Mathematical Modeling and Analysis of an Interfacial Polycarbonate Polymerization in a Continuous Multizone Tubular Reactor.
Aromatic polycarbonates derived from bisphenol A (BPA) are an important class of engineering polymers with a wide variety of applications such as in water bottles, food containers, optics, mobile phones, electronic components, data storage, automotive, and medical devices. There are two major BPAbased industrial polycarbonate processes: two-phase interfacial process (or simply phosgene process) and melt transesterification process , In the interfacial process, a two-phase mixture of BPA, phosgene (carbonyl dichloride), and a small amount of chain stopper dissolved in methylene chloride is polymerized with a tertiary amine catalyst and sodium hydroxide solution added to maintain the appropriate pH (10-12) at low temperature (40[degrees]C). The interfacial process is industrially very important due to its high productivity and controllability of the polymer molecular weight and molecular weight distribution. Moreover, the interfacial process can be readily retrofitted for the production of terpolymers or multicomponent polycarbonates by introducing comonomers or reactive additives such that branched polycarbonates can be easily synthesized. For example, the copolymer of BPA-polycarbonate and polydimethylsiloxane (PDMS) exhibit excellent thermal stability and good weathering properties. Siloxane-polycarbonate copolymers can be produced by introducing functionalized siloxane blocks in the interfacial polymerization of BPA and phosgene .
The interfacial polycarbonate synthesis can be carried out using either a continuous stirred tank reactor or a tubular reactor. Since the reaction involves multiple phases, efficient mixing is important. The overall reaction steps in interfacial polycarbonate synthesis are quite complex . Scheme 1 shows a simplified overall reaction scheme for the interfacial polycarbonate synthesis reaction with BPA and phosgene as two reactants.
Although Scheme 1 shows the simplified overall reaction chemistry, the actual interfacial polycarbonate synthesis reaction proceeds in several reaction steps. The first step is a monomer make-up process where BPA and sodium hydroxide dissolved in water react to di-sodium bisphenate (DSB). In the second step, DSB is reacted with phosgene (carbonyl dichloride, CDC) dissolved in methylene chloride to bis-chloroformate (BCF) which further reacts with DSB to polycarbonate oligomers in presence of a small amount of a tertiary amine catalyst. The oligomers may contain either chloroformate end group or sodium bisphenate group. Excess phosgene is used to ensure complete conversion of phenolic groups in BPA. A monohydroxylic phenol is usually added to the organic phase as a chain stopper to control the polymer molecular weight. The actual reaction occurs at the interface of an organic phase (solvent) where phosgene and polymer are dissolved and an aqueous phase where BPA is dissolved in presence of NaOH. In the aqueous sodium hydroxide phase, BPA dissolves to produce a mono- or di-sodium bisphenate, which react with phosgene at the interface.
Since the initial reaction bccurs at the interface of aqueous phase and solvent phase, the interfacial area or volume, acid-base equilibria of BPA with NaOH, stirring rate (when an agitated reactor is used) are the important factors that affect the performance of interfacial polymerization. At the interface, BPA dissolved in the aqueous phase (dispersed liquid droplets) and phosgene dissolved in the organic phase (e.g., methylene chloride) react. The reaction product, oligomers, may form a thin film, causing mass transfer resistance for the reactants [4, 5]. Aqueous sodium hydroxide is added to the organic phase with phosgene to scavenge the reaction byproduct (HC1). To quantitatively analyze the interfacial polycarbonate process, the mass transfer and reaction phenomena at the liquid-liquid interface and the main polymer chain growth reactions in the organic phase need to be understood and modeled.
Despite of its industrial importance and its relatively long history of industrial production, there is a dearth of open literature on the modeling and analysis of interfacial polycarbonate processes. It is perhaps due to the lack of experimental data reported in the literature because one of the reactants, phosgene, is a chemical that is extremely difficult to be handled safely due to its toxicity in any academic research laboratories and the only source of possible experimental data would be either pilot plants or commercial plants for polycarbonate manufacturing. If a quantitative reaction or reactor process model is available, such model can be employed to design advanced interfacial polycarbonate processes such as polycarbonate-siloxane copolymers.
