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Decreasing the Cycle Time for In-Mold Coating (IMC) of Sheet Molding Compound (SMC) Compression Molding.

INTRODUCTION

Sheet molding compound (SMC), consisting of a thermosetting resin (usually polyester or vinyl ester), particulate filler (usually calcium carbonate), and glass fiber reinforcement, is the material of choice for compression molding exterior truck body panels. A downside of SMC compression molded parts is that they are prone to surface defects such as porosity, waviness, roughness, and sinks [1-4]. A well-established technique, to overcome this surface defects as well as make the part conductive for subsequent electrostatic painting is to inject and cure a coating compound on the SMC molding after its cure is complete but before removing it from the mold. This added operation fills porosity as well as provides a conductive primer-like surface. This process is called inmold coating (IMC) and the compound used is called IMC.

The basic concept of the IMC process is to integrate priming with the molding process to eliminate emissions and reduce costs [5, 7]. A schematic representation of IMC application on SMC substrate is shown in Fig. 1. In the IMC process, a liquid coating material is injected onto the surface of the SMC at the end of the molding process while the part is still in the mold. A paint-like thin solid layer of coating material is formed after the coating material solidifies by chemical reaction [1-4]. The coated part is removed from the mold once it is cured. Fully cured IMC is 100% solids, and no volatile chemicals are released. IMC is currently an integral part of the SMC compression molding process for exterior automotive and truck body panels where IMC is used as an environmentally friendly conductive primer to allow for electrostatic application of the top coat [1-4, 8, 9], In addition to automotive and trucking industries, applications of commercial IMC can be found in marine, agricultural, residential, and food service industries.

The typical IMC compound contains polyvinyl acetate in styrene and unsaturated urethane oligomers. Chemical polymerization of vinyl-based resins is usually done via a free-radical polymerization mechanism; activation is usually achieved by using a binary, redoxcuring agent consisting of peroxide and an aromatic, tertiary amine [10, 11]. Curing agent decomposes to generate free radicals that initiate the reaction even at ambient temperature, not allowing sufficient working time at a higher temperature. The inhibitor is added to retard the reaction and to extend the working time (pot life) of the mixed coating. Inhibitor molecules act as radical scavengers, when added to the resin they prevent premature polymerization during the mixing or when the material is exposed to high temperature during molding. Materials such as hydroquinone and benzoquinone inhibit or slow down the polymerization reaction rate. Inhibitors mainly inhibit the polymerization reaction by reacting with initiating and propagating radicals and converting them to either nonradical species or a very low reactivity to undergo the propagation reaction. This inhibitory action occurs mainly due to hydrogen transfer to the reactive radical, producing a free radical with a delocalized unpaired electron, making it unable to initiate the polymerization reaction (double bond cannot be opened) [11].

A cure model was developed to predict the flow and cure time. From the molder point of view, the three controllable variables (CVs) at this disposal are: mold temperature, weight percentage (wt%) of initiator and wt% of inhibitor and two most important performance measures (PMs) are flow time, tz and cure time, tc. Inhibition time of the IMC is the maximum flow time before the polymerization reaction starts at molding temperature. For practical reasons, flow time is set at half of the inhibition time. Cure time is the minimum time at which the mold can be opened without damaging the surface integrity. It has been found that correlates well with the time when conversion reaches to 0.9 [12].

The typical molding temperature of SMC is 130[degrees]C-160[degrees]C. The heat activated one component commercial IMC works very well at this temperature with an adequate cure rate [1-4, 12]. To make the IMC process successful, it is essential to have short cycle time while maintaining adequate flow time and pot life so that the molder gets enough time to fill the mold cavity before solidification. However, increasing the flow time also increases the cycle time. We can thus say that there is no single optimal solution but a set of best compromises, which define the efficient or Pareto frontier (PF). A PF is a set of solutions that represent the best compromises among different PMs [13-17]. A multiple criteria optimization (MCO) method was used to obtain the PF. In summary, the objective of this study is to identify the IMC CVs at the molder disposal mainly, molding temperature, level of initiator and inhibitor that provide the best compromises among flow time and cure time.

