Mathematical modeling of nucleation and growth kinetics of polymer nanoparticles in emulsion polymerization process using conductometry results

Number of pages: 184 File Format: word File Code: 31788
Year: 2010 University Degree: Master's degree Category: Chemical - Petrochemical Engineering
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  • Summary of Mathematical modeling of nucleation and growth kinetics of polymer nanoparticles in emulsion polymerization process using conductometry results

    Master's Thesis in Chemical Engineering, Thermodynamics and Kinetics

    Abstract

    A major part of the final properties of the product in emulsion polymerization is determined by the particle size distribution. In this project, an accurate model based on population balance equations (zero-one model) which includes the phenomena of nucleation and particle growth has been chosen to predict the particle size distribution. The finite volume method has been used to solve population balance equations. In this study, the effect of the initial surfactant concentration parameter on the conversion percentage and particle size distribution has been investigated experimentally and with the help of simulation. Based on the results, the size of the particles increases with the decrease in the amount of surfactant. In all the above cases, the simulation and experimental results are in good agreement. In this project, appropriate relationships for the experimental calculation of CMC were presented using laboratory data as y=A Ln(x) + B at two temperatures of 25 and 60 degrees Celsius, as well as at 60 degrees Celsius the experimental formula for the combination of two electrolytes Na2CO3 and KPS which is used in the emulsion polymerization of better quality polybutadiene nanoparticles as a buffer and initiator with the method of least squares as z=A(x)m(y)n It was found that in all the above cases, coefficients were obtained that best match the laboratory data. Also, the initial electrical conductivity of the system in terms of ion concentration, in the presence of electrolytes in the emulsion polymerization of butadiene at two temperatures of 25 and 60 degrees Celsius, was obtained by four methods. First, by experimental method and using laboratory data, a formula as y=A(x) has been obtained for conducting the above electrolytes at two temperatures of 25 and 60 degrees Celsius. Then the two methods presented in the articles are reviewed, and finally an innovative method for calculating the electrical conductivity of the above solutions is mentioned and the error percentage of each of the methods is given in tabular form. Finally, the electrical conductivity of the butadiene emulsion polymerization system has been obtained without the addition of monomer and online in the presence of the reaction. The validity of these relationships was confirmed through laboratory data.

    Key words: emulsion polymerization, butadiene, particle size distribution, population balance, modeling

    Introduction

    Polymer refers to very large molecules that are made of multiple units with internal connections. In other words, it can be stated that a polymer is a large molecule made of many smaller molecules. The small molecules that are used as the building blocks of these large molecules are called monomers [1].

    In this chapter, after defining the word polymer and types of polymerization, in this chapter, we will briefly review emulsion polymerization and examine its general mechanism, describe and expand its general steps, and interpret it schematically. After that, we have a brief overview of butadiene monomer and explain the general properties of this monomer. Finally, we will have an overview of the work that has been done in the field of emulsion polymerization modeling and simulation.

    The final goal of this study is to control the particle size distribution in the discontinuous polybutadiene emulsion polymerization reactor. As mentioned, there are few articles in the field of particle size distribution in emulsion polymerization. In order to fully control the distribution of particle size, accurate simulation and modeling of the process is required. Due to the heterogeneous nature of the emulsion polymerization environment, there are many phenomena such as nucleation, particle growth, repulsion and absorption of radicals to particles, etc. It happens in the system that all these phenomena have been seen in modeling. For each of these phenomena, several relationships have been presented in the articles, and the most appropriate ones have been selected after review.

