Direct Production of Propene from the Thermolysis of Poly(β

Article pubs.acs.org/JPCA

Direct Production of Propene from the Thermolysis of Poly(β-hydroxybutyrate) (PHB). An Experimental and DFT Investigation Jared M. Clark,† Heidi M. Pilath,‡ Ashutosh Mittal,‡ William E. Michener,† David J. Robichaud,† and David K. Johnson*,‡ †

National Bioenergy Center and ‡Biosciences Center, National Renewable Energy Laboratory, Golden, Colorado 80401, United States ABSTRACT: We demonstrate a synthetic route toward the production of propene directly from poly(β-hydroxybutyrate) (PHB), the most common of a wide range of high-molecular-mass microbial polyhydroxyalkanoates. Propene, a major commercial hydrocarbon, was obtained from the depolymerization of PHB and subsequent decarboxylation of the crotonic acid monomer in good yields (up to 75 mol %). The energetics of PHB depolymerization and the gas-phase decarboxylation of crotonic acid were also studied using density functional theory (DFT). The average activation energy for the cleavage of the R′C(O)O−R linkage is calculated to be 163.9 ± 7.0 kJ mol−1. Intramolecular, autoacceleration effects regarding the depolymerization of PHB, as suggested in some literature accounts, arising from the formation of crotonyl and carboxyl functional groups in the products could not be confirmed by the results of DFT and microkinetic modeling. DFT results, however, suggest that intermolecular catalysis involving terminal carboxyl groups may accelerate PHB depolymerization. Activation energies for this process were estimated to be about 20 kJ mol−1 lower than that for the noncatalyzed ester cleavage, 144.3 ± 6.4 kJ mol−1. DFT calculations predict the decarboxylation of crotonic acid to follow second-order kinetics with an activation energy of 147.5 ± 6.3 kJ mol−1, consistent with that measured experimentally, 146.9 kJ mol−1. Microkinetic modeling of the PHB to propene overall reaction predicts decarboxylation of crotonic acid to be the rate-limiting step, consistent with experimental observations. The results also indicate that improvements made to enhance the isomerization of crotonic acid to vinylacetic acid will improve the direct conversion of PHB to propene.

■

INTRODUCTION Propene is a major industrial chemical intermediate that feeds into the synthesis of an array of plastic, chemical, and liquid fuel products. The larger part of all propene produced (∼60%) is consumed in the production of polypropylene, a thermoplastic polymer used in a wide variety of applications.1,2 In 2012, 42 million metric tons of polypropylene were produced globally, with a market valued at nearly U.S. $77 billion.3 Industrially, propene is also essential in the production of phenol through the formation and subsequent oxidation of the phenolic intermediate cumene.4,5 Global phenol production was in excess of 8 million metric tons in 2012, with an estimated market value of U.S. $9 billion. Propene is also used in the formulation of gasoline, gasoline components, and distillate fuels through oligomerization and cracking.6,7 Poly(β-hydroxybutyrate) (PHB), one of many polyhydroxyalkanoates,8 is a biopolymer synthesized by a number of microorganisms as an intracellular energy and carbon storage material. Through decarboxylation of the dehydrated monomer unit of PHB, crotonic acid (2-butenoic acid, CH3CHCHCO2H), PHB represents a renewable and sustainable source of propene.9 Recent activities to maximize PHB production from microorganisms has resulted in PHB formation that can constitute as much as 80 wt % of dry cell mass10−12 and be produced at a rate of 5 g L−1 h−1. With a production capacity of 60 000 L, © XXXX American Chemical Society

a moderate size production facility can produce in excess of 300 kg h−1 of PHB.13 The thermal conversion of PHB to crotonic acid has been studied8,9,14−40 using various analytical procedures, including thermogravimetric analysis (TGA), differential scanning calorimetry (DSC), nuclear magnetic resonance spectroscopy (NMR), among others. A comprehensive summary of this work identifying the various techniques is provided by Nishida.41 These studies indicate that PHB thermally degrades primarily through a statistical intramolecular β-elimination process that results in the production of an olefin and a carboxylic acid. This process is illustrated in reaction 1 for the simplest analogue of PHB, ethyl acetate.

Received: September 22, 2015 Revised: December 17, 2015

A

DOI: 10.1021/acs.jpca.5b09246 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A Reaction 1 has been studied both experimentally42,43 and computationally,44 with barrier heights of 205.3 ± 1.5 and 210.0 ± 6.3 kJ mol−1, respectively. This reaction provides a baseline for comparison to the β-elimination reactions that result in PHB depolymerization. For PHB, the result of β-elimination is the production of the observed major products, crotonic acid and crotonyl-terminated oligomers,16,17,32,45 reaction 2 (major), and the formation of small quantities of isomeric isocrotonic acid and isocrotonyl-terminated oligomers,27,46 reaction 2 (minor).

melt. Reaction 4 is included in the present model studies to verify that it does not play a contributing role in PHB depolymerization in melt. It has been reported that the rates of reactions 2 and 3 are sensitive to the reactivity of the β-C−H bonds.27,33 This is evident by comparing the activation energy for reaction 1 with that for reaction 2, which is herein reported to have an average value of 165.3 ± 3.7 kJ mol−1. The reduction in activation energy between ethyl acetate and PHB in excess of 40 kJ mol−1 is the result of the increased acidity of the β-hydrogen induced by the neighboring carbonyl functionality. A number of experimental reports25,27,33 of PHB depolymerization have noted the presence of an autoacceleration effect. As herein defined, autoacceleration refers to an intrinsic increase in the rate of PHB depolymerization caused by a weakening of the PHB ester linkage. In these reports, the autoacceleration phenomenon has been attributed to the formation of carboxyl and crotonyl end groups formed at the chain ends of fractured PHB oligomers, Scheme 1. Scheme 1

In addition to reaction 2, which involves the transfer of a β-methylene hydrogen to the carbonyl oxygen, a second, minor β-elimination pathway exists that leads to the production of vinylacetic acid and vinylacetyl-terminated oligomers,27 through the transfer of the β-methyl hydrogen, reaction 3.

To date, the authors are aware of only one other report dealing with the modeling of PHB depolymerization,39 and this was limited to the calculation of activation energies relating to the β-elimination of PHB-like compounds. This work describes the combined efforts of experimental measurements and DFT modeling methods to describe the reactions and mechanisms at play in the conversion of PHB to propene toward a viable “one pot” conversion process.

