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Modeling Copolymerization of Styrene and Acrylic Acid via the Free-Radical Retrograde-Precipitation Polymerization (FRRPP) Process Yi Zhao, Yadunandan L. Dar,† and Gerard T. Caneba* Department of Chemical Engineering, Michigan Technological UniVersity, Houghton, Michigan 49931
The free-radical retrograde-precipitation polymerization (or FRRPP) process is a free-radical-based chain polymerization process that occurs above a lower critical solution temperature (LCST). The unique features of FRRPP have been exploited for the synthesis of novel amphiphilic materials under industrially practicable conditions. In the work described here, the copolymerization of styrene and acrylic acid via FRRPP is modeled and simulated to derive greater understanding behind the polymerization mechanism. The penultimate model is used to calculate the reactivity ratios. These reactivity ratios are used to calculate conversion, composition, and molecular weight distributions using the mole balance equations for the different species in the system and the Achilias Kiparissides model for the calculation of reaction rate coefficients. The results suggest that precipitation and the resulting phase separation and change in diffusivities have a strong impact on the polymerization kinetics. The penultimate model provides a better representation of the reactivities, in comparison to other approaches. Introduction The free-radical retrograde-precipitation polymerization (FRRPP) process is a chain polymerization process wherein monomers undergo free-radical polymerization in solution. However, the polymer molecules form an immiscible polymerrich phase when polymer molecules of a critical size are produced at a critical concentration above a minimum temperature called the lower critical solution temperature (LCST).1 The mechanism proposed for polymerization control using FRRPP is based on radical occlusion and trapping in precipitated domains when the temperature is above the LCST. The LCSTtype behavior is proposed to be assisted by the exothermic nature of polymerization reactions, which leads to physical immobilization and radical longevity.2,3 This is especially relevant close to the spinodal curve, where termination as well as propagation rate coefficients vanish.3 In a study of FRRPP of styrene in ether, it was observed that up to 84% of polymer molecules are attached to live radicals, even after time periods equal to four times the initiator half-life.3 The mechanism of polymer occlusion was studied4 and related to the coil to globule transition of polymer chains, even under dilute conditions.6-10 The added effect of the exotherm in the chain polymerization system not only could result in chain collapse but also could result in knotting of the collapsed chains.11 Both chain collapse and knotting would contribute to a reduction in mutual diffusion coefficients. The trapped radicals can then react with a variety of different monomers, leading to block copolymers. In cases where the monomers exhibit a significant difference in hydrophilicity, the copolymer can be amphiphilic. The ability of FRRPP to synthesize novel amphiphilic copolymers has been demonstrated in previous work.1-5 Amphiphilic copolymers have been of interest in many areas of science and industry, because of their affinity for interfaces and their ability to stabilize certain dissimilar interfaces. The ability to extend polymer radical lifetimes can be used to develop an approach to determine a way around reactivity ratio limitations * To whom correspondence should be addressed. Tel.: (906) 4872051. Fax: (906) 487-3213. E-mail address:
[email protected]. † Present address: Applied Research Group, Imperial Chemical Industries plc., 10 Finderne Ave., Bridgewater, NJ 08807.
