3558
J . Phys. Chem. 1991, 95, 3558-3564
correlations with the assignments for ClCB and FCB in exchanging the characterizations of these modes. Ring-Puckering Mode. Both 1-halocyclobutenes have appreciably lower ring-puckering frequencies than CB due to the anchoring effect of the halogen substituent. With the heavier halogen atom substituent, ClCB has the lower ring-puckering frequency. Table V shows the relationships between ring-puckering frequencies and halogen substitution on cyclobutene. Included in Table V is our revision of the assignment for cis-3,4-dichlorocyclobutene as well as some other ring-puckering frequencies for halocyclobutenes from work in our laboratory. Halogen substitution on the methylene carbon causes a larger frequency decrease than does substitution on the vinyl carbon. The greater effect is surely due to inhibition of the motion of the singly bonded methylene carbon atoms, which have greater excursions than the vinyl carbon atoms in unsubstituted cyclobutene. Substituting chlorine atoms on each of the methylene carbons causes about twice the frequency lowering as adding a chlorine atom to one. Substituting two fluorine atoms on each of the methylene carbons has the same effect as substituting one chlorine on each carbon. Thus, the effect seems largely a mass effect. Simplicity of the pattern of changes in ring-puckering frequencies due to halogen substitution is consistent with this out-of-plane mode being rather free of mixing with other modes.
Conclusions Gas-phase infrared spectra and liquid-phase Raman spectra havc provided complete assignments of the 24 vibrational fundamentals of I -chlorocyclobutene and 1-fluorocyclobutene and have confirmed the previously disputed cyclobutene structure for the chloro compound. A close correlation exists between the
CH-rich modes of these isotopomer-like molecules. The relationship between the skeletal modes of the two molecules has also been interpreted qualitatively in terms of mixing of symmetry coordinates. Despite several detailed studies in the past, the fundamentals of cyclobutene itself remained unsettled. The Raman spectrum of liquid cyclobutene near -100 'C and correlation with the fundamental frequencies of two 1-halocyclobutenes have provided good evidence for the five unsettled a, and bl fundamentals. New assignments in cm-I are as follows: (a,) vg = 2944, v I I = 1011, and v I 2 = 846; (b,) v19 = 903 and v20 = 888. The ring- puckering frequencies for halogen-substituted cyclobutenes fit into an understandable pattern. Chlorine substitution has a larger effect than fluorine substitution. Substitution on a methylene carbon atom has a larger effect than substitution on the vinylic carbon atom. Due to two single bonds, the methylene carbon atoms in cyclobutene undergo greater out-of-plane motion than do the vinylic carbon atoms. Thus, anchoring a methylene carbon atom with a halogen atom has a larger frequency-lowering effect than anchoring a vinylic carbon atom.
Acknowledgment. We are grateful to Michael A. Fisher for some of the experimental work. We also acknowledge the help of Professor James Gano of the University of Toledo in obtaining the initial NMR spectra of precursor molecules. National Science Foundation Grants CSI-8750723 and CHE-850737 helped support the purchase of the FT-IR and the N M R spectrometers. We acknowledge the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. Y.-Z.X.was a Shansi Faculty Fellow at Oberlin College for 2 years.
Thermodynamics of Gas-Phase Mixed-Solvent Cluster Ions: Water and Methanol on K+ and Ci- and Comparison to Liquid Solutions D. H. Evans, R. C.Keesee, and A. W. Castleman, Jr.* Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802 (Received: October 9, 1990)
The enthalpy, entropy, and Gibbs free energy values for the gas-phase ion-molecule association reactions Qf(CH30H),,(H2O), + CH30H + Q*(CH30H),(HzO), and Q(CH30H),(HzO),l + H 2 0+ Q*(CH30H),(H20), for Q = W a n d K+ were determined. The thermodynamic values of the association reactions were used to calculate the thermodynamic values of the switching reactions, Q*(CH30H),,(H20), + (CH30H) * Q*(CH30H),(HzO),, + (H2O).Results for reactions with up to a total, n + m,of four ligands are presented; these data are used to determine the preferential clustering of solvent molecules onto the ions as a function of the composition of the gas phase. The difference of the free energies of clustering of a solvent onto the two separate ions shows a good correlation with the corresponding bulk-phase reaction. This correlation does not hold for the enthalpy and entropy changes.
