THE EFFECT OF HYDROCARBON STRUCTURAL ARRANGEMENT ON THE AUTO IGNITION TEMPERATURE AND ITS POTENTIAL USE IN CATALYTIC ACTIVATION OF OXYGEN

MSc Chemistry

Molecular Design, Synthesis and Catalysis

Literature Thesis

T

HE EFFECT OF HYDROCARBON STRUCTURAL ARRANGEMENT

ON THE AUTO IGNITION TEMPERATURE AND ITS POTENTIAL USE

IN CATALYTIC ACTIVATION OF OXYGEN

by

T.A. van Westen

10894187

October 2016

12 ECTS

Examiner 1:

Examiner 2:

Prof. dr. G. Rothenberg

Dr. D. Eisenberg

University of Amsterdam University of Amsterdam

VAN ‘T HOFF INSTITUTE FOR MOLECULAR SCIENCES

2

A

BSTRACT

The auto ignition temperature (AIT) is one of the most critical safety parameters in industry when dealing with hazardous and flammable materials. It is defined as the lowest temperature at which a substance will ignite in the absence of an ignition source, like a spark or a flame [1].

Ignition or combustion is a chain reaction of oxidation reactions. For hydrocarbons, oxidation reactions are exothermic but a kinetic barrier must first be overcome [2]. This means that the AIT for hydrocarbons can be described as the minimum temperature to which the substance must be raised so that the amount of oxidation reactions and the amount of energy released thereby is higher than can be lost to the surrounding and a chain reaction of oxidations takes place.

Since the AIT is such an important safety parameter, a lot of research has been conducted to develop a universal computer model to predict the AIT of a compound [7-12]. After reviewing several of these studies it is found that AIT is a property that has a complex dependency on the molecular structure and is therefore challenging to model. Nonetheless, (amount of) aromaticity and flexibility of the molecule are reoccurring parameters in the different studies.

By reviewing the reaction steps in hydrocarbon oxidation it is found that the energy required for abstraction of a hydrogen atom in the vicinity of the site of initial radical formation has a direct influence on the AIT. The energy required for hydrogen abstraction comprises of both the strength of the bond being cleaved as well as the steric hindrance around the hydrogen atom.

This knowledge could potentially be used to develop high performance fuels or in reactions were oxygen gets activated. This includes oxygen reduction reactions for fuel cells or low temperature catalytic oxidation.

3

C

ONTENTS

1.1 Auto ignition temperature ... 7

1.2 Measurement methods and databases ... 7

2. Trends in AIT ... 8

2.1 Plots of AIT data ... 11

2.1.1 AIT versus carbon number ... 11

2.1.2 AIT versus amount of hydrogens ... 12

2.1.3 AIT versus the ratio between carbon and hydrogen atoms ... 13

2.2 Observed trends ... 14

2.2.1 Stability of initial radical ... 14

2.2.2 Structure ... 14

3. Explaining the AIT ... 15

3.1 Computer models ... 15

3.1.1 QSPR study by mitchell and jurs ... 15

3.1.2 QSPR Study by Tsai, Chen and liaw ... 16

3.1.3 QSPR study by Borhani, Afzali and Bagheri ... 17

3.1.4 Group contribution method by Pan et al ... 18

3.1.5 Group contribution method by Albahri ... 19

3.1.6. Computer models: Summary ... 20

3.2 Hydrocarbon oxidation ... 21

3.2.1 Mechanism of hydrocarbon oxidation ... 21

3.2.2 Temperature regimes of hydrocarbon oxidation ... 22

3.3 Hydrogen abstraction ... 23

3.3.1 Stability of the resulting carbon based radical ... 23

3.3.2 Ease of reach ... 23

4

4. Possible implications ... 26

4.1 Engine knock ... 26

4.2 Activating oxygen at low temperature ... 26

4.2.1 Oxygen activation on nitrogen doped carbon for ORR ... 26

4.2.2 Low temperature oxidation ... 26

5. Conclusions ... 27

5

L

IST OF

A

BBREVIATIONS

ADAPT - Automated Data Analysis and Pattern recognition Toolkit AIChE - American Institute of Chemical Engineers

AIT - Auto Ignition Temperature

ANN - Artificial Neural Network

ARR - Aromatic Ratio

ASTM - American Society for Testing and Materials BDE - Bond Dissociation Energy

CNN - Computational Neural Networks DIPPR - Design Institute for Physical Properties

GA - Genetic Algorithm

GCM - Group Contribution Method

ICSC - Internal Chemical Safety Cards ORR - Oxygen Reduction Reaction

QSPR - Quantitative Structure-Property Relationship

RBF - Rotatable Bond Fraction

RMS - Root Mean Square

6

L

IST OF

F

IGURES

Figure 1

Experimentally determined AIT data for selected hydrocarbons versus the number of carbon atoms ... 11

Figure 2 Experimentally determined AIT data for selected hydrocarbons versus the number of hydrogen atoms ... 12

Figure 3 Experimentally determined AIT data for selected hydrocarbons versus the carbon/hydrogen ratio ... 13

L

IST OF

T

ABLES

Table 2 Experimentally determined AIT of selected Isoalkanes ... 9

Table 3 Experimentally determined AIT of selected Alkenes ... 9

Table 4 Experimentally determined AIT of selected aromatic compounds ... 10

Table 5 The sixteen by Pan et al identified atom types and their E-state indices symbol ... 18

7

1. I

NTRODUCTION

The auto ignition temperature of hydrocarbons is influenced by the structural properties of the compound. By exploring the chemical effects lying behind this observation, it is found that the energy required for

abstraction of a hydrogen atom in the vicinity of the site of initial radical formation has a direct influence on the auto ignition temperature. This knowledge could potentially be used to lower the energy required in catalytic activation of oxygen.

1.1

A

The auto ignition temperature (AIT) is defined as the lowest temperature at which a substance will ignite in the absence of an ignition source, like a spark or a flame [1]. This makes it an important parameter for handling, storing and processing hazardous and flammable materials.

