Anal. Chem. 2005, 77, 7434-7441
Equilibrium Partitioning Model Applied to RDX-Halide Adduct Formation in Electrospray Ionization Mass Spectrometry Michael E. Sigman,* Paul A. Armstrong, Jean M. MacInnis, and Mary R. Williams
National Center for Forensic Science and Department of Chemistry, University of Central Florida, Orlando, Florida 32826
An equilibrium partitioning model is applied for the first time to the sequential formation of 1:1 and then 2:1 adducts between the high explosive cyclo-1,3,5-trimethylene-2,4,6-trinitramine (RDX) and halide anions fluoride, chloride, bromide, and iodide in electrospray ionization interface (ESI) mass spectrometry. The equilibrium partitioning model is developed and model calculations are presented to demonstrate the generic behavior of the system, which is in qualitative agreement with the observed changes in 1:1 (RDX-halide) and 2:1 (RDXhalide) responses in ESI-MS. The model is successfully applied to the experimental data with the use of octanolwater partitioning coefficients to predict interior-to-surface partitioning behavior of the complexes in droplets formed in the ESI. The data and model suggest that the significantly more hydrophobic 2:1 complexes are readily observed in ESI-MS, even though their formation constants may be several orders of magnitude less than that of the 1:1 complex. Structures for RDX-halide 1:1 and 2:1 complexes are proposed based on ion-dipole attractions and destabilizing dipole-dipole interactions. Electrospray ionization mass spectrometry (ESI-MS) has been examined as an alternative to gas chromatography-mass spectrometry for the analysis of high explosives1-5 and inorganic oxidizers.6,7 The relatively mild conditions in the ESI interface can facilitate the analysis of the high explosives and provide an attractive alternative to APCI-MS analysis,8-11 although APCI-MS * To whom correspondence should be addressed. E-mail: msigman@ mail.ucf.ude. (1) Gapeev, A.; Sigman, M. E.; Yinon, J. Rapid Commun. Mass Spectrom. 2003, 17, 943-948. (2) McClellan, J. E. Fundamentals and Applications of Electrospray IonizationQuadrupole Ion Mass Spectrometry for the Analysis of Explosives. Ph.D. dissertation, University of Florida, Gainesville, FL, 2000. (3) Zhao, X.; Yinon, J. J. Chromatogr., A 2002, 977, 59-68. (4) Yinon, J.; McClellan, J. E.; Yost, R. A. Rapid Commun. Mass Spectrom. 1997, 11, 1961-1970. (5) Schreiber, A.; Efer, J.; Engewald, W. J. Chromatogr., A 2000, 869, 411425. (6) Zhao, X.; Yinon, J. Rapid Commun. Mass Spectrom. 2002, 16, 1137-1146. (7) Zhao, X.; Yinon, J. Rapid Commun. Mass Spectrom. 2001, 15, 1514-1519. (8) Zhao, X.; Yinon, J. J. Chromatogr., A 2002, 946, 125-132. (9) Sanchez, C.; Carlsson, H.; Colmsjo, A.; Crescenzi, C.; Batlle, R. Anal. Chem. 2003, 75, 4639-4645. (10) Evans, C. S.;. Sleeman, R.; Luke, J.; Keely, B. J. Rapid Commun. Mass Spectrom. 2002, 16, 1883-1891. (11) Zhao, X.; Yinon, J. J. Chromatogr., A 2002, 946, 125-132.
