2363
TUNNEL EFFECT, IR CONTINUUM, AND SOLVATE STRUCTURE
Tunnel Effect, Infrared Continuum, and Solvate Structure in Aqueous and Anhydrous Acid Solutions by Ilse Kampschulte-Scheuing and G . Zundel Physikalisch-Chemisches Institut, Unisersitdt Mfinchen, Munich, West Germany
(Received October 31, 1969)
Continuous absorbance occurs in the ir spectrum of hydrous acid solutions, if the acid is dissociated. This indicates that the excess protons tunnel in hydrogen bonds between solvent molecules. A pair of bands shows whether the nondissociated acids are associated. If the solvent molecules have no hydrogen bond acceptors, the p-toluenesulfonicacid molecules, nondissociated and associated, are found. If the solvent molecules have acceptor groups, the acid is all the more disassociated and dissociated, the more basic the solvent molecules. The continuous absorbance shows that the tunnel protons have a continuous energy level distribution, Le., are in energy bands. Two mechanisms which give rise to the energy bands are discussed. The first is the interaction of the tunneling protons by proton dispersion forces and the second, the interaction of the tunneling protons with the Coulomb fields of the neighboring anions. A saturation effect of the intensity of the continuous absorbance in the case of the dimethyl sulfoxide (DMSO)solution is found. With solutions in water and in methanol, the continuous absorbance in the range 2500-650 cm-1 is independent of the wave number. With the DMSO solution, however, the continuous absorbance shows a structure. This is explained by considering the nature of the solvate structure of the DMSO solution.
Introduction Continuous absorbance is observed in the ir spectra of hydrous solutions of acids and bases when dissociated‘ and also especially in the spectra of hydrated acidic and basic polyelectrolytes with dissociated This indicates that the protons and defect protons exist in energy bands.3 This continuous absorbance is closely connected with the tunneling of the protons in hydrogen bonds of the hydrate structures. A proton tunneling in a hydrogen bond isolated from its environment leads merely to a splitting up of the energy levels but in no case to a continuity of levels. The continuity results because the tunneling of the proton is connected with a fluctuation of the electromagnetic field near the hydrogen bond. Neighboring tunneling protons are now coupled via these fluctuating fields.* This coupling via the so-called proton dispersion forces leads to a shifting or splitting up, respectively, of the energy levels of the tunneling protons. A second cause of the energy level shift of the tunneling protons is the interaction with the Coulomb fields of the neighboring anion^.^ The magnitude of the shifts and splitting up depend on the distance and orientation of the hydrogen bonds with the tunneling protons as well as on that of the anions and the hydrogen bonds with the tunneling protons. The distances and orientations have random statistical distributions in the solutions and with the polyelectrolytes. The distances of the energy levels thus also have a random statistical distribution, which leads to the continuous ir absorbance observed. The proton dispersion forces, like the interaction of the tunneling protons with the anions, cause a decrease in the tunneling frequency which, however, does not
fundamentally affect the forces themselves. A more detailed discussion of the interplay of the proton dispersion forces and the anion fields on occurrence of the continuous absorbance is shortly to appear. If acids such as toluenesulfonic acid, for instance, are not dissociated, a pair of bands is observed when the acid groups are associated. (One band in the range 3000-2700 cm-l and one in the range 2450-2150 cm-l.) These bands show that the acid groups are cross-linked via extremely strong hydrogen bonds.1° These bonds are so strong, because on the one hand the hydrogen bond donator property of these OH acid groups is extremely large, and on the other the acceptor property of the two double-bonded 0 atoms of the -SOzOH group is quite considerable. The latter ensues from the fact that the bonding electrons in this ion are rearranged when the corresponding excess proton approaches. l1 (1) T. Ackermann, 2. Phys. Chem. (Frankfurt am Main), 27, 253 (1961). (2) G. Zundel, H. Noller, and G.-M. Schwab, 2. Elektrochem., 66, 129 (1962). (3) G. Zundel and H . Metzger, 2. Phys. Chem. (Frankfurt am Main), 58, 225 (1968). (4) G. Zundel and H. Metzger, 2. Naturforsch. A , 22, 1412 (1967). (5) T.Ackermann, G. Zundel, and K . Zwernemann, 2. Phys. Chem. (Frankfurt am Main), 49, 331 (1966). (6) G. Zundel and H. Metzger, 2. Phys. Chem. (Leipzig), 240, 50 (1969). (7) G. Zundel, “Hydration and Intermolecular Interaction,” Academic Press, Inc., New York, N. Y., 1969. (8) E. G. Weidemann and G. Zundel, 2. Phys., 198, 288 (1967). (9) E. G. Weidemann and G. Zundel, 2. Naturforsch, A , in press. (10) G. Zundel, H. Metzger, and I . Scheuing, 2. Naturforsch. B, 22, 127 (1967). (11) G. Zundel, 2. Naturforsch., A, 22, 199 (1967).