Introduction The study of ion-molecule complexes in the gas phase has revealed much about the nature of ionsolvent interactions.Iv2 Gas-phase studies provide data on the forces operating in individual complexes without the interferences arising from the presence of the bulk solvent or counter ions. Thermodynamic data for the clustering of a few molecules onto an ion have been particularly useful in evaluating single-ion heats of s ~ l v a t i o n . ~The . ~ success ( I ) Kebarle. P . Mod. Aspects Electrochem. 1974, 9, 1. (2) Castleman, A. W., Jr.; Kecsee, R.G. Acc. Chem. Res. 1986, 19, 413. (3) Arshadi, M.;Yamdagni, R.;Kebarle, P . J. Phys. Chem. 1970, 74, 1475. (4) Lee, N.; Keesee, R.G.;Castleman, A. W., Jr. J. Colloid Interface Sci. 1980, 75, 555.
of gas-phase results for single-component solvents suggests a natural extension to examine the utility of gas-phase data for binary solvents. The properties of alcohol-water solutions have received considerable and methanol is the simplest of the alcohols. ( 5 ) Franks, F.; Ives, D. J. G. Q.Reu. 1966, 20, I . (6) Simonson, J. M.;Bradley, D. J.; Busey, R.H. J. Chem. Thermodynam. 1987, 19. 479. (7) Abraham, M.H.; Hill, T.; Ling, H. C.; Schulz, R.A,; Watt, R. A. C. J. Chem. Soc., Faraday Trans. I 198480, 489. (8) Blandamer, M.J.; Burgess, J.; Clark, B.; Duce, P. P.;Hakin, A. W.;
Gosal, N.; Radulovic, S.;Guardado, P.; Sanchez, F.;Hubbard, C. D.; AbuGharib, E. A. J. Chem. Soc., Faraday Trans. I 1986, 82, 1471. (9) Wells, C. F. In Hydrogen-BondedSolvent Systems; Covington, A. K., Jones, P., Eds.; Taylor and Francis: London, 1968; pp 224, 323.
0022-365419 112095-3558$02.50/0 0 1991 American Chemical Society
Gas-Phase Mixed Solvent Cluster Ions 103
. 0
CI-
--
CI-M
, '
I
CIW a
CI-MW CI-ZM
;10'
G
I
EE
IO'
U
"
10'
"
"
" " " '
'
J ,-
1.5
2.5
3.5 10
1000/T(l/KI
-
Figure 1. Experimental van't Hoff plots for methanol addition onto CI--methanol-water cluster anions. M = methanol, W = water.
Mixed solvents are frequently used to attempt to design certain desired solvent properties. For aqueous mixtures, the systems can help to understand the structure of water and hydrogen-bonded networks. In a mixed solvent, the composition of the solvent in the neighborhood of the ions often differs from that of the bulk solvent. This preferential solvation is a consequence of the different specific interactions between the ions and each component of the solvent.I0 There appears to be no general agreement on the direction of preferential solvation of ions in aqueous methanol solution^.^ In the gas phase, a few studies of the ionic methanol-water clusters, i.e., the protonated clusters H+(H20),(CH3OH),,lI-I3 and the deprotonated (anionic) system [(H,O),(CH,OH), - HI-," have been reported. The purely hydrogenic ionic systems present some complications due to the possibility of proton mobility in the hydrogen-bonded network and ambiguity in the locality of the ~ h a r g e * * ~ The J ~ Jpresent ~ study focuses on ionic species with a clearer distinction in a hydrogen-bonded solvent, namely, the potassium cation and the chloride anion. Preliminary thermodynamic results for K+ have been communicated previ~usly;'~ complete data for both the C1- and K+ data are reported here.
Experimental Section The apparatus used to conduct these experiments has been described previously.16 Briefly, chloride ions are formed in a high-pressure region ( 1-20 Torr) by dissociative electron attachment. Trace amounts (0.1%)of CCl, are added to the reaction mixture as a source gas to produce Cl-. The reaction mixtures consist of 2-12% water and 0.610% methanol in either a helium, carbon dioxide, nitrogen, or methane buffer gas. Potassium ions are formed by thermionic emission from a resistively heated platinum filament coated with potassium nitrate in an alumina and silica matrix. Voltages are applied to various focusing electrodes to direct the ions toward a field-free, thermally controlled region. The primary ions and cluster ions leak through a 75-pm diameter orifice into a high-vacuum region ( l(r5Torr or less). In this latter region, the ions are mass analyzed with a quadrupole mass spectrometer and counted. Various tests as described elsewhere16 are performed to ensure that equilibrium is established. The equilibrium constant is calculated from the ratio of the measured (IO) Padova, J. J. Phys. Chem. 1968, 72, 796. (1 1) Kebarle, P.; Haynes, R. N.; Collins, J. G. 1.Am. Chem. Soc. 1967, 89, 5153. (12) Stace, A. J.; Shukla. A. K. J . Am. Chcm. Soc. 1982, 104, 5314. (13) Meot-Ner, M. J . Am. Chem. Soc. 1986, 108,6189. (14) Holland, P.M.;Castleman, A. W . ,Jr. J. Chem. Phys. IWU), 72,5984. (15) Keesee, R. G.; Evans, D.H.; Castleman, A. W., Jr. In Physics and
Chemistry of Small Clusters: Jena, P., Rao, B. K., Khanna, S.N., Eds.; NATO AS1 Series B, 1987; Vol. 158, p 687. (16) Castleman, A. W.. Jr.; Holland, P. M.;Lindsay, D.M.; Peterson, K. I. J. Am. Chcm. Soc. 1918,100,6039.
