Quantitative NMR Spectroscopy for the Analysis of Fuels: A

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Combustion

Quantitative NMR Spectroscopy for the Analysis of Fuels: A Case Study of FACE Gasoline F Andrew David Ure, John O'Brien, and Stephen Dooley Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.9b01019 • Publication Date (Web): 07 Sep 2019 Downloaded from pubs.acs.org on September 7, 2019

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Quantitative NMR Spectroscopy for the Analysis of Fuels: A Case Study of FACE Gasoline F Andrew D. Ure1, John E. O’Brien2 and Stephen Dooley1 1 2

School of Physics, Trinity College Dublin, Dublin, Ireland

School of Chemistry, Trinity College Dublin, Dublin, Ireland

Keywords: NMR Spectroscopy, Combustion, FACE Gasoline, Surrogate Fuel, Liquid Hydrocarbon Fuels, Heteronuclear Single Quantum Coherence (HSQC) Abstract A detailed experimental methodology is outlined which allows for the measurement of quantitative 1H and 13C Nuclear Magnetic Resonance (NMR) spectra of liquid hydrocarbons. Optimal experimental conditions are identified that allow for the collection of entirely quantitative 1H and 13C NMR spectra, the most significant among these are shown to be the choice of solvent and the delay time utilized. A best practice for the interpretation of the measured spectra that utilizes Heteronuclear Single Quantum Coherence (HSQC) NMR spectroscopy is outlined. Use of the HSQC method allows for the expeditious determination of fuel specific integral regions. Importantly, the use of HSQC is shown to be a convenient method for the identification of overlapping peaks. The fidelity of both 1H and 13C NMR spectroscopy for the analysis of liquid fuels is demonstrated through the analysis of a range of reference fuels of known composition. Atom type populations are calculated for the reference fuels using a defined set of operating equations. In general, the NMR spectroscopy measured atom type populations show a strong agreement with the known atom type populations. The uncertainty associated with these measurements is determined to be 99%) and m-xylene (>99%) were all purchased from Sigma-Aldrich. n-Decane (99%) and cyclopentane (95%) were purchased from Alfa Aesar. 2,2,4-trimethylpentane (>99.0%), n-dodecane (>99%) and ethyl benzene (>99%) were purchased from Tokyo Chemical Industry UK Ltd. n-Heptane (99.8%) was purchased from VWR international. 2-Methylbutane (99.39%) and hex-1-ene extra pure (SLR) were purchased from Fisher Scientific. Deuterated dichloromethane was purchased from Apollo Scientific. All chemicals were used as received, without further purification. All NMR spectra were collected in 7 inch Wilmad 5 mm thin wall precision NMR sample tubes in accordance with ASTM E438.71 1H and 13C{1H}

(13C herein) NMR spectra were collected using a Bruker Avance III 400 MHz NMR

spectrometer. NMR spectra were processed and analyzed using Bruker’s TopSpin 3.5 pl 7 software. Inversion recovery experiments were processed using the Bruker Dynamics Center software package. The compositions of the reference fuels used in this work are given in Table 1. Mole Fraction Component

PRF89 TRF

0.11 n-Heptane n-Decane 0.89 iso-Octane Toluene Methylcyclohexane 2.25 H:C

Model Model Fuel 1 Fuel 2

0.50 0.22 0.28 -

0.44 0.35 0.21 -

0.42 0.17 0.24 0.17

1.99

2.05

1.98

Table 1 - Compositions of the Primary Reference Fuel “89” (PRF89), the Toluene Reference Fuel (TRF) and the Model Fuels used in this work.

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3. Methodology Of the numerous instances reported in the literature regarding the use of 1H NMR spectroscopy in the quantitative analysis of liquid fuels, there are few reports which provided sufficient technical experimental information to allow for their critical evaluation. Of those that do provide the necessary information (Table S1) there is an apparent lack of consensus on the optimal experimental conditions that must be employed to generate useful, truly quantitative data. This is one of the two core issues addressed herein. A concise summary of the recommended experimental conditions for the measurement of quantitative 1H

and 13C NMR spectra of liquid fuels are given in Table 2. A comprehensive fundamental justification

and, where appropriate, experimental information to evidence these proposed standard experimental conditions can be found in the supporting information. The reader is strongly advised to consult this discussion.

Parameter

1H

Solvent Mass Solvent / g Mass Solute / g Concentration Cr(acac)3 / M Field Strength* / MHz Flip Angle / ° Acquisition Time / s Delay Time / s Time Domain Points (x 103) Sweep Width / Hz Dwell Time / μS Number of Scans Line Broadening / Hz

NMR CD2Cl2 1.0 0.05 0 400 90 4 60 64 8012 62.4 16 0.30

13C

NMR CDCl3 0.8 0.2 0.05 101 90 1.4 10 64 24038 20.8 3200 1.00

Table 2 – Recommended experimental parameters to obtain quantitative 1H and 13C NMR spectra of typically encountered liquid transportation fuels. *The parameters listed are universal and can be implemented irrespective of field strength. 12 ACS Paragon Plus Environment

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3.1 Spectral Interpretation Interpretation of 1H and 13C NMR spectra can be divided into two broad tasks; 1. The assignment of the observed peaks to the appropriate atom type. 2. Treatment of the assigned spectral regions in order to extract quantitative data. The former must be performed carefully, and on a sample-to-sample basis as is discussed by the case studies below. The latter is a far more general process and can be expressed as a series of operating equations that are applicable regardless of the liquid fuel sample. 3.1.1 Determination of Hydrogen Mole Fraction from 1H NMR Spectroscopy While it is not possible to definitively pre-assign specific regions of 1H (or 13C NMR) spectra to a given atom type, it is possible to say which atom types can be expected to be measured using this technique. These are listed in Table 3 and have been assigned a corresponding label (a-k). Once the ppm range of the peak for a given atom type has been determined (vide infra), the integral for that atom type from 1H NMR spectroscopy, 𝐼𝑥, (where 𝑥 = a-j) can be measured. In a 1H NMR spectrum, the measured relative integrals are directly proportional to the number of 1H nuclei associated with that atom type in the analyte. The sum of these relative integrals, HTotal is directly proportional to the total number of 1H nuclei in the sample. 𝑗