    In the second chapter, the kinetics of emulsion polymerization of butadiene has been fully discussed and the methods of numerical solution of population balance equations have been presented and briefly explained.In the third chapter, the critical micelle concentration (CMC) parameter, which is one of the unknown parameters of the model, has been calculated at C?25 and C?60 (reactor temperature) using conductometric results, and a formula for this parameter in the solution in the presence of initiator ions and surfactant has been presented. In the fourth chapter, the simulation results of the conversion degree and particle size distribution in emulsion polymerization are given. The modeling of particle size distribution in emulsion polymerization has a population balance structure that includes a set of partial-integral and ordinary differential and algebraic equations that must be solved simultaneously. As mentioned earlier, due to the large difference in the speed of system phenomena, the equations are very stiff and their solution is very difficult. After simulation, its results have been compared with experimental data. Also, in this chapter, the effect of parameters such as the initial amount of surfactant on the conversion percentage and particle size distribution has been investigated experimentally and with the help of simulation. In the fifth chapter, the electrical conductivity of the unreacted system (only in the presence of initiator ions and surfactant in the solution) has been investigated at both C?25 and C?60 (reactor temperature) and the formulas available in the articles to predict the electrical conductivity of the system have been presented. After that, a formula has been proposed to better predict the electrical conductivity of the system, and the accuracy of this formula has been checked with various experimental data. Finally, the online guidance of the system has been predicted at a temperature of 60°C (reactor temperature) and acceptable results have been obtained, which show a very good agreement with the experimental results. Step polymer is obtained during step polymerization [1] and the product of a chain polymerization [2] will be a chain polymer. In addition, the characteristics of these two mechanisms are very different. The main difference between these two methods is the time required for the full growth of the size of the polymer molecules.

    Stepwise polymerization progresses through the step-by-step reaction of the functional groups of the reactants, so that in such reactions, the size of the polymer molecules grows at a relatively slow rate. The reaction starts from monomer to dimer, trimer, tetramer, etc. and continues in this way:

    where M is the molecule of monomer or monomers. The termination of the reaction will be to reach large molecules containing a large number of monomer molecules. During the stepwise polymerization process, there is a possibility that both types of molecules react with each other, which is completely different from chain polymerization. In chain polymerization, almost very quickly after the start of the reaction, complete and equal polymer molecules are obtained [2]. In chain polymerization, only monomers have the ability to become dimers that can be activated (radically or ionized) at the beginning. In the next step, only these activated dimers attack other monomers and increase their chain length and quickly become long chains. This phenomenon occurs while there are still many unreacted monomers in the reaction medium.

    In the polymerization of chains with the passage of time, the monomer concentration shows a constant decrease. In the first stage, a polymer with a high molecular weight is suddenly created and this molecular weight does not change much with the progress of the reaction. The molecular weight of the polymer increases steadily during the reaction. Prolonging the reaction time increases the molecular weight and is a necessary factor to reach a very high molecular weight. In all stages of the reaction, there are all kinds of molecular particles, ranging from dimers to polymers with a high degree of polymerization [1]. In chain polymerizations, the presence of an active center is necessary to start the reaction, for this reason, the presence of an initiator is essential in these types of reactions. The type of initiator determines the properties of the active center.

    ABSTRACT

    Particle size distribution determines the major end-use properties of latex produced by emulsion polymerization.

  • Contents & References of Mathematical modeling of nucleation and growth kinetics of polymer nanoparticles in emulsion polymerization process using conductometry results

    List:

    Table of Contents

    The first chapter. 1

    Overview of polymerization processes. 1

    1-1- Introduction. 2

    1-2- Classification of polymers based on polymerization mechanism. 3

    chain polymerizations. 5

    Stage polymerizations. 5

    Only monomers that have active centers (such as free radicals or ions) enter the reaction. 5

    Both monomers that have two different active agents at their two ends have the ability to enter into the reaction. 5

    Monomer concentration decreases uniformly during the reaction. 5

    Monomers are quickly destroyed in the initial stages of the reaction. 5

    Polymers with high molecular weight are formed quickly. 5

    The molecular weight of the polymer chains all together increases slowly over time. 5

    The reaction speed is very high. 5

    The reaction speed is slow and slow. 5

    From the beginning of the reaction, chains with a high degree of conversion are obtained. 5

