Ion-Palr Formation and Anion Relaxation in Aqueous Solutions of Group 1 Perchlorates. A Raman Spectral Study Ray L. Frost, Chemistry Department, Queensland Institute of T e c h n q y , Brlsbene, Australla 4000
Davld W. James,' Roger Appleby, and Raymond E. Mayes Chemistry Department, Unlverslty of Queensland. Brlsbane, Awtralie 4067 (Received: October 7, 1981; I n Final Form: June 8, 1982)
The Raman line shape of the vl(Al) mode of the perchlorate anion has been measured over a wide range of concentrations with various group 1counterions. The line shapes and line parameters are interpreted in terms of equilibria between the free aquated perchlorate anion, the solvent-shared ion pair, and the contact ion pair. (4M) and 3.7 X lo-' (4 M) dm3mol-' for the first equilibrium are calculated Association constanta of 3.6 X for lithium and sodium perchlorates, respectively. The vibrational relaxation times of the three perchlorate species have been measured, and the variation in the perchlorate anion vibrational relaxation time is described in terms of strength of the anion-water hydrogen bond.
Introduction The association of electrolytes in aqueous and mixed aqueous/nonaqueous solutions has been measured by c~nductimetric'-~ and spectroscopic4methods. Association studies are usually made in solvent or solvent mixtures of low dielectric constant, where association is promoted! In solvents of high dielectric constant, especially water, association is often slight and the measurement of association constanb more difficult. The manifeatations of ion pairing or association of electrolytes can be determined spectroscopically by NMR,&" and Raman technique~.'~-'~Recently, Popov has identified ion pairing of sodium perchlorate in pyridine solutions by Raman spectroscopy where a new spectral feature at 470 cm-' in the region of the E fundamental was identified.15 Loss of degeneracy can indicate a lowering of symmetry of the anion and, in solution, the formation of ion pairs would provide the necessary perturbation to split the spectral band. The formation of ion pairs may also shift nondegenerate fundamentals leading to a multiple spectral feature. A weak interaction may not lead to resolvable splitting of the spectral bands, and such interactions have been observed as broadening of the band of the -1048 cm-' nitrate symmetric mode ul(A1').l6 Techniques for (1)C. W. Davies, Trans. Faraday SOC.,23, 351 (1927). 91,211(1969). (2)A. DAprano and R. M. Fuoss, J. Am. Chem. SOC., (3)A. DAprano, J. Phys. Chem., 75, 3290 (1971);76, 2920 (1972). (4)T. G. Chang and D. E. Irish, J. Solution Chem., 3, 175 (1974). (5)A. I. Popov, Pure Appl. Chem., 41, 275 (1975). (6) J. F. Coetzee and W. R. Sharpe, J. Solution Chem., 1, 1 (1972). (7)M. K. Wong, W. J. McKinney and A. I. Popov, J.Phys. Chem., 75, 56 (1971). (8) G. K. Templeman and A. L. Van Geet, J.Am. Chem. SOC.,94,5578 (1972). (9)H. A. Berman and T. R. Stengle, J.Phys. Chem., 79,1001(1975). (10)P.Relmarsson, H. Wennerstrom, S. Engstrom, and B. Lindum, J . Phys. Chem., 81, 789 (1977). (11)Y. M. Cahen, P. R. Handy, E. T. Roach, and A. I. Popov, J. Phys. Chem., 79,80 (1975). (12)R. E.Heater, R. A. Brown, and D. R. Kester, J. Chem. Phys., 38, 249 (1963). ~. (13)F. P. Daly, C. W. Brown, and D. R. Kester, J.Phys. Chem., 76, 3664 (1972). (14)R. M. Chatterjee, W. A. Adams, and A. R. Davis, J.Phys. Chem., 78,3 (1974). (15)M.S . Greenberg and A. I. Popov, J.Solution Chem., 5,653(1976). ~
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component band analysis have been developed17Jsand have been applied to spectral bands arising from nondegenerate vibrations of aqueous solutions of metal nit r a t e ~ . ' ~Association ~~~ equilibria involving a range of associated species have been studied with both solventshared ion pairs and contact ion pairs being identified for smaller cations. Similar techniques have been applied to solutions of lithium perchlorate in acetone and ether.21 The association processes were found to be highly dependent on the solvent, and in acetone separate component bands were identified for the isolated anion, the solventshared ion pair, and the contact ion pair.21 There was also a band component in concentrated solutions which could be assigned to ion aggregates in solution. This paper presents a parallel study of the vibrational band corresponding to the ul(A1) vibration of the isolated perchlorate anion in aqueous solutions of monovalent perchlorates. Experimental Section Electrolyte solutions were prepared from recrystallized salts and water triply distilled from an all-glass still. Solution concentrations were verified by appropriate means. Each solution was filtered through O.l-rm Millipore filters into a l-cm path length silica fluorimeter cell which was maintained at a constant temperature (25 "C). The temperature was measured by using a stainless-steel-sheathed chromel-alumel thermocouple placed in the solution adjacent to the focused beam. All spectra were obtained by using a Cary 82 Raman spectrophotometer employing the 514-nm radiation from a C.R.L.Model 52A laser with an incident power of 600 mW at the sample. All experiments were carried out by using 90" scattering geometry. The laser beam, weakly focused by using a 12.5-cm focal length lens, was passed only once through the cell with beam direction being (16)D. W. James and R. L. Frost, Discuss. Faraday SOC.,64,42 (1978). (17)R. L. Frost, R. Appleby, M. T. Carrick, and D. W. James, Can. J. Spectrosc., in press. (18)D. W. James, M. T. Carrick, and R. L. Frost, J. Raman Spectrosc., in press. (19)R. L.Frost and D. W. James, J. Chem. SOC.,Faraday Trans. 1, in print. (20) D. W. James and R. L. Frost, Aust. J. Chem., in press. (21)D. W.James and R. E. Mayes, Aust. J. Chem., in press.