Besides these safety concerns, the AIT is also an important parameter for dealing with engine knock [2]. Engine knock occurs when the air/fuel mixture ignites spontaneously in the cylinders of an internal

combustion engine instead of in response to the spark created by the spark plug [3]. These unwanted ignitions of the fuel decrease the performance of a combustion engine.

Ignition or combustion is a chain reaction of oxidation reactions. For hydrocarbons, oxidation reactions are exothermic but a kinetic barrier must first be overcome [4]. This means that the AIT for hydrocarbons can be described as the minimum temperature to which the substance must be raised so that the amount of oxidation reactions and the amount of energy released thereby is higher than can be lost to the surrounding and a chain reaction of oxidations takes place.

1.2

M

The measured AIT of a material is dependent upon the measurement method. Parameters like total pressure, partial pressure of oxygen, concentration of substance or size of the measurement vessel influence the measured AIT [1, 5]. For this, the American Society for Testing and Materials (ASTM) has developed a standardized measurement method to measure AIT and in literature reported values for AIT should only be compared if they are measured via the same method.

Among the vast amount of AIT data that can be found in databases and on the internet the International Chemical Safety Cards (ICSC) [9] and the by the American Institute of Chemical Engineers (AIChE) created Design Institute for Physical Properties (DIPPR) [18] are in literature considered to be the most reliable [5-12]. In this thesis only AIT data will be used that originates from either of these databases.

8

2. T

RENDS IN

AIT

Below are four tables with the experimentally determined AIT data for 126 different hydrocarbons [6-10]. The compounds are sorted by classification. Table 1 contains the AIT data for linear straight chain alkanes and cycloalkanes. Table 2 contains the collected data for isoalkanes and tables 3 and 4 the data for unsaturated hydrocarbons, alkenes and aromatics respectively.

Table 1 Experimentally determined AIT of selected Alkanes and Cycloalkanes

Alkanes Cycloalkanes

Compound: AIT (°C) Compound: AIT (°C)

Methane 537 Cyclopropane 498 Ethane 515 Cyclopentane 361 Propane 470 Cyclohexane 260 Butane 365 Methyl-cyclopentane 329 Pentane 260 Ethyl-cyclopentane 260 Hexane 234 Methyl-cyclohexane 283 Heptane 223 Propyl-cyclopentane 269

Octane 220 trans-1,3-dimethyl cyclohexane 306

Nonane 205 Ethyl-cyclohexane 262 Decane 210 1,2-Dimethyl-cyclohexane 304 Undecane 202 1,3,5-Trimethyl-cyclohexane 314 Dodecane 205 Propyl-cyclohexane 248 Tridecane 202 Isopropyl-cyclohexane 283 Tetradecane 220 Cyclodecane 235 Pentadecane 202 Butyl-cyclohexane 245 Hexadecane 202 4-Isopropyl-1-methyl-cyclohexane 306 Heptadecane 202 Decalin 250 Octadecane 235 Dicyclohexyl 245 Nonadecane 230 Icosane 230

9

Table 2 Experimentally determined AIT of selected Isoalkanes

Isoalkanes

Compound: AIT (°C) Compound: AIT (°C)

Isobutane 460 2,2,3-Trimethyl-pentane 430 2-Methyl-butane 420 2,2,4-Trimethyl-pentane 447 2,2-Dimethyl-propane 450 2,3,3-Trimethyl-pentane 425 2-Methyl-pentane 306 3-Methyl-octane 220 2,3-Dimethyl-butane 420 4-Methyl-octane 225 2,2-Dimethyl-butane 425 2,2,3,3-Tetramethyl-pentane 430 3-Methyl-pentane 278 2,3,3,4-Tetramethyl-pentane 437 2,3-Dimethyl-pentane 337 2,4-Dimethyl-3-ethyl-pentane 390 2,4-Dimethyl-pentane 337 2-Methyl-nonane 214 2-Methyl-hexane 280 4-Ethyl-octane 235 3-Methyl-hexane 280 2,3-Dimethyl-octane 231 2,2,3-Trimethyl-butane 450

Table 3 Experimentally determined AIT of selected Alkenes

Alkenes

Compound: AIT (°C) Compound: AIT (°C)

Ethylene 450 4-Methyl-pentene 300 Propylene 460 2-Ethyl-1-butene 315 1-Butene 385 2,3-Dimethyl-1-butene 370 2-Butene 325 2,3-Dimethyl-2-butene 401 Isobutene 465 1-Heptene 260 Butadiene 420 1-Octene 250 1-Pentene 272 1,7-Octadiene 230 Cyclopentene 395 2,3,4-Trimethyl-1-pentene 391 2-Methyl-1-butene 365 2,4,4-Trimethyl-2-pentene 308 2-Methyl-2-butene 240 3,4,4-Trimethyl-2-pentene 325 3-Methyl-1-butene 365 1-Decene 235 2-Methyl-1,3-butadiene 220 1-Dodecene 255 cis-2-Pentene 288 Cyclododecene 258 1-Hexene 253 1-Tetradecene 235 Trans-2-hexene 245 Hexadecene 240 Cyclohexene 310

10

Table 4 Experimentally determined AIT of selected aromatic compounds

Aromatics

Compound: AIT (°C) Compound: AIT (°C)

Benzene 560 Butyl-benzene 412 Toluene 530 sec-Butyl-benzene 418 Styrene 490 Isobutyl-benzene 428 p-Xylene 530 o-Diethyl-benzene 395 m-Xylene 527 m-Diethyl-benzene 450 o-Xylene 463 p-Diethyl-benzene 430 Ethyl-benzene 430 p-Isopropyl-toluene 436 Naphthalene 525 1,2,3,4-Tetrahydronaphthalene 385 Propyl-benzene 450 Divinyl-benzene 470 Cumene 424 p-Tert-butyl-toluene 510 1,2,3-Trimethyl-benzene 470 1-Methyl-3,5-diethyl-benzene 461 1,2,4-Trimethyl-benzene 515 Biphenyl 540 1,3,5-Trimethyl-benzene 550 Methyl-biphenyl 482 1-Methyl-2-ethyl-benzene 448 Diphenyl-methane 486 2-Vinyl-toluene 494 Diphenyl-ethane 480 α-Methyl-styrene 445 Phenanthrene 556 Anthracene 540

11

2.1 P

AIT

By plotting the data from table 1-4 possible trends in AIT could potentially be spotted more easily. The most straightforward plots are the AIT versus the amount of carbon or hydrogen atoms, or the ratio between these two.

