Kinetic and mechanistic aspects of myrcene production via thermal-induced β-pinene rearrangement

J. Anal. Appl. Pyrolysis 83 (2008) 26–36

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Kinetic and mechanistic aspects of myrcene production via thermal-induced b-pinene rearrangement A. Stolle a, W. Bonrath a,b, B. Ondruschka a,* a b

Institute of Technical Chemistry and Environmental Chemistry, Friedrich-Schiller-University Jena, Lessingstr. 12, D-07743 Jena, Germany R&D Chemical Process Technology, DSM Nutritional Products, P.O. Box 2676, CH-4002 Basel, Switzerland

A R T I C L E I N F O

A B S T R A C T

Article history: Received 3 March 2008 Accepted 4 June 2008 Available online 12 June 2008

The production of myrcene (2) is an industrially important reaction because 2 is a building block for the syntheses of various fine chemicals. The production of 2 through rearrangement of b-pinene (1) is a process carried out at elevated temperatures in flow-type reactors made of quartz or stainless steel with residence times below 1 s. Herein the thermal rearrangements of 1 and 2 are investigated in a quartz flow-type reactor using N2 as carrier gas. Experiments were carried out in a temperature range of 300– 600 8C with residence times of 0.5–2.5 s. Results showed that the main product 2 can be formed with a maximal overall yield of 77%. Consecutive reactions of 2 lead to a decrease in yield due to the formation of isomerization products. Neither the formation of gaseous or lower molecular products was observed nor polymerizations occurred in the temperature range investigated. Kinetic experiments allow for the calculation of activation parameters for the initial reactions. A reaction model of competitive parallel first-order reactions describes well the thermal reaction network of C10H16 hydrocarbons based on 1. ß 2008 Elsevier B.V. All rights reserved.

Keywords: Activation parameters Diradicals Cyclobutane fragmentation Kinetic model Pericyclic reactions

1. Introduction Acid-catalyzed as well as thermally initiated rearrangements of monoterpenes play a major role in industrial-scale synthesis of fine chemicals (e.g. flavors, fragrances, pharmaceuticals) [1–6]. Using aor b-pinene (1) as starting materials for chemical syntheses is advantageous considering sustainability and environmental impacts, because these are widely available and can be obtained from natural resources by distillation of turpentine or crude sulphate turpentine (CST) [1–3]. CST is a side product from pulp and paper industry. Syntheses based on pinane-type monoterpenes (e.g. 1, a-pinene) often require a thermally induced isomerization step yielding acyclic trienes (alloocimene, myrcene (2)) [7–15]. 2 itself is an important starting material for the commercial production of terpenic alcohols (e.g. geraniol, nerol) and of flavoractive compounds (e.g. citral, menthol, ionones) being initial starting molecules for syntheses of vitamins A and E [16–19]. The most commonly used method for production of 2 is the thermally induced rearrangement of 1 in a temperature range of 450–600 8C [7,11–14,20–26]. Under these conditions, different side-reactions occur leading to the formation of limonene (3) and c-limonene (D-1(7),8-p-menthadiene; 4), as shown in Scheme 1

[9,11,21–23]. Consecutive reactions of the target compound 2 lead to the formation of further isomerization products (5, 6; Scheme 1) [11–14,23] and coke [24] resulting in a decreased selectivity for 2. Another possible synthetic route to 2 is based on the reaction of ethyl acetoacetate with isoprene bromide yielding b-keto esters which can be converted into 2 via Wittig reaction [18,19,27]. However, the pyrolysis route using 1 as substrate is the more commonly used variant. Myrcene (2) is an industrially important intermediate but there is little data found in literature dealing with the consecutive reactions of 2 [23–25,28]. In the current work the thermal rearrangement of 1 and also of 2 is investigated using a flowtype reactor. The reactions described in Scheme 1 are also interesting from a kinetic point of view. Whereas for the initial reaction of 1–4 kinetic data have been published already [12– 14,22,26,29] the side-reactions of 2 have not been investigated by means of kinetic measurements. Therefore, kinetic data (Arrhenius and Eyring parameters) are presented allowing for the kinetic modeling of the initial reactions within the pyrolysis reaction of 1. 2. Experimental 2.1. Materials

* Corresponding author. Tel.: +49 3641948400; fax: +49 3641948402. E-mail address: [email protected] (B. Ondruschka). 0165-2370/$ – see front matter ß 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jaap.2008.06.001

(–)–b-Pinene (1; purity: ca. 99%, enantiomeric excess (ee): 97%), and myrcene (2; purity: ca. 90%) were purchased from Fluka

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the corrected peak areas from the GC-analyses (Eq. (1)). Conversions of 1 and 2 (Xi) were calculated according to Eq. (2), wherein [i] are the corrected and normalized peak areas for 1 or 2. Eq. (3) used for calculation of the selectivities (Sj) for the formation of the primary formed isomerization products (2–4). S2 calculated according to Eq. (3) did not include products formed consecutively. S3 and S4 describe the initial reaction routes starting from 1, whereas S2 describes the overall S including loss of 2 due to side reactions. Therefore, Sp2 (Eq. (4)) considers these reactions (Scheme 1) and allows for the description of S for the formation of 2 according to S3 and S4. Every data-point presented herein representing either Yi, Xi, or Si represents mean values of at least two individual pyrolysis experiments. Y i ¼ ½i;

i ¼ 16

(1)

Scheme 1. Products within the reaction network based on b-pinene (1).

and were used without further purification. Purity was determined by capillary gas chromatography. Myrcene (2) used for these studies comprise of 90% 2 and 10% c-limonene (4). Pyrolysis experiments reveal that the content of 4 remains constant over the whole temperature range investigated herein.

