Modeling of Fuel-System Icing Inhibitors - Energy & Fuels (ACS

992

Energy & Fuels 1999, 13, 992-998

Modeling of Fuel-System Icing Inhibitors Steven Trohalaki* and Ruth Pachter Materials and Manufacturing Directorate, Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio 45433-7702

John R. Cummings Naval Air Systems Command, Patuxent River, Maryland 20670 Received November 20, 1998. Revised Manuscript Received May 10, 1999

In our continuing efforts to design nontoxic and biodegradable fuel-system icing-inhibitor (FSII) compounds with improved fuel solubility and anti-icing ability, and nontoxic deicers for aircraft and runways, we describe experimental and molecular modeling efforts that allow us to predict the relative performance of FSII candidates. A small-scale, recirculating simulator containing a mixture of jet fuel, FSII, and water was employed to measure the time needed for the water to freeze and the lowest temperature to be achieved before freezing. The molecular model is based on classical molecular dynamics (MD) simulations of a two component mixture consisting of FSII and water. We assume that anti-icing performance is proportional to the degree of hydrogen bonding between FSIIs and water and, therefore, inversely proportional to the degree of hydrogen bonding between water molecules. FSII performance should therefore increase with decreasing water-cluster size, which is calculated from the MD equilibrium trajectories and defined as the average number of water molecules hydrogen bonded to a given water molecule. A good agreement is found between the theoretical and experimental performance rankings for twelve FSIIs and FSII candidates.

Introduction A fuel-system icing inhibitor (FSII) is added to U.S. and NATO military jet fuel in order to prevent ice formation from trace amounts of water. The FSII currently used is diethylene glycol monomethyl ether (DGME) at a concentration of about 0.1%. DGME is under scrutiny by the U.S. Environmental Protection Agency due to its human toxicity. Ethylene glycol monomethyl ether, which has an even higher toxicity than DGME, was only recently replaced due to a production ban imposed by the U.S. EPA. In the event that a production ban of DGME is also imposed, alternate FSIIs will be required. DGME partitions between the water “bottoms” that form in fuel and storage tanks from condensation or from leaking of ambient water. The DGME-containing water bottoms are disposed of by various means, depending on state and local regulations.1 In many cases, DGME, albeit in low concentrations, is released into the environment. Partitioning also depletes the FSII in fuel and may result in the FSII concentration falling below specification. Military and civilian airports also employ large quantities of similar, toxic (glycol-based) runway and * Author to whom correspondence should be addressed at AFRL/ MLPJ Building 651, 3005 P Street, Suite 1, Wright-Patterson AFB, OH 45433-7702. Telephone: (937) 255-6671-x3147. Fax: (937) 2551128. E-mail: [email protected]. (1) Diethylene Glycol Monomethyl Ether, Glycerol Formal, and Dipropylene Glycol Use, Handling, and Disposal; SEMCOR, Inc., 1996; iii-iv, pp 41-46.

wing deicers. Current deicers may soon be regulated as hazardous chemicals because of their toxicity to aquatic organisms,2 thus requiring the construction of extremely expensive containment systems.3 Such systems are inherently inefficient because Type-II deicers,4 composed of ethylene glycol and a thickening agent, prevent ice formation by coating the aircraft wing with a gellike protective layer that flows off only after application of sufficient shear stress experienced during takeoff. For example, flow-off of deicer has been recently blamed for a 3-4 min downpour of “green rain” in San Francisco.5 Partition coefficients serve as QSAR (Quantitative Structure-Activity Relationship) predictors for toxicity and other biological activities6 and are also important indicators of anti-icing ability. Toxicity screening will not be addressed here but will be the subject of a separate study. We have previously reported hexadecane-water partition coefficients calculated using molecular orbital methods for carbohydrate-based FSII candidates.7 The recently suggested FSII candidates8 considered in this study are summarized in Table 1. The mechanism by which FSIIs function is uncertain. It could be suggested that FSIIs extract water from fuel (2) Hartwell, S. I.; Jordahl, D. M.; May, E. B. Environ. Toxicol. Chem. 1995, 14, 1375. (3) O’Connor, R.; Douglas, K. New Scientist 1993, 137, 22. (4) Ross, J. F.; Connolly, J. T. J. Aircraft 1993, 30, 10. (5) Weiss, P. Valley Times, April 15, 1994. (6) Hansch, C.; Leo, A. J. Exploring QSAR; American Chemical Society: Washington, DC, 1995. (7) Trohalaki, S.; Pachter, R. Energy Fuels 1997, 11, 647. (8) Mushrush, G. Personal communication.

