Reduction of Bisphenol A Residue in Polycarbonates in a Two-Stage

Mar 27, 2009 - A theoretical modeling and simulation study is presented for the design of operational policies for a two-stage polycondensation proces...
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Ind. Eng. Chem. Res. 2009, 48, 4274–4282

Reduction of Bisphenol A Residue in Polycarbonates in a Two-Stage Step-Growth Polymerization Process Yuesheng Ye† and Kyu Yong Choi* Department of Chemical and Biomolecular Engineering, UniVersity of Maryland, College Park, Maryland 20742

A theoretical modeling and simulation study is presented for the design of operational policies for a twostage polycondensation process to achieve a significant reduction of bisphenol A (BPA) residue in high molecular weight bisphenol A polycarbonate (BAPC). In the first stage, low molecular weight polycarbonate prepolymers are prepared in a semibatch melt transesterification reactor under reduced pressure, and in the second stage, a solid-state polymerization is used to further increase the polymer molecular weight and to reduce the BPA residue. The residual BPA concentration in the final polymer can be significantly reduced by employing an optimally determined excess amount of diphenyl carbonate (DPC) in the transesterification stage. However, there is a narrow window of operating conditions that will satisfy the multiple process requirements of the lowest BPA concentration, high molecular weight, and economically feasible short reaction time. The proposed method can also be applied to optimally blending prepolymers of different reactive end group concentrations for the subsequent solid-state polymerization to reduce the BPA content and to obtain high molecular weight. The proposed methods are illustrated through model simulations. 1. Introduction In recent years, the public awareness and concerns about the potential health risks posed by bisphenol A (BPA) leaching out from certain plastic products became acute, and often, they have been the subject of controversial debates between different interest groups.1 For example, BPA has been reported to cause the estrogenic endocrine-disrupting effect because it can act like human body’s hormone and lead to similar physiological effects on the body.2 Some studies on mice and rats suggest that an exposure to low-dose BPA may develop obesity,3 permanent change to the genital tract,4 urethra malfunction,5 and carcinogenic effects such as breast cancer.6 There is also a concern about the long-term low dose exposure to BPA, which may induce chronic toxicity in humans.7,8 It has been reported that when BPA-containing polymer products are exposed to high heat or alkaline conditions, BPA can leach out of the solid polymer into a liquid phase. The potential risk of BPA leaching out from polycarbonate baby-feeding bottles can be a serious concern for parents.9 There is a report that BPA leaching out from waste plastics at landfill sites can also cause an environmental problem.10 On the other hand, it has been reported that BPA is not carcinogenic and does not selectively affect animal reproduction or development.11 The potential human exposure to BPA-derived polymers such as polycarbonates and epoxies have also been claimed to be too low to pose any known health risk.12,13 BPA is a common monomer for many polymers such as bisphenol A polycarbonate (BAPC) and epoxy resins. These BPA-based polymers are widely used for food packaging, beverage and milk bottles, dental sealants, and lacquer lining of food or beverage cans.14 The total annual production capacity of BPA in the world is about 3.2 million metric tons in 2002.14 About 70% of BPA is used for BAPC polymers and approximately 25% is for epoxy resins, while the remaining BPA is used in other products including phenolic resins, unsaturated * To whom correspondence should be addressed. Phone: (301) 4051907. Fax: (301) 405-0523. E-mail: [email protected]. † Current address. 3141 Chestnut Street, Chemical and Biological Engineering Department, Drexel University, PA 19104.

polyesters, can coatings, antioxidants, additives for tires, flame retardants, etc.14 To manufacture BAPC, two completely different processes are used in general: base-catalyzed melt transesterification of BPA with diphenyl carbonate (DPC) and amine-catalyzed interfacial condensation of phosgene and BPA. Because of environmental concerns, the phosgene-free melt transesterification process is regarded as a more environmentally benign process than the old interfacial process. In the melt transesterification process, BPA monomer is reacted with DPC in presence of catalyst such as LiOH · H2O at a reaction temperature of 180-230 °C and at reduced pressure (2-100 mmHg).15 The polymerization is a reversible reaction and it proceeds via a step-growth polymerization mechanism, which is commonly referred as polycondensation. To increase the polymer molecular weight, phenol condensate needs to be removed continuously from the reaction mixture so that the reverse reactions can be suppressed. However, a rapidly increasing melt viscosity at high molecular weight makes the removal of phenol difficult from the reaction mixture, limiting the maximum obtainable molecular weight in a practically reasonable reaction time frame. To obtain high molecular weight polymers suitable for injection molding applications, a postmelt polymerization process such as a solidstate polymerization (SSP) can be employed. The reaction temperature in a SSP process is maintained well above the glass transition temperature (Tg) to provide the mobility of reactive end groups but below the polymer’s melting point (Tm) to prevent the partial fusing and sticking of polymer particles. In a typical SSP process for BAPC manufacturing, relatively low molecular weight prepolymer particles are first crystallized.16 The crystalline portion of the polymer provides a structural support for the particle to maintain its dimensional stability by preventing a partial fusion of the polymer during the SSP. The SSP is usually carried out for more than 10 h because the slow diffusion of a condensate limits the increase of molecular weight. As mentioned earlier, a number of mass media and technical papers report the health related problems caused by BPA monomer leaching out of the BAPC plastic articles.8,17,18 It was reported that the residual BPA in polycarbonate food contact

10.1021/ie8014318 CCC: $40.75  2009 American Chemical Society Published on Web 03/27/2009