𝐻𝑇𝑜𝑡𝑎𝑙 =

∑𝐼

𝑥

#(𝟏)

𝑥=𝑎

Therefore, the hydrogen mole fraction from 1H NMR spectroscopy for a given atom type 𝑥, 𝜒𝐻𝑥(1𝐻), can be calculated as:

𝜒𝐻𝑥(1𝐻) =

𝐼𝑥 𝐻𝑇𝑜𝑡𝑎𝑙

#(𝟐)

From Equation 2 it is clear that the units of relative quantitative measurements from 1H or 13C NMR spectroscopy are fundamentally mole fraction hydrogen. Note, that for the purpose of the chemical functionality approach to the analysis of liquid fuels, there is no benefit gained from 13 ACS Paragon Plus Environment

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converting the measured mole fractions into mass fractions. This is converse to the assertion previously made by Jameel et al.51 3.1.2 Determination of Carbon Mole Fraction from 1H NMR Spectroscopy The major drawback of using hydrogen mole fraction as the metric to describe the atom type population is that it cannot account for quaternary carbon atom types, as they are not bonded to any hydrogen atoms. Therefore, the mole fraction hydrogen does not accurately depict the atom types in the sample as a whole. However, given that all H atoms are attached to a carbon atom in liquid hydrocarbon fuels,

1H

Atom Type

NMR Measured Integral (𝑰𝒙)

H Integral to “C” Integral Conversion 𝐼𝑎

Inferred Integral (𝑰𝒙∗ )

𝐼𝑎∗

Paraffinic CH3

𝐼𝑎

Paraffinic CH2

𝐼𝑏

Paraffinic CH

𝐼𝑐

Cycloparaffinic CH2

𝐼𝑑

C6H5-CH3

𝐼𝑒

C6H5-CH2-R

𝐼𝑓

C6H5-CH-R2

𝐼𝑔

Olefinic CH2

𝐼ℎ

Olefinic CH

𝐼𝑖

𝐼𝑖

𝐼𝑖∗

Aromatic CH

𝐼𝑗

𝐼𝑗

𝐼𝑗∗

Aromatic qC

n/a

𝐼𝑓

𝐼𝑘∗

Paraffinic qC

n/a

n/a

𝐼𝑙∗

3 𝐼𝑏 2 𝐼𝑐 𝐼𝑑 2 𝐼𝑒 3 𝐼𝑓 2 𝐼𝑔 𝐼ℎ 2

𝐼𝑒 3

+ 2 + 𝐼𝑔

𝐼𝑏∗ 𝐼𝑐∗ 𝐼𝑑∗ 𝐼𝑒∗ 𝐼𝑓∗ 𝐼𝑔∗ 𝐼ℎ∗

Table 3 – Assignment of standard notation and conversion procedures for the atom types discussed herein. Atom types are converted according to the attached number of H atoms. Note that 𝐼𝑙∗ is an effective integral determined through deduction, not an experimentally measured quantity.


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hydrogen mole fraction can be readily converted to carbon mole fraction; which can account for quaternary carbon atoms types. Thus, the atom type populations are herein discussed in terms of carbon mole fraction. a) Conversion of the Measured 1H Integrals to “Inferred” C Integrals In order to calculate the mole fraction carbon of a given atom type, the integrals measured from the 1H NMR spectrum, 𝐼𝑥, must be converted to give the equivalent number of carbon atoms. This is achieved using the number of H atoms in the atom type (Table 3). This requires the assumption that the designated number of H atoms in the atom type is correct e.g. CH3 has 3 attached H atoms; so, the measured integral must be divided by three. Thus, it is crucial that the integral regions are accurately assigned. In practice, this value may vary slightly due to overlapping peaks. Conversion of the 1H NMR measured integrals provides experimentally measured “Inferred Integrals”, represented as 𝐼𝑥∗ , for ten out of the twelve defined atom types (Table 3). b) Determination of Quaternary Carbon Inferred Integrals 𝑰𝒌∗ and 𝑰𝒍∗ Quantification of the quaternary carbon atom types 𝐼𝑘∗ and 𝐼𝑙∗ , by 1H NMR spectroscopy can be achieved utilizing two inductive assumptions. This process must be carried out before the inferred integrals are normalized to the total carbon content, so that all of the carbon atom types are represented. Assumption #1 – All aromatic quaternary carbon atoms have at least one corresponding non-aromatic alpha hydrogen atom. This is based on the fact that the C6H5–CH3, C6H5–CH2-R and C6H5–CH-R2 atom types all have a corresponding aromatic quaternary carbon atom. This requires the assumption that this is the only type of aromatic quaternary carbon atom present in the sample. For gasoline, this is a reasonable assumption as light end distillates do not typically contain polycyclic aromatics.77 However, this assumption may become invalid for samples that contain large fractions of poly aromatics i.e. kerosene and diesel.78 This is because the ring junction quaternary carbon atom types in poly aromatics do not have alpha hydrogen


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atoms therefore, are not quantifiable using this method. Note that the presence of polycyclic aromatics is indicated by aromatic CH peaks in the 7.5 – 8.0 ppm range.79 Assumption #2 – Any observed inequality between the actual 𝐻: 𝐶 and 𝐻: 𝐶𝑁𝑀𝑅 results entirely from the absence of any paraffinic quaternary carbon atom contribution to 𝐻: 𝐶𝑁𝑀𝑅. Using the inferred integrals, a-k (Table 3), the equivalent number of carbon atoms, 𝐶𝑇𝑜𝑡𝑎𝑙, can be estimated as: 𝑘

∑𝐼

∗ 𝑥

𝐶𝑇𝑜𝑡𝑎𝑙 =

#(𝟑)

𝑥=𝑎

𝐶𝑇𝑜𝑡𝑎𝑙 does not account for the presence of any paraffinic quaternary carbon atoms. It follows that, the 𝐻:𝐶 ratio according to NMR spectroscopy (𝐻:𝐶𝑁𝑀𝑅) is given by Equation. 4, as previously shown by Myers et al.48

𝐻:𝐶𝑁𝑀𝑅 =

𝐻𝑇𝑜𝑡𝑎𝑙 𝐶𝑇𝑜𝑡𝑎𝑙

#(𝟒)

