J. Phys. Chem. 1961, 85,1814-1820
1814
Several r e ~ e a r c h e r have, s ~ ~ ~in~ fact, ~ reported that calculated equilibrium pressures are lower than experimentally obtained values. This error could, in part, be due to the approximate nature of the Kihara size and energy parameters used. Such approximate Kihara parameters would be expected to produce random deviations between experimental and predicted dissociation pressures. The fact that calculated pressures are, in general, lower than the corresponding experimental values regardless of the gas species forming the hydrate implies that the error in dissociation pressures is due to cavity characterization rather than gas characterization; the error might be caused by ~~
~
(8) Mazo, R. M. Mol. Phys. 1964,8,515. (9)Davidson, D. W. In “Water-A Comprehensive Treatise”; Franks, F., Ed.;Plenum Press: New York, 1973,Vol. 2.
inappropriate radii for the spherical cells. Values of cell radii suggested here lead to smaller Langmuir constants and will to some degree compensate for the error. The effective cell radii and coordination numbers proposed herein are those which are needed to obtain a spherically smoothed cell potential which is equivalent to the discretely summed potential; these radii and coordination numbers, in effect, define the equivalent smoothed cell cavity. This cell characterization is independent of the size and energy parameters of the molecule occupying the cavity and is applicable to guest molecules whose interactions with the cell are through dispersion-type forces. Acknowledgment. This material is based upon work supported by the National Science Foundation under Grant No. ENG79-21022.
Ion-Solvent Molecule Interactions in the Gas Phase. The Potassium Ion and Benzene Jan Sunner, Kazushige Nishizawa, and Paul Kebarle’ Chemistty Department, University of Alberta, Edmonton, Canada T6G 2G2 (Received December 12, 1980)
The gas-phase equilibria ( n - l , n ) , K+B,-’ + B = K+B,, where B is benzene were measured for n = 1 to n = 4. The temperature dependence of the equilibrium constants K,,-’,, provides, through van’t Hoff plots, values for AHon-l,n, L L S O , , - ~ ~ ,and AGon-lfi, These data are compared with corresponding data for the reactions K+W,l + W = K+W,, where W is HzO. Exchange equilibria K+W,B, + B = KWx-lBy+lwere also measured. These provide data for the reactions K+W, + nB K+B, which can be checked against the K+ + nB K+B, results and earlier K+ + nW K+W, data. Generally good to fair agreement is observed. It is found that -AHon-l,n for B are somewhat larger than -AHon-l,n for W for n = 1-4. The larger binding energy for B is surprising considering that benzene has no permanent dipole. The free energy changes at 298 K, -AGon-l,n, for B are larger than those for W for small n,i.e., = 1 and 2 then a reversal occurs. This is due to the entropy changes ASon-l,n for B which become rapidly more unfavorable as n is increased to n = 4. A theoretical analysis based on ab initio calculations and improved classical electrostatic calculations shows that the most stable structure in K+B is obtained by placing K+ on the symmetry axis of B. This axial structure makes full use of the quadrupole moment of benzene. The ion-quadrupole and ion-induced dipole attractions make about equal contributions to the bonding. However, a substantial contribution is also made by dispersion forces. In K’W the far dominant contribution to bonding is the ion-permanent dipole attraction. Little bonding can be expected for the last molecule in K+BSsince that molecule must go to a far removed position and the bonding to B is short range. This is not so for K+W5and higher n. The bonding in K+B is compared with that of the isoelectronic C1-B on basis of experimental and theoretical information. The bonding to the negative ion is much weaker.
-
-
Introduction A continuing effort from this laboratory’,* has been to try t o show that some of the major features of ionic solvation in condensed media can be explained on basis of the interactions of the ion with a small number of solvent molecules. The pertinent experimental data are obtained from measurement of gas-phase ion, ion*, solvent moleand cules, S1, equilibria ( n - 1, n ) , eq 1. The ion*(S1),-l
+ S1 = ion*(Sl),
(1)
AHon-l,nobtained by this method represent the often de(1)Dzidic, I.; Kebarle, P. J . Phys. Chem. 1970,74, 1466. Kebarle, P. In “Ions and Ion Pairs in Organic Reactions”; Szwarc, M., Ed.; WileyInterscience: New York, 1972. Kebarle, P. In “Modern Aspects of Electrochemistry”; Vol. 9,Conway, B. E.; Bockris, J. OM., Ed.; Plenum Press: New York, 1974. Kebarle, P. Annu. Reu. Phys. Chem. 1977,28, 445. (2) Kebarle, P.; Davidson, W. R.; French, M. A.; Cumming, J. B.; McMahon, T. B. Faraday Discuss. Chem. SOC.1977,No. 64,220. 0022-3654/81/2085-1814$01.25/0
-
cisive energetics of the initial, intimate ion-solvent molecule interactions. Earlier studies of the alkali and halide ions with hydrogen-bonding molecules like HzO, or dipolar solvent molecules like acetonitrile and dimethyl sulfoxide, have formed an integral part of this work. The present study involves, for the first time, a nonpolar solvent molecule, namely, benzene. The scope and significance of our earlier work on the alkali and halide ions and water were significantly extended by theoretical ~ t u d i e s . ~In particular, Clementi4 showed that extended Hartree-Fock calculations predict bonding energies in good agreement with the experimental results from gas-phase ion equilibria. Pair potential functions based on the H F calculation were (3)Diercksen, G.H.F.; Kraemer, W. P. Theor. Chim. Acta (Berlin) 1972,23,387,393.Kollman, P. A.; Allen, L. C. J . Am. Chem. SOC. 1970, 92,6101.Pullman, A.; Armbuster, A. M. Chem. Phys. Lett. 1975,36,558. Kistenmacher, H.;Popkie, H.; Clementi, E. J . Chem. Phys. 1974,61,699. (4)Clementi, E. “Determination of Liquid Water Structure, Coordination Numbers for Ions and Solvation for Biological Molecules”, Lecture Notes in Chemistry; Springer Verlag: Berlin, 1976;Vol. 2.
