P. F. Rusch and J. J. Lagowski
21 0
probably, the monomer bound dye interacts with the benzene rings of the PSS chain through the T orbitals, such interactions are mainly of the same nature as those ruling the stacking of the dye molecules. For this reason an energy compensation may be expected in the dimerization process. We would also like to bring to the reader's attention the negative A§, values as compared with the positive one in water. This fact might suggest that hydrophobic interactions41.42 are much lese involved in the process of dye aseociation along the polyelectrolyte chain than in the corresponding process in water. Finally we have studied the effect of added NaCl on the PSS-A0 equXhrium1. As expected the addition of an excess of salt dacreases the binding strength of the dye and
increases the concentration of free dye in solution (see Figure 9A). This effect may be attributed mainly to the decrease of the { potential on the macroion due to addition of salt.29 On the other hand, the salt increases the stacking coefficient of the dye, as found for other polyelectrolytesl4 and for the free dye in ~ a t e r . ~ 3 A . ~plot 4 of the 41 stacking coefficient as a function of the NaCl concentration a t 20" is given in Figure 9B. G. Nemethyand H. Scheraga, J. Chem. Phys., 36,3382 (1962). G. Nemethyand H. Scheraga, J. Chem. Phys., 36, 3401 (1962). G. Barone, L. Costantino, and V. Vitagliano, Ric. Sci., 34 (11-A), Vol. 6, No. 1, 87 (1964). The q 2 parameter must be taken only as a fitting parameter for these runs. We have only used spectrophotometric data obtained at low D I P values ( D I P < 0.02-0.03) which are more reliable for computing the 9, parameter.
Metal- Am moni Solutions. IX. Vibrational Spectroscopy of the Solvent
. F. Rusch and J. J. Lagowski" Department of Chemistry, The Universityof Texas at Austin, Austin, Texas 78712 (Received July 12, 1972) Publioafion costs assisted b y the National Science Foundation and the Robert A. Welch Foundation
The infrared absorption spectra of liquid ammonia and of lithium and potassium ammonia solutions have been obtained in the 3 - p region at -70" using a spectrophotometric cell incorporating sapphire windows. The envelope of strongly overlapping bands in the 3-r region was mathematically resolved into components which are assigned to 2V4, v l , and v3 in order of increasing energy. The N-H stretching frequency of the solvent shifts to lower energy with increasing concentration of both lithium and potassium metal. The shift is independent of the nature of the metal over the concentration range 5 X to 5 X 10 - 2 M.The results are interpreted in terms of the formation of new solvent-containing species in the presence of solvated electrons. The solvent in these new species is polarized primarily by the electron; the weakening of the N-H bond arises from the increased electron density on solvent molecules associated with the solvated electron and from coordination by the cations present in these systems.
Introduction Solutions of alkali metals in liquid ammonia have been the subject of many experimental and theoretical investigationsl.2 sintee this solvent appears to be uniquely suited for stabilizing the soivated electron. By necessity, successful theoretical descriptions of these systems require that the solvent be intimately involved in the process of stabilizing the solvated electron. For the most part both theoretical and experimental investigations of metal-ammonia solutions have been concerned with the properties of the solvated electron, only a relatively small amount of experimental work being directed toward the description of the nature of the solvent in such solutions. We present here the results of an investigation of the vibrational spectrum of liquid ammonia and of metal-ammonia solutions using conventional traQsmission techniques in an attempt to clarify the role ofthe solvent in the latter systems. Previous investigations have used proton magnetic resonance and optical reflection techniques to probe the nature of the solvent in metal-ammonia solutions. Proton magnetic resonance studies of metal-ammonia solutions3 are complicated by the fact that the magnetic properties The Journal of Physical Chemistry, Vol. 77, No. 2, 1973
of the solvated electrons cannot be completely eliminated. Optical reflection studies in the fundamental region of the infrared have proved to be only moderately successful. Beckman and Pitzer4 reported specular reflection data for sodium-ammonia solutions in the region from 1 to 20 1.1, over a wide range of concentrations. Reflection bands attributed to the solvent were observed in the 3-r region. The positions of these reflection bands cannot be directly related to the absorption bands since the optical constants *of the solutions were not obtainable from the experimental procedure used. Burow and Laguwski5 used a silicon prism to obtain internal reflection spectra of sodium-, lithium-, and potassium-ammonia solutions over a wide range of concentrations. Severe noise difficulties prevent(1) G. Lepoutre and M. J. Sienko, Ed., "Metal-Ammonia Solutions Physiochemical Properties," W. A. Benjamin, New York, N.Y., 1964. (2) . . J. J. Laaowski and M. J. Sienko, Ed., "Metal-Ammonia Solutions," Butterworths, London, 1970. (3) (a) T. R. Hughes, Jr., ref 1, p 211; (b) T. R . Hughes, Jr., J. Chem. Phys., 38,202 (1963). (4) T. A. Beckman and K. S. Pitzer, J. Phys. Chem., 65,1527 (1961) (5) D. F. Burow and J. J. Lagowqki, J. Phys. Chem., 72,169 (1968).
