The SAFT-γ-Mie EoS is used to predict physical properties when no experimental or other more accurate method is unavailable. The SAFT-γ-Mie EoS attempts to accurately model the Helmhotz free energy (A), by decomposing A into different parts. A is obtained through the following equation: A = A i d e a l + A m o n o + A c h a i n + A a s s o c (1) where A i d e a l is the Helmholtz free energy obtained through the ideal gas law, A m o n o is the residual accounting for monomeric Mie segment interactions, A c h a i n is the residual accounting for molecule formation, and A a s s o c is a term that accounts for association interactions. With each additional term in the expansion, a more realistic chemistry is obtained, and a more realistic representation of A is realized. An exact expression for A i d e a l is known, and the other terms can be determined through group contribution theory perturbation theory or Wertheim’s first-order perturbation theory (TPT1) (Barker and Henderson, 1967; Wertheim, 1984a; Wertheim, 1984b; Wertheim, 1986a; Wertheim, 1986b). Once A is known, physical properties can be determined using simple partial derivative relations i.e., such as Maxwell’s equations.

Using the coefficients of a balanced combustion reaction, the enthalpy of combustion can be calculated using a quantum chemistry composite method, such as, CBS-QB3 method (Montgomery et al., 2000). The energy required to vaporize the cycloalkane is accounted for by using the standard heat of vaporization, which is calculated using the SAFT-γ-Mie Equation of State (EoS). The enthalpy of combustion, once calculated, is then converted to the specific energy by using the molecular weight as a conversion factor. The energy density is calculated by multiplying the Specific Energy by the density of the target molecule at 25°C. The SAFT-γ-Mie EoS is used to calculate densities, and a description of the SAFT-γ-Mie EoS is provided above.

The flashpoint of a pure molecule is calculated using an empirical equation that has been shown to be accurate for a wide range of compounds (Catoire and Naudet, 2004). The inputs to the flashpoint equation, Eq. 2, are the number of carbon atoms, the normal boiling point, and the standard heat of vaporization (Catoire and Naudet, 2004). This equation is accurate for flashpoints that are between −100 and 200°C, normal boiling points (NBP) that are between 250 and 650 K, standard enthalpies of vaporization ( △ H v a p ( 298.15 ) ) between 20 and 110 kJ mol⁻¹, and number of carbon atoms ( C n u m ) between 1 and 21. NBP are obtained from the literature, when possible, but, if not possible, are calculated using the SAFT-γ-Mie EoS. T f p = ( 1.477 × N B P 0.79686 × △ H v a p 0.16845 × C n u m − 0.05948 ) − 278.15   (2)

O-ring swelling behavior of cycloalkanes were investigated by using the framework provided by Hansen (1967). The framework, called Hansen Solubility Parameters (HSP), relies on the ability to calculate a dispersion, polar, and hydrogen bonding term. These terms form the basis of a three coordinate system, often called Hansen space. Molecules can be plotted using this coordinate system, and the closer two molecules are on this space, the more alike they are. The framework provided by HSP allows for the determination of the likelihood of o-ring swelling. The more alike a cycloalkane is with a polymer, the more likely the cycloalkane can permeate through the polymer and cause o-ring swelling. Once the three HSP are known, the distance between two molecules (Ra) can be calculated as follows: R a 2 = 4 ( δ d 2 − δ d 1 ) 2   + ( δ p 2 − δ p 1 ) 2   + ( δ h 2 − δ h 1 ) 2 (3)

Each polymer also has an interaction radius (Ro) ascribed to it. For a cycloalkane and a polymer, if Ra/Ro is less than 1, the two molecules a alike, and o-ring swelling behavior is predicted to occur. If Ra/Ro is greater than 1, then the two molecules are not alike, and o-ring swelling is not predicted to occur. One important aspect of cycloalkanes is that they are not very polar, and they do not hydrogen bond with other hydrocarbon cycloalkanes. This simplifies Eq. 3, where now, only the first term is important. In this work, the dispersion term is calculated through the following equation: H v a p V m (4) where, H v a p is the standard enthalpy of vaporization, and V m is the molar volume at 25°C.

