Modeling of Toluene Sulfonic Acid Catalyzed Oxide Addition Reaction

Dec 5, 2014 - Polyols were sampled in 20 mL containers at room temperature and the .... goes to infinity as the same extent of reaction as PDP goes to...
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Modeling of Toluene Sulfonic Acid Catalyzed Oxide Addition Reaction for Soy-Based Polyol Rima Ghoreishi*,† and Galen J. Suppes† †

Department of Chemical Engineering, University of MissouriColumbia, W2033 Lafferre Hall, Columbia, Missouri 65211, United States S Supporting Information *

ABSTRACT: Polyol oligomers formed from reactions of mono-, di-, and triethylene glycols with epoxidized soybean oil were synthesized and the reaction conversions were modeled. The data verified the effectiveness of a model that is based on the simultaneous solution of eight ordinary differential equations. In addition, the data demonstrated that di- and triethylene glycols produced lower viscosity oligomers than monoethylene glycol. Since the model is fundamentally based, it provides insight into the reaction mechanisms and allows for simulation of reaction conditions with reasonable extrapolation. Within the accuracy of the data, the reaction rate coefficients for all alcohol and epoxy moieties were equal, independent of the molecule to which they were attachedreaction rates varied based only on temperature and dilution of reacting moieties. The model provides an effective means to simulating concentration, viscosity, and temperature profiles including estimates of degrees of polymerization, which are dependent on a parameter related to inter versus intra-oligomerization.

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catalyst. Reactions took place at 130 °C and the products had hydroxyl numbers of 143−207 mgKOH/gr, depending on ESBO’s water content.10 Dai et al. used tetrafluoroboric acid as a catalyst to study the effect of different low molecular weight alcohols on soybean oil-based polyols.11 Guo et al. studied properties of halogenated and nonhalogenated ESBO-based polyols that were prepared by epoxy ring opening with hydrogen, methanol, hydrochloric, and hydrobromic acids.12 Lozada et al. evaluated formic acid, phosphoric acid, POLYCAT 5, p-toluenesulfonic acid monohydrate, POLYCAT SA-1, and DABCO BL17 as catalysts to produce soy-based polyols from oxirane ring opening using alcoholysis.13 Pathways different from the one implemented here have been investigated for soy-based polyol production. Preparation of soy-based polyols from bodied soybean oil (BSBO) by alcohol addition and acid reduction using dicyclopentadiene (DCP) catalyzed polymerization was investigated by Lozada et al. and the polyols’ hydroxyl numbers were in the range 42− 126 mgKOH/gr, respectively. In this study, polyols are produced from ESBO by alcohol addition and the final hydroxyl (OH) numbers are relatively higher than the work done by Lozada et al.14 Kiatsimkul et al. also used eight lipases for removing fatty acids from epoxidized soybean oil, thus performing selective hydrolysis.15 Using partial hydrolysis, they were able to replace the saturated fatty acids on epoxidized soybean oil molecules with hydroxyl moieties, therefore producing a product with higher epoxy and hydroxyl numbers compared to regular ESBO. Plant and animal oils can be directly converted to polyols during a single process. The polyol can then react with

INTRODUCTION The addition-reaction of alcohols to epoxidized soybean oil (ESBO) is used in a number of recently introduced soy-based polyol products which are used in the polyurethane industry. These polyol products are oligomers, which meet a range of market needs and specifications. Products attain market success by meeting performance criteria, which, in turn, depend upon having the right combination of molecular weight, hydroxyl functionality (number of hydroxyl moieties per molecule), and viscosity. Molecular weights are typically between about 500 and 4000, hydroxyl moieties between 2 and 6, and viscosities between 500 and 30 000 cP at ambient temperature. These complex combinations of polyol properties go handin-hand with equally complex combinations of reagents, reaction temperatures, catalysts, and reaction times. The paper provides experimental and reaction modeling data on the oxide addition of glycols to expoxidized soybean oil (ESBO) to produce polyols. The complete reaction scheme is representative of a sustainable biobased materials industry where vegetable oils costing $0.35 to $0.55 per pound have value added to in excess of $1.00 per pound. Vegetable oils with triglyceride groups are counted as sustainable renewable resources for polyurethane polyol production.1,2 Researchers have studied different pathways and catalysts to produce vegetable oil based polyols for the past decade.3−6 Soy based polyols can be used as substitutes for petroleum based polyols in the polyurethane industry. They can be used to produce rigid foams7 and bioelastomers,8 which are comparable with the petroleum based products.9 Foam properties would be improved based on polyol’s viscosity, functionality, hydroxyl number, etc. Different catalysts have been used for epoxy ring opening polymerization. Petrovic at al. studied making ESBO based polyols using a mixture of alcohol, water, and fluoboric acid as © 2014 American Chemical Society

Received: Revised: Accepted: Published: 91

December 19, 2013 November 26, 2014 December 5, 2014 December 5, 2014 DOI: 10.1021/ie404316v Ind. Eng. Chem. Res. 2015, 54, 91−99