Spectroscopyof Metal-Ammonia Solutions ed an unambiguous assignment of the solvent bands reported in this investigation. The purpose of the present study is to investigate the vibrational spectrum of the solvent in the fundamental region of the infrared using a transmission Lechnique. ~ x ~ e ~Secti ion ~ ~ i ~ t ~ ~
An attempb was made to obtain the infrared transmission spectra of me1,al-ammonia solutions over as wide a spectral range as possible. Spectral data in the near-infrared region were used to estimate the metal concentration using the extinction coefficients of the absorption band6 near 1 5 attributed to the solvated electron. Decomposition of the solutions was monitored by the chargetransfer-to.solvent ( CTTS) absorption' at 0.335 p attributed to the amide ion. From previous investigations on liquid amrnonia,s 9 i t in known that the N-H stretching vibrations have fundamental frequencies in the region about 3 p while the bending fundamental vibrations occur in the regions around 6 and II p. Design of ti suitable optical cell required the use of a window material whkh satisfied the following criteria: (I) optical tra,nsparenc:y throughout a broad spectral region, particularly in the infrared; (2) chemical inertness toward metal-ammonia solutions; (3) thermal stability over the liquid range of ammonia (from -70 to -33"); (4) ability to form vacuuin-tig,ht seals to prevent decomposition of the solutions. Obtaining the infrared spectrum of a liquid at ambient temperatures requires that only the first two criteria be satisfied. For this reason most references on techniques of infrared spleci roscopy of liquids indicate that alkali metal halide windows and amalgamated cells can be used. For studies of aqLeous solutions alkaline earth fluoride optics are used. Unfortunately, the alkali metal halides are soluble in liquid ammoiilia and the thermal stability of alkaline earth fluorides is not acceptable. Synthetic sapphire meets most of the design criteria for use as a window material for these experiments. It is transparent in the region from 0.2 p to more than 4.5 p and is commercially available in the form of optical flats sealed to Pyrex. The graded seals have exceptional thermal stability and sapphire is inert to metal-ammonia solutions. The optical cell used in these experiments incorporated the basic design used by Gold and Jolly.10 Using ammonia gas 9 and metal-ammonia solutions of known concentrations, the cell path length was determined to be (4.2 mm which is adequate for the infrared studies of liquids. The sapphire optical cell was attached by means of ball and socket joints to a solution-preparation vessel which was similar to that reported previously6 and was contained in an evacuable dewar12 vessel described by Quinn.13 Optical windows on the dewar assembly were sodium chloride of sufficient thickness to withstand a differential pressurt? of 1 atm. Solution preparation and other techniques were those described earlier.6 The entire dewar solution vesset asseirkbly was placed in a specially constructed support stand which was designed to permit reproducible positioning in both easy-14 and Beckman IR-7 spectrophotometers. The optical cell assembly containing a freshly prepared metal-ammonia solution was transported to the Cary 14 to determine its ultraviolet-visible-near-infrared spectrum and then to the Beckman IR-7 for its infrared spectrum. After the infrared spectrum was recorded, the cell was returned i o the Cary 14 to rerecord the ultraviolet-
21 1
visible-near-infrared spectrum to determine whether decomposition had occurred and to check the concentration of the solvated electron. Initial experiments involving the pure solvent demonstrated the need far a compromise to achieve the best instrument settings. The fundamental vibrations of ammonia in the 3-,44 region are quite intense and severely tax the ability of the instrument to perform well nn the doublebeam mode for the sample thickness employed. Although the black-body energy curve of the source of the IR-7 is highest in this region, the grating used in the double monochromator system is operating in the fourth order. Furthermore, the double-beam mode of operation was not useful because of the difficulties arising when an optical null instrument is used to obtain spectra of low-temperature ~ a m p 1 e s . lThe ~ inherent intensities of the bands of interest dictated the use of the 0-10% T scale on the IR-7 which further required a single-beam mode of .operation. The instrument settings selected proved to be the best compromise for scan speed, noise level, and resolution, and gave reproducible spectra with E 10-cm-I resolution in the region of the solvent absorptions.