0 1981 American Chemical Society
Ion-Solvent Molecule Interactions in the Gas Phase
The Journal of Physlcal Chemlstry, Vol. 85, No. 73, 7987 130
-
8 Figure 1. Ion source and reaction chamber: (1) filament painted with potassium salt producing potassium ions by thermionic emission; (2 and 3) drift electrodes and thermal shields; (4) field-free reaction chamber in which equilibria occur. Some of the ions and gas escape through the molecular flow slit at the bottom of 4 and are mass analyzed with sector fieid magnetic mass spectrometer. There are three channels (5). Gas flows in and out of the ion source through two of the channels and the third channel leads to a capacitance manometer. Ion source is heated by eight cartridge heaters placed in boxes (6). Cooling is obtained by passing liquid or gas through channels (7). The reaction chamber temperature is measured with a thermocouple (8).
then used to calculate the energies of large assemblies of water molecules and a given ion. These in turn led to thermodynamic data4v5via the statistical method by Metropolis. The experimental measurements of the ion-dipolar aprotic solvent equilibria showed that positive ions have much stronger binding energies to the solvent molecules than have negative ions of the same radiw6r7 It was also demonstrated that solvation by dipolar aprotic solvents like acetonitrile and dimethyl sulfoxide is relatively unsensitive to changes of radius or charge delocalization in the negative ion.6,’ Both these findings were a confirmation of long-held beliefs by workers in condensed media.s Hardly any theoretical calculations of ion-molecule clusters have been made for dipolar aprotic solvents. We hope that the availability of experimental data for these systems will stimulate theoretical work. Alkali cations are often the counterions in important synthetic and polymerization reactions involving carbanions as reaction intermediates. Frequently, such reactions are undertaken in weakly polar media. Little quantitative experimental information on ionic solvation in nonpolar or weakly polar media is available because of extensive ion pairing in such solvents. Also very few theoretical calculations of binding energies between alkali cations and weakly polar molecules seem to exist. One may expect a special theoretical difficulty when nonpolar systems are involved. In the absence of strong dipole forces, dispersion forces will be relatively important, yet a good account of dispersion forces is not given by calculations which do not consider electron correlation. For these reasons we believe that gas-phase measurements involving the alkali ions and benzene are of interest. ( 5 ) Abraham, F. F.;Mruzik, M. R. Faraday Discuss.Chem. SOC.1976, 61, 34. (6) Yamdagni, R.; Kebarle, P. J. Am. Chem. SOC.1972, 94, 2540. Davidson, W. R.; Kebarle, P. Zbid. 1976,98, 6125. (7) Magnera, T. F.; Sunner, J.; Kebarle, P. J. Am. Chem. Soc., sub-
mitted for publication. (8)Parker, A. J. Q.Reu. Chem. SOC.1962, 16, 163.
O ’ I 306
L L #01 # 0 8 ,
I ,
- 1 L------
1815
1
02
IO
03
torr
12
14
+
Flgure 2. Equilibrium constants for reaction K+ B = KB+ where B = benzene. (A)Results from pulsed experiments, pressure given is that of neat benzene used in these experiments. Numbers beside curves give temperature in OC. (a)Results from measurements with major gas methane containing 3.6% benzene. Pressure shown is total pressure.