■

PHB may pass through a minor depolymerization pathway, described as an intramolecular transesterification, that results in the formation of cyclic oligomers,26 typically trimers, as shown in reaction 4.

METHODS Experimental Section. Chemicals. Crotonic acid was purchased from Sigma-Aldrich with a purity of 98%. PHB was also purchased from Sigma-Aldrich (no purity claim). Stainless Steel Tube Reactor. All reactions were performed using a stainless steel tube reactor with a measured internal volume of 74 mL. Two shut-off valves were built into the top of the reactor; one attached to a pressure gauge allowed for measurement of the postreaction pressure, and the other allowed direct collection of product gases via gas sampling bags (SKC-West Inc., Houston, TX). A thermocouple inserted through the top of the reactor permitted measurement of the internal temperature. The reactant was added to an open glass tube that was then inserted into the reactor. The steel reactor was sealed and leak tested using an inert gas (He) to verify a good seal during the reaction period. Any air present was removed from the reactor by a pressurization and evacuation cycle with the inert gas. Reactions were performed by submerging the reactor in a fluidized sand bath for predetermined times and temperatures. No agitation of the mixture during the reaction was attempted. At the end of each experiment, the reactor was rapidly quenched in an ice water bath. For the depolymerization experiments, the reactor was rinsed with acetone to dissolve unreacted crotonic

These cyclic oligomers, however, have only been obtained in solution26 and have not been observed from depolymerization in B

DOI: 10.1021/acs.jpca.5b09246 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

the flow rate was 1.0 mL min−1. An injection volume of 10 μL was used. Retention time was converted into molecular weight by applying a calibration curve established using polystyrene standards of known molecular weight (from 1.3 × 106 to 3 × 103). The molecular weight distribution parameters were calculated using Cirrus GPC software (Varian Inc.). Theoretical. The calculations presented in this article were performed using the Gaussian09 suite of programs.47 The structures were fully optimized, and the energies and kinetic parameters of all species were obtained through use of the hybrid meta-GGA functional M06-2X of Truhlar and Zhao48 with the 6-311++G(2df,p) basis set. The M06-2X method has been shown to perform exceptionally well against databases involving thermochemistry (TC177), diverse barrier heights (DBH76), and noncovalent interaction energies (NCIE53) with mean errors of 5.4, 5.0, and 5.5 kJ mol−1, respectively.49 All transition states were identified as first-order saddle points, evidenced by the presence of a single imaginary frequency corresponding to the motion along the reaction coordinate. Further, intrinsic reaction coordinate (IRC) calculations with a step size of 0.1 amu0.5 bohr were carried out to establish a connection for each transition state with the appropriate reactants and/or products. Vibrational frequencies were modeled using the rigid rotor harmonic oscillator (RRHO) approximation. No effort was taken to include hindered rotor or anharmonic corrections. Kinetic rate constants and parameters where obtained according to

acid and its oligomers. The solution was subsequently analyzed via high-performance liquid chromatography (HPLC) and gel permeation chromatography (GPC). Solutions were vacuum filtered or centrifuged to determine the weight of undissolved solids, which were minimal. In the decarboxylation experiments, the final pressure and temperature were noted and the generated gas collected in a sampling bag for subsequent gas chromatography (GC) analysis. Any residual contents were treated the same as above for the depolymerization experiments. GC Analysis. Gas samples were analyzed by gas chromatography using an Agilent 7890A GC (Agilent Technologies, Palo Alto, CA) equipped with a flame ionization detector (FID) and a thermal conductivity detector (TCD). Sample compounds were separated using a GS-Q column (J&W, length 30 m, ID 0.53 mm). HP ChemStation software (Agilent Technologies, Santa Clara, CA) was used to quantify compounds. Each sample was manually injected at various volumes into an inlet split of 5:1 at an injection temperature of 250 °C. Helium served as the carrier gas at 10 mL min−1. The column oven temperature was increased at a rate of 20 °C min−1 from a temperature of 35 °C (held initially for 3 min) to 135 °C. The concentrations of propene and CO2 were quantified by use of external standards (50 ± 1% in a balance of CO2; Air Liquide, Longmont, CO). Various volumes of the mixture were injected into the GC to establish a six-point calibration curve. A secondary standard (Air Liquide, 3% propene and 3% CO2 in N2) was used to verify the initial calibration. The mole fraction of each gas was determined from the concentration and the volume of gas injected. The molar yield of each gas was calculated from this mole fraction multiplied by the total moles of gas produced divided by the initial moles of crotonic acid used in each reaction. HPLC Analysis. The crotonic acid and its oligomers formed by acid-catalyzed depolymerization of PHB and the amount of unreacted crotonic acid remaining after decarboxylation reactions were measured using an Agilent 1100 HPLC equipped with a photodiode array UV detector (Agilent Technologies) set to a wavelength of 210 nm. For the quantification of crotonic acid oligomers, the concentration was calculated using the peak area for all oligomers relative to the peak area of the crotonic acid standard. A Rezex RFQ Fast Acids column (100 × 7.8 mm, 8 μm particle size, Phenomenex) and Cation H+ guard column (BioRad Laboratories, Hercules, CA) operated at 85 °C were used to separate the crotonic acid and its oligomers present in the reaction solutions. The eluent was 0.01 N H2SO4 at a flow rate of 1.0 mL min−1. Samples and crotonic acid standards were filtered through 0.45 μm pore size nylon membrane syringe filters (Pall Corp.) prior to injection. The HPLC was controlled and data were analyzed using Agilent ChemStation software (rev. B.03.02). GPC Analysis. GPC analysis was performed for molecular weight determination of crotonic acid oligomers formed by acidcatalyzed depolymerization of PHB and unreacted crotonic acid remaining after decarboxylation reactions. Samples were dissolved in tetrahydrofuran (THF, Baker HPLC grade) at 1−2 mg mL−1 and then filtered (0.45 μm) prior to analysis. Analyses were performed using an Agilent 1050 HPLC with a photodiode array UV detector set to a wavelength of 220 nm to measure the concentration of the samples as they eluted from the columns. Three GPC columns (Agilent Polymer Laboratories, 300 × 7.5 mm) packed with polystyrene−divinylbenzene copolymer gel beads (10 μm diameter) having nominal pore diameters of 102, 103, and 104 Å connected in series in order of decreasing pore diameter were used. The eluent was THF, and

k(T ) = κ

kBT QTS exp[−(E TS − E R )/RT ] h QR

(eq 1)

where kB is Boltzmann’s constant, h is Planck’s constant, R is the ideal gas constant, T is temperature in Kelvin, QTS is the molecular partition function of the transition state, QR is the molecular partition function of the reactant, ETS and ER are the energies of the transition state and reactant, respectively, and κ(T) is the asymmetric Eckart tunneling factor.50−53 Transition state theory corrected for tunneling effects has been successfully used to calculate the rate coefficients for hydrogen abstraction reactions.54−59 The tunneling-corrected rate constants, κ(T), were then fit to a standard Arrhenius expression, eq 2, to obtain the kinetic rate parameters A and Ea k(T ) = A exp( −Ea /RT )

