Modeling particle size distribution in emulsion polymerization reactors

Abstract A review of the use and limitations of Population Balance Equations (PBE) in the modeling of emulsion polymerisation (EP), and in particular of the particle size distribution of the dispersed system is presented. After looking at the construction of the general form of PBEs for EP, a discussion of the different approaches used to model polymerization kinetics is presented. Following this, specific applications are presented in terms of developing a two-dimensional PBE for the modeling of more complex situations (for example, the particle size distribution (PSD) and the composition of polymerizing particles). This review demonstrates that while the PBE approach to modeling EP is potentially very useful, certain problems remain to be solved, notably: the need to make simplifying assumptions about the distribution of free radicals in the particles in order to limit the computation complexity of the models; and the reliance of full models on approximate coagulation models. The review finishes by considering the different numerical techniques used to solve PBEs.

[1]  Xavier Joulia,et al.  Accuracy, temporal performance and stability comparisons of discretization methods for the numerical solution of Partial Differential Equations (PDEs) in the presence of steep moving fronts , 2001 .

[2]  M. Morbidelli,et al.  Coagulation phenomena in emulsion polymerisation of vinyl chloride , 1999 .

[3]  F. K. Hansen,et al.  Particle nucleation in emulsion polymerization. III. Nucleation in systems with anionic emulsifier investigated by seeded and unseeded polymerization , 1979 .

[4]  J. Hsu,et al.  Critical Coagulation Concentration of a Colloidal Suspension at High Particle Concentrations , 1998 .

[5]  D. H. Napper,et al.  Chain-length-dependent termination rate processes in free-radical polymerizations. 1. Theory , 1992 .

[6]  M. Morbidelli,et al.  Modelling of aggregation kinetics of colloidal systems and its validation by light scattering measurements , 2004 .

[7]  T. Gu,et al.  Surfactant adsorption at solid-liquid interfaces , 1991 .

[8]  W. H. Ray,et al.  Tubular reactors for emulsion polymerization: I. Experimental investigation , 1994 .

[9]  J. Asua,et al.  Factors affecting kinetics and coagulum formation during the emulsion copolymerization of styrene/butyl acrylate , 2001 .

[10]  John R. Richards,et al.  Mathematical modeling of emulsion copolymerization reactors , 1989 .

[11]  Mf Maartje Kemmere,et al.  Aspects of coagulation during emulsion polymerization of styrene and vinyl acetate , 1998 .

[12]  W. Harmon Ray,et al.  Mathematical Modeling of Emulsion Copolymerization Reactors. I. Model Formulation and Application to Reactors Operating with Micellar Nucleation , 1998 .

[13]  En Sup Yoon,et al.  On the solution of population balance equations (PBE) with accurate front tracking methods in practical crystallization processes , 2002 .

[14]  M. Borkovec,et al.  Charging and Aggregation Properties of Carboxyl Latex Particles: Experiments versus DLVO Theory , 2000 .

[15]  Joakim Majander,et al.  Simulation of the population balances for liquid–liquid systems in a nonideal stirred tank. Part 2—parameter fitting and the use of the multiblock model for dense dispersions , 2002 .

[16]  J. Asua,et al.  Agitation effects in the semicontinuous emulsion polymerization of styrene and butyl acrylate , 2001 .

[17]  M. Borkovec,et al.  Aggregation in sulfate latex suspensions: The role of charge for stability predictions , 1998 .

[18]  J. Seinfeld,et al.  Numerical solution of the dynamic equation for particulate systems , 1978 .

[19]  Chi-Wang Shu,et al.  High order finite difference and finite volume WENO schemes and discontinuous Galerkin methods for CFD , 2001 .

[20]  Emulsion copolymerization in continuous loop reactors , 1994 .

[21]  A. Sood.  Particle size distribution control in emulsion polymerization , 2004 .

[22]  R. Hidalgo-Álvarez,et al.  Electrokinetic properties, colloidal stability and aggregation kinetics of polymer colloids , 1996 .

[23]  Francis J. Doyle,et al.  Population balance PSD model for emulsion polymerization with steric stabilizers , 2003 .

[24]  R. Gilbert,et al.  Conditions for secondary particle formation in emulsion polymerization systems , 1995 .

[25]  T. McKenna,et al.  Continuous Tubular Reactors for Latex Production: Conventional Emulsion and Miniemulsion Polymerizations , 2004 .

[26]  José M. Asua,et al.  Modeling Particle Size Distribution (PSD) in Emulsion Copolymerization Reactions in a Continuous Loop Reactor , 2001 .

