Article pubs.acs.org/IECR
Kinetic Modeling and Simulation of Emulsion Grafting Copolymerization of Styrene and Acrylonitrile in the Presence of Polybutadiene Seed Latex Particles Xiang Liu*,† and Mamoru Nomura‡,§ †
Key Laboratory of Flexible Electronics (KLOFE) & Institue of Advanced Materials (IAM), National Jiangsu Synergistic Innovation Center for Advanced Materials (SICAM), Nanjing Tech University (NanjingTech), 30 South Puzhu Road, Nanjing 211816, China ‡ Department of Material Science and Engineering, University of Fukui, Fukui, 910-8507, Japan S Supporting Information *
ABSTRACT: A two-phase kinetic model is proposed for the emulsion grafting copolymerization of styrene and acrylonitrile in the presence of polybutadiene seed latex particles. The experimental results observed by conducting the polymerizations at 50 °C are compared with those predicted by the proposed kinetic model and confirm that the model is valid for predicting the rate of this emulsion grafting copolymerization. In the model predictions, thermodynamic equilibrium equations proposed in our previous papers are used for calculating the monomer concentrations in poly(styrene-co-acrylonitrile) domains and continuous polybutadiene matrix in acrylonitrile−butadiene−styrene terpolymer particles as emulsion grafting copolymerization proceeds. In addition, it is shown that the model is also applicable to predict grafting efficiency, copolymer composition of free and grafted chains.
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INTRODUCTION Acrylonitrile−butadiene−styrene terpolymer (ABS) is the largest-volume engineering thermoplastic resin which exhibits high impact resistance, sufficient thermal stability, excellent processability, and good mechanical strength. The emulsion grafting copolymerization of styrene (St) and acrylonitrile (AN) in the presence of polybutadiene (PB) seed latex particles is still the most important route in preparing high-impact ABS resin.1,2 Although such a graft copolymerization process has been industrialized for several decades and extensive researches in terms of the effects of various process parameters and relevant structural features have been done to attain a good balance of elastomeric and thermoplastic properties that exhibit excellent toughness, good elongation at break, and excellent processability,3−11 only little work has been devoted so far to the modeling and simulation of the emulsion copolymerization despite its industrial importance.12−16 The graft copolymerization of St and AN in the presence of PB starts from a homogeneous system, and becomes heterogeneous soon after the beginning of the process, because great differences exist in the physical characteristics such as solubility parameter and polarity between poly(styrene-co-acrylonitrile)(SAN) and PB. The phase separation of ABS latex particles obtained by this method shows a two-phase composite with a sea−island structure, in which small spherical SAN domains (islands) are randomly dispersed in the continuous PB matrix (sea), as shown in Figure 1a.17 A quantitative treatment of the emulsion grafting copolymerization involves many complex heterogeneous processes containing heterogeneous polymerization, partition behaviors of monomers and free radicals, and phase separation. Some phase equilibrium models have been developed to estimate partition coefficients of monomers and free radicals in heterogeneous polymerization systems, such as © 2014 American Chemical Society
Figure 1. Comparison of the image of ABS resin particles: (a) high impact ABS resin particles produced with 0.3−0.4 μm PB seed latex particles and (b) high gloss ABS resin particles produced with ca. 0.1 μm PB seed latex particles.
emulsion polymerization or dispersion polymerization of St.18−20 In our previous study, a two-phase swelling model was proposed on the basis of the thermodynamic approach and on the assumptions that SAN domains are randomly dispersed in a continuous PB matrix of an ABS latex particle, and equilibrium swelling is attained among the SAN domains, PB matrix, and Received: Revised: Accepted: Published: 17580
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monomer conversion Xt = 78.5% (St conversion Xs = 98%, AN conversion Xa = 59%). The large size particle is an ABS particle that originated from PB seed latex particles, and the average diameter of these particles (dps) is 0.42 μm. On the other hand, the smaller monosized particles with the diameter of dp = 0.22 μm are newly formed SAN copolymer particles (secondary particle nucleation). The number of these newly formed particles (Np) could be estimated by calculation using the following material balance equation on polystyrene (PSt), polyacrylonitrile (PAN), and PB to be 1.8 × 1013 particles/cm3water, which is 5.6 times the initial concentration of PB seed particles. In deriving this material balance equation, the volume of each polymer is assumed to be additive.