All chemicals and solvents were obtained from commercial sources and used as received unless otherwise specified. NbOPO₄ was heated to 100°C in a vacuum oven overnight prior to use. ¹H and ¹³C NMR spectra were collected at room temperature on a Bruker AV400 MHz spectrometer, with chemical shifts referenced to the residual solvent signal. GC-MS analysis was carried out using an Agilent 7890 GC system equipped with an Agilent 5975 mass selective detector, a flame ionization detector (FID) and a Polyarc system. The Polyarc system is a catalytic microreactor that converts all organic compounds to methane after chromatographic separation and prior to detection.

Combustion calorimeter measurements were performed using an IKA C1 compact combustion calorimeter. Higher heating values were measured in triplicate using approximately 0.3 g sample and averaged. The lower heating values (reported as the specific energy) were calculated by subtracting the contribution due to hydrogen content from the higher heating value. Flash point was measured on an Ametek Miniflash FP flash point tester according to ASTM D6450 (ASTM D6450, 2021). In each run, around 1 ml of sample was injected into the sample cup and the heating rate was set to 5.5°C/min. Viscosity and density measurements were performed using an Anton Paar SVM 3001 according to ASTM D7042 (ASTM D7042, 2021) and ASTM D4052 (ASTM D4052, 2019). Freeze point (ASTM D5972) (ASTM D5972, 2016) and other cold flow properties such as cloud point (ASTM D5773) (ASTM D5773, 2021) and pour point (ASTM D5949) (ASTM D5949, 2016) were measured using Phase Technology PSA-70Xi-FP analyzer. Elemental analyses were performed by Atlantic Microlabs, Inc. (Norcross, GA, United States). Cyclohexane, cycloheptane, cyclooctane, cyclododecanone, cyclopentadecanone, (s)-(-)-limonene, and γ-terpinene were purchased from Sigma Aldrich. β-pinene and β-caryophyllene were purchased from Floraplex.

Figure 2 shows the melting point of unsubstituted rings as a function of the number of carbon atoms in the ring. Rings larger than 5 carbon atoms fail to meet the melting point specification for Jet-A. Melting point does not increase monotonically but rather reaches a plateau between 6 and 10 carbon atoms, before decreasing slightly, and then increasing to a melting point of 61°C, for cyclododecane. Drotloff and Moller used DSC (Differential Scanning Calorimetry) to investigate the phase transition of large cycloalkane rings (Drotloff and Moller, 1987). They observed that melting point behavior is correlated to the amount of disorder in the liquid phase and that cycloalkanes with lower ring strain can adopt multiple, different conformations. The degree to which these conformations can be accessed influences the melting point. Figure 3 shows the variation in flashpoint as a function of energy density. This relationship is mostly linear, with deviations occurring with larger ring sizes. The low energy density for small rings (cyclopropane and cyclobutane) is a byproduct of their much smaller densities. Conversely, their high specific energies are a results of their higher ring strain, which when broken releases more energy (Sirjean et al., 2006). The inference drawn from Figure 3 is that as ring size increases benefits to flashpoint and energy density are obtained. Unsubstituted cycloalkanes can be used in the design of SAFs so long as they are included as blends or contain other structural features that can decrease their melting point. Supplementary Tables S2–S5 shows experimental values for blending unsubstituted rings with Jet-A (POSF-10325) at 10 wt%. All blends meet the Jet-A specification for freeze point, viscosity, and specific energy. This is contrary to the neat cycloalkane physical properties where all of the cycloalkanes fail to meet the jet-A specification for melting point. In addition, pure solutions of cyclohexane, cycloheptane, and cyclooctane fail to meet jet-A specification for flashpoint. The data show that as modest (10 wt% blends), unsubstituted cycloalkanes can lead to acceptable jet-A fuels. Unfortunately, data for higher blends are not promising. Supplementary Tables S6–S9 show experimental measurements for unsubstituted cycloalkanes blended into Jet-A (POSF-10325) at 30 wt%. 30 wt% blends fail to meet many of the Jet-A specifications. The cyclododecane blend fails to meet the freeze point specification, the cyclohexane and cycloheptane blend fail to meet the flashpoint requirement, and the cyclododecane and the cyclopentadecane blend fail to meet the viscosity requirement for Jet-A. All unsubstituted cycloalkanes studied fail to meet at least one of the requirements for Jet-A, and at 30 wt% blends, unsubstituted rings cannot be used.