EXPERIMENTAL

Materials and Samples Preparation Methods

The commercial reactive IMC resin was used in this study which was supplied by OMNOVA Solutions Inc., a leading IMC manufacturing company. It is a one-component heat activated system. The density of the resin is 1.258 kg/L and its viscosity is 4.500-8.200 Pas at 30[degrees]C. r-Butyl peroxybenzoate (TBPB) and p-benzoquinone were used as initiator and inhibitor and purchased from Akzo Nobel and EASTMAN, respectively. A standard heat activated IMC material contains unsaturated oligomers and monomers to yield adequate hardness and adhesion to the SMC substrate [1-4]. The components of a representative commercial thermally activated IMC are given in Table 1.

A precalculated amount of resin was placed in a clean beaker and mixed carefully with the weighted inhibitor, p-benzoquinone. The mixture was adequately stirred by using a tongue depressor for 10 min at room temperature. Then, precalculated amount of initiator, TBPB was added into the mixture. TPBP is the recommended organic peroxide for the range of 130[degrees]C-160[degrees]C which is the typical molding temperature range of compression molded SMC processes. The sample was mixed for another 10 min.

Differential Scanning Calorimetry

Differential scanning calorimetry (DSC) experiments were carried out using a TA Instruments, DSC Q20 under nitrogen atmosphere. Carefully weighted 10-15 mg sample was placed in a Tzero hermetic pan and sealed with Tzero lid upon compression. Isothermal DSC experiments were conducted at 80[degrees]C, 90[degrees]C, and 100[degrees]C with 0.02, 0.04, and 0.06 wt% of p-benzoquinone. A dynamic scan from the isothermal temperature to 250[degrees]C with a ramp rate of 10[degrees]C/min was carried out for each sample following the isothermal scan to determine the residual heat. The same procedure was followed for all the samples.

To calculate the kinetic parameters, isothermal scans at three different temperatures 80[degrees]C, 90[degrees]C, and 100[degrees]C were carried out for all concentrations of TBPB and benzoquinone. For example, DSC graphs for 1.00 wt% TBPB, 0.02 wt% of benzoquinone, and at three different temperatures and followed dynamic scans are shown in Fig. 2. DSC scans for all other experimental conditions can be found in Ref. 18.

Cure Model

Curing is the process by which a liquid thermoset polymer is transformed into a crosslinked solid polymer by chemical reaction. The commercial thermally activated IMC has vinyl groups which react by the free-radical mechanism [1, 2]. A series of kinetic models for free-radical polymerization materials have been developed by Stevenson [19], Lee et al. [20-22], and Castro et al. [1,2, 23-25] to describe the reaction mechanism including three steps: initiation, propagation, and termination, in this study, the freeradical polymerization model was used to determine inhibition time.

[mathematical expression not reproducible] (1)

where [t.sub.z] is the inhibition time in second, [k.sub.do] is the frequency factor for decomposition, [C.sub.z0] is the initial concentration of inhibitor, [C.sub.IO] is the initial concentration of initiator, [E.sub.d] is the activation energy of decomposition, R is the ideal gas constant, T is the temperature in [degrees]K, q and / are the efficiencies for inhibitor and initiator, respectively. The derivation of this equation can be found in Ref. [23], Equation 1 can be simplified as follows:

[mathematical expression not reproducible] (2)

where "a" is a function of [C.sub.z0] and [C.sub.IO] and [E.sub.d] is a constant. The parameters a and [E.sub.d] were calculated by fitting the experimentally measured inhibition times versus temperature for each value of inhibitor and initiator concentration (Table 2), as described by Bhuyan [18]. They are listed in Table 3. These values should be used only to interpolate between the extreme experimental values.

To predict the cure time, a phenomenological autocatalytic model is used since it gives the best fit [12, 18, 26]. The autocatalytic model is represented by Eq. 3.

d[alpha]/dt = ([[alpha].sub.0] + [k.sub.p][[alpha].sup.m]) [([[alpha].sub.max]- [alpha]).sup.n] where [[alpha].sub.0] = 0.001 (3)

where [k.sub.p] is the kinetic rate constant, m and n are the reaction orders, and [[alpha].sub.max] is the maximum conversion.

The kinetic rate constant, [k.sub.p] is assumed to have an Arrhenius temperature dependence and can be expressed as

[mathematical expression not reproducible] (4)

where [E.sub.p] is the activation energy and [k.sub.p0] is the pre-exponential factor.