continuous water phases by a St and AN monomer mixture.21−23 In this work, therefore, we aim first to propose a two-phase kinetic model that describes the emulsion grafting copolymerization of St and AN in the presence of PB seed latex particles, taking into account the fact that the kinetic model proposed in our previous study could successfully predict the rate of emulsion copolymerization of St and AN.14 Second, the emulsion copolymerization of St and AN in the presence of PB latex particles as seed is conducted at 50 °C with varying the initial number of PB seed particles, the initiator and monomer concentrations, to confirm the validity and utility of the proposed two-phase kinetic model by comparing the experimental and predicted conversion versus time curves.
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M M X M X π π (d ps)3 NT + (d p)3 NP = 0B + 0s s + 0a a 6 6 ρPB ρps̅ ρPa ̅ ̅
MODELING EQUATIONS Preliminary Seeded Experiments. For industrial production of multipurpose high impact grade ABS resins, comparatively larger size PB latex particles with a diameter of 0.3−0.4 μm are employed as seed, as shown in Figure 1a. In the production of high gloss grade ABS resins, on the other hand, smaller size PB seed latex particles with the diameter of ca. 0.1 μm are used. We first tried to carry out a preliminary experiment under the recipe and conditions corresponding to the industrial production of multipurpose high impact grade ABS resins using 0.30 μm PB latex particles offered by Nippon Zeon Co. (average diameter = 0.30 μm, solid content = 54%, gel content = 73%, and specific gravity of the latex = 0.95 and of PB polymer = 0.91). The recipe and conditions employed were as follows: the initial concentration of PB seed particles, NT = 3.1 × 1012 particles/cm3-water; the weight of AN and St initially charged per unit volume of water, M0a = M0s = 0.10 g/cm3water; potassium persulfate initiator (KPS) = 2.5 g/dm3-water; sodium dodecyl sulfate emulsifier (SDS) = 0.30 g/dm3-water to prevent coagulation between particles; and reaction temperature = 50 °C. In seeded emulsion polymerizations, it is essential to confirm whether the number of polymer particles increased by the so-called secondary particle nucleation or decreased by coagulation between particles. This is usually possible by checking an electron micrograph of polymer particles, as shown in Figure 2, which was taken at the total
(1)
where M0B, M0a, and M0s are the weight of PB seed particles initially charged, the weight of AN and St initially charged per unit volume of water, respectively, and ρ̅PB, ρ̅Pa, ρ̅Ps are the densities of PB, PAN, and PSt, for which ρ̅PB = 0.91, ρ̅Pa = 1.08, and ρ̅Ps = 1.05 g/cm3.14 Thus, it was confirmed that a large number of SAN polymer particles are produced under the recipe and conditions corresponding to the industrial production of multipurpose high impact grade ABS resins. At the present stage, we have no pertinent theory that can predict the number of polymer particles produced by secondary nucleation in emulsion polymerization. It is, therefore, almost impossible to devise such a general two-phase kinetic model that is applicable to the industrial production of multipurpose high impact grade ABS resins, where secondary nucleation would take place. On the other hand, when another preliminary seeded experiment was conducted under the recipe and conditions corresponding to the industrial production of high gloss grade ABS resins using 0.1 μm PB seed latex particles offered also by Nippon Zeon Co. (average diameter = 0.10 μm, solid content = 35%, gel content = 80%, and specific gravity of the latex = 0.98 and of PB polymer = 0.94), no secondary particle nucleation was confirmed by checking the number of polymer particles with the same method as adopted in “Experimental Procedure” section. The recipe and conditions employed in this seeded experiment were the same as those in Figure 3 shown later. Moreover, it was found by analyzing the observed conversion versus time curves with the knowledge of our previous study14 that the average number of radicals per PB particle is far lower than 0.5. Considering