(eq 2)

All kinetic calculations are based on geometric and thermochemical quantities as established at the M06-2X/ 6-311++G(2df,p) level of theory. The performance of the employed computational methods in describing four-center and six-center proton-transfer transition states was established previously.44

■

RESULTS/DISCUSSION Thermal Conversion of PHB to Crotonic Acid. The thermal depolymerization of PHB has been studied over a range of temperatures (170−250 °C) and heating rates (1−50 °C min−1), which has led to a wide range of estimates of the activation energy Ea (111−550 kJ mol−1).41 The work by Nishida et al.41 represents a comprehensive review regarding the pyrolysis of PHB and subcategorizes the large range of activation energies into three groups. The first of these has a range of 111−140 kJ mol−1, calculated from the weight loss of PHB under C

DOI: 10.1021/acs.jpca.5b09246 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

Figure 1. PHB depolymerization experiments performed at 250 °C. (A) GPC chromatograms resulting from depolymerization experiments run over five different lengths of time. The peak corresponding to crotonic acid elutes at approximately 25 min. (B) The distribution of PHB oligomers produced after 30 min (red) compared to crotonic acid (black).

Figure 2. Production of (A) total oligomers and (B) crotonic acid obtained during PHB thermal depolymerization at various temperatures as detected by HPLC.

multiple constant heating rate methodologies.9,32,35,39 The second group is characterized by activation energies ranging between 178 and 247 kJ mol−1, as determined by isothermal degradation analyses based on changes in the molecular weight.16,17,19,35,45 The last group has the highest ranging activation energies, 235−550 kJ mol−1, which were calculated from weight loss data obtained from single constant heating routines.14,25,28,29,36 The ensuing discussion details both the nonisothermal experimental and isothermal computational efforts of the present work as a first step in understanding the mechanistic aspect of PHB depolymerization and the identification of possible experimental strategies to improve conversion of PHB to crotonic acid. Experimental Section. A kinetic analysis of the depolymerization of PHB to crotonic acid was performed by conducting experiments at temperatures between 200 and 250 °C and reaction times between 30 and 90 min, which are severe enough to depolymerize PHB but low enough to suppress further decomposition of the crotonic acid (99%. The loss of the tetramer occurs early ( 400 °C should be used.

Table 5. Kinetic Scheme Used to Model the Depolymerization of PHBa Tetramer Reactions bTETRAMER ↔ bTRIMER + CA bTETRAMER ↔ bDIMER + cDIMER bTETRAMER ↔ BHBA + cTRIMER bTETRAMER + ACIDb ↔ bTRIMER + CA + ACID bTETRAMER + ACID ↔ bDIMER + cDIMER + ACID bTETRAMER + ACID ↔ BHBA + cTRIMER + ACID Trimer Reactions bTRIMER ↔ bDIMER + CA bTRIMER ↔ BHBA + cDIMER cTRIMER ↔ cDIMER + CA cTRIMER ↔CA + cDIMER bTRIMER + ACID ↔ bDIMER + CA + ACID bTRIMER + ACID ↔ BHBA + cDIMER + ACID cTRIMER + ACID ↔ cDIMER + CA + ACID cTRIMER + ACID ↔ CA + cDIMER + ACID Dimer Reactions bDIMER ↔ BHBA + CA cDIMER ↔ CA + CA bDIMER + ACID ↔ BHBA + CA + ACID cDIMER + ACID ↔ CA + CA + ACID BHBA Decomposition BHBA ↔ CA + H2O a BHBA denotes 3-hydroxybutyric acid. bACID represents the total concentration of −C(O)OH groups present. This value is updated at each evaluation step to represent the new −C(O)OH groups formed.

Figure 4. Kinetic simulation involving the depolymerization of the PHB tetramer at 250 (A), 300 (B), 400 (C), and 450 °C (D), based on kinetic parameters derived using the M06-2X/6-311++G(2df,p) model chemistry. Stoichiometric conversion of the tetramer to crotonic acid is denoted in the upper right-hand box of each graph. Simulation time = 3600 (A), 1200 (B), and 3 s (C and D). The starting concentration of the PHB tetramer was set to 71.4 mg cm−3. H

DOI: 10.1021/acs.jpca.5b09246 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

lower molecular weight byproducts, relative to crotonic acid, were produced. Comparison of the UV spectra of crotonic acid with those of the byproducts indicated that they are likely to be chemically different from crotonic acid and thus unlikely to be crotonic acid oligomers. The kinetics of crotonic acid decarboxylation was following by quantifying the amount of CO2 produced as a function of time. GC analysis of the gaseous products from these decarboxylation experiments indicates that CO2 and propene constitute the majority of the product gas composition, with only minor contributions from CO, H2, methane, and ethane. The data obtained from the decarboxylation of crotonic acid at various temperatures between 300 and 400 °C are given in Table 6. Figure 6 depicts second-order kinetic analysis of the decarboxylation of crotonic acid based on the formation of CO2, represented as a conversion frequency, denoted 1 − CAconv (CAconv = [CO2]t/[CA]t=0). An Arrhenius analysis of the rate constants determined from the data in Figure 6 gives an activation energy of 146.9 kJ mol−1 and a pre-exponential factor of 8.3 × 108 s−1. Theoretical. The theoretical thermolysis behavior of crotonic acid has been discussed previously.44,63 These studies have indicated that crotonic acid thermally degrades primarily through decarboxylation, leading to the formation of CO2 and propene. Loss of CO2 may result from four-centered, unimolecular decomposition, with an activation energy of 277.4 kJ mol−1, reaction 11