The kinetic parameters of the autocatalytic model are determined by using the graphic-analytical method described by Bhuyan [18]. The average values of n, m, and [E.sub.p] were taken. The generalized linear regression model is used to predict the "[k.sub.p0]" values which are a function of TBPB (wt%) and benzoquinone (wt%). For [[alpha].sub.max], average values for each temperature are taken and then average values versus temperature fitted to a straight-line equation to obtain the temperature dependency. The detail information can be found in Bhuyan's dissertation [18], The final cure parameters are listed in Table 4.

A good agreement between experimental and predicted values has been observed. The comparison between experimental and predicted values of [t.sub.z] and [t.sub.c] for commercial IMC with different levels of benzoquinone at different temperatures and initiator levels are shown in Figs. 3 and 4, respectively.

Multiple Criteria Optimization

The MCO method developed by Villarreal et al. [27-29] is used to find the best compromises between inhibition time and cure time. The general strategy to find the best compromises among several PMs is schematically shown in Fig. 5.

The method starts with an experimental design for which a simulation run is performed by using the cure model to get the output values at each design point. The set of nondominating solutions or best compromises are identified based on Definition 1, described below, and is called incumbent PF.

Definition 1: It stated that "A feasible solution x, of the optimization problem minimize ([f.sub.1(x), [f.sub.2](x), ... , [f.sub.m](x)) is said to dominate [x.sub.2] if: [f.sub.i] ([x.sub.1]) [less than or equal to] [f.sub.i]([x.sub.2]) for i = 1, ... , m, and [f.sub.i] [x.sub.1]) < [f.sub.i]([x.sub.2] ) for some i [member of] {1, ... , m}" [30], The nondominated solutions are called Pareto set, and the corresponding output values are called PF.

A metamodel for each PM is constructed at each iteration using all the available data. The metamodels are used to predict the values of the PMs at a grid of input combinations. Next, the PF of the predicted data is identified, and it is called predicted PF. The nondominated predicted solutions are then simulated and compared against the incumbent PF for updating purposes. The software checks whether the number of the predicted Pareto solutions are larger than the number of remaining simulations or the maximum number of simulations allowed to be performed per iteration. If so, a subset of solutions is selected based on a max-min distance criterion on the outputs space. Finally, a series of stopping criteria are evaluated. The method stops based on the following three criteria: (1) if the coefficient of determination, [R.sup.2] for all metamodels is larger than (1 - [epsilon]), where [epsilon] is a small number; (2) if the incumbent PF does not change after a given number of iteration; and (3) if the number of simulations exceeds from the specified maximum. If at least one criterion is met, the method stops and the incumbent PF is reported; otherwise, the new simulated points are added to the existing set of points, and a new iteration begins. At each iteration, the metamodels are updated to obtain good approximations of the output responses closer to the PF.

RESULTS AND DISCUSSION

The range of the CVs is selected based on the ranges typically available for SMC molders. For instance, the mold temperature for IMC is set between 130[degrees]C and 160[degrees]C which is also the typical molding temperature range for SMC. Similarly, weight percent of TBPB and benzoquinone is set in the range of 0.5-2.5 and 0.02-0.06, respectively. It has been seen that beyond this range, inhibitor and initiator have minimal effect on cure. For simplicity, only the two most important PMs, inhibition ([t.sub.z]) and cure time ([t.sub.c]) are considered. The optimization problem is mathematically expressed as follows:

Find mold temperature ([T.sub.w]), wt% of initiator (TBPB) and wt% of inhibitor (Benzoquinone) to maximize inhibition time ([t.sub.z]) in minute and minimize cure time (fc) in minute (5)

Subjected to 130[degrees]C [less than or equal to] [T.sub.w] [less than or equal to] 160[degrees]C 0.50 wt% [less than or equal to] TBPB [less than or equal to] 2.50 wt% 0.02 wt% [less than or equal to] Benzoquinone [less than or equal to] 0.06 wt%

To solve Eq. 5, the previously described MCO method was used. A central composite design (CCD) is chosen as the initial design of experiment (DOE) [27], A maximum of 60 total simulations and a maximum of 20 predicted Pareto solutions to be evaluated per iteration were set in the MCO software. An e value of 0.002 was also set as stopping criteria for all metamodels. The procedure is as follows:

Initialization (Iteration 0)

Step 1: Run an initial experiment: An initial DOE for the three CVs is generated based on an inscribed CCD with one central point and an a value of 1.4 when the CVs are scaled between -1 and +1. Therefore, the corresponding axial points are at a distance 1 from the center point and the factorial points range between -0.7 and +0.7. The total number of initial points is 15 (eight (23) factorial points, six axial points, and one in the center). The design points are shown in Table 5 (Columns second to fourth).

