Ind. Eng. Chem. Res. 1996, 35, 1795-1800
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KINETICS, CATALYSIS, AND REACTION ENGINEERING Degradation of Poly(methyl methacrylate) in Solution Giridhar Madras, J. M. Smith, and Benjamin J. McCoy* Department of Chemical Engineering and Materials Science, University of California, Davis, California 95616
The rate of degradation of poly(methyl methacrylate) (PMMA) to methyl methacrylate (MMA) was investigated in the liquid phase with toluene as the solvent. The degradation experiments were carried out in a tubular flow reactor at 1000 psig (6.8 MPa) and at four different temperatures (200, 225, 275, and 300 °C). The polymer concentration was varied from 1 to 4 g/L. A discrete model for the first-order rate of polymer degradation was derived and compared to the continuous kinetics approach. Both models lead to the same expression for monomer concentration increasing linearly with time. Rate constants were evaluated using the moments of the molecular weight distributions of the reacted and unreacted polymer. The rate was first order in polymer concentration, and the activation energy was 8.4 kcal/mol (34 kJ/mol). This activation energy suggests that the rate controlling step for the thermal degradation of PMMA is the depropagation process. Introduction Disposal of plastic wastes has become a worldwide problem, with the current costs of dumping these wastes in landfills as high as $150 per ton (Ng et al., 1995). With increasing governmental regulations and increasing consumption of plastics, the cost of conventional disposal is likely to increase. These economic factors, coupled with increasing environmental concerns, have prompted researchers to investigate plastics recycling by degradation as an alternative. Apart from recycling, degradation can be used in conjunction with chromatography to characterize polymeric structure (Flynn and Florin, 1985). Most investigations of polymer degradation have centered on determining the yield of monomer and rate of change of average molecular weight. Rate equations were typically based on free-radical mechanisms (Simha and Wall, 1958). Thermal degradation of various polymers has been extensively investigated under pyrolysis conditions. However, there are few commercial applications because of low heat-transfer rates and high viscosity of the melting polymer. Thermal degradation in solution provides a potential alternative technique by ameliorating these problems. Degradation of polystyrene (Sato et al., 1990), poly(R-methylstyrene) (Murakata, 1993a), and poly(p-methylstyrene) (Murakata, 1993b) was studied in various solutions, but rates of degradation were not evaluated. Recently, our research group investigated the degradation of poly(styrene-allyl alcohol) (Wang et al., 1995; Madras et al., 1995a) and poly(R-methylstyrene) (Madras et al., 1995b) in solution and determined rate parameters as well as the dependence of the rate constants on polymer concentration and temperature. This technique using a steady-state tubular reactor for polymer degradation has several advantages. Since the reactions occur in the liquid phase, the reactant and all the products have the same reactor residence time, * Author to whom correspondence should be addressed. E-mail:
[email protected]. Telephone: (916) 752-1435. Fax: (916) 752-1031.
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which is directly controlled by the flow rate through the system. Since the temperature is uniform for all fluid elements, the temperature dependence is accurately determined. The continuous-mixture concept provides an effective, yet simple, procedure to analyze the change in molecular weight distributions (MWDs) on degradation of a polymer containing molecules of different molecular weights. Continuous-mixture models have been used previously to determine the kinetics for the liquefaction of coal (Wang et al., 1994), for catalyst deactivation (Subramanian and McCoy, 1994), and for polymer degradation (Wang et al., 1995). The objective of the present paper is to employ a steady-state tubular reactor to determine the rate constants of the degradation of poly(methyl methacrylate) (PMMA) to methyl methacrylate (MMA) in toluene solution. Experiments were conducted at 1000 psig (6.8 MPa), temperatures from 200 to 300 °C, and polymer concentrations, from 1 to 4 g/L. Rate constants were determined by analyzing the MWDs of the reactor effluent at various residence times. Reaction order was determined from the dependence of the rate constants on polymer concentration and the energy of activation from the dependence of rate constants on temperature. A mechanism for the degradation and a framework for the kinetics are proposed. Experiments Pretreatment of PMMA. PMMA was obtained from Aldrich Chemical Co., Inc. The MWD of PMMA was determined by dissolving 0.200 g of PMMA in 100 mL of tetrahydrofuran (THF) (Fisher Scientific) and analyzing this sample by gel permeation chromatography (GPC). Mass MWDs, which can be converted to molar MWDs by dividing by MWs, conveniently display the peaks. The mass MWD in Figure 1 indicates a number average MW of 300 and a weight average MW of 11 900. The graph shows many peaks in the lower MW range of the raw PMMA that would interfere with the product(s) of degradation. To eliminate these low MW peaks, © 1996 American Chemical Society
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Figure 1. MWD of untreated PMMA (Mn ) 300, Mw ) 11 900).