Experimental Section The measurements were made with the ion source reaction chamber shown in Figure 1. The potassium ions are obtained by thermionic emission from the filament 1 which is made of platinum gauze painted with potassium salt. The ions drift through the electrodes 2 and 3 into the reaction chamber 4. The total potential from 1 to 4 is usually 300 V. Lowering this voltage to much lower values decreased the sensitivity of ion detection but had no effect on the measured equilibrium constants. The space containing 1-4 is filled with the reactant gas. The electrodes 2 and 3 act as heat shields between the filament and 4. The thermal ion equilibria occur in the field-free space 4. Some of the ions and gas escape through the molecular flow slit (15 X 2000 pm) a t the bottom of 4. These ions are accelerated and subjected to magnetic mass analysis and detection. There are three tubes 5. Gas is passed into and out of the ion source by use of two of the tubes. The third tube leads to a capacitance diaphragm manometer which measures the pressure. The ion source can be heated by heater cartridges placed in 6 and cooled by circulating gas or fluid through the channels 7. The ion source temperature is measured with the thermocouple 8. The above apparatus is similar to that used earlier by Davidsone6 A more massive construction was used in the new version. Also, the filament was placed farther away from the reaction chamber 4. These two changes should lead to a more uniform temperature in the reaction chamber. The ion signals detected with this source were generally in the lo00 counts per second range, at -0.5 torr. Unfortunately, the ion signal decreased rapidly with ion source pressure. Results Measured equilibrium constants
of equilibria 2,
K+B,-I + B = K+B, (n - 1, n) (2) where B represents benzene, are shown in Figure 2. Experiments with neat benzene gave equilibrium “constants” which increased with pressure in the range 0.1-0.5 torr. Subsequent experiments in which the potassium ion supply
1816
The Journal of Physical Chemistry, Vol. 85, No. 13, 1981
Sunner et ai.
TABLE I : Thermodynamic Data"
1030
-AGO
-AH"
(298 1
-AS"
exptb cord exptb cord exptb cord
1
I d I
L3)1
1
I
(45f
13,4j I
I
20
,
,
15,6) ,
,
,
,
30
,
40
1 0 3 / ~K-1
+
Figure 3. van't Hoff plots of equilibria (n-l,n), K+B,-, B = K'B,,, where B = benzene: full line: (0)major gas methane containing 3.6% benzene, see Figure 1; (A)neat benzene, pulsed experiments, see Figure 1; (A)neat benzene. Dashed lines give van't Hoff plots for equilibria K+W,-l W = KW ' , from earlier work,' for comparison. Spacings between (n-1,n) and ( n , n + l ) plots correspond to decrease of binding free energy for the addition of one molecule to the n cluster. Much narrower spacings in the water plots show that binding free energies decrease much more slowly for this smaller molecule. Dlfference in slopes shows that superior binding free energies for water are due to more favorable entropy. Single data point (W) is the value for the equilibrium constant for the reaction CiB = CIB-. Comparison of this result with equilibrium constants for K+ shows that the posithre ( i o n i c ) ion has vastly stronger interactions with benzene.
+
K+ + B = K'B K'B + B = K'B, K+B, + B = K+B3 K'B, + B = K+B,
19.2 18.8 14.5 12.6
1 8 . 3 24.6 17.0 33.9 13.1 32.7 41.4
K+ + W = K+W K'W + W = K'W, K'W, + W = K'W, K'W, + W = K+W, K+W, + W = K+W, K+W, + W = K+W6
17.9' 16.2' 13.2' 11.8' 10.7' 10.Oc
17.9 16.0 12.9 11.1 9.6 8.4
22.4 1 1 . 9 1 1 . 6 25.1 8.8 9.5 32.8 4 . 7 3 . 3 0.3
21.6' 21.6 1 1 . 5 11.5 24.2' 24.1 9 . 0 8.8 23.0' 22.1 6 . 3 6 . 3 24.7' 22.2 4 . 4 4.5 25.2' 21.8 3 . 2 3.1 25.7' 19.2 2 . 3 2.7 Enthalpies and free energies in kcal/mol. Entropies in cal K-' mol-'. Standard state 1 atm. From van't Hoff plots, Figure 3. ' Experimental values from Searles and Kebarle.9 Corrected values for K'W, are from Sunner and Kebarle." Correction is to take into account the effect of unimolecular dissociation of ions under vacuum. The corrected values for K+B, were obtained from K+W, corrected and the exchange equilibria K'W, + nB = K+B, + nW, see Figures 4 and 5. Potassium ion K+ and water W or benzene a (AH')
kcalimol
+
1.0
1
(W,;B,)
.. . .O.0.
1
( -ll\ -19.2)
0.
