J. Phys. Chem. 1988, 92, 1655-1664 corresponds to an effective Hamaker constant of 4 X J, compared to approximately 6 X J for hydrocarbon across water and 2 X J for mica across water. That charge fluctuations of neutral surfaces are an unlikely candidate is supported experimentally by the numerous cases where no long-range attraction is observed between uncharged or weakly charged surfaces that are not h y d r o p h o b i ~ . ~ @The ~ ~ above notwithstanding we have recently obtained some indications that an increased ionic strength decreases the range of the hydrophobic interaction measured between surfactant monolayer surfaces. This point, which is complicated by the fact that we also observe an increased charge density with increasing electrolyte concentration, will be addressed in a forthcoming publication. No hydrophobic attraction acts between surfaces composed of mixtures of hydrophobic and hydrophilic groups. Examples include surfaces of ethylene oxide groups3' and surfaces with adsorbed tetraalkylammonium ions.3z This indicates that a longrange hydrophobic attraction exists only between homogeneous hydrophobic areas larger than some critical size. For surfaces with 0, > 90° the range and magnitude of the attraction are rather insensitive to the exact value of the contact angle, provided the surfaces have been prepared under identical conditions. This suggests strongly that the hydrophobic interaction is related to the metastability of water films between hydrophobic surfaces."-13,33 The system is close to a liquid-vapor phase transition,
1655
and small density fluctuations might well lead to an attraction of sufficient magnitude to explain the results. If this interpretation is correct, the important parameter is the difference between the surface energy of the solid against the vapor and against the liquid. For an isolated, macroscopic surface this difference is related to the contact angle but the proximity of the two hydrophobic surfaces may cause a change in the relative magnitudes of the surface energies. In other words, the difference between stability and metastability in such thin films is not necessarily directly related to a macroscopic contact angle of 90'. An alternative and often invoked explanation is that the hydrophobic attraction is due to water structure. This appears less and less likely as the range and decay of the attraction is increased by more accurate measurements. We are observing an attraction at a separation in excess of 300 molecular diameters! Given the present state of theories, it seems as if the best recourse is to push on with experiments. Which we will do. Acknowledgment. We acknowledge helpful advice from R. G. Horn. We are indebted to B. W. Ninham for many valuable discussions and to V. A. Parsegian for stimulating correspondence. We are grateful to our other colleagues in the Department of Applied Mathematics for their interest and support of this work. P.M.C. acknowledges a travel grant from the Swedish Board for Technical Development (STU). Registry No. DDOA, 3700-67-2; N-(a-trimethylammonioacety1)O,O'-bis(lH,lH,2H,2H-perfluorodecyl)-~-glutamatechloride, 88185-
(30) Marra, J.; Israelachvili, J. Biochemistry 1985, 24, 4068. (31) Claesson, P. M.; Kjellander, R.; Stenius, P.; Christenson, H. K. J . Chem. Soc., Faraday Trans. I 1986, 82, 2735. (32) Claesson, P. M.; Horn, R. G.; Pashley, R. M. J. Colloid InferfaceSci. 1984, 100, 250.
38-0. (33) Yushchenko, V. S.;Yaminsky, V. V.; Shchukin, E. D. J . Colloid Interface Sei. 1983, 96, 307.