Xi ¼ 1 

Si ¼

Yi ½i ¼ ; X1 X1

Sp2 ¼ 2.2. Analyses Analyses were carried out with a 6890 Series GC from Agilent Technologies. Products were identified by comparing retention times and mass spectra with those of pure reference compounds. GC-FID: HP 5, 30 m  0.32 mm  0.25 mm, H2: 5 psi, program: 35 8C (hold 1 min), 4 K min1 up to 80 8C, 4.5 K min1 up to 90 8C, 35 K min1 up to 280 8C (hold 3 min), injector temperature: 250 8C, detector temperature: 280 8C. The enantiomeric excess of the optical active primary products (3, 4) and of residual 1 was determined with a permethylated bcyclodextrine column. Analyses were carried out in a HP 6890: Supelco Beta-DexTM 120, 30 m  0.25 mm  0.25 mm, H2: 12 psi, program: 68 8C (hold 13.12 min), 25 K min1 up to 240 8C (hold 10 min), split ratio: 3.4, injector temperature: 240 8C, detector temperature: 280 8C. 2.3. Pyrolysis experiments Dilution gas pyrolyses were carried out in an electrically heated quartz tube of 500 mm length and with a pyrolysis zone of an approximate length of 200 mm, using the apparatus reported in Ref. [11]. Temperatures (T) were regulated with thermocouples and in addition the actual T was measured inside the reactor. The Tgradient vertical to the flow direction is below 20 K. The T-gradient was measured on the maximum T (800 8C) and the maximal flowrate (1.2 L min1 N2; t: 0.32 s). The discrepancies between adjusted T and measured T inside the reactor are due to heat transfer phenomena. In all experiments, oxygen-free nitrogen with a purity of >99.999% was used as the carrier gas. The substrates (15 mL) were introduced onto a quartz ladle at the top part of the pyrolysis apparatus using a glass syringe (50 mL) and carried along with the nitrogen stream into the reactor. Vaporization of the starting material was supported by heating the ladle to 200 8C with a hot blast. Pyrolysis products were collected in a cold trap (liquid nitrogen) and were dissolved in 1.5 mL of ethyl acetate. The liquid products obtained were analyzed by GC-FID and GC– MS adding 5 mL hexadecane as internal standard. Comparison of both residence times and mass spectra with those of reference compounds allowed for identification of the main products (2–6). Yields Yi of reaction products (2–6) and residual 1 are expressed by

½i ; 100

i ¼ 1; 2

(2)

i ¼ 2; 3; 4

(3)

100  ð½1 þ ½3 þ ½4Þ X1

(4)

2.4. Kinetic experiments The kinetic experiments were carried out in temperature ranges from 635 to 708 K and of 743–783 K for 2 and 3, respectively. Variation of the carrier gas velocity in a range from 0.4 up to 1.2 L min1 N2 allows for the modulation of the average residence time (t). Calculations of t were accomplished according to Eq. (5), wherein VR is the reactor volume, VE the substrate flow rate, VN 2 the carrier gas flow rate, TR and Trt are the reactor and ambient temperatures, both in K.

t¼

VR ðV˙ E þ V˙ N2 ÞT R =T rt

(5)

Studying the influence of the surface-to-volume-ratio (S/V) on the product selectivity as well as on the activation parameters another quartz tube (insert I or II; Table 1) was placed inside the reactor. Therefore, the actual reactor geometry was similar to a hollow cylinder. Calculated reactor volumes (VR), S/V, and t based on a reaction zone with an approximately length of 200 mm. Within this zone the T-gradient in flow-direction was lower than 10 K. Pyrolysis experiments used for calculation of rate constants were individually carried out three times. For calculation of the parameters all experimental results were considered. If outliers were present within a data set the corresponding experiments were redone individually four times and the data were recalculated considering the additional experiments. 3. Results and discussion It is well known, that the thermal isomerization of b-pinene (1) primarily leads to the formation of myrcene (2), limonene (3) and C-limonene (4), according to Scheme 1. Side reactions of 2 (enecyclization, formation of dimers) contribute to the loss of the main target product at either higher temperatures (T) or longer residence times (t). Therefore, two processes have to be considered investigating the production of 2 via rearrangement of 1: (a) the primary biradical reaction pathway leading to 2–4, and (b) consecutive reactions of 2.

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Table 1 Properties of the pyrolysis reactor depending on the quartz inserts used

(

)

Scheme 2. Diels–Alder dimerization products of myrcene (2).

Entry

dI (mm)a

dA (mm)b

VR (mL)c

SR (cm2) d

Scs (cm2) e

S/V (cm1) f

No insert Insert I Insert II

15.2 15.2 15.2

– 6.2 9.1

36.1 30.0 23.0

95.2 134.1 152.4

1.80 1.50 1.15

2.64 4.47 6.61

a b c d e f

Inner reactor diameter. Outer diameter of the quartz insert. Reactor volume. Surface area of the reactor. Cross-sectional area of the reactor. Surface-to-volume-ratio (SR/VR).

