Density Functional Theory Investigation of the Interaction between

Dec 4, 2008 - Takahiro Yamada,*,‡ John L. Graham,‡ and Donald K. Minus§ ... (1) Graham, J. L. The swelling of nitrile rubber by selected species ...
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Energy & Fuels 2009, 23, 443–450

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Density Functional Theory Investigation of the Interaction between Nitrile Rubber and Fuel Species† Takahiro Yamada,*,‡ John L. Graham,‡ and Donald K. Minus§ Energy and EnVironment, UniVersity of Dayton Research Institute, 300 College Park, Dayton, Ohio 45469, and Air Force Research Laboratory, United States Air Force, Wright-Patterson Air Force Base, Dayton, Ohio 45433 ReceiVed July 30, 2008. ReVised Manuscript ReceiVed October 21, 2008

The interactions between a nitrile rubber O-ring model polymer and selected fuel species were investigated using one of the hybrid density functional theories (DFT), B3LYP. The primary objective of this study was to examine whether theoretical investigation can be used as a potential tool to predict the intensity of the polymer-fuel species interaction, namely, swelling, and if so, which calculated properties have a strong correlation with experimentally observed swelling behavior. The fuel species investigated were ethylbenzene, phenol, methylphenol, phenylmethanol, phenylethanol, phenylbutanol, 1-butanol, 1-hexanol, cyclohexanol, and di- and triethylene glycol monomethyl ether (diEGME and triEGME, respectively). The model polymer created to represent the nitrile rubber O-ring was cis-butadiene-acrylonitrile-trans-butadiene (cis-C4H7-CH2CHCN-transC4H7). The properties investigated were charge distribution, intermolecular distances, binding energies, and vibrational frequency shifts corresponding to the cyano group stretching mode of the model polymers because of the interaction. Some of the cyano group vibrational frequency shifts were compared to an experimentally observed infrared absorption peak shift associated with the nitrile rubber cyano group because of polymer-fuel species interactions. There is a strong correlation among calculated intermolecular distances, binding energies, and frequency shifts. The order of interaction intensities between polymer and fuel species based on the calculated parameters is also consistent with the order of interaction intensities based on the experimentally derived partition and swelling coefficients. The B3LYP/6-311G(d,p) derived vibrational frequency shift associated with the cyano group stretching mode showed good agreement with the experimentally measured adsorption peak shift.

Introduction There has been considerable interest in O-ring swelling behavior in different types of fuels. The swelling occurs when fuel dissolves in the polymeric materials, increasing its volume and causing the material to swell and soften.1,2 A limited amount of swelling is often considered beneficial, improving the quality of the seal.1,2 The swelling character of petroleum distillate fuels has long been attributed to the aromatic species in these fuels.1,2 Switching from a petroleum distillate to synthetic fuels, such as those produced by the Fischer-Tropsch (F-T) process, may cause excessive shrink-back from the swollen state and fail the seal, because synthetic fuels do not contain aromatics.1,2 The simple solution to avoid O-ring swelling-shrinking is to add aromatic species into F-T fuel, but the addition of aromatics will increase the cost of F-T fuel production and enhance molecular growth to form polyaromatic hydrocarbons (PAHs), which will consequently enhance soot formation during the † Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Research Laboratory or the U.S. Government. * To whom correspondence should be addressed. Fax: 937-229-2503. E-mail: [email protected]. ‡ University of Dayton Research Institute. § United States Air Force. (1) Graham, J. L. The swelling of nitrile rubber by selected species in a synthetic jet turbine fuel. Ph.D. Dissertation, University of Dayton, Dayton, OH, 2006. (2) Graham, J. L.; Striebitch, R. C.; Myers, K. J.; Minus, D. K.; Harrison, W. E., III. Energy Fuels 2006, 20, 759–765.