To date, the most comprehensive mathematical modeling study on the interfacial polycarbonate process in a semibatch stirred tank reactor process has been reported by Mills [6, 7], He considered a well-mixed, liquid-liquid dispersion where the dispersed aqueous phase was assumed to contain BPA and NaOH and the continuous organic phase (methylene chloride) was assumed to contain dissolved phosgene. In the process modeled, phosgene gas was added to the liquid phase as gas bubbles, and hence the entire reaction system was a three-phase system (gas-liquid [aqueous phase]-liquid [organic phase]). Mass transfer resistances for low molecular weight compounds (e.g., phosgene, BPA, mono-functional chain stopper) between the various phases were described using the two-film theory. Mills assumed equal reactivity of end groups in the kinetic model for simplicity and all the reactions were assumed to follow the elementary reaction kinetics. With these assumptions, an infinite set of differential equations was derived but they were simplified with an additional assumption that the liquid-liquid mass transfer rate was much more rapid than the rate of reactions. The z-transform technique was used to reduce the number of differential equations and the solutions to the reduced equations yielded the concentration of each species as the first three moments of the polymer chain length distribution. The method of moments was used to calculate the instantaneous molecular weight averages. In another study on the interfacial polycondensation reactions by Gu and Wang , the ratio of the phosgenation kinetic constant to the hydrolysis kinetic rate constant was estimated to be about 8.0 and they reported that 58 mol% excess amount of phosgene is needed to obtain complete phosgenation of BPA.
Another important type of commercial interfacial polycarbonate reactor system is a tubular reactor that offers high throughput production of bisphenol A polycarbonates. The reaction kinetics are same as in the stirred tank reactor but in the tubular reactor system, static mixers are commonly inserted in the tube to provide intensive mixing of the multiphase mixture. Unfortunately, however, no report is available on the modeling and analysis of tubular interfacial polycarbonate reactor process. In this article, we present a mathematical model to describe the two phase interfacial polymerization of BPA and phosgene in a continuous tubular reactor and the simulation results are discussed.
For the reactor modeling, we consider the reaction process that involves the reaction between BPA dissolved in a dispersed caustic aqueous phase, and phosgene dissolved in a continuous organic phase (e.g., methylene chloride). The aqueous phase is forced to flow through a tubular reactor section filled with static mixers where small aqueous droplets are generated and dispersed in the organic phase. Therefore, the initial reaction locus is the interface between the dispersed aqueous phase and the continuous organic phase. The first stage (phosgenation) is the reaction between di-sodium bisphenate (in the aqueous phase) and phosgene (in the organic phase) at the interface between the dispersed aqueous phase and the continuous organic phase:
[formula not reproducible] (R1)
It is assumed that the dispersed phase consists of uniform sized aqueous liquid droplets. In the tubular reactor system, the upstream portion of the reactor is packed with high shear static mixers to generate small aqueous droplets containing BPA. Although the actual reaction mixture contains the droplets of non-uniform size distribution, we assume that the droplets are of uniform size for modeling purposes. A di-sodium bisphenate can react with a phosgene molecule to yield bisphenol-A monochloroformate. If di-sodium bisphenate reacts with two phosgene molecules, bisphenol-A bischloroformate is produced:
[formula not reproducible] (R2)
Mono/bischloroformates formed at the interface dissolve in the organic phase and it is assumed that they migrate to the organic phase and continue to react to higher molecular weight polymers. The subsequent chain growth reactions occur in the organic phase. In this stage, two major reactions occur: the reaction between two monochloroformates (R3) and the reaction between a monochloroformate and a bischloroformate (R4):
[formula not reproducible] (R3)
[formula not reproducible] (R4)
These reactions produce polycarbonate oligomers that differ in the types of functional end groups. The oligomers further react with chloroformates or other oligomers, depending on the available functional groups, to produce long chain polycarbonates.
The final step in the reaction process is the reaction of polymer end groups with an end capping agent (chain stopper) to control the molecular weight of the polymer and to stabilize the remaining reactive end groups. The following reaction scheme shows the chain stopping reaction with p-tert-butyl phenol as an end capping agent.
[formula not reproducible] (R5)
The schematic of the overall reactions that occur at the liquid-liquid interface and in the bulk organic phase in a continuous tubular reactor process is presented in Fig. 1. Notice that the reaction process is modeled as a two-phase process where aqueous droplets containing BPA and NaOH are dispersed in a continuous organic solvent phase where phosgene as well as oligomers and polymers are dissolved.