Importantly, as 𝐻: 𝐶𝑁𝑀𝑅 does not account for paraffinic quaternary carbon atoms, it will always be greater than the actual 𝐻:𝐶. It is assumed that this inequality is entirely due to the omission of paraffinic quaternary carbon atoms. Thus;

𝐶𝐴𝑐𝑡𝑢𝑎𝑙 = 𝐶𝑇𝑜𝑡𝑎𝑙 ×

𝐻:𝐶𝑁𝑀𝑅 𝐻:𝐶

#(𝟓)

𝐼𝑙∗ = 𝐶𝐴𝑐𝑡𝑢𝑎𝑙 ― 𝐶𝑇𝑜𝑡𝑎𝑙 #(𝟔) where 𝐶𝐴𝑐𝑡𝑢𝑎𝑙 is the total inferred integral representative of all carbon atom types present in the sample and 𝐼𝑙∗ is the effective inferred integral for paraffinic quaternary carbon atoms. Each individual inferred integral (𝐼𝑥∗ ) must then be normalized against 𝐶𝐴𝑐𝑡𝑢𝑎𝑙 to give the mole fraction carbon derived from 1H NMR spectroscopy, 𝜒𝐶𝑥(1𝐻), for each atom type 𝑥:


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𝜒𝐶𝑥( 𝐻) =

𝐼𝑥∗

1

𝐶𝐴𝑐𝑡𝑢𝑎𝑙

#(𝟕)

c) Determination of the Average Degree of Aromatic Substitution The ability to determine the aromatic quaternary carbon content also allows us to estimate the average degree of substitution of the aromatic rings according to:

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑆𝑢𝑏𝑠𝑡𝑖𝑡𝑢𝑒𝑛𝑡𝑠 =

𝜒𝐶𝑘(1𝐻) 𝜒𝐶𝑗(1𝐻) + 𝜒𝐶𝑘(1𝐻)

× 6 #(𝟖)

Note, that using Equation 8 it is not possible to determine the distribution of the substituents between molecules e.g. a mixture of benzene and xylene in equal mole fractions will have an average number of substituents equal to one. d) Determination of Mole Fraction Carbon from 13C NMR Spectroscopy Quantitative 13C NMR spectroscopy can also be used to quantify mole fraction carbon of atom types in liquid fuels. The advantage of using 13C NMR over 1H NMR spectroscopy is that all carbon atom types, including quaternary carbon atoms, can be measured experimentally. Assuming the peaks in the 13C NMR spectrum can be assigned, the 𝑛 discrete integrals (𝐶𝐼𝑥𝑛) corresponding to each atom type, 𝑥, can be combined to give 𝐶𝐼𝑥𝑇𝑜𝑡𝑎𝑙, the total integral for atom type 𝑥 according to; 𝐶

𝐼𝑥𝑇𝑜𝑡𝑎𝑙 = 𝐶𝐼𝑥1 + 𝐶𝐼𝑥2 + 𝐶𝐼𝑥3 + … 𝐶𝐼𝑥𝑛 #(𝟗)

this value is directly proportional to the number of carbon atoms present as atom type 𝑥, therefore 13

𝐶𝑇𝑜𝑡𝑎𝑙 is given by; 𝑘

13

𝐶𝑇𝑜𝑡𝑎𝑙 =

∑𝐼 𝐶

𝑥𝑇𝑜𝑡𝑎𝑙

#(𝟏𝟎)

𝑥=𝑎

and is directly proportional to the total number of carbon atoms in the sample. The mole fraction of carbon atoms in the atom type 𝑥, according to 13C NMR (𝜒13𝐶𝑥), is then given by; 17 ACS Paragon Plus Environment

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𝐶

𝜒𝐶𝑥( 𝐶) = 13

𝐼𝑥𝑇𝑜𝑡𝑎𝑙

13

𝐶𝑇𝑜𝑡𝑎𝑙

#(𝟏𝟏)

The prerequisite to the fidelity of Equation 9, Equation 10 and Equation 11 is the accurate assignment of every peak in the spectrum to the correct atom type. For complex mixtures this is not a trivial task and cannot be simplified in the same manner as for 1H NMR spectra. This is the significant complication applying 13C NMR spectroscopy for the quantitative analysis of liquid hydrocarbon fuels. It is possible to distinguish between CH3, CH2, CH, paraffinic qC, aromatic CH and aromatic qC relatively quickly using distortionless enhancement by polarization transfer (DEPT) experiments. However, it is not possible to resolve these carbon atom types into more specific atom types without a significant input of intellectual effort.73 For example, DEPT experiments alone cannot specify if CH2 atom types are present as paraffins, cycloalkanes, olefins or C6H5-CH2-R whereas, crucially, 1H NMR spectroscopy can. This is a principle justification for applying 1H NMR spectroscopy as the primary technique for the analysis of liquid fuels herein. e) Calibration of the 13C NMR Spectrum using 1H NMR Data In the appropriate scenario, data obtained from the 1H NMR spectrum can be used to convert the measured 13C NMR spectrum integrals into units of carbon mole fraction. This allows mole fraction carbon to be calculated from the 13C NMR spectrum, without the need to integrate all of the peaks. This methodology is used herein to determine the carbon mole fraction of individual molecules within mixtures; rather than atom types. If a peak, 𝛼, assignable to the same atom type within a single known molecule, can be identified in both the 1H and 13C NMR spectra then;


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𝜒𝐶𝛼(1𝐻) ≡ 𝐶𝐼𝛼 #(𝟏𝟐) which allows the following calibration constant to be established;

Calibration constant (mole fraction per integral unit) =

𝜒𝐶𝑥(1𝐻) 𝐶

𝐼𝑥

#(𝟏𝟑)This calibration constant can be

used to convert integral units measured in the 13C spectrum into units of mole fraction carbon. Carbon mole % of the molecule can then be calculated according to Equation 14.