    To obtain chains with a high degree of conversion, the reaction should be continued to more than 90%. 5

    The reaction takes place in several stages, initiation, release and termination. 5

    The reaction takes place only in one step. 5

    It produces only linear polymers or molecules with little branching. 5

    It gives molecules with different structures, from simple linear molecules without branches to bulky networks with many transverse connections. 5

    1-2-1- free radical polymerization reactions. 5

    1-2-1-1- the beginning. 6

    1-2-1-2- growth (release) 6

    1-2-1-3- end. 6

    1-2-1-4- chain transmission. 7

    1-2-2- Classification of polymerization methods or systems based on the reaction environment. 7

    1-2-2-1- homogeneous polymerization. 8

    1-2-2-1-1- Bulk Polymerization method 8

    1-2-2-1-2- Solution Polymerization method 9

    1-2-2-2- Heterogeneous polymerization. 10

    1-2-2-2-1- Suspension Polymerization method 10

    1-2-2-2-2- Emulsion Polymerization method 10

    Polymerization method. 14

    Advantages 14

    Disadvantages. 14

    Polymerization. 14

    Todhai. 14

    Discontinuous process. 14

    Simplicity of the process, flexibility, low cost of separation. 14

    Heterogeneity of the reaction, wide molecular weight distribution, strong increase in viscosity and as a result the problem of mixing and heat transfer during the reaction 14

    Continuous process. 14

    Controllability of the reaction by temperature, controllability of molecular weight, product properties and as a result low separation cost 14

    Low conversion degree, separation of monomer from polymer, need for high temperature and sometimes need for high pressure, adhesion of polymer to the reactor wall 14

    Solution polymerization. 14

    Compared to the mass system of lower viscosity and as a result of better mixing and heat transfer, controllability of the reaction by temperature control, direct consumption of the reaction solution, low adhesion of the polymer to the reactor body 14

    The cost of using solvents, pollution of the environment due to the presence of solvents, the cost of drying and separation, the problem of the phenomenon of radical transfer 14

    Suspension polymerization. 14

    Controllability of product quality and reaction by temperature control, direct consumption of dry solid grains and as a result low cost of separation, low viscosity and as a result suitable heat transfer. 14

    The impossibility of using continuous processes, the need for a stirrer and special additives, the adhesion of polymer particles to the reactor body 14

    Emulsion polymerization. 14

    Controllability of the reaction by temperature, high reaction speed, lower viscosity (compared to solution and mass systems), suitable heat transfer, usability of production Lanx. 14

    The need for a high concentration of emulsifier, the need to stabilize the particles, the adhesion of the particles to the reactor body 14

    1-2-3- The importance of emulsion polymerization. 14

    1-2-4- Emulsion polymerization mechanism. 15

    1-2-5- stages of emulsion polymerization. 18

    1-2-6- particle creation mechanism 22

    1-2-6-1- mycelial nucleation. 22

    1-2-6-2- homogeneous nucleation. 23

    1-2-6-3- Nucleation of diameters. 23

    1-2-7- butadiene emulsion polymerization. 24

    1-2-8- Introduction of butadiene monomer.24

    1-2-9- Materials used in emulsion polymerization of butadiene. 27

    1-2-9-1- emulsifier. 27

    1-2-9-2- Starter. 28

    1-2-9-3- Buffer. 29

    1-2-10- An overview of the works done in the field of simulation and control of particle size distribution. 29

    The second chapter. 35

    Emulsion polymerization kinetics. 35

    2-1- Introduction. 36

    2-2- continuous phase events. 36

    2-3- Monomeric droplet phase events. 36

    2-4-Phase phenomena of polymer particles. 37

    2-5- micelles swollen with monomer. 38

    2-6- Modeling. 42

    2-6-1- Initial reactions. 42

    2-6-2- Oligomers of the aqueous phase. 43

    2-6-3- Nucleation. 44

    2-6-4- Balance of monomers 45

    2-6-5- Balance of surfactant. 47

    2-6-5-1- model zero - one. 48

    2-6-5-2- pseudo mass model. 49

    2-6-6- Equations of pseudo-mass model for population balance of polymer particles. 49