[27]  J. A. V. BUTLER,et al.  Theory of the Stability of Lyophobic Colloids , 1948, Nature.

[28]  B. Finlayson.  Nonlinear analysis in chemical engineering , 1980 .

[29]  J. Berg,et al.  Electrosteric Stabilization of Colloidal Latex Dispersions , 1993 .

[30]  C. Kiparissides,et al.  Steric stabilization in emulsion polymerization using oligomeric nonionic surfactants , 1999 .

[31]  D. Ramkrishna,et al.  On the solution of population balance equations by discretization—II. A moving pivot technique , 1996 .

[32]  C. Kiparissides,et al.  The Effect of Oxygen on the Kinetics and Particle Size Distribution in Vinyl Chloride Emulsion Polymerization , 2002 .

[33]  M. Hounslow,et al.  A discretized population balance for nucleation, growth, and aggregation , 1988 .

[34]  C. Chern,et al.  Shear-induced coagulation kinetics of semibatch seeded emulsion polymerization , 1996 .

[35]  Costas Kiparissides,et al.  CFD analysis of turbulence non-homogeneity in mixing vessels: A two-compartment model , 2002 .

[36]  A. Hamielec,et al.  Transport Phenomena in Emulsion Polymerization Reactors , 1997 .

[37]  Alexander Penlidis,et al.  Mathematical modeling and computer simulator/database for emulsion polymerizations , 2002 .

[38]  Shi-Yow Lin,et al.  Determination of adsorption of an ionic surfactant on latex from surface tension measurements , 2002 .

[39]  M. Morbidelli,et al.  A model for the coagulation of polyvinyl acetate particles in emulsion , 2000 .

[40]  Ville Alopaeus,et al.  Simulation of the population balances for liquid-liquid systems in a nonideal stirred tank. Part 1: Description and qualitative validation of the model , 1999 .

[41]  Hans-Jörg Bart,et al.  Numerical solution of the spatially distributed population balance equation describing the hydrodynamics of interacting liquid–liquid dispersions , 2004 .

[42]  E. Giannetti.  Nucleation mechanisms and particle size distributions of polymer colloids , 1993 .

[43]  M. Morbidelli,et al.  Kinetics of multimonomer emulsion polymerization. The pseudo-homopolymerization approach , 1989 .

[44]  R. Hidalgo-Álvarez,et al.  Sequential Adsorption of Triton X-100 and Sodium Dodecyl Sulfate onto Positively and Negatively Charged Polystyrene Latexes. , 2001, Journal of colloid and interface science.

[45]  H. Arenhövel,et al.  Comparison of theory and experiment , 1991 .

[46]  D. H. Napper,et al.  Free radical exit in emulsion polymerization. I. Theoretical model , 1994 .

[47]  M. Smoluchowski.  Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen , 1918 .

[48]  E. Matijević,et al.  Kinetics of heterocoagulation. 3. Analysis of effects causing the discrepancy between the theory and experiment , 1992 .

[49]  R. H. Ewart,et al.  Kinetics of Emulsion Polymerization , 1948 .

[50]  Costas Kiparissides,et al.  Prediction of particle size distribution in suspension polymerization reactors: effect of turbulence nonhomogeneity , 2000 .

[51]  Chi-Wang Shu.  Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws , 1998 .

[52]  J. Asua,et al.  Radical desorption in emulsion polymerization , 1989 .

[53]  Doraiswami Ramkrishna,et al.  Population Balances: Theory and Applications to Particulate Systems in Engineering , 2000 .

[54]  G. Poehlein.  Reaction Engineering for Emulsion Polymerization , 1997 .

[55]  Stelios Rigopoulos,et al.  Finite‐element scheme for solution of the dynamic population balance equation , 2003 .

[56]  C. D. Immanuel,et al.  Nonisothermal Modeling and Sensitivity Studies for Batch and Semibatch Emulsion Polymerization of Styrene , 2003 .

[57]  R. Burton.  A MECHANISTIC APPROACH , 1990 .

[58]  D. H. Napper,et al.  Surfactant-free emulsion polymerizations: predictions of the coagulative nucleation theory , 1987 .

[59]  Mohamed S. El-Aasser,et al.  Emulsion polymerization and emulsion polymers , 1997 .

[60]  The Loop Process , 1997 .

[61]  Costas Kiparissides,et al.  Part I: Dynamic evolution of the particle size distribution in particulate processes undergoing combined particle growth and aggregation , 2004 .

[62]  Doraiswami Ramkrishna,et al.  Efficient solution of population balance equations with discontinuities by finite elements , 2002 .