The IMC cure model was run at each initial design point. The values of inhibition time ([t.sub.z]) and cure time ([t.sub.c]) are shown in the last two columns of Table 5 as well as graphically in Fig. 6 by dots.

Step 2: Identified PF: The incumbent PF is identified from the current data (Step 1) according to Definition I. The nondominated solutions are solutions: 4, 8, 9, 13, and 14. The solutions in circles in Fig. 6 correspond to the incumbent PF for the initial points.

Main Iteration (Iteration I)

Step 3: Construct a metamodel for each PM: Regression models with 14 (n-1 = 15-1) parameters were constructed for each process output. Equations 6 and 7 are the regression models for [f.sub.1] = [t.sub.z] and [f.sub.2] = [t.sub.c], where [x.sub.1], [x.sub.2], and [x.sub.3] represent the mold temperature, the wt% of initiator, and the wt% of inhibitor, respectively. The corresponding [R.sup.2] values are 0.9979 and 0.9977.

[f.sub.1](.) = -0.1903 + 0.4302[x.sub.1] + 0.2783[x.sub.2] -0.0934x3 -0.2747[x.sub.1][x.sub.2] + 0.1917[x.sub.1][x.sub.3] + 0.1408[x.sub.2][x.sub.3] -0.1898[x.sub.1.sup.2] -0.1871[x.sup.2.sup.2] + 0.0068[x.sub.3.sup.2] - 0.1008[x.sub.1][x.sub.2][x.sub.3] -0.0016[x.sub.1] [x.sub.2.sup.2] -0.1909[x.sub.1][x.sub.3.sup.2] +0[x.sub.1.sup.2][x.sub.2] (6)

[f.sub.2](.) = 1.2062-1.2539[x.sub.1] -0.5948[x.sub.2] + 0.1 16[x.sub.3] + 0.53[x.sub.1][x.sub.2] -0.2378[x.sub.1] [x.sub.3] -0.1749[x.sub.2][x.sub.3] + 0.5285[x.sub.1.sup.2] +0.2613[x.sub.2.sup.2] -0.011[x.sub.3.sup.2] + 0.0646[x.sub.1] [x.sub.2] [x.sub.3] -0.0688[x.sub.1] [x.sub.2.sup.2] + 0.237[x.sub.1] [x.sub.3.sup.2] + 0[x.sub.1.sup.2][x.sub.2] (7)

Step 4: Evaluate metamodels: Once the metamodels are constructed, the values of the process outputs for 1,000 input combinations are predicted. The 1,000 points corresponded to 10 equally spaced levels of mold temperature (each representing 3[degrees]C), wt% TBPB (each one representing 0.2 wt%) and wt% benzoquinone (each one representing 0.004 wt%). The predictions are shown as dots in Fig. 7.

Step 5: Identified predicted PF and Set: The PF from the predicted data (Step 4) was identified. A total of 24 predicted Pareto solutions were found and shown in Fig. 7 as circles. Since the maximum number of simulations allowed per iteration was set to 20; therefore, 20 out of the 24 solutions were selected based on max-min distance criteria. The selected 20 predicted Pareto set is shown in Table 6 (Columns second to fourth) and graphically represented in Fig. 7 as squares.

Step 6: Simulate predicted PF: The IMC cure model was run at the additional 20 selected Pareto points. The output of inhibition time ([t.sub.z]) and cure time ([t.sub.c]) are shown in the last two columns of Table 6.

Step 7: Update incumbent PF: The values of the new solutions, as well as the previous PF were used to update the incumbent PF. At this point, the incumbent PF has 19 solutions. Solution Numbers 4 and 8 are from initial DOE and remaining Numbers 18-22 and 24-35 are from Iteration 1. The new incumbent PF (Iteration 1) is shown in Table 7 (Columns fifth and sixth) and graphically in Fig. 8 as crosses.