'
.
--E; l o * -.
-%
.
;lo,
r
101.
0
n-z n-3
///
-
K+.
a
n-I
n-z n-3
I
L 10 1
L
2.0
2.5
3.0
3.5
4.a
4.5
1000/T (1/Kl
Experimental van't Hoff plots for the equilibria K+(CH3OH),I(H20) + CH3OH + K+(CH30H)n(HzO). Figure 4.
ion intensities and known partial pressure of the clustering neutral. A number of such measurements at various temperatures results in a van't Hoff plot from which the enthalpy and entropy changes for a particular clustering reaction can be determined. Two of the reactions, CI-(CH,OH)(H20)
+ H2O + CI-(CH,OH)(H,O),
(1)
were studied by using D 2 0 (99.8% D, MSD Isotopes) and CH30D (99S+% D, Aldrich Chemical Co.) to avoid overlapping the mass peaks of interest with a contaminant ion, Cl--HCI, and clusters containing CI-.HCI. CI--HCl is produced by reactions in the source and many times was of larger intensity than the ion of interest of the same mass, CI-(H20)2. In the deuterated system, the ions of interest and contaminant ions were thereby separated.
Results The van't Hoff plots for the association of C1- with water and methanol are shown in Figures 1 and 2. Those for K+ are shown in Figures 3-5. The data are based on the conventional standard state of 1 atm. van't Hoff plots were obtained over a range of
Evans et al.
3560 The Journal of Physical Chemistry, Vol. 95, No. 9, 1991
t
A
K’MU
r““l
cI
(10.0)
I
1 2 , K.d 1Y.6 2.5
2.0
3.0
3.1
4.0
1 OOO/T( I / K )
Figure 5. Experimental van7 Hoff plots for water addition onto K+-
methanol-water ions.
Figure 7. Same as Figure 7 for entropy changes, -MO (in cal/K mol).
??:’-I
l->yz
i
,O.O1
1
iauu QM]
1
I O 9
,
a:ur 121
Figure 6. Enthalpy changes, -AH (in kcal/mol), in the methanol (M) and water (W)clustering onto K+ and CI-.Values beneath ion desig nation are the cumulative enthalpy changes for the cluster ion from its ion and component gas-phase solvent molecules. Values in parentheses are determined by closure of thermodynamic cycles. For measured values, the indicated error is 1 standard deviation of least-squares fit to the van’t Hoff plot: (a) from ref 17; (b) from ref 18; (c) from ref 19.
conditions that produced at least a decade change in the equilibrium constants. The plots are linear over these ranges. The resulting thermodynamic values for each clustering step are displayed in Figures 6-8. The uncertainties in enthalpy and entropy are 1 standard deviation in the least-squares fit of the van? Hoff plots. The K+-water results are from Searles and Kebarle,” and the CI--water results are from earlier work in this laboratory.I* Hiraoka and Mizuse19 have also recently examined the single-solvent CI--water and Cl--methanol clusters. The results from their laboratory and ours are in excellent agreement. The cumulative thermodynamic functions for the formation of the cluster ions from its ion and component gas-phase solvent molecules are also indicated in Figures 6-8. In cases for which more than one route to the same cluster is experimentally de(17) Searles, S. K.;Kebarle,
(18) (19)
P. Cum J . Chem. 1969, 47, 2619.
Kegee, R.G.; Castleman, A. W.,Jr. Chem. Phys. Lett. 19W74.139. Hiraoka, H.; Mizuse, S.Chem. Phys. 1987, 118,457.