[63]  James B. Rawlings,et al.  The modeling of batch and continuous emulsion polymerization reactors. Part I: Model formulation and sensitivity to parameters , 1988 .

[64]  D. Ramkrishna,et al.  ON THE SOLUTION OF POPULATION BALANCE EQUATIONS BY DISCRETIZATION--I . A FIXED PIVOT TECHNIQUE , 2003 .

[65]  R. Gilbert,et al.  Particle Size Distributions , 1997 .

[66]  G. Chauveteau,et al.  Colloidal Stabilization of Polystyrene Particles by Adsorption of Nonionic Surfactants: I. Adsorption Study , 1998 .

[67]  W. Ray,et al.  Tubular reactors for emulsion polymerization: II. Model comparisons with experiments , 1994 .

[68]  Mf Maartje Kemmere,et al.  Colloidal stability of high‐solids polystyrene and polyvinyl acetate latices , 1999 .

[69]  Robert G. Gilbert,et al.  Modelling particle size distributions and secondary particle formation in emulsion polymerisation , 1998 .

[70]  Douglas W. Fuerstenau,et al.  Mutual coagulation of colloidal dispersions , 1966 .

[71]  R. LeVeque.  Finite Volume Methods for Hyperbolic Problems: Characteristics and Riemann Problems for Linear Hyperbolic Equations , 2002 .

[72]  M. Buback,et al.  Free-Radical Termination Kinetics Studied Using a Novel SP-PLP-ESR Technique , 2004 .

[73]  R. Gilbert,et al.  Measurement of transfer constant for butyl acrylate free-radical polymerization , 1998 .

[74]  P. Bataille,et al.  Emulsion copolymerization in a tubular reactor , 2000 .

[75]  Francis J. Doyle,et al.  Control of particle size distribution described by a population balance model of semibatch emulsion polymerization , 2000 .

[76]  Francis J. Doyle,et al.  Modeling of particle size distribution in emulsion co-polymerization: comparison with experimental data and parametric sensitivity studies , 2002 .

[77]  R. LeVeque.  Numerical methods for conservation laws , 1990 .

[78]  D. Ramkrishna,et al.  On the solution of population balance equations by discretization - III. Nucleation, growth and aggregation of particles , 1997 .

[79]  Alvin W. Nienow,et al.  CFD modelling of continuous precipitation of barium sulphate in a stirred tank , 2003 .

[80]  Stuart W. Prescott.  Chain-Length Dependence in Living/Controlled Free-Radical Polymerizations: Physical Manifestation and Monte Carlo Simulation of Reversible Transfer Agents , 2003 .

[81]  D. Bassett,et al.  Emulsion Polymers and Emulsion Polymerization , 1981 .

[82]  E. Pefferkorn,et al.  Kinetics of heterocoagulation , 1993 .

[83]  S. Katz,et al.  Some problems in particle technology: A statistical mechanical formulation , 1964 .

[84]  S. Chen,et al.  Emulsion polymerization: Theory of particle size distribution in copolymerization system , 1988 .

[85]  W. Ray,et al.  Mathematical modeling of emulsion copolymerization reactors: Experimental validation and application to complex systems , 1997 .

[86]  W. H. Ray,et al.  The computer simulation of batch emulsion polymerization reactors through a detailed mathematical model , 1978 .

[87]  Bo-geng Li,et al.  Prediction of the average number of radicals per particle for emulsion polymerization , 1993 .

[88]  E. Matijević,et al.  An assessment of heterocoagulation theories , 1992 .

[89]  W. Ray,et al.  On the Mathematical Modeling of Emulsion Polymerization Reactors , 1974 .

[90]  C. Kiparissides,et al.  A Comprehensive Experimental and Theoretical Investigation of the Styrene/2-Ethylhexyl Acrylate Emulsion Copolymerization , 2003 .

[91]  Robert G. Gilbert,et al.  Emulsion polymerization : a mechanistic approach , 1995 .

[92]  L. Spielman.  Viscous interactions in Brownian coagulation , 1970 .

[93]  Alexander Kurganov,et al.  Semidiscrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton-Jacobi Equations , 2001, SIAM J. Sci. Comput..

[94]  G. Froment,et al.  Chemical Reactor Analysis and Design , 1979 .

[95]  S. Swanton.  Modelling colloid transport in groundwater; the prediction of colloid stability and retention behaviour , 1995 .

[96]  Francis J. Doyle,et al.  Computationally efficient solution of population balance models incorporating nucleation, growth and coagulation: application to emulsion polymerization , 2003 .