One of the factors to consider in developing a two-phase model of the polycarbonate process is to identify what reactive species are present in the aqueous phase and in the organic phase, respectively. BPA is not soluble in the organic phase but phosgene has a slight solubility in the aqueous phase. The solubility of phosgene in water at 25[degrees]C has been estimated as 0.069 mol/L and it is assumed that as phosgene diffuses from the bulk solvent phase to the liquid-liquid interface, it reacts rapidly with BPA. Polycarbonate oligomers can be generated in the aqueous phase as a result of reaction between BPA and phosgene dissolved in the caustic aqueous phase. The oligomers with chain length x are assumed to remain soluble in the aqueous phase until the critical chain length is reached. Upon reaching the critical chain length at which oligomers are no longer soluble in the aqueous phase, the oligomers precipitate out into the organic phase and there they react further with other oligomers and phosgene to higher molecular weight polymers.
According to Brunelle et al. , BPA-bis-chloroformate and oligomeric bis-chloroformates are not soluble in the aqueous phase. For the reaction modeling, we postulate that di-sodium bisphenate ([A.sub.0]) in the aqueous phase and phosgene ([B.sub.0]) in the organic phase diffuse from their respective bulk phases to the liquid-liquid interface to react. As these two species react at the interface, the reaction product (A) dissolves in the bulk organic phase and it continues to react with phosgene to generate bischloroformate BPA (B). The species A and B are the basic monomer units that react in the organic phase to oligomers and eventually, to high molecular weight polymers. [Z.sub.1] is the end group of sodium bisphenate and [Z.sub.2] is the end group of monochromate bisphenate. The chain stopper ([P.sub.0]) is present in the organic phase, p-tert-butyl phenol (PTBP) is a commonly used chain stopper that can react with A and B, and the end groups of the growing polymer chains.
Based on the assumptions in the above, the following reaction scheme is postulated. Phosgenation (reaction at the liquidliquid interface)
[mathematical expression not reproducible] (1)
End unit conversion to monomer B (organic phase)
[mathematical expression not reproducible] (2)
Reactions between monomer units (organic phase)
[mathematical expression not reproducible] (3)
[mathematical expression not reproducible] (4)
Reactions between monomer units and polymer species (organic phase)
[mathematical expression not reproducible] (5)
[mathematical expression not reproducible] (6)
[mathematical expression not reproducible] (7)
Chain stopper end unit conversion (organic phase)
[mathematical expression not reproducible] (8)
Reactions between monomer units and chain stopper (organic phase)
[mathematical expression not reproducible] (9)
[mathematical expression not reproducible] (10)
[mathematical expression not reproducible] (11)
Reactions between polymer species and chain stopper (organic phase)
[mathematical expression not reproducible] (12)
[mathematical expression not reproducible] (13)
Reactions between polymer species (organic phase)
[mathematical expression not reproducible] (14)
In the reaction scheme above, [A.sup.*.sub.0] and [B.sup.*.sub.0] represent the [A.sub.0] (BPA) and B0 (phosgene) at the liquid-liquid interface, respectively. The species X represents the carbonate linkages between monomer units in the polymer species. The reactions at the interface and the end unit conversion of monomer units do not generate any carbonate linkages. For the reactions between monomer units, each reaction generates one carbonate linkage. Further, each reaction generates a growing polymer chain with two functional end groups on each end. Reactions between A and A produces [Z.sub.1] end group and one [Z.sub.2] end group. Reactions between A and B produce one [Z.sub.2] end group on both chain ends. For the reactions between monomer units and growing polymer species, one functional end group of a growing polymer chain reacts with a monomer unit, each reaction generating one carbonate linkage. The functional end group is consumed as it reacts with a monomer species but a new functional end group is generated depending upon which monomer unit has reacted. The reaction of chain ends with the chain stopper does not produce carbonate linkages. In the reactions between polymer species, the reactive end group of each growing polymer chain reacts with each other to yield one carbonate linkage. The number of carbonate linkages generated during the polymerization process is tracked so that the number average molecular weight can be calculated.