2.1.1 AIT

By comparing the experimentally determined AIT data versus the number of carbon atoms in the molecules, the plot in figure 1 is obtained.

Figure 1 Experimentally determined AIT data for selected hydrocarbons versus the number of carbon atoms Alkanes

By comparing the number of carbon atoms to the AIT for alkanes, displayed as green triangles in figure 1, it can be seen that the AIT decreases sharply with increasing carbon number in the beginning and levels of around 220 °C from hexane onwards. A second observation is the striking drop in AIT between propane and pentane.

Cyclo-alkanes

The gathered AIT data versus carbon number for cyclo-alkanes, displayed as red squares in figure 1, follows suit compared to the data for alkanes for the lower carbon numbers, with a sharp decrease in AIT with increasing number of carbons.

Iso-alkanes

No trends in the AIT of alkanes versus the number of carbons can be detected in figure 1, where the iso-alkanes are displayed as blue diamonds.

Alkenes

The AIT data gathered for alkenes compared to the carbon number, the light blue crosses in figure 1, falls between that of the alkanes (green triangles) and iso-alkanes (blue diamonds). In the data given in table 3 it can also be seen that branched alkenes have AIT comparable to iso-alkanes and straight alkenes to alkanes. It

0 100 200 300 400 500 600 0 2 4 6 8 10 12 14 16 18 20 AI T (° C)

Number of carbon atoms

Experimentally determined AIT versus number of carbon atoms for selected hydrocarbons Alkanes Cyclo-alkanes Iso-alkanes Alkenes Aromatics

12 can therefore be debated whether or not the alkenes should be displayed as a separate class. This will be addressed in a later section (3.4).

Aromatics

The aromatic compounds, displayed as purple circles in figure 1, have notably the highest AIT of these selected classes of hydrocarbons. Mutually between the aromatic compounds no trends can be discovered in the AIT data versus the amount of carbon atoms.

2.1.2 AIT

As the first step in hydrocarbon oxidation is the abstraction of a hydrogen atom (see section 3.2) a correlation between the AIT and the amount of hydrogen atoms could perhaps be expected. As can be seen in figure 2 no such correlation exists.

Figure 2 Experimentally determined AIT data for selected hydrocarbons versus the number of hydrogen atoms

The graph in figure 2 resembles the graph in figure 1, which was to be expected since for these relatively simple hydrocarbons more carbon atoms means more hydrogen atoms.

0 100 200 300 400 500 600 0 5 10 15 20 25 30 35 40 45 A IT (° C)

Number of hydrogen atoms

Experimentally determined AIT versus the number of hydrogen atoms for selected hydrocarbons Alkanes Cyclo-alkanes Iso-alkanes Alkenes Aromatics

13

2.1.3 AIT

A last straightforward plot is a plot of the AIT versus the ratio between carbon and hydrogen atoms. This plot is displayed in figure 3.

Figure 3 Experimentally determined AIT data for selected hydrocarbons versus the carbon/hydrogen ratio

As can be seen in figure 3, no linear correlation can be found between the AIT and the ratio of carbon versus hydrogen atoms. 0 100 200 300 400 500 600 0 0.25 0.5 0.75 1 1.25 1.5 A IT (° C)

Carbon/hydrogen atom ratio

Experimentally determined AIT versus the ratio between carbon and hydrogen atoms Alkanes Cyclo-alkanes Iso-alkanes Alkenes Aromatics

14

2.2

O

While it is challenging to discover trends in the AIT data by comparing the AIT to straightforward descriptors as is done in section 2.1, two trends appear in the tables with AIT data. The first is that the stability of the initial radical after hydrogen abstraction has an effect; the second is the structure of the hydrocarbon in the direct vicinity of the expected site of oxidation, based on the stability of the initial radical formation.

2.2.1 S

Hydrocarbon oxidation, and thus combustion, is a radical process [4]. The stability of the initial radical on the carbon molecule has an effect on the AIT; a more stable radical results in a lower AIT. In the tables 1-4 this can be seen in the data for a hydrocarbon with solely a primary carbon, methane with an AIT of 537 °C, versus a hydrocarbon with solely secondary carbons, for example cyclopentane with an AIT of 361 °C, versus a simple saturated hydrocarbon that possesses a tertiary carbon, like 3-methyl pentane with an AIT of 278 °C. The stability of the initial radical is not the whole story however. As can be seen in figures 1 and 2, iso-alkanes (blue diamonds) have on average a higher AIT than straight chain alkanes (green triangles). This would be the other way around if the stability of the initial radical would be the sole parameter influencing the AIT of hydrocarbons.

2.2.2 S

The structure in the direct vicinity of the expected initial radical formation based on stability thereof also has an effect. In the tables this can be seen for example for the AIT data of propane, butane and pentane. All three molecules comprise of secondary and primary carbons, yet their AIT is 470 °C, 365 °C and 260 °C, respectively.

Also, the differences between p-xylene (530 °C), m-xylene (527 °C) and o-xylene (465 °C) points to an effect of the molecules structures, since these three molecules comprise of exactly the same amount and type of carbons, but differ slightly in their structural arrangement.

Lastly, in table 2 it can be seen that the more heavily branched alkanes have higher AIT than the iso-alkanes with only 1 tertiary carbon.

15

3. E

XPLAINING THE

AIT

The two observed trends in section 2.2 must have a chemical or physical explanation. By determining the origin of these effects, they can potentially be controlled. This should lead to a better control of chemical reactions in which oxygen reacts with hydrocarbons.

3.1 C

Various research groups have tried to develop a universal model or equation to predict the AIT of an organic compound based on its structure [6-10]. The approach of most of these groups is to collect a large amount of AIT data, load it into a certain statistics program along with various arbitrarily chosen descriptors and let the software generate an equation or model [6-8].