The Journal of Physical Chemistry, Vol. 74, N o . 11, 1970
2364
ILSE KAMPBCHULTE-SCHEUING AND G. ZUNDEL Wavelength,
@.
0.0 C
;0.2
0
-e
$ 0.4 0.7 1.0 1.5
tso
380036003400 32003000 2800 2600 2400 2200 2000 1800 1600 1400 1200 1000 800650 Wave number, cm-’
Figure 1. Ir spectra of solutions of p-toluenesulfonic acid in dependence on the concentration, at 30’: (a) rolution in DMSO, thickness of film 10 p, spectrum 1 saturated solution (3.29 M ) ; spectra 1 to 8 decreasing concentration; 9 is the spectrum of the pure DMSO; (b) solution in HzO, thickness of film 5 p, spectrum 1 saturated solution (5.08M ) , spectra 1 to 9 decreasing concentration; (c) solution in CHsOH, thickness of film 10 p, spectrum 1 (concentration 1.96 M ) ; spectra 1 to 8 decreasing concentration; 9 is the spectrum of pure methanol.
Both bands are caused, according to Hadii, et al.,12013a without hydrogen bond acceptors, the above-mentioned pair of bandslo is always observed, thus indicating the by the stretching vibration and by the overtone of the bending vibration of the OH group. These vibrations association of the -SOtOH groups. According to this, the acid groups of the p-toluenesulfonic acid molecules are coupled by Fermi resonance (for details see ref 13b). are not dissociated in these solvents, but associated via The present work deals with continuous absorbance, extremely strong hydrogen bonds. the tunnel effect, the interaction of tunneling protons with their environment, and solvate structure of p-toluThe picture is quite different in the case of solvents with hydrogen bond acceptors. A band a t 907 cm-’, enesulfonic acid in water and in anhydrous solvents with and without hydrogen bond acceptors. which is ascribed to the stretching vibration of the SO single bond in the nondissociated -SOzOH groupll gives Hydrogen Bond Acceptors of the Solvent
and Behavior of the Acids If anhydrous p-toluenesulfonic acid is dissolved in CC14, CHCI,, CH2C12,CaHa,C7Hs, that is, in solvents The Journal of Physical Chemistry, Vol. 74, No. 11, 1970
(12) D.Hadii, Pure A p p l . Chem., 11, 435 (1965). (13) (a) D. Had% and N. Kobilarow, J. Chem. Soc., 439 (1966); (b) see ref 7,pp 124-142; ( 0 ) see ref 7,p 124 ff.
2365
TUNNEL EFFECT, IRCONTINUUM, AND SOLVATE STRUCTURE information on the dissociation. This band disappears with dissociation and thus constitutes a measure of the true degree of dissociation.7 This band cannot be observed in the spectra of the solutions in dimethyl sulfoxide (DMSO) and water (Figures la-lc); accordingly almost all acid protons are removed from the anions also in the saturated solution a t 25'. The spectra of the solutions in methanol show this band at 907 cm-1. It disappears with increasing dilution; i.e., the acid groups dissociate increasingly. With concentrations greater than 1.96 M acid in methanol, one broad intensive band at about 2935 cm-l and one somewhat weaker a t 2425 cm-l are found in the spectrum. (These spectra are not shown in Figure IC.) These bands show that some acid groups are associated. The disassociation and dissociation of the acid in dioxane is even slighter. I n general, the acid is the more disassociated and dissociated the more basic the solvent molecules are. With these solvents the pK, values of the removal of the H+ attached to the solvent molecules are very small and thus difficult to determine. Values of the DMSO are given by Andersen, et aZ.,14 and Arnett.15 With regard to the pK, value of water data are given in the publication of Arnett.ls The pK, value of methanol . ~ ~ was investigated by Weston, et ~ 1 Unfortunately, the used methods are very different from one another. Consequently, these values are not comparable and can not be used in this work as a quantitative measure for the basicity. I n summary, we can state that the p-toluenesulfonic acid dissolves undissociated as an associate in solvents without hydrogen bond acceptors. Disassociation and dissociation occur in solvents with hydrogen bond acceptors. This disassociation and dissociation is larger, the greater the proton acceptor property, that is, the basicity of the solvent.