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articles ranges from 3 to 141 ppm, with about 10 ppm as a median value.19 The potential adverse effects caused by BPA migrating from a polycarbonate container to food or drinks may be significantly reduced if the polycarbonate contains a negligible amount of BPA residue. However, little or none has been reported in the open literature on how to make polycarbonates with minimal content of BPA at their manufacturing stages by significantly reducing the amount of BPA in the polymer. In this paper, we illustrate that indeed the BPA content in polycarbonate products can be reduced during the polymer manufacturing stage by judiciously designing the reaction conditions with the aid of theoretical process models. We present a method to minimize the BPA content in BAPC polymers through theoretical modeling and simulation studies for a twostage process system of melt transesterification and SSP.20 For a bottle-grade high molecular weight polycarbonate as an example for simulation study, we will show that the optimal conditions for a process system of transesterification and SSP can be found to achieve both high molecular weight and very low BPA content in a practically acceptable total reaction time. Although this work is limited to theoretical model simulations, we expect that the proposed technique may provide a new insight into the design of commercial BAPC process conditions to obtain lowest possible BPA content in polycarbonates. 2. Modeling of a Two-Stage Polycarbonate Polymerization Process To investigate whether the BPA content in the final BAPC product can be reduced significantly by designing the process operational conditions, we shall use a mathematical process modeling technique. The polycondensation process we consider consists of a semibatch melt transesterification process to prepare a low molecular weight prepolymer and a subsequent SSP process in a single polymer particle to obtain high molecular weight suitable for bottle-grade polycarbonate products.20,21 It should be noted that one can also develop a continuous multistage melt transesterification process where reaction temperature and pressure are varied with reaction time to raise the polymer molecular weight. However, here we only consider a semibatch melt transesterification and a subsequent SSP as an example system to illustrate how we can obtain high molecular weight polycarbonates containing minimum possible amount of BPA residue. The bisphenol A polycarbonate process is a typical AA-BB polymerization system where two bifunctional monomers AA (DPC) and BB (BPA) are polymerized. Initially, the reaction of BPA and DPC occurs between the phenyl carbonate end group (EA) in DPC and the hydroxyl end group (EB) in BPA with a catalyst such as lithium hydroxide. The transesterification can be represented as:

different chain ends. The modeling techniques and validation for both methods are well documented elsewhere.15,20-22 In our model simulation study, we shall use a molecular species model. For a BAPC polymerization process with DPC and BPA monomers, three molecular species can be defined as follows:

In the above, A0, B0, and C0 are diphenyl carbonate monomer, bisphenol A monomer, and phenol, respectively. In the molecular species modeling framework, the polycondensation reactions are represented as An + Bm T Cn+m+1 + P (n, m g 0)

(1.1)

An + Cm T An+m + P (n g 0, m g 1)

(1.2)

Bn + Cm T Bn+m + P (n g 0, m g 1)

(1.3)

Cn + Cm T Cn+m + P (n, m g 1)

(1.4)

where n and m are the chain lengths and P is the phenol condensate. The monomers (A0 and B0) in the reaction mixture are included in the kinetic scheme so that we can calculate the concentrations of unreacted monomers during the polymerization. To obtain high molecular weight polymers, the condensate (P) is removed from the reaction mixture by vacuum or inert gas purging in the melt polymerization and SSP processes. In the polycarbonate process, one of the monomers (DPC, A0) is partially removed from the reactor with phenol because of its relatively high vapor pressure. The molecular weight averages can be calculated using the method of molecular weight moments. For each polymeric species, the kth molecular weight moments are defined as follows: ∞

µA,k )

∑ n [A ], k

n

∞

µB,k )

n)1

∑ n [B ], k

n

∞

µC,k )

n)1

∑ n [C ] k

n

n)1

(2) The polymerization is a reversible reaction with phenol (P) as a condensate that needs to be removed from the mixture to shift the reaction equilibrium to the right (chain propagation reaction). The polycondensation process can be modeled using either a molecular species model or a functional group model. Both modeling approaches yield the predictions of conversions of functional end groups and polymer molecular weights. However, the molecular species model provides direct information about the concentrations of monomer and polymer molecules of

where [An], [Bn], and [Cn] denote the concentrations of corresponding polymeric species and the subscript n is the chain length. The number-average and the weight-average molecular weights of the polymer are calculated as j n ) wm M

µ1 , µ0

j w ) wm M

µ2 µ1

(3)

where wm is the molecular weight of a repeating unit, µ0, µ1, and µ2 are the sum of the zeroth, first, and second moments of

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the three different molecular weight species (e.g., µ0 ) µA,0 + µB,0 + µC,0). Here, we assume that the contributions of the chain end units to the overall molecular weight of the polymer are negligible as the chain length is sufficiently large. For the melt polymerization process we consider, phenol condensate is removed by high vacuum. Although BPA has a negligibly low vapor pressure at a reaction temperature (180-230 °C), the vaporized DPC is not negligible because its vapor pressure is as high as 114 mm Hg at 230 °C. As the melt polymerization proceeds, DPC vaporizes together with phenol as high temperature and low pressure are applied from the beginning of the polymerization. Although most of the vaporized diphenyl carbonate is condensed and refluxed back to the reactor, a small amount of DPC might be lost from the reactor. In our modeling, we ignore the vaporization of BPA and assume that the vapor-liquid equilibrium is quickly established in the reactor and in the reflux column for a binary mixture of phenol and DPC.15 In other words, the melt polymerization process in the semibatch reactor is treated as a reactive separation process.23,24 Thus, the amounts of phenol and DPC removed from the reactor and the reflux column are calculated using the vapor-liquid phase equilibrium model.15,22 The computational procedure to calculate the vapor- and liquid-phase compositions and the amounts of volatile components removed from the reaction system is briefly given as follows: (i) for a given small time step, the species mass balance equations are solved; (ii) the vapor-liquid phase equilibria in the reactor and reflux column are computed with the composition of the reaction mixture calculated in step i; (iii) the amount of DPC in the reactor is updated by incorporating the amount of DPC condensed and refluxed back to the reactor at the end of the time step i; (iv) steps i-iii are repeated until the final reaction time is reached. The detailed calculation procedure is documented elsewhere.15 For the semibatch transesterification, the rate equations for the monomers and phenol are expressed as follows:22 Diphenyl carbonate: d[A0] ) -2k1,0[A0][2(µB,0 + [B0]) + µC,0] + dt k2,0[P](µC,0 + 2µA,0) (4) Bisphenol A: d[B0] ) -2k1,0[B0][2(µA,0 + [A0]) + µC,0] + dt k2,0[P](µC,0 + 2µB,0) (5) Phenol: d[P] ) k1,0[4(µA,0 + [A0])(µB,0 + [B0]) + dt 2µC,0(µA,0 + [A0] + µB,0 + [B0]) + µC,02] + k2,0[P][µC,0 - 2(µA,1 + µB,1 + µC,1)] (6) The molecular weight moment equations for the polymeric species take the following form: dµA,0 ) 2k1,0[-2µA,0(µB,0 + [B0]) + µC,0[A0]] + dt k2,0[P](µC,1 - µC,0 - 2µA,0) (7)