10.1021/ef9802577 CCC: $18.00 © 1999 American Chemical Society Published on Web 07/31/1999

Modeling of Fuel-System Icing Inhibitors

Energy & Fuels, Vol. 13, No. 5, 1999 993

Table 1. Chemical Names, Designations, and Formulas or Molecular Structures

and prevent ice formation by depressing the freezing point of water, or that FSIIs inhibit the growth of ice crystals so that they remain small enough to pass through fuel filters and injectors. Antifreeze proteins, which are found in certain plants, insects, and fish, are one class of compounds that are related to FSIIs by function. Another class promotes vitrification in aqueous solutions of cells or in tissue. Antifreeze proteins function through a noncolligative mechanism to lower water’s nonequilibrium freezing point without depressing its melting point. Thermal hysteresis is the term used to describe the difference between freezing and melting points.9-12 Antifreeze (9) DeVries, A. L. Science 1971, 172, 1152. (10) DeVries, A. L. Methods in Enzymology; Academic Press: New York, 1986; Vol. 127, pp 293-303.

proteins not only inhibit nucleation13-15 but they also hinder the growth of ice crystals.16 It has been demonstrated by experimental and molecular modeling studies17 that antifreeze proteins preferentially bind in (11) Duman, J. G.; Xu, L.; Neven, L. G.; Tursman, D.; Wu, W. D. Insects at Low Temperatures; Chapman and Hall: New York, 1991; pp 94-127. (12) Duman, J. G.; Wu, W. D.; Olsen, T. M.; Urrutia, M.; Tursman, D. Advances in Low-Temperature Biology, Vol. 2; JAI Press: London, Greenwich, CT, 1986; pp 131-1182. (13) Parody-Morreale, A.; Murphy, K. P.; DiCerca, E.; Fall, R.; DeVries, A. L.; Gill, S. J. Nature 1988, 333, 782. (14) Olsen, T. M.; Duman, J. G. J. Comput. Physiol. B 1997, 167, 105. (15) Olsen, T. M.; Duman, J. G. J. Comput. Physiol. B 1997, 167, 113. (16) Knight, C. A.; Cheng, C. C.; DeVries, A. L. Biophys. J. 1991, 59, 409. (17) Madura, J. D.; Wierzbicki, A.; Harrington, J. P.; Maughon, R. H.; Raymond, J. A.; Sikes, C. S. J. Am. Chem. Soc. 1994, 116, 417.

994 Energy & Fuels, Vol. 13, No. 5, 1999

specific orientations to the bipyramidal and prism ice faces. Restriction of ice growth normal to the binding surface can be explained by the Kelvin effect.18 The ice crystal grows faster in the area between two peptides than near them so that the surface of the ice crystal becomes curved. According to the Kelvin effect,18 the free energy for the addition of a molecule to a crystal is higher for curved than for flat surfaces so that crystal growth is inhibited. The freezing point is locally depressed without altering the melting point. Vitrification-promoting agents also do not display a colligative effect when suppressing crystal formation and promoting glass formation. Several groups of isomeric compounds have been found to exhibit very different behavior when cooled well below the thermodynamic melting point.19 For example, different concentrations of butanediol isomers are required to achieve the same reduction in freezing point.19 NMR experiments indicate that the role of vitrification-promoting agents is 2-fold:19 (1) suppressing anomalous structuring, which occurs in supercooled water and causes rapid nucleation of ice, and (2) decreasing molecular mobility so that the probability of nucleation is decreased and glass formation occurs at a relatively high temperature. Both (1) and (2) are a result of strong hydrogen bonding between vitrification-promoting agents and water. Intuitively, FSII performance must also be due to hydrogen bonding to water. The chemical structures of FSIIs are more similar to vitrification-promoting agents than to antifreeze proteins, and it is therefore reasonable to assume that the mechanisms for these two classes of compounds are similar, i.e., that formation of ice crystals is suppressed. One objective of this study is to provide evidence regarding this assumption. In this paper we describe an experimental apparatus and protocol used to measure the performance of FSII candidates. We also describe a molecular model based on molecular dynamics (MD) simulations of bulk aqueous FSII solutions to predict FSII performance. The hydrogen bonding of this system is analyzed using standard statistical mechanics. We compare the calculated ranking with that found experimentally and find a surprisingly good correlation. Methods Experimental. The Fuel System Icing Simulator (FSIS), employed here to test the effectiveness of FSII candidates at varying concentrations, is a small-scale, recirculating simulator fitted with a 30 µm filter. A schematic diagram for the FSIS is shown in Figure 1. The test fluid mixture consisted of 3500 mL of jet fuel, 235-265 ppm of water, and FSII at a concentration in the range of 0.01-0.050 vol %. The flow rate was 40 mL/s. While the test fluid was circulated, the FSIS was cooled to beween -37 and -39 °C. Circulation was maintained until the pressure differential across the filter reached 35 psi, indicating significant ice formation and triggering an automatic shutdown, or until 6 h of continuous circulation was reached. Extensive testing has demonstrated that once 6 h of continuous circulation was reached without automatic shutdown, the test can (18) Wilson, P. W. Cryoletters 1993, 14, 31. (19) MacFarlane, D. R.; Forsyth, M. Cryobiology 1991, 27, 345.