Continuous Absorbance and Continuous Energy Level Distribution of Tunneling Protons in the Anhydrous Solutions I n Figures l a and IC, spectra 1 are the spectra of the anhydrous solution of p-toluenesulfonic acid in DMSO or methanol, respectively. The spectrum in Figure 2 is that of p-toluenesulfonic acid-& in CH30D. These figures show that the acid protons cause continuous absorbance in the anhydrous solutions, too. This begins, if H + is present, a t 3200 cm-' and, inasfar as D+ is present, a t 2400 cm-l, and extends to smaller wave numbers. The acid protons removed from the anion form hydrogen bonds between DMSO or between methanol molecules, respectively. The continuous absorbance shows that the excess protons occur in continuous energy level distribution, i.e., in energy bands. This continuity is caused, as previously discussed, by symmetrical hydrogen bonds with double minimum potential well
Wove number, cm-'.
Figure 2. Ir spectrum of p-toluenesulfonic acid-& in CHsOD.
I
X.
C H 3 - 0 . . . . . t ~ , , . , H20-CH3 I
H
Figure 3. (a) Symmetric potential well with double minimum; (b) proton boundary structures.
(see Figure 3a) in which the proton tunnels. Therefore this hydrogen bond is represented by two proton boundary structures (Figure 3b). Thus, with these systems, too, the fluctuating fields connected with the tunneling may cause proton dispersion forces which act between the groupings. A second cause of the continuity of energy levels is the interaction of the tunneling proton with coulomb fields of neighboring anions. The result, that the acid proton is bound between the DMSO molecules and does not remain in a hydrogen bond between an oxygen atom of the -SO3- ion and one DMSO molecule, is confirmed by the nature of the band of the antisymmetric stretching vibration of these ions observed a t 1200 cm-'. I n hydrous or hydroxylic solvents this band shows a doublet structure because the degeneracy is removed by varying degrees of interaction of the three oxygen atoms in hydrogen bonds.17"tb This band, however, does not show doublet structure in the case of the DMSO solution (Figure la). This tells us that the acid proton does not remain in a hydrogen bond between the -SOa- ion and a DMSO molecule. According to the above, it must be bound in a hydrogen bond between the 0 atoms of two DMSO molecules.
Concentration Dependence of Continuous Absorbance Figures la-lc show that the absorbance of the continuous spectrum increases with increasing acid concentration. The concentration dependence for (14) K. K. Andersen, W. H. Edmonds, J. B. Biasotti, and R. A. Strecker, J . Org. Chem., 31, 2859 (1966). (16) E. M. Arnett, Progr. Phys. Org. Chem., 1 , 283 (1963). (16) R. E. Weston, S. Ehrenson, and K. Heinzinger, J . Amer. Chem. Soc., 89, 481 (1967).
(17) (a) G. Zundel and A. Murr, 2. Naturforsch., A , 21, 1640 (1966); (b) see ref 7, pp 37 ff and p 172; (c) see ref 7, pp 119 ff.
The Journal of Physical Chemistry, Vol. 74, No. 11, 1970
2366
ILSE KAMPSCHULTE-SCHEUINC AND G. ZUNDEL
0)
5: 0.6
Concentrotion, M.
Concentiation, M,
a
b
Co nce n t rat io n ,
M.
C
Figure 4. Absorbance of the continuous spectrum of t'he solution of p-toluenesulfonic acid in dependence on the molar concentration: (a) Solution in DMSO; (b) Solution in HnO; (c) Solution in CHIOH.