dµB,0 ) 2k1,0[-2µB,0(µA,0 + [A0]) + µC,0[B0]] + dt k2,0[P](µC,1 - µC,0 - 2µB,0) (8) dµC,0 ) k1,0[4(µA,0 + [A0])(µB,0 + [B0]) dt 2µC,0(µA,0 + [A0] + µB,0 + [B0]) - µC,02] + k2,0[P][-µC,0 + 2(µA,1 + µB,1)] (9) dµA,1 ) 2k1,0[-2µA,1(µB,0 + [B0]) + µC,1(µA,0 + [A0])] + dt k2,0[P] [µC,2 - µC,1 - 2(µA,2 + µA,1)] (10) 2 dµB,1 ) 2k1,0[-2µB,1(µA,0 + [A0]) + µC,1(µB,0 + [B0])] + dt k2,0[P] [µC,2 - µC,1 - 2(µB,2 + µB,1)] (11) 2 dµC,1 ) 2k1,0[2(µA,1 + µA,0 + [A0])(µB,1 + µB,0 + [B0]) dt µC,1(µA,0 + [A0] + µB,0 + [B0]) - 2µA,1µB,1] + k2,0[P](µA,2 + µA,1 + µB,2 + µB,1 - µC,2) (12) dµA,2 ) 2k1,0[-2µA,2(µB,0 + [B0]) + µC,2(µA,0 + [A0]) + dt k2,0[P] [2µC,3 - 3µC,2 + µC,1 2µA,1µC,1] + 6 8µA,3 - 6µA,2 + 2µA,1] (13) dµB,2 ) 2k1,0[-2µB,2(µA,0 + [A0]) + µC,2(µB,0 + [B0]) + dt k2,0[P] [2µC,3 - 3µC,2 + 2µB,1µC,1] + 6 µC,1 - 8µB,3 - 6µB,2 + 2µB,1] (14) dµC,2 ) 2k1,0[2(µA,2 + µA,1 + µA,0 + [A0])(µB,2 + µB,1 + dt µB,0 + [B0]) - 2µA,2(µB,1 + µB,2) - 2µB,2(µA,1 + µA,2) + 2µB,1(µA,1 + µA,0 + [A0]) + 2µA,1(µB,1 + µB,0 + [B0]) 2µA,1µB,1 + 2µA,2µB,2 - µC,2(µA,0 + [A0] + µB,0 + [B0]) + k2,0[P] (2µA,3 + 3µA,2 + µA,1 + 2µB,3 + 3µB,2 + µC,12] + 3 µB,1 + µC,1 - 4µC,3) (15) In the above equations, k1,0 and k2,0 are the forward and reverse reaction rate constants. The catalyst concentration is incorporated in each rate constant.15 At each time step, the concentrations of the molecular species are calculated by solving the above ordinary differential equations (ODEs). The amounts of volatile species (phenol and DPC) removed from the reactor and the reflux column are determined using the vapor-liquid phase equilibrium model.15 The activity coefficients of the volatile species in the reactor and in the reflux column are estimated by the Flory-Huggins equation:

[ (

ln γj ) ln 1 - 1 -

)

] (

)

1 1 (1 - Φj) + 1 (1 - Φj) + mj mj χj(1 - Φj)2 (16)

where γj is the activity coefficient of component j, χj is the Flory interaction parameter, mj is the ratio of molar volumes of the polymer and solvent (volatiles), and Φj is the volume fraction

Ind. Eng. Chem. Res., Vol. 48, No. 9, 2009 4277

of volatile component j. The molecular weight moments and the concentrations of polymeric species at the end of the melttransesterification process are used as the initial conditions for the subsequent SSP model simulations. The SSP of BAPC can be carried out in a continuous reactor system such as a moving packed bed reactor, but the overall SSP reactor performance is easily followed by solving the SSP model for a single polymerizing particle. Here, we consider a partially crystallized, relatively low molecular weight single polycarbonate prepolymer particle. The BAPC particles can be easily crystallized by solvent-induced crystallization techniques.16 In general, the prepolymer particles are broadly size distributed and for a large prepolymer particle, intraparticle concentration gradients may be present for the diffusing species such as phenol. Then, the chain end group concentrations and molecular weight are radially distributed because the polymerization rate is dependent on the rate of phenol removal, which is a diffusion-controlled process.21,25 In presence of intraparticle compositional and molecular weight nonuniformity, the overall molecular weight averages in a particle are calculated by the following equations:

(∫

j N ) R3 3 M

j W ) 1 (3 M R3

R

0

∫

)

r2 dr j n(r) M

2k1 ∂µB,0 ) [-2µB,0(µA,0 + [A0]) + µC,0[B0]] + ∂t 1 - xc k2[P] (µ - µC,0 - 2µB,0) (22) 1 - xc C,1 k1 ∂µC,0 ) [4(µA,0 + [A0])(µB,0 + [B0]) ∂t 1 - xc 2µC,0(µA,0 + [A0] + µB,0 + [B0]) - µC,02] + k2[P] [-µC,0 + 2(µA,1 + µB,1)] (23) 1 - xc ∂µA,1 2k1 ) [-2µA,1(µB,0 + [B0]) + µC,1(µA,0 + [A0])] + ∂t 1 - xc k2[P] [µ - µC,1 - 2(µA,2 + µA,1)] (24) 2(1 - xc) C,2

-1

(17.1)

R 2 j

0

2k1 ∂µA,0 ) [-2µA,0(µB,0 + [B0]) + µC,0[A0]] + ∂t 1 - xc k2[P] (µ - µC,0 - 2µA,0) (21) 1 - xc C,1

r Mw(r) dr)

(17.2)

where r is the radial position in the particle, R is the particle j n(r) and M j w(r) are the number-average and weightradius, M average molecular weights of the polymer particle at the radial position of r.21,25 The isothermal model equations for the SSP in a partially crystallized spherical particle take the following form:20,21 Diphenyl carbonate: -2k1[A0] ∂[A0] ) [2(µB,0 + [B0]) + µC,0] + ∂t 1 - xc k2[P] (µ + 2µA,0) (18) 1 - xc C,0 Bisphenol A: -2k1[B0] ∂[B0] ) [2(µA,0 + [A0]) + µC,0] + ∂t 1 - xc k2[P] (µ + 2µB,0) (19) 1 - xc C,0 Phenol: k1 ∂[P] ) [4(µA,0 + [A0])(µB,0 + [B0]) + ∂t 1 - xc 2µC,0(µA,0 + [A0] + µB,0 + [B0]) + µC,02] + k2[P] 1 ∂ 2 ∂[P] [µ - 2(µA,1 + µB,1 + µC,1)] + DP 2 r 1 - xc C,0 ∂r r ∂r (20)

( (

))

DP is the diffusivity of phenol. The molecular weight moment equations for three polymeric species can be derived as follows.

2k1 ∂µB,1 ) [-2µB,1(µA,0 + [A0]) + µC,1(µB,0 + [B0])] + ∂t 1 - xc k2[P] [µ - µC,1 - 2(µB,2 + µB,1)] (25) 2(1 - xc) C,2 ∂µC,1 2k1 ) [2(µA,1 + µA,0 + [A0])(µB,1 + µB,0 + ∂t 1 - xc [B0]) - µC,1(µA,0 + [A0] + µB,0 + [B0]) - 2µA,1µB,1] + k2[P] (µ + µA,1 + µB,2 + µB,1 - µC,2) (26) 1 - xc A,2 2k1 ∂µA,2 ) [-2µA,2(µB,0 + [B0]) + µC,2(µA,0 + [A0]) + ∂t 1 - xc k2[P] [2µ - 3µC,2 + µC,1 - 8µA,3 2µA,1µC,1] + 6(1 - xc) C,3 6µA,2 + 2µA,1] (27) 2k1 ∂µB,2 ) [-2µB,2(µA,0 + [A0]) + µC,2(µB,0 + [B0]) + ∂t 1 - xc k2[P] [2µ - 3µC,2 + µC,1 - 8µB,3 2µB,1µC,1] + 6(1 - xc) C,3 6µB,2 + 2µB,1] (28) 2k1 ∂µC,2 ) [2(µA,2 + µA,1 + µA,0 + [A0])(µB,2 + µB,1 + ∂t 1 - xc µB,0 + [B0]) - 2µA,2(µB,1 + µB,2) - 2µB,2(µA,1 + µA,2) + 2µB,1(µA,1 + µA,0 + [A0]) + 2µA,1(µB,1 + µB,0 + [B0]) 2µA,1µB,1 + 2µA,2µB,2 - µC,2(µA,0 + [A0] + µB,0 + [B0]) + k2[P] (2µ + 3µA,2 + µA,1 + 2µB,3 + 3µB,2 + µC,12] + 3(1 - xc) A,3 µB,1 + µC,1 - 4µC,3) (29) In the above equations, k1 and k2 are the forward and backward rate constants. The effect of varying crystallinity on the effective rate constant is expressed as k1 )

k1,0 1 - xc

(30)

4278 Ind. Eng. Chem. Res., Vol. 48, No. 9, 2009 Table 1. Reaction Conditions and Model Parameters Used in the Model Simulation parameter

value

unit

melt polymerization process reactor volume reaction temperature reaction pressure reflux column temperature catalyst (LiOH · H2O) concentration initial charge of BPA reaction time forward reaction rate constant, k1,0 backward reaction rate constant, k2,0 vapor pressure of DPC

4 230 5 80 8 × 10-5

L °C mm Hg °C mol/L

6.75 2 4.248

mol h L/(mol · h)

2.166

L/(mol · h)

sat ln PDPC ) -[1.48 × 104/RT] + 19.55

mm Hg

solid-state polymerization process reaction temperature particle size, dp forward reaction rate constant, k1,0 backward reaction rate constant, k2,0 diffusivity of phenol, DP initial crystallinity, xc,in rate of crystallization, kc maximum crystallinity, xmax

200 1.0 × 10-4 2.736

°C m L/(mol · h)

1.953

L/(mol · h)

1.08 × 10-9 0.25 3.76 × 10-2 0.62

m2/h 1/h

where k1,0 is the rate constant for melt polymerization. Here, xc is the degree of polymer crystallinity. The term 1 - xc represents the fraction of the amorphous region where the polymerization occurs. The crystallinity increases during the SSP process, affecting the reaction rate. We employed the following equation for the rate of change in the polymer crystallinity:26 dxc ) kc(xmax - xc) dt