Figure 2. MWD of the polymer portion of the reacted (Figure 3) and unreacted (feed) polymer.
the polymer was fractionated (Kamide and Matsuda, 1989) by partially dissolving 50 g of polymer in 500 mL of toluene at 30 °C. This solution was continuously stirred using a magnetic stirrer and 750 mL of the precipitating agent, n-butanol, slowly added. The precipitated polymer was dried to constant weight in an oven maintained at 110 °C and stored under nitrogen in a sealed bottle. The number-average MW of the treated polymer increased to 6850; the MWD is shown in Figure 2. Degradation of PMMA. The thermal degradation of the treated PMMA in toluene was conducted in a steady-state tubular-flow reactor 0.45 m length with 0.028 m internal diameter). Detailed descriptions of the apparatus and experimental procedure are provided elsewhere (Zhang et al., 1992; Wang et al., 1993). Treated PMMA was dissolved in toluene to the desired concentration (1-4 g/L) at 35 °C and passed through the reactor maintained at constant pressure, 6.8 MPa, and at the desired temperature. The solution was cooled by a water cooled heat exchanger and flowed through a pressure-reduction valve. The flow rate was controlled by a rotameter placed after the pressurereduction valve. Thermal degradation experiments at each temperature and polymer concentration were performed at four different flow rates (6, 9, 12, and 20 mL/min at STP conditions). At each condition, two effluent samples of 10 mL were taken for GPC analysis. The residence time in the reactor was determined by calculating the density of the solvent at reactor conditions (Lee and Kesler, 1975).
Figure 3. MWD after thermal degradation at 225 °C, 6.8 MPa, and t ) 17.1 min.
Analysis of Degradation Products. The samples are analyzed using HPLC-GPC. The HPLC (HewlettPackard 1050) system consists of a sample loop of 100 µL, a gradient pump that pumps THF at a constant flow rate of 1.0 mL/min, and an on-line UV detector. The GPC system consists of three PL gel columns (Polymer Lab Inc.) of 300 × 7.5 mm. The three columns of crosslinked poly(styrene-divinylbenzene) had pore sizes of 100, 500, and 104 Å and were used in series for efficient separation and resolution of the peaks. Various wavelengths were investigated in the range of 200-330 nm, and 205 nm was chosen because of the separation of the MMA and toluene peaks. The first sample of 10 mL is concentrated to 2 mL by evaporating toluene (Fisher Scientific) at 70 °C under vacuum. This is dissolved in THF (Fisher Scientific), and a sample of 100 µL is injected into the HPLC-GPC. Since MMA is evaporated during the concentration of the sample, the chromatograph of this sample provides only the polymer portion of the reacted polymer. To evaluate the concentration of MMA in the sample, the second sample of 10 mL is dissolved in THF and injected into the GPC system, and the concentration is calculated from the area of the peak. A calibration curve (retention time versus MW) was constructed by using polystyrene standards (MW ranging from 162 to 1.5 million) obtained from Polymer Lab Inc. Styrene and R-methylstyrene were dissolved in THF and analyzed in the GPC. The calibration was thus extended to the lower MW range. The monomer peak was also calibrated quantitatively by injecting known amounts of MMA in the GPC. The standard deviation between the peak area and the known amount of MMA was 3.5%. Mechanism The thermal degradation mechanism for polymers depends on the molecular structure and experimental conditions. Two extremes are possible, pure random degradation and pure depolymerization. Random degradation of a polymer occurs by bond scission at any position along the chain backbone. Depolymerization occurs by scission at the chain end, which for homopolymers yields monomers. The reacted polymer shown in Figure 3 has three distinct peaks in the MWD below 1000. To identify these peaks, the effluent from the GPC was separated based on retention time, and the samples were analyzed
Ind. Eng. Chem. Res., Vol. 35, No. 6, 1996 1797