Results and Discussion The infrared spectrum of gaseous ammonia indicates that the molecule has C3" symmetry. A molecule with this symmetry has four normal modes of vibration, all of which are both infrared and Raman active.15 The most striking feature of the gas-phase infrared spectruml6 of ammonia is that two of the normal modes occur very close together in the region near 3 p. These modes, labeled v1 and v3, are of symmetry types A1 and E, respectively, and are attributed to N-H stretching motions. The normal modes involving the H-N-H angle deformation are labeled v2 and v4 for the A1 and E modes, respectively. The intensities of the bending modes are markedly greater than the stretching modes and their normal frequencies are beyond the region where sapphire is transparent. Pure Solvent. The spectrum of liquid ammonia in the 0.2-mm sapphire cell is shown in Figure 1. Prominent features include the intense solvent cut-off at 0.225 iu. and the series of intense, narrow bands in the near-infrared region. The fundamental region of the infrared spectrum near 3 p exhibits an envelope of overlapping bands. Previous investigatorss.9 have attempted to resolve this envelope into components using the method of symmetrical contours, an acceptable method of area resolution which suffers from the disadvantage that only one symmetric contour may be developed at a time. The envelope appears to have three components. Two of these components are the N-H (6) D F Burow and J J Lagowski, Advan Chem Ser, No. 50, 125 (1965) (7) R E Cuthrell and J J Lagowski, J Phys Chem 71,1298 (1967) (8) I V Demidenkova and L D Scherba, Izv Akad Mauk SSSR, Ser f ( z , 22, 1122 (1958), Bull Acad S o USSR, Phys Sei-, 22, 1110 (1958) (9) C A Plint, R M B Small, and H L Welsh Can J Phys, 32, 653 (1954) I O ) M Gold and W L Jolly, lnorg Chem , 1,818 (1962) 11) F A Gunther, J H Barkley, M J Kolbezen R C Blinn, and E A Staggs, Anal Chem, 28,1985 (1956) 12) For detailed drawings specifications, and procedures, see P F Rusch, Ph D Dissertation, The University of Texas at Aubtin, 1971 (13) R K Quinn and J J Lagowski, J Phys Chem, 72,1374 (1968) (14) W J Potts, Jr , Chemical Infrared Spectroscopy, Vol I, Wiley, New York, N Y , 1963 (15) G Herzberg, 'Molecular Spectra and Molecular Structure Part II Infrared and Raman Spectra of Polyatomic Molecules, Van Nostrand-Reinhold New York, N Y , 1945 (16) R H Pierson, A N Fletcher, and E S Gantz, Anal Chem, 28, 1218 (1956) The Journal of Physical Chemistry, Vol. 77, No. 2, 1973
P. F. Rusch and J. J. Lagowski
21 2 4.0
5.0,
3.0
-
1
30
I
I -I
2.0
I
U hi
W
h:
2.0 z
a
Iix
m 0
v) 0
u) Iu
a
m
LO
4
I
1.0
d Y
Q
v
5.0
z 0 v) 2
s
i n 5.0 2 d
Lz
t-
I-
z a
0 02
4.0
W 0 I I : W
3.0
0
0.5
10
1.5
2.0
25
WAVELENGTH.
3.0
4.0
35
44
+
Figure 1. Typical spec:tra obtained in a 2 cell at -70": ,,a) liquid ammonia; (b) 5 X tion.