-
n
r
I -8.6 -.-tKCB2 (-18.8)
a
t ( +- 0 . 75 )
-4.7 d + B (-14.5)
K+wB2
3
-0.3
K+B4
(-12.61
(a1
-11.6
-19.9
-24.3
fkcal/mol)
(b)
-11.9
-20.5
-25.2
(kcal/mol)
(a)
-18.3
-35.4
48.7
fbl
-19.2
-38.0
52.5
Figure 5. AGOa8 and AHo values for potassium-benzene (n-1,n) equilibria, (potassium-water (n-1, n ) equilibria (from earlier work this laboratory ), and water-benzene exchange equilibria. Consistency of l o / , , , (W3, B,Wz,621 , =these results can be checked by means of thermodynamic cycles. The O1 20 30 results from such cycles are shown on the figure. Agreement for ~o~/T(K-') AGOm results is within less than 1 kcal/md even for the longest cycle. Agreement for the AHo results is not as good, but, on the whole, the Fyure 4. van't Hoff plots of exchange equilibria K+W,B, B = data are mutually supportive. K Wx-,By+, annotated on figure as (W,B,; W,-l,B,+,) where W = water and B = benzene: (0)P w / P B = 1; (0)P w / P B = 4.9. at lower temperature where the kinetics were faster. The (W4i W3B)
+
was pulsed gave ion signals which were time resolved. These revealed that the rate of the (0,l) reaction was slow and that the low equilibrium constants a t low benzene pressure (unpulsed experiments) were due to incomplete approach to equilibrium. Experiments with neat benzene at higher pressures, time-resolved experiments with pulsed K+ at lower pressure, and experiments with methane containing 3.6 % benzene a t higher pressure gave equilibrium constants which were in fair agreement with each other (see Figures 3 and 4). These data were used in the (0,l) van't Hoff plot shown in Figure 3. The equilibrium constants for the higher (n-1,n) equilibria were measured by using neat benzene vapor. These measurements were
observed equilibrium constants were found largely independent of benzene pressure. The AGO,,-I,~,AHon-la,and obtained from the van't Hoff plots of Figure 3 are shown in Table I. Measurements of the water-benzene exchange equilibria (3) were also made. van't Hoff plots of these equilibria K+W,B, W = K+W,-1BY+1+ B (W,B,; W,-1BY+1) (3) are shown in Figure 4. These experiments were made with two different reaction mixtures: 0.73% B, 3.6% W and 3.5% B, 35% W, the rest being methane for both mixtures. The total pressures of the gas were changed from about
+
Ion-Solvent Molecule Interactions in the
Gas Phase
0.5 to 3 torr with both mixtures. The enthalpy and free energy changes obtained from the van't Hoff plots in Figure 4 are summarized in Figure 5. Also given in Figure 5 are (n-1,n) association equilibria of K+ and W obtained in earlier work by S e a r l e ~ . ~ Thermodynamic cycles between the two sets of data are made possible by the W,B exchange equilibria (3). Cycles made up of the branch K+ + nW = K+W, followed by the K+W, + nB = K+B, + nW exchange are compared with the direct branch K+ + nB = K+B, in Figure 5. Agreement within less than 1 kcal/mol between the two branches is observed for the results. The AH data agree less well. The direct K+B, enthalpy branch is consistently more exothermic than the K+W, K+B, route. Most of the (n-1,n) K+B, equilibria were measured with neat benzene and experimental equilibrium constants extend at high temperatures to values as low as Kn-l,n = 0.1 (t0rr-I). A recent analysis1° has shown that unimolecular decomposition of ion clusters n to clusters n - 1can occur in the vacuum of the mass analysis system. This dissociation is possible only for species n which, when leaving the ion source, have an internal energy which is larger than the dissociation energy -AH,,+,. The effect of the dissociation is to reduce the values of the observed equilibrium constants Kn-l,nat higher temperature. This in turn leads to and -AS,,, data that are somewhat larger than the true values. Unfortunately, the measurements of the K+B, equilibria with neat B fall partly in the temperature range where one might expect this effect to operate. These measurements were made before we knew that ion dissociation in the mass analysis vacuum may distort the results. The error will be more serious for the K+B, than for K+W, equilibria because of the large number of internal vibrations of the benzene molecule.1° A set of corrected values for the K+B, (n-1,n) equilibria can be obtained by using K+W, enthalpies which were approximately corrected for the dissociation effect.'O These corrected K+W, are given in Table I. Combining these data with the K+W, K+B, exchange enthalpies, i.e., following the long branch of the cycles in Figure 5 one obtains a set of corrected enthalpies for the K+B, equilibria. These are given in Table I as AHOn-l,n(cor).These corrected values are probably closer to the true values. The ASon-l,n(cor)and AGo,-l,n(cor) also given in Table I were obtained in the same manner. The benzene-water exchange equilibria were obtained under experimentally different conditions as compared to the (n-1,n) equilibria. For example, the temperature range for the equilibrium K+W B = K+B + W is considerably lower (29G470 K, see Figure 4) than the temperature range (400-598 K, see Figure 3) used for the K+ + B = K+B equilibrium. This is the case also for the other cycles. Therefore it is very likely that problems connected with unimolecular dissociation in the mass analysis system did not occur in exchange equilibria 3.
-
-
+
Discussion The results given in Table I show that both -AHo,, and -AGoo,l for K+B are somewhat larger than those for K+W. This result is surprising, since one would have expected the water molecule with its large permanent dipole to have a stronger bonding interaction than benzene, which is devoid of a permanent dipole. We will describe here the results of calculations which provide additional information on the situation. We have performed STO-3G calculations" for the species Na+C6HG.The four structures shown (9) Searles, S. K.; Kebarle, P. Can. J. Chern. 1969, 47, 2620. (10) Sunner, J.; Kebarle, P. J. Phys. Chern. 1981, 85, 327.