Article

Industrial & Engineering Chemistry Research Table 1. Reactions, Reaction Rates, and Stoichiometric Coefficients for Each Component rxn #

reaction

1 2 3 4

ESBO ESBO ESBO ESBO

+ + + +

EG → P DEG → P TEG → P PALCOHOL → P

5 6 7 8

PEPOXY PEPOXY PEPOXY PEPOXY

+ + + +

EG → P DEG → P TEG → P PALCOHOL → P

9

PEPOXY → P

rate expression

dCEPOXY/dt dCESBO/dt dCEG/dt dCDEG/dt dCTEG/dt dCP/dt

r(1) = k(1)f ESBOCESBO f EGCEG r(2) = k(2)f ESBOCESBO f DEGCDEG r(3) = k(3)f ESBOCESBO f TEGCTEG r(4) = k(4)f ESBOCESBO(MALCOHOLp − ∑3i fAlcoholi*CAlcoholi) r(5) = k(5) (MESBO − f ESBOCESBO)f EGCEG r(6) = k(6) (MESBO − f ESBOCESBO)f DEGCDEG r(7) = k(7) (MESBO − f ESBOCESBO)f TEGCTEG r(8) = k(8) (MESBO − f ESBOCESBO) (MALCOHOLp− ∑i 3= 1fAlcoholi* CAlcoholi) r(9) = k(9)*CEPOXY

−1 −1 −1 −1

−1 −1 −1 −1

−1 0 0 0

0 −1 0 0

0 0 −1 0

1 1 1 0

−1 −1 −1 −1

0 0 0 0

−1 0 0 0

0 −1 0 0

0 0 −1 0

0 0 0 −DPn

−1

0

0

0

0

0

attain desired products. Since the mathematical models are based on fundamental reaction mechanisms, this simulation can be used to extrapolate the performances of the products and to better understand these set of reactions.

isocyanate forming polyurethanes as well as reactive intermediates containing epoxy and hydroxyl moieties.16−19 Research has also been done on producing polyols from different natural oils. Suresh et al. developed two different pathways to synthesize polyurethane polyols from cardanol.20 Sonnenschine et al. used canola or high oleic sunflower oils in addition to soybean oil to produce methyl esters, which were transformed to polyol ester subsequently.21 Petrovic et al. examined ozonolysis to prepare primary polyols from canola and soybean oils,22 Javni et al. studied the effect of isocyanates on soybean oil based polyols,23 Zlatanic et al. tested the effect of structure of vegetable oils on polyols and polyurethanes.24 The works mentioned above provide insight into natural oil based polyols properties, production pathways, and their applications but none include a model to simulate the polymerization process. As briefly described in the previous paragraphs, considerable work has been done on isolated applications of chemistry to meet product goals. Also, a few polymerization processes producing petroleum based polyols have been simulated. Torres et al. performed modeling for glycerol hydrogenolysis to produce 1,2-propanediol and reported the kinetic parameters of these reactions.25 In a review on modeling polymerization processes, Villa reported modeling pathways for simulating polyol production by ring opening.26 It is apparent that fundamental modeling of polyol production from triglycerides is not available. Simulation of this reaction can lead to a more efficient process and to reduce the effort needed to implement soy-based polyols in polyurethane production. Since soybean oil does not contain hydroxyl groups, it is first epoxidized and the epoxy functional groups are reacted with an alcohol to yield hydroxyl groups. In this paper, the epoxy rings on ESBO were reacted with ethylene glycol using toluene sulfonic acid as a catalyst to produce the desired polyols. The model is capable of simulating oligomerization process and epoxy number and degree of polymerization profiles. Zhao et al.,27 Ghoreishi et al.,28 and Shen et al.29 used a similar code based on this approach to simulate urethane reactions and foam and/or gel’s temperature and density profiles. The goal of this paper is to apply modeling methods that have been successfully used to simulate urethane-forming reactions to the oxide addition reaction that occurs between epoxidized soybean oil and glycols. This modeling approach is a more sophisticated modeling method than commonly used for simple molecules. In particular, the presence of multifunctional reagents leads to a larger array of intermediates and products. A successful approach to follow the ESBO-glycol reaction can provide concentration, temperature, and viscosity profiles (functions of time) that are needed to design reactors and

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MODELING BASIS The series of reactions that describe the oligomerization process are summarized in Table 1. The reactions and rate expressions are related through the matrix comprised of stoichiometric coefficients. Each reaction constant [k(i)] is further expressed in terms of the Arrhenius equation A and E. Reactions 1 through 9 in Table 1 correspond to alcohol moieties reacting with an epoxy moieties to form new ether and alcohol moieties. C, f represent concentration and functionality, respectively. MESBO, EG, DEG, and TEG stand for total epoxy moieties, ethylene glycol, diethylene glycol, and triethylene glycol monomers, respectively. ESBO and P stand for epoxidized soybean oil monomer and polymer molecule. EPOXY and ALCOHOL subscripts represent epoxy and alcohol moieties on the polymer molecule. Reaction 9 shows a unimolecular reaction during which epoxy moieties react and are unavailable for polymerization. One possible product of these side reactions would be ketones. The model neither follows nor depends on the products of this reaction. The code is written such that all epoxy moieties (on monomer as well as polymer) undergo reaction 9. Figure 1 illustrates a linolein-based epoxidized soybean oil molecule as well as representative reactions with ethylene glycol, diethylene glycol, triethylene glycol, and polymer. As it is shown in part a, ESBO is a big monomer, therefore one part of the ESBO and/or polymer molecule containing epoxy and/ or alcohol moieties was selected to illustrate the reactions for parts b−f. A key point of the discussionas provided lateris an evaluation of whether or not, within the accuracy of the data, all epoxy-alcohol reaction rate constants are in fact equal, regardless of the type of monomer. The reactions conserve alcohol moieties and will consume epoxy moieties. The alcohol functional group of the products (Figure 1) may further react with another epoxide group of another oligomer to form crosslinks. The basis for reaction rate expressions (as presented in Table 1) is the following: the hydroxyl moieties on alcohol monomer or polymer/oligomer molecule react with the epoxy moieties on ESBO monomer or polymer/oligomer molecule, resulting in epoxy ring opening and hydroxyl group formation on the polymer or oligomer product. Reaction rate expressions are related to concentration of the reactants as well as their 92