on copolymer composition and microstructure obtained from conventional copolymerization kinetics. This can be achieved by manipulating monomer feed compositions, combined with long radical lifetimes. This effect was demonstrated by the synthesis of tapered styrene-acrylic acid block copolymers,5 despite the fact that unfavorable reactivity ratios (based on literature values) lead to large proportions of homopolymers and random copolymers.12 The work described in this manuscript is directed toward the modeling and simulation of the free-radical retrograde-precipitation copolymerization of styrene and acrylic acid, with the intention of providing a better understanding of the cause-andeffect relationships that drive the novel properties of the polymer that is produced.4 The approaches used to model the physical effects concerned have been selected for their simplicity, while maintaining sufficient ability to describe complex thermodynamic and kinetic behavior. Experimental Section Materials Used. Styrene (St) and acrylic acid (AA) monomers, which were purchased from Aldrich Chemical Co., were distilled under reduced pressure to remove any inhibitors. Analytical-grade diethyl ether and pyridine solvents were purchased from Fisher Scientific, Inc. The 2,2′-azobis(2,4dimethylvaleronitrile) (V-65) initiator was obtained from Wako Chemical Co. All fluids used in the reactor were bubbled with nitrogen gas for at least 15 min to purge any dissolved oxygen. Phase Equilibria Work. The LCST of the polystyrene-ether system has been shown to be located at ∼42 °C for a polystyrene molecular weight of 20.4 kDa.13 The theoretical value of the LCST should be based on an infinite molecular weight and zero pressure. For the ternary styrene-polystyrene-ether system, the phase behavior above the LCST has been measured in the past,3,14 which showed a dependence on the polymer molecular weight of the phase envelope. (Essentially, the larger the molecular weight, the larger the phase envelope.) Using the same apparatus, we have determined that, relative to our operating temperatures (60-80 °C), poly(acrylic acid) phase-separates in ether above the LCST. The same apparatus was used to verify that pyridine and cyclohexane dissolve polystyrene within the
10.1021/ie0712176 CCC: $40.75 © 2008 American Chemical Society Published on Web 04/26/2008
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operating temperature range, whereas poly(acrylic acid) phaseseparates below the UCST in ether and cyclohexane. Polymerization Apparatus and Procedure. The stirred-tank apparatus and polymerization procedure have been described elsewhere.3,4 The experimental procedure is reproduced below for reference: (1) A 200-mL quantity of solvent was bubbled with nitrogen for ∼15 min. (2) The reactor was first purged with nitrogen and then filled with ∼80 mL of solvent. (3) All the liquid lines were purged with nitrogen to make the reactor oxygen-free. (4) The reactor assembly included a stirrer, which was maintained at 50% of its maximum speed, at ∼230 RPM. (5) The temperature controller was programmed to heat the reactor to its operating temperature within 30 min and then maintain the temperature at that value. (6) The monomer mixture was prepared by mixing the monomer(s), solvent, and initiator. (7) The monomer(s)-initiator-solvent mixture was bubbled with nitrogen for ∼15 min. (8) After the reactor reached the steady-state temperature, the monomer(s)-initiator-solvent mixture was pumped into the reactor (using an Eldex metering pump) for 28-35 min. At this point, the timer was started. (9) A small amount of solvent was pumped into the reactor, to flush the lines. (10) Nitrogen gas was pushed through the lines to clear any of the material left behind in the liquid lines. The liquid inlet valve was then closed. (11) Samples and reactor product were collected inside a sealed bottle that was immersed in an ice bath, and then the sample bottle was stored in a refrigerator. Preparation and Analysis of Products and Samples. Liquid samples and products from the reactor were air-dried on aluminum pans and then completely dried in a vacuum oven. Solid products and samples were analyzed for molecular weight distribution using size exclusion chromatography. To obtain an idea of the tapered block copolymer contents of the products, they were first dissolved in tetrahydrofuran (THF). The THFproduct solutions were heated while water was added to replenish the vaporized THF. At the same time, ammonia was added to neutralize the acid in the copolymer. When all the THF had vaporized, the resulting emulsion in water was isolated, and its solid content was determined gravimetrically. Also, the residue from this emulsification process was weighed. Another approach to estimate the copolymer content was to try to dissolve the solid