combustion process. Therefore, the goal is to introduce aromatics that will be both effective and swell the O-ring as little as possible. The swelling behavior of polymers in a fluid can be examined experimentally in a variety of ways, including volume and weight gain, hardness change, and polymer-fuel partition coefficient.1,3 Graham1 had also recently reported that the intensity of the frequency shift of the infrared absorbance associated with the cyano group (-CtN) was qualitatively correlated with partition and swelling coefficients. Recent rapid improvements of computational capability, including the faster clock speed of the microprocessor unit and increased memory, enable us to perform relatively high-level molecular orbital (MO) calculations for relatively large molecular systems within a reasonable time scale. The properties that can be obtained from MO calculations include optimized geometry, total energy, vibrational frequency, and electrostatic potential (charge distribution), etc. If the calculated properties have good correlation with polymer swelling behavior, then computational modeling can be a potential tool to predict the intensity of the polymer-fuel species interaction and also gives us the molecular level insight to elucidate polymer-fuel interactions. One study was found that applied a theoretical investigation for fluid-polymer interactions. Alfonso and Cugini3 applied a local MP2 (LMP2) method with two basis sets, cc-pvDZ and (3) Alfonso, D. R.; Cugini, A. V. Prepr. Pap.-Am. Chem. Soc., DiV. Fuel Chem. 2003, 48 (2), 508–509.

10.1021/ef8006189 CCC: $40.75  2009 American Chemical Society Published on Web 12/04/2008

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Table 1. Most Negatively and Positively Charged on Terminal Atoms for the Model Polymer and the Most Positively Charged on Terminal Atoms for the Fuel Species Based on B3LYP/ 6-311G(d,p) Optimized Geometries and CHelp Scheme molecule

atom

charge

model polymer model polymer ethylbenzene phenol methylphenol phenylmethanol phenylethanol phenylbutanol butanol hexanol cyclohexanol diEGME triEGME

N in cyano group H attached to second carbon of trans-butadienea H at benzene meta position H in OH group H in OH group H in OH group H in OH group H in OH group H in OH group H in OH group H in OH group H in OH group H in OH group

-0.487 +0.108 +0.059 +0.431 +0.398 +0.328 +0.378 +0.345 +0.418 +0.355 +0.238 +0.338 +0.349

a

See Figure 1b.

cc-pvTZ, to investigate the interaction between nitrile polymer and small hydrocarbons. Isobutylnitrile was used as a model polymer, and methane, acetylene, ethene, ethane, and benzene were employed as fuel species. Binding energies between model polymer and fuel molecules were calculated. The binding energies were calculated with and without basis set superposition error (BSSE) correction. The BSSE-corrected binding energies using cc-pvTZ basis set indicated that the binding energies are the strongest with acetylene followed by ethylene and benzene and that the weakest binding energies were with methane and ethane. Alia et al.4 conducted detailed studies of vibrational spectroscopic properties (band position and infrared and Raman intensities) of the cyano group stretching mode of complexes of CH3CN with 27 organic and inorganic acids using the density functional theory (DFT) [B3LYP/6-31++G(2d,2p)]. They concluded that the observed cyano group stretching mode and consequent vibrational stretching blue shift promoted by hydrogen-bond formation have been reasonably well-reproduced using DFT calculations. Their systematic computational work further demonstrated that, even in relatively complex systems, the energetic, geometric, and vibrational characteristics of hydrogen-bond complexes can be predicted using DFT with an acceptable level of confidence. We compared our calculation results to experiments directly and indirectly. For the indirect comparison, we determined the relative order of polymer-fuel interaction intensity based on the calculated parameters, such as intermolecular distance, binding energies, and vibrational frequency shift associated with the cyano group stretching mode because of the interaction, then we compared the calculation-based relative order of interaction intensity with the experimentally determined relative order of interaction intensity to examine whether the calculation can provide results consistent with experiments. We also plotted the experimentally derived swell coefficient against intermolecular distance, binding energy, and frequency shift associated with the cyano group stretching mode to examine if there are good correlations. For the direct comparison, we compared our calculated frequency shift to the experimentally observed infrared absorption peak shift associated with the nitrile rubber cyano group conducted by Graham.1 Fourier transform infrared spectroscopy (FTIR) analysis was conducted for nitrile rubber aged with a variety of fuel species blended in the synthetic jet (4) Alia, J. M.; Edwards, H. G. M. J. Phys. Chem. A 2005, 109, 7977– 7987.

