Prediction of Acrylonitrile-Based Copolymers

Prediction of Acrylonitrile-Based Copolymers Microstructures by Monte Carlo Simulation Method Zahra Hoseinzadeh Nik1, Seyed Hassan Jafari1, Saeed Houshmand Moayed1, Neda Sanatkaran2, 1

School of Chemical Engineering, University of Tehran, P.O. Box 11155-4563, Tehran, Iran 2 Chemical Engineering Department, Amirkabir University of Technology, P.O. Box: 63516-43659, Mahshahr Campus, 415 Mahshahr, Iran

Abstract: A Markov chain Monte Carlo simulation was carried out using MC method, to predict the microstructure of copolymer and investigate the effect of reactivity ratio on variation of microstructural properties, randomness and monomer sequence length, during copolymerization reaction in a batch process. For this purpose copolymerization of acrylonitrile (AN) with methacrylic acid (MAA), acrylic acid (AA) and itaconic acid (IA) were investigated. According to the simulation results, reactivity ratio had a strong effect on the randomness, monomer sequence length, homogeneity and blockiness of obtained copolymers. Considering the randomness and monomer sequence length versus conversion for these three systems, there was a certain value of conversion where the difference between reactivity ratios of each pair monomers had a positive effect on the randomness and homogeneity, while beyond this point it affected negatively. In addition an individual value of conversion for each copolymerization process, in which block formation suddenly increased, was obtained. Keywords: Monte Carlo Simulation, randomness, monomer sequence length

copolymerization,

microstructure,

INTRODUCTION Copolymerization can dramatically alter the properties of the resultant material from those of either homopolymer that is formed from a single monomer. It usually leads to the formation of macromolecular chains in which the different monomer groups are statistically distributed. The arrangement of the monomers along the copolymer chains is responsible for the different distributions of the properties in the final product. These „„statistical‟‟ polymers can have interesting properties that are a compromise between those of the homopolymers (Dadmun, 2001; Bouzo and Pflüger, 2003). In order to optimize the key properties of the copolymer, it is very important to predict the copolymer microstructure factors prior to synthesis. Monomer sequence length and comonomer distributions are two important factors which can result in a better understanding of the possible microstructure (Anantawaraskul et al., 2003). Our description of the system is based on the simple “Markov chain” model, which is a mathematical description of a copolymerization process. Monomers are added to the chain in some random fashion. The theory gives a mathematical expression for the probability distribution of monomers along each chain (Odian, 1991; Read, 1998). Monte Carlo (MC) simulations are one of the computational methods for modeling Markovian processes. These MC simulations are based on conditional probabilities, but they vary with regard to the simulation algorithm and are often tailored to the specific problem to be solved (Tobita, 1994). Zetterlund et al. (2003) used Monte Carlo methods to explore the effects of rate constants, reactant stoichiometry and extent of reaction on the microstructure of the chain. Using MC simulations and the lattice bond-fluctuation model, Starovoitova et al. (2005) performed the computer-aided sequence design of a twoletter copolymer with quenched primary structure near a chemically homogeneous impenetrable surface. Study on monomer sequence distribution of ethylene copolymers by using MC simulation was carried out by Al-Saleh (2006). Using MC method, we intend to predict the microstructure of copolymer and investigate the effect of reactivity ratio on variation of microstructural properties, randomness and monomer sequence length, during the reaction. The simulation was carried out with three acidic comonomers at amount of 5 mol% which was in the proper range for acrylonitrile copolymers used as carbon fiber precursors (Bajaj et al., 1996).

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MODEL DISCRIPTION In this work, the MC method was utilized to model a free radical copolymerization system. In this model, following assumptions have been applied to reduce complexity of the proposed model and to focus on the parameters by which the microstructure of the copolymers, is mostly determined: 1. The number of primary radicals that are born in each moment is correlated with the number of initiator molecules that are decomposed in that moment. The initiator is decomposed into two radicals based on the following equation:

I

I

0

exp( k d t )

(1)

where [I]0, [I] are the initiator concentrations at time zero and time t, respectively, and kd is the rate constant of the initiator decomposition reaction. According to the Quasi steady-state approximation (QSSA) theory, there is no accumulation of radicals in the polymerization course. Hence, it seems that the number of generated radicals in each polymerization time interval is nearly proportional to the area under the initiator dissociation curve in that interval. Therefore the number of copolymer chains that must be simulated in a time interval between t i-1 and ti [np(ti)] is given by: ti

np (t i )

0

exp( k d t )dt tf 0

ti 0

1

exp(k d t )dt

Np

(2)

exp( k d t )dt

where Np and tf are the total number of copolymer chains that must be simulated and final copolymerization reaction time, respectively. 2. Initiation probability of each macroradical depends on the instantaneous feed composition by equation 3.