3.1.1 QSPR

Mitchell and Jurs conduct such a quantitative structure-property relationship (QSPR) study [6]. In their study they have collected the AIT of 327 organic compounds, including hydrocarbons (104) but also compounds containing heteroatoms (223). Here the focus will lay on their work on hydrocarbons.

The QSPR models in their study were developed using several aides. Two sets of data were created, a training set for model development which contained around 90 compounds and a set used for model validation containing the remaining compounds. The compounds from the development set were put into their energetically minimal configuration, as calculated by MOPAC [13]. The automated data analysis and pattern recognition toolkit (ADAPT) [14] was then used to calculate descriptors. The resulting descriptor pool was analyzed and reduced by objective feature selection, which is the removal of descriptors with little or redundant information. Pairwise correlations were examined and only one descriptor retained. Descriptors with more than 80% identical values were also removed from the pool. A reduced descriptor pool of around 60 descriptors remained.

Since it is not feasible to examine all possible combinations of descriptors which such a large pool a genetic algorithm (GA) routine [15] and a simulated annealing routine (SAR) [16] were used to generate linear regression models. The quality of the model was based on root mean square (RMS) error and statistical integrity. Good models were further investigated using an interactive regression analysis routine, which allowed descriptors to be added or removed and the effect thereof on the model statistics to be determined. The linear regression models developed by the above method were subsequently improved by computational neural networks (CNN) [17]. This can be seen as a nonlinear mathematical function that identifies the weights and biases of the descriptors by adjusting these and looking for the minimal squared error between observed and calculated AIT.

When the above techniques were applied to the complete subset of 104 hydrocarbons a poor result was obtained. An eight-descriptor model resulted, with a root mean square error of 38.2 °C.

The subset was then split into two sub-subsets, one containing the data of hydrocarbons with an AIT below 350 °C and one with an AIT above 350 °C. The choice for this temperature lies in the switch in oxidation mechanism (see section 3.2.2). It can be debated whether such a division can be made, or whether the model should incorporate the underlying reasons leading to this effect.

Logically, when the subset is divided into two, a low-temperature subset and a high-temperature sub-subset, good models are obtained. The low-temperature model comprises of five descriptors and has a RMS

16 error of 8.8 °C. The five descriptors found to be most relevant were the total charge weighted partial negative surface area, the difference in atomic charge weighted partial surface area, the valence corrected second order molecular connectivity, the count of forth order paths and the count of primary sp2_-carbons.

For the high-temperature sub-subset, comprising of 51 compounds, a six descriptor model was obtained with a RMS error of 18.5 °C. The six descriptors in this model were the charge on the most negative atom, the fractional charge weighted partial positive surface area, the number of aromatic bonds, the count of forth order path clusters, the total weighted number of paths/number of atoms and the count of primary sp3 -carbons.

Mitchell and Jurs fail to give coefficients for these descriptors, so the weight that has to be given to each is unclear. Also, while eventually two reasonable models are obtained based on their RMS errors, the statistical manipulation that has to be executed has to be kept in mind. They divide the subset of hydrocarbon data in two sub-subsets, based on the expected mechanism. The resulting models comprise of five and six descriptors for the low-temperature and high-temperature compounds, respectively. Both the necessity for the division into two sub-subsets and the relatively large amount of descriptors needed to obtain a reasonable model point towards auto ignition being a complex sequence of events to model, where the speed and occurrence of events is dependent upon the temperature.

Lastly, it should be noted that in both models descriptors for electronic as well as topological information are incorporated.

3.1.2 QSPR

S

T

,

C

In a separate study, Tsai, Chen and Liaw attempt to develop a model to predict AIT via a QSPR study as well [7]. Their approach is similar as the study discussed in section 3.1.1, although a larger database with AIT data was obtained. For their study they have acquired the AIT data of 820 organic compounds from the DIPPR database [18].

As before, first the compounds energetically favoured structure is calculated using chemical software. Tsai et al use the HyperChem software with the MM+ and AM1 molecular mechanics force field [19, 20, 21]. Next molecular descriptors are calculated using the Dragon software [22]. This software can calculate up to 3224 molecular descriptors. After dropping the descriptors with equal values across the entire database, 1707 molecular descriptors remain.

This set of descriptors is loaded into a multiple linear regression (MLR) model. Stepwise regression is subsequently adopted. Stepwise regression is a method that begins with an initial model and then compares larger and smaller models for their predictive behaviour. The p-value of an F-statistic is calculated for models with and without a potential regressor. If a regressor is currently in the model the null hypothesis is that the regressor has a zero coefficient. If a regressor is currently not in the model, the null hypothesis is that a regressor would have a zero coefficient. If the null hypothesis is rejected, the regressor is either removed or added. The p-value of both scenarios is then chosen such that the chance for a regressor to leave the model is higher than for it to enter. This ensures a final model is as small as possible. Lastly, they use the random search technique introduced in their previously reported work [23] to automatically set up the initial model to prevent an obtained model to be locally optimal instead of globally.

17 The model they eventually obtained consists of four molecular descriptors, with a correlation coefficient of 0.90 and an average error of 36.0 K, for the compounds in their database. Their suggested model is shown below.

AIT (K) = 495.39 (±8.07) + 57.79 (±3.15) MS + 194.80 (±6.33) ARR – 388.70 (±18.08) RBF + 49.06 (±3.17) C-040

MS stands for mean electro topological state and is calculated by dividing the sum of electro topological state of the ith _{atom in the molecule by the total number of non-hydrogen atoms in the molecule. The electro} topological state of an atom is a variable which encodes the intrinsic electronic state of an atom as perturbed by the electronic influence of all other atoms in the molecule. For a detailed explanation, the reader is referred elsewhere [24].

ARR is the ratio of the number of aromatic bonds over the total number of bonds, excluding bonds to hydrogen.

RBF is the number of rotatable bonds divided by the total number of bonds in a molecule.