2.0
cm sapphire M lithium solu-
X lo-*
stretching f u ~ ~ ~ m e n tVaI land s v3 while the third is attributed to an unusually intense bending overtone which appears becauw of Fermi r e s ~ n a n c e . ~The s infrared spectrum of the pure solvent showed little spectral change as a function of te mperature. Throughout this investigation a non-linear least-squares method was employed to perform the resolution of the envelope in the 3-/®ion into its components, using a program17 which was executed on a CDC-6600 computer system.12 The band positions reported in the 3-p region were obtained from this resolution and can be considered accurate to within the resolution of the spectrophotometer. All resolutions were performed using three component bands described by either Lorentzian or a combination of Gaussian and Lorerntzian functions.18 Valid objections to the use of computer methods for resolving overlapping spectral bands exist. In general, the best least-squares fit of the data is obtained with an infinite or very large number of bands. However, in practice any envelope of overlapping bands has certain prominent features which limit the number of components to be resolved. In the absence of any well-defined structure in the envelops there may be pertinent theories which help predict the number of bands. With judicious use, the resolution of o v e r l ~ p ~ ~spectral ng bands using programs of the type described herein provides a standard method of analysis which can be kept relatively free from bias. Resolution of the envelope into three overlapping bands in the 3 - p region for the pure solvent gave the following band positions: 3151 r m - j / 2 v g ) , 3286 cm-1 ( V I ) , and 3453 cm -1 ( u s ) . The assignments are consistent with previous data and were verified in the fallowing way. Using the simple valence force field (VFF) equations for a molecule of CaU symmetrjP the positions of v3 and vq ( = 2v4/2) were used to calculate the force constants for bond stretching ant3 bond angle deformation modes. These force constants were then used to calculate the positions of V I and v2. With the frequencies of all the normal vibrations, the positions of overtone and combination bands were calculated. The results of this last calculation lead to an assignment of ail bands observed in this investigation which is in agreement with a11 past reports.*.9J5 ~ e ~ ~ l - A Solutions. ~ ~ ~ AF t high z ~ concentrations ~ of alkali mletals, metal-ammonia solutions exhibit properties more like metah, than like normal ionic solutions and they The Journal of Physic& Chemistry,
VO/.
77, NO. 2, 1973
I.0
U U 3500 3300 SI00
WAVE N U M B E R ,C m-'
Figure 2. Typical spectra of 5 X monia at -70".
M Li and K in liquid am-
reflect electromagnetic radiation4J9 very strongly. Thus only metal-ammonia solutions in the dilute to intermediate concentration range are suitable for infrared transmission experiments. From previous investigations,G it appears that there is little dependence of the spectrum of the solvated electron on the nature of the alkali metal in solution. The spectral properties of N&-, on the other hand, show some dependence on the nature of the cation. The position of the "2CTTS band varies regularly as the cation changes from Li+ to K+; for the larger cations t,he position of the CTTS band is constant.20 Based on previous data on the optical properties of metal-ammonia solutions as a function of concentration, metal, and temperature, the range of experiments was limited to the study of lithium and potassium solutions a t -70". The metal concentration was in the range 5 X 10 - 3 to 5 x M . Attempts to observe the infrared spectrum of solutions more concentrated than 5 x 10-2 M failed because the solutions were opaque to infrared radiation even in the 0.2-mm cell. The spectrum of a 5 X M Li-NH3 solution is shown in Figure 1. Even though the intense solvated electron absorption band is present a t about 1.5 p, several overtone and combination bands of the pure solvent we easily observed. The spectrum shows no evidence of the amide ion CTTS absorption at 0.335 p. Resolution of the overlapping bands in the 3-p region yields the three vibrational frequencies for 2 ~ 4 ,V I , and us. A simplified VFF calculation was performed to calculate the frequency of vp. Using this calculated value and the positions of the resolved bands, the positions of the overtone and combination bands were determined. The assignments of the fundamental frequencies of the solvent in 5 X M lithium and potassium solutions are identical with those of the pure solvent. In (17) Program RESOL was written by Dr. D. D. Tmicliff, Sheil Development Co., Emeryville, Calif., who kindly supplied t h e initial version. (18) R. P. Young and R. N. Jones, Chern. Rev., 71,219 (1971). (19) W. H. Koehler and J. J. Lagowski, J. Phys. Chem., 73, 2329 (1969). (20)J. A. Caruso, J. H. Takemoto. and J. J. Lagowski, Specbosc. Lett., 1,311 (1968).