0 1982 American Chemical Society
Ion-Pair Formation and Anion Relaxatlon
The Journal of Physical Chemlstry, Vol. 86, No. 19, 1982 3841
TABLE I: Band Parameters for the u,(A,) and v,(F,) Fundamentals of Group 1 Perchloratesn concn, electrolyte mol dm-3 VMqa+a2 W,p M,,a, (cm-l)’ Tc, PS 7&2’/’/(2nc) T V , W ’ / ~ , PS Wl/l,a NH,ClO, 0.2 933.8 58.0 0.78 0.79 1.53 3.45 0.74 1.53 3.45 64.0 0.70 0.5 933.8 1.51 3.50 0.63 0.71 1.0 933.6 72.0 72.0 0.63 0.71 1.51 3.55 2.0 933.6 LiClO, 0.2 933.7 42.0 1.28 1.10 1.53 3.45 0.5 933.7 42.0 1.28 1.10 1.53 3.50 1.10 1.47 3.60 1.0 933.7 42.0 1.28 2.0 933.8 49.0 1.10 1.02 1.38 3.85 3.0 933.9 56.0 0.96 0.96 1.26 4.20 4.0 934.0 56.0 0.99 0.99 1.18 4.50 5.0 934.2 64.0 0.87 0.93 1.08 4.90 0.2 933.7 58.0 0.91 0.92 1.538 3.45 NaClO, 0.5 933.9 64.0 0.84 0.89 1.495 3.55 1.0 934.0 72.0 0.81 0.91 1.29 4.10 2.0 934.2 120.0 0.51 0.74 1.23 4.30 3.0 935.0 138.0 0.47 0.73 1.14 4.65 4.0 936.0 938.0 138.0 0.50 0.78 1.08 4.90 6.0 937.5 938.0 144.0 0.52 0.83 0.95 5.60 8.0 939.8 940.0 169.0 0.56 0.97 0.85 6.2 10.0 939.9 941.0 169.0 0.56 0.97 0.56 9.5 64.0 0.73 0.78 1.58 3.35 KClO, 0.1 933.5 64.0 0.73 0.78 1.58 3.35 933.5 CSClO, 0.07 46.0 0.84 0.76 1.71 3.10 TEAClO, 0.1 933.5 a uMa,p = band maximum of isotropic ( a ) and anisotropic ( p ) bands (cm-l). M,,a = second moment of isotropic band. ~ ~ = ~vibrational 1 1 2 relaxation calculated from band half-width. w I/apr = half-width (k0.5) isotropic T~ = modulation time. ~ band (hwhh) (cm-I).
maintained parallel to the collecting lens. A GlanThompson prism was used to ensure the polarization orientation. The scattered light was collected from a solid and the two polarization components were angle of Go, studied by using a Polaroid sheet followed by a quartz wedge scrambler. Slits corresponding to constant spectral band-pass of 0.5 cm-l were employed throughout. To facilitate computer analysis, we collected the spectral data at 0.2-cm-l sampling intervals on paper tape. At least nine spectra were recorded for each solution and were “band averaged” and then smoothed by using the Savitzky-Golay techniques. The isotropic and anisotropic peak positions, half-widths, and band intensities were then calculated,16 and the bands were Fourier transformed by using standard fast Fourier transform routines.