0.2
$ 0.4 0
e
a
n
0.7 1.0
1.5 a,
Wave number, cm-'
Figure 5. Ir spectra; - - - -, p-toluenesulfonic acid in , p-toluenesulfonic acid-& in (CD3)2SO. DMSO;
-
to a concentration of the tunneling protons of approximately 2 M ; then the slope diminishes subsequently. The linear increase is immediately comprehensible. The absorptivity coefficient of the tunneling protons is independent of the concentration in the concentration range investigated in the case of the HzO and methanol solutions. The same holds good for the solution in DMSO with concentrations up to 2 M . With larger concentrations, however, the absorbance per tunneling proton decreases as the concentration increases. A saturation effect of the absorbance of the continuous spectrum is observed. A similar saturation effect mas studied in detail with polystyrenesulfonic acid.lsaIb
Structure of the Continuous Absorbance various wave numbers is plotted in Figures 4a-4c. The wave numbers used for evaluation were so chosen that a superposition of the continuous absorbance by solvent bands was avoided as far as possible. The absorbance of the continuous spectrum dependent on the concentration of the tunneling protons and not of the acid concentration is of interest. I n DAIS0 and in HzO the acid is almost wholly dissociated; thus these two concentrations are equal. I n CHIOH a t higher concentrations the dissociation is incomplete. The concentration of dissociated acid groups and hence the concentration of tunneling protons can be calculated from the integral absorbance of the 907-cm-l band. The absorbance of the continuous spectrum dependent on the calculated tunneling proton concentrations is shown as the points on the straight line in Figure 4c. Figure 4 demonstrates the following findings : first, with HzO and CHIOH solutions the absorbance of the continuous spectrum increases in linear proportion to the concentration of the tunneling protons in the concentration range shown in Figure 4 (in the case of HzO up to the saturated solution). Second, in the case of the solution in DMSO a linear relationship is found up The Journal of Physical Chemistrv, Vol. 743N o . 11, 1970
With the solution in water or methanol, respectively, the absorbance of the continuous spectrum is independent of the wave numbers in the range 2500-650 cm-l; this can be seen from Figures l b and I Cas well as from Figures 4b and 4c. Contrary to this, in the solution in DMSO the continuous absorbance in the range of large wave numbers is considerably smaller than in the range of smaller wave numbers; thus it shows a distinct structure; this is illustrated by Figures l a and 4a. The rise in intensity of the continuous absorbance of the DMSO solution a t about 1600 cm-l with decreasing wave numbers is caused by the tunneling protons since it cannot be observed when, instead of tunneling protons, tunneling deuterons are present (see Figure 5 ) . Then, a rise at about 1200 cm-l is found, however, largely masked by the SO bands. The rise observed in the spectra of the solution in methanol results from the extremely widened OH bending vibration of the methanol molecules. This finding, that the continuous spectrum with the DMSO solution has a structure, con(18) (a) G. Zundel and H. illetzger, 2.Phys. Chem. (Leipzig), 235, 33 (1967); (b) see ref 7, pp 187-192.
2367
TUNNEL EFFECT, IRCONTINUUM, AND SOLVATE STRUCTURE
I
H-
-5
0
,.
b
Figure 6. Solvate structures of solutions of p-toluenesulfonic acid in: (a) DMSO, (b) HzO, (c) CHIOH. I n considering such schematic representations, we should keep in mind the fact that the solvate structures are continually being rearranged by thermaI motion^.^^-^^ Any attachment position is in dynamic equilibrium with analogous alternative positions. Thus the pictures show temporary equilibrium configurations.
trary to the water and methanol solution, can easily be understood when comparing the nature of the solvate structures in Figure 6.19-22 I n the hydrous solution, the excess proton tunnels in the hydrogen bond of HbOZf or bonds of HP04+, respectively.23~ The external water molecules of this grouping are linked via hydrogen bonds with further water molecules or acceptor groups of anions (Figure 6b).23b The network of the solvate structure of the CHaOH solution does not differ considerably from that of the hydrous solution, since in the spectra-as shown in Figure le-no band of the stretching vibration of free OH groups occurs, ie., of groups not bound in hydrogen bonds. Thus, as in the case of the hydrous solution, the groupings around the tunneling excess proton are linked with further CHIOH molecules or acceptor groups of anions. The linking of the HzO and CH30H molecules with the anions is indicated by the doublet structure of the band of the antisymmetric stretching vibration of the anions a t 1200 cm-l (Figures l b and IC); this splitting up-as already mentioned above-is brought about by the elimination of the degeneracy of this vibration. The elimination of the degeneracy, however, results from the varying engagement of the individual 0 atoms of the -SO3- ions with hydrogen bonds of the solvate structure and thus indicates the linking of anions with the CH30H molecules. The nature of the solvate structure of the DMSO solution differs considerably from this as indicated by this band too, since in this case the band a t 1200 cm-l h.as no doublet structure (Figure la). Following this, the DMSO-H +-DMSO complexes are not cross-linked (Figure 6a). Contrary to the solution in HzO and CH30H in the DMSO solution no steric constraint is exerted by the network of the hydrogen bonds on the groupings with the tunneling excess proton. The groupings with the tunneling protons are therefore