3.1. Thermal behavior of b-pinene and of myrcene Fig. 1 illustrates the temperature dependency of various parameters important for the description of the title reaction presented in Scheme 1. Obviously, 1 is converted within a narrow T-range (350–450 8C) yielding 2 as the main product with an overall selectivity (S2; Eq. (3)) of approximately 76%. As the conversion of 1 (X1; Eq. (2)) reaches its maximum, S2 drops in favor of the formation of consecutive products (cp; e.g. 5, 6). 2 itself decomposes at higher T starting at 475 8C. Within the T-range investigated herein (300–600 8C) neither the formation of coke and other higher molecular products was observable, nor products with a molecular weight smaller than 136 g mol1 were detected in the product mixtures. In contrast to previous studies at temperatures below 600 8C no decomposition of 2–4 occurred yielding lower molecular weight products (e.g. isoprene) [24,25]. The formation of myrcene dimers via intermolecular Diels–Alder reaction took place only when T was above 625 8C leading to products presented in Scheme 2 in amounts below 5% [30,31]. Obviously, dilution with N2 as carrier gas suppresses bimolecular reactions leading to dimers and higher molecular products (coke).

Fig. 1. Temperature dependency (T) of X1, S2, and of the conversion of myrcene (2) for pyrolysis of 2 (X2) and calculated from pyrolysis experiments of 1 (X2 (1); Xi and S2 calculated according to Eqs. (2) and (3); mean values of at least two experiments; 15 mL starting material, carrier gas: N2, flow rate: 1.0 L min1, t: 0.47–0.72 s, S/V: 6.61 cm1).

Because of these facts the conversion of 2 (X2, Fig. 1) in the temperature range investigated (400–600 8C) yields C10H16 isomers exclusively (5, 6; Scheme 1). Whereas products with structures similar to 5 are known from various analogous compounds of 2 (b-citronellene, isocitronellene, linalool; Table 2), substituted products with cycloheptene skeleton (6) yield from the rearrangement of 2 only [11,23,28]. Studying the thermal rearrangement of various 1,6-dienes with hydrogen in aposition, the generation of cyclopentane-type products is known to occur [12–14,28,32–41]. For instance, the thermal treatment of linalool yields 1,2-dimethyl-3-isopropenylcyclopentanol (Table 2) [28,38], and consecutive reactions of the acyclic main product from the pyrolysis of nopinone lead to the formation of 2-methyl-3isopropenylcyclopentanone (Table 2) [12,13,35,36]. The cyclization of 1,7-dienes with a-hydrogen leads to the formation of substituted cyclohexenes, whereas the ring-formation of systems with fused rings failed [32,33]. The cyclization proceeds via concerted ene-type reaction (Table 2). As evident from Fig. 1, the selectivity for the formation of 2 (S2; Eq. (3)) remains constant until 1 is completely converted (X1). Exceeding of this point by increasing T leads to an obvious decline in S2 yielding isomerization products (5, 6). Fig. 2a depicts the dependency of Sp2 (Eq. (4)) to X1 (Eq. (2)) indicating that the initial formation is essentially independent from X1 in the range of 20% < X1 < 90%. The mean values for the selectivities expressing the initial formation of 2–4 from 1 are listed in Table 3. Conversions of lower than 20% were not considered calculating the mean values because these resulted in signals below the detection limit of the GC-FID (especially 4). On the other hand, for conversions higher than 90% 2 started to isomerizes, forming products 5 and 6, and these values were not included for averaging either. The listed medians (Table 3) indicate that pyrolysis of 1 yields the primary formed products 2–4 with selectivities of 82.7%, 12.7%, and 4.6%, respectively. It is also shown that the covariances for all reaction routes are low. Investigating the influence of the average residence time (t; Eq. (5)) no statistically significant dependencies were observed. Product distribution for the initially formed products (2– 4) found herein are in accordance with results from previous studies [9,11,22,26,42]. In addition to the influence of X1 on Sp2 (Fig. 2a and Table 3) the relation between T and Sp2 (Fig. 2b) was also investigated. Fig. 2b clearly indicates that higher temperatures applied for pyrolysis of 1 lead to the formation of product mixtures with higher Sp2. The coherence found between Sp2 and T is nearly linear and seemed to be independent from S/V (Fig. 2b). The calculation of the average values depending on S/V seems to indicate that the higher the S/V-value the higher are the corresponding Sp2 as shown in Table 3. However, the calculated average values are within the error limits expressed by the covariances. Results reveal that the selectivity for the initially formed 2 (Sp2; Eq. (4)) seems to be independent form X1 and t, whereas higher T are shown to be advantageous for the formation of 2. S/V seems to have little influence on the initial reactions via the formed biradical pictured in Scheme 1. Investigations exemplified for Sp2 were accomplished for the selectivity of 2 considering consecutive reactions (S2; Eq. (3)) also with the same results, S2 showing no clear dependence neither to X1 and T, nor to t or S/V.

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Table 2 Compounds which form substituted cyclopentanes via ene-cyclization according to the formation of 5 from myrcene (2)

(

)

Scheme

Bicyclusa

1,6-Diene

R1

R2

A A A B B B B B

b-Pinene (1) Nopinone Verbanone – Norpinane Pinane Pinane 2-pinanol

Myrcene (2) 7-Methylocta-1,6-dien-3-one 5,7-Dimethylocta-1,6-dien-3-one 1,6-Octadiene 7-Methylocta-1,6-diene b-Citronellene Isocitronellene Linalool

CH2 O O H CH3 CH3 CH3 CH3

H H CH3 H H H CH3 H

a

R3

H H CH3 H CH3

R4

Reference

H H H H OH

[12,23,28] [12,35,36] [36,39] [33] [32] [32,34,40] [41] [28,38]

Pinane-type precursor compound from which the listed 1,6-diene can be generated from via thermal rearrangement.