An alternative route to meet Jet-A specification is to add alkyl substituents to unsubstituted cycloalkane rings. Figure 4 shows the flashpoint vs. density plot for monosubstituted linear cycloalkanes. The homologous series of 3, 4, and 5 membered rings is depicted, and a clearly discernable trend is that as density increases so too does the flashpoint. Strikingly, the curves for 3, 4, and 5 membered rings are nearly overlapping, suggesting that ring size plays little to no role in this trend. Figure 5 shows the density vs. melting point for the homologous series of 5 and 6 membered monosubstituted linear cycloalkanes. The literature shows that the orientational dependence, upon freezing, plays a large role in understanding the melting properties of monosubstituted linear cycloalkanes. Hasha and Huang observed a coupling between the rotational and translational motion of methylcyclohexane using NMR (Hasha and Huang, 1979). They postulated that this coupling plays a large role in the melting properties of methylcyclohexane. The crystal structure of methylcyclopentane was investigated and found to be oriented in an envelope conformation, with the methyl group adopting a pseudo-equitorial position (Bream et al., 2006). Upon freezing, the methylcyclopentanes adopt a zig-zag pattern with each other, with some methyl groups pointed diagonally upwards, and some pointed diagonally downwards. Finally, Milhet et al. used DSC to observe the melting behavior of n-alkyl cyclohexanes. Their observations revealed that melting temperature increases as chain length increases, but that odd carbon length chains behaved differently from even carbon length chains (Milhet et al., 2007). Adding an extra CH2 to an alkyl chain with an odd number of carbons increased the melting temperature more than if a CH2 was added to an alkyl chain length with an even number of carbons. This suggests that indeed orientational dependence does play a role, but that as alkyl chain length increases the number of orientations that can be adopted in a crystalline structure decreases, and solidification becomes easier. The plot in Figure 5 captures this orientational dependence by plotting the density and shows that melting point increases as the linear alkane length increases. The linear relationship between density and energy density is shown in Figure 6. For all homologous series studied, the energy density is a linear function of the density and if large energy densities are desired, large densities are needed. The conclusions drawn from Figures 4–6 are that density is an overriding factor in determining what role monosubstituted linear cycloalkanes can play in the generation of SAFs. Higher densities lead to higher energy densities, but at the expense of higher melting points, and trade-offs are required to ensure that existing fuel requirements are met. If a mixture of simple linear cycloalkanes were generated with densities at the top range of the jet-A specification (840 kg/m³), such a mixture would likely fail to meet the jet-A specification for melting point. Figure 6 indicates that it would have a melting point estimate of >50°C. In order to meet the melting point specification, it would need to have a density < ∼810 kg/m³.

Due to the structural complexity available in this group, there are no easily identifiable trends within the data however, all structures exceed the minimum Jet-A specification for specific energy of 42.8 MJ/kg. A few cycloalkanes in this group are notable in that they have specific energy in excess of 0.5% above the median Jet-A while achieving comparable energy density. These structures, and their properties are shown below in Table 2. A pattern that emerges from this data is that multiply substituted molecules with rings greater than 6 carbons are suitable cycloalkanes for the development of SAFs. These are suitable molecules, because they feature large densities and flashpoints while maintaining very low melting points. In addition, although viscosity is not covered in this work, there is evidence in the literature that they can have good viscosities (Rosenkoetter et al., 2019). A mixture of 1,4 and 1,5 dimethylcyclooctane was prepared using a [4 + 4] cycloaddition of isoprene catalyzed by an Iron catalyst (Rosenkoetter et al., 2019). Measured physical properties of this mixture show that its freezing point is <−78°C, and its viscosity at −20°C is 4.17 mm²/s (Rosenkoetter et al., 2019). These values are well below the maximum value for Jet-A, as indicated in Table 1. The structural reasons for why polysubstituted ring expanded cycloalkanes have good cold flow properties is not known, but, as discussed previously, it may be related to greater flexibility conferred by the addition of multiple alkyl chains to the ring. Running quantum mechanics calculations on 1,4-dimethylcyclooctane, the lowest energy configuration is the crown configuration. This is different from the boat-chair conformation adopted by cyclooctane. Another pattern that emerges from the data is that cyclic structures which have di-methylated carbon atoms can have very good physical properties.