C-040 is the number of the description in a molecule. This variable is defined by Todeschini and Consonni and includes R-C(=X)-X / R-C#X / X=C=X; in which R represents any group linked through carbon, X represents any electronegative atom (e.g. O, S, halogens), - represents a single bond, = a double bond and # a triple bond [25].

As can be seen by the coefficients, the most important parameter is the RBF. It is also the only negative coefficient, meaning the more flexible a molecule is the lower is the expected AIT. The large positive coefficient before the ARR variable shows that more aromaticity in a molecule increases the AIT. The two other variables have less of an impact and incorporate the electronic nature of the molecule (MS) and the presence of heteroatoms (C-040).

3.1.3

QSPR

B

,

A

B

In their recently published work, Borhani, Afzali and Bagheri develop a model for prediction of AIT after a QSPR study [8]. They combine the genetic algorithm (GA) with MLR for construction of their model. From the DIPPR database [18] the AIT data of 813 hydrocarbons is obtained. As with the previously

discussed QSPR studies, the energetically most favoured structure of the compounds is first determined (here again with HyperChem [19]) and then descriptors are calculated (via Dragon [20]).

From here on the approach of this group starts to differ from that discussed in section 3.1.2. Here the GA is used, where the previously discussed group uses stepwise regression. The GA is a powerful method to find the global optimal model. This algorithm is developed to mimic processes observed in natural evolution. More details can be found elsewhere [26].

Using this GA they obtain the best MLR model. Logically they find better models by incorporating more descriptors. The correct amount of descriptors is determined at three by keeping an eye on the RP (redundancy) and RN (overfitting) parameters as discussed in the work by Todeschini et al on regression analysis [27].

18 The model they propose is based on three descriptors and has a correlation coefficient of 0.81 with a RMS error of 43.0 °C for the compounds in their database.

AIT (°C) = 201.46 (±6.18) ARR – 308.49 (±17.21) RBF + 753.53 (±22.01) Ms0.25 _{– 278.32}

Interestingly, these three descriptors are also reported in the model discussed in section 3.1.2. As before, the more aromaticity in a molecule (ARR) the higher the AIT and the more flexible a molecule is (RBF) the lower is its AIT. The third descriptor in this model (Ms) is also encountered in the model in section 3.1.2. It has a much lower coefficient in the latter, most likely due to the presence of a forth descriptor, which also

incorporates the presence of heteroatoms. In the model suggested by the group in this section the presence of heteroatoms has to be incorporated by one descriptor, which then logically has a larger coefficient.

3.1.4 G

P

A different approach is to use a group contribution method (GCM), where several chemical groups of hydrocarbons are identified and an approach is taken to identify the effect each additional group has on the observed AIT [28].

One group that uses the GCM to obtain a model to predict the AIT is the group of Pan et al [9]. In their study they identify 16 different chemical groups encountered in hydrocarbons. These groups are based on the electro topological state of the carbon atom and are called the E-state indices [24]. The groups selected are given in table 5.

Table 5 The sixteen by Pan et al identified atom types and their E-state indices symbol

Symbols: − for single bond, = for double bond, ≡ for triple bond, a for aromatic bond and > for two single bonds. The R in subscript stands for a ring structure.

No. Atom-type E-State indices symbol [24]

1 −CH3 SsCH3 2 =CH2 SdCH2 3 ≡CH StCH 4 ≡C− StsC 5 −CH2− SssCH2 6 (−CH2−)R SssCH2 7 >CH− SsssCH 8 (>CH−)R SsssCH 9 >C< SsssC 10 (>C<)R SsssC 11 =CH− SdsCH 12 (=CH−)R SdsCH 13 aCHa SaaCH 14 =C< SdssC 15 (=C<)R SdssC 16 saCa SsaaC

A database with AIT data of 118 hydrocarbons is obtained from the ICSC [9] and for each the E-state indices of all the atom types are calculated. The relationship of these E-state indices versus the AIT is subsequently modelled via both the artificial neural network (ANN) method as well as the MLR method.

19 The MLR analysis was performed using SPSS statistical software [29]. Two E-State indices were found to be non-significant, numbers 10 and 15 in table 5. The resulting model thus comprises of 14 E-State indices and is displayed below. It has a correlation coefficient of 0.87 and a RMS error of 39.07, for the hydrocarbons in their database.

AIT (°C) = 498.858 – 25.162{1} – 10.264{2} – 24.232{3} – 6.075{4} – 13.065{5} – 22.332{6} + 58.852{7} + 24.950 {8} + 335.108 {9} – 21.480 {11} + 8.581 {12} – 6.408 {13} + 20.274 {14} + 51.376 {16} Looking at their suggested model, two observations can be made. Intuitively, the prefix of 335.108 for a quaternary carbon seems too large. Using this model the compound 2,2,3,3-tetramethyl pentane, possessing two quaternary carbons, would have a calculated AIT of 1005 °C (498.585 – 6 * 25.162 – 13.065 + 2 * 335.108), far too high compared to its actual value (430 °C, table 3).

Second, in this proposed model aromaticity has a decreasing effect on the AIT (negative prefix for #13). This contradicts the previously discussed models, where aromaticity was determined to have a large increasing effect on AIT.

The developed model suffers most likely from non-linear dependencies, as well as being developed with a too small database of AIT values (118 hydrocarbons). The former is attempted to be overcome by applying a non-linear method of data analysis. The method used is ANN with back-propagation learning, for a detailed explanation of this method the reader is referred elsewhere [30].

The same set of E-state indices is used as given in table 5. Pan et al fail to mention the coefficients obtained for the E-State indices using the ANN method. It is however mentioned a better overall result is obtained, with the model having a correlation coefficient of 0.96 and a RMS error of 34.8 °C.

3.1.5 G

A

A different study that develops a model to predict AIT based on the group contribution method is the study of Albahri [10]. He obtains a database with AIT data of 131 hydrocarbon compounds from the DIPPR database [18]. He has identified 20 different chemical groups based on the Joback method [31]; these are given in table 6 together with their identified contribution to the AIT. The derivation of the contributions as well as the general formula will be discussed below.