Using the kinetic scheme presented in the above, we shall develop a reactor model for the interfacial polymerization that is carried out in a continuous tubular reactor. We assume that the fluid flow (mixture of dispersed aqueous phase and continuous solvent phase) is of the plug flow and that both phases move at the same speed. This assumption is justifiable because the flow rate is high and the tubular reactor is charged with high shear static mixer elements to break up the aqueous phase into finely divided droplets. To develop a mathematical model, we also assume that the pseudo-steady state approximation is applicable for the mass transfer and reaction at the aqueous droplet-solvent interface. That is, we assume that the amount transferred to the interface from the aqueous phase and the organic phase is equal to the amount that is consumed at the interface for BPA/phosgene and phosgene/di-sodium bisphenate reactions.
The mass transfer rate of di-sodium bisphenate ([A.sub.0]) from the aqueous phase to the liquid-liquid interface and that of phosgene ([B.sub.0]) from the bulk organic phase to the interface can be expressed by the following equations:
[r.sub.Ao,m] = -[k.sub.LA]a([[A.sub.o]] - [[A.sup.*.sub.0]]) (15)
[r.sub.Ho,m] = -*[k.sub.BL]a([[B.sub.0]] - [[B.sup.*.sub.0]]) (16)
where [k.sub.LA] and [k.sub.LB] are the mass transfer coefficients of disodium bisphenate and phosgene, respectively, and a is the specific interfacial area. [[A.sup.*.sub.0]] and [[B.sup.*.sub.0]] are the interfacial concentrations of Ao and Bo, respectively and [Bo] is the bulk concentration of phosgene. Then, the interfacial reaction rate (or consumption rate) between di-sodium Bisphenate and phosgene can be expressed by the following equation:
[r.sub.p] = 4[k.sub.1][[A.sup.*.sub.0]][[B.sup.*.sub.0]] (17)
where [k.sub.1] is the reaction rate constant for the two end groups of [A.sup.*.sub.0] and [B.sup.*.sub.0] at the interface.
As we apply the quasi-steady state approximation to the phosgene mass transfer and reaction processes, the mass transfer rate is equal to the consumption rate:
[k.sub.LB]a([[B.sub.0]]-[[B.sup.*.sub.0]]) = 4[k.sub.1][[B.sup.*.sub.0]][[A.sup.*.sub.0]] (18)
Solving for [[B.sup.*.sub.0]], we obtain the following equation for the concentration of phosgene at the interface.
[[B.sup.*.sub.0] = [k.sub.LB]a[[B.sub.0]]/[k.sub.LB]a + 4[k.sub.1][[A.sup.*.sub.0]] (19)
Similarly, for the concentration of di-sodium bisphenate at the interface, we obtain
[[A.sup.*.sub.0] = [k.sub.LB]a[[A.sub.0]]/[k.sub.LB]a + 4[k.sub.1][[B.sup.*.sub.0]] (20)
Both [[A.sup.*.sub.0]] and [[B.sup.*.sub.0]] are calculated from Eqs. 19 and 20.
To derive a continuous tubular reactor model, we assume that phosgene is completely dissolved in the bulk organic phase and that aqueous droplets of equal size are dispersed uniformly in the organic phase. The overall fluid velocity (u) is assumed to be constant along the reactor length. It is also assumed that both the organic phase and the aqueous droplet phase move at the same speed in the reactor. Then, the non-steady state mass balance equation for the dissolved phosgene in the organic phase takes the following form:
[mathematical expression not reproducible] (21)
At steady state, [partial derivative][[B.sub.0]]/[partial derivative]t = 0 and the steady state model equation for phosgene is reduced to
ud[[B.sup.0]]/dz = -[k.sub.L]a [[B.sub.0]] - [[B.sup.*.sub.0]] - 2[k.sub.2][A] [[B.sub.0]] - 2[k.sub.3][[B.sub.0]][[P.sub.0]] (22)
Similarly, the steady state model equations for [A.sub.0] and all intermediate and polymeric species are derived from the reaction kinetics for each species:
u d[[A.sub.0]]/dz = -[k.sub.L]a [[A.sub.0]] - [[A.sup.*.sub.0]) (23)
[mathematical expression not reproducible] (24)
u d[B]/dz = 2[k.sub.2][A][[B.sub.0]] - 2[k.sub.1][B][A] - 2[k.sub.3][B][[P.sub.0]] - 2[k.sub.1][B][[Z.sub.1]] (25)
u d[[P.sub.0]]/dz = 2[k.sub.3][[P.sub.0]][[B.sub.0]] - 2[k.sub.3][[P.sub.0]][A] - 2[k.sub.3][[P.sub.0]][B] - [k.sub.3][[P.sub.0]][[Z.sub.2]] (26)
u d[[P.sub.1]]/dz = 2[k.sub.3][[P.sub.0]][[B.sub.0]] - [k.sub.3][[P.sub.1]][A] - [k.sub.3][[P.sub.1]][A] - [k.sub.3][[P.sub.1]][[Z.sub.1]] (27)
u d[[P]/dz = [k.sub.3][P.sub.1]] + [k.sub.3][[P.sub.0]][[Z.sub.2]] (28)
[mathematical expression not reproducible] (29)
[mathematical expression not reproducible] (30)
Here we assume that the chain length of polymeric species does not affect the reactivity of its end groups (i.e., the rate constants do not change during the interfacial process).