The Journal of Physical Chemistry, Vol. 85, No. 13, 198 1
1817
Na+
I
Na+ Ir
Ir
d
a
E(kcallmo1) -25.6 r
(A)
21
-20.4
-4.7
2.34
2.9
+
Figure 6. Possible structures for Na+-benzene considered in STO-3G calculations. The axial structure (a) is predicted to be the most stable. The same result is expected also for K+-benzene. The complex d, analogous to the most stable structure of protonated benzene, was found to be nonbonding (repulsive). More thorough geometry search may lead to a weakly bonding structure.
in Figure 6 were considered. The structure in which Na+ lies on the c6 symmetry axis of benzene was found to be the most stable. We shall call this structure the axial structure. The STO-3G calculated stabilization energies for systems like Na+C6H6are probably unreliable; however, the structural predictions are useful. We assume that the K+C6H6complex will have the same most stable geometry as the Na+C6HG.Recently, Huzinaga12has performed an ab initio SCF calculation for the systems K+H20 and K+C6&, using a newly composed minimal basis set.13 The stabilization energies obtained were -18.7 kcal/mol for HzO and -12.4 kcal/mol for the axial structure. The geometry optimization showed12that the presence of the potassium ion causes an increase of the C-C and the C-H bonds by approximately 0.05 8, each and a slight (2.3') out-of-plane bending of the C-H bonds away from the potassium ion. Huzinaga'slZ stabilization energy for K+H20 is in fair agreement with the AHo,,(K+H2O)= -17.9 kcal/mol, see Table I. However, the stabilization energy for K+C6H6of 12.4 kcal/mol is appreciably lower than the experimental AHo,, of -18.3 kcal/mol. SCF calculations do not give a good account of the London dispersion energies. These can be estimated, see below, to be about -1.5 kcal/mol for K+H20and -4 to -5 kcal/mol for K+C&. This changes the stabilization energies to -20.4 kcal/mol for K+H20and -17 kcal/mol for K+C&. This corrected K+C6H6result is now close to the experimental AHo,l but the K + H 2 0 result has overshot somewhat the AHo for water. An electrostatic calculation performed in our laboratory provides insight into the nature of the bonding in K+C,&. The energy between the K+ ion and benzene was calculated as the sums of the energies due to electrostatic (ES), induction (ion-induced dipole) (I), dispersion (D), and electronic repulsion (ER) interactions as shown in eq 4. E = EES E' + ED EER (4) The electrostatic interaction is due to the quadrupole moment of benzene. The axial structure of K+C6& makes maximum use of the benzene quadrupole moment which, due to the A electron cloud and the nuclear charges in the C6H6plane, has the charge distribution minus, plus, plus, minus along the c6 symmetry axis of benzene, Le., the quadrupole moment Bzz is negative. Details regarding the experimental parameters for the quadrupole moment, polarizability, dispersion, and electron repulsion and the calculation are given in the The numerical
+
+
(11) Hehre, W. J.; Latham, W. A.; Ditchfield, R.; Newton, M. D.; Pople, J. A. Gaussian 70, Quantum Chemistry Program Exchange, Indiana University, Bloomington, IN. (12) Huzinaga, S., private communication. (13) Hatewaki, H.; Huzinaga, S. J . Cornput. Chern. 1980, I , 205. (14) Claverie, P. In "Intermolecular Interactions: From Diatomics to Biopolymers"; Pullman, B., Ed.; Wiley: New York, 1978; p 167.
1818
The Journal of Physical Chemistry, Vol. 85, No. 13, 1981
Flgure 7. Resuits from electrostatic calculations for K+-benzene in axial structure, Le., structure a in Figure 6. The largest contribution to bonding at the equilibrium position is due to ion induced dipole, E’. Nearly equal is the Stabilization energy due to the interaction of the ion with the quadrupole moment of benzene ps.A significant contribution, ED, is also made from the dispersion forces.
results are shown in Figure 7. The calculation predicts a stabilization energy of -20 kcal/mol which is in fairly good agreement with AHo,,. However, this agreement is not too significant, since there is some latitude in the choice of the parameters. What is useful is the description of the bonding. From the figure we see that, at the equilibrium distance, the ion-benzene quadrupole ES and the ion-induced dipole E1 energies are nearly equal and provide the two major contributions to the bonding. Each of these is about -10 kcal/mol. However the dispersion interaction ED at -5.4 kcal/mol is also significant. The relative contributions of the interactions for K+OH2predicted by the electrostatic model are quite different (Davidson6). The ion-permanent dipole interaction ES at -17.8 kcal/mol is dominant. E1 is only -3.4 kcal/mol and ED at -1.7 kcal/mol is even smaller. The fact that the ion-permanent dipole interaction is by far the dominant bonding term for the potassium water complex indicates directly that the binding energy in this complex will decrease relatively slowly with increasing ion-ligand distance. The opposite will be true for benzene where all important interactions, ion-quadrupole, ion-induced dipole, and dispersion, are short range. Thus, we expect that bonding of additional benzene molecules will be adequate only so long as these molecules can be close to the potassium ion, i.e., in the first shell. Furthermore, as the benzene molecules accumulate in the first shell, expansion of the average K+C6H, distance will be very unfavorable. This fact combined with a consideration of the large size of the benzene molecules leads one to expect that the motions of the benzene molecules in the K+B, complexes will by much more restricted than will be the case for the water molecules. A detailed analysis of the vibrations and rotations of the water molecules in K+W, has been perf~rmed.~JO This predicts very considerable freedom of movement. It is probably this difference (15) French, M. A.; Kebarle, P., to be submitted for publication. (16) Buckingham, A. D. In “Intermolecular Interactions: From Diatomics to Biopolymers”; Pullman, B., Ed.; Wiley: New York, 1978; p 20. (17) Shoemaker, R. L.; Hygave J. Chem. Phys. 1969, 51, 2988. (18) Denbigh, K. G. Trans. Faraday SOC.1940, 36, 936. (19) Hirshfelder, J. 0.; Curtis, C. F.; Bird, R. B. “Molecular Theory of Gases and Liquids”; Wiley: New York, 1964. (20) Pitzer, K. S. Adu. Chem. Phys. 1959, 2, 59.