Step 8: Evaluate stopping criteria: None of the stopping criteria is satisfied. Therefore, a second iteration is started. The optimization process continues from Step 3.

In the second iteration, new metamodels are constructed with 34 (n-1 = 35-1) parameters for each process output. The corresponding [R.sup.2] values of the metamodels are 1 and 0.9999. The number of predicted Pareto solutions at Iteration 2 is five. Since the remaining number of simulation is 25 (60-35) and number of predicted Pareto solutions is 5 which does not reach the maximum number of simulation per iteration (20), all five solutions are evaluated at this stage. The IMC cure model was run for these new five solutions, and the output values are compared with the previous PF. The PF is updated. The new Pareto solutions are 4, 8, 18-22, 24-35, and 40. These solutions are graphically shown in Fig. 9 with squares. The stopping criteria were evaluated and since the [R.sup.2] values of both metamodels are larger than 0.998; the method stopped and the final Pareto set and the final PF of the IMC process is reported. The final Pareto set (Columns second to fourth) and frontier (Columns second and sixth) are shown in Table 8 as well as graphically in Fig. 9 as squares.

As can be seen from Table 8, the number of final Pareto solutions for the IMC process is 20. Among them, two solutions: four and eight are from the initial DOE; 17 solutions: 18-22 and 24-35 are from first iteration; and the only one solution: 40 is generated on the second iteration.

In Fig. 9, it is observed that at each iteration of the MCO method, the PF is improved by moving toward the ideal solution. The movement of the PF toward the ideal location maximized the inhibition time and minimized the cure time. The ideal solution should be at the southeast comer of the plot. However, the ideal solution does not exist in reality. Therefore, the values of the control variables must be chosen from the final Pareto set to achieve the best compromises.

CONCLUSIONS

The effect of inhibitor (p-benzoquinone) has been experimentally investigated. Inhibitor delays the polymerization reaction by reacting with free radicals which increases both inhibition and cure time. However, to improve the IMC process, it must have short cycle time while maintaining adequate inhibition time and pot life. An attractive approach to increase the inhibition time while decreasing the cure time is to add inhibitor and initiator simultaneously. This allows IMC molding to be run at moderately higher temperature. This approach will also help in keeping the pot life at a reasonable level due to a higher percentage of inhibitor.

An MCO method was employed to identify the setting parameters of the controllable process variables that result in the best compromises between flow time and cure time. The results indicate that the addition of inhibitor improves the PF by moving toward the ideal location.

ACKNOWLEDGMENTS

This research was partially sponsored by OMNOVA Solution Inc. The authors would like to thank the support received by U.S. Department of Commerce (EDA Award No. 06-49-06019) grant through Center for Design and Manufacturing Excellence (CDME), College of Engineering, OSU.

REFERENCES

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Mohammad S.K. Bhuyan (ID), (1) Seunghyun Ko (ID), (1) Maria G. Villarreal, (2) Elliott J. Straus, (3) Lee James, (4) Jose M. Castro (1)

(1) Department of Integrated Systems Engineering, The Ohio State University, Columbus, Ohio, 43210

(2) Modeling Optimization and Computing Technology SAS de CV, Monterrey 64700, Nuevo Leon, Mexico

(3) OMNOVA Solutions Inc., Akron, Ohio, 44305

(4) Department of Chemical and Biomolecular Engineering, The Ohio State University, Columbus, Ohio, 43210

Correspondence to: J. M. Castro; e-mail: castro.38@osu.edu

Contract grant sponsor: U.S. Department of Commerce; contract grant number: EDA Award No. 06-49-06019.

DOI 10.1002/pen.25095

Published online in Wiley Online Library (wileyonlinelibrary.com).

Caption: FIG. 1. Schematic representation of the stages of IMC during the SMC process. [Color figure can be viewed at wileyonlinelibrary.com]

Caption: FIG. 2. DSC graphs of commercial IMC with 1.00 wt% TBPB and 0.02 wt% of benzoquinone at three different temperatures.

Caption: FIG. 3. A comparison between experimental and predicted values of [t.sub.z] for commercial IMC.

Caption: FIG. 4. A comparison between experimental and predicted values of [t.sub.c] for commercial IMC.

Caption: FIG. 5. Flowchart of the MCO method [30].

Caption: FIG. 6. Output values at initial design points (dots) and Pareto solutions (circles).