In the step-growth polymerization with AA and BB type monomers where BB monomers are in excess, the number average polymer chain length is calculated using Eq. 31. Here, NA0 denotes the initial number of sodium bisphenate groups, Nm the initial number of chloroformate groups, r the ratio of A groups to B groups (<1; B groups in excess), and p the conversion of A groups.
[X.sub.n] = [r + 1]/[2r(1 - p) + 1 - r] = [[N.sub.A0] + [N.sub.B0]]/[2[N.sub.A] + [N.sub.B0] - [N.sub.A0]] (31)
Since X is the number of moles of carbonate linkages,
[N.sub.A0p] = X = [N.sub.A0] - [N.sub.A] (32)
[N.sub.A0] = [N.sub.A] + X (33)
[N.sub.B0] = [N.sub.B] + X (34)
Thus, the number average molecular weight is calculated using the following equation:
[M.sub.n] = ([X.sub.n])(mw) = [[[N.sub.A] + [N.sub.B] + 2X]/[[N.sub.A] + [N.sub.B]]] (mw) = (1 + 2X/NA + [N.sub.B])(mw) (35)
where mw is the molecular weight of a repeating unit.
We shall consider an interfacial polycondensation in a tubular reactor with side injection of various components. Figure 2 illustrates a tubular interfacial polycondensation reactor process that consists of a mixing zone and a reaction zone. This reactor configuration is commonly used in industrial processes as reported in patent literature [10-14]. One of the advantages of a tubular polycondensation reactor is that reactants and other additives can be easily added to the reactor as side streams. In the mixing zone, gaseous phosgene is completely dissolved in a solvent phase (e.g., methylene chloride). As the phosgenecontaining solvent exits the mixing zone, a caustic aqueous solution of BPA is added.
In the tubular reactor model, we consider two side injections and we assume that the overall tubular reactor is divided into three virtual reaction sections divided by the two side injection stream points and a mixing zone. Since organic solvent phase and aqueous phase containing BPA are immiscible, they are forced to flow at high flow rate through the mixing zone packed with stack mixer units where aqueous phase is dispersed as finely divided liquid droplets (Reaction Zone). In the main reaction zone, additives such as chain stopper (e.g., PTBP) are injected as a side feed to control the polymer molecular weight. In the downstream zone, additional sodium hydroxide (NaOH) can be introduced to the reactor to maintain the desired pH in the aqueous phase. The pressure and temperature are kept constant in the reactor (e.g., 85 psi and 35[degrees]C). The reactor model derived in the above is applied to each reaction zone and solved numerically (The dimension of the industrial reactor considered in this work is proprietary).
To simulate the reactor model, the kinetic rate constants and other relevant parameters need to be estimated. We used a total of four proprietary industrial plant data sets for the interfacial process in this tubular reactor system. The data includes the polymer production rate, weight-average and number average molecular weights for each polymer grade. The model parameters were estimated using the MATLAB[R] optimization protocol to minimize the error between the plant data of molecular weight ([M.sub.n]) and polymer production rate and the simulated values.
The MATLAB protocol that was used in the optimization process is called fminsearch which is used to find the minimum of a scalar function of several variables starting at an initial estimate. This protocol is an example of unconstrained nonlinear optimization. The function used in this protocol was our polymerization model and the variables were the kinetic rate constants [k.sub.1], [k.sub.2], and [k.sub.3]. The number of iterations for this protocol can be set to a desired value. With the previously reported parameter values as initial estimates, this protocol implements the function (polymerization model) for the four different grades of polycarbonate and calculates the average error between experimental and calculated values for the number average molecular weight and polymer production rate for each grade. Then, the parameter values are slightly adjusted for each iteration to minimize this error and this process was repeated until the minimum error was reached. Table 1 lists the optimized parameter values.