Binding Energies for AI Atom Association Complexes with Simple Alkenes and Arenest S. A. Mitchell,* B. Simard, D. M. Rayner, and P. A. Hackett* Laser Chemistry Group, Division of Chemistry, National Research Council of Canada, 100 Sussex Drive, Ottawa, Canada, K I A OR6 (Received: July 13, 1987)
A1 atom association reactions with simple alkenes and arenes in the gas phase are investigated by time-resolved resonance fluorescence excitation of ground-state A1 atoms following pulsed visible laser photolysis of trimethylaluminum in a gas cell. Ar buffer gas pressure effects on the reaction rates are observed and interpreted in terms of collision-complex lifetimes in termolecular reactions. The limiting high Ar pressure bimolecular rate constants are near the gas kinetic values, implying negligible activation energies and large Arrhenius preexponential factors for these reactions. For reactions involving truns-2-butene, tetramethylethylene, benzene, toluene, and o-xylene, an equilibration is observed between free AI atoms and A1 atoms bound in complexes with the reactant molecules. Equilibrium constants for the association reactions are obtained from an analysis of kinetic data at different pressures of reactant. Binding energies are derived from observations of the temperature dependence of the equilibrium constant in the range 283-333 K, or by estimating the standard entropy change for the association reaction. Evidence is presented which indicates that monoligand complexes are formed in all cases. A1 atom binding energies (kcalmol-I) are reported for C2H2(>13), CzH4(>16), 1-butene (>15), trans-2-butene (14.2 f l), tetramethylethylene (13.5 f l), 1,4-cyclohexadiene (>14), benzene (11.7 A l), toluene (14.1 & l), and o-xylene (14.3 A 1). Kinetic and thermochemical results are discussed in terms of alternate bonding schemes for AI-alkene and Al-arene complexes.
Introduction Doublet spin multiplicity, monoethylene complexes of Al(3s23p1) atoms have recently been prepared in low-temperature rare gas' and hydrocarbon2 matrix supports and studied by ESR spectroscopy. According to the analysis of Kasai,' the unpaired electron resides mainly in a p-orbital of A1 but is delocalized onto the CzH4 molecule because of a bonding interaction between the A1 p-orbital and the **-antibonding molecular orbital of CzH4. +Issued as NRCC No. 28176.
0022-3654/88/2092-1655$01.50/0
It was suggested that this bonding interaction accounts for the stability of the Al[C2H,] adduct, which was characterized as a a-complex with the A1 atom bound symmetrically below the C2H4 molecular plane. Alternative bonding schemes, involving formation of a charge-transfer complex, Al+[C2H4]-, a AI-C a-bonded radical, AI-CH2-CHz, or an aluminocyclopropane (1) Kasai, P. H. J. Am. Chem. SOC.1982, 104, 1165. (2) Howard, J. A.; Mile, B.; Tse, J. S.;Morris, H. J . Chem. Soc., Da[fon Trans. 1987, 83, 3701.
Published 1988 by the American Chemical Society
1656 The Journal of Physical Chemistry, Vol. 92, No. 6, 1988 Aq I H 2 'CH2
were ruled out as being iqcompatible witb the ESR spectral data. An AI @tomcomplex with benzene has also been observed in matrix-ipolatioa ESR studies, and a similar r-bonding scheme has been invoked to explain its ~ t a b i l i t y . ~An unusual feature of the Al[C6H6Jqmplex is the interaction of the A1 atom with ss (:bond, rather than with the full +system apparently just ~ n c Another example of r-type bonding inof tbc g r o q t i c volving A1 and an qnsaturatd ligand is found in A1(C0)2, which has been charactwized by matrix-i~olation-ESR~~~ and -1Rvibrationaf3' spectrercopic studies as a planar n-radical with a ZBl electronic groupd state in C2"symmetry. Curiously, in this case there is no evidence far formation of a stable monoligand complex AlCO? Reactions of A1 atoms with unsaturated organic molecules are rot limited to addwt formation processes involving n-interactions. This is &pwn by observations of the AI-C o-bonded radicals A I - C H A H and
.d""'T C'
Hp-
CH
formed by reaetion of A1 atoms with ClH21 and CH2=CH-CH==CH219 respectively, under matpx-isolation conditions (cocondensation mctions). Very recently, Howard et al.1° reported the observation of a spectrum that was attributed to aluminocyclopentane Al/cH2-pn, c' Hp-CH2