7434 Analytical Chemistry, Vol. 77, No. 22, November 15, 2005
typically gives more structural information through increased fragmentation. Reviews of explosives analysis by LC-MS methods are available in the recent literature.12,13 The formation of chloride attachment ions to form [M + Cl]in negative ion ESI-MS greatly enhances the analysis of analytes that lack acidic sites and therefore exhibit weak [M - H]signals.14 Chloride attachment to nonacidic organics has been proposed to occur primarily at electrophilic hydrogens.14 The stability of these anionic adducts has been shown to increase as the difference between the gas-phase basicities of the deprotonated analyte ([M - H]-) and the anion is minimized.15 In addition, the stability of adducts has been shown to generally increase with rising gas-phase basicities of the two species. Specific interactions, such as hydrogen bonding, have also been shown to play an important role in stabilizing some adduct ions.15 Negative ion electrospray-tandem mass spectrometry has been utilized to investigate the collision-induced decomposition of the adducts as a method of evaluating the gas-phase acidities of the analyte.16 Although the explosive cyclo-1,3,5-trimethylene-2,4,6-trinitramine (RDX) does not contain acidic hydrogens, both 1:1 and 2:1 attachment ions formed between RDX and chloride, as well as other anions, have previously been reported.1,2 However, 3:1 and higher complexes involving RDX have not been reported. The gas-phase and in-crystal chemical conformations of RDX are depicted in Figure 1.17 The peak widths at 10% maximum intensity, W10%, in a quadrupole ion trap mass spectrometer have been shown to be very low for both RDX-Cl and HMX-Cl adducts, indicating that these ions are fairly stable.18 In this paper, we examine the formation of RDX attachment ions with fluoride, chloride, bromide, and iodide by ESI-MS and ESI-MS/MS. Although a sizable ESI response is observed here for 2:1 RDX-halide adducts, a recent report failed to detect significant 2:1 adducts between RDX and several anions.19 (12) Yinon, J.; Zhao, X.; Gapeev, A. Tracking the terrorists: Identification of explosives residues in post-explosivon debris by LC/MS methods. In Vapour and Trace Detection of Explosives for Anti-Terrorism Purposes; Krausa, M., Reznev, A. A., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2004; pp 51-62. (13) Yinon, J. Forensic Sci. Rev. 2001, 13, 19-28. (14) Zhu, J.; Cole, R. B. J Am Soc Mass Spectrom 2000, 11, 932-941. (15) Cai, Y.; Cole, R. B. Anal. Chem. 2002, 24, 985-991. (16) Zhu, J.; Cole, R. B. J. Am. Soc. Mass Spectrom. 2001, 12, 1193-1204. (17) Tsiaousis, D.; Munn, R. W.; Smith, P. J.; Popelier, P. L. A. Chem. Phys. 2004, 305, 317-323. (18) McClellan, J. E.; Murphy, J. P., III; Mulholland, J. J.; Yost, R. A. Anal. Chem. 2002, 74, 402-412. 10.1021/ac058037v CCC: $30.25
© 2005 American Chemical Society Published on Web 10/11/2005
Figure 1. Chemical structures of RDX (a) in the gas phase and (b) in the crystal.
In the electrospray interface, excess charge is deposited on the surface of forming droplets. The excess surface charge is formed at a constant rate, and it is thought that the surface charge carriers are eventually the source of ions observed in the mass spectrometer. An equilibrium model has been proposed based on competition between ions in solution for the limited number of surface sites that accounts for observed concentrationresponse behavior in ESI-MS.20 The model is based on a series of adduct-forming equilibria occurring on the interior and surface of the droplet, with equilibrium partitioning of all species between the interior and exterior surface of the droplet. Partitioning between the droplet interior and surface has been described by a surface selectivity factor, which depends strongly on structural characteristics of the analyte.21 The equilibrium model has recently been applied to 1:1 host-guest complex formation in ESI-MS;22 however, this model has not previously been applied to the stepwise formation of 1:1 and 2:1 RDX-halide complex formation in the ESI interface. In this paper, the equilibrium partitioning model is applied to the stepwise formation of 1:1 and 2:1 explosive-halide complexes and shown to account for the experimentally observed formation of these adduct ions by ESIMS. Although the complexes could be studied by direct infusion of solutions containing RDX and halide salts into the ESI-MS, this paper examines the complexes formed after HPLC chromatographic separation of RDX in a mixture of common high explosives because those are the conditions under which most analyses of explosives mixtures occur. MATERIALS AND METHODS RDX was obtained as a 1000 ppm acetonitrile solution along with other high explosives in an EPA 8330A mixture (Ceriliant Corp., Round Rock, TX). Methanol and water (HPLC grade, Burdick and Jackson, Muskegon, MI) and salts NH4F, NH4Cl, NH4Br, and NH4I (reagent grade, Sigma-Aldrich Chemical Co., Milwaukee, WI) were used as received. Liquid chromatography-mass spectrometry experiments were performed on a Thermo Finnigan LCQ-DUO equipped with an ESI interface. The interface spray voltage was set at 4.2 kV with a capillary voltage of -43 V and capillary temperature of 140 °C. The sheath gas and auxiliary gas flows were set at 50 and 52 (arbitrary units), respectively. The circuit current in the interface (19) Mathis, J. A.; McCord, B. R. Rapid Commun. Mass Spectrom. 2005, 19, 99-104. (20) Enke, C. G. Anal. Chem. 1997, 69, 4885-4893. (21) Cech N. B.; Enke, C. G. Anal. Chem. 2001, 73, 4632-4639. (22) Sherman, C. L.; Brodbelt, J. S. Anal. Chem. 2003, 75, 1828-1836.