Mole % C (Molecule) = Mole % C (Atom Type) × #

# of C Atoms in Molecule # of C Atoms Represented by Signal

#(𝟏𝟒)

This methodology is most conveniently explained by a specific example and is therefore discussed below. f) Heteronuclear Single Quantum Coherence Spectroscopy HSQC spectroscopy is a 2-dimensional NMR experiment in which the 1H spectrum is given on the xaxis while the 13C spectrum is given on the y-axis. A cross-peak is observed in the center of the spectrum indicating a single C-H bond between the corresponding nuclei responsible for the peaks in the 1H and the

13C

spectrum. In the phase edited version of this experiment, C atoms with an odd number of

attached H atoms (i.e. CH3 and CH) appear in the opposite phase (a different color) to those with an even number of attached H atoms (i.e. CH2).73 This allows for CH3, CH2 and CH peaks to be readily distinguished. Phase edited HSQC is similar to the commonly used 13C DEPT 135 experiment however, phase edited HSQC is significantly more sensitive as the 13C nucleus is attached to the more abundant 1H

nucleus.73

Unlike 1H and 13C NMR spectroscopy, HSQC is purely a qualitative technique. The main benefit of using this technique is that overlapping peaks in the 1H spectrum (x-axis) are resolved along the y-axis according to their 13C chemical shift. This can crudely be thought of as a chromatogram of the peaks contributing to a given peak in the 1H spectrum. Importantly, this allowed the peaks that contribute to each peak in the 1H NMR spectrum to be identified and therefore any exposure to overlapping peaks to


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be assessed. The assignment of integral regions using HSQC spectroscopy is discussed in more detail below.


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4 Results: Method Validation After careful review of the existing literature it was surprising to find that there were no reported studies that systematically applied NMR spectroscopy to the analysis of fuel like mixtures of known composition, in order to validate the technique. Therefore, this was adopted as the starting point to this study. To do this, four model fuels that contain the range of atom types commonly found in gasoline fuels were selected (Table 1). 4.1 Analysis of Primary Reference Fuel “89” (PRF89) a)

1H

NMR Spectroscopy

Primary Reference Fuels (PRFs) are mixtures of n-heptane and iso-octane (Table 1). Based on the chemical structures of these molecules, peaks are expected in the 1H NMR spectrum corresponding to paraffinic CH3, paraffinic CH2 and paraffinic CH atom types. As PRF89 is a simple mixture, the peaks in the 1H NMR spectrum were readily assigned to their corresponding atom types (Figure 1a). The measured integrals were treated as described above to generate the atom type population of PRF89 (Table 4).

Figure 1 – a) 1H NMR spectrum of PRF89 (0.05 g) in CD2Cl2 (1.0 g) at 400 MHz. b) 13C NMR spectrum of PRF89 (0.2 g) with 0.05 M Cr(acac)3 in CDCl3 (0.8 g) at 101 MHz. Experimental conditions are given in Table 3. The y-axis of all spectra are truncated for clarity. Un-truncated 1H NMR spectra including integral regions and integral values as well as 13C NMR resonance assignments are available as supporting information.


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Mole % Carbon Atom Type

Actual

Paraffinic CH3 Paraffinic CH2 Paraffinic CH Paraffinic Quaternary C

59.0 18.4 11.3 11.3

1H

NMR

58.9 18.6 11.3 11.2

Absolute Difference 0.1 0.2 0.0 0.1

13C

NMR

58.6 18.8 11.3 11.3

Absolute Difference 0.4 0.4 0.0 0.0

Table 4 – Comparison of the carbon mole % atom type populations from 1H and 13C NMR spectroscopy of PRF89 with the actual value.

These results are compared with the expected values; as calculated from the known mole fractions of each component (Table 1). An excellent agreement between the known values and those measured by 1H

NMR spectroscopy was observed. The strong agreement can be attributed to the fact that there is no

overlap between any signals in the 1H NMR spectrum therefore, the measured integrals are entirely unambiguous. This confirmed that the conditions outlined in Table 4 were suitable for measuring quantitative 1H NMR spectra of liquid fuels. Of particular significance is the fact that the value for the mole % C of the paraffinic quaternary carbon atom type from 1H NMR spectroscopy (11.16 mole % C) was in excellent agreement with the expected value (11.25 mole % C). This is an important result as it validates assumption #2 and shows that the discrepancy between 𝐻:𝐶 and 𝐻:𝐶𝑁𝑀𝑅 can be used to accurately approximate 𝐼𝑙∗ as per Equation 5 and Equation 6. b)

13C

NMR Spectroscopy

The quantitative

13C

NMR spectrum for PRF89 was also acquired and assigned (Figure 1b). The

assignment of the 13C NMR spectrum is slightly more complex than the 1H NMR spectrum due to both the increased number and dispersity of the peaks (Figure 1a). Therefore, this problem was addressed with the use of the corresponding heteronuclear single quantum coherence (HSQC) spectrum. This technique is discussed in more detail below. The measured integrals were treated as discussed above to derive the atom type populations of PRF89 from 13C NMR spectroscopy (Table 4). Quantitation of the atom types using 13C NMR spectroscopy showed an excellent agreement with the actual values (Table 4). This demonstrates that the conditions outlined in Table 4 are suitable to measure quantitative 13C NMR spectra of liquid fuel-like mixtures. 22 ACS Paragon Plus Environment

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In spite of the accuracy of the atom type populations derived from 13C NMR spectroscopy, it is clear from inspection of the spectra (Figure 1), that while the 1H NMR spectrum can be divided into broad regions corresponding to specific atom types, the same cannot be achieved for the 13C NMR spectrum. Even in the simple case of a PRF, the paraffinic CH3 peaks are spread over a ~20 ppm range which overlaps with the paraffinic CH2 peaks; that are also spread over a ~35 ppm range. Furthermore, peaks from paraffinic CH3, paraffinic CH2 and paraffinic quaternary carbons are all present within a 5 ppm window, centered at 30 ppm. This observation suggests that the application of generic integral regions for the analysis 13C is inadvisable as there is significant overlap between the peaks for different atom types, even in this simple binary system. 4.2 Analysis of Ternary Mixtures: Toluene Reference Fuel (TRF) and Model Fuel 1 Next, more complex mixtures, a TRF and Model Fuel 1 (Table 1), that consist of a n-paraffin, isooctane and toluene were analyzed.

Figure 2 - a) 1H NMR spectrum of the TRF (0.05 g) in CD2Cl2 (1.0 g) at 400 MHz. b) 13C NMR spectrum of the TRF (0.2 g) with 0.05 M Cr(acac)3 in CDCl3 (0.8 g) at 101 MHz. Experimental conditions are given in Table 3. The y-axis of all spectra are truncated for clarity. Un-truncated 1H NMR spectra including integral regions and integral values as well as 13C NMR resonance assignments are available as supporting information.