Fig. 2. Dependency of overall myrcene selectivity (Sp2; according to Eq. (4)) from conversion of b-pinene (X1; (a)) and reaction temperature (T; (b)) for different surface-tovolume-ratios (S/V, cf. Table 1; 15 mL starting material, carrier gas: N2, flow rate: 0.4–1.2 L min1, t: 0.49–2.52 s).

Due to the fact that neither a-pinene (7) nor camphene was found in the mixtures of trapped products in every experiment side reactions such as intramolecular double-bond shifts could be ruled out. Acid-sites in a reactor or catalysts with acidic centers are able to isomerize 1 yielding 7 [43], and further reactions would lead to the formation of camphene and similar products via non-classical carbenium-ions formed initially by H+-addition [44–47]. Table 4 lists the ee for both 1 and the optical active products formed from 1 (3, 4). It is obvious that the ee found initially for 1 (97%) remains constant while increasing T (X1, respectively). Monocyclic products primarily yielded from pyrolysis of 1 have comparable ee-values

suggesting that the process leading to their formation is highly enantiospecific. Concordantly, to previous studies it is believed that the formation of 2–4 from pyrolysis of 1 proceeds via biradical transition states (Scheme 1) [21,42]. Scheme 3 pictures the initially formed biradical for both 1 and 7, whereby all chiral centers have Sconfiguration. Whereas in case of 1 the resonance-stabilized biradical is optically active, the optical activity is lost for 7 because the transition state has a mirror plane (point symmetry group: CS). Therefore, pyrolysis of ()-7 as well as of (+)-7 yields a racemic mixture of 3 (dipentene) [10,21,42]. The mechanistic routes described in Scheme 3 leading to the formation of 3 and 4 in case of 1 are [1,7]-H and [1,5]-H-shifts, respectively [11].

Table 3 Mean values for the selectivities (Si, Sp2) for the formation of the primary formed products from thermal isomerization of b-pinene (1; 15 mL starting material, carrier gas: N2, flow rate: 0.4–1.2 L min1, t: 0.49–2.52 s; based on experiments with X1: 20% < X1 < 90%)

Table 4 Enantiomeric excess (ee) for ()-1 and the optical active products (3, 4) depending on reaction temperature (T) and conversion of 1 (X1)a

Entrya

Si (%) b

Comment

ee (%)

Sp2 Sp2 Sp2 Sp2 S3 S4

82.7  0.9 82.3  1.0 82.6  0.9 83.1  0.9 12.7  0.8 4.6  0.5

c

a b c

S/V: 2.64 cm1 S/V: 4.47 cm1 S/V: 6.61 cm1 c

Entry 1 2 3

T (8C) 375 400 425

t (s)b 0.63 0.61 0.59

X1 (%) 9 33 72

()-1c 96 96 96

()-3 – 98 97

d

c

Calculated according to Eqs. (3) and (4). Variances calculated based on 95% certainty limits using t-distribution. Mean values from experiments with different S/V (cf. Table 1).

a b c d

15 mL ()-1 as starting material; carrier gas: N2; flow rate: 1.0 L min1. Calculated using Eq. (5). Initial ee: 97%. X1 to low.

()-4 –d 98 97

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concentration (1, 2). Due to the fact that for parallel first-order reactions the sum of the rate constants for each reaction channel leading to product P (kP) equals the overall rate constant for the disappearance of the starting material (kd; Eq. (7)) allows in combination with the mass balance (Eq. (8)) for setting up the general equation describing the formation of P (Eq. (9)). Determination of various rate constants by performing kinetic pyrolysis experiments at various temperatures allows for the calculation of both Arrhenius (Ea, log10A) as well as Eyring parameters (DH#, DS#) expressed by Eqs. (10) and (11), respectively. Calculation of the Arrhenius and Eyring parameters was performed by simply plotting ln kT or ln (kT T1), respectively, against inverse reaction temperature T1 in K. d½A ¼ kd ½A ) ½A ¼ ½A0 ekd t dt X kP kd ¼ ½A0 þ Scheme 3. Formation of limonene (3) and c-limonene (4) from b-pinene (1; A) and dipentene (racemic 3) from a-pinene (7, B).

3.2. Kinetic considerations

X

½P0 ¼ ½A þ

d½P kP ½A0 ¼ kP ½A ) ½P ¼ ½P0 þ ð1  ekd t Þ dt kd kT ¼ A eEa =RT

For calculation of the residence times (t) and rate constants (k), it had to be ensured that no gaseous products were formed and that the liquid pyrolysis products were completely condensed. The reaction products did not undergo further degradation to lower molecular weight products and were able to be trapped completely in the temperature range in which the conversion of the starting material (1, 2) increases linearly with increasing temperature. A high carrier gas to substrate ratio (e.g. 3000 at 500 8C) suppresses bimolecular reactions leading to dimers, oligomers and coke. Cycloreversion and ene-reactions are monomolecular reactions, therefore, first-order kinetics were chosen to describe the rearrangements of both bicyclic and acyclic products. Kinetic experiments with 1 were carried out in order to describe the rearrangements of the bicyclic starting material to the primarily formed products (2–4). The corresponding concentrations for compounds resulting from consecutive reactions of 2 (5, 6) were added to the respective primarily formed product (2). Studying the thermal rearrangement of 2 allows for the estimation of the rate constant for the isomerization of the acyclic substrate. The parallel first-order reaction model was chosen to describe the thermal behavior of the compounds investigated [12–14]. General rate equations used for the description of disappearance of starting materials (kd) are given in Eq. (6), wherein [A] is the substrate Table 5 Kinetic dataa for the gas-phase isomerization reactions of b-pinene (1) and myrcene (2; VR: 23.0 mL, S/V: 6.61 cm1; cf. Table 1)