Fz7
I
(1.1)
Figure 8. Same as Figure 8 for Gibbs free energy changes, -AGO at 298 K (in kcal/mol).
termined, the cumulative value is determined from the average of the paths in a sequence from lowest rank to highest. Following Meot-Ner,” the rank r of a cluster refers to the total number (n + m) of solvent molecules in the cluster. The self-consistency of the measured values can be checked by calculating thermodynamic cycle errors. For example, Cl-(CH30H)2H,0 can be produced from Cl-(CH30H) through two different routes. The thermodynamic values for these two routes
Gas-Phase Mixed Solvent Cluster Ions
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3561
TABLE I: Comparison of Alternate Routes from Cl-(CH30H) to Ct(CH30H)z(H20) AHo, kcal/mol CI-(CHjOH) + CH,OH + CI-(CHjOH)2 -13.7 0.2 -7.7 f 0.7 CI-(CHjOH)z + H20 = CI-(CH,OH)ZH20 -21.4 f 0.7 net: CI-(CH,OH) + CH,OH + H 2 0* CI-(CH30H)2H20 CI-(CH,OH) + H2O * CI-(CH,OH)(H20) Cl-(CH,OH)(H,O) + CH,OH * CI-(CHIOH)2H,O net: CI-(CH,OH) + CH,OH + H20 + CI-(CH30H)2H20 should be identical if the clustering system is at equilibrium. The comparison of these two routes is shown in Table I. The overall thermodynamic values for the two routes agree quite well. Other examples show similarly good agreement. The cumulative uncertainties are determined as the square root of the sum of the squares of the standard deviation for each component path. The agreement for enthalpy is typically better than that for entropy because the entropy determinations have possible systematic errors due to mass discrimination that are not accounted for in the statistical uncertainties and that do not influence the enthalpy determinations.I6 The statistical uncertainties in the enthalpy and entropy determinations are coupled and so do not transform directly into uncertainties in the Gibbs free energy. Uncertainties in the free energy are largely due to the systematic errors and to the extrapolation of data to the reference temperature of 298 K. On the basis of the consistency of the thermodynamic cycles and our experience on the typical agreement with other laboratories, the uncertainty in is estimated to be about 0.3 kcal/mol for each clustering step. The thermodynamic values for the switching reactions
e
where is CI- or K+, are calculated from thermodynamic cycles and shown in Figures 6-8. As anticipated from the internal consistencies noted above, thermodynamic values for switching determined from the averaged cumulative clustering are in good agreement with values determined from parallel reactions involving water versus methanol addition to a given cluster.
Discussion Neat Clusters. For neat clusters, the stepwise addition of methanol molecules onto K+,up to the experimentally measured limit of four solvent molecules, is consistently more exothermic than the respective water solvation step. In addition, the methanol additions have a significantly more negative entropy change. As a result, only the first methanol addition is more exoergic than the corresponding water clustering step. For the proton, MeotNer13 found that each methanol clustering step is more exothermic for methanol (with the possible exception of the fourth clustering step) for up to seven solvent molecules, but the water addition s t e p are more exoergic from the fourth step onward. Thus,similar to K+,entropy changes have a significant influence on the relative exoergicities of the clustering steps. With C1-, methanol clustering steps are more exothermic than those for water for the first two steps but not the third step. The clustering steps also have the same pattern in exoergicity since the entropy changes are similar for both water and methanol addition. Since the influence of the ion is expected to diminish for large clusters, the thermodynamic functions for each clustering step should approach the values for condensation of the clustering species (at 298 K, AHoWnd = -9.08 versus -10.52 kcal/mol, ASo,,,,, = -26.98 versus -28.41 cal/mol K, and AGOmd = -1.04 versus -2.05 kcal/mol for methanol versus water). Thus, water addition should eventually become more exothermic as well as more exoergic than methanol addition for all these ions. For the completely solvated ions in the pure liquids, the transfer from water to methanol is endoergic for all three ions (AG,W'M = 2.5, 2.3, and 3.2 kcal/mol for H+, K+,and CI-,respectivelyz0) while the transfer of H+ and K+ is exothermic and C1- endothermic (20) Marcus, Y . Pure Appl. Chem. 1983, 55,917.