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Atom type

Actual

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Mole % Carbon Absolute 1H NMR 13C NMR Difference

Absolute Difference

Paraffinic CH3

29.0

29.3

0.3

29.0

0.0

Paraffinic CH2

37.6

38.1

0.5

37.7

0.1

Paraffinic CH Paraffinic Quaternary Carbon C6H5-CH3 Aromatic CH Aromatic Quaternary Carbon

3.1 3.1 3.9 19.4 3.9

3.2 2.1 3.9 19.5 3.9

0.1 1.0 0.0 0.1 0.0

3.3 3.1 4.0 19.1 3.8

0.2 0.0 0.1 0.3 0.1

Table 5 - Comparison of the carbon mole % atom type populations from 1H and 13C NMR spectroscopy of the TRF with the actual value.

Mole % Carbon Atom Type Paraffinic CH3 Paraffinic CH2 Paraffinic CH Paraffinic Quaternary Carbon C6H5-CH3 Aromatic CH Aromatic Quaternary Carbon

Actual 30.6 44.3 4.1 4.1 2.4 12.1 2.4

1H

NMR

30.6 44.8 4.1 3.6 2.4 12.1 2.4

Absolute Difference 0.0 0.5 0.0 0.5 0.0 0.0 0.0

13C

NMR

30.5 44.7 4.1 4.1 2.3 11.9 2.4

Absolute Difference 0.1 0.4 0.0 0.0 0.1 0.2 0.0

Table 6 - Comparison of the carbon mole % atom type populations from 1H and 13C NMR spectroscopy of Model Fuel 1 with the actual value.

a)

1H

NMR Spectroscopy of Ternary Mixtures

The 1H NMR spectra for the TRF and Model Fuel 1 were acquired, and integral regions a-c, e and j were assigned (Figure 2a). The measured integrals were treated as described above to give the atom type populations for the TRF and Model Fuel 1, which are shown in Table 5 and Table 6 respectively. As with PRF89, the measured values for the TRF and Model Fuel 1 are in excellent agreement with those expected based on the mixture composition (Table 1). For both the TRF and Model Fuel 1, the largest discrepancy for measured values was found for the paraffinic CH2 atom types. This is most likely due to the fact that this integral region is comprised of multiple overlapping, high multiplicity, peaks. This consistently results in a slight overestimation of the carbon mole % of the paraffinic CH2 atom type in PRF89, the TRF and Model Fuel 1. A consequence of this is that in the TRF and Model Fuel 1,


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the carbon mole % of the paraffinic quaternary carbon atom type is underestimated. This is because 𝐻: 𝐶𝑁𝑀𝑅 is affected by the overestimation of the carbon mole % of the paraffinic CH2 atom type, i.e. assumption #2 is not strictly true. Using Equation 11, it was shown that the average degree of aromatic substitution in both the TRF and Model Fuel 1 was 1.0. This reflects the fact that the only aromatic present in these mixtures is the monosubstituted toluene. Most importantly, the results summarized in Tables 7 and 8 demonstrate the applicability of calculating the aromatic quaternary carbon content based on non-aromatic alpha carbon atoms i.e. the validity of assumption #1. b)

13C

NMR Spectroscopy of Ternary Mixtures

The respective 13C NMR spectra for the TRF (Figure 2b) and Model Fuel 1 were assigned with the aid of the corresponding HSQC spectrum. The measured integrals were treated as described above to derive the atom type populations of the TRF (Table 5) and Model Fuel 1 (Table 6). In general, the atom type populations in the TRF and Model Fuel 1, show excellent agreement with the actual values. The absolute difference between the actual and 13C NMR values for the paraffinic CH2 atom type in Model Fuel 1 is slightly larger than that observed for the TRF. This is due to clustering of the CH2 peaks from n-decane which complicates the integration in the 13C NMR spectrum of Model Fuel 1 c.f. the TRF. It is again noteworthy that the 13C NMR spectra for the TRF and Model Fuel 1 both show a tight cluster of peaks from different atom types centered around 30 ppm. As with PRF89, this suggests that it is not possible to prescribe a generic ppm range within the spectrum to a given atom type. The results obtained from the 1H and 13C NMR analysis of PRF89, TRF and Model Fuel 1 served an important purpose. Comparison of the 1H and 13C NMR analysis shows that measurements of the atom types of comparable fidelity can be obtained using either of the two techniques. This is important as the ability to utilize 1H NMR spectroscopy to carry out this analysis represents a significant reduction in both the required experimental time as well as in the complexity of the spectral assignment.


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4.3 Analysis of Model Fuel 2 Although the three examples discussed above serve excellent demonstrative purposes, they are ideal examples, with a low total number of components and no overlapping peaks from different atom types. In order to progress this analysis towards real fuels that do contain a high number of component molecules and consequently often have overlapping peaks from different atom types, the use of phase edited HSQC NMR spectroscopy was pursued. a) Analysis using HSQC Spectroscopy In order to demonstrate the utility of this technique, Model Fuel 2 was formulated (Table 1). The addition of methylcyclohexane causes significant peak overlap c.f. Model Fuel 1. This is because the CH2 peaks in methylcyclohexane are distributed over an unusually wide chemical shift range for hydrocarbons (0.90 – 1.77 ppm). This distribution occurs because the presence of the methyl group reduces the symmetry of the molecule (c.f. cyclohexane). Thus, there are three unique CH2 carbon atoms within methylcyclohexane, each of these carbons is bonded to two non-equivalent hydrogen atoms

Figure 3 – Phase edited HSQC spectrum of Model Fuel 2. Region 1 shows overlap between the CH of iso-octane with three of the CH2 atom types in methyl cyclohexane. Region 2 shows overlap of the CH in methylcyclohexane, two of the CH2 atom types in methylcyclohexane and all of the CH2 atom types in n-decane. Region 3 shows overlap of a CH2 atom type from methylcyclohexane, the CH3 atom type from methylcyclohexane and the CH3 atom type from n-decane. Data was collected on Model Fuel 2 (0.05 g) in CD2Cl2 (1.0 g) at 600 MHz