Sunner et al.
Figure 8. A shematic drawing to scale of the complex K+(CeHe),, The distance between K+ and the symmetry plane of benzene is taken as 3.2 A which is somewhat larger than the 2.7-A distance for K+C6H6 of Figure 7. Even at this distance the CeHe molecules are quite crowded and their motions except internal rotation will be very restricted. I t is also obvious that a fifth benzene molecule will be very weakly held due to lack of space near the ion and the short-range forces involved in the K’B bonding.
between benzene and water that is reflected in the very different -ASo.-,,, for B and W. As is clear from Table I and van’t Hoff plots in Figure 3, the entropy changes for water addition are much less unfavorable than are those for benzene addition. This difference is seen to increase as n increases, which is to be expected because crowding will occur much faster for the benzene molecules. A scale drawing of the K+B4complex is shown in Figure 8. The radius of K+ shown is the Pauling radius of 1.33 A, the height of the a system of the benzene, Le., the thickness of benzene is 3.2 A and the radius of hydrogen 1 A. The distance between K+ center and the symmetry plane of the benzene is taken as 3.2 A. This is somewhat larger than the 2.7-A equilibrium distance in K+B, Figure 7. The drawing in Figure 8 shows that four benzene molecules can be accommodated in a tetrahedral arrangement around the K+ ion, but the structure is very tightly packed. The motions of the benzene molecules, apart from internal rotations around the c6 axis, will be very restricted. A fifth molecule will have to be far removed from the K+ and, considering the short-range forces involved in the bonding interactions, will be very weakly held indeed. We could not detect a K+B5 complex at temperatures where the detection of K+W5 and K+W6 was easy (see van’t Hoff plots Figure 3). The van’t Hoff plots in Figure 3 show a single point for the equilibrium constant of the reaction 5. This is an
c1- + C6H6 = C1-C&6
(5)
experimental result from a study of the interactions of C1with a series of different solvent m~lecules.’~Inspection of Figure 3 immediately shows that the bonding of benzene to C1- is vastly weaker than the bonding to the isoelectronic K+. The equilibrium constant K 5 obtained at 300 K can be converted to AGO5 = -RT In K 5 = -3.8 kcal/mol. Assuming a reasonable value of ASo5 = -22 cal K-’ mol-’ (see Table I) one obtains AHoo,l(C1-)= A H 5 = AGO5 + TAS05 = -10.4 kcal/mol. The binding enthalpy of C1- to benzene is some 8-9 kcal/mol lower than that for K+. This must be a consequence of the somewhat larger radius of C1- and more importantly of the sign of the quadrupole moment of benzene. The ES interaction in the axial complex (see eq 4 and Figure 7) is repulsive for C1-, i.e., the ES energy is positive. An approximate idea for the bonding in the Cl--benzene axial complex can be obtained by plotting the
The Journal of Physical Chemistry, Vol. 85,No. 13, 1981 1819
Ion-Solvent Molecule Interactions in the Gas Phase
data of Figure 7 with Em being positive. Such a plot leads to a shallow minimum of about 1 kcal/mol. Comparing this result with the experimental AHo,l= -9 kcal/mol one concludes that the axial complex cannot be the most stable structure of the Cl--benzene complex. Of course this is to be expected from the fact that the axial structure maximizes the quadrupole repulsion with the negative ion. An investigation of the bonding in C1--benzene has not been made yet; however, it is clear from the experimental result that the bonding in C1-B is much weaker than that in K+B and that this difference is due to the fact that the negative ion cannot make use of the large quadrupole moment of benzene in the z direction because of its negative sign. Potassium chloride is very soluble in liquid water, while it is almost insoluble in liquid benzene. The gas-phase energetics described in the preceding paragraphs fit into this situation as follows. The first four molecules of water and benzene interact almost equally well with K+;however, the bonding of the ion with benzene essentially stops after n = 4, while for water strong bonding, i.e., bonding stronger than that to bulk water, continues to much higher n. For C1- the situation in benzene is even worse since even the first bonding interactions are much weaker than those with water. Of course in addition to these intimate ion-solvent interactions one has to consider the solvation (free) energies of the clusters in the liquid solvent. Obviously, the much higher dielectric constant of water and the much smaller size of the K+W, species and Cl-W, clusters as compared to the benzene clusters will lead to an additional large differential lowering of the energy in favor of the aqueous solution. The major contribution to the interactions of the ion cluster with the liquid solventz1is the Born charging term given in eq 6, where r is the radius of
"(.