products in toluene. The dissolved polystyrene homopolymer portion was isolated from the residue. NMR Spectroscopy. The composition of the St-AA copolymer was determined using nuclear magnetic resonance spectroscopy (1H NMR or 13C NMR). The copolymer spectra were obtained using a Varian-400 MHz spectrometer. Pyridined5 was selected as the reference solvent. The solid copolymer sample was dissolved in a 5-mm-diameter NMR test tube at a concentration of 0.1 g/mL. The 1H NMR analysis was performed at 50 °C, using the following measurement parameters: acquisition time, 2.502 s; spectral width, 5000 Hz; pulse width, 4.5 s; and number of scans, 16. For the 13C NMR test, which was performed at 25 °C, the measurement parameters were given as follows: acquisition time, 0.640 s; spectral width, 25 000 Hz; pulse width, 4.5 s; and number of scans, 2000-8000. The molar fraction of styrene units in the copolymer was calculated using the ratio of the aromatic groups to the backbone repeat
units from both 1H NMR and 13C NMR analysis. The acrylic acid molar composition was obtained by subtracting the styrene composition from the total. Theory Polymer Reactivity Ratios. Theoretical studies of the polymerization of two or more monomers have been conducted on various reaction systems since Dostal15 first proposed the concept of the terminal model in 1936. In the terminal model, it is assumed that the reactivity of the growing polymer chain is determined merely by the last added monomer unit (i.e., terminal unit), independent of the chain length and composition. For a two-component copolymerization, the terminal model leads to four propagation reaction equations and two reactivity ratios.16,17 It was discovered that the penultimate unit also affects the reactivity of the growing polymer chain for many copolymerization systems,18,19 especially for highly polar monomers or monomers with bulky side chains. After the penultimate model was developed by Merz et al.,20 many investigations have been conducted to explore the applicability and limitations of this approach. Eight propagation equations are required to describe the penultimate model as both penultimate and terminal units affect the reactivity of the growing radicals: k111
M1M1* + M1 98 M1* k112
M1M1* + M2 98 M2* k121
M1M2* + M1 98 M1* k122
M1M2* + M2 98 M2* k211
M2M1* + M1 98 M1* k212
M2M1* + M2 98 M2* k221
M2M2* + M1 98 M1* k222
M2M2* + M2 98 M2*
(1) (2) (3) (4) (5) (6) (7) (8)
Using the aforementioned reactions, four reactivity ratios can be determined:
r1 )
k111 k112
(9)
r2 )
k222 k221
(10)
r′1 )
k211 k212
(11)
r′2 )
k122 k121
(12)
where r1 and r2 are the reactivity ratios of monomers for the growing radicals with the same penultimate and terminal units.
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The terms r′1 and r′2 represent the reactivity ratios of monomers for the growing radicals with different penultimate and terminal units. Steady-state conditions are assumed for all the radicals and, combined with the consumption rate equations for monomers, produce the following copolymer composition equation:21
1 + [r′1Z(r1Z + 1)/(r′1Z + 1)] F1 ) 1 - F1 1 + {r′2(r2 + Z)/[Z(r′2 + Z)]}
(13)
where
Z)
f1 1 - f1
(
)(
)
r2 r2 H G ) r1 + R+H R R+H R
(
)
r2 r2 ξR R
η ) r1 +
(18)
where R is an arbitrary constant to make the variables η and ξ lie within the interval (0, 1). Kelen and Tu¨do˜s23 suggested the following optimal value for R:
R ) xHmHM
(19)
in which Hm and HM are, respectively, the smallest and biggest values among the H values. Plotting η vs ξ should give a straight line, from which r1 and r2 can be obtained. In addition, the following equations are given for r1 and r2, using the leastsquares method:
r1 )
∑ ηξ(n - ∑ ξ) - ∑ η(∑ ξ - ∑ ξ2)
r2 )
(20)
∑ ξ - (∑ ξ) ∑ ηξ ∑ ξ - ∑ η∑ ξ2 2
n
∑
n
ξ2 - (
2
∑
(21) ξ)2
where n is the number of sets of experimental data. To overcome the errors created by the approximation for instantaneous copolymer composition and the drift in monomer feed ratio, the following equation (called the integration composition equation) was used to determine the monomer reactivity ratios:24
ln x2 ) r2 ln x1 +
)[
(
]
1 - r1r2 (1 - r2)x2 - (1 - r1)x2x ln 1 - r1 (1 - r2)x2 - (1 - r1)x1x
(22)
in which
xi )
(15)
[Mi] [Mi]0
(23a)
and
where
x)
([M1]f/[M2]f) + ([M1]0/[M2]0) 2
(16a)
dM1 dM2
(16b)
x(y - 1) y
(16c)
x2 y
(16d)
y) G)
H)
[M1]f is the final molar concentration of M1, and [M1]0 is the initial molar concentration of M1. If we let
η) and
(17b)
eq 15 can be written as
(14)
Equation 13 can be used to calculate the reactivity ratios by obtaining a series of monomer mole fractions (f1) and their corresponding instantaneous copolymer compositions (F1). The most common experimental procedure is to perform a set of copolymerizations, varying the feed ratios of M1 to M2 from 0.1 to 0.9 and keeping the conversions at