The activation energy for the formation of crotonic acid from PHB has been determined from the model to be 169.4 kJ mol−1. This value is ∼41 kJ mol−1 higher than that measured using the current experimental method (129 kJ mol−1), which involves variable-temperature programming (i.e., a period of heating followed by a sustained reaction temperature). However, as the modeling of PHB degradation has been carried out isothermally, it is more reasonable to compare the calculated activation energy to experiments run isothermally.16,17,19,35,45 Activation energies for the isothermal depolymerization of PHB have been reported in the range of 178−182 kJ mol−1. Consequently, the nonisothermal result found herein compares favorably with similar results reported by the same groups in the range of 119−141 kJ mol−1. It can be concluded from the DFT modeling that PHB depolymerization strictly adheres to the random β-elimination paradigm throughout the entirety of the reaction. In addition, the model does not predict any autoacceleration to the depolymerization of PHB, either from the formation of carboxyl and crotonyl end groups or from acid catalysis. The autoacceleration effect measured by some experimental methods is likely the result of process methodologies (e.g., uneven heat transfer through the melt) and not intrinsic mechanistic phenomena. Additionally, the data in Figure 4 A and B indicate that the ideal temperature for depolymerization without crotonic acid decomposition ranges between 250 and 300 °C. Thermal Conversion of Crotonic Acid to Propene. Experimental Section. A thorough kinetic analysis of the decarboxylation of crotonic acid to propene and carbon dioxide was performed by conducting experiments at various temperatures (325−400 °C) and reaction times (30−90 min) severe enough to ensure decarboxylation of crotonic acid. GPC analyses, Figure 5, of the residues from decarboxylation experiments indicated that small amounts of both higher and

or through bimolecular self-reactions, which may pass through either a six- or eight-centered transition state, with activation energies of 205.4 and 141.0 kJ mol−1, respectively, reactions 12 and 13.

Figure 5. GPC chromatograms resulting from the decarboxylation of crotonic acid at 375 °C.

Table 6. CO2 Yields Resulting from the Decarboxylation of Crotonic Acida 325 °C

a

350 °C

375 °C

400 °C

time, (min)

CO2, (mol %)

time, (min)

CO2, (mol %)

time, (min)

CO2, (mol %)

time, (min)

CO2, (mol %)

20 40 65 80 100

7 19 32 ± 5b 37 42

10 15 20 30 60 90

9 15 24 36 58 ± 5b 67 ± 1b

10 15 20 30 45 60

23 39 51 59 ± 5b 76 76 ± 4b

6 8 10 15

37 52 66 ± 3b 81 ± 8b

CO2 yields represent the theoretical maximum production of propene. bValues obtained represent one standard deviation based on three replicates. I

DOI: 10.1021/acs.jpca.5b09246 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A Scheme 2

Figure 6. Second-order reaction kinetics for the decarboxylation of crotonic acid. The slopes of the straight lines, which represent linear fits to the experimental data, equal the rate of the bimolecular reaction, %conv−1 s−1.

catalysis (G). At elevated acid concentrations of crotonic acid, specifically that required for bimolecular chemistry, the acidcatalyzed pathway will dominate. The decarboxylation of crotonic acid has been kinetically modeled according to the scheme in Table 7, and the results are shown at 400 °C in Figure 7. The scheme shown in Table 7 is meant to be generic. Terms such as ACID, KETENE, and DIOL designate the state of any of the three acids during the reaction scheme. Whenever two ACID designations appear on the same side of a reaction arrow, the second ACID term is assumed catalytic. The model was run from 325 to 400 °C in order to calculate the Arrhenius parameters for the entire decomposition of crotonic acid, resulting in an activation energy of 147.5 kJ mol−1 and a pre-exponential factor of 2.8 × 108 s−1. An Arrhenius plot for both the experimental and theoretical decarboxylation of crotonic acid is shown in Figure 8. The model predicts (Figure 7) that crotonic acid reaches a crotonic acid-to-propene conversion efficiency of 78% at a reaction time of 15 min. This result compares favorably with that measured experimentally at the same reaction time, crotonic acid-to-propene = 74 ± 3%. In an effort to understand the mechanism of crotonic acid decomposition, the amount of propene formed directly from crotonic acid was compared to that derived from vinylacetic acid. The results of this comparison indicate that >99% of the propene formed is derived from vinylacetic acid, indicating that crotonic acid first isomerizes to vinylacetic acid and then decarboxylates to propene. Of the various isomerization pathways shown in Scheme 2, the bimolecular, acid-catalyzed conversion of crotonic acid to vinylacetic acid is expected to dominate under high acid conditions. Direct Thermal Conversion of PHB to Propene. The direct production of propene from PHB was studied experimentally and computationally at 350 and 400 °C. It has been shown, both experimentally and theoretically, that the PHB depolymerization is very rapid and that the decarboxylation of

The blue dotted−dashed line around the −ROH moiety of the acid catalyst in reaction 12 indicates that like crotonic acid itself (R = C(O)CHCHCH3), water (R = H) and similar protic molecules may also be able to catalyze the decomposition of crotonic acid. On the basis of reactions 11−13, the overall rate of crotonic acid decarboxylation will be determined by the balance of reaction 11 to reactions 12 and 13. At 300 °C, the concentration of crotonic acid at which the reaction transitions between uni- and bimolecular chemistry is ∼2 × 10−4 mg cm−3. As the temperature rises to 400 °C, the transitional concentration increases by 2 orders of magnitude to ∼2 × 10−2 mg cm−3. As a point of reference, typical concentrations of crotonic acid used in this study are ∼7 × 101 mg cm−3, indicating that crotonic acid concentrations are large enough for degradation reactions to be governed by bimolecular decomposition kinetics. The calculated decarboxylation activation energy for crotonic acid, as previously reported, is 141.0 kJ mol−1,63 which compares very well to that currently measured experimentally, 140.2 kJ mol−1. This correlation seems to indicate that reaction 13 acts as the primary decomposition route under bimolecular conditions, as concluded previously.63 However, crotonic acid represents only one isomer of a set of three (crotonic, isocrotonic, and vinylacetic) that are known to interconvert. The formation and subsequent decomposition of isocrotonic acid and vinylacetic acid represents alternative schemes leading to the production of CO2 and propene. Interestingly, vinylacetic acid can decompose unimolecularly to form propene with relatively low activation energy, 142.3 kJ mol−1. This value also agrees with that measured experimentally and raises the interesting possibility that crotonic acid decomposition requires initial isomerization to vinylacetic acid, as shown in the scheme below. The isomerization pathways considered in Scheme 2 include direct unimolecular conversion (A), conversion through the formation of common intermediates (B−F), and acid J