PA

MA MA MB

(3)

Where PA is the initial feed fraction of the monomer A, MA and MB are the number of monomers A and B, respectively. 3. The propagation of the chain is considered as a sequential addition of monomer units of the type A or B to the free active end of macroradical. There are four possible ways in which monomer can be added. Assuming kij are the rate constants for a propagating chain ending in i adding to monomer j, reactivity ratio parameters are defined by rA= kAA/kAB and rB= kBB/kBA. The propagation reactions which actually take place are selected by a random number generator with the condition PAA + PAB =1, and PBA + PBB =1 imposed on the probabilities Pij of monomer j addition to the active center i. The probability of a particular reaction occurring is proportional to the product of the reactivity ratios and concentration of the monomers, assuming the reactions follow the concept of the first-order Markov chain model:

PAA PBB

rA M A rA M A M B rB M B rB M B M A

(4) (5)

4. To consider the termination step, the propagation of generated macromolecules is limited to 3000 monomers. 5. Elementary reactions are not diffusion-controlled, so the reaction rate constants of the propagation are assumed to remain unchanged in the course of the simulation. 6. The polymerization reaction time which is twice the initiator half time, is divided in to 3.5×105 identical time intervals and the magnitude of simulated copolymer chains is 3.5×107. Considering the above assumptions, a suitable and optimized subroutine was written in C++ language and compiled under the Windows XP operating system (V2002, Pack2) on a 2.66-GHz (dual-core Intel processor) personal computer. The optimization was conducted in such way that the runtime of the simulation was minimized. This model enabled us to predict the copolymer microstructure variations as the copolymerization proceeds. Monomer sequence length (MSL) and comonomer dispersion in the copolymer chain have an important role on the copolymer microstructure.


Randomness used as a quantitative measure of the comonomer dispersion. This parameter which is the fraction of hetero-dyads (AB and BA) is defined by the equation 6.

Randomness

N AB

N AB N AA

(6)

N BB

Where NAA, NBB are the number of homo-dyads of A and B, respectively, and NAB is the number of hetero-dyads, both AB and BA.

RESULTS AND DISCUSSION In this work, a Monte Carlo simulation method has been carried out to investigate copolymerization of acrylonitrile (AN) with various vinyl acids, i.e., acrylic acid (AA), methacrylic acid (MAA), and itaconic acid (IA) with the reactivity ratios represented in Table 1. α,α'-azobisisobutyronitrile (AIBN) was used as initiator, with the half time, t1/2, equal to 4.8 h and kd= 4.01×10-5, at 70°C (Bajaj et al., 1996). Initial feed composition was 95 mol% of AN. Table 1. Reactivity ratios of AN monomer and various vinyl acid comonomers (Bajaj et al., 1996) AN/IA rAN 0.575

AN/AA rIA 2.05

rAN 0.495

AN/MAA rAA 2.502

rAN 0.265

rMAA 3.452

Figure 1, depicts the variation of randomness versus conversion for three copolymerization systems which differ in the type of comonomer. According to the simulation results, randomness is decreasing during the reaction. A higher difference between the reactivity ratio values in each copolymerization system leads to a higher decreasing rate of randomness. Since rMAA> rAA> rIA, for AN/MAA system, the number of MAA units which could be found in the copolymer chain and consequently randomness values at the low conversions (up to 35%) are the highest. As the copolymerization proceeds, due to higher reactivity ratio and higher consumption rate of the MAA, in comparison with IA and AA, the MAA concentration decreases more severely. Therefore beyond the conversation value of 35%, the randomness in AN/MAA system becomes lower in comparison with the AN/AA and AN/IA systems, while, in AN/IA system, the randomness gradually tends to reach higher values as compared to the other systems, during the copolymerization reaction. It means that after a certain conversion, reactivity ratio effect become negligible and feed composition has the main influence.

Randomness

0.25

0.2

0.15

0.1

0.05

0

0

0.2

0.4

0.6

0.8

1

Conversion

Fig. 1. Randomness as a function of conversion in AN/IA(■), AN/AA(○)and AN/MAA(▲) systems at fA0= 0.95. According to Figure 1, randomness of AN/IA and AN/AA systems during the reaction is not zero up to completion of the reaction (conversion=100%), while for AN/MAA system at conversion of about 85% randomness becomes zero. It means from this conversion onwards for AN/MAA system just chains with very long blocks are formed. In addition, at high conversion (more than 35%), higher difference between reactivity ratios of two types of monomers in a copolymerization leads to increase in block lengths and heterogeneity of products, however, at the low conversions (less than 35%), this leads to an increase in randomness and homogeneity of products.