The droplet size of suspended aqueous phase is an important process parameter because the total interfacial area for mass transfer and reaction is determined by the droplet size. In the industrial tubular reactor system considered in this work, the aqueous phase is forced to flow through a tubular section packed with static mixers when the aqueous phase is broken up to fine droplets and suspended in a continuous organic phase (methylene chloride). The rate of mass transfer is hence dependent upon the total available interfacial area that is a function of dispersed aqueous droplet size and its holdup. For a tubular section filled with static mixers, the size of dispersed droplets depends on the flow rate. At a given flow rate, the mean energy dissipation rate per mass unit can be regarded as a measure of turbulence at any point in the mixer. High flow rate produces a finer dispersion at equilibrium and requires shorter residence time to reach equilibrium. The estimation of dispersed droplet size in a static mixer system has been reported in the literature [15-17]. In this work, we fitted the droplet size versus flowrate data reported in the literature by the following equation:
[d.sub.L] = 105.8 exp (- 4 X [10.sup.-5]u) (36)
where [d.sub.L] is the average droplet size (microns) and u is the linear fluid velocity (m/h). Using this droplet size and total volume of the aqueous phase, we can estimate the number of droplets and specific surface area (a). Here we assume that the consumption of BPA from the aqueous phase and the consumption of phosgene from the organic phase will not significantly change the total reaction volume. The specific surface area is calculated by
a = 4[pi]N[d.sub.L.sup.2]/4[V.sub.mix] (37)
where N is the total number of dispersed aqueous droplets and [V.sub.mix] is the total reaction volume.
RESULTS AND DISCUSSION
Using the simulation model, we can predict the concentration profiles of various species in the reaction mixture and molecular weight profiles in the tubular reactor. The tubular reactor process that was simulated in this work has a residence time of 70 s and reactor temperature of 30[degrees]C. The average aqueous droplet size was 4.6 pm. Figure 3 shows the axial concentration profiles of BPA and phosgene in the bulk phases as well as at the liquid-liquid interface. We can observe that BPA concentrations at the interface and in the bulk aqueous phase drop to near-zero value at x = 1/3 and the phosgene concentrations at the interface and in the bulk phase are identical and they are much higher than the BPA concentrations.
Figure 3 shows that the mass transfer resistance for phosgene is insignificant at the interface. The estimated mass transfer coefficient of BPA is 9.00 X [10.sup.-7] m/s, whereas the mass transfer coefficient of phosgene is 2.71 X [10.sup.-5] m/s, indicating that the mass transfer resistance for the BPA from the bulk aqueous phase to the liquid-liquid interface is much larger than that for the phosgene in the organic phase. The interfacial BPA concentration lower than in the bulk phase as shown in Fig. 3 confirms that indeed the BPA mass transfer resistance is present. As discussed previously, we have assumed the quasi-steady state for the mass transfer and reaction at the interface.
Figure 4 shows the concentration profiles of chain stopper (PTBP) after being injected at the 1/3 position of the tubular reactor. Note that as the reaction progresses, PTBP ([P.sub.0]) is consumed and end-capped units ([P.sub.1] and P) are produced. In the above model simulation, an excess amount of chain stopper was used and hence the conversion of chain stopper was not very high.
Figure 5 depicts the concentration profiles for intermediate and polymeric species. We can see that carbonate linkages (X) is steadily produced throughout the process. However, the monomer consumption rate becomes negligible after about the first third of the tubular reactor length. After this point, even though BPA and phosgene consumption rates are close to zero, the chloroformates and oligomers/polymers continue to react in the organic phase increasing the number average molecular weight, as shown in Fig. 6. In fact, the molecular weight grows more in the latter half of the process due to these reactions.
Figure 7 compares the model simulated number average molecular weight ([M.sub.n]) and polymer production rate with the actual plant data. It is seen that the agreement between the simulation model predictions and the data are quite satisfactory. In fact, the model predicts the number average molecular weight within the average error of 2 chain lengths (~500 g/mol) and the polymer production rate within the average error of about 3%.