Spectroscopyof Metal- Ammonia Solutions
21 3
TABLE I: Typical Resolved Band Positions from the 3-p Envelope 2V4 Solution
NH3
M Li 1W3M K
5 X 10-3
5 X
6 x i 0 - - 2 dM Li 6 X IO-->N K
Vt
v3
cm-1
Errora
cm-'
Error"
cm-1
Erma
31 55 31 58 31 56 31 53 3152
fl.4 f1.4 f1.4 12.0 11.4
3281 3265 3268 3250 3252
13.0 f2.7 f2.a f4.0 f3.0
3449 3429 3426 3409 341 3
k3.6 rfr2.5 12.5 f5.0 14.3
a 95% confidence levell
2.0
stroyed by the addition of an alkali metal if the general theoretical description of metal-ammonia solutions are valid .22 -23 The effect on the N-H vibrational modes when ammonia becomes associated with ions and/or forms hydrogen bonds can be deduced from the spectrum of salt solutions in liquid ammonia reported by Corset, Huong, and Lascombe.24 A series of overlapping bands with two prominent peaks assigned to 2 1 4 and v3 were observed in the 3 - p region of the spectrum of these solutions. The frequency of the v3 (asymmetric N-H stretching fundamental) vibration shifted to lower energy as a linear function of the quantity Z / x 2 where Z is the cation charge and x is the sum of the crystal radius of the cation and the radius of the ammonia molecule. In solutions of alkali metal iodides v3 of the solvent was shifted more than in solutions of the corresponding alkali metal nitrates. This anion effect i s attributed to increased hydrogen bonding between the ammonia molecules in a cation solvation layer and the iodide ion. In effect, the system can be described in terms of a solvent separated ion pair (M+ . .NH3 -X-). The infrared spectra of concentrated salt solutions in liquid ammonia suggest that two effects may be operating to weaken the solvent N-H bond in metal-ammonia solutions: coordination of the lone electron pair of the ammonia molecule to a cation and/or formation of additional hydrogen bonds. These two effects operating either separately or collectively could result in the observed lowering of the N-H stretching frequency in metal-ammonia solutions. The presence of an alkali metal in liquid ammonia has an effect on the solvent which is quite different from that of the corresponding alkali metal salts. First, in metalammonia solutions the shift of v3 i s independent of the cation (Table I). On the other hand, the cation dependence of this band in salt solutions is attributed to an ion dipole interaction of the cation with the solvent. In addition, the magnitude of the shift in v3 as a function of solute concentration is greater for metal-ammonia solutions than for the salt solutions. Thus, a 10.25 M solution of KI in ammonia leads to a decrease in v p which is 18 cm-1 lower than the pure solvent under similar conditions of pressure and temperature,24 whereas a Q.05 A4 solution of potassium metal in ammonia produces a shift of 363 cm-' in u3 relative to the pure solvent under the same conditions. The magnitude of the shift in u3 per unit solute
-
0 I 0 0 i-
LL_ILL_J 3500 3300 3100
WAVENUMBER, cm-'
Figure 3.
Typical spectra of 5
X
M Li and K in liquid am-
monia at -70".