Figure 2, shows the monomer sequence length (MSL) of AN as a function of conversion for three copolymerization systems. As copolymerization proceeds, for each system at a certain conversion level, slope of MSL curves severely increases, which is a measure of block formation in chains due to decrease of comonomer content in the feed. These critical conversion levels for AN/MAA, AN/AA and AN/IA are about 40%, 60% and 70%, respectively. The observed differences between he critical conversion levels are due to the differences between the reactivity ratio of AN monomer and the three comonomers. A higher difference in the reactivity ratio leads to a lower value of the critical conversion level. The initial value of MSL of AN increases as the difference between the reactivity ratios becomes smaller. Up to conversion of 35%, increase in the difference between the reactivity ratios leads to lower amounts of MSL. Because higher amounts of a comonomer with a higher reactivity ratio goes into copolymer chain and hence MSL of AN monomer decreases. But beyond the conversation value of 35%, AN monomer sequence length in AN/MAA system becomes higher as compared to the AN/AA and AN/IA systems. This is due to the fact that consumption of a comonomer with a higher reactivity ratio is high and therefore the feed becomes depleted from this active comonomer. Thus when a certain conversion is reached, the amount of the more active comonomer in the copolymer structure decreases and hence the MSL in AN/MAA system becomes higher than the others. 100

MSL Of AN

80

60

40

20

0

0

0.2

0.4

0.6

0.8

1

Conversion

Fig. 2. MSL of AN as a function of conversion in AN/IA (■), AN/AA (○) and AN/MAA (▲) systems at fA0= 0.95.

CONCLUSION In this work it was aimed to predict and trace the variation of microstructural properties of AN copolymer with MAA, AA and IA, during a copolymerization process. It was found that in a copolymerization reaction, the difference between reactivity ratios of monomers had a strong influence on degree of randomness and MSL and their trend of variations with degree of conversion. The higher amount of the difference between reactivity ratios of monomers led to copolymer chains with higher randomness, lower MSL and consequently more homogeneity and less blockiness in copolymer microstructure at conversion values up to 35%. Beyond this conversion value, the difference between reactivity ratios of monomers showed an inverse effect. In addition, an individual value of conversion for each copolymerization process in which block formation suddenly increased was determined.

REFERENCES Al-Saleh, M. A. and L. C. Simon (2006). Monte Carlo Simulation of Ethylene Copolymers: A Look into the Monomer Sequence Distribution, Macromol. Symp., 243, 123–131. Anantawaraskul, S., J. B. P. Soares, P. Wood-Adams, B. Monrabal (2003). Effect of molecular weight and average comonomer content on the crystallization analysis fractionation (Crystaf) of ethylene α-olefin copolymers. Polymer., 44, 2393-2401. Bajaj, P., K. Sen, S.H. Bahrami (1996). Solution Polymerization of Acrylonitrile with Vinyl Acids in Dimethylformamide. J. Appl. Polym. Sci., 59, 1539-1550. Bouzou, B. and F. Pflüger (2003). Biospecific Properties of Random Copolymers, Monte Carlo Simulation of the Radical Random Terpolymerization. Macromol. Theory Simul., 12, 243–250. Dadmun, Mark D. (2001). Quantifying and Controlling the Composition and Randomness Distributions of Random Copolymers. Macromol. Theory Simul., 10, 795–801. Odian, G. (1991). Principles of Polymerisation, chapter 6. Wiley, New York.


Read, D. J. (1998). Mean Field Theory for Phase Separation during Polycondensation Reactions and Calculation of Structure Factors for Copolymers of Arbitrary Architecture. Macromolecules, 31, 899-911. Starovoitova, N. Y., A. V. Berezkin, Y. A. Kriksin, O. V. Gallyamova, P. G. Khalatur, A. R. Khokhlov (2005). Modeling of Radical Copolymerization near a Selectively Adsorbing Surface: Design of Gradient Copolymers with Long-Range Correlations. Macromolecules, 38, 2419-2430. Tobita, H., Y.Takada, M. Nomura (1994). Molecular Weight Distribution in Emulsion Polymerization. Macromolecules, 27, 3804-3811. Zetterlund, P. B., R. G. Gosden, A. F. Johnson (2003). New aspects of unsaturated polyester resin synthesis. Part I: modeling and simulation of reactant sequence length distributions in stepwise polymerization. Polym. Int., 52, 104–112.