this, it will be possible to presume that every PB particle contains at most one SAN domain and only one radical is growing in this domain on the time-averaged scale. On the basis of the above presumptions, the following simple two-phase kinetic model applicable to the production of high gloss grade ABS resins using ca. 0.1 μm PB seed latex particles is proposed as the first step to develop a general twophase kinetic model that does not depend on the diameter of PB seed particles. Expressions for Rate of Emulsion Copolymerization, Grafting Efficiency, Copolymer Composition. The following descriptions are aimed to establish a two-phase kinetic model describing the emulsion copolymerization of AN and St using smaller size (0.10 μm) PB latex particles as seed. To simplify the model derivation, the following assumptions are considered: (1) Phase separation between SAN copolymer and
Figure 2. A representative electron micrograph discriminating the original PB seed particles from newly formed SAN particles by secondary nucleation in the seeded emulsion copolymerization of St and AN with PB seed latex particles conducted under the conditions of NT = 3.1 × 1012 particles/cm3-water, M0a = M0s = 0.10 g/cm3-water, KPS = 2.5 g/dm3-water, SDS = 0.30 g/dm3-water, and reaction temperature = 50 °C. 17581
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in SAN domains can never be grafted to PB simply because it is never in contact with PB. Therefore, the grafting reaction only takes place in the PB matrix, the grafting copolymerization rate for each monomer can be expressed as follows: g R pa = M 0a
dXag = (k paanag + k psansg )[MA]PB NT dt
(4)
R psg = M 0s
dXsg = (k pssnsg + k pasnag )[MS]PB NT dt
(5)
nga ,
where are the number of the grafted chain radicals with acrylonitrile unit at its end, and that with styrene unit at its end, respectively. The grafting efficiency is defined as the fraction of SAN or homopolymer chains which become chemically bound to the PB. Therefore, the grafting efficiency can be expressed by
Figure 3. Comparison between the experimental and predicted conversion versus time curves under the conditions: NT = 1.8 × 1014 particles/cm3-water, M0t = 0.2 g/cm3-water, M0a/M0s = 1.0 (M0a = M0s = 0.1 g/cm3-water), [I0]w = 1.25 g/dm3-water, S0 = 0.3 g/dm3-water and 50 °C.
ϕ=
R ps = M 0s
ya̅ f =
M 0a(Xa − Xag) M 0a(Xa − Xag) + M 0s(Xs − Xsg)
(7)
ya̅ g =
M 0aXag M 0aXag + M 0sXsg
(8)
Instantaneous copolymerization composition of the free chain and of the grafted chain yfa and yga are given by the following expressions: yaf =
yag =
M 0a dX M 0a dt a
(
−
M 0a dX g M 0a dta
(
dXag dt
dX a dt
−
dXag dt
)+M ( 0s
) dX s dt
−
dXsg dt
)
(9)
dXag dt
+ M 0s
dXsg dt
(10)
Thus, if the average number of various radicals and the concentrations of monomers absorbed in two phases involved above can be calculated by using the values of the operational variables of an emulsion copolymerization system, one can predict the properties such as the rate of emulsion copolymerization, grafting efficiency, copolymer composition by means of eq 2 to eq 10. Subsequently, the concentrations of monomers absorbed in two phases are derived. The derivation of the equations which predict the average number of various radicals, mean rate coefficient, and mean termination rate coefficient is presented in the Supporting Information (SI). Prediction of Monomer Concentrations in ABS Particles. The prediction of the concentrations of respective monomers in the ABS particles, regardless of whether they are expressed as a function of either the reaction time or the monomer conversions, is critically important for the accurate use of the kinetic model. In the previous paper, it was demonstrated that a two-phase swelling model consisting of thermodynamic swelling equations and empirical equations
(2)
dX s = {k pss([MS]PB ns,PB + [MS]SAN ns,SAN) dt
+ k pas([MS]PB na,PB + [MS]SAN na,SAN)}NT
(6)
Xgs
where are the conversions of AN and St monomers grafted onto the PB, respectively. Accumulated copolymerization composition of the free chain and the grafted chain yfa̅ and yga̅ is given by the following expressions:
dX = M 0a a = {k paa([MA]PB na,PB + [MA]SAN na,SAN) dt + k psa([MA]PB ns,PB + [MA]SAN ns,SAN)}NT
M 0aXag + M 0sXsg M 0aXa + M 0sXs
Xga,
PB occurs and produces a SAN domain as soon as the emulsion copolymerization of St and AN takes place in a PB seed particle, so that the early homogeneous stage of the reaction can be neglected.24 (2) Since the average particle size of the PB latex particles used is as small as ca. 0.1 μm in diameter, every ABS latex particle contains only one SAN domain by fast coalescence between the existing domain and a newly born domain at the embryo stage. (3) The total number of radicals per ABS particle is assumed to be partitioned between the SAN domain phase and the PB matrix phase on the basis of the volume fraction of each phase.19 (4) The equilibrium of radical concentrations between the SAN domain and the PB matrix is assumed to be attained instantaneously, so that radical desorption from the small spherical SAN domain into the continuous PB matrix is unnecessary to be considered, and hence, only free radical desorption from the PB matrix into the continuous water phase is taken into account. (5) On the basis of assumption 4, the radical termination and chain transfer reactions between the SAN domain and PB matrix phases are also unnecessary to be considered. Therefore, the rate of St and AN copolymerization for each monomer in an ABS latex particle should be the sum of each rate in the SAN domain and PB matrix phases, namely, R pa
ngs
(3)
where M0a and M0s are the weight of AN and St initially charged per cm3-water, Xa and Xs the conversion of each monomer, kpij is the propagation rate constant of i-radical to j-monomer, [Mi]PB, [Mi]SAN are the concentrations of i-monomer absorbed in PB matrix and SAN domains, respectively; na,PB, na,SAN, ns,PB, and ns,SAN are the number of A-radicals and S-radicals in PB matrix and SAN domain, respectively; NT is the number of PB seed particles per unit volume of water. To predict the grafting efficiency onto the PB latex particles, it is further assumed that two monomers which are converted 17582
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Table 1. Approach of Predicting Monomer Concentrations in ABS Particles When Monomer Droplets Are Present14,21,22,25 equation Thermodynamic equations are applied to predict St and AN concentrations in a continuous PB matrix:
(ΔG /RT )SPB = ln ΦSP + (1 − mSA )ΦAP + ΦP + χSA ΦAP2 + χS,PB Φp2 + χS,PB − χAP mSA ) +
2VS̅ γ ΦP1/3 = (ΔG /RT )Sd RPRT
= ln ΦSd + (1 − mSA )ΦAd + χSA ΦAd 2 2 2 (ΔG /RT )PB A = ln ΦAP + (1 − mAS)ΦSP + ΦP + χSA ΦSP + χA,PB Φp + χA,PB
− χSP mAS) +
2VA̅ γ ΦP1/3 = (ΔG /RT )dA RPRT
= ln ΦAd + (1 − mSA )ΦSd + χSA ΦSd 2 ΦSPρS ΦAPρA [MA]PB = MS MA The saturation concentration of each monomer in SAN domains could be correlated by the following empirical equation: βj [MS]SAN MS [MA]SAN MA 1 = aj + ⇒ Φ̅ SP = Φ̅AP = [Mj]SAN ϕjd ρS ρA
[MS]PB =
The values of αj and βj are tabulated in Table 3 in the previous paper. The overall material balance equations on each monomer in three phases can be expressed: ΦSP + ΦAP + ΦP = 1
ΦSd + ΦAd = 1 A 0(1 − X a)/ρA = ΦAPVPB + Φ̅APVSAN + ΦAd Vd + VAW
S0(1 − Xs)/ρS = ΦSPVPB + Φ̅ SPVSAN + ΦSd Vd + VSW (1 − Φ̅ SP − Φ̅AP)VSAN =
(1 − ΦSP − ΦAP)VPB =
S0Xs A X + 0 a ρS ρA
1 3 πd p NT 6
⎞ ⎛ ΦAd VAW = 0.14⎜ ⎟ ⎝ 0.72 + 0.73ΦAd ⎠
⎛ ⎞ 1 − ΦAd VSW = 5.65 × 10−4⎜ ⎟ ⎝ 1.62 − 0.98ΦAd ⎠
the same as those employed in the preliminary experiment (Nippon Zeon Co.: average diameter = 0.10 μm, solid content = 35 %, gel content = 80 %, and specific gravity of the latex = 0.98, and specific gravity of PB polymer = 0.94). The experimental procedures are the same as those employed in the previous study. 14 Latex samples were withdrawn successively from the reactor to determine the total monomer conversion gravimetrically using methyl alcohol as precipitant for ABS copolymers and the conversion of each monomer by gas chromatography. The number of polymer particles (NP) per unit volume of water was calculated using the average particle diameter (dp) determined by electron microscopy and the material balance equation for each polymerized monomer and PB seed particles initially charged.