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In which DP is degree of polymerization, Ci0 is the initial concentration of species i and Ci is the concentration of species i at time t. As shown in Figure 1, polymer/oligomer molecules contain both epoxy and alcohol moieties, resulting in the molecules undergoing inter- and intrapolymerization. When intrapolymerization happens, moieties on one polymer molecule react with each other, reducing the number of epoxy moieties and therefore decreasing the reaction rate of the interpolymerization. As the polymerization proceeds, the polymer molecules become larger and the probability of the occurrence of intrareactions increase. The ratio of inter- versus intrapolymerization is a function of the degree of polymerization (DP). As presented in Table 1, the stoichiometric coefficient for the polymer-forming reaction is expressed as a function of DP, namely −DPn. At the beginning of the reactionwhere all reactions are intermolecularthe stoichiometric coefficient (−DPn) is −1 as DP is 1. As the reaction proceeds, more intramolecular reactions take place and also DP gets larger and increases to infinity, leading to the stoichiometry coefficient to be reduced to −1/∞ or 0. The value of the parameter n would theoretically vary from 0 (all intermolecular polymerization,) to −1/3 (maximum intramolecular polymerization,). When n = 0, −DPn is equal to −1 for all DP, which corresponds to Flory’s assumption of zero intrapolymerization. A value of n = 1/3 as the lower limit of interpolymerization is based on a model using the following three assumptions: (a) the polymer molecule is assumed to have the geometry of interconnected strings of diameter d and cumulative length L, with surface area πdL and volume π(d/2)2L, (b) when the string is coiled into a sphere it will have the greatest tendency for intramolecular reaction. At this point the radius of the sphere will be [3/4L(d/2)2L]1/3, which is derived by noting that the volume of the sphere is the same as the volume of the coiled string, and (c) when coiled into the sphere the fraction of reactions that are intermolecular is equal to the surface area of the sphere divided by the surface area of the string per eq 3. surface area of polymer coiled into sphere = 4πr 2 ⎡ 3 ⎛ d ⎞ ⎤2/3 = 4π ⎢ ⎜ ⎟L ⎥ ⎣4⎝2⎠ ⎦

Figure 1. Linolein a major component of epoxidized soybean oil (a), Ring opening reaction of the epoxy group on epoxidized soybean oil with ethylene glycol (b), diethylene glycol (c), and triethylene glycol (d), reaction of ethylene glycol with epoxy moieties on polymer molecule (e) and reaction of alcohol moieties with epoxy moieties on polymer molecule (f) to yield polyols.

where L is the length of the string and d is the diameter of its cross sectional area. L is proportional to DP and all terms except DP are presented as a constant: surface area of polymer coiled into sphere surface area of polymer ≈ constant × DP−1/3

functionalities. Within the Matlab simulation, one matrix represents reaction rates and another matrix represents stoichiometric coefficients of all moieties and components. A multiplication of these two matrices result in a set of differential reactions that are simultaneously solved by ODE45 Matlab function, with initial parameters and rate expressions listed in the table provided as Supporting Information. The code simulates the concentration profiles of all the components. Average number degree of polymerization is also calculated by the code using eq 1.

DP =

∑ Ci0 ∑ Ci

(2)

(3)

The minimum interpolymerization occurs when the molecule is wound into the geometry of a sphere, which is the geometry with the minimum surface area to volume ratio. This equation must be valid in the limit of performance of low DP. The lowest limit for step growth polymerization of monomers, each having a functionality of 2, is interpolymerization = 1 at DP = 1. Under these conditions the constant in eq 3 is 1. For functionalities greater than 2 and for cases where the functionality is not lost in the reaction (e.g., alcohol reacting with an epoxy), the constant can be less than one indicating that the equivalent of DP = 1 may has some potential for intrapolymerization. The limit should be correct; however, it

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Industrial & Engineering Chemistry Research Table 2. Chemical Recipe for Polyols ESBO

EG

DEG

TEG

batch #

polyol

mass (g)

mol.

mass (g)

mol.

mass (g)

mol.

mass (g)

mol.

catalyst (g)

1 2 3 4 5

EE ED ET EED EET

815.5 753.9 632.6 792.2 769.8

0.81 0.75 0.63 0.79 0.77

84.5 0 0 54 54

1.35 0 0 0.86 0.86

0 146.9 0 53.8 0

0 1.35 0 0.5 0

0 0 208.6 0 76.2

0 0 1.37 0 0.5

5 5 5 5 5

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RESULTS AND DISCUSSION The EE polyol was synthesized at both 140 and 160 °C with the profile and model fit as summarized by Figure 2. The model

needs not represent actual performance at DP = 1 since this equation is only applied to molecules of DP greater than or equal to 2. This constant having values less than or equal to one, is primarily a function of the average functionality of the monomers and may be used as a fitted parameter or it may be derived based on theory.