The main biological route to branched cycloalkanes is through the MEP pathway. Using computational modeling the production of limonene in cyanobacteria was increased 100 fold (Wang et al., 2016). The computational modeling identified a bottleneck to the production of limonene, which once removed, allowed for increased limonene production. Through genetic engineering of R. turuloides researchers were able to achieve titers of α-bisabolene and 1,8-cineole of 2.6 and 1.4 g/L, a several fold increase over previously reported efforts (Kirby et al., 2021). Chemical routes reported in the literature are sparse and rely on reduction of a starting oxygenate. Starting from diacetone alcohol, a dehydration/diels alder process was developed, which when hydrogenated furnished a mixture of cyclopentanes. Branched cyclopentanes were a major fraction of the products formed, and the overall mixture has a freezing point of −56.6°C (Chen et al., 2016a). Starting from a lignocellulosic oxygenated by product, hydrodeoxygenation afforded a 12 C branched cycloalkane (Li et al., 2020). One important feature of branched cycloalkanes is their low melting points. In the database, constructed for this paper, isopropyl and isobutyl substitutions lead to melting points of at least 50°C below the jet-A specification. Tert-butyl linkages also have good melting points, but tert-butylcyclohexane’s melting point of −41.2°C hovers just below the jet-A specification. No melting point data outside of 5 and 6 membered rings are available hence, a correlation between ring size and branching substituent is not possible. Of the branched cycloalkanes examined, specific energies increased by an average of 1.04%, and energy densities fell by an average of 1.73% over median jet-A values. The molecules with the highest specific energies were those with an isopropyl group. Most molecules with a tert-butyl group showed the largest decreases in energy density. Reasons for this include lower specific energies, but also lower physical densities.

Polysubstituted branched cycloalkanes do not show any benefit over monosubstituted branched cycloalkanes. Specific energies and energy densities calculated are commensurate with those calculated for monosubstituted branched cycloalkanes. Additionally, not a lot is known about the melting points of polysubstituted branched cycloalkanes. Further, because they have multiple substitution sites, they are likely to have higher YSI yields. Given the difficulty of producing polysubstituted branched cycloalkanes, it is unlikely that there will be benefits to including them in SAFs.