X ½P ¼ 1

kT ¼

kB T ðDH T DSÞ=RT e h

(6) (7) (8) (9) (10) (11)

The calculated activation parameters for the most important reactions with respect to the formation of myrcene (2) from 1 are listed in Table 5 for S/V being 6.61. Comparison of the energyrelated values (Ea, DH#) indicates that the formation of the biradical from 1 (k1), the formation of 2 and 4 (k2, k4) afford the same Ea or DH# for its course, whereas the formation 3 (k3) and the loss of 2 due to side reactions (k5) need less energy. This would suggest that the pyrolysis of 1 would yield 3 as main product. Consideration of log10A allows for the unequivocal conclusion that the formation of 2 (k2) is the most dominant reaction in the whole network based on pyrolysis of 1, because the frequency factor is two magnitudes of order higher as for k3 and k4. The value log10A can be interpreted as probability for the formation of a transition state and the higher log10A the higher the desired probability [48]. Focusing on the activation entropies (DS#) listed in Table 5 obvious differences points the reader’s eyes. The equality for all values in case of k1 and k2 points out the predominance of these reactions. Log10A around 14.0 and DS# ranging from 10 to 10 J K1 mol1 are clear indicators for a normal transition state (TS) the reaction passes through [48,49]. Those TS are characterized by rotational and torsional degrees of freedom similar to those of the initial molecules. Hence, the formation of a biradical pictured in Scheme 1 and reported as an intermediate for the formation of 2 in literature [11–13,21,23–25] yields a biradical TS with higher degree of freedom in rotation and torsion, this route is obviously

)

(

Ea (kJ mol1) log10A (s1) DH# (kJ mol1) DS# (J K1 mol1)

b-Pinene (1) k1 180.8  6.4 2 3 4 Myrcene (2) a

k2 k3 k4 k5

182.7  6.2 168.5  6.6 180.7  10.4 167.6  6.8

13.9  0.48 14.0  0.48 12.1  0.52 12.6  0.81 11.3  0.47

Error limits are 95% certainty limits.

175.2  6.4 177.1  6.2 162.9  6.7 175.1  10.5 161.5  7.0

6.8  0.3 8.1  0.4 28.6  1.7 19.2  1.7 45.1  2.7

Scheme 4. Possible transition state (TS1) for the formation of myrcene (2) from bpinene (1).

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Scheme 5. Possible transition states leading to limonene (3) and c-limonene (4) from b-pinene (1).

contrarily to the activation entropies presented in Table 5. Fragmentation of four-membered rings (cyclobutane, oxetane) can proceed via two different reaction mechanisms: (a) concerted [2 + 2]-cycloreversion or (b) stepwise fragmentation passing through biradical intermediates. According to the rules of conservation of orbital symmetry by Woodward and Hoffmann pericyclic reactions passing through an antiaromatic transition state with 4np-electrons are thermally forbidden [50–52]. Therefore, the initial reaction of 1 leading to the formation of 2 is the formation of a biradical TS (TS1) whose subsequently fragmentation yields acyclic 2 (Scheme 4). The reported activation parameters for k1 and k2 are reported to be typical for fragmentation of four-membered rings [48,53–55]. The negative values in activation entropy found for the formation of 3 and 4 (k3, k4; Table 5) are typical for tight TS typical for reactions with a cyclic six-membered TS [48,49]. Therefore, their formation via concerted [1,n]H-shift reactions seems to be confirmed (Scheme 5). Tight TS are characterized by a lack of degrees of movement as present in the initial molecule. Homogenolysis of C(1)-C(6) in 1 yields the biradical TS1 which rearranges forming TS1a. From thermodynamical viewpoint the initially formed TS is more stable than the mesomeric form because of the better stabilization. Subsequently [1,5] or [1,7]Hshift via TS1–4 and TS1a–3 lead to pyrolysis products 4 and 3, respectively. Due to the fact that activation parameters presented herein determine the rate-determining step of the reaction the initial formation of the biradical from 1 is fast compared to the hydrogen shifts leading to products 3 and 4. Table 3 revealed that the ratio of 3 found in the reaction mixture is three times that of 4. Therefore, it can be concluded that the route shown in Scheme 5 starting from 1 and yielding 3 on its end is preferred. Activations parameters listed in Table 5 for the disappearance of 2 (k5) indicate that the reaction proceeds via a six-membered tight TS. As the main reaction route starting from 2 yielding 5 as the main product proceeds as concerted ene-reaction (Table 2), the calculated parameters found for k5 are in accordance with the experimental results [12,13,23,28]. Table 6 lists Arrhenius parameters (Ea, log10A; Eq. (10)) for the initial reactions according to Table 5 published earlier [22,29,56]. Unfortunately, data result from pyrolysis experiments under different conditions and therefore a comparison of the results concerning yield of 2 is difficult. Hawkins and Vogh investigated the pyrolysis of 1 in the gas-phase using similar techniques to these presented herein but analysis and kinetic