AGBom
2r
- 1)
the cavity that the cluster will occupy, t is the dielectric constant of the liquid solvent, and L is Avogadro's number. A comparison of the numerical value of A G B ~ ~for , K+benzene and K+-water is instructive. The free energies for cluster formation involving the gaseous ion and molecules from the liquid solvent, eq 7-9, can be evaluated from K+(g)+ 4%) = K+B4(g)
(7)
AGO, = -20.7 kcal/mol AGoh,,(K+B4) = -13 kcal/mol
(r = 7 8)
K+(g)+ 4Ww = K+W4(g)
(8)
AGO, = -23.0 kcal/mol K+(g)+ 6W(l) = K+W6(g)
(9)
AGO9 = -24.4 kcal/mol
t
Electrostatic Calculation" of Interaction Energy in K+-C,H, qc = - 0 . 0 9 2 4 5 q H = + 0.09245 e z z = - 5.6 X esu cmz I K t = 31.7 eV JK+ = 25.5 IC,H, = 9 . 3 eV a
a ~ = +0 . 8 9 A S e C - C , t = 0.48 C Y C - ~=, 2.25 ~ A'
0.58 A 3 0.79 l i s a,(b'enzene) = 6.35 A 3 a,,l,,(benzene) = 1 2 . 3 A ' 0c-H.t = LYC-H 1 =
Jc,H, = 2.5 See Appendix.
The radius for K+B4,r = 7 A, was estimated from a consideration of the dimensions of K+B4shown in Figure 7. The radius for K+W4of 5.8 A is based on geometries for the complex obtained from electrostatic calculations.1° The sum of AGO8 and AGB,, for water is -51.4 kcal/mol while the corresponding sum for benzene is only -33.7 kcal/mol. The total free energy of hydration of K+(g)is believed to be around -81 kcal/mo1.z2 The large difference between -51.4 and -81 kcal/mol indicates considerable additional bonding of the K+W4in the liquid water. This is an expected result as there will be eight relatively strong hydrogen bonds from the K+(OHJ4 to water molecules in the solvent. Much additional bonding for K+B4 in liquid benzene is not expected. Therefore the total free energy of solvation of K+ in benzene should be lower than -33.7 kcal/mol but not%y more than 10 kcal/mol.
Appendix. Electrostatic Calculations for K+-Benzene The interaction energy between the potassium ion and benzene was calculated from eq 4. The first three terms Em, E', and EDwere calculated with the classical equations in multicenter expansion^.'^ For the ES term the charge distribution in benzene was approximated with net atomic charges q as shown in eq 10, where the sum i is over all
Em
= qICqi/ri,I
(10)
atoms in benzene, qi being the respective atomic charges and ri,Ithe distances between the atoms and the ion, and qI is the charge of the ion. The atomic charge distribution in benzene is determined by the quadrupole tensor.16 The experimental value for the quadrupole moment Ozz = -5.6 X esu cm2was taken from Sh~emaker.'~ The atomic charges are given in Table 11. The induction energy E' was calculated by using bond polarizabilities, eq 11, where E' = -1/x(ab,t sinz o b + ab,e cos2 ob)IEI1z (11) b
= 2.274
AGh,,(K+W,) = -28.4 kcal/mol
TABLE 11: Numerical Values of Parameters Used for
(r = 5.8 A) (9)
b is summed over all bonds in benzene and CUbJ and a b , $ ar_e the lateral and transverse polarizabilities of bond b. EI is the electric field vector of the ion at the center of the bond, and o b is the angle between that vector and the bond. The bond polarizabilities were taken from Denbigh.l8 They add up to the experimental polarizability of benzene.lg The dispersion energy was calculated with the London formula in multicenter expansion as shown in eq 12. I K
= 80
data in Table I and the free energies of evaporation at 298 K, AGoeva,(C6H6)= -1.26 kcal/mol, AGoevap(HzO)= -2.05 kcal/mol. Also shown are the AGhm obtained from eq 6. (21) For a description of more detailed calculations and difficulties that arise if one wishes to obtain accurate solvation energies see Saluja, P. P. S. MTPZnt. Rev. Sci., Phys. Chem., Ser. Two 1976,6.
(22) Desnoyers, J. E.; Jolicoeur, C. In "Modern Aspects of Electrochemistry";Bockris, J. O'M.; Conway,B. E., Ed.;Plenum Press: New York, 1969;Vol. 5.
1820
J. Phys. Chem. 1981, 85, 1820-1823
and IBare the ionization potentials of K+ and benzene while JK and JB are the respective correction factors suggested by Pitzerm and O b is the angle between the vector from the ion to the center of the bond and the vector in
the direction of the bond. No experimental information is available for the electron repulsion energy EER. This term was equated to the STO-3G calculated energy between argon and benzene.