was typically 3.9 × 10-7 A, corresponding to an excess charge [Q] at the instant of droplet formation of 1.21 × 10-6 equiv/L.20 RDX was isolated from the other explosives in the mixture by chromatography at a flow rate of 200 µL/min through a reversedphase column (Restek Allure, C18, 5-mm particle size, 150 × 2.1 mm) by isocratic elution with a 1:1 methanol to water mobile phase. Individual halide salts were added to the postcolumn eluent at a rate 5 µL/min. The initial concentration of each salt was adjusted to give a final concentration of 0.1 mM in the eluent stream. RESULTS AND DISCUSSION ESI-MS Experimental Response Curves. When RDX is analyzed by ESI-MS with postcolumn addition of halide, both the 1:1 and 2:1 complexes are observed. The fluoride, chloride, bromide, and iodide adduct spectra are shown in Figure 2 at an RDX analytical concentration of 2.5 × 10-5 M. The 1:1 and 2:1 RDX-halide complexes are the dominant species in the chloride, bromide, and iodide spectra. The 1:1 and 2:1 complexes are also present in the fluoride spectra, although other species are also present. The intensity of both adduct ions and the ratio of 1:1 and 2:1 adducts can be seen to vary as the concentration of RDX was increased. The chloride anion was introduced postcolumn at a rate of 5 µL/min at a constant concentration of 4.0 × 10-3 M prior to dilution in the 200 µL/min column effluent stream. The final concentration of halide in the effluent entering the ESI interface was 1.0 × 10-4 M. The analytical concentrations of the RDX samples were 2.5 × 10-5, 1.2 × 10-5, 5.0 × 10-6, and 5.0 × 10-7 M. The RDX in each 5-µL injection eluted from the column with a peak width of ∼0.3 min in a total column effluent flow rate of 205 µL/min. The average diluted concentrations of RDX in the eluting solution corresponded to 2.0 × 10-6, 1.0 × 10-6, 4.0 × 10-7, and 4.0 × 10-8 M, respectively. It is important to differentiate between the analytical concentration and the diluted concentration entering the electrospray interface when discussing the analyte behavior within electrospray droplets. Throughout the remainder of this paper, estimated analyte concentrations in the electrospray interface will be used to facilitate comparison with theoretical models. Similar sets of chromatographic isolation of RDX were performed with fluoride, bromide, and iodide anions added into the postcolumn effluent, with each halide at a concentration of 1.0 × 10-4 M (prior to dilution). The ratios of 1:1 and 2:1 RDX-halide adduct ions varied with the concentration of RDX as shown in Figure 3. The data in Figure 3 reflects the integrated areas for the respective extracted ion chromatograms measured by mass scanning, and the concentrations are the estimated concentration in the electrospray interface (not the analytical concentration) as discussed above. The 2:1 adduct response is seen to exceed the 1:1 response for RDX-fluoride adducts at all RDX concentrations in Figure 3a. When the halide is chloride and bromide, the 1:1 adduct response exceeds that for the 2:1 adduct at low concentrations of RDX, Figure 3b and c, respectively. However, the 2:1 adduct response exceeds that of the 1:1 adduct with chloride and bromide at higher RDX concentrations. The 1:1 adduct response is seen to exceed the 2:1 response of RDX-iodide adducts at all RDX concentrations investigated, Figure 3d. The RDX-halide adducts exhibit progressively less propensity for 2:1 adduct formation through the series Fl-, Cl-, Br-, and I-. Analytical Chemistry, Vol. 77, No. 22, November 15, 2005
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Figure 2. (a) Fluoride, (b) chloride, (c) bromide, and (d) iodide adduct spectra shown at an RDX analytical concentration of 2.5 × 10-5 M.
Figure 3. ESI-MS intensities of 1:1 (solid symbols) and 2:1 (open symbols) RDX-halide adduct ions for halides (a) fluoride, (b) chloride, (c) bromide, and (d) iodide.