-10.9 f 0.7 -10.8 f 0.8 -21.7 f 0.8
ASo,cal/mol K
AG20a,kcal/mol
-22.0 f 0.5
-7.1 -4.4
-11 f 2 -33 f 2.1
-11.5
-16.9 f 0.4 -19 i 2 -35.9 2
-5.9 -5.1 -1 1.0
(AHIWdM= -3.9, -4.5, and 2.0 kcal/m~l'-~'). The magnitudes of the entropy changes for H+ and K+ are relatively large compared to that for C1- (ASlw-M = -21.3, -22.5, and -4.2 cal/mol K) * Qualitatively, comparison of the trends in water and methanol clustering onto these ions is in accord with expectations from the liquid-phase properties. For the free energy changes, both condensation and ion solvation favor solvation by water over methanol and, although the ion-methanol interaction is stronger for the simple adduct, the switchover to greater exoergicity in stepwise water addition occurs at small clusters (two to four solvent molecules). Both the single-ion AH, and AH,, favor water in the case of CI-,but the single-ion heats of transfer for K+ and H+ are in the opposite direction. In keeping with the bulk-phase comparison, the crossover between methanol and water in the enthalpy change occurs at the third step for C1- but has not yet occurred at the fourth step for K+ or the seventh step for H+ (excepting the anomaly for the fourth step). With the difference in AS-,, between methanol and water being small, the comparison of entropy changes for the gas-phase clustering reactions of water and methanol is consistent with the bulk phase ASl', i.e., large differences for H+ and K+, but small ones in the case of CI-. Mixed Clusters. Next we examine the mixed clusters and consider trends in the cumulative clustering thermodynamics (or equivalently the replacement of water molecules by methanol) for clusters with a given number of solvent molecules (referred to as the rank r). For H+, Meot-NeP found a consistent increase for a given rank (up to the highest rank measured, r = 7 ) in both exothermicity and exoergicity for clustering as the cluster ion goes from water rich to methanol rich. The greater proton affinity of methanol is largely responsible for the observed trend. The largest change occurs with the replacement of the first water molecule. The difference between the neat water and neat methanol clusters in enthalpy and free energy is nearly independent of the rank. In fact, the cumulative free energy change for each rank exhibits a very similar dependence with respect to the mole fraction of methanol molecules in the product cluster. For the potassium cation, there is a consistent increase in exothermicity for forming clusters in a given rank as the composition shifts from water to methanol (see Figure 6). In comparison to water, the large exothermicity and entropy decrease for methanol addition onto K+ is probably related to the interaction of the ion with hydrogen atoms (which are slightly negatively charged centers) of the methyl group, thereby inhibiting free rotation of methanol about the ion-dipole axis. The net result for the free energy is that mixed clusters have the largest exoergicity in a given rank. The most striking aspect in the results for the chloride ion is the relatively small enthalpy and entropy changes for addition of water onto clusters containing methanol. The excellent agreement for independent routes, as shown in Table I, indicates that the peculiar feature is reliable. Hiraoka and MizuseIg suggest that methanol has a "chelate" interaction of its methyl group with the CI- ion. They also propose that the configuration gradually shifts to an "open" more linear hydrogen bond with increasing numbers of methanol molecules in the cluster. Inspection of Figure 7 for CI- shows that the cumulative entropy change for the mixed clusters are smaller than those for the neat clusters within a given rank. If the entropy changes were independently additive for each ( 2 1 ) Marcus, Y . Pure Appl. Chem. 1985, 57, 1103.
3562 The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 ligand (Le., about -20 eu per H 2 0 addition and -22 eu per C H 3 0 H addition), the cumulative entropy change for CI-(CH30H)(H20) would be expected to be about 2 eu more negative (larger -AS) and those for C1-(CH30H)(H20)2and CI-(CH30H)*(H20) about 5-8 eu more negative. A forcing by water of methanol into an “open” configuration from the “chelate” form would result in a less negative entropy change. Releasing of the methyl group leads to less hindered internal rotations and lower vibrational frequencies associated with bending modes and CI--ligand stretching. It is worth noting that the smallest entropy change is observed in the addition of water to the neat methanol cluster with the most ligands, i.e., CI-(CH,OH),. The conjectured transformation from the “chelate” to “open” configuration appears to reduce the -AS for addition of water by 4 or 5 eu per methanol molecule. In the cumulative enthalpy change, replacement of the last water molecule with a methanol molecule leads to the largest (most negative) change or, alternatively, the addition of water to a neat methanol cluster of C1- has a noticeably smaller -AH than the other addition reactions within a given rank. The conclusion is that water and methanol interfere with water having a particularly strong effect on the interaction of methanol with CI-. Preferential Soloation. The preference factor for a particular species in mixed cluster ions of a given rank r (number of solvent molecules) relative to the binary vapor composition can be expressed as the ratio of methanol to water molecules in the family of clusters of rank rover the ratio of methanol to water molecules in the gas phase.” The ratio of methanol to water molecules for cluster ions of a given rank can be calculated in a straightforward manner from the Gibbs free energies for the switching reactions Q*A,j+lBj-l
+B
Q*APjBj
+A
(4)
with the equilibrium constant
where [I,] and [Ihl] represent the concentrations of the cluster ions Q*.AP,Bj and Q*-Arj+lBl-l, respectively, and pA and pB are the partial pressures of the clustering species. Each cluster concentration is related by
By normalizing to the total concentration of cluster ions of rank r, the fraction li of cluster ions QfA,,Bi in rank r is (7)
and the fraction zB of clustering molecules that are species B is r
zB = ( I / r ) C i I i i- I
ZA
= 1 - ZB
(8) (9)
so the preference factor for clusters of rank r is a, =
ZB/ZA
PB/PA
A preference for species B occurs when a, is greater than unity, and a preference for species A occurs when a, is less than unity.