Caption: FIG. 7. Metamodel's predictions (dots), Pareto solutions (circles), and selected Pareto solutions (squares).

Caption: FIG. 8. Initial solutions (circles), Iteration 0 Pareto front (plus signs), and Iteration 1 Pareto front (cross signs).

Caption: FIG. 9. Initial solutions (circles), Iteration 0 Pareto front (plus sign), Iteration 1 Pareto front (cross signs), and Iteration 2 PF/final PF (squares).
TABLE 1. Components of a single component IMC [1].

Component                                               Weight (%)

LP90 (polyvinyl acetate in styrene)                       17.00
Urethane 783 (unsaturated urethane oligomers)             20.00
Chemlink 600 (polyoxyethylene glycol dimethacrylate)      10.00
Hydroxypropyl methacrylate                                10.00
Styrene                                                   15.00
2% Benzoquinone                                            1.70
t-Butyl peroxybenzoate                                     1.00
Zinc stearate                                              2.00
12% cobalt octoate                                         0.10
Vulcan XC-72 (conductive carbon black)                     2.80
Talc                                                      20.20

TABLE 2. The experimental result of DSC.

TBPB     Benzoquinone   T([degrees]C)   [t.sub.z]
(wt%)       (wt%)                         (min)

1.00         0.02           80.00         91.67
                            90.00         23.67
                           100.00          9.92
1.75         0.02           80.00         26.00
                            90.00          7.27
                           100.00          2.80
2.50         0.02           80.00         11.48
                            90.00          3.03
                           100.00          1.23
1.75         0.04           80.00         60.00
                            90.00         18.67
                           100.00          6.45
1.75         0.06           80.00         73.33
                            90.00         23.33
                           100.00          7.90

TABLE 3. Parameter to calculate inhibition time.

Kinetic                           Value
parameter

[E.sub.d]                       130,247.12
a            (0.04524 - 0.02010 x TBPB (wt%) + 0.1676 x TBPB
                (wt%) x benzoquinone (wt%)} x [10.sup.-14]

TABLE 4. Kinetic parameter to predict cure time.

Kinetic                             Value
parameter

n                    0.8250
m                    0.9227
[E.sub.p]            54,566.44
                     {-0.0445 + 0.35 X TBPB (wt%) +
[k.sup.p0]           1.0777 X TBPB (wt%) X benzoquinone
                     (wt%)) x [10.sup.6]
[[alpha].sub.max]    0.0025 x (T[degrees]K) + 0.0162

TABLE 5. Initial DOEs with corresponding evaluations.

Point      [T.sub.w]     TBPB    Benzoquinone   [t.sub.z]   [t.sub.c]
number    ([degrees]C)   (wt%)      (wt%)         (min)       (min)

1            134.39      0.793      0.0259       0.2643      4.7260
2            134.39      0.793      0.0541       0.2952      4.3660
3            134.39      2.207      0.0259       0.0702      1.5100
4            134.39      2.207      0.0541       0.1562      1.4820
5            155.61      0.793      0.0259       0.0394      2.0500
6            155.61      0.793      0.0541       0.0440      1.8790
7            155.61      2.207      0.0259       0.0105      0.6593
8            155.61      2.207      0.0541       0.0233      0.6207
9            130.00      1.500      0.0400       0.2986      2.7830
10           145.00      0.500      0.0400       0.1185      5.0980
11           145.00      1.500      0.0200       0.0584      1.5320
12           160.00      1.500      0.0400       0.0202      0.8248
13           145.00      2.500      0.0400       0.0297      0.8344
14           145.00      1.500      0.0600       0.0897      1.3970
15           145.00      1.500      0.0400       0.0741      1.4600

TABLE 6. Selected predicted Pareto solutions.