DOI: 10.1021/acs.jpca.5b09246 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A Table 7. Kinetic Scheme Used to Model the Thermal Decomposition of Crotonic Acid Decarboxylation ACIDa ↔ C3H6 + CO2 ACID + ACID (↔6)b C3H6 + CO2 + ACID ACID + ACID (↔8) C3H6 + CO2 + ACID ACID + H2O ↔ C3H6 + CO2 + ACID VAc (↔6) C3H6 + CO2 Dehydration ACID ↔ KETENEd + H2O ACID + ACID (↔8) KETENE + H2O ACID + H2O ↔ KETENE + H2O iCAe (↔6) KETENE + H2O Diol Formation ACID ↔ DIOLf ACID + ACID (↔8) DIOL + ACID ACID + H2O ↔ DIOL + H2O iCAe (↔6) DIOL Diol Dehydration DIOL ↔ KETENE + H2O DIOL + ACID (↔6) KETENE + H2O + ACID DIOL + ACID (↔8) KETENE + H2O + ACID DIOL + H2O ↔ KETENE + H2O + H2O Isomerization CA ↔ iCA CA ↔ VA iCA ↔ VA ACID + ACID ↔ ACID + ACID

Figure 8. Arrhenius plot depicting the experimental (blue) and modeled (red) decarboxylation of crotonic acid from 325 to 400 °C.

Table 8. Reaction Results Obtained from the Thermal Depolymerization of PHB and Subsequent Decarboxylation of Crotonic Acida substrate

temperature (°C)

pressureb (psig)

CO2 yields (mol %)

crotonic acid PHB crotonic acid PHB

350 350 400 400

23 ± 3 24 ± 1 76 ± 2 71 ± 7

15 ± 7 20 ± 2 74 ± 3 78 ± 6

Each reaction represents a minimum of five replicates and a reaction time of 15 min. bAutogenic pressure measured at 25 °C after thermal treatment. a

separately, these reaction conditions should ensure complete depolymerization of PHB and conversion of crotonic acid to propene and carbon dioxide in yields of ∼75%. The results of this study are shown in Table 8. Comparison of the data in Tables 6 and 8 shows that the conversion of either PHB or crotonic acid to propene at 350 and 400 °C is consistent, with conversions of ∼15 and ∼70 mol %, respectively. These results show that the decarboxylation of crotonic acid represents the rate-limiting process in the conversion of PHB to propene. As the depolymerization of PHB tends to progress readily at low temperatures (250−300 °C), efforts to improve decarboxylation rates should prove more beneficial to the development of a pathway leading from PHB to propene. Theoretical. A kinetic model incorporating the elementary steps of PHB tetramer depolymerization and crotonic acid decarboxylation was run at 400 and 450 °C with a simulation time of 15 min (900 s). The results are shown in Figure 9A and B. The depolymerization of the PHB tetramer to form crotonic acid is complete at ∼2 and ∼0.2 s for the simulations at 400 and 450 °C, respectively. On the scale shown in Figure 9, this rapid depolymerization is difficult to see (purple line) and is labeled “tetramer” for clarity. The associated rate of decarboxylation of crotonic acid is, by comparison, much slower. In an effort to identify a means of increasing the rate of decarboxylation, varying amounts of initial water were incorporated into the model. It was shown in a previous publication63 that water can act as a gas-phase catalyst and increase the rate of decarboxylation of organic acids. At 400 °C and with an initial water concentration of 1 × 103 times that of the maximum modeled crotonic acid concentration, an increase of 7 mol % in the production of propene was predicted. If the concentration of water is increased by a factor of 1 × 105, the conversion of PHB to propene is increased to ∼99 mol %. These concentrations of water are not feasible, indicating that water is not a practical gasphase catalyst.

a

ACID represents crotonic, isocrotonic, and vinylacetic acids with a rate expression defined for each or the combination of each. The second ACID term of each bimolecular expression is catalytic. bThe number next to the reaction arrow denotes the number of atoms in the transition state. cVinylacetic acid can decarboxylate via a six-center transition state. dKETENE represents the ketene dehydration product of crotonic, isocrotonic, and vinylacetic acids. eIsocrotonic acid can dehydrate or form the 1,1-diol intermediate through a six-center transition state. fDIOL represents the 1,1-diol product of crotonic, isocrotonic, and vinylacetic acids.

Figure 7. Kinetic simulation involving the decarboxylation of crotonic acid at 400 °C, based on kinetic parameters derived using the M06-2X/6-311++G(2df,p) model chemistry. Simulation time = 15 min (900 s). The starting concentration of crotonic acid was set to 13.5 mg cm−3.

crotonic acid to propene represents the rate-limiting conversion step of the overall process. Experimental Section. An analysis of the direct conversion of PHB to propene was performed at 350 and 400 °C, both at a reaction time of 15 min. On the basis of data obtained for PHB depolymerization and crotonic acid decarboxylation, considered K

DOI: 10.1021/acs.jpca.5b09246 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

Figure 9. Kinetic simulation involving the depolymerization of PHB tetramer and the subsequent decarboxylation of crotonic acid at 400 (A) and 450 °C (B), based on kinetic parameters derived using the M06-2X/6-311++G(2df,p) model chemistry. Stoichiometric conversion of the tetramer to propene is denoted in the upper right-hand box of each graph. Simulation time = 15 min (900 s). Starting concentration of the PHB tetramer was set to 74.1 mg cm−3.