EXPERIMENTAL SECTION

A series of polyols were synthesized by reacting fully epoxidized soybean oil (ESBO) with different combinations of ethylene glycol (EG), diethylene glycol (DEG), and triethylene glycol (TEG). PToluenesulfonic acid monohydrate (TSA) was used as a catalyst. Epoxidized soybean oil used in the experiments had 7% oxirane oxygen and a molecular weight of 1000. Table 2 summarizes the recipes used for the five batches synthesized in this study. The different products are referred to as EE, ED, ET, EED, and EET. As presented in Table 2, EE, ED, ET, EED, and EET stand for ESBO-EG, ESBODEG, ESBO-TEG, ESBO-EG-DEG and ESBO-EG-TEG systems, respectively. The EE, ED, and ET polyols contained 9.5 wt % alcohol while EED and EET polyols contain 6 wt % EG. As presented in Table 2, the total number of moles of alcohol was kept constant for all recipes. All mixtures contained 0.5 wt % catalyst. All experiments were conducted in a 1000 mL type Erlenmeyer flask equipped with a magnetic stirrer. A hot plate used to provide most of the heat input was augmented with a heating lamp connected to a PID controller to control temperature based on a set point. Experiments were initiated by heating ESBO and EG to 125 °C; at which point, TSA (catalyst) was added. A combination of exothermic heat of reaction and heat input was used to bring the mixture to a final temperature of 160 or 140 °C. It took about 15 min for the mixture to reach the set point temperature. Equation 4 was used to empirically determine the temperature profile of the reaction at different times. The equation was then used to calculate the temperature in the Matlab model.

T = T0 + (T∞ − T0 + 5)

t (t + 500)

Figure 2. Epoxy number profiles for EE polyol produced at 161 °C (circles) and 140 °C (squares). Solid lines represent modeling results.

provides a good fit to the data accurately characterizing a faster reaction rate constant at 160 °C and a slower initial reaction due to the lower initial temperature. The Arrhenius parameters of the fitted model are summarized in Table 3. The same values of the pre exponential factor (A) and activation energy (E) were able to characterize reaction rate coefficients for epoxy-EG reactions (reactions 1, 4, 5, and 8 of Table 1). Within the accuracy of the data, the reaction rates between the alcohol and epoxy moieties were the same, independent of whether the moieties were attached to the monomer or polymer. Kinetic parameters for reaction 9 were obtained using the experimental results presented by Figure 3. As the reaction is first order, pre-exponential factor (A) and activation energy (E) were gained from a linear regression of the experimental data points on the graph. The kinetic parameters are presented in Table 3. The value of activation energy (E) for epoxy-alcohol reaction is typically 80 kJ/mol, which is lower than the value presented in Table 3. Figure 4 shows a comparison between simulation results for E = 80 KJ and E = 134 KJ. Epoxy number profiles for ED and ET polyols are presented by Figure 5. It is shown that the ET-forming reaction was faster than the ED-forming reaction, and the EE-forming reaction was faster than the ET-forming reaction. The model-lines of Figure 5 were generated using the same Arrhenius parameters as provided in Table 3. Within this range of diols, the reactivity of the reactants was independent of the monomer and/or polymer to which they were attached. The slower reaction rates observed for oligomers ED and ET were primarily due to the lower concentration of (C−C−O)n units in the diol reagents. Primary conclusions of the results presented by Figures 2 and 3 are that the model effectively simulates the concentration profiles and that temperature, reaction time, and alcohol

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T is temperature at any given time, t is time, and T0 and T∞ are initial and final temperatures, respectively. For EED and EET polyols, ESBO and EG were heated up for 90 min (during which catalyst was added and temperature was kept at 161 °C). Then, hot DEG or TEG were added to the mixture according to the recipe. Epoxy number, hydroxyl number, and viscosity profiles were used to characterize products and intermediates. Epoxy number of the polyols was determined using oxirane oxygen titration (AOCS Cd 9−57). Hydroxyl numbers were determined using AOCS Ts 1a-66 method. Polyols were sampled in 20 mL containers at room temperature and the dynamic viscosities were measured using a rotational Cole−Parmer basic viscometer, with a number 4 spindle. To verify the reaction rate coefficient of the first order epoxy unimolecular reaction, epoxy titration was performed on two mixtures of ESBO and TSA (0.5 wt %). Experiments were initiated by heating ESBO and TSA to 160 or 180 °C. Then the mixture’s temperature was kept constant for 2 h. 94

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Industrial & Engineering Chemistry Research Table 3. Kinetic Parameters Based on the Modeling Results for EE Polyol kinetic params. epoxy and alcohol monomer kinetic params. unimolecular epoxy degradation

A

k (L·mol−1·s−1) (161 °C)

E (J/mol)

5.5 × 10

1.34 × 10

17

05

A

E (J/mol)

1.05 × 107

8.5 × 104

35.47 k (1/s) (160 °C) 6 × 10−4

k (L·mol−1·s−1) (140 °C) 5.39 k (1/s) (180 °C) 1.7 × 10−3

Figure 3. Epoxy number profiles for ESBO and TSA reactions at 160 °C (squares) and 180 °C (diamonds). The solid lines represent linear regression.