Table 6 Group contributions for estimation of the AIT as found by Albahri

Groups 17-20 are all non-fused

No. Hydrocarbon Type Group (AIT)i

1 Paraffins −CH3 -0.8516 2 >CH2 -1.4207 3 >CH− 0.0249 4 >C< 2.3226 5 Olefins =CH2 0.4682 6 =CH− -1.9356 7 >C= -2.242 8 ≡CH -3.118 9 ≡C− -1.136 10 Cyclic >CH2 -1.160 11 >CH− 0.0372 12 >C< 8.960

20

No. Hydrocarbon Type Group (AIT)i

13 Cyclic =CH− 0.0037 14 >C= -12.33 15 Aromatics =CH− 0.4547 16 >C= (fused) 0.0246 17 >C= -1.889 18 >C= (ortho) 0.9125 19 >C= (meta) 2.465 20 >C= (para) 2.097

The general equation used by Albahri is one that has been developed by his previous research, in which the equation below was found to be the best to predict the target property in a nonlinear form [32].

Φ = a + b ( Σ(Φi)) + c ( Σ(Φi))2 _{+ d ( Σ(Φi))}3 _{+ e ( Σ(Φi))}4

An ANN was constructed using MATLAB code [46] to derive the contributions of each group, as given in table 6, as well as the value for a, b, c, d and e in the above equation. He arrives at the equation displayed below to predict the AIT which has, for his database, a correlation coefficient of 0.92 and an average deviation of 28 K.

AIT (K) = 780.42 + 26.78 ( Σ(Φi)) – 2.5887 ( Σ(Φi))2 _{– 0.3195 ( Σ(Φi))}3 _{– 0.007825 ( Σ(Φi))}4

The coefficients found by Albahri for the various chemical groups are more in line with the results from the QSPR studies discussed above than the coefficients found in the GCM discussed in the previous paragraph. Quaternary carbons and aromaticity increase the AIT and addition of groups with free rotating bonds (e.q. >CH2) decrease the AIT.

3.1.6.

C

:

S

Two approaches to develop a model to predict the AIT of hydrocarbons are encountered most in literature, the QSPR method and the GCM. After reviewing several studies via both of these methods it is clear that AIT is a property that has a complex dependency on the molecular structure of the substance and is therefore challenging to model.

From the QSPR studies discussed above it is clear both electronic properties as well as structural properties from the molecules influence the observed AIT. These groups also mention that they see different results depending on the initial descriptors they use in their model when running their various optimization methods. Nonetheless, (amount of) aromaticity and flexibility of the molecule are reoccurring descriptors in the

different studies.

By looking at the data in the tables 1-4, one can already see that the AIT is not the best property to be modelled by the group contribution method. For straight chain alkanes the AIT decreases sharply with increasing carbon number up to C5 and then remains almost the same for C6 up to C20, indicating effects that cannot be modelled via the group contribution method have the largest effect on AIT.

It is exactly these effects which need to be explored in order to be able to use and steer the reactions

occurring during hydrocarbon combustion. In order to explain the trends, the sequence of events during auto ignition needs to be determined.

21

3.2 H

3.2.1 M

Combustion of hydrocarbon species is an exothermic process and results in the formation of the species CO2, CO and H2O. However, before forming these species various radical intermediates are formed and a chain reaction of these radical species has proceeded. A radical chain reaction comprises of several steps: initiation, propagation, termination and in certain cases branching.

The initiation step of hydrocarbon oxidation is endothermic and accounts for the observed kinetic barrier during oxidation. The initiation comprises of two steps [5]:

(1) RH +O2 R· + ·OOH (2) R· + O2 ROO·

The subsequent steps, propagation, branching and termination, are exothermic. The peroxyradical formed in reaction (2) can propagate the radical chain by either decomposing to an aldehyde and an alkoxy radical via reaction (3), by hydrogen abstraction, either externally (4) or internally (5) or by formation of an alkene and hydroperoxyl radical (6):

(3) ROO· → R’CHO + R”O· (4) ROO· + R’H → ROOH + R’·

(5) ROO· → ·ROOH

(6) ROO· → Alkene + ·OOH

The ratio of these reactions is dependent upon the structure of the hydrocarbon and the temperature [33-38]. Three other possible propagation steps are the reaction of the hydroperoxyalkyl radical with another

molecular of oxygen (7) or the abstraction of hydrogen by hydroperoxyl radical (8) or hydroxyl radical (9): (7) ·ROOH + O2 → ·OOROOH

(8) R + ·OOH → R· + HOOH (9) R + ·OH → R· + H2O

Branching can occur in several ways. The hydroperoxide formed in reaction (4) splits homolytically (10), the aldehydic hydrogen with a relatively weak C-H bond formed in reaction (3) gets abstracted by oxygen (11), the species formed in reaction (7) undergoes isomerization giving complex compounds and two hydroxyl radicals (12) or by the decomposition of in reaction (8) formed hydrogen peroxide (13) [4, 33, 34]:

(10) ROOH → RO· + ·OH

(11) RCHO + O2 → RC·O + HOO· (12) ·OOROOH → products + 2 ·OH (13) HOOH → HO· + ·OH

Branching results in the formation of one or two new radicals. These radicals can create new radical sites on surrounding hydrocarbon chains by hydrogen abstraction and result in an acceleration of oxidation rate. This forms the basis of autoignition of hydrocarbons [36, 37].

22

3.2.2

T

In hydrocarbon oxidation various temperature regions can be distinguished. The ratio of the above reactions and the displayed equilibria vary with temperature. While the exact temperature is dependent upon the structure, temperature regimes can be appointed.

Below 130 °C

At temperatures below 130 °C hydrocarbons do not notably undergo oxidation. Hydrocarbons comprise of relatively strong C-H bonds and the initiation reaction (1) is extremely slow in this temperature regime [4].

Between 130 and 330 °C

With increasing temperature up to 330 °C an increase in the speed of oxidation can be observed [34]. The equilibrium represented in reaction (2) lies increasingly to the right [33] and the increase in secondary initiation through reactions (4) followed by (10) as well as (5) followed by reactions (7) and (12) accounts for the observed increase in oxidation rate.