■

■

CONCLUSIONS

ACKNOWLEDGMENTS Funding was provided from the DOE Bioenergy Technology Office (BETO) under Contract Number DE-AC3699GO100337. Part of this work was performed within the computational pyrolysis consortium, also funded by DOE-BETO under Contract Number DE-AC36-99GO100337. Additional support came from the Department of Energy (DOE) Office of Energy Efficiency and Renewable Energy (EERE) Postdoctoral Research Awards under the EERE Biomass Program administered by the Oak Ridge Institute for Science and Education (ORISE) for the DOE. ORISE is managed by Oak Ridge Associated Universities (ORAU) under DOE Contract Number DE-AC05-06OR23100. All opinions expressed in this paper are the authors’ and do not necessarily reflect the policies and views of DOE, ORAU, or ORISE. The authors would also like to acknowledge Dr. Luc Moens for useful discussions and advice of the potential chemistries involved in the depolymerization and decarboxylation reactions studied in this work.

In this study, the thermal conversion of PHB to crotonic acid and crotonic acid to propene has been explored to determine the feasibility of a direct conversion route from PHB to propene. The experimental results demonstrated that it is possible to achieve up to ∼75% conversion of PHB to propene, with limitations to the process arising from the rate-limiting decarboxylation step of crotonic acid. The kinetic models also identified decarboxylation as the rate-limiting step. The autoacceleration of ester bond cleavage arising from nearby carboxyl and crotonyl end groups is unclear, with differences in activation energy falling within the theoretical uncertainty of the currently modeled chemistry, ±6.3 kJ mol−1. This suggests that the observed autoacceleration of PHB depolymerization, if not an artifact of experimental methods, cannot be attributed to the formation of carboxyl and crotonyl end groups but to other reaction mechanisms, such as intermolecular catalysis via carboxyl groups. However, gas-phase depolymerization model results indicate that bimolecular, acidcatalyzed depolymerization pathways, although lower in energy by approximately 20 kJ mol−1, are insufficient to explain the autoacceleration effect, again indicating that the autoacceleration phenomenon is of nonmechanistic origins. This result may vary, however, if the magnitude of the pre-exponential factor varies significantly in melt from that in the gas-phase. Efforts to improve decarboxylation, including the addition of a catalyst, may make it possible to engineer an efficient route from PHB to propene. The present kinetic models demonstrate that water, and likely similar homogeneous catalysts, will be unable to increase the rate of conversion of PHB to propene in reasonable amounts. This being said, the model indicates that the decomposition of crotonic acid takes place through the initial isomerization of crotonic acid to vinylacetic acid, which more readily decarboxylates. Future work to improve crotonic acid-topropene conversion should focus on the isomerization of crotonic acid to vinylacetic acid.

■

■

REFERENCES

(1) Wan, V. Y. Propylene Production via Metathesis of Ethylene and Butenes; iHS: Menlo Park, CA, 2011. (2) McDaniel, M. P. Controlling Polymer Properties with the Phillips Chromium Catalysts. Ind. Eng. Chem. Res. 1988, 27, 1559−1564. (3) Polypropylene Market for Packaging, Automotive, Consumer Products, Electrical & Electronics, Construction and Other End-User Industries Global Industry Analysis, Size, Share, Growth, Trends and Forecast, 2013− 2019; Transparency Market Research: Albany, NY, 2013. (4) Tian, Z.; Qin, Z.; Dong, M.; Wang, G.; Wang, J. A Comparative Study on the Alkylation of Benzene with Propene over HBeta Zeolites in Different Phases. Catal. Commun. 2005, 6, 385−388. (5) Wang, G.; Qin, Z.; Liu, J.; Tian, Z.; Hou, X.; Wang, J. Critical Properties of the Reacting Mixture in the Alkylation of Benzene with Propene. Ind. Eng. Chem. Res. 2003, 42, 6531−6535. (6) Tabak, S. A.; Krambeck, F. J.; Garwood, W. E. Conversion of Propylene and Butylene over ZSM-5 Catalyst. AIChE J. 1986, 32, 1526− 1531. (7) Marchionna, M.; Di Girolamo, M.; Patrini, R. Light Olefins Dimerization to High Quality Gasoline Components. Catal. Today 2001, 65, 397−403. (8) Gonzalez, A.; Irusta, L.; Fernández-Berridi, M. J.; Iriarte, M.; Iruin, J. J. Application of Pyrolysis/Gas Chromatography/Fourier Transform Infrared Spectroscopy and TGA Techniques in the Study of Thermal Degradation of Poly (3-hydroxybutyrate). Polym. Degrad. Stab. 2005, 87, 347−354. (9) Ariffin, H.; Nishida, H.; Shirai, Y.; Hassan, M. A. Highly Selective Transformation of Poly[(R)-3-hydroxybutyric Acid] into trans-