(31)

where xmax is the maximum obtainable crystallinity. The lamellar thickness may also affect the molecular weight in SSP,27 but its effect is assumed negligible in the present modeling study. The following boundary conditions are used for phenol and other species (polymeric species, DPC, BPA), respectively: [P] ) 0 at r ) R; ∂[X] ) 0 at r ) R; ∂r

∂[P] ) 0 at r ) 0 ∂r

(32.1)

∂[X] ) 0 at r ) 0 ∂r

(32.2)

where X denotes species other than phenol. The boundary condition for phenol at the surface of particles shown in eq 32.1 represents the situation where external mass transfer resistance for phenol is negligible at the surface of particles because of high purge gas flow rate. The second boundary conditions shown in eq 32.2 indicate that all other species are not removed from the particle. In this model, we ignored the effect of diffusive movement of polymers within the particle. 3. Results and Discussion The model equations in the above have been solved using a MATLAB ODE solver (“ode45”) for the melt transesterification and a MATLAB PDE solver (“pdepe”) for the SSP process. Table 1 lists the reaction conditions and model parameters used for the numerical simulations of the melt transesterification and the SSP processes.

In our model simulations, we have chosen a bottle-grade bisphenol A polycarbonate of weight average molecular weight about 80 000 as an example.28 Later in this paper, we shall discuss the effect of molecular weight on the design of polymerization conditions. The initial DPC/BPA molar charge ratio (rm) is one of the major process operational parameters because this ratio affects the actual concentrations of reactive end groups, polymer molecular weight, the conversion of BPA, and the residual BPA concentration in the final polymer. In our previous paper,15 we have shown that a slight excess of DPC needs to be used in the first-stage melt transesterification process to obtain a desired target molecular weight in the shortest reaction time. The evaporative loss of DPC during the reaction is compensated by the excess amount of DPC and thereby the molar ratio of the reactive end group can be kept to its stoichiometric value as closely as possible. For the semibatch melt transesterification process considered in our simulations, the initial monomer charge ratio of 1.0631 has been found by direct search to make the end group mole ratio ([EA]/[EB], phenyl carbonate group/hydroxyl end group) close to unity at the end of the semibatch melt-transesterification process. We shall call this value the “optimal stoichiometric” value. We would like to note that the optimal stoichiometric value may change from one process to another where different reactor/reflux column systems are employed. Therefore, the value 1.0631 is applicable to the system considered in this work, but not universally applicable to all other polycarbonate synthesis processes. We have chosen two other initial DPC/BPA molar charge ratios (rm) for comparison: 1.0566 and 1.0694. These values are either smaller than or larger than the optimal stoichiometric ratio by less than 1%. But as will be shown later, this small difference in the initial monomer charge ratio can make a huge difference in the final polymer properties as well as in the process performance. The parametric sensitivity of the charge ratio on the performance of the polycarbonate process is one of the most important characteristics of the BAPC process. Figure 1a shows the profiles of end group molar ratio for these three different initial monomer charge ratios during the semibatch melt polymerization. When rm ) 1.0631, the end group mole ratio is maintained very closely at 1.0 (stoichiometric value) during the polymerization. In other words, just right amount of excess DPC has been used to compensate for the evaporative loss of DPC from a reflux condenser. However, when the slightly smaller initial charge ratio of rm ) 1.0566 is used, the end group ratio decreases and deviates significantly from the stoichiometric value. Similarly, for rm ) 1.0694, the deviation of the end group mole ratio from the stoichiometric value is also quite significant, although the reaction mixture becomes rich in the phenyl carbonate end group as reaction time increases. Figure 1b shows the corresponding molecular weight profiles. Notice that the difference in the end group mole ratio has little effect on the prepolymer molecular weight during the first 2 h of reaction. The three transesterification products obtained at t ) 2 h in this simulation cases will be used as precursors for the subsequent SSP. In our model simulations, we assume that the prepolymers are crystallized before the SSP. Figure 2a shows the molecular weight profiles for the three different prepolymers during the SSP in a single polymer particle. The simulation results clearly illustrate that indeed, the deviation from the stoichiometric mole ratio of the reactive end groups results in a large difference in the obtainable molecular weight. For rm ) 1.0631 (optimal stoichiometric value), the polymer molecular weight increases almost linearly with time, but for rm ) 1.0566 and 1.0694, the final molecular weights

Ind. Eng. Chem. Res., Vol. 48, No. 9, 2009 4279

Figure 1. Simulation results in a semibatch melt polymerization process: (a) End group ratio ([EA]/[EB] ) phenyl carbonate group/hydroxyl end group); (b) Weight-average molecular weight.

level off at about 82 000 after 20 h of polymerization. It is also interesting to notice that for both rm ) 1.0566 and 1.0694, the polymers of almost identical final molecular weight are obtained. To reach the target molecular weight of 80 000, the latter two cases need about 13 h more than the stoichiometrically balanced case (i.e., rm ) 1.0631). However, the end group ratio profiles for these three cases are dramatically different, as illustrated in Figure 2b. When the monomer charge ratio of 1.0631 is used, the end group mole ratio is nearly constant during the polymerization. The end group mole ratio profiles for rm ) 1.0566 and rm ) 1.0694 are quite different: For rm ) 1.0566, the end group mole ratio decreases during the SSP whereas for rm ) 1.0694, the end group mole ratio increases because more hydroxyl end group is consumed by the excess amount of phenyl carbonate groups. Due to the severe molar imbalance of the reactive end groups, the reaction rate is greatly reduced. Figure 3a shows the BPA concentrations in the reaction mixture during the melt prepolymerization stage, and Figure 3b shows the BPA content in a particle during the SSP. The unreacted BPA concentrations at the end of 2 h melt transesterification for the three different initial monomer charge ratios are in the range of 100-300 ppm (inset); however, Figure 3b shows the strong effect of initial monomer charge ratio on the final BPA concentrations in the polymer particle during the SSP. The prepolymers with rm ) 1.0566 and rm ) 1.0694 yield the same molecular weight, but the final BPA concentrations in the polymer are significantly different: After 20 h of the SSP, the BPA content in the polymer is 31.5 ppm for rm ) 1.0566, while the BPA content is 0.017 ppm for rm ) 1.0694. When rm ) 1.0631 is used, the target molecular weight (Mw ) 80 000)

