptive reactor model with a detailed particle approach is presented introducing the formulation of the mass balance for the solid phase in counter-current moving systems. The system studied here is the enzymatic inversion of sucrose into fructose and glucose and subsequent separation of glucose/fructose; the reaction occurs both in the outer fluid phase and inside particles. Model equations include film mass transfer, intra-particle diffusion resistance, axial dispersion for the outer fluid phase, plug flow of the solid phase and linear adsorption equilibrium of glucose/fructose. This new model is compared with previous LDF-type approximations for reactive systems and applied to pure separative TMB process. The numerical solution of model equations is obtained for transient and steady state with commercial and public domain packages (gPROMS and COLNEW). The influence of the particle size and reaction rate constant is analyzed in the (γ₂×γ₃) reactive/separation region.     

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.