evaluation are based on refractive indices (RI) of the product mixtures [22]. Results are in accordance with those listed in Table 5 revealing that the formation of 2 via pyrolysis of 1 is the most preferred reaction. Same analysis technique (RI) was applied in the studies of Hunt and Hawkins pyrolyzing 1 in sealed quartz tubes [29]. Authors found lower values for Ea and log10A for k2 and higher ones for k3. Apparently, the formations of 2 and 3 from 1 in liquid-phase are pari passu. The first attempt describing the formation of 2 yielding from pyrolysis of 1 considering consecutive reaction of 2 was made by Anikeev and co-workers [56]. Experiments were carried out in supercritical ethanol and the Ea was estimated from a mathematical model of the reactor used. Thus, results are not comparable to those presented herein. Nevertheless, the overall trend concerning the absolute differences in Ea are quite similar. As described in the section before (Fig. 2 and Table 3) the surface-to-volume-ration (S/V) has shown to have only little effect on the overall formed 2. Investigating the influence of S/V on the activation parameters (Ea, log10A, DH#, DS#) experiments were carried out allowing for calculation of these according to Eqs. (10) and (11) in dependence of S/V. Exemplarily for Ea the results are summarized in Fig. 3, indicating that activation energy for the main reactions (k1, k2, and k3) are influenced by S/V. Same dependencies were found for the other activation parameters (log10A, DH#, DS#). Apparently, increase of S/V leads to a decrease of Ea for the formation of the biradical from 1 (k1) and for the formation of 2

Table 6 Comparison of kinetic data (Ea, log10A) for the thermal isomerization reaction of bpinene (1) and myrcene (2) log10A (s1)

Commentb

204 209 189

15.6 15.9 13.5

Gas-phase, flow-type reactor, RI

k2 k3

197 209

15.4 16.2

Liquid-phase, sealed tubes, RI

k2 k3 k4 k5

276  17 275  18 215  19 158  33

Reference

ki a

Ea (kJ mol1)

[22]

k1 k2 k3

[29]

[56]

a

– – – –

Supercritical ethanol, flow-type reactor, GC

According to Table 5. RI: analysis of the reaction products via refractive index. GC: analysis of the reaction products via GC-FID and GC–MS. b

32

A. Stolle et al. / J. Anal. Appl. Pyrolysis 83 (2008) 26–36

coefficients for the reactions important for the model in the range of 300–600 8C with an increment of 10 K. The model of competitive first-order reactions for the formation of the primary products 2–4 was used and consecutive reactions of 2 were taken into account. Eqs. (12)–(15) express the mole fractions of 1–4, respectively, for a desired reaction temperature T. Reactant 1 used within these experiments has a purity of higher than 99%. For this reason the starting concentration in the model ([1]0) was set 1.00 (equal to 100%) and contributing to the mass balance (Eq. (8)) the overall molar fraction is not allowed to exceed this value. Consideration of experimental conditions (VR, VE , VN ) allows for the calculation of t (Eq. (5)). Consecutive 2 reaction products of 2 (5, 6) are summarized (cp). [cp]T is calculated according to Eq. (16) despite the fact that the difference between 2 formed directly from 1 ([2]form,T) and the amount present in the reaction mixture [2]T (Eq. (13)) is equal to the molar fraction of cp. ½10 ¼1

Fig. 3. Activation energies (Ea) for different surface-to-volume-ratios (S/V) for the conversion of b-pinene (1, k1), the formation of myrcene (2, k2) and consecutive reactions of 2 (k5; error limits are 95% certainty limit).

(k2), while higher S/V give rise to the activation energy needed for consecutive reactions of 2 (k5). The observed decrease is nearly linear for both k1 and k2 (R2 being 0.996 and 0.987, respectively). A statistically significant trend for k3 was not found. Higher surface area or lower reactor volume seem to support the initial formation of 2, whereas consecutive reactions leading to lower concentrations of 2 are suppressed because more activation energy is needed. 3.3. Kinetic model With the help of the Arrhenius parameters (Ea, log10A) presented in Table 5 it was possible to design a kinetic model describing the temperature dependent reaction composition of the isomerization reaction of 1 including consecutive reactions responsible for decreasing the yield of 2. The use of Eq. (10) allows for the calculation of the temperature dependent rate

Fig. 4. Mole fraction vs. T for experimental data (symbols) and modeling data (lines) for the thermal isomerization of b-pinene (1: b-pinene, asterisk and dashed blue line; 2: myrcene, filled diamonds and red line; 3: limonene, filled squares and green line; 4: c-limonene, triangles and brown line; cp: consecutive products from 2, empty diamonds and red dotted line) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.).

½1T ¼ ½10 ek1;T t ! ½1T ¼ ek1;T t

(12)

½2T ¼

k2;T ð1  ek1;T t Þek5;T t k1;T

(13)

½3T ¼

k3;T ð1  ek1;T t Þ k1;T

(14)

½4T ¼

k4;T ð1  ek1;T t Þ k1;T

(15)

½cpT ¼ ½2form;T  ½2T ¼

k2;T ð1  ek1;T t Þð1  ek5;T t Þ k1;T

(16)