Figure 2. Simulation results in a solid-state polymerization process: (a) Weight-average molecular weight; (b) End group ratio ([EA]/[EB] ) phenyl carbonate group/hydroxyl end group).

is reached at t ) 7.2 h, but the corresponding residual BPA concentration is about 10 ppm. Figure 4a shows the effect of initial monomer charge ratio on the residual BPA content and the SSP time to reach Mw ) 80 000 (model simulations) for five different rm values. Note that the melt polymerization time is same for all the cases (i.e., 2 h). The results in Figure 4a indicate that the shortest reaction time to reach the target molecular weight is obtained for rm ) 1.0631 (7.2 h) and the corresponding residual BPA content in the polymer is 9.8 ppm. The residual BPA content can be further decreased to 0.9 ppm if the initial monomer charge ratio of 1.0680 is used but then, the reaction time increases to 10.1 h. The BPA content can be reduced even further to 0.06 ppm for rm ) 1.0694, but again, the reaction time to reach the target molecular weight (Mw ) 80 000) increases to 16.1 h. These residual BPA contents shown in Figure 4a for rm ) 1.06001.0694 are far less than those reported in the literature for most of the bottle-grade polycarbonates with 10 ppm BPA as a median value.19 Although the reaction times for both rm ) 1.0680 and rm ) 1.0694 are longer than the case of the balanced end group ratio (rm ) 1.0631) to reach a desired target molecular weight of 80 000 in this example, the BPA content in the final product is very low to justify the longer reaction time. We have also found that for rm smaller than 1.050 or rm larger than 1.070, the target molecular weight of 80 000 is not obtainable in less than 20 h of the SSP. In other words, there is a small window of rm to obtain low BPA content, high molecular weight, and reasonable reaction time. The weight-average molecular weight of the bottle-grade polycarbonate is in a certain range depending on the applica-

4280 Ind. Eng. Chem. Res., Vol. 48, No. 9, 2009

Figure 3. Model-calculated BPA concentration (a) in a semibatch melt polymerization process and (b) in a solid-state polymerization process.

tions. In the above simulation results, the weight average molecular weight is taken as 80 000. To compare BPA content and reaction time for the different molecular weights of polycarbonate, we also carried out the model simulations for the molecular weight of 60 000, and the results are given in Figure 4b. It clearly shows that for a given initial monomer charge ratio, the higher the molecular weight is, the lower the BPA content will be. It is because longer reaction time is needed to reach higher molecular weight and more BPA is consumed during the extended reaction time. The simulation results shown in Figure 4 suggest that the initial monomer charge ratio can be optimized to balance the requirements of low BPA content, desired polymer molecular weight, and economically profitable reaction time. The use of initial monomer charge ratio that is slightly larger than the ratio that gives rise to the stoichiometric end group ratio during the polymerization (e.g., rm ) 1.064) might be the most desirable. Since the operating window of monomer ratio is narrow, we shall check the feasibility of implementing the initial monomer charge ratio (rm) designed by the method presented in this work in a commercial scale production. For the reactor volume of 50 m3 with the initial load volume of 80%, the amounts of DPC and BPA for the initial charge mole ratio of rm ) 1.0631 are 24 615 and 24 674 kg, respectively. Figure 5 shows the initial charges of DPC and BPA for different monomer ratios. It is seen that although the difference in the initial monomer charge ratios looks very small, the differences in the actual amounts of DPC and BPA might be large enough for practical implementation into an existing polymerization process system. It also indicates that the accuracy of initial charge ratio in practical implementation is important to obtain BAPC polymers with low BPA content in the two-stage process considered in this work.

Figure 4. Model-calculated BPA contents in bottle-grade polycarbonates for different rm values. (a) Mw ) 80 000; (b) Mw ) 60 000.

Figure 5. Initial charge of BPA and DPC monomers for different monomer ratios. The “*” mark represents the optimal stoichimetric ratio (rm ) 1.0631) (model simulations).

In the above, we considered adding a slight excessive amount of DPC in the beginning of the melt prepolymerization so that monomer BPA can be consumed to a maximum extent at the end of SSP. However, this method can also be extended to blending two prepolymers of different end group concentrations and using the blend in the subsequent solid-state polymerization. To illustrate, let us consider blending prepolymer A and prepolymer B of different end group mole ratios. First, we need to calculate the molecular weight moments for each prepolymer using the method reported in our previous paper.20 According to this method, an objective function is first defined:

Obj )

(

j w,cal - M j w,exp M j w,exp M

) ( 2

+

Ind. Eng. Chem. Res., Vol. 48, No. 9, 2009 4281

r′a,cal - r′a,exp r′a,exp

)