by GC-MS. The GC-MS analysis confirmed that the peak at MW ) 100 was MMA. The peak at MW ) 380 is an oligomer of THF, formed by the exposure of the GPC eluent, THF, to air. The peak at MW ) 1000 was identified as methyl silicones in the MW range 9001100. Used as additives to increase the thermal stability of the polymer (Reich and Stivala, 1971), methyl silicones are nondegradation products that are inert in these experiments. Because they detach from the polymer only at high temperatures, methyl silicones are not removed during the pretreatment of the polymer. Figure 2 compares the polymer portions of the reacted (Figure 3) and unreacted (feed) polymer. Calculations for the curves in Figure 3 show that the first moment of the unreacted polymer is nearly the same as that of the reacted polymer, indicating an absence of random scission. Based on this experimental evidence, one may conclude that the degradation of PMMA to MMA under these experimental conditions is by chain-end scission only. The degradation of PMMA is a radical chain reaction that occurs in three irreversible steps (Grassie and Scott, 1985; Reich and Stivala, 1971) : Initiation. The polymer PN degrades randomly into two radicals by breakage of the bond in the β position (indicated by the vertical arrow):
MW is a continuous variable. The MWD is, therefore, a continuous function of MW. We allow pˆ (x,t) to be the molar MWD of the polymer. The subscript 1 indicates that pˆ 1(x,t) is the molar MWD of the monomer. With the continuous kinetics approach and for a first-order degradation, the steady-state reactor equation can be written in terms of the residence time, t, as follows (Madras et al., 1995b):
dpˆ 1(x,t) dt
)
∫x∞kpˆ (x′,t) δ(x-x1) dx′
(1)
where k is the degradation rate constant (assumed to be independent of the MW x). The initial condition is
pˆ 1(x,0) ) 0
(2)
The moment operation defined as
p1(j)(t) )
∫0∞xjpˆ 1(x,t) dx
(3)
is applied to obtain
dp1(j)(t) ) kx1jp(0)(t) dt
(4)
It was shown (Wang et al., 1995) that the molar concentration of the polymer is constant,
p(0)(t) ) p(0)(0) ) p0(0) ) pN0
(5)
Equation 4 is solved using eq 5 and the initial condition
p1(j)(0) ) 0
(6)
p1(j)(t) ) ktx1jpN0
(7)
to yield Depropagation. The depropagation step consists of the production of the monomer from the newly created radicals:
This is the reverse of the propagation step in the polymerization process. Termination. The termination occurs by interaction of the pair of radicals to reform a polymer:
which is valid for j ) 0, 1, 2, ... and, in particular,
p1(0)(t) ) ktpN0 (j ) 0)
(7a)
p1(1)(t) ) ktx1pN0 (j ) 1)
(7b)
Equation 7b along with the experimental data can be used to evaluate the degradation rate constant, k. Next a discrete model, similar to the one derived by Jellinek (1955), is developed for polymer degradation by chain-end scission and compared to the continuous kinetics model. Consider a polymer, PN, of MW Nx1 that degrades by chain-end scission to the monomer, P1, having MW x1. The overall reaction is first-order in polymer concentration as discussed in the mechanism section. The reactions and the corresponding rate equations can be written in terms of the molar concentration pN, pN-1, ..., pn, ... p2 for polymers PN, PN-1, ..., Pn, ..., P2, respectively:
PN f PN-1 + P1 This model, with the stationary-state assumption for all radical concentrations, leads to a rate equation that is first-order in polymer concentration.
PN-1 f PN-2 + P1
dpN/dt ) -kpN
dpN-1/dt ) k(pN - pN-1)
(8) (9)
l Theoretical Model We have previously developed continuous kinetics models for two types of polymer degradation: degradation by both random-chain scission and chain-end scission (Wang et al., 1995) and degradation by chainend scission only (Madras et al., 1995b). In these models, the polymer is considered to be a mixture with a large number of different size molecules, so that the
Pn f Pn-1 + P1
dpn/dt ) k(pn+1 - pn) n ) 2, 3, ..., N (10) l
P2 f P1 + P1
dp2/dt ) k(p3 - p2)
(11)
As in the continuous mixture kinetics model, we assume
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that the rate constant, k, is independent of the MW. This assumption was satisfactory in the analysis of our previous data for polymer degradation (Wang et al., 1995; Madras et al., 1995a). The rate equations are solved with the initial conditions
molecule undergoes N - 1 first-order degradation reactions until the polymer is completely converted to monomer. The molar concentration and mass concentration of the feed polymer are given, respectively, by
pN(t)0) ) pN0
(12)
p(0)(θ)0) ) p0(0) ) pN0
(21)
(13)
p(1)(θ)0) ) p0(1) ) Nx1pN0
(22)
pn(t)0) ) 0
n