EFFECT OF BISPHENOL A MASS TRANSFER RATE ON POLYMER PROPERTIES
In the foregoing model simulations, we have seen that the mass transfer resistance of phosgene at the liquid-liquid interface was insignificant. The mass transfer rate of monomers from their respective bulk phases to the interface depends on the difference between the bulk and interface concentration of each monomer. Also, the rate of mass transfer is affected by the total surface area available for mass transfer and the mass transfer coefficient. This surface area is determined by the size of the dispersed aqueous droplets with an assumption that the aqueous phase liquid hold-up remains constant. The droplet size is dependent upon the type of static mixers in the tubular reactor and the flow rates of the aqueous phase and the organic phase.
Figure 8 shows the polymer molecular weight and the interfacial surface area as the diameter of aqueous drop size is varied. Note that the polymer molecular weight is strongly dependent on the droplet size up to about 20 pm. When the droplet size is larger than 20 pm, the interfacial surface area is not large enough for the reactions to proceed and as a result, the polymer molecular weight fails to reach high values. With the same liquid hold-up of the aqueous phase, varying the dispersed aqueous droplet size significantly affects the specific surface area (surface area to volume ratio) and thus the rate of mass transfer. The total surface area available for mass transfer decreases when the droplet size increases. Thus, with larger average droplet diameters, the availability of BPA for the reaction at the interface decreases and the rates of BPA mass transfer/reaction decrease resulting in lower molecular weights. The effect of aqueous droplet size has a smaller impact at larger diameters. Increasing the diameter from 1 to 20 pm results in a 60% decrease in average molecular weight, whereas, increasing the diameter from 50 to 100 [micro]m only results in an 8% decrease.
We can also see the effect of the BPA mass transfer coefficient on the average molecular weight in Fig. 9. For a small mass transfer coefficient (i.e., 1.0 X [10.sup.-7] m/s), the average molecular weight of the polymer is quite low. Due to the slow rate of BPA transfer to the interface, the reactions at the interface progress at a slow rate as well. In this case, the process is diffusion controlled; the reaction rate is quick, but the diffusion rate hinders the rate of polymerization. As the mass transfer coefficient increases, the obtainable molecular weight increases as well. However, after a certain point (a mass transfer coefficient of about 4.0 X [10.sup.-6] m/s), we see no increase in molecular weight. At this point, the process is reaction controlled: the diffusion of BPA to the interface is very fast, but the rate of reaction limits the obtainable molecular weight.
In this study, the kinetics of the interfacial polycarbonate process in a tubular reactor was investigated through mathematical modeling and simulation based on a simplified reaction model for a two-phase reaction process. The functional end group modeling approach has been employed to model the polymer growth process and the model was applied to a continuous steady state tubular reactor model. The model parameters were estimated using the proprietary plant data and MATLAB-based optimization tool. One of the major model outputs is the polymer molecular weight and excellent agreement between the model and the plant data has been obtained.
For the interfacial polymerization system modeled in this study, it was shown that the mass transfer of BPA at the interface was a crucial process. The linear velocity has a strong effect on the size of dispersed aqueous phase which is directly related to the available interfacial area for mass transfer. At high fluid velocities, the average size of the dispersed aqueous droplets becomes small and the overall mass transfer efficiency increases to yield high polymer molecular weight. The model simulations indicated that the mass transfer resistance of phosgene was much smaller than that of BPA.