fuel (S-5) to measure infrared adsorption peaks associated with the cyano group with and without interactions.1 Computational Details Fuel Species and Model Polymers. The fuel species investigated were ethylbenzene, phenol, methylphenol, phenylmethanol, phenylethanol, phenylbutanol, 1-butanol, 1-hexanol, cyclohexanol, and di- and triethylene glycol monomethyl ether (diEGME and triEGME, respectively). With the exception of the latter two species, these are some of the candidate additives that can be used to enhance swelling in F-T fuels. The last two species were the agents used to prohibit fuel icing, and their interaction intensity was also examined. These species were also chosen to investigate the interaction difference among different types and sizes of species. A nitrile rubber is a random copolymer of polyacrylonitrile and polybutadiene. Most commercial polymers have a range of acrylonitrile up to 30 wt %. To represent these properties, cisbutadiene-acrylonitrile-trans-butadiene (cis-C4H7-CH2CHCNtrans-C4H7) was developed and used as a model polymer for the calculations. Properties Calculated and Theory Used. The charge distribution, intermolecular distance, binding energies, and vibrational frequency shifts corresponding to the cyano group stretching mode were calculated using hybrid DFT, B3LYP,5 with a basis set of 6-311G(d,p). B3LYP has been successfully employed to assess the geometries, energies, and vibrational spectra of hydrogen-bonded complexes,6-9 and recently, its accuracy and good agreement with MP2 and coupled-cluster methods has been confirmed for hydrogen bonds.4,10 The Gaussian 03 computer code11 was used for all DFT calculations. The geometries of the each compound, both fuel species and model polymer, were optimized using the B3LYP/6-311G(d,p) level of theory, and charge distributions were calculated prior to the interaction studies. The charges were calculated using the CHelp12 scheme implemented in the Gaussian 03 computer code11 to determine a possible interaction complex configuration. We assumed that the most positively charged terminal hydrogen of the fuel species forms the strongest hydrogen bond with the most negatively charged atom of the model polymer. The calculation and discussion presented in this paper are based on the geometries that we examined under this assumption. Although few other hydrogenbond configurations, such as the hydrogen bond between the cyano group and hydrogens in the fuel species other than OH, were examined for the limited number of fuel species, all of calculations (5) Becke, A. D. J. Chem. Phys. 1993, 98, 5648–5652. (6) George, W. O.; Jones, B. F.; Lewis, R.; Price, J. M. Phys. Chem. Chem. Phys. 2000, 2, 4910–4917. (7) Dimitrova, Y. Spectrochim. Acta, Part A 2004, 60, 1–8. (8) Schlucker, S.; Singh, R. K.; Asthana, B. P.; Popp, J.; Kiefer, W. J. Phys. Chem. A 2001, 105, 9983–9989. (9) Burneau, A.; Genin, F.; Quiles, F. Phys. Chem. Chem. Phys. 2000, 2, 5020–5029. (10) Ireta, J.; Neugebauer, J.; Scheffler, M. J. Phys. Chem. A 2004, 108, 5692–5698. (11) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03. Gaussian, Inc., Wallingford, CT, 2004. (12) Chirlian, L. E.; Francl, M. M. J. Comput. Chem. 1987, 8, 894– 904.

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Energy & Fuels, Vol. 23, 2009 445 showed either nearly zero or even slightly negative binding energies. Therefore, we stick to this assumption. The initial input geometries of polymer-polymer and polymer-fuel species complexes for DFT calculation were generated using semi-empirical MO theory, PM5, which is part of the CAChe package.13 The geometries of the complexes were, then, optimized using the B3LYP/6-311G(d,p) level of theory, and intermolecular distances were measured at the closest point. Binding energies were calculated on the basis of the enthalpies of reactions at 298 K, the energy difference between reactants, and polymer-polymer or polymer-fuel species complexes. The BSSE corrections were taken into account using the counterpoise method. The origin of BSSE lies in the possibility that the unused basis functions of the second unit in the associated complex may augment the basis set of the first unit, thereby lowering its energy compared to a calculation of this unit alone. The first unit will cause a similar error on the second. The counterpoise correction proposed by Boys and Bernardi14 has been the most popular means of correcting for BSSE and was applied in this study. The vibrational frequencies were also calculated at the B3LYP/ 6-311G(d,p) level. The frequency of the cyano group stretching mode without fuel interaction was compared to the one with interactions, and the frequency shift was calculated. The vibrational modes corresponding to the specific frequencies were identified using the GaussView visualization program.15 Among the fuel species, the calculation results of ethylbenzene, 1-butanol, phenol, methylphenol, and phenylmethanol were compared to the measured infrared absorption peak shift associated with the nitrile rubber cyano group.1