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(axial and equatorial), giving rise to six unique CH2 peaks in the spectrum. The wide ppm range over which these peaks occur is a result of strong H-H coupling interactions between the axial and equatorial H atoms attached to the same carbon atom (germinal coupling). This phenomenon can be expected in all substituted cycloalkanes. A phase edited HSQC spectrum for Model Fuel 2 is shown in Figure 3. The region of the spectrum containing the aromatic CH and C6H5-CH3 peaks has been omitted as these peaks are discrete therefore readily identified from the 1H NMR spectrum alone. The spectral region shown in Figure 3 contains all of the paraffinic peaks for Model Fuel 2. CH2 peaks (blue) can be quickly distinguished from CH3 and CH peaks (red). [N.B. the CH3 peak at the top of region 3 appears both red and blue due to non-ideal phasing of the spectrum. This is a result of strong overlap with the oppositely phased CH2 peak along the x-axis.] It is immediately apparent that there are three regions of the spectrum in which there is significant overlapping of peaks. Region 1 (Figure 3) shows overlap between the CH of iso-octane with three of the CH2 groups in methyl cyclohexane. Region 2 shows overlap between the CH of methylcyclohexane, two of the CH2 groups from methylcyclohexane and all of the CH2 groups from n-decane. Region three shows overlap between a CH2 group from methylcyclohexane, the CH3 group from methylcyclohexane and the CH3 groups from n-decane. Thus, every peak in the paraffinic region is overlapped by a peak from a different atom type. This observation has a significant impact on the analysis of the spectrum. Without the use of the HSQC spectrum, it is likely that region 1 would be assigned as purely CH, region 2 as purely CH2 and region 3 as purely CH3 when in fact, this is clearly not the case. The implication of the overlapping peaks is that it is not possible to accurately convert the integrals measured from the 1H NMR spectrum, according to Table 3, because the number of hydrogen atoms attached to the CHx atom type is unknown. In this instance, there is no scientifically justifiable method for converting the measured 1H integrals to their corresponding inferred integral therefore the analysis of Model Fuel 2 using 1H NMR spectroscopy was not performed.


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This is a somewhat unusual example and is a result of a combination of the complexity of the 1H NMR spectrum of methylcyclohexane and Model Fuel 2 consisting of only 4 components. Consequently, the effect of overlap arising from methylcyclohexane, which accounts for ~17 mol % of the entire mixture, is significant. In this respect, the analysis of more complex real fuels is more straightforward as it can be considered a “sloppy” problem.39 The vast number of individual components allows for compensatory effects within the system; it is possible for the overlap in one region to be compensated for by overlap in another region. This is reflected in the high fidelity of the analysis of more complex mixtures discussed below. b) Analysis using 13C NMR Spectroscopy The atom type population of Model Fuel 2 was, however, accurately measured using quantitative 13C spectroscopy (Figure 4, Table 7). The biggest discrepancy between the 13C NMR value and the actual value was found for the paraffinic CH3 and paraffinic CH2 atom types. This is because of multiple instances of overlap between peaks arising from these atom types at both 30.0 and 26.0 ppm. It is clear from Figure 4 as to why quantitative 13C NMR spectroscopy cannot be routinely applied to real fuels. As shown with previous examples, peaks from different atom types are tightly grouped. Thus, generic integral regions cannot be ascribed to these 13C NMR spectra. The considerable complexity in the 13C NMR spectrum of Model Fuel 2 arises from only four components, the accurate assignment of

Mole % Carbon Atom Type Paraffinic CH3 Paraffinic CH2 Paraffinic CH Paraffinic Quaternary C C6H5-CH3 Aromatic CH Aromatic Quaternary C

Actual

NMR

Absolute Difference

22.2 51.9 4.0 2.1 2.8 14.2 2.8

22.6 52.2 3.9 2.1 2.7 13.8 2.7

0.4 0.3 0.1 0.0 0.1 0.4 0.1

13C

Table 7 – Comparison of the carbon mole % atom type populations from 13C NMR spectroscopy of Model Fuel 2 with the actual value.


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Figure 4 – 13C NMR spectrum of Model Fuel 2 (0.2 g) with 0.05 M Cr(acac)3 in CDCl3 (0.8 g) at 101 MHz. Spectra were collected using the conditions given in Table 3. All spectra have been truncated on the y-axis for clarity. Colored regions indicate the integral regions utilized. Resonance assignments are given in Table S2.

these peaks took considerable time c.f. the assignment of a 1H NMR spectrum. For this reason, quantitative analysis of more complex mixtures using 13C NMR spectroscopy was not pursued. 4.4 Analysis of Model Fuel 3 In order to demonstrate that the high-fidelity 1H NMR analysis shown for PRF89, the TRF and Model Fuel 1 was not due to the simplicity of the mixture and that the failure of the method in analyzing Model Fuel 2 was related to the “sloppiness” of the problem, Model Fuel 3 was formulated. The composition of Model Fuel 3 (Table 8) constitutes an atom type population typical of a gasoline fuel. Four separate iso-paraffins were selected to reflect the fact that this group of compounds is the most structurally diverse found in typical gasolines. Consequently, these components convey a higher degree of complexity to the resulting 1H NMR spectrum.

Component n-dodecane 2-methylbutane 2,3-dimethylbutane 2,3-dimethylpentane iso-octane Cyclopentane Hex-1-ene m-xylene Ethylbenzene

Mole %

Mole % Carbon

4.98 22.19 11.66 14.15 15.47 12.85 10.63 6.75 1.31

9.11 16.91 10.66 15.10 18.87 9.80 9.72 8.23 1.60

Table 8 - Mixture mole fraction and mole % carbon of components in Model Fuel 3.


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Figure 5 - Phase edited HSQC spectrum of Model Fuel 3. The y-axis of all spectra are truncated for clarity. Data was collected on Model Fuel 3 (0.05 g) in CD2Cl2 (1.0 g) at 600 MHz. * Denotes the residual solvent signal. Un-truncated 1H NMR spectra including integral regions and integral values as well as 13C NMR resonance assignments are available as supporting information.