Trohalaki et al.

Figure 1. Schematic diagram of fuel system icing simulator (FSIS).

be run virtually nonstop without the filter differential pressure ever reaching 35 psi. Time-temperature baseline curves were generated from statistical analyses of numerous runs using EGME and DGME for the FSII component. Time-temperature profiles of all test runs were compared to the baselines in order to ensure proper performance of the FSIS. Test time and fuel temperature were both monitored for test fluids containing FSII at several concentrations. Computational. To a first approximation, it was assumed that water and FSIIs segregate from the fuel and that interactions between water and fuel and between FSII and fuel can be neglected. Molecular dynamics (MD) simulations were used here to simulate that portion of the mixture containing only FSII and water. In a classical MD simulation, Newton’s equations of motion for a system of atoms are solved, thereby determining the time evolution of molecular motion on a potential energy surface. The empirical fit to the potential energy surface employed in MD simulations is the force field, which defines the coordinate system, form of the mathematical representation, and the parameters adjusted in the fit. Potential energy force fields include equations that describe “bonded terms” that include bond stretches, bond-angle bends, and dihedral distortions, as well as “nonbonded” terms that govern van der Waals and electrostatic interactions between atoms. The PCFF force field20 was employed here. Periodic boundaries were employed in order to minimize surface effects of the bulk liquid. A periodic cell is set at the center of a periodic lattice of identical cells. As a molecule diffuses through a periodic boundary and out of the central cell, its periodic image diffuses into the central cell from the opposite periodic boundary. Also applied was the minimum-image convention, in which each molecule interacts only with those molecules and periodic images within a distance of half the cell. A potential energy cutoff of 8.5 Å was adopted for the nonbonded interactions in order to improve computational efficiency. The model used here to predict relative FSII performance consists of a cubic periodic cell containing a 50 weight % mixture of water and FSII with a total of 500 molecules, except for DPGME for which the total number of molecules equaled 750 because a larger



Table 2. Stereochemical Composition FSII Components in the Molecular Model dipropylene glycol dipropylene glycol monomethyl ether