[A] Molar concentration of bisphenol-A monochloroformate in organic phase, mol/[m.sub.3] [[A.sup.*. sub.0]] Molar concentration of di-sodium bisphenate at the interface, mol/[m.sub.3] [[A.sub.0]] Molar concentration of di-sodium bisphenate in bulk (aqueous) phase, mol/[m.sub.3] [B] Molar concentration of bisphenol-A bischloroformate in organic phase, mol/[m.sub.3] [[B.sup.*. sub.0]] Molar concentration of phosgene at the interface, mol/[m.sub.3] [[B.sub.0]] Molar concentration of phosgene in bulk (organic) phase, mol/[m.sub.3] [P] Molar concentration of capped end groups, mol/[m.sub.3] [[P.sub.1]] Molar concentration of PTBP with chloroformate end group, mol/[m.sub.3] [[P.sub.0]] Molar concentration of para-tertiary butyl phenol (end capping agent), mol/[m.sub.3] [X] Molar concentration of carbonate linkages, mol/[m.sub.3] [[Z.sub.1]] Molar concentration of sodium end groups, mol/[m.sub.3] [[Z.sub.2]] Molar concentration of chloroformate end groups, mol/ [m.sup.3] a Specific surface are of dispersed aqueous phase, [m.sup.2]/[m.sub.3] [d.sub.p] Dispersed aqueous droplet diameter, m [k.sub.1] Kinetic rate constant for phosgenation/polymerization, [m.sub.3]/mol s [k.sub.2] Kinetic rate constant for monomer end group conversion, [m.sub.3]/mol s [k.sub.3] Kinetic rate constant for PTBP (end-capping agent), [m.sub.3]/ mol sec [k.sub.LA] Mass transfer coefficient of di-sodium Bisphenate, m/sec [k.sub.LB] Mass transfer coefficient of phosgene, m/sec [M.sub.n] Number average molecular weight, g/mol N Total number of dispersed aqueous droplets p Extent of reaction [V.sub.mix] Total reaction volume, [m.sub.3]
[1.] H. Schnell, Chemistry and Physics of Polycarbonates, Interscience, New York (1964).
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Woo Jic Yang, (1) Moo Ho Hong, (2) Kyu Yong Choi (iD) (1)
(1) Department of Chemical and Biomolecular Engineering, University of Maryland, College Park, Maryland 20742
(2) LG Chem Research Park, 104-1 Moonji-dong, Yuseong-gu, Daejeon 305-380, Korea
Correspondence to: K.Y. Choi; e-mail: email@example.com Contract grant sponsor: LG Chem, Korea.
Caption: SCHEME 1. Overall interfacial polycarbonate synthesis reaction with bisphenol A and phosgene.
Caption: FIG. 1. A schematic illustration of mass transfer and reaction processes for the interfacial polymerization of PC in a tubular reactor.
Caption: FIG. 2. A tubular reactor for interfacial polymerization.
Caption: FIG. 3. (a) Normalized concentration profiles for the di-sodium bisphenate in the aqueous phase ([A.sub.0]), di-sodium bisphenate at the interface ([A.sub.0.sup.*), (b) phosgene in the organic phase ([B.sub.0]), and phosgene at the interface ([B.sub.0.sup.*).
Caption: FIG. 4. Normalized concentration profiles for para-tertiary butyl phenol ([P.sub.0]), modified para-tertiary butyl phenol ([P.sub.1]), and end-capped species (P). Simulation results.
Caption: FIG. 5. Normalized concentration profiles for intermediate species: monochloroforamte (A), bischloroformate (B); polymeric species: [Z.sub.1], [Z.sub.2]; and carbonate linkages (X). Simulation results.
Caption: FIG. 6. Evolution of normalized number average molecular weight (M.,). Simulation results.
Caption: FIG. 7. Comparison of experiment and predicted values of number average molecular weight and polymer production rate.
Caption: FIG. 8. The effect of dispersed aqueous droplet size on the specific surface area of interface and number average molecular weight obtainable. The relationship between drop size and molecular weight exhibits an exponential decay. Simulation Results.
Caption: FIG. 9. The effect of BPA mass transfer coefficient on the number average molecular weight obtainable. With small mass transfer coefficients, this process exhibits diffusion controlled behavior, while at large mass transfer coefficients, this process exhibits reaction controlled behavior. Simulation Results.
TABLE 1. Optimized parameter values. Parameters Definition [k.sub.1] Reaction rate constant [k.sub.2] Reaction rate constant [k.sub.3] Rate constant for PTBP [k.sub.LB] Mass transfer coefficient of [B.sub.0] [k.sub.LA] Mass transfer coefficient of [A.sub.0] Parameters Parameter value [k.sub.1] 9.58 x [10.sup.-5] [m.sup.3]/mol s [k.sub.2] 2.24 x [10.sup.-6] [m.sup.3]/mol s [k.sub.3] 7.20 x [10.sup.-6] [m.sup.3]/mol s [k.sub.LB] 2.71 x [10.sup.-5] m/s [k.sub.LA] 9.00 x [10.sup.-7] m/s
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|Author:||Yang, Woo Jic; Hong, Moo Ho; Choi, Kyu Yong|
|Publication:||Polymer Engineering and Science|
|Date:||Mar 1, 2018|
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