The SEED plot for molecules in the MC group are shown in Figure 7. Most multicyclic molecules are located within a band bounded between 42 and 43 MJ/kg, and 33 and 43 MJ/L. The remaining seven molecules are cis-carane, and a group of molecules that belong to a class of molecules called ladderanes. Further, there is no correlation between molecular weight and where a molecule falls in the SEED plot. This finding indicates that the type of carbon-carbon bond is important, and that low molecular weight, ring strained molecules can lead to elevated energy densities and specific energies. Focusing on decalins, in 2009, researchers using an ignition quality tester, IQT, determined that the cetane number of cis-decalin was significantly higher than trans-decalin (Hasha and Huang, 1979). Although cis-decalin does not have great physical properties for jet fuel, the authors suggested those physical properties may be improved by adding a single isoparaffin group to the cis-decalin core (Heyne et al., 2009). Also, in 2019 researchers upgraded cyclopentanone to a series of alkyl-decalins. The measured freezing point of the isomerization mixture was reported to be −23.45°C. In this work, several derivatives of cis-decalin were evaluated as possible candidates for inclusion into SAFs. Table 3 lists these derivatives along with their physical properties. Cis-decalin has a measured energy density of 38.7 MJ/L. This is 10.8% higher than the median Jet-A value. However, its specific energy of 42.98 MJ/kg is 0.51% lower than the median Jet-A value. As a jet fuel component, its melting point of −38.8°C is slightly above the −40°C upper limit of the jet-A fuel specification, and has a low temperature viscosity, at −20°C, of 11.3 mm²/s (see Table 1). In this work, a series of dimethyl cis-decalins have been evaluated. The physical properties of cis-decalin, and its derivatives, are tabulated in Table 3. Dimethyl cis-decalins have lower densities and thus lower energy density than cis-decalin. A 2016 paper outlined a conversion strategy, starting from cyclopentanol, which generated a mixture of C10 decalin and C15 polycycloalkanes. Measured physical properties of this mixture show that it has a melting point that is less than −110°C, and a density, measured at 20°C, of 876 kg/m³ (Chen et al., 2016b). The clear suggestion here is that decalin mixtures can yield promising physical properties. However, SAF generating process are unlikely to derive large benefits from the inclusion of dimethyl cis-decalins. Adding larger alkyl substituents, like an n-butyl substituent to cis-decalin recovers most of the density lost from alkylation of cis-decalin, but likely have melting points that are too high to be useful as SAF components. Of course, cis-decalin is not the only fused bicyclic compound available. Other bicyclic compounds, such as octahydropentalene (two fused cyclopentanes), and mixed cyclic fused molecules are also available. Table 4 shows the physical properties for octahydropentalene and its derivatives. Octahydropentalenes show only modestly higher specific energy values but show elevated energy density. Additionally, they show densities that are too high to meet Jet-A requirements. Octahydropentalene’s flashpoint is 20.7°C, 17.3°C below the Jet-A specification. It is likely that octahydropentalenes will require blending to meet the requirements for Jet-A fuel. Octahydropentalene can be chemically synthesized through a number of routes (Gunbas et al., 2005). Further, iodination and bromination can serve as sites for further derivatization by alkyl substitution (Gunbas et al., 2005). Other derivatizations are also possible (Kendhale et al., 2008). A biological pathways to octahydropentalene derivatives is available, starting from glycerol (Li et al., 2014). Some work has been reported on other fused rings containing 5 and 6 membered rings. Starting from aromatic aldehydes and methyl isobutyl ketone a pathway to the formation of octahydroindanes was reported (Muldoon and Harvey, 2020). The route yields a mixture that has a freezing point that hovers around the −40°C upper limit and features a density of 885 kg/m³. The formation of a binary mixture of perhydrofluorene and dicyclohexamethane from aromatic building blocks, yielded a melting point of −40°C, and a density of 930 kg/m³ (Muldoon and Harvey, 2020). A class of molecules called ladderanes consist of fused cyclobutanes. They can be prepared chemically in a variety of ways, and are natural products produced by planctomycetes. Anammox planctomycetes, which is the species responsible for producing ladderanes, plays an important part in the remediation of nitrogen-rich wastewater. Table 5 shows the ladderane structures examined in this work, along with the measured and predicted physical properties. Ladderanes, even the simples bicyclic ladderane, possess remarkably high specific energy and energy density. An analysis from NIST reveals that the bicyclic ladderane possesses a viscosity of 0.77 mm²/s at −13.15°C (Kazakov et al., 2002). It is likely therefore, that it meets the maximum viscosity of 8 mm²/s at −20°C. Further, the density of the bicyclic ladderane at 15°C is 828.2 kg/m³, below the maximum of 840 kg/m³. When the bicyclic ladderane is alkylated, our work shows that the energy density increases while the specific energy remains elevated. This suggests that alkylation of ladderanes can serve as routes to improve physical properties.

Strained, multicyclic cycloalkanes are also possible. In the literature, these are often hydrogenated terpenes, and in this work, those which were studies, along with their physical properties, are tabulated in Supplementary Table S13. Cis-carane, pinane, and sabinane all have the same chemical formula (C10H18). Cis-Carane has higher specific energy and energy density values, and has a viscosity, measured at −40°C, of 6.83 mm²/s, and a density, measured at 15°C, of 842 kg/m³. Pinane has somewhat lower specific energy and energy density, compared to cis-carane, but still higher than the median value of Jet-A fuels. At −40°C, the viscosity of pinane is 11.23 mm²/s, and has a freeze point of −53°C. Its flashpoint is 39.7°C.