formed by qondensation reaction of A1 with two molecules of C2H4 This latter speck resembles in some respects products that were suqopeted by Skell and Wolf" (on the basis of deuterolysis studies) to be formed by cocondensation reaction of A1 a t o m with propew. The above studies demonstrate that both u- and n-bonded species are formed in reactions of A1 atoms with unsaturated hydrocarbons. A1-C u-bonds are well-known in orgaooaluminum chemistry,I2 but the r-type interactions are novel and hence interesting from a fundamental point of view. Ab initio molecular orbital calculations for the AI-C o-bonded species A1-CH3l3 and A l - - C H d v 1 4 provide descriptions of the bonding which correlate well with available experimental information, but the situation is less ytisfactory for the case of s-bonding. For Al[C2H,] there are contradictory indications from theory and experiment, the experimental results pointing to a r-complex,' as noted above, and the theoretical work predicting no significant chemical binding for a +complex configuration.'sq16 Recent results of Howard et al.2 indicate that the Al[C2H4] adduct (3) Kasai, P. H.; McLeod, D., Jr. J . Am. Chem. Six.1979, 101, 5860. (4) Kasai, P. H.; Jones, P. M. J. Am. Chem. SOC.1984, 106, 8018. (5) Cheniq, J. H. 8.; Hampson, C. A.; Howard, J. A.; Mile, B.; Sutcliffe, R. J . P h w . Chem. 1986, 90, 1524. (6) Hinchcliffe, A. J.; Ogden, J. S.; Oswald, D. D. J . Chem. Soc., Chem. Commun. 1972, 338. (7) C h d e r , J. €4. B.; Hampson, C. A,; Howard, J. A.; Mile, B. J . Chem. Soc., Chem. Commun. 1986, 730. (8) Balaji, V.; Sunil, K. K.; Jordan, K. D. Chem. Phys. Lett. 1987, 136, 309 . .
(9) Chenier, J. H. B.; Howard, J. A,; Tse, J. S.; Mile, B. J . A m . Chem. SOC.1985, 107,7290. (10) Chenitr, J. H. B.; Howard, J. A.; Mile, B. J . Am. Chem. SOC.1987, 109, 4109. (11) Skell, P. S.; Wolf, L. R. J . A m . Chem. SOC.1972, 94, 7919. ( 12) Eisch, J. J. In Comprehensive Org~nomtallicChemistry; Pugamon: Oxford, U.K., 1982; Vol. 1. (13) Fox, D. J.; Ray, D.; Rubesin, P. C.; Schaefer, H. F.,I11 J . Chem. Phys. 1980, 73, 3246. (14) Scbeiner, A.; Schaefer, H. F., 111J. Am. Chem. Soc. 1983,107,4451. (15) Trenary, M.; Schaefer, H. F., 111 J. Chem. Phys. 1978, 68, 4047. (16) Trenary, M.; Casida, M. E.: Brooks, B. R.: Schaefer. H. F.. 111J. Am. Chem. SOC.1979, 101, 1638
Mitchell et al. previously characterized as a n-complex1 is stable up to 297 K in an adamantane matrix. In view of the diverse nature of the observed and proposed interactions of Al atoms with unsaturated organic molecules and the lack of agreement between certain experimental and theoretical results, there is a need for basic structural and thermochemical characterization of reaction products. In this paper we report measurements of binding energies for complexes of A1 atoms with simple alkenes and arenes in the gas phase. We find binding energies in the range 11->16 kcal.mol-', indicating significant chemical interaction for these paramagnetic molecular complexes. Our experiments involve direct, time-resolved observations of equilibration in gas-phase complexation reactions, with the initial condition produced by introduction of free A1 atoms into a large excess of complexing ligand Q A1
+Q
A1Q 4 A1 atoms are produced by pulsed visible laser photolysis of trimethylaluminum (TMAl)" and monitored by resonance fluoreswnce excitation at 394.4 nm. For the equilibration process I, the time dependence of the A1 atom concentration is given by an expression of the formI8 [All = Ae-Bf C
+
where CIA = k q / k ~ [ Q ]= KJQ1-l. Here kQ and k, are effective bimolecular and unimolecular rate constants, respectively, and K , is the equilibrium constant for the reverse of reaction I (dissociation equilibrium constant) in concentration units
Provided that Q is present in large excess, the dissociation equilibrium constant may be obtained from kinetic data at different pressures of Q by plotting CIA versus [ Q ] - ] . Binding energies for the A1Q complexes may be obtained from the equilibrium constants either directly by observing the temperature dependence of K, (second-law method by using the van't Hoff relation) or through estimates for the standard entropy change ASPTfor reaction I at the temperature T of the experiment (third-law method). Here we report results obtained using both methods, with good agreement between the two approaches. This provides a verification that our analysis of the equilibration data in terms of the formation of monoligand complexes is correct. We also report data for the rate constants kQ and k, which control the rate of the equilibration process I.