M1 M2 M3

M6 M7

glycerol formal

periodic cell was required. The stereochemical composition of the FSII components, where appropriate, is given in Table 2. Each molecular species was constructed using the Builder module in InsightII, release 4.0.0,21 which is a comprehensive graphical molecular modeling program. Optimal molecular conformations were obtained by minimizing the potential energy of the individual molecules with Discover, version 2.9.7.21 The periodic cells were built using the AmorphousCell module in InsightII, release 4.0.0.21 The AmorphousCell program places molecular components randomly in a periodic cell taking into consideration their excluded volume. Before MD is run, the potential energy is minimized, i.e., a configuration corresponding to a local minimum on the potential energy surface is found. MD simulations were performed using Discover, version 2.9.7.21 The canonical ensemble was applied, i.e., the number of molecules per periodic cell, the cell volume, and the temperature were all held constant. A density of 1.0 g/cm3, which approximates known experimental densities, and a temperature of 300 K were applied in all cases. The Verlet leapfrog integrator22 with a time step of 1 fs was chosen to numerically integrate Newton’s equations of motion. Initially, atomic velocities were assigned according to a Maxwell-Boltzmann distribution but during the equilibration stage velocities were scaled uniformly in order to maintain 300 K. After equilibrium was attained, constant temperature was maintained through coupling of the system with a temperature bath using a method introduced by Berendsen.23 Atomic coordinates were collected every 0.5 ps from 100-ps equilibrium trajectories. Construction of the periodic cells typically took an hour of CPU time on a Silicon Graphics Indigo2 Extreme equipped with one 100 MHz IP22 processor, 64 MB main memory, and a data cache of 8 KB. All MD runs were run on a Silicon Graphics Power Challenge (20) Hwang, M. J.; Stockfisch, T. P.; Hagler, A. T. J. Am. Chem. Soc. 1994, 116 (6), 2515. (21) Molecular Simulations, Inc., 9685 Scranton Rd., San Diego, CA 92121-3752.

25% [R-(R*,R*)]1,1′-oxybis-2-propanol 25% [S-(R*,R*)]1,1′-oxybis-2-propanol 50% [R-(R*,S*)]1,1′-oxybis-2-propanol 25% [R-(R*,R*)]-1-(2-methoxypropoxy)-2-propanol 25% [S-(R*,R*)]-1-(2-methoxypropoxy)-2-propanol 25% [R-(R*,S*)]-1-(2-methoxypropoxy)-2-propanol 25% [S-(R*,S*)]-1-(2-methoxypropoxy)-2-propanol 50% (R)-2,2-dimethyl-1,3-dioxolane-4-methanol 50% (S)-2,2-dimethyl-1,3-dioxolane-4-methanol 50% (R)-1,3-dioxolane-4-methanol 50% (S)-1,3-dioxolane-4-methanol 25% (2R-cis)-2-methyl-1,3-dioxolane-4-methanol 25% (2S-cis)-2-methyl-1,3-dioxolane-4-methanol 25% (2R-trans)-2-methyl-1,3-dioxolane-4-methanol 25% (2S-trans)-2-methyl-1,3-dioxolane-4-methanol 50% (5R)-2,2-dimethyl-5-ethyl-1,3-dioxane-5-ethanol 50% (5S)-2,2-dimethyl-5-ethyl-1,3-dioxane-5-ethanol 25% (2R-cis)-5-ethyl-2-methyl-1,3-dioxane-5-ethanol 25% (2S-cis)-5-ethyl-2-methyl-1,3-dioxane-5-ethanol 25% (2R-trans)-5-ethyl-2-methyl-1,3-dioxane-5-ethanol 25% (2S-trans)-5-ethyl-2-methyl-1,3-dioxane-5-ethanol 20% (R)-1,3-dioxolane-4-methanol 20% (S)-1,3-dioxolane-4-methanol 30% R-1,3-dioxan-5-ol 30% β-1,3-dioxan-5-ol

equipped with eight 194 MHz IP25 processors (although only one was used at a time), 1024 MB main memory, and a data cache of 32 KB. Equilibrium was typically achieved in 200 000 integration steps requiring a CPU time of about 15 h. For DPGME, 200 000 integration steps required almost 24 h due to the larger system size. Results and Discussion The set of performance graphs for DGME, using data obtained with the FSIS, is presented in Figure 2. Test time, t, is plotted as a function of FSII concentration in Figure 2a with the data fit to a sigmoidal function of the form:

t ) at + b/[1 + exp{c (V - d)}]f

(1)

where at is the time in minutes it takes the water in the test mixture to freeze with no FSII present, b is the upper limit of the test time (360 min), c is the slope coefficient, V is the FSII concentration (vol %), d is the FSII concentration at the inflection point of the curve, and f is the symmetry parameter. Note that water in the test fluid froze when t < 360 min. The lowest temperature of the test mixture before the water freezes, termed the pre-freezing temperature, Tpf, is plotted as a function of FSII concentration in Figure 2b, and the data is fit with an exponential decay of the form