Blends of hydrogenated terpenes can often be beneficial. Experimental measurements using 10 and 30 wt % of pinane, carryophyllane, limonene, and p-menthane were carried out. Blends were generated using the POSF 10325 Jet-A fuel. Supplementary Tables S10–S13 shows the neat physical properties of these hydrogenated terpenes, followed by their blended physical properties. The viscosity of pinane at −40°C is 12.256 mm²/s, which is at the border of pass/fail. At 10 wt% blends with Jet-A, the viscosity is measured to be 8.94 mm²/s, within the Jet-A specification. Carryophyllane fails to meet viscosity requirements for Jet-A. As a 10 wt% blend, it still fails to meet viscosity specification. Smaller blends are possible, but will dilute the elevated energy density and specific energy neat values of carryophyllane. Limonane and terpinane have neat properties that meet Jet-A specifications. As blends, low temperature viscosities increase, specific energies decrease, and flashpoints increase. In this scenario, a trade-off needs to be made between decreasing specific energy and increasing flashpoints.

O-ring swelling behavior was inspected by using the framework provided by Hansen Solubility Parameters (HSP). This framework allows for the identification of molecules with similar interactional forces. It is described in further detail in the methodology section. A number of polymer materials were analyzed, and the results of the analysis are shown in Table 6. HSPs were obtained from (Accu Dyne Test, 2021) Polymers which have a Ra/Ro that is less than 1 indicate that o-rings made out of that polymer will exhibit o-ring swelling behavior when exposed to cycloalkanes. Polymer materials with low polarity and hydrogen bonding terms, but a high dispersion term show the best promise for o-ring swelling behavior. All cycloalkanes studied indicate they will produce o-ring swelling in o-rings made from polybutadiene. Di methyl and tri methyl cyclohexanes and cyclopentanes show Ra/Ro values that were closest to 1, indicating that they may produce minimal amounts of o-ring swelling. Ra/Ro values were all significantly above 1 for o-rings made with polyacrylonitrile polymers, indicating that cycloalkanes are less likely to induce o-ring swelling in polyacrylonitrile than in polybutadiene. The best performing cycloalkanes were fused cycloalkanes. Octacyclopentalene (two five membered rings fused together), and decahydro-1H-cyclopenta[a]pentalene (three five membered rings fused together) were best performers. Research has indicated that disruption of the interaction of nitrile groups is important to inducing o-ring swelling. Although no definitive conclusions can be drawn, it appears that many of the cycloalkanes studied do not possess the ability to disrupt these interactions in acrylonitrile. O-ring swelling in acrylonitrile-butadiene-styrene polymers were also examined, by analyzing the results of HSP. Results indicate that cycloalkanes may produce some o-ring swelling in o-rings made from acrylonitrile-butadiene-styrene material. Ra/Ro values hover around 1. It is unclear which cycloalkanes may provide o-ring swelling. The standard deviation is small (0.03), and because of uncertainty it is difficult to ascertain which cycloalkanes may be considered best performers. Overall, what can be said of this analysis is that fused cycloalkanes tend to provide the best opportunities for o-ring swelling. This seems to be true regardless of the o-ring material. This does not mean that o-ring swelling is guaranteed, merely that fused cycloalkanes provide the best opportunity to induce sufficient o-ring swelling. Future experimental work may shed more light, but computational simulations may also aid in understanding the criteria necessary for cycloalkanes to induce o-ring swelling in different materials. Some of the molecules studied in this work have physical properties that are at least commensurate with those of Jet-A. As blends, these molecules offer the best opportunities for providing adequate o-ring swelling while maintaining the physical properties of the blended fuel.