Figure 4. Comparison of epoxy number profile simulation results for EE polyol at 140 °C (squares) and 161 °C (circles). The solid lines represent simulation results for E = 134 KJ at 140 °C (top) and 161 °C (bottom). The dashed lines represent simulation results for E = 80 KJ at 140 °C (top) and 161 °C (bottom).

coreagent can be used to create final products with a range of performances. The use of this information to produce improved products resides in being able to meet a range of performance criteria for various applications that includes the following characteristics: • Most markets require product viscosities less than about 10 000 cP at ambient temperature to allow pumping and mixing with existing infrastructure. Viscosities up to 20 000 cP may find acceptance in some of the larger markets if they bring other benefits. • The primary polyol properties used to match a polyol with a urethane application are the polyols functionality and hydroxyl number. The profiles of Figures 3c and 3d include the addition of DEG and TEG, respectively, after the first 4800 (DEG) and 6300 (TEG) seconds of reaction. This addition resulted in an immediate change in epoxy number due to dilution and hence a slower subsequent reaction rate. Both are properly accounted for by the model. These profiles provide epoxy numbers for oligomers formed by EG and ESBO which were then capped with DEG (c) or TEG (d). By adding the DEG and TEG at the

Figure 5. Epoxy number profile for ED (a), ET (b), EED (c) and EET (d) polyols at 161 °C. Symbols represent experimental data and solid lines the modeling results.

end of the reaction, more of these longer straight-chain segments will be branches as opposed to cross-links. Longer 95

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it impacts the polyol’s functionality and viscosity. However, extensive degrees of polymerization can lead to viscosities so high as to make a product undesirable and unmarketable. Model-based sensitivity analyses are performed on the following parameters so as to better understand how they impact epoxy number and degree of polymerization: • Amount of EG in the recipe. • Water content of the initial reaction mixture. • The impact of epoxy degradation. Epoxy number is related to the number of functional groups according to eq 5, where MW, W, and f are molecular weight, sample weight and functionality of ESBO.

branches on the oligomer have the potential to reduce viscosity, especially dynamic viscosity. Figure 6 compares the viscosities of the EE, EED, and EET polyols.

epoxy functional groups =

W f MW

(5)

As illustrated by the sensitivity analysis of Figure 7, increased loadings of EG result in a slight dilution of the ESBO moieties and, at least from 6% to 12%, an increase in reaction rate. Lower EG loadings will result in an increased tendency to form high degrees of polymerization with respective high viscosities. Most importantly, the assumption of conservation of alcohol moieties was used by model and implicitly validated by the good fit of the modeling results; the initial loading of ethylene glycol determines the hydroxyl number of the oligomers. Sensitivity analyses simulation results are provided by Figure 8 for both n = 0 versus n = −0.3334. The polymer degree of polymerization (PDP) is plotted rather than DP, which includes unreacted monomers. PDP is defined by eq 6, where

Figure 6. Epoxy number vs ambient temperature−viscosity for EE, EED, and EET polyols produced at 160 °C. The dotted lines show trend lines.

As presented by Figure 6, capping with DEG and TEG was effective in reducing viscosity. At the same final epoxy number, EE has a greater viscosity than EED which has a greater viscosity than EET. For an epoxy number of 2.6, EE, EED, and EET have viscosities of 4800, 2800, and 2200, respectively. Polyols showed an increase in viscosity during storage at room temperature. This could be due to the residual epoxy present in polymer molecules that continue to react and increase the viscosity. The dilution impact would adjust the epoxy number by about 2.5% of 6.2 (about 0.16 change in epoxy number). The impact of the capping was much greater than can be accounted for by dilution and can be attributed to less entanglement and more alignment of longer branches on the SBO backbone. The oligomers with longer branches should also show relatively improved resilience and respectively better performance in flexible urethane foam applications. As a fundamentally based model, the results can be extrapolated to determine the sensitivity to various reagent and reaction parameters. The goal is to identify conditions leading to suitable viscosities, hydroxyl numbers, and epoxy numbers. An additional goal is to provide further insight into the fundamental reaction mechanisms. Figures 7−10 summarize sensitivity analyses using the model with the goal of being able to control the final product’s epoxy number and degree of polymerization. Degree of polymerization is important because

Figure 8. Impact of 100% inter- (n = 0), 100% intra- (n = −0.3334), and side reaction on polymerization reactions (a), Comparison of actual performance of the model and − [constant]DP1/3 modification (b).