Results Atomic Charges, Optimized Geometries, and Binding Energies. Table 1 shows atomic charges using the CHelp scheme12 for the model polymer and fuel species. The most negatively charged atom and the most positively charged terminal hydrogen are presented for the model polymer, and the most positively charged terminal hydrogen atoms are presented for the fuel species. The most negatively charged atom in model polymer was nitrogen, and the most positively charged terminal hydrogen in the model polymer was found at the hydrogen attached to the second carbon of trans-butadiene shown in Figure 1b. With the exception of ethylbenzene, hydrogen at the OH group were the most positively charged atoms within the molecule. Hydrogen at the meta position of ethylbenzene was the most positively charged atom within the molecule. On the basis of the charge distribution analysis of all species, initial bonding configurations of polymer-polymer and polymer-fuel species complexes were determined. Figure 1 shows optimized geometries of model polymer-model polymer and model polymer-fuel species complexes. Both N-C and N-H interaction configurations are shown for the polymer-polymer interaction. The intermolecular distances are shown in the second column of Table 2. For polymer-polymer interaction, the strongest interaction occurred when two cyano groups were placed in parallel as shown in Figure 1a, and the intermolecular distance was measured between nitrogen in the cyano group of one polymer and carbon in the cyano group of the other polymer. The other polymer-polymer interaction was a hydrogen bond as shown in Figure 1b. The intermolecular distances for both configurations were relatively long compared tothepolymer-fuelspeciesdistance.Forthepolymer-ethylbenzene Figure 1. Optimized geometries of model polymer-model polymer and model polymer-fuel species complexes optimized with the B3LYP/ 6-311G(d,p) level of theory. White, gray, blue, and red indicate hydrogen, carbon, nitrogen, and oxygen, respectively. Intermolecular distances are shown in Table 2.

(13) CAChe6.1. Fujitsu Limited, Chiba, Japan, 2005. (14) Boys, S. F.; Bernardi, F. Counterpoise (BSSE). Mol. Phys. 1970, 19, 553. (15) Dennington, R., II.; Keith, T.; Millam, J.; Eppinnett, K.; Hovell, W. L.; Gilliland, R. GaussView, version 3.09. Semichem, Inc., Shawnee Mission, KS, 2003.

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Table 2. Intermolecular Distances, Binding Energies, and Vibrational Frequencies Corresponding to the Cyano Group Stretching Mode Calculated by the B3LYP/6-311G(d,p) Level of Theory binding energy (kcal/mol) intermolecular distance (Å)

BSSE corrected

vibrational frequency (cm-1)a

BSSE uncorrected

frequency

shift

model polymer

3.863

1.44

2.98

model polymer

2.753

0.69

1.35

ethylbenzene phenol methylphenol phenylmethanol phenylethanol phenylbutanol 1-butanol 1-hexanol cyclohexanol diEGME triEGME

2.686 2.014 2.020 2.071 2.106 2.115 2.123 2.122 2.124 2.094 2.084

-0.43 4.80 4.02 3.06 3.29 2.94 3.02 2.86 2.75 3.47 3.49

0.08 5.99 5.22 4.20 4.52 4.08 3.98 4.04 3.92 4.73 4.74

2342.4 2342.8b 2345.2c 2346.9d 2348.1 2356.6 2356.6 2356.2 2354.0 2353.2 2353.4 2353.8 2353.3 2354.6 2354.7

-4.5 -4.1 -1.7 0.0 +1.2 +9.7 +9.7 +9.3 +7.1 +6.3 +6.5 +6.9 +6.4 +7.7 +7.8

bond type C-N H bond H bond H bond H bond H bond H bond H bond H bond H bond H bond H bond H bond

a Vibrational frequency corresponding to the cyano group stretching mode without interaction is 2346.9 cm-1. b Two frequencies correspond to cyano group stretching for two model polymers in Figure 1a. c Vibrational frequency corresponding to the cyano group stretching mode for the upper molecule in Figure 1b, not interacted. d Vibrational frequency corresponding to the cyano group stretching mode for the bottom molecule in Figure 1b, interacted.