Between 330 °C and 630 °C

Remarkably, further increase in temperature results in a decrease in oxidation rate [5, 33, 34]. The equilibrium of reaction (2) lies increasingly to the left and alternative reactions, with higher activation energies, of ROO· start to dominate the reactions occurring between 130 and 330 °C [38]. Reaction (6) starts to dominate reactions (4) and (5). This reaction results in the formation of the hydroperoxyl radical and an alkene. The hydroperoxyl radical is a relatively stable species [34, 39] and is less prone to propagate the radical chain by hydrogen abstraction than hydroxyl radicals formed in the previous temperature regime. This results in a decrease in secondary initiation through branching reactions and subsequently a decrease in oxidation rate.

Above 630 °C

At temperatures above 630 °C an increase in oxidation rate with increasing temperature is once again

observed [34]. At these temperatures, the relatively stable hydroperoxyl radical formed in reactions (1), (6) and (11) abstracts a hydrogen atom from a hydrocarbon chain and forms a new alkyl radical and hydrogen

peroxide (reaction (8)). Subsequently, a these high temperatures the hydrogen peroxide decomposes into two new hydroxyl radicals via reaction (13).

With increasingly higher temperature the hydroperoxyl radical can also decompose into hydroxyl radical and oxygen radical, without prior abstraction of hydrogen [34].

23

3.3 H

Hydrogen abstraction reactions play an important role in hydrocarbon oxidation reactions. The initiation step, reaction (1) as well as several propagation steps, reactions (4), (5), (6), (8) and (9), comprise of hydrogen abstraction.

For auto ignition especially the propagation steps (4) and (5) are important, since at elevated temperatures the formed peroxide will split homolytically into an alkoxy radical and hydroxyl radical and thus create two additional radical sites.

The energy required for hydrogen abstraction can be divided into two categories.

3.3.1 S

Here we only look at abstractions of hydrogen from hydrocarbons. This simply means that the more stable the resulting carbon based radical is, the easier is the abstraction of hydrogen from that carbon [4]. This can simply be evaluated by looking at the bond dissociation energies (BDE) of various C-H bonds and results in the following general order of C-H bond strength [4, 40]:

Aromatic (112.9) > methane (105.0) > primary (101.1) > secondary (98.6) > tertiary (96.5)

The numbers in parentheses are an indication of the BDE in kcal/mol [41]. A conjugated π-bond provides stability by resonance, as can be seen for by slightly lower BDE values for such molecules. For example propylene, CH2=CH−CH2−H BDE of 88.8 kcal/mol, or toluene, phenyl−CH2−H BDE of 89.7 kcal/mol [41].

The stability of the carbon based radical has an effect on the observed AIT. In the tables 1-4 it can be seen that aromatic molecules, with the strongest C-H bonds based on the BDE, have the highest observed AIT. Also the order of carbon radical stability methane > primary > secondary can be seen in table 1. The AIT of methane, ethane and propane decreases respectively, as would be expected.

While the stability of the carbon based radical influences the AIT, additional effects must play a role as well. The AIT of iso-alkanes, table 2, is on average higher than that of straight-chain alkanes, table 1. Tertiary carbons have weaker C-H bonds than secondary carbons and this AIT data thus contradicts the in this paragraph discussed effect of radical stability on AIT.

3.3.2 E

The energy required for hydrogen abstraction comprises of two parts. Besides the in the previous paragraph discussed bond strength the ease of reach also has an effect. The bond strength is an indication of the energy required for the homolytical splitting of the C-H bond. However, during hydrogen abstraction reactions the C-H does not split homolytically into two radicals. The hydrogen atom gets abstracted, which means the energy required for the atom abstracting the hydrogen (be it intra- or inter-molecular) to reach that hydrogen needs to be incorporated.

For internal hydrogen abstraction, as displayed in reaction (5), it can thus be said that the more rigid the molecules backbone is or the more steric hindrance there is around the tertiary carbon the more energy is required for hydrogen abstraction.

For external hydrogen abstraction, as displayed in reactions (4), (8) and (9), only steric hindrance affects the ease of reach for hydrogen abstraction.

24

3.4 P

HYDROCARBONS

Looking at the trends in AIT, I propose that the internal hydrogen abstraction by the peroxyradical plays a key role in auto ignition. This abstraction can be from C-atoms in α, β, γ or δ position relative to the peroxidized carbon [5].

In aliphatic hydrocarbons the abstraction is expected to take place most from the carbons in β and γ-position. Abstraction from these positions results in transition state comprising of five or six-membered rings, which are the ring sizes that experience the least amount of strain [42]. Abstraction of hydrogen from a carbon in δ position would result in a transition state with a ring size of seven, also virtually strain free [42], but this requires the correct rotation of more bonds and is therefore expected to happen less. Generally speaking, incorporating both the ring-strain and the need for the correct orientation of the atoms, the speed of ring closing reactions follows the order 5-membered >> 6-membered >>> other ring-sizes [42].

For AIT, the presence of an easy to abstract hydrogen at the β-carbon seems to be dominant over the stability of the initial radical. Looking at straight chain alkanes, the drop in AIT from methane (537 °C) via ethane (515 °C) to propane (470 °C) can be attributed to the stability of the initial radical, being a methyl, primary and secondary, respectively.

On the other hand, the more significant drop in AIT from propane (470 °C) via butane (365 °C) and pentane (260 °C) to hexane (234 °C) can be explained by the presence and amount of hydrogens at the β-carbon. For all these molecules the initial radical formation is on a secondary carbon. The difference lies in the fact that the secondary carbon in propane has no β-carbons; either secondary carbon in butane has three hydrogens at a β-carbon; the centre secondary carbon in pentane has six and the other two secondary carbons two (average of 3.33) and hexane an average of 3.5 (4 secondary carbons with 2, 5, 5 and 2 hydrogens present at β-carbons). Additional −CH2− groups have an increasingly lower effect on this average amount of hydrogens at

β-carbons, which explains the levelling off of the AIT at longer carbon chains.