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. L

DOI: 10.1021/acs.jpca.5b09246 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A Crotonic Acid by Catalytic Thermal Degradation. Polym. Degrad. Stab. 2010, 95, 1375−1381. (10) Johnson, K.; Jiang, Y.; Kleerebezem, R.; Muyzer, G.; van Loosdrecht, M. C. M. Enrichment of a Mixed Bacterial Culture with a High Polyhydroxyalkanoate Storage Capacity. Biomacromolecules 2009, 10, 670−676. (11) Albuquerque, M. G. E.; Torres, C. A. V.; Reis, M. A. M. Polyhydroxyalkanoate (PHA) Production by a Mixed Microbial Culture using Sugar Molasses: Effect of the Influent Substrate Concentration on Culture Selection. Water Res. 2010, 44, 3419−3433. (12) Jiang, Y.; Marang, L.; Kleerebezem, R.; Muyzer, G.; van Loosdrecht, M. C. M. Polyhydroxybutyrate Production from Lactate using a Mixed Microbial Culture. Biotechnol. Bioeng. 2011, 108, 2022− 2035. (13) Wang, F.; Lee, S. Y. Poly(3-hydroxybutyrate) Production with High Productivity and High Polymer Content by a Fed-Batch Culture of Alcaligenes latus under Nitrogen Limitation. Appl. Environ. Microbiol. 1997, 63, 3703−3706. (14) Liu, Q. S.; Zhu, M. F.; Wu, W. H.; Qin, Z. Y. Reducing the Formation of Six-Membered Ring Ester during Thermal Degradation of Biodegradable PHBV to Enhance its Thermal Stability. Polym. Degrad. Stab. 2009, 94, 18−24. (15) Morikawa, H.; Marchessault, R. H. Pyrolysis of Bacterial Polyalkanoates. Can. J. Chem. 1981, 59, 2306−2313. (16) Grassie, N.; Murray, E. J.; Holmes, P. A. The Thermal Degradation of Poly(-(d)-β-hydroxybutyric Acid): Part 1Identification and Quantitative Analysis of Products. Polym. Degrad. Stab. 1984, 6, 47−61. (17) Grassie, N.; Murray, E. J.; Holmes, P. A. The Thermal Degradation of Poly(-(d)-β-hydroxybutyric Acid): Part 2Changes in Molecular Weight. Polym. Degrad. Stab. 1984, 6, 95−103. (18) Ballistreri, A.; Garozzo, D.; Giuffrida, M.; Impallomeni, G.; Montaudo, G. Analytical Degradation: An Approach to the Structural Analysis of Microbial Polyesters by Different Methods. J. Anal. Appl. Pyrolysis 1989, 16, 239−253. (19) Kunioka, M.; Doi, Y. Thermal Degradation of Microbial Copolyesters: Poly(3-hydroxybutyrate-co-3-hydroxyvalerate) and Poly(3-hydroxybutyrate-co-4-hydroxybutyrate). Macromolecules 1990, 23, 1933−1936. (20) Gogolewski, S.; Jovanovic, M.; Perren, S. M.; Dillon, J. G.; Hughes, M. K. The Effect of Melt-Processing on the Degradation of Selected Polyhydroxyacids: Polylactides, Polyhydroxybutyrate, and Polyhydroxybutyrate-co-valerates. Polym. Degrad. Stab. 1993, 40, 313−322. (21) Abate, R.; Ballistreri, A.; Montaudo, G.; Impallomeni, G. Thermal Degradation of Microbial Poly(4-hydroxybutyrate). Macromolecules 1994, 27, 332−336. (22) Hoffmann, A.; Kreuzberger, S.; Hinrichsen, G. Influence of Thermal Degradation on Tensile Strength and Young’s Modulus of Poly(hydroxybutyrate). Polym. Bull. 1994, 33, 355−359. (23) Lehrle, R. S.; Williams, R. J. Thermal Degradation of Bacterial Poly(hydroxybutyric acid): Mechanisms from the Dependence of Pyrolysis Yields on Sample Thickness. Macromolecules 1994, 27, 3782− 3789. (24) Lehrle, R.; Williams, R.; French, C.; Hammond, T. Thermolysis and Methanolysis of Poly(β-hydroxybutyrate): Random Scission Assessed by Statistical Analysis of Molecular Weight Distributions. Macromolecules 1995, 28, 4408−4414. (25) Kopinke, F. D.; Remmler, M.; Mackenzie, K. Thermal Decomposition of Biodegradable PolyestersI: Poly(β-hydroxybutyric Acid). Polym. Degrad. Stab. 1996, 52, 25−38. (26) Melchiors, M.; Keul, H.; Höcker, H. Depolymerization of Poly[(R)-3-hydroxybutyrate] to Cyclic Oligomers and Polymerization of the Cyclic Trimer: An Example of Thermodynamic Recycling. Macromolecules 1996, 29, 6442−6451. (27) Kopinke, F. D.; Mackenzie, K. Mechanistic Aspects of the Thermal Degradation of Poly(lactic Acid) and Poly(β-hydroxybutyric Acid). J. Anal. Appl. Pyrolysis 1997, 40−41, 43−53.

(28) Galego, N.; Rozsa, C. Thermal Decomposition of some Poly(βhydroxyalkanoates). Polym. Int. 1999, 48, 1202−1204. (29) Li, S. D.; Yu, P. H.; Cheung, M. K. Thermogravimetric Analysis of Poly(3-hydroxybutyrate) and Poly(3-hydroxybutyrate-co-3-hydroxyvalerate). J. Appl. Polym. Sci. 2001, 80, 2237−2244. (30) He, J. D.; Cheung, M. K.; Yu, P. H.; Chen, G. Q. Thermal Analyses of Poly(3-hydroxybutyrate), Poly(3-hydroxybutyrate-co-3-hydroxyvalerate), and Poly(3-hydroxybutyrate-co-3-hydroxyhexanoate). J. Appl. Polym. Sci. 2001, 82, 90−98. (31) Lee, M. Y.; Lee, T. S.; Park, W. H. Effect of Side Chains on the Thermal Degradation of Poly(3-hydroxyalkanoates). Macromol. Chem. Phys. 2001, 202, 1257−1261. (32) Aoyagi, Y.; Yamashita, K.; Doi, Y. Thermal Degradation of Poly[(R)-3-hydroxybutyrate], Poly[ε-caprolactone], and Poly[(S)lactide]. Polym. Degrad. Stab. 2002, 76, 53−59. (33) Nguyen, S.; Yu, G.; Marchessault, R. H. Thermal Degradation of Poly(3-hydroxyalkanoates): Preparation of Well-Defined Oligomers. Biomacromolecules 2002, 3, 219−224. (34) Li, S. D.; He, J. D.; Yu, P. H.; Cheung, M. K. Thermal Degradation of Poly(3-hydroxybutyrate) and Poly(3-hydroxybutyrate-co-3-hydroxyvalerate) as Studied by TG, TG−FTIR, and Py−GC/MS. J. Appl. Polym. Sci. 2003, 89, 1530−1536. (35) Kim, K. J.; Doi, Y.; Abe, H. Effects of Residual Metal Compounds and Chain-end Structure on Thermal Degradation of Poly(3hydroxybutyric Acid). Polym. Degrad. Stab. 2006, 91, 769−777. (36) Carrasco, F.; Dionisi, D.; Martinelli, A.; Majone, M. Thermal Stability of Polyhydroxyalkanoates. J. Appl. Polym. Sci. 2006, 100, 2111− 2121. (37) Kawalec, M.; Adamus, G.; Kurcok, P.; Kowalczuk, M.; Foltran, I.; Focarete, M. L.; Scandola, M. Carboxylate-Induced Degradation of Poly(3-hydroxybutyrate)s. Biomacromolecules 2007, 8, 1053−1058. (38) Kim, K. J.; Doi, Y.; Abe, H. Effect of Metal Compounds on Thermal Degradation Behavior of Aliphatic Poly(hydroxyalkanoic Acid)s. Polym. Degrad. Stab. 2008, 93, 776−785. (39) Ariffin, H.; Nishida, H.; Shirai, Y.; Hassan, M. A. Determination of Multiple Thermal Degradation Mechanisms of Poly(3-hydroxybutyrate). Polym. Degrad. Stab. 2008, 93, 1433−1439. (40) Ariffin, H.; Nishida, H.; Shirai, Y.; Hassan, M. A. Anhydride Production as an Additional Mechanism of Poly(3-hydroxybutyrate) Pyrolysis. J. Appl. Polym. Sci. 2009, 111, 323−328. (41) Nishida, H.; Ariffin, H.; Shirai, Y.; Hassan, M. A. Precise Depolymerization of Poly(3-hydoxybutyrate) by Pyrolysis. In Biopolymers; Elnashar, M., Ed.; InTech: Rijeka, Croatia, 2010; pp 369−386. (42) McMillen, D. F.; Lewis, K. E.; Smith, G. P.; Golden, D. M. Laserpowered Homogeneous Pyrolysis. Thermal Studies under Homogeneous Conditions, Validation of the Technique, and Application to the Mechanism of Azo Compound Decomposition. J. Phys. Chem. 1982, 86, 709−718. (43) Keller, P. J.; Fetting, F. Kinetische Untersuchung der Thermischen Nachverbrennung von Essigsäureethylester in einem Strömungsrohr-Reaktor. Chem. Ing. Tech. 1982, 54, 1079−1079. (44) Clark, J. M.; Nimlos, M. R.; Robichaud, D. J. Comparison of Unimolecular Decomposition Pathways for Carboxylic Acids of Relevance to Biofuels. J. Phys. Chem. A 2014, 118, 260−274. (45) Grassie, N.; Murray, E. J.; Holmes, P. A. The Thermal Degradation of Poly(-(d)-β-hydroxybutyric Acid): Part 3The Reaction Mechanism. Polym. Degrad. Stab. 1984, 6, 127−134. (46) Ballistreri, A.; Montaudo, G.; Garozzo, D.; Giuffrida, M.; Montaudo, M. S. Microstructure of Bacterial Poly(β-hydroxybutyrateco-β-hydroxyvalerate) by Fast Atom Bombardment Mass Spectrometry Analysis of the Partial Pyrolysis Products. Macromolecules 1991, 24, 1231−1236. (47) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, revision B.01; Gaussian, Inc: Wallingford, CT, 2009. (48) Zhao, Y.; Truhlar, D. The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two M