Figure 7. Modeling results for epoxy number profiles for different amounts of alcohol monomers. 96

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Industrial & Engineering Chemistry Research C0,monomer, Ct,monomer, and Cpolymer represent initial concentration of monomers, concentration of monomers at time t and polymer concentration, respectively. PDP =

oligomer molecule into two oligomer molecules. Figure 10 illustrates simulation results for the impact of ESBO water

(C0,monomer − Ct ,monomer) Cpolymer

(6)

The basis for this is that when the polymer reaches its gel point creating a system of infinite viscosity. At the gel point, cross-linking results in combining of polymers, which is mathematically represented as the concentration of the polymers decreasing to zero; at the gel point, any remaining monomers would be entrapped in the cross-linked network. Viscosity is a measured property to which simulation results can be compared. PDP is the simulation result that is compared with viscosity where increased PDP leads to increased viscosity and where viscosity goes to infinity as the same extent of reaction as PDP goes to infinity (gel point). It is clear from Figure 7 that the gel point is not reached as indicated by Figure 8. Comparison of actual performance to that of the geometrybased −[constant]DP1/3 model performance reveals that the constant must have a value less than 1.0 and/or side reactions may be consuming epoxy moieties. Independent studies were performed to quantify the known side reaction. A side reaction of particular interest is the one reported by Rios et al.30 during which epoxy moieties undergo a unimolecular reaction to form ketones. This unimolecular reaction happens when TSA is present in the mixture and at high temperatures. The effect of this side reaction on polymer concentration and PDP is shown in Figure 8 were PDP and polymer concentrations change more slowly when a side reaction is taken into account. Figure 9 shows the impact of the constant on simulated PDP. Viscosity is in correlation with PDP and as is shown by thin

Figure 10. Impact of ESBO’s water content on degree of polymerization for EE polyol.

content on degree of polymerization for EE polyol. One half of a percent water in ESBO can have significant impacts on reducing degree of polymerization. This reaction would increase hydroxyl number. As mentioned earlier, the model simulates reactions where alcohol moieties are conserved (neglecting the impact of trace water). Figure 11 presents the hydroxyl number profile for EE

Figure 11. Hydroxyl numbers EE polyol (circles) and ESBO+EG mixture (square).

polyol. Hydroxyl values of EE polyol (circles) and cold ESBO and EG mixture (square) were determined using AOCS Ts 1a66 method. According to the experimental data, polyol’s hydroxyl number increases over time and reached the value of the ESBO+EG mixture; however, the final hydroxyl number is consistent both is the final hydroxyl number calculated based on the amounts of the reactants and also the measured hydroxyl number of the epoxy-alcohol mixture at ambient temperature before the reaction. Two different analytical methods were used to determine hydroxyl numbers. In the first analytical method, the hydroxyl numbers of two mixtures of ESBO and EG, one with and without TSA were measured using AOCS Ts 1a-66 titration method. As seen in Figure 12, the mixture with TSA shows a lower hydroxyl value. Two possible explanations for the decrease in hydroxyl number illustrated by Figure 12 are (a) the pyridine used in the titration mixture increases the tendency for TSA to react with alcohols and interferes with the analysis and (b) TSA reacts with alcohol groups to form esters, thus consuming the alcohol moieties. To determine which explanation is correct, gel runs

Figure 9. Correlation between PDP and viscosity. The diamonds represent measured viscosity of EE polyol with the dashed line added to show the trend. Solid lines represent simulation results for different values of the constant multiplied by DP.

vertical lines in Figure 9, the point at which PDP and viscosity go to infinity is used to identify the mpst appropriate constant (0.47) for PDP. Another factor that can increase theDP of the product is the presence of water in the reaction mixture. Hydrolysis of ester groups of the fatty acid backbone can lead to formation of one alcohol and one acid moiety for each water molecule that reacts. Both the acid and alcohol can then, irreversibly, react with epoxy moieties. The net impact is the splitting of one 97

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blowing agents. The EET, EED, and EE products all exhibited high reactivity indicative of primary hydroxyl groups on the polyol. No difference in reaction rate could be determined within the standard deviation of the data. It is anticipated that the EET polyol will result in foams of greater flexibility and resilience than the EE polyol. The chemical compositions of all gels are listed in Table 4. Table 4. EE, EED, and EET Gel Chemical Recipes

Figure 12. Hydroxyl number titration results for ESBO and EG mixtures, with and without TSA.

material

polyol (g)

isocyanate (g)

cat. eight (g)

TCPP (g)

L6900 (g)

EE EED EET

16.93 16.99 16.9

26.09 27.48 27.45

0.123 0.122 0.123

1.34 1.36 1.37

0.26 0.26 0.26

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were performed with mixtures of ESBO and EG, one with TSA and one without. Both mixtures had the same isocyanate index and alcohol concentration. Gel temperature profiles presented in Figure 13 show that both samples had equal peak temperature, that is, heat of