For iso-alkanes, the ease of reach of the hydrogens at β-carbons starts to play a role. Looking at the data in table 3, the AIT for iso-alkanes can be divided into two. The first group are the iso-alkanes with only one branch and a low-temperature autoignition and the second group is the iso-alkanes with multiple branches and high-temperature autoiginition.

For all iso-alkanes the initial hydrogen abstraction in the oxidation initiation step is expected to take place from a tertiary carbon. Now, the more heavily branched the carbon chain backbone, the more steric hindrance is encountered when the carbon chain backbone needs to be folded in order to reach a hydrogen attached to a β-carbon. This results in the requirement of more energy and thus a higher AIT. For the heavily branched iso-alkanes so much steric hindrance is required that temperatures are reached from the next temperature regime in hydrocarbon oxidation (see section 3.2.2). In this temperature regime, the equilibrium of reaction (2) is expected to lie more towards the alkyl radical than the peroxyradical. The result is that the auto-catalytic effect of branching reactions is less encountered and a lot of extra energy has to be put in before ignition takes place. This is exactly as is encountered in the data for iso-alkanes, where a large jump is made in AIT between the low-temperature and the high-temperature compounds.

The AIT data for alkenes can be discussed briefly. The initial hydrogen abstraction in the initiation step is expected to take place from the saturated part in the molecules as the abstraction of hydrogen from a sp2 -hybridized carbon atom requires more energy (11 kcal/mol difference based on the BDE [41]).

25 Aromatics are a different story. As was already discussed, aromatic C-H bonds are among the strongest [41]. A fully aromatic compound like benzene is thus expected to have a high AIT, as is indeed the case (560 °C). It gets more interesting when alkyl substituents are placed on the ring.

Due to the lower C-H bond strength initial hydrogen abstraction takes place from the substituent. Because of the stabilizing effect of the phenyl ring by resonance, the carbon attached directly to the ring is expected to be the site of initial hydrogen abstraction and thus, after reaction with oxygen, the peroxyradical. Two β-carbons are now aromatic carbons, with their high C-H bond strengths and only for the substituents propyl and longer carbon chains are other β-carbons present. However, since the initial abstraction will take place from the carbon directly attached to the ring, two of the possible three β-carbons1 _{will be aromatic. This explains the} high AIT for aromatic molecules.

Nonetheless, the effect of sp3_{-carbons with hydrogens attached in the γ-position can be seen in table 4. For} example, para and meta-xylene have virtually identical AIT of 530 °C and 527 °C, respectively. Ortho-xylene on the other hand has an AIT of 463 °C. The only difference between ortho and para/meta-xylene is that the former has a sp3_{-hybridized carbon with hydrogens attached in reach from the site of initial radical formation} (γ-position), where the latter have not (δ- and ε-position).

1 _{A sp}3_{-hybridized carbon can have four β-carbons when it is quaternary. However, since hydrogen abstraction needs to} take place for the site to oxidize, the maximum number of carbons is three.

26

4. P

OSSIBLE IMPLICATIONS

4.1 E

Engine knock occurs when the air/fuel mixture in an internal combustion engine ignites spontaneously instead of in response to a spark from the sparkplug [3]. This undesired event has already been linked to the autoignition of the fuel (i.e. hydrocarbons) long time ago [43]. Incorporating hydrocarbons with high AIT in the fuels should thus prevent engine knocking from taking place, as is indeed found to be the case [44, 45].

4.2 A

Various chemical processes require the activation of oxygen. Some examples of processes in which oxygen needs to be activated are oxygen reduction reactions (ORR) in for example fuel cells and oxidation reactions.

4.2.1 O

ORR

It is known that nitrogen doped carbon catalyses ORR. The exact mechanism by which this takes place is still under debate.

One research group proposes oxygen to attack at the carbon β to the incorporated nitrogen; after which a ring-structure is formed that incorporates both of the oxygen atoms and the nitrogen [46]. The O-O bond then opens up and a hydroxyl group and a hydroxyl amine are formed upon reaction with two protons and electrons.

A different research group proposes the carbon next to the incorporated nitrogen to be the site of attack. After this initial attack the outer oxygen atom forms a hydroperoxide by reaction with a proton and an electron. By reaction with two more protons and electrons, water and a hydroxyl group are formed [47]. In either case incorporating sp3_{-hybridized carbons in the vicinity of the nitrogen is likely to lower the} energetic barrier. In the former case because the initial attack of the oxygen is likely to require less energy on a sp3_{-hybridized carbon than an aromatic carbon. In the latter case the hydroperoxide is likely to form quicker} and with less energy.

4.2.2 L

Using nitrogen doped carbon as a support for oxidation catalysts has been shown to have a beneficial effect [48, 49]. I predict that incorporating sp3_{-hybridized carbons in the vicinity of the catalyst might lower the} energy required to activate the oxygen, due to the easier abstraction of hydrogen from a close by sp3 -hybridized carbon. However, it may have undesired effects due to blocking of micropores and surface hydrophibization. The ultimate trade-off between the trends is best determined experimentally.

27

5. C

ONCLUSIONS

Oxidation of hydrocarbons is a radical chain process. The initiation step is endothermic and the subsequent steps, propagation, branching and termination, are exothermic.

Once the energy released by the exothermic reactions is higher than can be lost to the surroundings, an auto-catalytic chain reaction of oxidations takes place known as ignition.

For ignition to take place, the amount of branching reactions should be maximized. Branching reactions result in the formation of more radical sites, which forms the basis for the auto-catalytic effect.

The temperature to which a substance must be raised before ignition takes place is dependent upon the structure of that substance.

The structure influences this temperature in two ways. First, the stability of the initial radical site has an influence. The more stable the initial radical is the less energy is required for the radical site to form. Second, the presence of hydrogens attached to sp3_{-hybridized carbons in β- or γ-position with respect to the carbon} where initial oxidation has taken place also influences the AIT. The more of these easy to abstract hydrogens present the lower the AIT.

Incorporating sp3_{-hybridized carbons with hydrogens attached in the vicinity of catalytic activation of oxygen} can potentially lower the energy required therefore.

28

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