could be applied to the prediction of monomer concentrations in ABS latex particles constituted a sea−island structure with spherical SAN domains in a PB matrix.21,22 Therefore, a twophase swelling model and the overall material balance equations on each monomer in three phases, corresponding to three intervals of emulsion copolymerization are listed in Tables 1 and Tables 2 without being explained further. The parameters and constants used in the equations are also presented in Table 3.
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EXPERIMENTAL RESULTS AND DISCUSSION Experimental Procedure. St and AN monomers of commercial grade were distilled under reduced nitrogen pressure and stored at −20 °C in the refrigerator prior to use. Reagent grade sodium dodecyl sulfate (SDS) and potassium persulfate (KPS) were used as emulsifier and initiator, respectively, without further treatments. A small amount of SDS was added to the reactor so as to be S0 = 0.30 g/dm3-water, which is far lower than the CMC of SDS, to prevent both coagulation between particles and secondary nucleation of new SAN particles during the course of the copolymerization. The seeded emulsion copolymerization experiments were carried out at 50 °C in the same reactor system as used in the previous study.14 Stirring speed was maintained at 250 rpm. The PB latex particles used as seed are
⎛M M X M X ⎞ π 3 d p NP = ⎜⎜ 0B + 0a Ma + 0s Ms ⎟⎟ ρpa̅ ρps̅ ⎠ 6 ⎝ ρpB̅
(11)
where M0B is the weight of PB seed particles initially charged per unit volume of water and ρ̅pB is the density of PB polymer. The constancy of the number of particles during the course of polymerization was checked at the end of polymerization by comparing the number of polymer particles (NP) calculated by eq 11 with that of PB seed particles initially charged (NT). If the calculated value of NP is within the range of (1 ± 0.1) × NT, we 17583
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Rate Constants and Comparison of Model Predictions with Experimental Results. The numerical values of the rate constants and other parameters at 50 °C used in this study are listed in Table 3. Most of the numerical values of rate constants and coefficients are the same as those used in the previous study.14,26 It should be noted here that the value of ktrsB is literature value, while the value of ktraB has not been reported yet.28 Moreover, there are no experimental data on the grafting efficiency that can be used to determine the value of ktraB by fitting with the predicted value under similar conditions. As an alternative approximation, the value of ktraB is estimated to be about 10 times higher than that of ktrsB by comparing Cmas = 4.0 × 10−4 with Cmss = 5.0 × 10−5, although the value of ktraB used is subject to some errors. The main process variables involved in the experiments to be carried out are the concentration ratio of AN to St (M0a/M0s) in the initial monomer feed and the initial initiator concentration ([I0]w) as long as the number of PB seed particles (NT) is fixed at 1.8 × 1014 particles/cm3-water, which ensure no secondary particle nucleation during the seeded copolymerization. In this study, therefore, the value of M0a/M0s was varied with M0t fixed at 0.20 g/cm3-water. First of all, an experiment with representative recipe and conditions shown in Figure 3 was conducted. In this experiment, 63 g of PB seed latex having 22 g of PB seed particles (0.10 μm) and 199 g of purified water having 0.075 g of SDS were first charged into the reactor, and then, 25 g of St and 25 g of AN were charged, respectively. Aqueous initiator solution was prepared by dissolving 0.313 g of KPS into 10 g of purified water. After the oxygen remaining in the reactor system was purged by using high-purity nitrogen gas (purity >99.995%), the polymerization was started by pouring the aqueous initiator solution into the reactor. Figure 3 shows a typical example of the comparison between the experimental and predicted conversion versus time curves observed in the seeded emulsion grafting copolymerization of St and AN in the presence of PB latex particles as seed. Open circles represent additional total conversions versus time data to confirm good reproducibility of the experiment. The solid lines show the predicted simulation results for the total and respective monomers. It is seen that the agreement between the experimental and predicted conversion versus time curves is fairly good from the initial to final conversions. Alternately, the solid lines shown in Figures 4 and 5 respectively display the calculated variations of the concentration of each monomer in the SAN domain and PB matrix