Kebarle and co-workers” found in small clusters of rank 6 and less that the proton is preferentially solvated by methanol compared to water with respect to the composition of the vapor. They also found that the extent of the preference, a,,diminished with increasing rank r and by extrapolation estimated that a preference for water would be observed for clusters containing more than nine solvent molecules. By examining competitive decomposition processes in cluster ions, Stace and Shukla12 verified the shift in preference. Kebarle et al.” also found that the preference factor for the H+-water-methanol system was nearly independent of the vapor
Evans et al.
I
K’,c3
i
‘
.I 0.0
0.2
0.4
0.6
0.8
I
I .o
Melhanal v a p o r male fraction
Figure 9. Preference factor a, versus methanol vapor mole fraction for water-methanol system for H+(rank r = 3 and 6) and CI-and Kt ( r = 3).
composition except for a possible indication of an increase in a, at low methanol vapor mole fraction. Kebarle determined a, directly from measured ion intensities at various vapor compositions. Thus experimental scatter a t low methanol vapor concentrations obscured the trend. The thermodynamic definition of a, shown above along with the free energies of Meot-Ner13 clearly confirm Kebarle’s results. The calculations for a3and a6 are shown in Figure 9. The sharp increase in a,below about 10% methanol in the vapor is due to the tendency of the clusters to incorporate readily the first methanol molecule owing to larger proton affinity of methanol compared to water. The preferential solvation for K+ and CI- clusters with three solvent molecules (the highest cluster rank with complete data), on the other hand, does vary with the gas composition as shown in Figure 9. The values for a, are calculated based on the cumulative free energies for clusters of rank 3 given in Figure 8 (Le., the free energies for switching that are given in parentheses). Calculation of a, based on free energies of switching reactions determined from the direct differences in experimental values for the addition (onto the cluster ions of rank 2) of water versus methanol yield similar trends; however the magnitudes of a3are up to a factor of 2 smaller for CI- and as much as a factor of 2 larger for K+. Within the experimental uncertainties, the values of a3and its dependence on methanol vapor mole fraction for C1and K+ are quite similar. The preference factors are much nearer unity than those for the small protonated clusters. Preference for methanol appears greatest in the neat vapors and lowest in the more mixed vapors. The ions even possibly have a preference for water (a< 1) in the mixed vapors (methanol mole fractions about 0.3-0.9). Larger cluster ranks were not measured, so no meaningful conclusions with regard to the number of solvent molecules can be made. Comparisons of the Difjrences of Ionic Solvation Reactions in the Gas Phase and Condensed Phase. For comparison with solvation of an ion in the condensed phase, one must recall that the clustering of molecules onto an ion in the gas phase involves both solvation of the ion and condensation of the solvent molecules. In the limit of very large cluster ions, the influence of the ion becomes negligible and the thermodynamic quantities for the stepwise clustering reaction approach those for condensation of the solvent molecules. For the very small clusters, the ionsolvent
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3563
Gas-Phase Mixed Solvent Cluster Ions
Y I
;:I
IO
01 0
'
'
I
'
2
' 4
3
'
'
5
6
, " ' . * 7""
1
1 4 0 ' '
i
2t -0
"
2
1
3
2
5
4
6
"
4
"
6
"!
"
a
0.
Number o f solvent Molecules
Figure 11. Same as Figure 1la except QI is CI- or K+, as indicated, and
7"-
Qsis H+.