The 1:1 RDX-halide adducts show strong deviations from linear behavior, breaking concave down as RDX concentrations increase. In contrast, 2:1 RDX-halide adducts show distinct induction-type behavior, breaking concave up at low RDX con7436
Analytical Chemistry, Vol. 77, No. 22, November 15, 2005
centrations and then breaking concave down at higher RDX concentrations, Figure 3. This behavior is consistent with stepwise formation of 1:1 RDX-halide adducts first, followed by addition of a second RDX molecule to form the 2:1 adduct.
The excess charge on a droplet at the time of formation is designated as [Q] and was calculated from our experimental parameters to be 1.21 × 10-6 equiv/L.20 The value of [Q] is equal to the sum of the concentrations of those ions on the surface of the droplet that contribute to the excess charge:
[Q] ) [X]s + [EX]s + [E2X]s
Figure 4. Equilibrium partitioning model for adduct formation between the explosive RDX (symbol E) and a halide (symbol X).
The quantitative analysis of RDX in the ESI-MS spectra by means of halide adduct formation is complicated by the formation of both 1:1 and 2:1 RDX-halide adducts and by the variation of the adduct ratios as a function of RDX concentration. Fluoride is the preferred adduct anion for quantitative analysis of RDX by ESI-MS given the large dominance of 2:1 RDX-fluoride complexes at all RDX concentrations examined. Quantitative analysis of RDX by LC-ESI-MS with the addition of nitrite has previously been reported.2 In that work, both 1:1 and 2:1 RDX-NO2- adducts were observed and the intensities were summed to produce a calibration curve with a linear dynamic range of 2-150 ppb (9 × 10-9-7 × 10-7 M) analytical concentrations. This concentration range corresponds to the two lowest concentration points in Figure 3. From a more fundamental perspective, the significant variation in 1:1 and 2:1 RDX-halide adduct formation as a function of the halide identity may offer an opportunity to gain additional insight into the factors controlling adduct formation. Application of the Equilibrium Response Model to Explosive-Halide Adduct Formation. The equilibrium partitioning model by Enke20 has recently been applied to the formation host-guest complexes in droplets within the ESI interface.22 The same model can be applied to the sequential formation of 1:1 and 2:1 RDX-halide adducts within droplets in the ESI interface. The model employed here is shown in Figure 4. The symbol E is used in Figure 4 and subsequent discussion to generically represent the explosive RDX. The halide anion is denoted in the model by X, where the formal charge has been dropped for simplicity, and the 1:1 complex is symbolized as EX, while the 2:1 complex is designated as E2X. The equilibrium constant for EX formation is denoted as K1, and the equilibrium constant for the formation of E2X from EX is given by K2. Both complexes, EX and E2X, exist in the interior of the droplet and on the surface of the droplet, as do the species E and X. The subscripts of i and s have been employed to designate the location of each species; i.e., EXi exists on the interior of the droplet, while Xs exists on the droplet surface. Similarly, the two equilibria described by K1 and K2 occur both on the interior and on the surface of the droplet. The notation K1i designates an equilibrium constant for 1:1 complex formation on the droplet interior, while K2s refers to the equilibrium constant for 2:1 complex formation at the droplet surface, etc. The equilibrium partitioning of each species (i.e., X) between the interior and surface of the droplet is designated by an equilibrium constant (i.e., KX), as shown in Figure 4.
(1)
The model presented here does not include a term for background ions. While these ions exist, their concentrations are relatively small in comparison to the 1.0 × 10-4 M halide concentration. Sodium chloride impurity levels in methanol have been estimated to be as large as 1 × 10-5 M range.22 Equation 1 will be applicable to RDX adducts with Cl-, Br-, and I-, where the 1:1 and 2:1 complexes are by far the most abundant species observed; however, eq 1 is not applicable to RDX adducts with F-, where species other than the 1:1 and 2:1 complexes are observed. Mass balance equations can be written for the two major components of the system, E and X, as
CE ) [E]s + [E]i + [EX]s + [EX]i + 2[E2X]s + 2[E2X]i (2) CX ) [X]s + [X]i + [EX]s + [EX]i + [E2X]s + [E2X]i (3) The concentrations CE and CX are the concentrations of E and X, respectively, in the effluent solution entering the ESI interface. The partitioning of each species between the droplet interior and surface are defined as shown in eqs 4-7, as done previously.22
KEX ) [EX]s/[EX]i
(4)
KE2X ) [E2X]s/[E2X]i
(5)
KX ) [X]s/[X]i
(6)
KE ) [E]s/[E]i
(7)
While these equilibrium constants define the partitioning between the droplet interior and surface for each species, it is more convenient to think in terms of the relative partitioning coefficients for the important chemical species. Equations 4, 5, and 7 are divided by eq 6 to define a set of partitioning constants that are relative to the halide partitioning, eqs 8-10.