Table 2. Approach of Predicting Monomer Concentrations in ABS Particles after Monomer Droplets Disappear14,22 equation At thermodynamic equilibrium, the partial molar free energy of i monomer in SAN domains must be equal to that in the PB matrix and that in the aqueous phase: aq 2 (ΔG /RT )PB A = (ΔG / RT )A = ln ΦAW + (1 − mAW )ΦW + χAW ΦW
(ΔG /RT )SAN = (ΔG /RT )aq A A (ΔG /RT )SPB = (ΔG /RT )SAN S [MS]PB =
ΦSPρS ΦAPρ A [MA]PB = MS MA
Φ̅ SPρS Φ̅ APρ A [MA]SAN = MS MA The overall material balance equations on each monomer in two phases can be expressed: ΦSP + ΦAP + ΦP = 1
[MS]SAN =
Φ̅ SP + Φ̅AP + Φ̅ P = 1 A 0(1 − Xa)/ρA = ΦAPVPB + Φ̅APVSAN + ΦAw Vw
S0(1 − Xs)/ρS = ΦSPVPB + Φ̅ SPVSAN + ΦSw Vw (1 − Φ̅ SP − Φ̅AP)VSAN = (1 − ΦSP − ΦAP)VPB =
S0Xs A X + 0 a ρS ρA
1 3 πd p NT 6
ΦSw = 0.0Φw + ΦAw = 1.0Φw Vw = 1.0
Φij is the volume fraction of i-monomer (a = AN, s = St) in j-phase (w = water, p = polymer); Φp, Φw are the volume fractions of polymer in the ABS particles and of water in the water phase; χip and χik are the interaction parameters between i-monomer and polymer, between imonomer and k-monomer; mik is the molar volume ratio of imonomer to k-monomer; γ is the interfacial tension between the particle and water phases; R is the gas constant; VPB, VSAN, and Vw are the volumes of PB matrix, SAN domains, and water phases per cm3water; dp is the diameter of ABS particles; Viw is the volume of imonomer dissolved in the water phase; Mi and ρi are the molecular weight and density of i-monomer, respectively; [Mi]PB, [Mi]SAN are the concentrations of i-monomer absorbed in PB matrix and SAN domains, mol/dm3 of particle, respectively.
regarded that appreciable secondary nucleation and coagulation between particles were both negligible and that the assumption of constancy in the number of particles during the course of the seeded emulsion copolymerization held within experimental error.
Table 3. Values of the Numerical Constants at 50 °C Used in Kinetic Equations14,26−28 constant
a
unita 3
kp γ δ Cm
[dm /mol sec] [−] [−] [−]
Dw md k̅tp
[cm2/sec] [−] [dm3/mol sec]
ktriB kdf
[−] [1/sec]
acrylonitrile
styrene
sources
3700 0.045 1.0 Cmaa = 6.0 × 10−6 Cmsa = 1.0 × 10−7 2.0 × 10−5 7.8 ktpaa = 3.0 × 108 ktpsa = 1.2 × 108 ktraB = 2.5 × 10−2 6.7 × 10−7
210 0.33 0.45 Cmss = 5.0 × 10−5 Cmas = 4.0 × 10−4 1.2 × 10−5 1300 ktpss = 1.8 × 106
26 26 14 14
ktrsB = 2.5 × 10−3
28 27
14 26 26
Notation: [−], unitless value. 17584
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mostly composed of AN monomer units. These oligoradicals cannot easily be absorbed into ABS particles consisting of PB matrix, because of the poor affinity for PB, although an AN monomer can enter each phase in the ABS particles even when no St monomer exists in this copolymerization system, as shown in Figure 4. This poor affinity will bring about a decrease in the number of oligoradicals entering the ABS seed particles to initiate polymerization and accordingly lead to a decrease in the average number of total radicals in an ABS particle. Additionally, we found also that polymerization is restarted as soon as a small amount of St monomer is added to the system after complete depletion of the St monomer in the system. Hagiopol et al.29 claimed that polyacrylonitrile macroradicals generated in the aqueous phase cannot easily be captured by PB particles in the absence of a St comonomer. Figure 6 shows, on the other hand, a typical example of the effect of changing the ratio M0a/M0s from 1.0 (Figure 3) to 2.33 Figure 4. Calculated variation of the concentration of each monomer in SAN domains and PB matrix in ABS copolymer particles with total monomer conversion under the conditions corresponding to those in Figure 3.