[97]  M. Hütter.  Coagulation rates in concentrated colloidal suspensions studied by Brownian dynamics simulation , 1999 .

[98]  I. Finar,et al.  Fundamental Principles , 2019, How to Engineer Software.

[99]  P. Wiersema,et al.  Effect of hydrodynamic interaction on the coagulation rate of hydrophobic colloids , 1971 .

[100]  J. Israelachvili.  Intermolecular and surface forces , 1985 .

[101]  S. Motz,et al.  Comparison of numerical methods for the simulation of dispersed phase systems , 2002 .

[102]  Stuart W. Prescott,et al.  Average termination rate coefficients in emulsion polymerization: Effect of compartmentalization on free‐radical lifetimes , 2005 .

[103]  Wei Zhou,et al.  Computational Fluid Dynamics Modeling of the Precipitation Process in a Semibatch Crystallizer , 2001 .

[104]  M. Morbidelli,et al.  Effect of fluid motion on the aggregation of small particles subject to interaction forces , 1999 .

[105]  Vanni,et al.  Approximate Population Balance Equations for Aggregation-Breakage Processes. , 2000, Journal of colloid and interface science.

[106]  R. Gilbert,et al.  First-principles calculation of particle formation in emulsion polymerization: pseudo-bulk systems , 2004 .

[107]  J. Asua.  Polymeric dispersions : principles and applications , 1997 .

[108]  E. Lavernia,et al.  An experimental investigation , 1992, Metallurgical and Materials Transactions A.

[109]  Michael J. Hounslow,et al.  Finite-element methods for steady-state population balance equations , 1998 .

[110]  N. Fuchs.  Über die Stabilität und Aufladung der Aerosole , 1934 .

[111]  John Ugelstad,et al.  Particle nucleation in emulsion polymerization. I. A theory for homogeneous nucleation , 1978 .

[112]  K. Landfester,et al.  Determination of the Adsorption Isotherm of the Nonionic Surfactant Triton X-405 on Polystyrene Latex Particles Using1H NMR , 1998 .

[113]  Stelios Rigopoulos,et al.  A hybrid CFD: reaction engineering framework for multiphase reactor modelling: basic concept and application to bubble column reactors , 2003 .

[114]  David J. Jeffrey,et al.  Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow , 1984, Journal of Fluid Mechanics.

[115]  C. Chern,et al.  Stability of acrylic latices in a semibatch reactor , 1996 .

[116]  J. Vanderhoff,et al.  Kinetics of agitation-induced coagulation of high-solid latexes , 1986 .

[117]  E. Matijević,et al.  Kinetics of heterocoagulation 1. A comparison of theory and experiment , 1992 .

[118]  E. Verwey,et al.  Theory of the stability of lyophobic colloids. , 1955, The Journal of physical and colloid chemistry.

[119]  Sengupta,et al.  Stability of Concentrated Colloids: The Controlling Parameters. , 1998, Journal of colloid and interface science.

[120]  R. Ottewill.  Stability of Polymer Colloids , 1997 .

[121]  M. Hounslow,et al.  Adjustable discretized population balance for growth and aggregation , 1995 .

[122]  K. Landfester,et al.  Competitive adsorption of the anionic surfactant SLS and the nonionic surfactant Triton X-405 on polystyrene latex particles. , 2000 .

[123]  A. Herk,et al.  Modeling of emulsion co‐ and terpolymerizations: Will it ever be possible? , 1998 .

[124]  Alexander Penlidis,et al.  Mathematical Modeling of Multicomponent Chain-Growth Polymerizations in Batch, Semibatch, and Continuous Reactors: A Review , 1997 .

[125]  José M. Asua,et al.  A New Model for Radical Desorption in Emulsion Polymerization , 2003 .

[126]  A. S. Dunn.  Latex particle nucleation in emulsion polymerization , 1989 .

[127]  Charles L. Weber,et al.  A Mathematical Model , 1987 .

[128]  G. Batchelor,et al.  Brownian diffusion of particles with hydrodynamic interaction , 1976, Journal of Fluid Mechanics.

[129]  Jose A. Romagnoli,et al.  Operation of semi-batch emulsion polymerisation reactors: Modelling, validation and effect of operating conditions , 2002 .

[130]  T. McKenna,et al.  High solid content latexes , 2002 .

[131]  M. Borkovec,et al.  Coagulation Rate Measurements of Colloidal Particles by Simultaneous Static and Dynamic Light Scattering , 1996 .

[132]  R. Olayo,et al.  On the kinetics of styrene emulsion polymerization above CMC. II. Comparison with experimental results , 2000 .