CONCLUSIONS This work introduced a model based on the simultaneous numerical solution of several ordinary differential equations describing the oligomerization of ESBO with glycols. The model accurately simulated concentration profiles over a range of conditions; and since the model is fundamentally based, it allows for reasonable extrapolation to simulate performances in a series of sensitivity analyses. The following are key findings of this study: • Pre-exponential factor and activation energy have similar values for all reactions regardless of the type of the alcohol used. This indicates that the reaction rate of the epoxy and primary alcohol moieties is not a significant function of the molecule to which it is attached for the range studied in this work. • The primary factor impacting reaction rates was the dilution of the reacting groups due to the different hydroxyl numbers between EG, DEG, and TEG reagents. • A side reaction where epoxy moieties undergo unimolecular reactions happens, which slows down the polymerization process, resulting in a lower final viscosity. • Viscosity and gel temperature profiles show that substituting a percentage of EG with DEG or TEG reduces the polyol viscosity. • Degree of polymerization is affected by polymer− polymer reactions. A model parameter was introduced that exhibits limits on intra- versus intermolecular oligomerization. The model is fundamentally correct and with inclusion of the parameter (eq 3 constant) that takes into account the high propensity for intrapolymerization, the rapid increase in viscosity is ultimately consistent with the model. A study of unimolecular degradation of ESBO indicates that TSA does catalyze the decomposition of epoxy moieties, and this explains, in part, the absence of a gel point in experimental data. Oligomerization modeling using the approach of this work provides greater detail than that provided by simplified models. The finding that moiety reaction rates do not vary much based on the size of the ethylene glycol oligomer provides a useful insight. The degree of polymerizationand respective estimate of viscosityis one of the properties this approach allows to be simulated, which is not possible with simplified models. The greater fundamental insight into the mechanisms provided by this approach allows for improved reaction engineering.

Figure 13. Gel temperature profiles for ESBO and ethylene glycol mixtures. Diamonds and squares represent mixtures with and without TSA, respectively.

reaction. Therefore, the same amount of isocyanate is consumed by the alcohols present in each mixture. Hence, it is concluded that the immediate reduction in hydroxyl number is not due to TSA irreversibly reacting with alcohol groups. Previous publications have demonstrated that the soy-based polyols produced by this approach are effective in rigid urethane applications;13 so, foam performance is not repeated in this work. However, it is desirable to know how the reaction rates of the polyol products presented here vary in a standard urethane reaction. Figure 14 shows temperature profiles for EE, EED, and EET gels, which are urethane formulations without

Figure 14. Temperature profile for EED and EET gels. 98

DOI: 10.1021/ie404316v Ind. Eng. Chem. Res. 2015, 54, 91−99

Article

Industrial & Engineering Chemistry Research

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(10) Petrovic, Z. S.; Javni, I.; Guo, A.; Zhang, W. Method of Making Natural Oil-Based Polyols and Polyurethanes Therefrom. U.S. Patent No. 6,433,121, Aug. 13, 2002. (11) Dai, H.; Yang, L.; Lin, B.; Wang, C.; Shi, G. Synthesis and Characterization of the Different Soy-Based Polyols by Ring Opening of Epoxidized Soybean Oil with Methanol, 1,2-Ethanediol and 1,2Propanediol. J. Am. Oil Chem. Soc. 2009, 86, 261. (12) Guo, A.; Cho, Y.; Petrovic, Z. S. Structure and Properties of Halogenated and Nonhalogenated Soy-Based Polyols. J. Polym. Sci. A1 2000, 38, 3900. (13) Lozada, Z.; Suppes, G. J.; Tu, Y. C.; Hsieh, F. H. Soy-Based Polyols from Oxirane Ring Opening by Alcoholysis Reaction. J. Appl. Polym. Sci. 2009, 113, 2552. (14) Lozada, Z.; Suppes, G. J.; Hsieh, F. H.; Lubguban, A.; Tu, Y. C. Preparation of Polymerized Soybean Oil and Soy-Based Polyols. J. Appl. Polym. Sci. 2009, 112, 2127. (15) Kiatsimkul, P.; Sutterlin, W. R.; Suppes, G. J. Selective Hydrolysis of Epoxidized Soybean Oil by Commercially Available Lipases: Effects Of Epoxy Group on the Enzymatic Hydrolysis. J. Mol. Catal. B: Enzym. 2006, 41, 55. (16) Casper, D. M.; Newbold, T. Methods of Preparing Hydroxy Functional Vegetable Oils. U.S. Patent 8,350,070, January 8, 2013. (17) Casper, D. M.; Newbold, T. Methods of Preparing Hydroxy Functional Vegetable Oils. U.S. Patent No. 7,893,287, February 22, 2011. (18) Yalamanchili, S.; Nodelman, N.; Casper, D. M.; Newbold, T. Methods of Preparing Hydroxy Functional Vegetable Oils. U.S. Patent 8,507,701, Aug. 13, 2013. (19) Newbold, T.; Newbold, S. M.; Yalamanchili, S. Preparation of an Active Intermediate. U.S. Patent No. 8,674,124, March 18, 2012. (20) Suresh, K. I.; Kishanprasad, V. S. Synthesis, Structure, and Properties of Novel Polyols from Cardanol and Developed Polyurethanes. Ind. Eng. Chem. Res. 2005, 44, 4504. (21) Sonnenschein, M. F.; Greaves, M. R.; Bell, B. M.; Wendt, B. L. Design, Polymerization, and Properties of High-Performance SeedOil-Derived Lubricants. Ind. Eng. Chem. Res. 2012, 51, 8386. (22) Petrovic, Z. S.; Zhang, W.; Javni, I. Structure and Properties of Polyurethanes Prepared from Triglyceride Polyols by Ozonolysis. Biol. Macromol. 2005, 6, 713. (23) Javni, I.; Zhang, W.; Petrovic, Z. S. Effect of Different Isocyanates on the Properties of Soy-Based Polyurethanes. J. Appl. Polym. Sci. 2002, 88, 2912. (24) Zlatanic, A.; Lava, C.; Zhang, W.; Petrovic, Z. S. Effect of Structure on Properties of Polyols and Polyurethanes Based on Different Vegetable Oils. J. Polym. Sci., Polym. Phys. 2004, 42, 809. (25) Torres, A.; Roy, D.; Subramaniam, B.; Chaudhari, R. V. Kinetic Modeling of Aqueous-Phase Glycerol Hydrogenolysis in a Batch Slurry Reactor. Ind. Eng. Chem. Res. 2010, 49, 10826. (26) Villa, C. M. Reactor Modeling for Polymerization Processes. Ind. Eng. Chem. Res. 2007, 46, 5815. (27) Zhao, Y.; Gordon, M. J.; Tekeei, A.; Hsieh, F. H.; Suppes, G. J. Modeling Reaction Kinetics of Rigid Polyurethane Foaming Process. J. Appl. Polym. Sci. 2013, 130, 1131. (28) Ghoreishi, R.; Zhao, Y.; Suppes, G. J. Reaction Modeling of Urethane Polyols Using Fraction Primary, Secondary, and HinderedSecondary Hydroxyl Content. J. Appl. Polym. Sci. 2014, 131, 12. (29) Shen, L.; Zhao, A.; Tekeei, A.; Suppes, G. J. Density Modeling of Polyurethane Box Foam. Polym. Eng. Res. 2014, 54, 1503. (30) Rios, L. A. Heterogeneously Catalyzed Reactions with Vegetable Oils: Epoxidation and Nucleophilic Epoxide Ring-Opening with Alcohols. PhD Thesis, Institute of Chemical Technology and Heterogeneous Catalysis, University of Technology RWTH, Aachen, 2003.