KEX/X ) ([EX]s [X]i)/([EX]i[X]s)
(8)
KE2X/X ) ([E2X]s [X]i)/([E2X]i [X]s)
(9)
KE/X ) ([E]s [X]i)/([E]i[X]s)
(10)
A surface selectivity factor (S) has previously been defined as the ratio of the fraction of analyte lost during droplet fission divided by the fraction of the total excess charge lost.21 The surface selectivity factor can vary from 0 to 1, with a larger number indicating that an ion has an affinity for the surface. In an ESIMS analysis of trimethyloctadecylammonium (TMOA+) chloride and cesium hydroxide in a 1:1 methanol-water mixture with 0.5% Analytical Chemistry, Vol. 77, No. 22, November 15, 2005
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acetic acid, S for the hydrophobic TMOA+ moiety was estimated to be near 1 while the S value for the cesium ion was estimated to be near 0.01.21 By analogy, in the case examined here, the more hydrophobic 1:1 and 2:1 explosive-halide adducts would be expected to demonstrate selectivity for the droplet surface. Consequently, the values of KEX/X and KE2X/X from eqs 8 and 9, respectively, would be expected to be significantly greater than 1. To the extent that the 2:1 adduct is more highly hydrophobic, KE2X/X would be expected to be larger than KEX/X. The last equilibrium constants to be defined are those for the formation of 1:1 and 2:1 explosive-halide adduct ions. Adduct ion formation can occur on the interior or surface of the droplet; hence, four equilibrium constants are defined as in eqs 11-14.
K1i ) [EX]i/([E]i[X]i)
(11)
K1s ) [EX]s/([E]s[X]s)
(12)
K2i ) [E2X]i/([E]i[EX]i)
(13)
K2s ) [E2X]s/([E]s[EX]s)
(14)
Equations 8-10 can be rearranged and substituted into eqs 12 and 14 to give eqs 15 and 16, which demonstrate that the equilibrium formation of adduct ions on the droplet surface are related to the analogous equilibria occurring on the droplet interior. The equilibria on the droplet surface and interior are related through the equilibria involving partitioning between the droplet interior and surface.
K2s ) (KE2XK2i)/(KEKEX)
(15)
K1s ) (KEXK1i)/(KEKX)
(16)
ESI Response Curves from Equilibrium Partitioning Model Calculations. The model presented above can be represented by a set of eight equations (1-3, 8-10, 11, and 13) with eight unknowns ([E]s, [E]i, [EX]s, [EX]i, [E2X]s, [E2X]i, [X]s, and [X]i). The set of equations can easily be solved analytically, whereas the symbolic solutions would likely be extremely complicated and offer little additional insight into the model.20-22 The analytical solution to the model was calculated at concentrations CX and CE corresponding to the approximate concentrations entering the ESI (1.0 × 10-4 M for the halide and 4.0 × 10-8-2.0 × 10-6 M for the explosive). These concentrations are less than the analytical concentration and are calculated based on the analytical concentration, the column flow rate, and the peak width, as discussed above. The total charge carrier concentration [Q] was held constant at the experimental value (1.21 × 10-6 equiv/ L). The effect of K1i and K2i on the droplet surface concentrations [EX]s and [E2X]s were examined while holding KEX/X, KE2X/X, and KE/X at a value of 50. The value of K1i was held at a value of 1.0 × 109, while K2i was varied from 1 × 108 up to 1 × 1011. The basis for these choices are as follows. The gas-phase chloride and fluoride affinities (∆H) for methanol have been reported to be 70 7438 Analytical Chemistry, Vol. 77, No. 22, November 15, 2005
Figure 5. Results of the model calculations showing (a) concentrations of EX on the outer surface of the droplet and (b) concentrations of E2X on the outer surface of the droplet. Calculations were performed holding KEX/X, KE2X/X, and KE/X at a value of 50, the value of K1i was 1.0 × 109, and K2i was varied from 1 × 108 up to 1 × 1011.