    2-6-6-1- average number of radicals in particles. 50

    2-6-6-2- growth of polymer particles. 51

    2-6-6-3- entry of oligomers into particles. 51

    2-6-6-4- Removal of oligomers from particles. 52

    2-6-6-5- Conclusion inside the particles. 52

    2-6-7- zero-one model equations for population balance of polymer particles. 52

    2-6-8- Numerical solution of population balance equations. 55

    2-6-8-1- Finite Elements 56

    2-6-8-2- Finite volume/difference. 57

    The third chapter. 59

    Calculation of CMC using conductometry results. 59

    3-1- Introduction. 60

    3-2- Test. 61

    3-3- Effects of electrolytes on CMC at 25?C. 62

    3-4-1- The effect of individual electrolytes on CMC at 60?C. 65

    3-4-2- The effect of mixing electrolytes on CMC. 68

    Chapter Four. 70

    Polybutadine emulsion simulation and comparison with experimental data. 70

    4-1- Introduction. 71

    4-2- Modeling. 73

    4-2-1- Modeling scale. 73

    4-2-2- Modeling steps in polymerization reactions and processes. 74

    4-2-3- Model selection methods in polymerization reactions and processes. 75

    4-3- Kinetic modeling of butadiene emulsion polymerization. 75

    4-4- Assumptions considered in the presented kinetic plan for emulsion polymerization of butadiene. 76

    4-5- Solving the equations obtained in kinetic modeling of emulsion polymerization of butadiene. 77

    4-5-1- Discretization of partial differential equations of population balance. 78

    4-6- Parameters used in kinetic modeling of butadiene emulsion polymerization. 79

    4-7- Comparing the results of kinetic modeling with laboratory data. 81

    4-7-1- Description of devices and equipment. 81

    4-7-2- Test method. 82

    4-7-3- feed for each experiment. 84

    4-7-4- Polymerization with sodium dodecyl sulfate. 84

    The fifth chapter. 103

    Conductivity prediction during the polymerization process. 103

    5-1- Introduction. 104

    5-2- Test. 105

    5-3- Prediction of electrical conductivity of solutions without chemical reaction. 106

    5-3-1 Prediction of electrical conductivity of SDS solutions in different concentrations of Na2CO3 and KPS electrolytes at 25?C and 60?C 106

    5-3-2 Prediction of electrical conductivity of SDS solutions in different concentrations of combining Na2CO3 and KPS electrolytes at 60?C 135

    5-4- Prediction of reaction electrical conductivity Emulsion polymerization of polybutadiene nanoparticles (online) 146

    Sixth chapter. 148

    Conclusions and suggestions. 148

    6-1 Conclusion. 149

    6-2- Suggestions. 150

    References. 152

    Appendices 158

    Calculation of CMC in the presence of 0.5 g of Na2CO3 in the medium with SDS titration at 25°C. 159

    Calculation of CMC in the presence of 0.75 g of KPS in the medium with SDS titration at 25°C. 160

    Calculation of CMC in the presence of 0.5 g of Na2CO3 in the medium with SDS titration at 60°C. 162

    Calculation of CMC in the presence of 1 g of KPS in the medium with SDS titration at 60°C. 164

     

     

    Source:

     

    1.       Haddadi Asl and., Technology of Polymers, Tehran, Amir Kabir University of Technology Publishing Center, 2010.

    Odian, G., Principles of Polymerization, 4th edition, John Wiley and Sons Inc. Publication, New York, 2003.

    3.

Mathematical modeling of nucleation and growth kinetics of polymer nanoparticles in emulsion polymerization process using conductometry results