ASSOCIATED CONTENT

S Supporting Information *

MATLAB code written for modeling chemical reactions and table presenting reaction rate expressions. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the United Soybean Board for financial support of the experimental studies used to validate the modeling work. The authors thank FSI. Company providing foam formulas and technology support. None of the authors has conflicts of interest with companies producing epoxidized soybean oil, ethylene glycol, diethylene glycol, triethylene glycol, p-toluenesulfonic acid monohydrate, N,N-dimethylcyclohexylamine(DMCHA), TCPP, and momentive L6900.

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ABBREVIATIONS ESBO = epoxidized soybean oil EE = ESBO−ethylene glycol ED = ESBO−diethylene glycol ET = ESBO−triethylene glycol EED = ESBO−ethylene glycol−diethylene glycol EET = ESBO−ethylene glycol−triethylene glycol TSA = toluenesulfonic acid DP = degree of polymerization PDP = polymer degree of polymerization.

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REFERENCES

(1) Kluth, H. G.; Meffert, B.; Huebner, W. Polyurethane Prepolymers Based on Oleochemical Polyols, Their Production and Use. U.S. Patent No. 4,742,087, May 3, 1988. (2) Hoefer, R.; Gruber, B.; Meffert, A.; Gruetzmacher, R. Polyurethane Casting Resins. U.S. Patent No. 4,826,944, May 2, 1989. (3) Guo, A.; Javni, I.; Petrovic, Z. S. Rigid Polyurethane Foams Based on Soybean Oil. J. Appl. Polym. Sci. 2000, 77, 467. (4) Petrovic, Z. S.; Guo, A.; Javni, I. Process for the Preparation Of Vegetable Oil-Based Polyols and Electron Insulating Casting Compounds Created from Vegetable Oil-Based Polyols. U.S. Patent No. 6,107,433, Aug. 22, 2000. (5) Goud, V. V.; Patwardhan, A. V.; Pradhan, N. C. Studies on the Epoxidation of Mahua Oil (Madhumica indica) by Hydrogen Peroxide. Bioresour. Technol. 2006, 97, 1365. (6) Petrovic, Z. S.; Javni, I.; Guo, A. Proceedings of Two-Component High-Solid Polyurethane Coating Systems Based on Soy Polyols. Polyurethanes EXPO’98, SPI, Polyurethane Division, Dallas; 1998. (7) Suppes, G. J.; Hsieh, F. H.; Tekeei, A.; Fan, H. Soy-Based Rigid Foams with Reduced Urethane Loadings. Am. Chem. C 2012, 545. (8) Suppes, G. J.; Lozada, Z.; Lubguban, A. Soy-Based Polyols for Production of Polyurethane Bioelasteromers. U.S. Patent No. 7,696,370, May 23, 2013. (9) Lubguban, A.; Tu, Y. C.; Lozada, Z. R.; Hsieh, F. H.; Suppes, G. J. Functionalization via Glycerol Transesterification of Polymerized Soybean Oil. J. Appl. Polym. Sc. 2009, 112, 2185. 99

DOI: 10.1021/ie404316v Ind. Eng. Chem. Res. 2015, 54, 91−99