DOI: 10.1021/acs.jpca.5b09246 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A New Functionals and Systematic Testing of Four M06-class Functionals and 12 Other Functionals. Theor. Chem. Acc. 2008, 120, 215−241. (49) Zhao, Y.; Truhlar, D. G. Density Functionals with Broad Applicability in Chemistry. Acc. Chem. Res. 2008, 41, 157−167. (50) Steinfeld, J. L.; Francisco, J. S.; Hase, W. L. Chemical Kinetics and Dynamics, 2nd ed.; Prentice Hall: New York, 1999. (51) Eckart, C. The Penetration of a Potential Barrier by Electrons. Phys. Rev. 1930, 35, 1303−1309. (52) Johnston, H. S.; Heicklen, J. J. Photochemical Oxidations: II. Methyl Iodide. J. Phys. Chem. 1962, 66, 532−533. (53) Louis, F.; Gonzalez, C. A.; Huie, R. E.; Kurylo, M. J. An ab Initio Study of the Kinetics of the Reactions of Halomethanes with the Hydroxyl Radical. 2. A Comparison between Theoretical and Experimental Values of the Kinetic Parameters for 12 Partially Halogenated Methanes. J. Phys. Chem. A 2000, 104, 8773−8778. (54) Chandra, A. K.; Uchimaru, T. J. Kinetics of Hydrogen Abstraction from Chloromethanes by the Hydroxyl Radical: A Computational Study. J. Phys. Chem. A 2000, 104, 8535−8539. (55) Korchowiec, J.; Kawahara, J. I.; Matsumura, K.; Uchimaru, T. J.; Sugie, M. Hydrogen Abstraction from Methane and Hydrofluoromethanes by •OH Radical: Modified GAUSSIAN-2 Study. J. Phys. Chem. A 1999, 103, 3548−3553. (56) Zhang, M.; Lin, Z.; Song, C. Comprehensive Theoretical Studies on the CF3H Dissociation Mechanism and the Reactions of CF3H with OH and H Free Radicals. J. Chem. Phys. 2007, 126, 034307. (57) Kaliginedi, V.; Ali, M. A.; Rajakumar, B. Kinetic Parameters for the Reaction of Hydroxyl Radical with CH3OCH2F (HFE-161) in the Temperature Range of 200−400 K: Transition State Theory and ab Initio Calculations. Int. J. Quantum Chem. 2012, 112, 1066−1077. (58) Ali, M. A.; Rajakumar, B. Computational Study on OH Radical Reaction with CHF2CHFCHF2 (HFC-245ea) Between 200 and 400 K. Int. J. Chem. Kinet. 2011, 43, 418−430. (59) Ali, M. A.; Upendra, B.; Rajakumar, B. Kinetic Parameters of Abstraction Reactions of OH Radical with Ethylene, Fluoroethylene, cisand trans-1, 2-Difluoroethylene and 1, 1-Difluoroethylene, in the Temperature Range of 200−400K: Gaussian-3/B3LYP Theory. Chem. Phys. Lett. 2011, 511, 440−446. (60) Bigley, D. B. 742. Studies in Decarboxylation. Part I. The Mechanism of Decarboxylation of Unsaturated Acids. J. Chem. Soc. 1964, 3897−3899. (61) Bigley, D. B.; Thurman, J. C. 1155. Studies in Decarboxylation. Part II. Kinetic Evidence for the Mechanism of Thermal Decarboxylation of βγ-Unsaturated Acids. J. Chem. Soc. 1965, 6202−6205. (62) Hoffmann, R. The Norcaradiene - Cycloheptriene Equilibrium. Tetrahedron Lett. 1970, 11, 2907−2909. (63) Clark, J. M.; Nimlos, M. R.; Robichaud, D. J. Bi-Molecular Decomposition Pathways for Carboxylic Acids of Relevance to Biofuels. J. Phys. Chem. A 2015, 119, 501−516.

N

DOI: 10.1021/acs.jpca.5b09246 J. Phys. Chem. A XXXX, XXX, XXX−XXX