(16.7 kcal/mol) and 124 kJ/mol (29.6 kcal/mol), respectively.23 The corresponding halide-methanol equilibrium constants for chloride and fluoride are calculated to be 1 × 109 and 4 × 1015, based on a ∆S ) -5.8 J/kmol calculated from the statistical conversion of 2 mol of reactant to 1 mol of complex. The values for K1i and K2i must exceed the equilibrium constants for solvent adduct formation; otherwise the explosive-halide adduct would not be observed in the ESI-MS.14 While the equilibrium partitioning model depends on equilibria formed in solution, the gas-phase data provide a basis for estimating the magnitude of RDX-halide interactions that must exist in order for complex formation to be observed in the presence of solvent. The values used here for K1i and K2i exceed the values previously used in an equilibrium partitioning model for the analysis of host-guest complexes.22 The results of the numerical model varying the values of K2i are shown in Figure 5. The graph in Figure 5a demonstrates that [EX]s increases with increasing initial explosive concentration, CE, and reaches a limiting value due to the formation of E2X. This is the behavior observed for 1:1 RDX-halide complexes in Figure 3. As the value of K2i increases, [EX]s decreases, as would be expected based on the model. At the highest calculated value of K2i, the concentration of EXs maximizes around a CE value of 1 × 106 and then decreases slightly. The model predicts the concentration of [E2X]s to increase as CE is increased; however, the (23) Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Lein, R. D.; Mallard, W. G. J. Phys. Chem. Ref. Data 1988, 17, Suppl. 1.
Figure 6. Results of model calculations showing the surface concentrations EX (open symbols) and E2X (filled symbols) where (a) both K1i and K2i equal to 1 × 109 and (b) K1i ) 1 × 109 and K2i ) 1 × 1011. The equilibrium partition constants KEX/X, KE2X/X, and KE/X are maintained at a value of 50.
Figure 7. Effects on the surface concentrations of (a) EX and (b) E2X from model calculations where KE2X/X is varied from 50 to 500, KEX/X and KE/X are maintained at constant values of 50, and K1i and K2i are maintained at values of 1 × 109.
behavior of [E2X]s differs significantly from that of [EX]s, as shown in Figure 5b. At low explosives concentrations, [E2X]s is seen to increase in a concave up quadratic fashion. As the explosive concentration, CE continues to increase, [E2X]s also increases, but the trend breaks concave down as the total concentration of charge carrier approaches the limit of Q. This behavior is analogous to that observed for the 2:1 RDX-halide concentrations in Figure 3. The model calculation results shown in Figure 5 demonstrate the general agreement between the model and the experimental data. Further model calculations were conducted to examine the influence of other parameters on the surface concentrations of EX and E2X. It is instructive to plot both [EX]s and [E2X]s as a function of CE on the same graph. Figure 6a shows the numerical simulation for both K1i and K2i equal to 1 × 109. Figure 6b shows the simulation for K1i ) 1 × 109 and K2i ) 1 × 1011. The equilibrium partition constants KEX/X, KE2X/X, and KE/X are maintained at a value of 50 in Figure 6a and b. Under the simulation conditions, the model predicts that [EX]s will exceed [E2X]s at low values of CE. When K2i exceeds K1i by 2 orders of magnitude, the curves showing the surface concentration of the two species cross, Figure 6b, and the populations are inverted at higher explosives concentrations. The model calculations in Figure 6a generically resemble the RDX-iodide response curves in Figure 3d, whereas Figure 6a resembles the RDX-chloride or RDX-bromide response curves in Figure 3b and c. The surface concentrations of the two
complexes are also affected by the equilibrium partitioning constants KEX/X and KE2X/X. The effects on the surface concentrations of EX and E2X resulting from changing KE2X/X from 50 to 500, while holding KEX/X and KE/X constant at values of 50, and holding K1i and K2i at 1 × 109, are shown in Figure 7. Increasing KE2X/X leads to an increase in [E2X]s and a decrease in [EX]s at any given CE, and while the effect is not large, [EX]s clearly reaches a maximum concentration at a CE value of ∼6 × 10-6 M, as seen in Figure 7a. The effect on [E2X]s is more pronounced, as shown in Figure 7b; however, the surface concentration [E2X]s did not exceed [EX]s at a KE2X/X value of 500 and a CE of 1 × 10-5 M, as shown in Figure 8. At values of KE2X/X greater than 600, [E2X]s does exceed [EX]s higher values of CE. The effects of changing KEX/X while holding KE2X/X constant were also examined. As KEX/X is decreased relative to KE2X/X, the surface concentration of EX also decreases (results not shown). The value of KEX/X should always be less than or equal to KE2X/X due to the greater hydrophobic nature of the 2:1 complex, as discussed earlier. On the contrary, changing the value of KE/X, while holding KEX/X and KE2X/X constant, has no effect on the surface concentrations of E2X or EX. This result is easily understood because KE/X changes the surface concentration of E, which is involved in the formation of both EX and E2X at the droplet surface. A comparison of the experimental data in Figure 3 with the model calculations in Figures 5-8 demonstrates a qualitative Analytical Chemistry, Vol. 77, No. 22, November 15, 2005
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Table 1. Calculated log(KOW) and KOW/KOW(RDX) Values for 1:1 and 2:1 RDX-Halide Complexes
Figure 8. Model calculation results from Figure 7 for [EX]s and [E2X]s plotted on the same graph for a partitioning constant KE2X/X of 500. Values of partitioning constants KEX/X and KE/X each had values of 50 in the model calculation and the values of K1i and K2i were 1 × 109.