Experimental Section Details of the experimental arrangement have been given previously,'* so only a brief description is included here. A1 atoms are produced by visible multiphoton dissociation of trimethylaluminum (TMAl), using the focused output of an excimer laser pumped dye laser." The pulse energy at 441 nm is 2-3 mJ, and the focal length of the focusing lens is 25 cm. Detection of ground-state A1(3s23p' 2Pl,2) atoms is by saturated resonance fluorescence excitation at 394.4 nm, using a second, independently triggered excimer/dye laser system with the photolysis and detection laser beams in a collinear and counterpropagating arrangement. The fluorescence signal is saturated to ensure a linear response with A1 atom density. The temporal behavior of the A1 atom concentration is observed by scanning the delay time between the photolysis and detection laser pulses, which are produced at a repetition rate of 20 Hz. Typically, the signals from 20 to 40 pulses are averaged at each delay setting. A computer scans the interpulse delay in preset increments and stores the kinetic data for later analysis. The reaction cell is a double-walled, 30-cm-long Pyrex tube fitted with angled end windows for passing the laser beams, a side (17) Mitchell, S. A.; Hackett, P. A. J . Chem. Phys. 1983, 79, 4815. (18) Mitchell, S.A.; Hackett, P. A.; Rayner, D. M.; Cantin, M. J . Phys. Chem. 1986.90, 6148.
Binding Energies: Al-Alkene and -Arene Complexes
The Journal of Physical Chemistry, Vol. 92, No. 6, 1988 1657
t A
1
400
800
1200
1600
2000
I .o
2.0
3.0
Po I Torr
Figure 2. Plots showing a linear dependence of the pseudo-first-orderrate constant B for removal of A1 atoms on the pressure of reactant for C6H6 and C2H4. The pressure scale is compressed by a factor of 2 for the C2H4 case only. The pressure of Ar was 100 Torr for the C2H4 case and 400 Torr for the C6H6 case.
B
tt
r
0,5
180
360
540
720
900
C
I .o
"
L.'...:, .... . 0
2 .o
3.0
Figure 3. Plots showing an inverse linear dependence of the ratio C I A on the pressure of reactant for C6H6 and C2(CH3)4.The pressure of Ar was 400 Torr in both cases. 400
800
1200
1600
2000
TIME DELAY I n s
FEgure 1. Kinetic traces for removal of ground-state AI atoms by reaction with benzene (A,B) and ethylene (C) at 296 K. Gas mixtures: (A) 20 mTorr of trimethylaluminum (TMAI), 0.5 Torr of C&, 400 Torr of Ar; (B) 20 mTorr of TMAI, 2 Torr of C6H6, 400 Torr of Ar; (C) 40 mTorr of TMA1, 5 Torr of C2H4, 100 Torr of Ar. 1 Torr = 133 Pa.
window for viewing fluorescence, and gas inlet and outlet ports for connection to an all-metal, high-vacuum line on the inlet side and a 4in. diffusion pump on the outlet side. Metal bellows valves are used to isolate the cell after preparation of the gas mixture. The temperature of the gas inside the cell is controlled by circulating a water/ethylene glycol mixture between the inner and outer glass walls of the cell, using a Polyscience Model 90 temperature controller. The gas temperature is monitored with a chromel-alumel thermocouple probe positioned near the fluorescence viewing zone. Pressure measurement is by Baratron capacitance manometers. Electronic grade trimethylaluminum was obtained from Alfa Products. Research purity argon and carbon monoxide, purified acetylene, chemical purity ethylene, and technical trans-2-butene were from Matheson of Canada. Research purity 1-butene was from the Phillips Petroleum Co. The highest purity grades of tetramethylethylene, 1,4-~yclohexadiene,benzene, toluene, and o-xylene were supplied by Aldrich. Liquid nitrogen condensable materials were extensively degassed and/or vacuum distilled before use.