Fig. 4 compares the experimental with the model data for the thermal isomerization of 1. Because of the high agreement between experiment and model the chosen kinetic model of competitive first-order reaction seems to be correct. The visible discrepancies are within the calculated error margins. Since reactions leading to gaseous products were not present within the T-range for which the activation parameters were determined, it is important to point out that the model is only valid if no decomposition reactions leading to gaseous products take place. For comparison reasons of the herein presented results with those from former studies the yields of 2 (Y2) were modeled of a wide range of t and T. The rate of Y2 is influenced by the conversion of 1 (X1) and the selectivity of 2 (S2) because X1 multiplied with S2 is equal to Y2 (Eq. (19)). Based on Eq. (17) and consideration of the rate equations used for modeling of the mole fractions of 1 and 2 (Eqs. (10) and (11)), it is possible to calculate X1, S2, and Y2 on the basis of Arrhenius-parameters (Table 5) using Eqs. (17), (18), or (19), respectively assuming that pure 1 is used as educt. Temperature dependent rate constants ki;T were calculated on the basis of the Arrhenius equation (10). As lower T boundary 200 8C was chosen because at lower T myrcene is not gaseous any more. The rate constants were determined for the gas-phase isomerization. Application of these values for liquid-phase reactions is not suitable. The upper boundary is 800 8C. Although it is possible to model the reaction parameters (X1, Y2, S2) at higher T, heating-up and cooling-down of the gaseous reaction mixture would afford special precautions and reactors for suppression of undesirable consecutive reactions in these phases of the reaction process. Reactions investigated herein took place in a residence time range of 0.1–10 s. Performing the reaction at higher T requires heat-up and cool-down times 10-fold smaller than t to inhibit a reaction during this phase. The time interval between 105 and

A. Stolle et al. / J. Anal. Appl. Pyrolysis 83 (2008) 26–36

33

Fig. 5. Conversion of b-pinene (X1), selectivity for myrcene (S2), and yield of myrcene (Y2, symbols) depending on temperature (T) for four different residence times (t: 104, 102, 1, and 100 s; log t: 4, 2, 0, and 2). Values are calculated using Eqs. (17)–(19) with respect to the Arrhenius parameters listed in Table 5. Every figure represents a transposed column vector of the matrices A, B, and C (Eqs. (20)–(22)) with the given t. (Diagrams of the three matrices are provided within the supplementary information of this article).

105 s was chosen as boundary conditions for t. Longer reaction times are inefficient and shorter reaction times are technically challenging. X 1;T;log t ¼ 1  ek1;T t S2;T;log t ¼

(17)

k2;T k5;T t e k1;T

Y 2;T;log t ¼ X 1;T;log t S2;T;log t ¼

(18) k2;T ð1  ek1;T t Þek5;T t k1;T

(19)

Modeling of the three reaction parameters (X1, S2, Y2) was performed by building up n  m matrices for each parameter (A, B, C; Eqs. (20)–(22)), wherein n are the columns represented by log t within a range from 5 to 5 with a step width for log t of 0.2. Log t was chosen for reasons of easier calculation. Within each row (m) T was varied from 800 to 200 8C with an increment of 10 K forming a matrix with 51 columns and 61 rows. Values for each matrix element were calculated using the corresponding Eqs. (17)– (19). 0 1 X 1;800;5 . . . X 1;800;5 B C ... ... AðX 1 Þ ¼ @ (20) A } X 1;200;5    X 1;200;5

0

S2;800;5 B .. BðS2 Þ ¼ @ . S2;200;5 0

... } 

1 S2;800;5 C .. A . S2;200;5

X 1;800;5  S2;800;5 . . . .. . } X 1;200;5  S2;200;5    0 1 Y 2;800;5 . . . Y 2;800;5 B C ... ... ¼@ A } Y 2;200;5    Y 2;200;5

B CðY 2 Þ ¼ A  B ¼ @

(21)

1 X 1;800;5  S2;800;5 C .. A . X 1;200;5  S2;200;5 (22)

Fig. 5a–d pictures the transposed column vectors of the matrices A, B, and C (Eqs. (20)–(22)) describing each reaction parameter (X1, S2, Y2) depending on T for different t (104, 102, 1, and 100 s). Fig. 5c (t ca. 1 s) corresponds to the experimental conditions applied for the previously described results (Figs. 1 and 4), considering temperature dependency of t according to Eq. (5). Therefore, this counterplot (Fig. 5c) is not a column vector, but t varies only between 0.38 and 0.87 s for 800 and 200 8C, respectively. The difference is between two increments of log t (<0.4). Generally, the graphs in Fig. 5 show that the shorter t the higher is the maximum possible yield of 2 (Y2), although the maximum in Y2 is at higher T for low t than for longer values of residence time. According to Eq. (19) Y2 is strongly influenced by conversion of 1

A. Stolle et al. / J. Anal. Appl. Pyrolysis 83 (2008) 26–36

34

Fig. 6. Conversion of b-pinene (X1), selectivity for myrcene (S2), and yield of myrcene (Y2; symbols) depending residence time (t) for four different temperatures (T: 350, 450, 550, and 650 8C). Values are calculated using Eqs. (17)–(19) with respect to the Arrhenius parameters listed in Table 5. Every figure represents a row vector of the matrices A, B, and C (Eqs. (20)–(22)) with the given T. (Diagrams of the three matrices are provided within the supplementary information of this article.).

Table 7 Comparison of the maximal overall yield of myrcene (2;Y2) and of the reaction parameters these results were obtained with T (8C)

t (s)a

403 450

6–11

Continuous flow-type reactor (stainless steel)

350 550

171 129

Continuous flow-type reactor (capillary reactor)

592 661 750

Continuous flow-type reactor (Pyrex, cg: N2)b

350 450

70 43

Flash vacuum pyrolysis (0.07 mbar) Flow-type reactor; supercritical ethanol (122 bar) Flow-type reactor (quartz, cg: N2)b

900 400 425

70e 0.98

Reactor Tubular flow type reactor (Pyrex, cg: N2) Flow-type reactor (vacuum)

a b c d e

b

0.04 0.01 0.01

S/V (cm1)

Y2 (%)

Reference

2.0

70 80

[20] [22]

3.5 3.5

4 54

[24]

28.6 28.6 28.6

75 80 85c

[7]

0.8 0.8

71d 39

[23]

6.6

77 72 69

[9] [26,56] This paper

Calculated according to Eq. (5) based on the reaction parameters published. cg: carrier gas. Pyrolysis at 6.6 mbar. Formation of polymeric product was observed but not considered in Y2. Taken from reference given.