all other metal-ammonia spectra the bands in the 3 - p region were assigned to 284, V I , and v~ in order of increasing energy. Details of tbe infirared spectra of dilute (5 X M) lithium- arid potassium-ammonia solutions are shown in Figure 2, where they are compared with the spectra of the pure solvent at the same temperature. Similar spectra are shown in Figure 3 for the more concentrated (5 X M) lithium and potassium solutions. Each of the infrared envelopes was resolved into three components assigned to 2v4, V I , and u3 in order of increasing energy. Typical resolved band positions are given in Table J and graphical representatnons of the data appear as Figures 4 and 5. The position of both the symmetric ( V I ) and asymmetric (v3) stretching fundamentals shifts to lower energy with increasing metai Concentration, the shift being independent of the nature of the cation in solution. The asymmetric bending overtone ( 2 ~ 4 )remains relatively unchanged as a function of metal concentration. Lowering of the N-H fundamental stretching vibration (VI) suggests a lower force constant for the vibration, thus implying a weakened bond. In othea syritems,21 a decrease in an N-H bond frequency has been attributed to the formation of hydrogen bonds (-H--.N-P-I) and it might be tempting to suggest a similar interpretation here. However, the normal hydrogen bonding which occurEi in pure ammonia should be de-
G. Pimentei and A. McClelian, "The Hydrogen Bond." W. ti. Freeman, San Francisco, Calif., 1960. E. Becker, R. H. Lindquist, and B. J. Alder, J. Chem. Phys., 25.
971 (1956).
D. A. Cogeland, N. R. Kestnev, and J. Jortner, J. Cham. Phys,, 53, 1189 (1970). J. Corset, P. V. Huong. and J. Lascombe, Spectrcchm. Acta., Part' ' A, 24,1385 (1968). The Journalof PhysicaiChemistry, Vol. 77, No. 2, 1973
P.F. Rusch and J. J. Lagowski
21 4
-
'E: d
3a001
34001
3900
t
Y170
I
I
5
3
3,5
oL.LL-20
[K] X 10'
Figure 4. Resolved band positions for tion of potassium concentration.
2v4, V I ,
and
v3
as a func-
concentration id approximately 400 times greater for potassium metal than for KI. Since the shift of the v3 solvent vibration 1s independent of the nature of the metal in solution (comparing Ld and K), it is inferred that the presence of the solvated edectron in liquid ammonia accounts for the observed shift. The solvated electron is a well-established species in metal-ammonia solutions and seems to be reasonably well described by the cavity mode1.23 In this model the solvated electron is supposed to be stabilized in a cavity formed by the orientation of four to six solvent molecules oriented so that the protons are closest to the center of the cavity. Solvent molecules which form a cavity have characteristics that can account for the observed infrared spectrum of the solvent in metal-ammonia solutions. First, such molecules would be expected to have weakened N-H bonds because of an increased electron density around the solvent protons which point toward the cavity. This arrangement should contribute to the observed lowering of the N-H stretching frequencies compared to that found in the pure solvent. Second, the solvent molecules in cavities are free from cation interactions because the cavities appear to be islolaled from the corresponding cations.l3 Finally, the solvated electron in a cavity polarizes the solvent molecules forming the cavity so that they have perturbed dipole a conclusion which shortly will be shown to be important. It is generally agreed that as the concentration of alkali metal is increased in liquid ammonia, aggregation of species occurs. The original description of the simplest aggregate species, +, e- was given by the expanded metal mode1.22 The basic unit of this model consists of a solvated metal cation containing an electron in an expanded metal orbital. The solvent molecules are oriented with the nitrogen atoms closest to the cation, and the electron orbital is in the region of the protons. More recently it has bem suggested10 that nonspecific aggregation of solvated ele:trons and solvated cations occurs as a function of concentration, much as would be expectedz5 for any collectam of oppositely charged species in a solThe Journal of Physical Chemistry, Vol. 77, NO. 2, 1973
[ ii] x 10' Figure 5. Resolved band positions for tion of lithium concentration.
2v4, v , ,
and
v3
as a func-
vent with low dielectric constant. In these aggregates we also would expect to find solvating ammonia molecules under the influence of cationic and electron fields. Solvent molecules in such environments can account for the observed shifts in the N-H stretching frequencies of the solvent in metal-ammonia solutions. In any case, the increased electron density about the solvent protons plus the coordination of the solvent by the cation results in a weakened N-H bond for the solvent molecules in this environment. The fundamental stretching vibrations of ammonia in metal-ammonia solutions display shifts, relative to the pure solvent, which are characteristic of a system in which hydrogen-bonded species are being formed as a function of increasing metal concentration. The formation of a hydrogen-bonded species is accompanied by a shift to lower energy for the fundamental vibration involving symmetrical N-H bond stretching.21 Often a new band, attributed to the hydrogen-bonded species containing molecules with weakened bonds, is observed as a low-energy component of the symmetric bond-stretching fundamental. Fundamental vibrations of the molecde which involve asymmetric bond stretching are also shifted to lower enetgy but usually to a smaller extent than the symmetric bond stretching fundamental. Bending fundamental vibrations are often not shifted by the formation of a hydrogen-bonded species. Assuming the most recent description of the solvated electron is correct, the concentration of solvent molecules forming the cavities should be four to six times the concentration of the alkali metal present depending on the coordination number of the electron. Using the smaller values of coordination number, the concentration of associated solvent molecules is between 0.2 and 0.3 M for an analytical concentration of alkali metal of 0.05 M, while the concentration of the bulk solvent is more than 200 times greater. If the results of nmr experi(25) (a) C . A. Kraus, J. Phys. Chern., 60, 129 (1956); (b) R . M. Fuoss, J. Arner. Chern. Soc., 80,5059 (1958).