Figure 2. BSSE-corrected binding energy against the intermolecular distance in the studied complex. The model polymer-ethylbenzene complex was excluded. Table 3. Comparison of Intermolecular Distances, Binding Energies, and Vibrational Frequency Shifts Using Two Different Basis Sets [6-311G(d,p) and 6-31++G(2d,2p)] basis set 6-311G(d,p) 6-31++G(2d,2p)

intermolecular BSSE-corrected binding frequency shift distance (Å) energy (kcal/mol) (cm-1) 2.014 1.971

4.80 5.36

+9.7 +13.8

interaction, the C-H group in the meta position formed a nearly coaxial configuration with the cyano group in the model polymer. The intermolecular distance is longer than those for other fuel species. For other compounds, OH groups formed a nearly coaxial configuration with the cyano group. In general, phenol and methylphenol formed the closest configuration with the model polymer, followed by di- and tri-EGME, phenyl alcohol, straight chain and cyclic alcohol, and ethylbenzene. Table 2 also shows calculated binding energies at the B3LYP/ 6-311G(d,p) level of theory. Both BSSE-corrected and -uncorrected energies are presented. The strongest binding energy was formed with phenol, calculated as 4.80 kcal/mol, followed by methylphenol, di- and tri-EGME, phenyl alcohol, straight chain

Figure 3. Vibrational frequency shift of the CtN stretching mode because of the interaction against the intermolecular distance. The model polymer-ethylbenzene complex was excluded.

alcohol, cyclic alcohol, and ethylbenzene. The order is consistent with the reverse order of the intermolecular distance. The binding energy between model polymer and ethylbenzene showed a negative value with BSSE correction. Those without BSSE correction are also only 0.08 kcal/mol, which indicates that the B3LYP/6-311G(d,p) level of theory may underestimate the binding energy. Alfonso and Cugini3 calculated the binding energies between isobutylnitrile and benzene as 1.475 and 0.816 kcal/mol, with BSSE correction using LMP2 with cc-pvDZ and cc-pvTZ basis sets, respectively. Except ethylbenzene, the binding energies of polymer-fuel species are stronger than the binding energies of polymer-polymer interactions. The binding energies of polymer-fuel species were plotted against intermolecular distance and are shown in Figure 2. The plot for the interaction between model polymer and ethylbenzene was excluded because it showed negative binding energy. The plots were relatively well-fitted with exponential expression. The calculations were also carried out for the phenol-model polymer interaction using a larger basis set, 6-31++G(2d,2p). The results using this basis set showed a stronger interaction than the results using 6-311G(d,p) as shown in Table 3. Intermolecular distance is shorter by 0.043 Å, and the binding energy is stronger by

Interaction between Nitrile Rubber and Fuel Species

Figure 4. Vibrational frequency shift of the CtN stretching mode because of the interaction against BSSE-corrected binding energy. The model polymer-ethylbenzene complex was excluded.

Figure 5. Total ion chromatogram for JP-5 (top) and S-5 (bottom) showing the similar molecular size range and complexity of these fuels.1

0.561 cal/mol. The calculation time using a larger basis set was nearly 7 times longer than the calculation using 6-311G(d,p). We could not afford to use a larger basis set for all of the compounds, even though it may give better results for the binding energies, especially for the ethylbenzene-model polymer interaction. Vibrational Frequency Shift Analysis for the Cyano Group Stretching Mode. Vibrational frequencies were also calculated using the B3LYP/6-311G(d,p) level of theory for polymer-polymer and polymer-fuel species complexes. The frequency shifts of the cyano group stretching mode because