2

(33)

j w,exp) and ra,cal j w,cal (M ′ (ra,exp ′ ) are the calculated where M (experimentally measured) weight-average molecular weight and initial end group mole ratio in a prepolymer. The prepolymerization conditions such as reaction time and initially charged end group ratio can be back-calculated by minimizing the objective function using a semibatch prepolymerization model. For example, let us assume that prepolymer A (Mw ) 15 470) and prepolymer B (Mw ) 10 200) have end group ratio ([EA]/ [EB] ) phenyl carbonate group/hydroxyl end group) of 2.888 and 0.097, respectively. Using a semibatch prepolymerization model and a numerical optimization routine (“fminsearch”) from MATLAB optimization toolbox, we can minimize the objective function (eq 33) and calculate the exact initial charged ratios of monomer for prepolymer A and reaction time as 1.08 and 120 min, respectively. The optimized values are 1.02 and 120 min for prepolymer B. Then, the molecular weight moments of the prepolymers can be calculated by solving the prepolymerization model using the optimized initial end group ratio and the reaction time. The overall kth molecular weight moments of the blend are given as µi,k ) w1µi,k + w2µi,k (i ) A,B,C; k ) 0, 1, 2)

(34)

where w1 and w2 denote the weight fractions of prepolymer A and prepolymer B, respectively, and i represents the three different molecular species (A, B, C). With the calculated values of the overall molecular weight moments, the SSP model is solved to calculate the final molecular weight and the BPA content. Figure 6 shows the effect of weight fraction of prepolymer A on the BPA content and the reaction time required to reach a target molecular weight. It is seen that BPA content decreases as the amount of prepolymer A is increased. In other words, more BPA is consumed as more prepolymer A having excessive phenyl carbonate end groups is added. For the optimal weight fraction of 0.72 which gives rise to the stoichiometric ratio of the end groups, the shortest reaction time is needed to reach the target molecular weight, but the BPA content has a moderate value of 10.8 ppm. To consume more BPA, adding an excess amount of prepolymer A is very helpful, but longer reaction time is required (e.g., 8.3 h for the weight fraction of 0.77). If the weight fraction of prepolymer A is increased to 0.82, the BPA content can be further reduced to 0.15 ppm, but much longer reaction time is required (14.1 h). Although the foregoing design requires a very accurate process model and some computational efforts, this example illustrates that minimizing the BPA residue in the final polymer product will be feasible using the proposed method for a prepolymer mixture. 4. Concluding Remarks In this paper, we have presented a method to minimize the content of residual BPA in a two-stage polymerization process that consists of melt transesterification and SSP stages. With the aid of theoretical modeling, we have demonstrated that the excess amount of DPC at the beginning of melt prepolymerization can be exactly calculated to satisfy the requirements of high molecular weight, low residual BPA content in the final product, and practically acceptable total reaction time. The reduction of BPA concentration in the final polymer product may require a longer reaction time, but the extended polymerization time, unless it is exceptionally long, should be acceptable

Figure 6. Model-calculated BPA content and reaction time for different weight fractions of prepolymer A in the prepolymer blends.

for the bottle-grade high molecular weight polycarbonates if the BPA content can be reduced to a practically negligible level. It is also illustrated through our model simulations that the adjustment of end group ratio of a prepolymer for the SSP can be made to reduce BPA content by blending two prepolymers of different end group ratios. Although the models developed for the melt polymerization and the subsequent SSP process were based on bench scale experimentation,15,20-22 the concept and method developed in this paper can be applicable to larger scale processes with some adjustment of the models and parameters to fit the plant data. It should be noted that the proposed method is based on the availability of accurate polymerization process models and that the operational window that allows for the significant reduction of residual BPA concentration in the final product can be quite narrow. The ideas introduced in this paper and the numerical simulation examples illustrate that any efforts for developing comprehensive and accurate models can be very worthwhile to retrofit the process conditions to achieve the lowest possible BPA content while meeting other process requirements. Notation A0 ) diphenyl carbonate (DPC) An ) polymeric species A B0 ) bisphenol A (BPA) Bn ) polymeric species B Cn ) polymeric species C dp ) particle diameter, m DP ) diffusivity of phenol, m2/h [EA] ) concentration of phenyl carbonate group in prepolymer, mol/L [EB] ) concentration of hydroxyl end group in prepolymer, mol/L k1 ) effective forward reaction rate constant, L/(mol · h) k2 ) effective reverse reaction rate constant, L/(mol · h) k1,0 ) forward reaction rate constant, L/(mol · h) k2,0 ) reverse reaction rate constant, L/(mol · h) kc ) crystallization rate constant, 1/min m ) polymer chain length mj ) the ratio of molar volumes of the polymer and solvent (volatiles) j n ) number average molecular weight, g/mol M j N ) number-average molecular weight of a polymer particle, M g/mol j w ) weight-average molecular weight, g/mol M j W ) weight-average molecular weight of a polymer particle, g/mol M n ) polymer chain length

4282 Ind. Eng. Chem. Res., Vol. 48, No. 9, 2009 P ) phenol r ) distance from particle center, m rm ) initially changed monomer ratio ([DPC]/[BPA]) in prepolymerization reactor R ) particle radius, m t ) reaction time, h xc ) degree of polymer crystallinity X ) species other than phenol, in eqs 32.1 and 32.2 wm ) molecular weight of a repeating unit, g/mol µi,j (i ) A,B,C; j ) 0,1,2) ) jth molecular weight moment of polymeric species i χj ) the Flory interaction parameter γj ) the activity coefficient of component j Φj ) the volume fraction of volatile component j