Mole % C Atom Type

Actual

Paraffinic CH3 Paraffinic CH2 Paraffinic CH Paraffinic Quaternary Carbon Cyclic CH2 C6H5-CH3 C6H5-CH2-R Olefin CH Olefin CH2 Aromatic CH Aromatic Quaternary Carbon

41.0 20.3 13.6 2.4 9.8 2.1 0.2 1.6 1.6 5.1 2.3

1H

NMR

39.9 22.3 12.9 2.3 9.2 2.2 0.2 1.6 1.6 5.4 2.4

Absolute Difference 1.1 2.0 0.7 0.1 0.6 0.1 0.0 0.0 0.0 0.3 0.1

Table 9- Comparison of the carbon mole % atom type populations from 1H and 13C NMR spectroscopy of Model Fuel 3 with the actual value.


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a) HSQC Analysis of Model Fuel 3 The HSQC spectrum of Model Fuel 3 was obtained in order to facilitate the assignment of the integral regions in the 1H NMR spectrum (Figure 5). The integral regions for aromatic CH, olefinic CH, olefinic CH2, C6H5-CH2-R and C6H5-CH3 all occur in characteristically discrete regions of the spectrum thus are easily identified and assigned (Figure 5). The paraffinic region of the spectrum (< 2.0 ppm), while considerably more complicated, nonetheless can be divided into the discrete regions (Figure 5). The cycloparaffinic CH2 integral region was assigned as 1.59 – 1.54 ppm while the paraffinic CH integral was assigned as two regions 1.81 – 1.59 and 1.54 – 1.43 ppm (Figure 5). This overlap could not have been identified without the use of the HSQC spectrum. Similarly, the HSQC spectrum was used to delineate between the paraffinic CH and paraffinic CH2 regions as well as the paraffinic CH2 and paraffinic CH3 (Figure 5). It is clear from this assignment of the integral regions of the enormous benefit that accompanies the implementation of HSQC spectroscopy. Bespoke integral regions can be quickly and accurately determined on a fuel by fuel basis. This ultimately allows us to measure integrals that accurately reflect the chemical composition of the fuel. This is an important achievement as the ultimate goal of this analysis is to interpret these measurements in terms of chemical reaction kinetics. The spectrum was integrated using the regions defined in Figure 5, and the resulting atom type description of Model Fuel 3 was derived using the previously described methodology (Table 9). The values measured from 1H NMR spectroscopy show a good agreement with the known measured values across all atom types. The biggest discrepancies were observed for the atom types with peaks that are exposed to the highest degrees of overlap, i.e. the paraffinic CH3, CH2, CH and cycloparaffinic CH2 atom types. This is in line with the observations made for PRF89, the TRF and Model Fuel 1. Importantly, the H:C ratio method for approximation of the quaternary carbon content has been shown to hold even in more complex mixtures. The results shown in Table 9 are important as they demonstrate that the NMR methodology developed using simple reference fuels can be applied to yield an accurate atom type population of considerably more complex mixtures. 31 ACS Paragon Plus Environment

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b) Average Degree of Aromatic Substitution The average degree of aromatic substitution in Model Fuel 3 was calculated to be 1.85 from 1H NMR spectroscopy. This is in strong agreement with the actual value, 1.84. This reflects the fact that the major aromatic component is the di-substituted m-xylene while the other, minor, aromatic component is the mono-substituted ethyl benzene. c) Relative Quantification of Individual Components from 13C NMR Spectroscopy As demonstrated above, complete quantitation of atom types using

13C

NMR spectroscopy is not a

trivial task. Even for a nine-component mixture such as Model Fuel 3, there are 40 discrete peaks in the 13C

NMR spectrum that must be assigned. However, 13C NMR spectroscopy is an incredibly powerful

tool for quantifying individual components within fuel mixtures. To achieve this, we require a peak assignable to the same atom type within a single known molecule, identifiable in both the 1H and 13C NMR spectra. In the 1H NMR spectrum of Model Fuel 3, the olefinic CH2 peak occurs at 5.10 – 4.90 ppm. The only atom type contributing to this peak is the olefinic CH2 in hex-1-ene. This peak, i.e. 𝜒𝐶ℎ(1𝐻), corresponds to 1.57 mole % carbon (Table 9). The corresponding CH2 peak in the 13C spectrum, 𝐶𝐼ℎ, was identified at 113.7 ppm using the HSQC spectrum (Figure 5). Since 𝜒𝐶ℎ(1𝐻) ≡ 𝐶𝐼ℎ according to Equation 12, a calibration constant of 1.57 carbon mole % per 13C NMR integral unit was calculated using Equation 13. This value was used to calculate the carbon mole % of iso-octane and cyclopentane present in Model Fuel 3 (Table 10) according to Equation 15. These measured values were in good agreement with the actual values and demonstrate how 1H and 13C NMR spectroscopy can be combined to expeditiously measure the carbon mole % of individual molecules. 13C

Chemical Component Shift / ppm Hex-1-ene 113.7 iso-octane 52.8 Cyclopentane 25.5

Molecular Fragment Measureda

C Mole % Represented by Integralb

CH2 CH2 C5H10

1.57 2.31 9.22

13C

NMR C Mole % (Molecule)

Actual C Mole % (Molecule)

Absolute Difference

9.42 18.50 9.22

9.72 18.87 9.80

0.30 0.37 0.58

Table 10 - Comparison of the 13C NMR spectroscopy derived carbon mole % of iso-octane and cyclopentane for Model Fuel 3 with the actual values. aIndicates the number of carbon atoms represented by the signal. bCalculated by multiplying the measured integral by the calibration constant defined by Equation 13


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The measurement of the cycloparaffinic CH2 atom type (of which cyclopentane is the sole contributor) of 9.16 mole % carbon from the 1H NMR spectrum (Table 9), agrees well with the corresponding value (9.22 mole % carbon) obtained using the calibrated 13C NMR spectrum (Table 10). Thus, comparison of HSQC divided 1H NMR values with those from a calibrated 13C NMR spectrum can, in appropriate instances, be used to assess the fidelity of the 1H NMR spectroscopy measurements. 4.7 Uncertainty Assignment of an absolute standard uncertainty to the atom type populations derived from NMR spectroscopy is not a trivial task. Typical values for the standard uncertainty in quantitative NMR measurements range from 0.5-2.0 %.80, 81 One of the major contributors to these values is the signal-tonoise ratio of the spectrum. (Note, other significant contributions arise from gravimetric sample preparations required for absolute concentration determinations. Such contributions are not applicable to this work.) It is estimated that for a signal-to-noise ratio of 30:1 the standard uncertainty on the measured integral is 3 %.80 For a signal-to-noise ratio of 2500:1, this value is < 0.2 %.81 It is important to note that these values are associated with absolute measurements on single compounds, not relative measurements on mixtures as investigated herein. The signal-to-noise ratio of the peaks in the Model Fuel 3 1H NMR spectrum are in the range of approximately 35-10000:1. Consequently, the standard uncertainty on the measured integrals is in the range 100 s to 10 s. The choice of solvent is also shown to be important. It is imperative that the residual solvent signal does not overlap with any signals that may be of interest. For this reason, CD2Cl2 is recommended for use for 1H NMR while CDCl3 is recommended for use for 13C

NMR.