Figure 6. Comparison between the experimental and predicted conversion versus time curves for the emulsion copolymerization of St and AN in the presence of PB seed latex particles under the conditions NT = 1.8 × 1014 particles/cm3-water, M0t = 0.2 g/cm3-water, M0a/M0s = 2.33 (M0a = 0.14 g/cm3-water, M0s = 0.06 g/cm3 -water), [I0]w =1.25 g/dm3-water, S0 = 0.30 g/dm3-water and 50 °C. The solid lines show the predicted results. Figure 5. Calculated variation of the average number of total radicals per ABS particle with total monomer conversion under the conditions corresponding to those in Figure 3.
on the total, and each monomer conversion versus time curve with keeping M0t constant at 0.2 g/cm3-water. The predicted values shown by the solid lines are in fairly good agreement with the experimental data points except for a higher range over 80% of the St monomer conversion. However, it is seen that disagreement of the St conversion between the observation and prediction becomes remarkable in the higher range of monomer conversion when the concentration of St monomer initially charged is decreased. Figure 7 shows a comparison between the experimental and predicted total conversion versus time curves observed when the initial weight ratio of AN and St (M0a/M0s) in the initial monomer feed was varied from 0.7 to 2.33 with keeping M0t constant at 0.2 g/cm3-water. It is seen that the predicted values shown by solid lines agree fairly well with the observed values. From these comparisons, we can regard that the two-phase kinetic model proposed in this study can provide a satisfactory explanation for the effect of comonomer composition in ABS particles on the kinetic features of this emulsion copolymerization system.
and of the average number of total radicals in an ABS copolymer particle with total monomer conversion under the experimental conditions corresponding to those in Figure 3. It is seen from Figures 3 and 4 that St monomer disappears from the system at the total monomer conversion of around 80%, and that the polymerization practically stops when St monomer in the ABS particles approaches zero, although almost half of AN monomer initially charged still remains in the ABS particles. This polymerization behavior is clearly different from that observed in the emulsion copolymerization of St and AN in the presence of PS seed particles.14 The reasons for this difference will be as follows: One reason is that the average number of total free radicals in an ABS particle sharply decreases when St monomer approaches zero, as shown in Figure 5. Furthermore, almost all the monomer left in the continuous water phase is the AN monomer after complete depletion of the St monomer from the ABS particles. This means that oligoradicals generated in the water phase are those 17585
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In addition, it is shown here that the proposed two-phase kinetic model is able to predict some structural features on which the properties of ABS strongly depend, such as accumulated and instantaneous composition of the free copolymer chain and the grafted copolymer chain, and the grafting efficiency of St and AN onto PB, although the values of the rate constants used here may not necessarily be perfect. Figure 9 shows the predicted variation of accumulated and instantaneous wt % PAN composition in the two phases in ABS particles with total monomer conversion.
Figure 7. Comparison between the experimental and predicted total conversion versus time curves observed when the initial weight ratio of AN and St (M0a/M0s) in the initial monomer feed is varied. M0t = 0.2 g/cm3water, [I0]w = 1.25 g/dm3-water, S0 = 0.3 g/dm3-water, NT = 1.8 × 1014 particles/cm3-water. The solid lines show the predicted results.