(X1) and selectivity of 2 (S2). The changeover between very low and high yields of 2 is very small. Small changes in T tremendously affects the overall yield of 2. It has to be pointed out that carrying out the process of myrcene production via pyrolysis of 1 at higher T (>600 8C) is advantageous with respect to the overall possible yield of 2. Furthermore, performing the reaction above 600 8C is beneficial because small changes in T affect Y2 not as strongly as at lower T.

The same conclusions derived from Fig. 5 can be drawn from inspection of the graphs in Fig. 6 where t is varied at constant T. The four diagrams in Fig. 6 represent row vectors of the matrices A, B, and C (Eqs. (20)–(22)) for four different T (350, 450, 550, and 650 8C) reveal that short t together with high T are beneficial due to three facts: (a) The maximal Y2 possible to reach is higher, (b) the gap with Y2 > 0.7 is wider, and (c) the decline to Y2 < 0.10 is not as sharp as for the opposite conditions (low T, long t). Nevertheless, it

A. Stolle et al. / J. Anal. Appl. Pyrolysis 83 (2008) 26–36

has to be stated that besides the advantages for producing 2 at T > 600 8C and t < 103 s some technical challenges would have to be overcome. While industrial processes at high T are not difficult to regulate with respect to heat control, the regulation of t is complex, because small changes (<1 ms) have a tremendous effect on Y2. Additionally, the warm-up and quenching of the reactants has to proceed with heating and cooling rates of 6000 K s1 (T: 200–800 8C, time for heat-up/cool-down: 0.1 s). Otherwise side reactions within these phases will yield side products (5, 6; Scheme 1) and lower the yield of 2. Furthermore, high heating rates can provoke the formation of coke and polymers. Table 7 compares the maximal reached yields of myrcene (2; Y2) from different studies in the literature with those found herein [7,9,20,23–26,56]. For a direct comparison with the model (Fig. 5) t are given as log t-values. Except for Refs. [26,56] all studies were carried out in gas-phase in flow-type reactors with Reynolds numbers (Re) below 100, also found for the experiments reported herein. Therefore, laminar flow (Re < 2300) is present and the flow behavior is similar to an ideal plug-flow without back mixing. Apparently, the results found in literature are only in accordance when similar reaction conditions were applied, with respect to pressure and S/V. Nevertheless, agreement is generally satisfactory, and the model describes the observed trends in a good manner. Short t and high T lead to high Y2 for both atmospheric [7] and reduced pressure [7,9]. Combination of low t and a high surface-tovolume-ratio (S/V) seem to be beneficial also because higher values in S/V improve heat transfer [7,9,20]. Additionally, the dilution effects from using a carrier gas suppress bimolecular reactions which lead to the undesired formation of coke or polymeric products [20,23]. Carrying out the reaction in supercritical ethanol at p of 120 bar seems to be possible too [26,56]. Results show that it is difficult to compare findings even if similar pyrolysis techniques are used. Various effects have to be considered: reactor geometry (S/V), carrier gas, pressure, operation mode, analytics, and of course T.

35

operation modes. Nevertheless, overall trends observed herein are in accordance to previously published findings. For modeling of the thermal rearrangement of 1 the model of competitive first-order reactions was chosen combining kinetic data with reaction parameters (T, t). The high accordance between calculated data and experimental data indicates that the chosen model is correct. The results show that it is generally possible to predict reaction conditions leading to product mixtures with high amount of 2. Specifically, the model shows that it is not possible to obtain 2 exclusively, but with the right choice of experimental condition (T > 500 8C, t < 0.1 s) its overall yield could be as high as 80%. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.jaap.2008.06.001. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]

[14]

4. Conclusion

[15] [16]

The production of myrcene (2) from b-pinene (1) via pyrolysis is an important industrial reaction. Besides 2 the thermal rearrangement of 1 leads to the formation of limonene (3) and c-limonene (4). Consecutive reactions of 2 at higher temperatures lead to decreased yields and various isomerisation products are formed depending on reaction temperature and residence time. Pyrolysis experiments with 1 and 2 in a range from 300 to 600 8C in a flow-type apparatus using N2 as carrier gas were carried out studying the influence of temperature, residence time and of the surface-to-volume-ratio on the conversion of 1 and 2 and the selectivity of the initially formed products (2–4). Experiments reveal that the pyrolysis temperature and the residence time have the highest influence, whereas experimental runs with different surface-to-volume-ratios showed little discrepancies. Investigating the ee of the optical active components (1, 3, 4) leads to the conclusion that the pyrolysis of 1 is a highly enantioselective reaction because the ee remains constant during the reaction. Arrhenius as well as Eyring parameters were calculated based on experimentally determined rate constants. Analysis of those allows for the conclusion that the pyrolysis of 1 passes through a biradical transition state. The formation of 2 from 1 is similar to a stepwise fragmentation of a cyclobutane ring, whereas products 3 and 4 yield from [1,n]H-shifts occurring in the initially formed biradical (Scheme 1). Comparison of activation parameters known from literature reveal differences, caused by different analytical methods or

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