Results Kinetic traces illustrating typical time-concentration profiles for removal of ground-state AI(3p' 2Plj2)atoms by reaction with
benzene and ethylene under pseudo-first-order conditions are shown in Figure 1. In this figure the laser-induced fluorescence (LIF) signal is proportional to the concentration of ground-state A1 atoms, and the time delay refers to the delay between the photolysis and detection laser pulses-the photolysis pulse producing A1 atoms by multiphoton dissociation of TMAl and the detection pulse exciting fluorescence from the atoms by resonance excitation. 3p' 2P1/2 4s' The solid lines drawn through the data points represent nonC linear least-squares fitted curves of the form A exp(-Bt) (exponential-plus-background, as in Figure 1, parts A and B), or A exp(-Bt) (simple exponential, as in Figure 1, part C). All of the reactions studied gave kinetic traces that were well described by one or the other of these forms. Those involving carbon monoxide, acetylene, ethylene, 1-butene, and 1,Ccyclohexadiene showed a simple exponential decay under all conditions investigated, whereas those involving trans-2-butene, tetramethylethylene (TME), benzene, toluene, and o-xylene showed decay traces of the form exponential-plus-background (see Figure 1, parts A and B). The significant features of the kinetic traces are contained in the value of 8, which measures the rate of the exponential decay, and in the ratio CIA, which measures the magnitude of the background signal relative to the difference between the initial and background signals. C I A is equal to zero in the case of a simple exponential decay. For all systems studied, the parameter B showed a linear dependence, and the ratio CIA (in cases where CIA # 0) an inuerse linear dependence, on the pressure of added reactant. Representative results are shown in Figures 1, 2, and 3. Also for all systems studied, B showed a linear dependence on the pressure of Ar buffer gas at low Ar pressure, and a leveling
-
+
Mitchell et al.
1658 The Journal of Physical Chemistry, Vol. 92, No. 6, 1988 TABLE I: Rate Constants for AI
+ Q Association Reactions at 296
T=323K
/
K
0
co C,H, C,H,
,
kO(*)(Pnr/ Torr) kA,(*) = (4.8 f 0.6) X (7.0 f 0.2) X lo-' (100) (1.05 f 0.08) X lo-' (100) 1.5 f 0.2 (100)
kWpL(*) (PA,/Torr)b r/psc >2.4 (>600) >0.3 (>300) ~ 3 . (-600) 2
0.3 310 37 970
0.8 0.6 \
0
L
1.2 f 0.2 (400)
>2.1 (>600)
180
0.4
=P
3.6 (>400)
1900
cm3 molecule-' s-' at the Bimolecular rate constant in units of indicated pressure of Ar (see eq 9). Uncertainties represent 2 standard deviations in least-squares slopes for plots of the type shown in Figure 2. bLimiting high Ar pressure bimolecular rate constant in units of cm3 molecule-' s-' for the indicated Ar pressure range (see eq 10). (Lifetime of AIQ* collision complex in reaction V, T = 1 / k l (see the text). dBimolecular rate constant in units of cm3 molecule-' s-I for 50 Torr of added C O (see the text).