Figure 8 shows a typical example of the effect of initial initiator concentrations on the total conversion versus time
Figure 9. Calculated variation of accumulated and instantaneous wt % PAN composition in the two phases in ABS particles with total monomer conversion under the conditions corresponding to those in Figure 3
According to the model prediction with the two-phase kinetic model, it is expected that AN content in the grafted SAN is lower than that in the free SAN in both the accumulated and instantaneous compositions, as shown in Figure 9. This may be due to the effect of solubility parameters on the partition of AN between SAN and PB. On the other hand, it is also expected that the difference of composition increases with increasing total conversion, especially for instantaneous composition. It should be noted here that a large difference in composition can lead to incompatibility of the grafted and free SAN in ABS copolymer. Figure 10 indicates the predicted variation of the grafting efficiency (GE) of St and AN onto PB matrix in the ABS particles with total monomer conversion. It is seen from Figure 10 that the GE decreases very sharply in the beginning of the copolymerization, and then gradually reaches a relatively constant value as the copolymerization proceeds. In the very beginning of the copolymerization, the penetration of free radicals into the PB matrix part is highly probable, because the volume of PB matrix is larger than that of the SAN domain in the ABS particle. This will result in a higher GE in the beginning of the copolymerization. On the other hand, Figure 10 also indicates that an increase in the ratio of the total amount of monomer initially charged (W0t) to PB seed particles (WPB) leads to a decrease in the value of GE.
Figure 8. Effect of the initial initiator concentrations on the course of copolymerization for the emulsion copolymerization of St and AN in the presence of PB seed latex particles under the conditions M0t = 0.2 g/cm3-water, M0a/M0s = 1.0, S0 = 0.3 g/dm3-water, NT = 1.8 × 1014 particles/cm3-water, and reaction temperature = 50 °C. The solid lines show the predicted results.
curves, in which the initial initiator concentration was varied about four times from 0.63 to 2.53 g/dm3-water. It is seen that agreement between the observed and predicted results is fairly good except for a higher range of monomer conversion in a lower initial initiator concentration. Considering a fairly good agreement between the experimental and predicted monomer conversion versus time curves so far presented, we can conclude that the two-phase kinetic model proposed in this study is valid and applicable for predicting the rate of emulsion grafting copolymerization of St and AN in the presence of PB seed latex particles with the diameter of ca. 0.10 μm. This also indicates that the several assumptions made in deriving the two-phase kinetic model represent the phenomena rather close to actual ones.
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CONCLUSIONS A two-phase kinetic model is proposed for the emulsion grafting copolymerization of St and AN in the presence of 17586
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smaller PB seed latex particles with the diameter of around 0.1 μm. The validity and utility of this kinetic model for predicting the conversion versus time curves of this copolymerization system was demonstrated by comparing the experimental and predicted monomer conversion versus time curves. It was found that the swelling behavior of AN in SAN domains and PB matrix in ABS latex particles is rather normal, even though no more St monomer exists in the copolymerization system. Nevertheless, the average number of total radicals in an ABS particle sharply decreases when the St monomer is completely consumed. This kinetic behavior is completely different from that observed in the emulsion copolymerization of AN and St in the presence of PS particles as seed.14 In addition, it was shown that this kinetic model is able to predict some structural features, on which the properties of ABS strongly depend, such as accumulated and instantaneous composition of the free copolymer chain and of the grafted copolymer chain, and the grafting efficiency of St and AN onto PB.
ASSOCIATED CONTENT
S Supporting Information *
Derivation of the equations which predict the average number of various radical, mean rate coefficient, and mean termination rate coefficient. This material is available free of charge via the Internet at http://pubs.acs.org.
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REFERENCES
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Figure 10. Calculated variation of the grafting efficiency of St and AN onto the PB matrix in ABS particles with total monomer conversion under the conditions M0t = 0.2 g/cm3water, M0a/M0s = 1.0, [I0]w =1.25 g/dm3-water, S0 = 0.3 g/dm3-water, NT = 1.8 × 1014 particles/cm3water, 50 °C. The lines show the predicted results. The arrow indicates the direction of a decrease in GE when the initial weight ratio of monomer to PB seed particles (W0t/WPB) is increased.
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Article
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Present Address §
M.N.: Institute of Advanced Materials, Nanjing Tech University, Box No. 138, No. 30, Puzhu Road(S), Nanjing 211816, China.
Notes
The authors declare no competing financial interest. 17587
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