Fluorescence Enhancement of Benzene Derivatives by Forming Inclusion Complexes with P-Cyclodextrin in Aqueous Solutions Miklo Hoshlno," Masashl Imamura, The Institute of Physical and Chemical Research, Wako-shi, Saitama 351, Japan
Klyoshl Ikehara, and Yoshlmasa Hama Science and Engineering Laboratory, Waseda University, Shinjuku-ku, Tokyo 160, Japan (Received: June 18, 1980; In Final Form: February 4, 198 1)
Benzene derivatives (benzene, phenol, ethoxybenzene, aniline, N-methylaniline, N,N-dimethylaniline, and NJV-diethylaniline)form inclusion complexes with P-cyclodextrin in aqueous solutions. The equilibrium constants of these inclusion complexes were obtained by absorption and/or fluorescence spectrophotometric methods. Fluorescence enhancement was observed upon inclusion for all benzene derivatives studied. Of the compounds, aniline and N-methylaniline showed marked effects of inclusion. These results are discussed on the basis of environmental changes around fluorescent molecules upon inclusion.
Introduction Cyclodextrins form inclusion complexes with organic solutes in aqueous solutions. The binding force between cyclodextrins and organic solutes has been assumed to be hydrogen bonding, van der Waals force, or hydrophobic interaction.'P2 Since absorption spectra of inclusion complexes differ from those of organic solutes dissolved in water, the absorption spectrophotometric method has been used for obtaining equilibrium constant^.^ A series of thermodynamic and kinetic studies on the formation of inclusion complexes showed that a molecule can be included when the size of the molecule is smaller than that of the cavity inside a cyclodextrin m ~ l e c u l e . ~ The first observation of fluorescence enhancement upon inclusion was reported for the aqueous P-cyclodextrin solutions of l-anilin0-8-naphthalenesulfonate.~ Recently, Kondo et al. studied fluorescence enhancement of 6-(pto1uidino)naphthalenesulfonate for the purpose of detecting ring opening of cyclodextrins catalyzed by Takaa m y l a ~ e . ~No other compounds were reported to show fluorescence enhancement in aqueous cyclodextrin solutions. In the present study, the spectra and the quantum yields of fluorescence were measured for benzene, phenol, ethoxybenzene, aniline, N-methylaniline, N,N-dimethylaniline, and N,N-diethylaniline in aqueous P-cyclodextrin solutions in order to elucidate the behavior of fluorescent molecules in their excited states upon inclusion. Experimental Section Reagent-grade benzene, ethanol, and phenol were used without further purification. Water, ethoxybenzene, aniline, N-methylaniline, N,N-dimethylaniline, and N,Ndiethylaniline were purified by distillation. P-Naphthol (1)Hall, E.S.;Ache, J. J. Phys. Chem. 1979,83,1805. (2)Hoffman, J. L.; Bock, R. H. Biochemistry 1970,9,3542. (3)Cramer, F.;Saenger, W.; Spatz, H. J.Am. Chem. SOC.1967,89,14. (4)Kondo, H.; Nakatani, H.; Hiromi, K. J. Biochemistry 1976,79,393. 0022-3654/81/2085-1820$01.25/0
was sublimed under reduced pressure before use. Reagent-grade P-cyclodextrin (P-CD) was purified by recrystallizing it twice from aqueous solutions. No fluorescent impurities were detected in aqueous solutions of the purified P-CD. Quinine sulfate was used as supplied. The purity of chemicals used was ascertained from absorption and fluorescence spectra. Absorption and fluorescence spectra were recorded on a Hitach 200-20 spectrophotometer and a MPF-4 spectrofluorimeter, respectively. All spectra were measured at 28 f 2 OC. Quantum fluorescence spectra were measured by calibrating the output of the spectrofluorimeter using the corrected fluorescence spectra of aniline and phenol in ethanol solutions, and quinine sulfate and @-naphtholin both aqueous and ethanol An acid aqueous solution of quinine sulfate was used as a standard for determination of fluorescence quantum yields. Solutions were not degassed because fluorescence intensities observed for deaerated aqueous solutions of benzene derivatives were decreased only by less than 2% after aeration.
Results Absorption Spectra. Figure 1 shows the absorption spectra of N-methylaniline (NMA) in aqueous solutions containing various amounts of P-CD. The absorption band around 283 nm shifts toward long wavelengths with increasing concentration of P-CD. The isosbestic points appearing at 270 and 280 nm indicate an equilibrium: NMA + P-CD F? NMA-P-CD The equilibrium constant, K (= [NMA.P-CD]/( [NMAI(5) Berlman, I. B. "Handbook of Fluorescence Spectra of Aromatic Molecules"; Academic Press: New York, 1965. (6) Lippert, E.; Nagele, W.; Seibald-Blankenstein, I.; Staiger, U.; Voss, W. Z. Anal. Chem. 1959,170, 1. (7) Parker, C. A.; Rees, W. T. Analyst (London) 1961,87, 83.
0 1981 American Chemical Society