A series of operating equations for the relative quantitation from both 1H and

13C

NMR spectra is

described. These equations are derived from first principles and show that the units of the measured data are inherently mole % H or mole % C respectively. It is shown how mole % H can be converted to give mole % C. This conversion is suggested as the paraffinic carbon content is otherwise unaccounted for; which is not possible using only mole % H. Importantly, these operating equations are applicable to all liquid hydrocarbon fuels.


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The described methodology is validated through the analysis of a series of reference fuels. In general, both the 1H and

13C

NMR measured values replicate the actual values to high fidelity; even in the

instance of a complex, nine component, reference fuel. However, substituted cycloalkanes such as methylcyclohexane are highlighted as being particularly difficult to quantify. The 1H NMR spectrum, rather than the 13C NMR spectrum, is proposed as the preferred spectrum from which to derive quantitative data. This is because in general, the signals from different atom types are more spatially resolved in the 1H spectrum c.f. the 13C spectrum. Two-dimensional heteronuclear single quantum coherence (HSQC) spectroscopy is shown to be invaluable in producing fuel specific integral regions. This avoids the common and unadvisable practice that prevails in the literature of employing generic and prescriptive integral regions. Furthermore, it is shown that HSQC NMR can be used to readily identify overlapping signals from different atom types. This newly developed comprehensive methodology was applied to the analysis of FACE gasoline F. The NMR measured values were compared with a similar analysis obtained using detailed hydrocarbon analysis (DHA). In general, the NMR and DHA measured values were in good agreement with one another. This is particularly true for the more spatially resolved signals e.g. aromatic CH, olefinic CH etc. The paraffinic CH, paraffinic CH2 and paraffinic CH3 measurements all agree within the uncertainty of the NMR measurement. It is important to note that it is not possible to say if the discrepancies originate from the NMR or the DHA analysis. Finally, 1H NMR was used to characterize the olefinic species in FACE F, which had been mis-identified in the DHA analysis. This highlights the potential for a complementary relationship between the various analytical techniques typically employed in the analysis of liquid hydrocarbon fuels. The NMR techniques described in this manuscript are suitable to measure atom type descriptors. Ultimately, identification of larger molecular fragments, in particular chemical functionalities, is sought. Efforts in our group are currently focused on the use of other two-dimensional NMR techniques such as Heteronuclear Multiple Bond Coherence (HMBC) spectroscopy towards this goal.


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Conflicts of Interest There are no conflicts to declare. Acknowledgements Work at Trinity College was funded by Science Foundation Ireland under award 16/ERCD/3685, and also as part of the “Future Fuels” Competitive Center Funding (CCF) program at King Abdullah University of Science and Technology.

References 1. Curran, H. J., Developing detailed chemical kinetic mechanisms for fuel combustion. Proc. Combust. Inst. 2019, 37, (1), 57-81. 2. Dryer, F. L., Chemical kinetic and combustion characteristics of transportation fuels. Proc. Combust. Inst. 2015, 35, (1), 117-144. 3. ASTM D6729-14, Standard Test Method for Determination of Individual Components in Spark Ignition Engine Fuels by 100 Metre Capillary High Resolution Gas Chromatography, ASTM International, West Conshohocken, PA, 2014, www.astm.org. 4. ASTM D6730-01(2016), Standard Test Method for Determination of Individual Components in Spark Ignition Engine Fuels by 100–Metre Capillary (with Precolumn) High-Resolution Gas Chromatography, ASTM International, West Conshohocken, PA, 2016, www.astm.org. 5. ASTM D6733-01(2016), Standard Test Method for Determination of Individual Components in Spark Ignition Engine Fuels by 50-Metre Capillary High Resolution Gas Chromatography, ASTM International, West Conshohocken, PA, 2016, www.astm.org. 6. Wang, F. C.-Y.; Qian, K.; Green, L. A., GC×MS of Diesel: A Two-Dimensional Separation Approach. Anal. Chem. 2005, 77, (9), 2777-2785. 7. ASTM D8071-17, Standard Test Method for Determination of Hydrocarbon Group Types and Select Hydrocarbon and Oxygenate Compounds in Automotive Spark-Ignition Engine Fuel Using Gas Chromatography with Vacuum Ultraviolet Absorption Spectroscopy Detection (GC-VUV), ASTM International, West Conshohocken, PA, 2017, www.astm.org. 8. ASTM D2699-19, Standard Test Method for Research Octane Number of Spark-Ignition Engine Fuel, ASTM International, West Conshohocken, PA, 2019, www.astm.org. 9. ASTM D2700-19, Standard Test Method for Motor Octane Number of Spark-Ignition Engine Fuel, ASTM International, West Conshohocken, PA, 2019, www.astm.org. 10. ASTM D613-18a, Standard Test Method for Cetane Number of Diesel Fuel Oil, ASTM International, West Conshohocken, PA, 2018, www.astm.org. 11. ASTM D1322-18, Standard Test Method for Smoke Point of Kerosene and Aviation Turbine Fuel, ASTM International, West Conshohocken, PA, 2018, www.astm.org. 12. Howard, M. S.; Issayev, G.; Naser, N.; Sarathy, S. M.; Farooq, A.; Dooley, S., Ethanolic gasoline, a lignocellulosic advanced biofuel. Sustainable Energy & Fuels 2019, 3, (2), 409-421. 42 ACS Paragon Plus Environment

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Quantitative NMR Spectroscopy for the Analysis of Fuels: A

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