able to orient themselves to one another and to the anions. Therefore, however, more definite distances and orientations occur preferably. A random statistical distribution of distances and orientations is, however, a necessary requisite for the occurrence of a continuity of energy levels. This is seen on examining the equations for the energy level shifts by the proton dispersion forcesz4 or by the influence of electric fieldsg of neighboring anions on the bonds with tunneling protons. The magnitude of the shift, for example, of the lowest energy level of a pair of hydrogen bonds with tunneling protons by the proton dispersion forces is according to ref 8 or ref 7 , p 205
AE
=
hvo[ 1
-d 1 +
(5&)"I
where vo is the tunnel frequency, p the dipole moment of a proton boundary structure, e the dielectric constant of the medium between the tunneling protons (if the tunnel frequencies are high, the optical dielectric constant is decisive). g is a factor which considers the orientation of the hydrogen bridges to one another. It assumes values at the interval 2 2 g 2 -2; R is the distance of the bridges between the tunneling protons. I n Figure 7 the energy levels are plotted as a function of the distance of the bridges for a pair of bridges with tunneling protons.7r8 If the distance R and the orientation factor g has an accumulation value for certain
(19) T. J. Swift and R.E. Conniok, J . Chem. Phya., 37, 307 (1962). (20) H. G. Hertz and M. D. Zeidler, Ber. Bunsenges. Phys. Chem., 67, 774 (1963). (21) H. G. Hertz and M. D. Zeidler, ;bid., 68, 821 (1964). (22) M.Eigen, Pure Appl. Chem., 6 , 97 (1963). (23) (a) See ref 7, p 166 and 179; (b) see ref 7, p 180 ff. (24) See ref 7, pp 203, 205, and 210. The Journal of Physical Chemistru, Vol. 74, No. 11, 1970
2368
ILSEKAMPSCHULTE-SCHEUING AND G. ZUNDEL
€0 -1
P aa I
QI
c 0
+
t
*' €0-0-
+ Y-
JinA
Eotot I
Figure 7 . Shift or splitting, respectively, of the energy levels of a pair of tunneling protons in dependence on the distance of the hydrogen bonds (after ref 7 ) . o+o- means, for instance, that one proton is in the state $ot and the other in the state
distances and orientations, the energies of the individual transitions have accumulation values as well. Therefore, if-as in the DMSO solution-no steric constraint is exerted on the groupings with the tunneling protons by the solvate structure network, the former can orient themselves more definitely in relation to their environment. Thus more definite distances and orientations are preferred, resulting in accumulation values of certain wave numbers. Thus the continuous absorbance, however, exactly as observed with the DMSO solutions, is given a structure.
ExDerimental Procedure The anhydrous p-toluenesulfonic acid was produced from the commercial monohydrate by drying under vacuum at 40". After approximately 130 hr a constant pressure of 5 x 10-5 Torr sets in. This indicates complete drying.
The Journal of Physical Chemistry, VoL 74,No, 11, 1070
The p-toluenesulfonic acid-dl was produced by repeated treatment of dry p-toluenesulfonic acid with DzO and subsequent drying. CH30H and DMSO were dried over a 3-A molecular sieve. I n the case of DMSO, the molecular sieve must be replaced once or twice. Towards the end of the drying process, warming must be undertaken for some hours with the DAISO. The solutions were examined in an ir cell with variable thickness of the film. This cell was improved as against the usual type in the following way. The cell windows consist of germanium. I n order to prevent loss by absorption, this must be ?+dotted (specific resistance > 50 ohm cm). The cell is completely lined with platinum, thus eliminating any acid corrosion. A vernier with 51 divisions permits a precise adjustment for the thickness of the film. A Teflon 0 ring with a groove ensures that the cell is well sealed. The cell is fitted outside with a channel all round which allows thermostatization of the cell by circulating water. All spectra are for 30". The measurements were effected with the PerkinElmer ir double-beam spectrophotometer Model 221, On account of the high loss of reflection of the germanium slit program 980 was used. Registering speed amounted to one wave number per second. The sensitivity was checked during plotting of the spectra. I n order to eliminate loss of energy through absorption of the water vapor in the air, the spectrophotometer was flushed with dry air. The spectra drawings are corrected by a calibration curve plotted with the help of the values given in ref 25. Acknowledgment. We should like to express our thanks to Dr. E. G. Weidemann of the Institute for Theoretical Physics, Munich University, for many valuable discussions. Our thanks are also due to the Deutsche Forschungsgemeinschaft and the Frauenhofer Gesellschaft for providing the facilities for this work, and to the VW-Stiftung for a grant. (25) "Tables of Wave Numbers for Calibration of Infrared Spectrometers" Butterworth and Co., London, 1961.