Point       [T.sub.w]     TBPB    Benzoquinone   [t.sub.z]   [t.sub.c]
numbers    ([degrees]C)   (wt%)      (wt%)         (min)       (min)

16            150.00      2.06       0.0200       0.0178      0.8886
17            150.00      2.28       0.0200       0.0101      0.7921
18            130.00      0.50       0.0600       0.4986      8.8290
19            130.00      0.94       0.0600       0.4383      4.3600
20            130.00      1.17       0.0600       0.4068      3.4790
21            130.00      1.39       0.0600       0.3767      2.9210
22            130.00      1.83       0.0600       0.3164      2.2110
23            133.33      1.83       0.0600       0.2301      1.8880
24            130.00      2.06       0.0600       0.2849      1.9560
25            133.33      2.06       0.0600       0.2072      1.6700
26            136.67      2.06       0.0600       0.1514      1.4330
27            140.00      2.06       0.0600       0.1112      1.2380
28            143.33      2.06       0.0600       0.0821      1.0750
29            146.67      2.06       0.0600       0.0609      0.9364
30            153.33      2.06       0.0600       0.0340      0.7199
31            130.00      2.28       0.0600       0.2548      1.7570
32            133.33      2.28       0.0600       0.1853      1.5000
33            136.67      2.28       0.0600       0.1354      1.2880
34            140.00      2.28       0.0600       0.0995      1.1120
35            143.33      2.28       0.0600       0.0735      0.9653

TABLE 7. The PF and set after the first iteration.

                          Pareto set

Point       [T.sub.w]        TBPB      Benzoquinone
numbers    ([degrees]C)     (wt%)         (wt%)

4             134.39         2.21         0.0541
8             155.61         2.21         0.0541
18            130.00         0.50         0.0600
19            130.00         0.94         0.0600
20            130.00         1.17         0.0600
21            130.00         1.39         0.0600
22            130.00         1.83         0.0600
24            130.00         2.06         0.0600
25            133.33         2.06         0.0600
26            136.67         2.06         0.0600
27            140.00         2.06         0.0600
28            143.33         2.06         0.0600
29            146.67         2.06         0.0600
30            153.33         2.06         0.0600
31            130.00         2.28         0.0600
32            133.33         2.28         0.0600
33            136.67         2.28         0.0600
34            140.00         2.28         0.0600
35            143.33         2.28         0.0600
                    PF

Point      [t.sub.z]   [t.sub.c]
numbers      (min)       (min)

4           0.1562      1.4820
8           0.0233      0.6207
18          0.4986      8.8290
19          0.4383      4.3600
20          0.4068      3.4790
21          0.3767      2.9210
22          0.3164      2.2110
24          0.2849      1.9560
25          0.2072      1.6700
26          0.1514      1.4330
27          0.1112      1.2380
28          0.0821      1.0750
29          0.0609      0.9364
30          0.0340      0.7199
31          0.2548      1.7570
32          0.1853      1.5000
33          0.1354      1.2880
34          0.0995      1.1120
35          0.0735      0.9653

TABLE 8. The final Pareto set and PF of the IMC process.

                            Pareto set

Solution      [T.sub.w]     TBPB (wt%)   Benzoquinone
             ([degrees]C)                   (wt%)

4               134.39         2.21         0.0541
8               155.61         2.21         0.0541
18              130.00         0.50         0.0600
19              130.00         0.94         0.0600
20              130.00         1.17         0.0600
21              130.00         1.39         0.0600
22              130.00         1.83         0.0600
24              130.00         2.06         0.0600
25              133.33         2.06         0.0600
26              136.67         2.06         0.0600
27              140.00         2.06         0.0600
28              143.33         2.06         0.0600
29              146.67         2.06         0.0600
30              153.33         2.06         0.0600
31              130.00         2.28         0.0600
32              133.33         2.28         0.0600
33              136.67         2.28         0.0600
34              140.00         2.28         0.0600
35              143.33         2.28         0.0600
40              160.00         2.28         0.0600

                      PF

Solution     [t.sub.z]   [t.sub.c]
               (min)       (min)

4              0.16        1.48
8              0.02        0.62
18             0.50        8.83
19             0.44        4.36
20             0.41        3.48
21             0.38        2.92
22             0.32        2.21
24             0.28        1.96
25             0.21        1.67
26             0.15        1.43
27             0.11        1.24
28             0.08        1.08
29             0.06        0.94
30             0.03        0.72
31             0.25        1.76
32             0.19        1.50
33             0.14        1.29
34             0.10        1.11
35             0.07        0.97
40             0.02        0.50
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Author:Bhuyan, Mohammad S.K.; Ko, Seunghyun; Villarreal, Maria G.; Straus, Elliott J.; James, Lee; Castro,
Publication:Polymer Engineering and Science
Article Type:Report
Geographic Code:1USA
Date:Jun 1, 2019
Words:5738
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