agreement between model and experiment. A better idea of the applicability of the model comes from attempting to fit the experimental data. Modeling the Experimental Results. To model the experimental data, estimates for some of the model parameters must be made. The gas-phase affinities of fluoride and chloride for methanol (∆H ) 124 and 70 kJ/mol, respectively) fall off as the inverse of the square of the ionic radii of the halide. Assuming an analogous behavior for bromide and iodide, we can estimate the ∆H values to be 61 and 47 kJ/mol, respectively. To facilitate model calculations, the formation constants K1i for fluoride, chloride, bromide, and iodide were set equal to 4 × 1015, 1 × 109, 7 × 107, and 1 × 106 as lower limit estimates based on gas-phase methanol affinities (∆H), as discussed above. The values for the relative partitioning constants between the inner and outer layers of the droplet (KE/X, KEX/X, and KE2X/X) are less straightforward to estimate. More highly hydrophobic moieties are thought to partition to the outer surface of the droplet to a greater extent than less hydrophobic compounds.20-22 The energy of hydration for a species can be used to help estimate the extent of partitioning; however, these values are not known for the complexes in question. As an alternative, we chose to use the octanol-water portioning coefficient (KOW) as a basis for estimating the partitioning coefficients. Values for KOW can be estimated from molecular formula and are readily calculated by hand or by several molecular modeling packages.24 The calculated values of log(KOW) for RDX and each complex are given in Table 1. These values were calculated by treating the halide as a halogen atom covalently bonded to a sp3-hybridized carbon. The calculation does not take into account the negative charge on the complex and therefore may overestimate the KOW value. The ratio of the KOW values for the complex and KOW(RDX), the calculated KOW for RDX, are shown in Table 1. The ratios reflect a substantially larger hydrophobicity for the 2:1 complex. The KOW ratios in Table 1 were used in the model calculations as estimates of the relative magnitudes of the partitioning constants KE/X, KEX/X, and KE2X/X. The implication of the estimated partitioning constants is that even if the formation constant K2i is much smaller than K1i, the (24) Viswanadham, V. N.; Ghose, A. K.; Revankar, G. N.; Robins, R. K. J. Chem. Inf. Comput. Sci. 1989, 29, 163.