off or saturation of the dependence at higher Ar pressures, the saturation pressure range characteristic of the particular reactant. The ratio C I A was in all cases independent of the Ar pressure. The parameter B is a pseudo-first-order rate constant for removal of A1 atoms. The bimolecular rate constant for reaction of A1 with the added gas Q is obtained as the slope of a plot of B against pressure of Q, as in Figure 2. Bimolecular rate constants obtained in this way are given in Table I under the heading kQ(2). These values apply for the pressures of Ar indicated in Table I. For the case of the reaction of A1 with CO, the bimolecular rate constant kA,(2)was obtained as the slope of a plot of B against pressure of Ar, for a constant partial pressure of 50 Torr of added CO. The reason for this is explained later. As noted above, the pseudo-first-order rate constant B is an increasing function of Ar pressure at constant partial pressure of Q, approaching a saturated value at high Ar pressure. From observations of the onset of this saturation effect, lower limits for the limiting high-pressure values of kQ(2)were obtained. These are given in Table I as kHpL(2), together with the Ar pressures at which the limiting values were observed. According to the analysis described below, the slope of a plot of the ratio C I A versus the reciprocal of the reactant pressure is related to the equilibrium constant for the reversible A1 Q A1Q association reaction. The effect of temperature on these plots was investigated for benzene and tetramethylethylene. Results for benzene are shown in Figure 4.
+
Kinetic Analysis The form of the A1 atom removal kinetics shown in Figure 1, parts A and B, is suggestive of an equilibration process as in reaction I, where some fraction of the free A1 atoms introduced into the system become bound in complexes with the reactant gas Q (present in great excess), and the remainder stay as free atoms. If the only removal process for AI is formation of a complex A1Q and initially all of the A1 is in the form of free atoms with concentration [AI],, then the mass balance relationship [AI] + [AlQ] = [AI], leads to the following expression for the time dependence of the A1 atom concentration
Note that diffusion of AI atoms out of the detection zone may
2.0
Pi'/ Torr-' Figure 4. Temperature dependence of plots of the type shown in Figure 3 for the case of benzene. The pressure of Ar was 400 Torr.
be disregarded because the diffusion rate is expected to be negligible relative to the observed reaction equilibration rate (half-life < 1 ~ ssee , Figure 1) under the relatively high Ar buffer gas pressure conditions ( e 4 0 0 Torr) of our experiments. Equation 3 is of the form observed experimentally [All = Ae-B'
+C
+
where B = k+ kQ[Q] and CIA = k,/kQ[Q]. The equilibrium constant for the reverse of reaction I, Kc, is defined in eq 2. From this it is seen that
C / A = Kc/ [QI = K p / p ~
(4)
where K p is the dissociation equilibrium constant in pressure units and Pa is the pressure of Q (assumed constant throughout the equilibration process). Kp =
[ 21
Eq
From this simple model we expect the parameter B to show a linear dependence on PQ, with slope kQ, and the ratio C I A an inverse linear dependence on PQ,with slope Kp. The experimental results shown in Figures 1-3 are consistent with these expectations. In the case of a simple exponential decay, as in Figure lC, the CIA ratio is vanishingly small, which implies a small value for Kp. Equation 4 may be viewed as a special case of a more general relationship which applies for a mechanism involving formation of both A1Q and AIQz complexes by coupled equilibration processes A1 Q * A1Q AIQ + Q * AlQ2
+
In this situation, the mass balance relationship [All + [AlQ] + [AlQ,] = [AI], and the definitions of the equilibrium constants
lead to the following expression for the ratio C I A
_C --
KciKcz
(5)
A Kcz[QI + [QI2 Note that A and C are defined as A = [All, - [AllEqand C = [Allq, since [All = A exp(-Bt) C. In the limit where [AIQ],, [A1Q2IEq,it is seen that C / A Kci/[QI which is the same as eq 4. In the intermediate situation, with [AlQ]& [A1Q2IEq,a mixed inverse linear and inverse square