Literature Cited (1) Layton, L. U.S. Cites Fears on Chemical in Plastics. The Washington Post 2008, April 16. (2) Krishnan, A. V.; Stathis, P.; Permuth, S. F.; Tokes, L.; Feldman, D. Bisphenol-A: An Estrogenic Substance Is Released from Polycarbonate Flasks during Autoclaving. Endocrinology 1993, 132, 2279–2286. (3) Grossman, E. Chemicals May Play Role in Rise in Obesity. The Washington Post 2007, March 12. (4) Markey, C. M.; Wadia, P. R.; Rubin, B. S.; Sonnenschein, C.; Soto, A. M. Long-Term Effects of Fetal Exposure to Low Doses of the Xenoestrogen Bisphenol-A in the Female Mouse Genital Tract. Biol. Reprod. 2005, 72, 1344–1351. (5) Timms, B. G.; Howdeshell, K. L.; Barton, L.; Bradley, S.; Richter, C. A.; vom Saal, F. S. Estrogenic Chemicals in Plastic and Oral Contraceptives Disrupt Development of the Fetal Mouse Prostate and Urethra. Proc. Natl. Acad. Sci. U.S.A 2005, 102, 7014–7019. (6) Soto, A. M.; Vandenberg, L. N.; Maffini, M. V.; Sonnenschein, C. Does Breast Cancer Start in the Womb. Basic Clin. Pharmacol. Toxicol. 2008, 102, 125–133. (7) Murray, T. J.; Maffini, M. V.; Ucci, A. A.; Sonnenschein, C.; Soto, A. M. Induction of Mammary Gland Ductal Hyperplasias and Carcinoma in Situ Following Fetal Bisphenol A Exposure. Reprod. Toxicol. 2007, 23, 383–390. (8) vom Saal, F. S.; Hughes, C. An Extensive New Literature Concerning Low-Dose Effects of Bisphenol A Shows the Need for A New Risk Assessment. EnViron. Health Perspect. 2005, 113, 926–933. (9) Austen, I. Bottle Maker to Stop Using Plastic Linked to Health Concerns. New York Times 2008, April 18. (10) Wintgens, T.; Gallenkemper, M; Melin, T. Occurrence and Removal of Endocrine Disrupters in Landfill Leachate Treatment Plants. Water Sci. Technol. 2003, 48, 127–134. (11) Howe, S. R.; Borodinsky, L. Potential Exposure to Bisphenol A from Food-Contact Use of Polycarbonate Resin. Food Addit. Contam. 1998, 15, 370–375.

(12) NTP (U.S. National Toxicology Program). Report of the Endocrine Disruptors Low-Dose Peer ReView; NTP: Research Triangle Park, NC, August 2001. (13) SCF (Scientific Committee on Food). Opinion of the Scientific Committee on Food on Bisphenol A; April 17, 2002. (14) Tsai, W. T. Human Health Risk on Environmental Exposure to Bisphenol-A: A Review. J. EnViron. Sci. Health Part C 2006, 24, 225– 255. (15) Woo, B. G.; Choi, K. Y.; Song, K. H.; Lee, S. H. Melt Polymerization of Bisphenol A and Diphenyl Carbonate in a Semibatch Reactor. J. Appl. Polym. Sci. 2001, 80, 1253–1266. (16) Fukawa, I.; Fukuoka, S.; Komiya, K.; Sasaki, Y. Porous, Crystallized, Aromatic Polycarbonate Prepolymer, a Porous, Crystallized Aromatic Polycarbonate, and Production Methods. U.S. Patent 5,204,377, April 20, 1993. (17) Biles, J. E.; McNeal, T. P.; Begley, T. H.; Hollifield, H. C. Determination of Bisphenol-A in Reusable Polycarbonate Food-Contact Plastics and Migration to Food-Simulating Liquids. J. Agric. Food Chem. 1997, 45, 3541–3544. (18) Amaral Mendes, J. J. The Endocrine Disrupters: a Major Medical Challenge. Food Chem. Toxicol. 2002, 40, 781–788. (19) Leo, L. W.; Wong, K. O.; Seah, H. L. Occurrence of Residual Bisphenol A and Its Migration Levels in Polycarbonate Baby Milk Bottles. Singapore J. Pri. Ind. 2005, 32, 106–108. (20) Ye, Y.; Choi, K. Y. Optimizing Polymer Reactivities for the SolidState Polycondensation of AA-BB Type Monomers. Polymer 2008, 49, 2817–2824. (21) Ye, Y.; Machado, B.; Choi, K. Y.; Kim, J. H.; Woo, B. G. Modeling of Solid-State Polymerization of Bisphenol A Polycarbonate. Ind. Eng. Chem. Res. 2005, 44, 2494–2505. (22) Kim, Y. S.; Choi, K. Y. Multistage Melt Polycondensation of Bisphenol-A and Diphenyl Carbonate to Polycarbonate. J. Appl. Polym. Sci. 1993, 49, 747–764. (23) Ravindranath, K.; Mashelkar, R. A. Modeling of Poly(ethylene terephthalate) Reactors: I. A Semibatch Ester Interchange Reactor. J. Appl. Polym. Sci. 1981, 26, 3179–3204. (24) Samant, K. D.; Ng, K. M. Synthesis of Prepolymerization Stage in Polycondensation Processes. AIChE J. 1999, 45, 1808–1829. (25) Goodner, M. D.; Gross, S. M.; DeSimone, J. M.; Roberts, G. W.; Kiserow, D. J. Broadening of Molecular-Weight Distribution in Solid-State Polymerization Resulting from Condensate Diffusion. J. Appl. Polym. Sci. 2001, 79, 928–943. (26) Mallon, F. K.; Ray, W. H. Modeling of Solid-State Polycondensation. I. Particle Models. J. Appl. Polym. Sci. 1998, 69, 1233–1250. (27) Kim, J.; Roberts, G. W.; Kiserow, D. J. Effect of Prepolymer Molecular Weight on Solid State Polymerization of Poly(bisphenol A carbonate) with Nitrogen as a Sweep Fluid. J. Polym. Sci., Part A: Polym. Chem. 2008, 46, 4959–4969. (28) Brunelle, D. J.; Kailasam, G. Polycarbonates; Technical Information Series; GE R&D Center, Schenectady, NY, 2002.

ReceiVed for reView September 23, 2008 ReVised manuscript receiVed February 3, 2009 Accepted March 9, 2009 IE8014318