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of the interactions are shown in Table 2. The results are later compared to the experimentally observed infrared adsorption peak. For the model polymer, the frequency associated with the cyano group stretching mode was 2346.9 cm-1 without interaction. When the cyano group interacted with another cyano group as shown in Figure 1a, the frequencies were reduced (red shift) by 4.5 and 4.1 cm-1 to 2342.4 and 2342.8 cm-1, respectively. Interestingly, when the model polymer formed a hydrogen bond with the other model polymer as shown in Figure 1b, the frequency of the cyano group stretching mode of upper polymer, which was not interacted, was reduced by 1.7 cm-1 to 2345.2 cm-1 but the frequency of the bottom polymer, which was interacted, was unchanged. Even though the cyano group-cyano group interaction shown in Figure 1a showed a large frequency shift, the probability to form this configuration in the actual polymer will not be high when steric hindrance and the number of possible polymer-polymer configurations are taken into account. Instead, the polymers will most likely form hydrogen bond as shown in Figure 1b, where calculation indicated no frequency shift. Therefore, when calculation results are compared to measured frequency shift, the DFT-derived frequency shifts were based on the frequency change from 2346.9 cm-1. The vibrational frequencies were increased (blue shift) when the polymer interacted with fuel species. The shift was highest when the polymer interacted with phenol, methylphenol, and phenylmethanol followed by di- and tri-EGME and alcohol species in general, and minimal shift was observed for the interaction with ethylbenzene. The degree of shift showed a similar trend with the binding energies and also intermolecular distance. The vibrational frequency shifts were plotted against the intermolecular distance and binding energy, as shown in Figures 3 and 4, respectively. Relatively good linear correlation was found between the intermolecular distance and frequency shift. Data was scattered for the correlation between the binding energy and frequency shift, but in general, it showed that the stronger the binding energy, the larger the frequency shift. The optimized geometries showed a slightly shortened cyano group bond length, as much as 0.1146%, when the model polymer interacted with phenol. Even though the change is small, it could be one of the reasons why the frequency shifted toward the blue side. Alia and Edwards4 also reported CtN bond length shortening and the blue shift of the cyano group bond length and the stretching mode frequency when acetonitrile interacted with all of compounds that they studied. One of compounds they studied, methanol, showed bond length shortening by 0.1556%, and the frequency shifted by 12.1 cm-1 using the B3LYP/631++G(2d,2p) level of theory. They elucidated this strengthening of the CtN bond and the resulting bond length shortening as follows:4 When a hydrogen bond formed with the cyanide group, there is an important depletion in the electronic population of the N lone pair, which accounts for almost all of the net charge transferred from the base (CH3CN) to the acid. There is also a relative decrease in the total antibonding population and a significant increase in the s character of the triple bond. Some of the calculation results were compared to FTIR measurements for nitrile rubber aged with a variety of fuel species blended in the synthetic jet fuel (S-5) that were conducted by Graham.1 The nitrile rubber film used was uncrosslinked polyacrylonitrile-co-butadiene, which contained approximately 30% molar/molar ratio of polyacrylonitrile (Aldrich Chemical Co., Milwaukee, WI). The fuel species common to Graham and this study were ethylbenzene, 1-butanol, phenol,

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Figure 6. FTIR spectrum of a nitrile rubber film aged in different fuels.1 Table 4. Partition (Kpf) and Volume Swell (Ks) Coefficients of Selected Fuel Species species

Kpf

Ks

S-5 ethylbenzene 1-butanol phenol methylphenol phenylmethanol

0.08 0.34 0.85 20.00 10.87 10.27

0.79 3.96 37.54 26.37 19.41

methylphenol, and phenylmethanol. The baseline fuel, S-5, was provided by Syntroleum Corporation (Tulsa, OK). S-5 and conventional jet fuel, JP-5, show similar molecular range and complexity, n-C9-n-C17 and n-C9-n-C15, respectively, but have some differences in their composition. JP-5 includes 78.8% paraffins, 19.9% aromatics, and 1.3% diaromatics, while S-5 is entirely paraffinic.1 Figure 5 shows the total ion chromatogram obtained from GC-MS analyses of the two fuels.

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Figure 7. Swelling coefficient against the (a) intermolecular distance, (b) binding energy, and (c) vibrational frequency shift of the CtN stretching mode for the selected complex.

Figure 6a shows the FTIR spectrum of a nitrile rubber film aged in S-5 jet fuel. The solid and broken lines represent source film and S-5-aged film, respectively. It also shows difference spectra plotted with a cubic spline fit through the data points. The peak shifts were determined using difference spectra. Without interaction, the peak was centered at approximately 2237 cm-1. There is almost no difference between source film and S-5-aged film, indicating S-5 does not strongly interact with nitrile rubber. Parts b-f of Figure 6 show FTIR spectrum of a nitrile rubber film aged in S-5 jet fuel blended with a 20% volume to volume ratio (v/v) of ethylbenzene, 40% (v/v) 1-butanol, 0.5% (v/v) phenol, 0.5% (v/v) p-methylphenol, and 0.5% (v/v) phenylmethanol, respectively. Ethylbenzene also showed almost no change between the source film and ethylbenzene-aged film as shown in Figure 6b. Our calculation showed the frequency shift of +1.2 cm-1. The spectra for 1-butanol shown in Figure 6c indicates interactions with the