The Journal of Physical Chemistry, Vol. 92, No. 6, 1988 1659
Binding Energies: Al-Alkene and -Arene Complexes
TABLE II: Equilibrium Constants, Partition Functions, and Binding Energies for AlQ Complexes'
B,b 0.0042 0.06 0.32 0.34
B" 0.65 0.13 0.18 0.18
K p / 1Od atm 13 kcal mol-'), this would imply an Al-C u-bond energy >84 kcal mol-'. This value seems high in comparison with the A1-C u-bond energies noted above, but this could be accounted for by the difference in the, hybridization state of carbon bonded to 41: sp3 for A1-CHz-CHz or A1(C2H& and sp2 for AI-CH=CH. It is worth noting that metal-phenyl bonds are generally stronger than metal-alkyl bonds, the former involving sp2 carbon and the latter sp3 carbon. A theoretical prediction of ( N 15 kcal mol-')I4 the A1 atom binding energy in AI-CH=CH is consistent with our experimental result (>13 kcal mol-'). Considering now the Al[CzH4] a-complex, the bonding interaction is envisaged to occur between the singly occupied porbital of A1 and the vacant ?r* antibonding molecular orbital of CzH4 The A1 atom is placed symmetrically below a nearly planar C2H4 molecule with the bonding A1 p-orbital oriented parallel to the C-C bond axis. This bonding scheme was suggested by Kasai' on the basis of ESR studies that directly probed the orbital character of the unpaired spin distribution. Following this scheme it may be expected that the strength of the Al-alkene interaction, and thus the binding energy, is related to the separation in energy between the Al p-orbital and the alkene a * orbitalsmaller energy separations leading to larger binding energies. In Figure 6 are shown approximate orbital energies for the A1 3s and 3p atomic orbitals and the ?r and a * molecular orbitals for various alkenes, as derived from ionization potentials:' optical spectra,31and atomic structure calculations.32 It is seen that the energy gap between the A1 3p atomic orbital and the a * alkene molecular orbital increases in the sequence C2H4, 1-butene, trans-2-butene, tetramethylethylene. As Table I1 shows, this is the order in which the binding energies decrease, in agreement with the expectation noted above. Thus the trend in binding energies is understandable in terms of the a-complex bonding scheme. It niay be noted that this scheme bears some resemblance to the Dewar-Chatt-Duncanson model for bonding in transition-metal-alkene complexes.33 A correlation similar to the one noted above has been demonstrated by T01man~~ for a series of nickel-alkene complexes. The binding energy for Al[CzH4] (>16 kcal mol-') may be compared with that for Ga[CzH4] (9 kcal mol-')I8 and with measured or estimated transition-metal-C2H4 bond strengths in Rh(C5HS)(CzH4),( 16 kcal-mol-'. Registry No. AI, 7429-90-5; CO, 630-08-0; C2Hz, 74-86-2; C&b, 74-85-1;1-butene,106-98-9;2-butene, 107-01-7; 2,3-dimethyl-2-butene, 563-79-1; 1,3-cyclohexadiene,592-57-4; benzene, 71-43-2; toluene, 10888-3; o-xylene, 95-47-6.
Rdantion in Supercrltlcal FluM Chromatography:
Influence of the Partial Molar Volume
of tho sdlute in the Stationary Phase Clement R. Yonker* and Richard D. Smith Chemical Methods and Separations Group, Chemical Sciences Department, Pacific Northwest Laboratory (Operated by Battelle Memorial Institute), Richland, Washington 99352 (Received: June 9, 1987)
Theoretical models for retention in supercritical fluid chromatography have described solute retention based on statistical thermodynamics or classical thermodynamic models of mobile-phase interactions with the solute. The shortcomings of these models largely reside in the assumption of pressure-independentsolutestationary phase interactions with supercritical fluids. The pressure dependence of the partial molar volume of the solute in the stationary phase and the role of the partial molar volume of the solute in the stationary phase on retention in supercritical fluid chromatography are discussed based upon experimental studies with C 0 2 over a wide range of fluid pressures.