Tpf ) aT + b exp{-crV}

(2)

where aT is the minimum temperature, b is the amplitude of the curve, and cr is the cooling rate constant. The performance curves of DGME are compared to those for EGME and the FSII candidates in Figures 3 and 4. Drawn according to the fit using eq 1, t is plotted as a function of FSII concentration in Figure 3a for the FSII candidates whose performance is similar to DGME’s performancesDPG, DPGME, M2, M3, MPD, and GF. (The fitted function for GF was omitted for clarity because it performs nearly identically to DGME.) These


Figure 2. (a) FSIS test time as a function of DGME concentration (+) with fit to data (solid line) drawn according to eq 1. (b) Pre-freezing temperature as a function of DGME concentration (+) with fit to data (solid line) drawn according to eq 2.

candidates will be considered for additional testing. Similarly, the fit of Tpf as a function of FSII concentration drawn according to eq 2 is presented in Figure 3b for this same set of FSII candidates. As expected, EGME is only marginally less effective than DGME. As seen in Figure 3a, a slightly higher concentration of EGME is needed for total inhibition of icing. Figure 3b shows that Tpf is a bit higher with EGME than with DGME at identical concentrations. By these same criteria, M2 is slightly less effective than DGME, while DPG and DPGME are slightly more effective. M3 performed less effectively than DGME, and its behavior as depicted in Figure 3 is unique. In contrast to DGME and the other candidates, t rises slowly with concentration and Tpf as a function of concentration is considerably flatter and lies above that for DGME. MPD performed slightly better than DGME at concentrations up to 0.06 vol %, slightly worse in the

Trohalaki et al.

Figure 3. (a) Fits to experimental data (FSIS test times as functions of FSII concentration) are drawn according to eq 1 for FSII candidates with performance similar to that for DGME. For clarity, the fitted function for GF is not included because it is virtually identical to that for DGME. (b) Fits to experimental data (pre-freezing temperatures as functions of FSII concentration) are drawn according to eq 2 for FSII candidates with performance similar to that for DGME. For clarity, the fitted function for GF is not included because it is virtually identical to that for DGME.

concentration range of 0.07-0.09 vol %, and almost identically to DGME for higher concentrations. Figure 4, parts a and b, are analogous to Figure 3 parts a and b, respectively, except that they correspond to the set of FSII candidates, namely M1, M4, M6, and M7, whose performance is poor in comparison to DGME’s performance. Also, raw data was plotted instead of the fitted curves for M4, M6, and M7 because their extremely poor performance prevented proper curve fitting. M1 is not a viable FSII because of the high concentrations (>0.29 vol %) required to provide any anti-icing protection. M1 exhibits a nearly on-off behavior in Figure 4a, and Tpf is observed to be almost



Figure 5. The pair distribution function, g(r), for oxygen atoms in water was calculated from the equilibrium molecular dynamics trajectory of the 50 wt % DGME-water mixture.

Figure 4. (a) FSIS test times as functions of FSII concentration for FSII candidates with performance that is poor in comparison to DGME are compared to the fit to analogous data (drawn according to eq 1) for DGME. The fit instead of the data is drawn for M1. Equation 1 could not be satisfactorily fit to the data for the other FSII candidates. (b) Pre-freezing temperatures as functions of FSII concentration for FSII candidates with performance that is poor in comparison to DGME are compared to the fit to analogous data (drawn according to eq 2) for DGME. The fit instead of the data is drawn for M1. Equation 2 could not be satisfactorily fit to the data for the other FSII candidates.

linear as a function of concentration in Figure 4b. M1, M4, M6, and M7, will not be considered for additional testing. Pair distribution functions, g(r), between oxygen atoms in the water molecules were calculated from the equilibrium molecular dynamics trajectories. Also known as the radial distribution function, g(r) provides information on local solution structure. Specifically, g(r) measures the probability that, given the presence of an atom at the origin of an arbitrary frame of reference, there will be another atom at a separation r with its center located within a spherical shell of infinitesimal thickness. Figure 5 shows g(r) calculated from the MD trajectory of the 50 wt % DGME-water mixture, which

is typical of all FSII-water mixtures. The first maximum is prominent and is located at a separation of about 2.9 Å, thereby indicating hydrogen bonding between water molecules.24 Hydrogen bonding between hydroxyl groups and water is also indicated by prominent 2.9 Å peaks in g(r) calculated between hydroxyl oxygens in FSII and oxygen atoms in water. It is noteworthy that g(r) calculated between ether oxygens and water oxygens and between carbonyl oxygens and water oxygens are small or negligible, indicating that hydrogen bonding occurs to a much lower degree between carbonyls and water and between ethers and water, at least as simulated with the PCFF force field. It is implicit in our analysis that all types of interactions between FSIIs and water affect hydrogen-bonding between water molecules. Integrating over the first peak of g(r) yields the average number of water molecules hydrogen bonded to a single water molecule, Nw, which can be interpreted as the average size of water clusters:

∫rr r2g(r) dr

Nw ) 4π Fo

2

1

(3)

where Fo is the number density of water oxygen atoms, r1 is zero, and r2 is the first minimum in g(r) after the first peak. Whenever r2 was difficult to discern from the raw data, g(r) was smoothed from 3.5 Å (considered to be the maximum oxygen-oxygen separation for a hydrogen bond) onward using a third-degree 5-point smoothing formula25 (r2 was always greater than 3.5 Å). We postulate that FSII performance is inversely proportional to Nw. Using the PCFF force field and a procedure similar to that outlined above, Rigby26 found that each hydroxyl (22) Verlet, L. Phys. Rev. 1967, 159, 98. (23) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; DiNola, A.; Haak, J. R. J. Chem. Phys. 1984, 81, 3684. (24) Narten, A. H.; Habenschuss, A. J. Chem. Phys. 1984, 80 (7), 3387. (25) Stark, P. A. Introduction to Numerical Methods; Macmillan: Toronto, 1970. (26) Rigby, D. Personal communication.


Figure 6. Pre-freezing temperature (left ordinate) and Nw (right ordinate) are plotted for FSIIs and FSII candidates.

group in bulk methanol and in bulk ethanol has, on average, 1.8 hydroxyl neighbors from other molecules at a distance of 2.8 Å, in excellent agreement with experiment.24 To compare our theoretical FSII performance ranking to experimental results in a straightforward manner, a single experimental point representative of the performance of each FSII candidate was required. We found that the set of Tpf values measured at a FSII concentration of 0.05 vol % is sufficient to reproduce the experimental performance ranking. We assume that a larger degree of hydrogen bonding between a FSII and water (and therefore decreased hydrogen bonding between water molecules) is reflected in a lower Tpf, which should correlate with Nw. In Figure 6, we use a double-y plot to demonstrate the correlation between Tpf and Nw. In general, the agreement is good. A linear least-squares fit of Tpf vs Nw has a slope of 0.0482 with a correlation coefficient of 0.94. To assess whether the results of our model are due to colligative effects, we calculated the freezing-point depression (FPD) from the composition of each periodic cell. We assumed ideal solutions but made no mathematical simplifications based on dilute concentrations. The correspondence between Tpf and FPD, shown in Figure 7, is not close (a linear least-squares fit of Tpf vs FPD has a correlation coefficient of only 0.53). As is the case with vitrification-promoting agents, the nature of FSII performance does not appear to be colligative. Conclusions In this paper, we described the development of experimental and theoretical methods to rank the

Trohalaki et al.

Figure 7. Pre-freezing temperature (left ordinate) and freezing point depression (right ordinate), calculated using the compositions the periodic cells used in the molecular model, are plotted for FSIIs and FSII candidates.

performance of FSII candidates. Using our molecular model, FSII candidates can be screened quickly so that the time-consuming steps of synthesis, purification, and experimental testing can be performed only for promising candidates. Indeed, this study enables us to gain insight into the ice-inhibiting mechanism and possibly offer predictive capabilities in general. Our results are consistent with the hypothesis that water and FSIIs segregate from fuel and that FSIIs function by preventing the formation of ice crystals in a noncolligative manner. Incorporation into the molecular model of a third component to represent fuel is currently underway. Future plans include modeling of FSII binding to ice surfaces to enable us to investigate the hypothesis that FSIIs also inhibit the growth of ice crystals. Our molecular model may also be of use in predicting aircraft and runway deicers. On the basis of the demonstrated and predicted performance we reported for the considered candidates, it is shown that GF, DPG, DPGME, M2, M3, and MPD are recommended for additional testing. Screening of these candidates on the basis of toxicity will be addressed in a separate study. Acknowledgment. It is a pleasure to acknowledge funding from the U.S. Air Force Office of Scientific Research.

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Modeling of Fuel-System Icing Inhibitors - Energy & Fuels (ACS

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