Spectroscopy of Metal-Ammonia Solutions
ments26.21 which suggest solvation numbers in the range 20-49 for the electron are correct, the concentration of associated solvont molecules would be even larger. The concentration of the bulk molecules can be estimated from the density of the pure solvent corrected for the concentration of the associated molecules in cavities. In the case of a 5 x M alkali metal solution in liquid ammonia, the bulk solvent molecules are more than 2000 times more abundant than the associated molecules using the lower value of electron solvation numbers. Based on the effect of concentration alone, the theoretical second component of the absorption would be too weak to produce the shift observed for a dilute metal-ammonia solution. Assuming that Beer’s law is obeyed by both the bulk and the associated solvent molecules for a given vibration leads to a consideration of the extinction coefficient of the two types of solvent molecules. It is reasonable to assume that the bulk solvent molecules in dilute metal-ammonia solutions will have the same absorptivity as in the pure solvent. The polarized state of the associated molecules23 suggests that they may have a larger absorptivity than the bulk molecules. Selection rules for infrared transitions require a change in the dnpole moment of the molecule for a fundamental vibration to give use to an absorption band. Solvent molecules which form a cavity may well have larger changes in dipole moment as a result of polarization by the solvated electron and therefore also have larger absorptivity leading to a significant contribution to the absorption spectrum even at very low concentration of solvating molecules. If these arguments are correct, the absorptivity of the associated molecules should be from 50 to 2 0 times greater than the bulk solvent molecules to produce spectral components of sufficient intensity to shift the resolved band position. ummary By analogy with systems where hydrogen bonding is
21 5
known to occur it is possible to account for the shift of the v1 and v3 band positions in metal-ammonia solutions. In dilute metal-ammonia solutions the formation of cavities effectively removes molecules from the bulk solvent. The solvent molecules which form the cavities have fundamental band stretching vibrations which are of lower energy than the bulk solvent molecules. Experimentally these lower energy vibrations appear as additional components in the spectrum. The sum of the two components, one for bulk molecules and one for solvent molecules forming the cavities, would then account for the resolved band position shift to lower energy. The success of the Copeland, Kestner, and Jortner cavity model23 in predicting spectral properties of the cavityassociated solvent is significant. The modelling of the cavity-associated solvent properties was necessary to describe the stability of the solvated electron. From the infrared spectra of the solvent in metal-ammonia solutions it appears that the properties of the cavity-associated solvent molecules are essentially correct. Recent calculations by O’Reilly28 predict the stability of a solvent cavity occupied by a pair of electrons. There is a distinct similarity between the cavity-associated solvent properties in this model and the one-electron cavity of Copeland, Kestner, and Jortner.23 If two-electron cavities are formed in these solutions, it is expected that solvent molecules associated with such cavities will also show increased integrated absorption coefficients relative to bulk solvent molecules.
Acknowledgment. We gratefu!ly acknowledge the financial assistance of the Robert A. Welch Foundation and the National Science Foundation. (26) D. E. O’Reilly, J. Chem. Phys., 50,4743 (1969). (27) R. A. Pinkowitz and T. J. Swift, J. Chem. Phys., 54,2858 (1971) (28) D. E. O’Reilly, J. Chem. Phys., 55,474 (1971).
The Journal of Physical Chemistry, Vol. 77,No. 2, 1973