IMradUction
Ecktrt, C . A.; Ziger, D. H.; Johnston, K. P.; Kim, S. J . Phys. Chem. 1986,90,2738. (2) Ziger, D.H. Ph.D. Thesis, University of Illinois, Urbana, 1983.
description of solute retention far applicable systems can be obtained. The mathematical complexity of the Lee-Kesler EOS constitutes the major drawback of this approach8~~Martire and Martire and Boehmlos'l have developed an alternative unified theory of chromatographic retention based on a statistical thermodynamic treatment using established lattice-gas models to describe the solute partition coefficient. Previous theoretical work by Martire et al.l2-I4for liquid chromatography has been expanded and applied to retention in supercritical fluid chromatography. Solute retention in Martire's work is related to molecular parameters that control retention. Yonker et aI.l5 have used a simple thermodynamic model of solute retention in SFC as a function of pressure to describe the chromatographic retention process, using the bulk macroscopic properties of partial molar volume of the solute in the mobile and stationary phases. The partial molar volume of the solute in the mobile phase at infinite dilution was calculated by using the Peng-Robinson EOS, which is a simple two-parameter, cubic EOS. Correlation with actual solute retention is similar to that seen for the more complex statistical thermodynamic model of Martirelo-" and has the advantage of ease of calculation as compared to Schoenmakers methodology. All the models discussed above determine the stationary-phase contribution to retention through an initial reference retention value to which all other calculated retention values are related. One reason for this approach is the difficulty in determining the interactions between the solute and the stationary phase, as well as uncertainties in the actual stationary-phase volume. These models all assume that the effect of pressure upon the interaction of the solute with the stationary phase is negligible. This as-
(3) Kim, S.; Johnston, K. P. AIChE J . 1987, 33, 1603. (4) Yonker, C . R.; Wright, B. W.; Petersen, R. C.; Smith, R. D. J . Phys. Chem. 1985,89, 5526. ( 5 ) Chester, T. L.; Innis, D. P. J. High Resolut. Chromatogr. Chromatogr. Coinmun. 1985, 8, 561. (6) Van Wasen, J.; Schneider, G. M. Chromatographia 1975, 8, 214. (7) Van Wasen, J.; Swaid, I.; Schneider, G. M. Angew. Chem., Int. E d . Engl. 1980, 19, 575. (8) Schoenmakers, P. J. J . Chromatogr. 1984, 315, 1.
(9) Lee, B. I.; Kesler, M. G. AIChE J . 1975, 21, 510. (10) Martire, D. E. J . Liq. Chromatogr. 1987, 10, 1569. (11) Martire, D. E.; Bochm, R. D. J . Phys. Chem. 1987, 91, 2433. (12) Martire, D. E.; Boehm, R. E. J . Phys. Chem. 1983, 87, 1045. (1 3) Jaroniec, M.; Martire, D. E. J . Chromatogr. 1986, 351, 1. (14) Martire, D. E.; Locke, D. C . Anal. Chem. 1971, 43, 68. (15) Yonker, C . R.; Gale, R. W.; Smith, R. D. J . Phys. Chem. 1987, 91, 3333.
The evcpanding applications of supercritical fluids in extraction, chromatography, and chemical reaction processes are primarily due to the ability to control solvent strength and other physicochemical properties as a function of density. The capability to alter the intermolecular interactions in the mobile phase for supetcritical fluid chromatography (SFC) is reflected in the partial molar voluihe of a solute as a function of density at infinite dilution.'S2 This solvation of the solute by a fluid can influence local fluid density and extend over multiple solvent shell^.^ The elucidation of the detailed retention mechanism in S F C is a complex problem. Yonker et aL4 have developed a simple thermodynamic model for solute retention as a function of temperature at constant pressure. Chester and InnisS developed an ehpirical thermodynamic model relating retention with temperature for SFC. Van Wasen et al.637have developed a simple thermodynamic model describing solute retention in S F C as a function of pressure. Schoenmakerss also derived a simple thermodynamic equation describing solute retention as a function of density and ressure based upon the Lee-Kesler equation of statb (EOS). hese workers calculated the fugacity coefficient of the solute at infinite dilution in the supercritical fluid mobile phase, which was used to determine solute retention. Although this method cannot yield retention for a solute a priori, once a reference retention value for a system is measured, a quantitative
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0022-3654/88/2092-1664$01.50/0
0 1988 American Chemical Society
