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Ind. Eng. Chem. Res. 2009, 48, 4810–4816
Study of Butyl Methacrylate Depropagation Behavior Using Batch Experiments in Combination with Modeling Wei Wang and Robin A. Hutchinson* Department of Chemical Engineering, Dupuis Hall, Queen’s UniVersity, Kingston, Ontario K7L 3N6, Canada
Michael C. Grady Central Research and DeVelopment, E. I. du Pont de Nemours and Co. Inc., Wilmington, Delaware 19880
Batch polymerization experiments are combined with simulations to investigate the depropagation behavior of butyl methacrylate (BMA). Experiments carried out between 110 and 145 °C and polymer contents between 9 and 34 wt %, including experiments conducted with added polymer, indicate that equilibrium monomer concentration ([M]eq) varies not only with temperature but also with polymer content. An extended Predici model provides a good fit to the monomer concentration and polymer molecular weight profiles, with the simulated monomer profiles at 132 and 145 °C sensitive to small changes in the depropagation activation energy. Thus, these data provide a better estimate of depropagation kinetics than those measured by the pulsed-laser polymerization/size-exclusion chromatography method. The entire data set is well-represented by [M]eq (mol · L -1) ) 1.76 × 106(1 - 0.778xwp) exp(-6240/T), in which xwp represents the weight fraction of polymer in the system. 1. Introduction In the classical analysis of free radical polymerization, the propagation reaction is treated as irreversible. However, thermodynamic considerations indicate that the assumption of irreversibility may be violated under certain conditions. The overall direction of the reaction is governed by the Gibbs free energy equation, which relates the change in free energy (∆G) to the change in enthalpy (∆H) and entropy (∆S) with the reaction temperature (T). ∆G ) ∆H - T∆S
(1)
Polymerization can only proceed when the sign of ∆G is negative. When the entropy and enthalpy of a polymerization reaction are both negative, a ceiling temperature (Tc) exists above which propagation will no longer occur because the reverse propagation (depropagation) reaction is favored. Thus, the propagation step should be written as an equilibrium equation: kp
• P•n + M {\} Pn+1
(2)
kdp
where kp and kdp are the rate coefficients for propagation and depropagation, respectively, Pn• represents a growing radical of length n, and M is the monomer. The change in enthalpy (∆H) and entropy (∆S) are calculated as follows: ∆H ) Ep - Edp
(3)
∆S ) R ln(Ap ⁄ Adp) + R ln[M]
(4)
E and A, respectively, are the activation energies and frequency factors of the forward and reverse rate coefficients expressed in the usual Arrhenius form: kp ) Ap exp(-Ep ⁄ RT)
(5)
kdp ) Adp exp(-Edp ⁄ RT)
(6)
* To whom correspondence should be addressed. E-mail:
[email protected].
The effective or net forward propagation rate, denoted by kpeff, is given by eq 7. keff p ) kp - kdp ⁄ [M]
(7)
At low temperature, the depropagation rate is insignificant and the second term in eq 7 can be neglected. This is not the case at high temperatures and low monomer concentrations, as the activation energy of kdp is higher than that of kp by ∆H; typical values of ∆H for alkyl methacrylates are in the range of -50 to -60 kJ/mol.1-3 The effective propagation rate becomes zero at the ceiling temperature Tc, where the forward and back reactions are exactly balanced. The standard free energy change at Tc is given by eq 8, which may be written either with the monomer concentration or with the temperature as the independent variable, where [M]eq is the equilibrium monomer concentration at a given temperature.4 ∆G0 ) -RTc(kp ⁄ kdp) ) RTc ln[M] ) RT ln[M]eq
(8)
The relationship between [M]eq and temperature can be examined in two ways. The first considers monomer concentration to be fixed and defines Tc as the ceiling temperature at which effective propagation rate Rp tends to zero: at a given [M], lim Rp f 0 TfTc
The second considers temperature to be fixed and defines [M]eq as the equilibrium monomer concentration below which polymerization will not proceed: at a given T,
lim
[M]f[M]eq
Rp f 0
The two approaches are equivalent: for a given ceiling temperature there exists an equilibrium monomer concentration, and vice versa. Since the reversibility of propagation was first reported by Ivin and Dainton,5 methacrylate depropagation behavior has been studied by Ivin et al.,6-9 Bywater,10 and others.11-13 The investigation of a series of methyl methacrylate batch polymerizations by Bywater10 indicated that the polymerization equili-
10.1021/ie900060x CCC: $40.75 2009 American Chemical Society Published on Web 04/09/2009
Ind. Eng. Chem. Res., Vol. 48, No. 10, 2009
brates at the same monomer concentration ([M]eq) for a given temperature, independent of the initial monomer concentration, and does not proceed when the initial monomer concentration is below this equilibrium value. The conclusion that [M]eq is only a function of temperature is not completely adequate when one takes a closer look at eq 8: [M]eq or Tc may be dependent on any factor that affects the free energy of polymerization, such as the solvent medium, the monomer concentration, the external pressure, the polymer concentration, etc.4 In particular, the variation of [M]eq with solvent14-17 and polymer concentration18-23 for different monomer systems (but not methacrylates) has been observed by several researchers. For instance, the equilibrium volume fraction of monomer (φm) declines by ∼20% as the polymer volume fraction (φp) is increased for the anionic polymerization of R-methylstyrene using tetrahydrofuran as the solvent. The decrease was represented by a linear relation φm ) A + Bφp, where A and B are two constants deduced using thermodynamic equations in terms of free energy change and interaction parameters between polymer, solvent, and monomer.21,22 More recently, Grady et al.24 have developed an empirical equation to represent [M]eq for butyl methacrylate (BMA) semibatch freeradical polymerizations conducted at 138 °C. [M]eq ) 1.76 × 106(1 - 0.778xwp) exp(-6339 ⁄ T)
(9)
The temperature dependence in eq 9 was estimated using Edp ) 75.60 kJ/mol, as estimated by a pulsed-laser polymerization/ size-exclusion chromatography (PLP/SEC) study of methacrylate depropagation kinetics.3 The PLP/SEC technique measures kpeff at elevated temperatures, then calculates kdp from eq 7 using a value for kp extrapolated from lower-temperature experiments.3,25 The values of Adp and Edp are estimated from the resulting Arrhenius plot for kdp. However, the methacrylate experiments were performed at low fractional conversion and conditions where the rate of propagation is significantly higher than that of depropagation. Because of the high correlation between the pre-exponential factor and the activation energy, the estimated Edp values vary between 71.1 and 80.8 kJ/mol for dodecyl methacrylate (DMA), depending upon the assumptions made during fitting.3 In addition, the decreased quality of PLP/SEC data at high temperatures increases the uncertainty in the kpeff data and, thus, affects the accuracy of the Edp estimates.26 Unfortunately, small differences in Edp, even