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species
log(KOW)
KOW/KOW(RDX)
RDX [RDX-F][RDX2-F][RDX-Cl][RDX2-Cl][RDX-Br][RDX2-Br][RDX-I][RDX2-I]-
9.42 9.76 19.18 10.05 19.47 10.35 19.77 10.35 19.77
1 2.2 5.8 × 109 4.3 1.1 × 109 8.5 2.2 × 1010 8.5 2.2 × 1010
Table 2. Estimated Model Parameters KEX/X, KE2X/X, KE/X, and K1s, and the Fitted Values of K2s
KEX/X KE2X/X KE/X K1i K2i
Cl
Br
I
43 1.1 × 1010 10 1.0 × 109 1.0 × 103
85 2.2 × 1011 10 7.0 × 107 5.0
85 2.2 × 1011 10 1.0 × 106 2.0 × 10-2
2:1 complex would be observed in the ESI due to the much larger partitioning constant KE2X/X. Using the values in Table 1, we further estimated the ratio of KE/X to be 10 for all halides due to the higher hydrophobicity for RDX relative to the halides. This estimate is reasonable based on previous reports.20-22 The values of KEX/X and KE2X/X were adjusted accordingly. The value of K2i for RDX-halide complexes with chloride, bromide, and iodide was adjusted to obtain the fits shown in Figure 9. The values for KEX/X, KE2X/X, KE/X, K1i, and K2i are given in Table 2. The data for fluoride were not fitted to the model because species other than the 1:1 and 2:1 complex with RDX were observed in the ESI-MS, and therefore, eq 1 was not valid. The fitted values demonstrate how, according to the model, a very large KE2X/X can compensate for a K2i that is much smaller than K1i. The fitted value of K2i varies over 5 orders of magnitude as the halide is varied from chloride to iodide. The ratio of K1i/K2i is seen to increase as the halide is varied from chloride (K1i/K2i ) 1 × 106) to bromide (K1i/K2i ) 1.4 × 107) to iodide (K1i/K2i ) 5 × 107). RDX-Halide Complex Structure. It has previously been proposed that chloride attachment to nonacidic organics occurs primarily at electrophilic hydrogens.14 The vapor-phase dipole moment of RDX has been calculated to be 6.404 D.17 The calculated vapor-phase configuration places the triamine ring in a chair conformation with the three nitro groups in pseudoequitorial positions on the same side of the ring, see Figure 1a, leading to the large resulting dipole directed perpendicular to the plane of the six-membered ring. In the conformation observed in-crystal, and depicted in Figure 1b, one of the nitramine nitrogens is inverted, producing a more highly strained structure with a 7.405 D dipole.17 In both the vapor-phase and crystalline conformations, the three hydrogens that occupy axial positions on the ring methylene carbons can be classified as electrophilic. The combined effects of the electrophilicity of these hydrogens and the sizable dipole moment support an anticipated ion-dipole interac-
Figure 10. Proposed gas-phase structures for EX and E2X adduct ions.
two RDX moieties. The structure shown in Figure 10b is not unreasonable, given that the attractive ion-dipole interactions will exhibit a 1/r2 distance dependence, while the repulsive dipoledipole interactions will exhibit a 1/r6 distance dependence. It can be expected that the average RDX-halide interaction energy in the E2X complex would be substantially weaker than the RDXhalide interaction energy in the EX complex because of the dipole-dipole repulsion. This trend is observed in the fitted values for K2i, which are 6-8 orders of magnitude less than K1i.
Figure 9. Experimental integrated areas of 1:1 (filled symbols) and 2:1 (open symbols) RDX-halide adduct ions and model-fitted data for (a) chloride, (b) bromide, and (c) iodide. Parameters used for model calculations are given in Table 2.
tion between a chloride (or other halide) and RDX. The iondipole interaction leading to EX formation can be represented as depicted in Figure 10a for the vapor-phase conformation. As the size of the halide increases, the strength of the interaction is expected to decrease inversely with the ion-dipole separation. The addition of a second RDX molecule to form the E2X complex may occur in a similar fashion, as depicted in Figure 10b. In order for the 2:1 complex to form, the average attractive RDX-halide interaction would need to be larger than the repulsive dipoledipole interaction resulting from the dipoles associated with the
CONCLUSIONS An equilibrium partitioning model has been shown to describe the experimentally observed formation of 2:1 RDX-halide complexes in ESI-MS. The model predicts association constants for the E2X complexes that are orders of magnitude less than the association constants for the EX complexes and may be explained as resulting primarily from ion-dipole interactions. The modeling results suggest that highly hydrophobic species formed in relatively low quantities may be readily observed in ESI-MS as a result of favored partitioning to the exterior of the charged droplet. This finding is significant for the analysis of RDX by HPLC-(ESI)MS with postcolumn adduct formation because it demonstrates that while the analyte of interest (RDX) partitions between two adduct species, the 1:1 complex predominates. ACKNOWLEDGMENT This work was supported under a Contract Award from the Counterterrorism and Forensic Science Research Unit of the Federal Bureau of Investigation’s Laboratory Division. Points of view in this document are those of the authors and do not necessarily represent the official position of the Federal Bureau of Investigation. Received for review July 19, 2005. Accepted August 23, 2005. AC058037V
Analytical Chemistry, Vol. 77, No. 22, November 15, 2005
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