Number o f molecules
Figure 10. (a) AGOzg8 versus cluster size n for reaction 12 where QI is CI-,Q2 is K+, and S is water or methanol, as indicated. (b) Same for AH'.
interactions dominate. Two approaches have been taken to negate the thermodynamic contribution of condensation to the gas-phase data in order to make the data for clustering onto gas-phase ions more directly comparable to single-ion liquid-phase values. One approach is to subtract the contribution of the formation of the neutral cluster^:^^'^
Q'
+ nS
--
(S), net:
Q*
Q'(S),
(lla)
nS
(lib)
+ nS + ( S ) ,
Q'(S),
+ nS
(1 1) Straightforward use of the thermodynamics for the bulk-phase condensation is not appropriate since one must consider the surface contribution (the Kelvin effect) for small cluster^.^ Information on neutral clusters, however, is quite limited. Curtiss and BlanderU have reviewed the thermodynamic information on uncharged clusters of hydrogen-bonded systems and some results for methanol-water trimers have been inferred from the thermal conductivity of the vapors of the binary mixture.23 Even in the case of adequate data, simply accounting for the thermodynamics of the neutral clusters may be unsatisfactory because of an especially stable neutral cluster as has been implied for the methanol tetramer. In this case, the trends implicated in the ionic solvation contribution are strongly perturbed by peculiar solvent-solvent interactions in the small neutral clusters. Hiraoka and Mizuse,I9 in their comparison, approximated the neutral contribution to be half that of the bulk phase condensation. The other approach considers the difference between two different ions QI and Q2:
QI + nS Q2(S)n
-
+
Qi(s),
(12 4
+ nS
(12b)
Q2
net: QI+ Q2(S)n Qi(S), + 42 (12) Arshadi et al.3 demonstrated the utility of this approach for comparing data on gas-phase clustering to bulk-phase single-ion solvation. In bulk-phase studies, measurements are usually conducted on ion pairs. To separate the individual contributions of the cation or anion into the thermodynamic functions for single ions, some particular extrathermodynamic assumption is neces+
L. A.; Blander, M. Chem. Reu. 1988, 88, 824. (23) Curtiss, L. A.; Frurip, D. J.; Blander, M. J . Chem. Phys. 1981, 75,
0.2
0.0
-
0.4
0.6
0 8
1 0
Methanol Mole Fraction
Figure 12. (a) Gibbs free energy change for the reaction CI-(solv), + K+(g) K+(solv), + CI-(g) in the water-methanol solvent system versus mole fractions of methanol as solvent molecules. Points are present data for these solvent molecules. Solid line is based on recent results for transfer of these ions from water to methanol-water solutions in ref 8 and the hydration values in ref 24. The dashed line indicates earlier data of ref 26. (b) Same for AHo.
saryUmThe gas-phase data do not involve any extrathermodynamic assumption. In Figure loa, we compare the free energy change for reaction 12 for solvation by water and methanol as a function of cluster size n, where QI is CI- and Q2is K+. The trends show a good correlation with the accepted values from the bulk-phase single ion free energies of s o l ~ a t i o n . ~ ~ ~ ~ ~ The enthalpy changes for clustering, on the other hand, do not exhibit a very good indication .of the bulk-phase values (see Figure lob). The gas-phase clusters include four to six solvent molecules, so one may argue that the primary solvation shells are not complete for one or both of the ions. However, the trend in enthalpy changes does not suggest that results for clusters with a few more solvent moleculas would significantly improve the agreement between the
(22) Curtiss, 5900.
a
a
(24) 1.
Desnoyers, J. E.; Jolicoeur, C. Mod. Aspects Electrochem. 1%9,5,
3564
J . Phys. Chem. 1991, 95. 3564-3568
gas-phase and bulk-phase enthalpy values. This situation appears to be another manifestation of enthalpy-ntropy compe.nsati~n.~J~ The bulk solvent surrounding the primary solvation shell will produce enthalpy and entropy contributions as a dielectric medium under the influence of an electric field, but the enthalpy and entropy contributions offset each other to produce little effect on the free energy of solvation. The enthalpy-entropy compensation effect indicates that the free energy of reaction 12 should compare well with the condensed phase at a rather small value for n, corresponding to the size of the primary solvation shell. Whereas, a large value for n may be necessary for a reasonable comparison of the enthalpy and entropy. It may be rather fortuitous that the free energy compares so well with the condensed phase a t a cluster size as small as n = 4. Considering the ion pair CI- and H+ (Figure 1l), the free energy difference for the water cluster ions closely approaches that for bulk-phase hydration. The comparison is much poorer in the case of methanol. Similar to CI- and H+ with methanol, the difference between K+ and H+with methanol does not agree well with that for the bulk phase. The difference for ions of like sign does not rely on extra thermodynamic assumptions, so there is little variance in the reported values for the bulk phase. The basis for the disparity with methanol thus rests elsewhere. Now consider the binary water-methanol system. Illustrated in Figure 12a is the free energy change for reaction 12 with three solvent molecules and for the bulk liquid as a function of methanol mole fraction. The ion cluster results follow the recent bulk-phase (25) Yu, H. A.; Karplus, K. J . Chem. Phys. 19%8,89,2366. R. Lumry, H. A.; Rajender, S.BiopoIymers 1910, 9, 1125.