Aromatics are well known to contribute substantially to soot production during combustion compared to most non-aromatic compounds found in conventional jet fuel (Aromatics perform an important seal-swelling function in jet fuel, and cyclic alkanes have been proposed as an alternative for aromatics to perform the seal-swelling function.). A number of indices have been developed to quantify the relative tendency of hydrocarbons to produce soot. One of the earliest indices, Smoke Point (SP), has been used since the 1930’s (Woodrow, 1933), and the measurement involves observing a flame from a standard lamp and measuring the fuel consumption rate (Schalla and McDonald, 1953) or flame height at which visible smoking occurred with lower SPs intended to indicate a greater tendency to produce soot. Systematic measurements of different molecular classes revealed qualitative structure property relationships for SP (Hunt, 1953; Calcote and Manos, 1983) with the general trend in sooting tendency following the pattern: n-paraffins < iso-paraffins < cycloalkanes < alkenes < alkynes < benzenes < naphthalenes. The Threshold Sooting Index (TSI) index was subsequently developed to provide an approximate adjustment for variations in SP related to the quantity of air consumed during combustion, with TSI defined as aMW/SP+b where MW is the molecular weight of the fuel and a and b are constants assigned through measurements of standard compounds to put all TSI measurements on a common scale. Using TSI values the additional trend if increasing soot tendency with increasing carbon number could be seen within different classes of hydrocarbons. In order to improve the reproducibility and precision of sooting tendencies compared to TSI values researchers have subsequently developed other indices that do not rely on SP measurements including Yield Sooting Index (YSI) (McEnally and Pfefferle, 2007; YSI database v2, 2021), Micropyrolysis Index (MPI) (Crossley et al., 2008), and Fuel Equivalent Sooting Index (FESI) (Lemaire et al., 2015). Quantitative structure property relationships based on group contribution methods have been developed for YSI (Crossley et al., 2008; John et al., 2017; Lemaire et al., 2021) for predicting sooting tendencies of uncharacterized hydrocarbons on the basis of their chemical structure.

As a specific example we can look at YSI values, which are derived from the maximum volume-fraction of soot measured by laser induced incandescence along the centerline of a methane co-flow diffusion flames doped with small quantity a specific hydrocarbon. YSI values on the current unified scale (Das et al., 2018) are scaled to give a value of 30 for n-hexane and 100 for benzene. The current YSI database includes 16 cycloalkanes with species in four ring sizes: cyclopentane, cyclohexane, cycloheptane, and cyclooctane. For cycloalkanes with the same molecular weight, higher YSI values are measured for cycloalkanes with multiple substitutions compared to cycloalkanes with longer alkyl side chains. The highest YSI value for a cycloalkane in the database is 82.8 for 1,2,4-trimethylcyclohexane, and the lowest two are cyclohexane and cyclopentane at 42.7 and 39.4, respectively. By comparison, naphthalene has a value of 466.1. The trends in measured YSI values (YSI database v2, 2021) for different structural classes of cycloalkanes is shown in Figure 8.

In an effort to understand the potential of including cycloalkanes into SAFs, a database of cycloalkanes, and their physical properties was developed. This database contains 178 cycloalkane structures, and includes information on specific energy, energy density, liquid density, flashpoint, and HSP. From this database, SPRs were developed based on cycloalkane structural features. These structural features include ring size, monosubstituted linear substitutions, polysubstituted linear substitutions, monosubstituted branched substitutions, polysubstituted branched cycloalkanes, and multicyclic cycloalkanes. The SPR developed indicate that unsubstituted cycloalkanes are of limited usefulness for the production of SAFs, because of their high melting points. Experiments, blending unsubstituted cycloalkanes into Jet-A (POSF-10325), show that 10 wt% blends meet the specifications outlined by ASTM D1655, but 30 wt% blends do not. Linear alkyl substitutions can greatly decrease melting points, while maintaining suitably high specific energies and energy densities. In particular, polysubstituted linear, ring expanded cycloalkanes offer large benefits, in terms of exceptional melting points, and large specific energies and energy densities. However, due to their larger YSI values, careful consideration must be taken to avoid sooting issues. Branched substitutions can be beneficial to lowering melting point however, their specific energies and energy densities are only commensurate with median Jet-A values. Given the difficulty of generating (biologically or chemically) branched cycloalkenes, their inclusion into SAFs may be challenging. HSP show that fused cycloalkanes are consistently amongst the most likely cycloalkanes to provide o-ring swelling. For that reason, they should also be considered as possible jet-fuel cycloalkane candidates. Experimental measurements show that some fused cycloalkanes can meet jet-A standards, as specified by ASTM D-1655, especially as 10 and 30 wt% blends. However, not all fused cycloalkanes are good fuel component candidates. Carryophyllane failed to meet Jet-A specifications, even at a modest 10 wt% blend into Jet-A (POSF-10325).