cyano group, whose absorption peak centered on 2244 cm-1, which is a +4 cm-1 frequency shift. Our calculation showed the vibrational frequency shift from 2346.9 to 2353.4 cm-1 (+6.5 cm-1). The large adsorption peak shifts were observed for phenol, methylphenol, and phenylmethanol as shown in parts d-f of Figure 6, respectively. These adsorption features centered at 2249 cm-1, which is a +9 cm-1 frequency shift. The calculated frequency shifts for the corresponding species are +9.7, +9.7, and +9.3 cm-1, respectively. Graham argued that the latter three spectra were taken with each species present at only 0.5% (v/v), illustrating that the interaction with the cyano group with these species is exceptionally strong.1 S-5 jet fuel was blended with 1-butanol and ethylbenzene at 40 and 20% of the concentration, respectively; however, shifts were smaller than phenol, methylphenol, and phenylmethanol blended fuels. Overall, the calculation results have good agreement with the measured infrared absorption peak shift. Frequency shift was

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also compared between two basis sets, 6-311G(d,p) and 6-31++G(2d,2p), for the phenol-model polymer interaction, as shown in Table 3. The frequency shift is larger by 4.1 cm-1 using the larger basis set. A comparison to experimental measurements indicated that the frequency shift was overestimated using a larger basis set. Volume Swell and Partition Coefficients and Relation to Calculation Results. Graham also derived partition (Kpf) and volume swell (Ks) coefficients.1 The Kpf provides a means to quantitatively measure the relative equilibrium concentration of specific species between the O-ring and fuel and was calculated on the basis of the following equation:1 Kpf ) [A]p/[A]f

(1)

where [A]p and [A]f are the concentrations of fuel component A in the polymer and fuel, respectively. The volume swell coefficient was calculated as follows:1 Ks ) (µ1 - µ0)/[A1]

(2)

where µ1 and µ0 are the volume swells when the concentration of the additive is at [A1] and zero, respectively. The volume swell µ was calculated as µ ) (Vi/V0 - 1) × 100%

(3)

where Vi and V0 are volumes of swelled and original O-ring. The results are shown in Table 4. Phenol has a very strong partition and swell coefficients, followed by methylphenol, phenylmethanol, 1-butanol, and ethylbenzene. The orders of these two coefficients are same as the order of calculated frequency shift, as well as the order of binding energies and reverse order of intermolecular distance. The swell coefficients were also plotted against the intermolecular distance, binding energy, and frequency shift, as shown in Figure 7. Ethylbenzene was again excluded from the plot. The swell coefficient showed a linear correlation with the intermolecular distance and binding energy. It was also well-fitted exponentially with frequency shift.

The results indicated that the theoretical investigation using DFT can be a potential tool to predict fuel-nitrile rubber interactions, at least in a relative manner. Conclusions The interactions between nitrile rubber and fuel species were theoretically investigated using model polymer and 11 fuel species. The model polymer used was cis-butadiene-acrylonitrile-trans-butadiene. The fuel species investigated were ethylbenzene, phenol, methylphenol, phenylmethanol, phenylethanol, phenylbutanol, 1-butanol, 1-hexanol, cyclohexanol, and di- and tri-EGME. Intermolecular distance, binding energy, and vibrational frequency shift associated with the cyano group stretching mode were three key parameters to be investigated. There was a correlation among the three parameters in general. These parameters also qualitatively correlated with experimentally derived partition and swelling coefficients. Good agreement between theoretical calculations and experimental observations suggests that theoretical investigation can be used as a potential tool to predict polymer swelling efficiency. The strongest interaction was found when the model polymer interacts with phenols, followed by methylphenol, di- and tri-EGME, phenyl alcohols, straight chain and cyclic alcohols, and ethylbenzene. The frequency shift calculation using B3LYP with a basis set of 6-311G(d,p) agreed with the measured FTIR frequency shift. Even though the binding energy calculation for the model polymer-ethylbenzene indicated that this level of theory underestimated the energy, the comparison of the computationally determined relative order of interaction intensity agreed with the experimentally determined relative order of interaction intensity. Acknowledgment. This paper is based on research sponsored by the Air Force Research Laboratory under Agreement F3361503-2-2347 (Technical Monitor, Mr. Robert W. Morris, Jr.). EF8006189