determinations. The earlier bulk-phase values% for the difference between C1- and K+ are obviously inconsistent with the present results on the gas-phase cluster ions. Similar to the situation for the one-component solvents, considerable disparity exists between the gas and liquid phase for the enthalpy (Figure 12b). The behavior of the entropy basically mirrors that of the enthalpy. Summary
The trends in the thermodynamic functions, AGO, AH’, and
ASo,for the clustering of water versus methanol onto H+, K+, and CI- are qualitatively consistent with the thermodynamics of condensation and ion transfer for the two solvents. For clusters containing three solvent molecules, C1- and K+ exhibit a much weaker preference for methanol than does H+ in the mixed methanol-water system. The differences in the changes in the free energy for clustering onto K+ and C1- show a good correlation with the corresponding values for solvation by the liquids. The enthalpy-entropy compensation effect appears to be operative since the comparison is rather poor for enthalpy and entropy changes. For C1- clusters, water appears to shift methanol from a “chelaten configuration with an interacting methyl group to an “open” more linear hydrogen bond.
Acknowledgment. Financial support by the National Science Foundation, Grant No. ATM-87- 14095, is gratefully acknowledged. Registry No. CH,OH, 67-56-1; K,24203-36-9; CI,16887-00-6. (26) Andrews, A. L.;knnetto, H. P.; Feakins, D.; Lawrence, K. G.; Tomkins, R. P. T. J . Chem. Soc. A 1968, 1486. Alfenaar, M.;Deligny, C. L. Recl. Trav. Chim. Pays-Bas 1967, 86, 929.
Spatial Distribution of Free Radicals in ?-Irradiated Alcohol Matrices Determined by the 24-1 Electron Spin Echo Method Vadim V. Kurshev, Arnold M. Raitsimring, and Tsuneki Ichikawa* Institute of Chemical Kinetics and Combustion, Novosibirsk 630090, USSR (Received: April 18. 1990; In Final Form: September 18, 1990)
The magnetic dipole-dipole interaction between hydroxyalkyl radicals in y-irradiated glassy matrices of alcohols has been selectively detected by means of the 2+1 electron spin echo method for determining the structure of spurs generated by y-irradiation at 77 K. The structure is approximately the same for all the alcohols examined. One spur consists of one radical pair with an intrapair distance distribution of exp(-P/r$) and an average distance of 5 nm. It is concluded that about 40% of the initial ion pairs recombine in the spur before being stabilized in the matrices at 77 K.
Introduction Ionization and bond dissociation of molecular substances necessarily result in the pairwise formation of paramagnetic species such as ion radicals and neutral free radicals. The pairwise correlation of the paramagnetic species is maintained in a lowtemperture solid, where the diffusion of the paramagnetic species is highly restricted. Such a spatial correlation is an important factor controlling the yield of stable products. For example, if free radicals are formed in close vicinity of the paired radicals, the molecular products of initial radical-radical reactions can be obtained with high efficiency even though the bulk concentration of the free radicals is quite low. To determine the local spatial
distribution of free radicals is therefore important for elucidating radical reactions. One of the most direct methods for determining the spatial distribution of free radicals is to measure their paramagnetic relaxation rates by means of an electron spin echo (=E) method. Paramagnetic relaxation is the recovery of electron spin states after excitation by microwave radiation to the thermal equilibrium states, and is categorized into longitudinal and transverse relaxations.’ Longitudinal relaxation is the recovery of electron spin energies at an on-resonant spectral position that is induced by the change of the spin quantum states of on-resonant spins (A spins) and by the spectral diffusion of the A spins to the off-resonant
*On leave from the Faculty of Engineering, Hokkaido University, Sapporo, 060 Japan, where correspondence should be addressed.
( 1 ) Salikhov, K. M.; Tsvetkov, Yu, D. In Time Domain Electron Spin Resonance; Kevan, L., Schwartz R. N., Eds.;Wiley-Interscience: New York, 1979; pp 231-277.
0022-365419 112095-3564%02.50/0 0 1991 American Chemical Society