Results and Discussion The perchlorate anion has nine vibrational degrees of freedom distributed into four normal modes of vibration: vl(A1), vZ(E),~3(Fz), and ~q(F2).The degenerate stretching vibration, v3, has been used to indicate perturbation of the perchlorate anion resulting in loss of degeneracy. This has been observed in both crystallinezzand solution23states. It is not possible however to readily use this loss of degeneracy to study ion association since the identification of separate vibrating species is neither easy nor definitive. Studies of the nondegenerate vibration, vl, however do not pose the same difficulty, and changes in band shape may be analyzed in terms of contributions from more than one sort of oscillator. The results collected in Table I refer to the complete band profile for the v1 band. The similarity in the band maximum for all solutes except NaC104 is evident while the second moment of the band emphasizes that the band half-width for the majority of solutes does not show marked changes. Solutions of NaC104 evidently behave rather differently with the band maximum and the second (22) W. H. Leong and D. W. James, A u t . J. Chem., 22,499 (1969). (23) A. D. E. Pullin and J. McPollock, Trans. Faraday SOC.,64, 11 (1958).
1
2
3
4
5
Time(ps)
Flgm 1. Time conelation functlons for perchlorate solutions in water: (A) LiCi04, 0.5 M (least slope)-4.5 M (greatest slope). Dotted line represents the value for 1 M NH4CI0,. (B) NaCIO,.
moment both showing a marked change with concentration. In addition, the appearance of an anisotropic component (indicated by vB) shows that marked perturbation of the perchlorate ion has occurred. The parameter r a Z /( 2 m ) indicates that all solutions are characterized by an intermediate mod~1ation.l~ The variations in the vibrational relaxation time r, reflect the changes in the total band half-width. A further discussion of vibrational relaxation will be given later. It has been shown elsewhere17that the Fourier transform of a band can give an indication of the presence of more than one component in the band envelope. Thus,a change in slope of the time correlation function (TCF) indicates a change in half-width, and a change in slope together with the development of a minimum indicates the presence of at least two components. The 8 function, which can be defined as tan-l 0 = imaginary/real for the Fourier transform, gives further information.18 The presence of more than one component in the spectral band yields a 8 function which oscillates with time, and it is possible to
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The Journal of phvslcal Chemlstfy, Vol. 80, No. 19, 1982 n
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Flgure 2. 6 functlons for aqueous perchlorate solutions: (A) LiCIO,. (e)NaCIO,. Dotted llnes represent the 6 functions for bands at 934 and 938 cm-'.
obtain semiquantitative information concerning the separation and relative intensity of the components. The 6 function analysis has proved to be much more sensitive to the presence of multiple bands than the TCF. The time correlation functions for solutions of NH4C104, LiC104, and NaC104 are shown in Figure 1. It is evident that in the presence of the cations NH4+and Li+ there is evidence for some increase in half-width for the band but little evidence for more than one component. Changes in the TCF in the presence of Na+ are much more pronounced with large changes in slope and inflections appearing. The 6 functions for solutions of LiClO, and NaC10, are shown in Figure 2. For LiC10, solutions there is a minimum at short times followed by an almost linear portion. The initial minimum corresponds to a separation of two bands by -10 cm-' with the major band being in the region of 934 cm-'. The weaker band is evident in the spectrum as a strong asymmetry on the low-energy side of the band. The increase in slope of the 6 function as the concentration increases indicates that the band maximum is moving to higher energy and may also indicate the presence of a weak band at higher energy than 934 cm-l. It is not possible however to establish this. The 6 functions for solutions of NaC104 shown in Figure 2B fall into two groups. Below 5 M the functions are related to the straight line corresponding to a major component at -934 cm-l while above 5 M the functions are related to the straight line corresponding to a major component at 938 cm-'. The oscillations of the functions about these straight lines clearly indicate the presence of several components in the band and the crossover points indicate separations between the bands of -5 cm-'. For all 6 functions the oscillation at short times indicates the presence of a weak band some 10 cm-I below the 934-cm-' band. Band component analysis was performed interactively by using a suite of p r o g r a m ~ ~including ~ p ~ ~ a nonlinear least-squares routine.26 The bands were described by a Lorentzian-Gaussian product function of the form I@) = Io e~p[-X,~(g- ij0)2]/[1+ X32(3- p0)2] where Io is the band intensity, vo is the position of the band maximum, and X3 and X4 are half-width parameters for ~
(24) D. Sweatman, Ph.D. Thesis, University of Queensland,Brisbane, Australia, 1982. (25) R. L. W. Frost, Ph.D. Thesis, Univemity Brisbane, . of Queensland, . Australia 1982. (26) P. Sampson "Program BMD 07R in Biomedical Computer Programs",W. J. Dixon, Ed.,University of California Press, Berkeley, CA, 1914, p 381.
Energy (cm-1)
Flgure 3. Fitted band contours for LiCIO, solutions: Upper curve represents both experimental and composite bands. Error function is shown at base.
E nergy(cm-1) Flgure 4. Fitted band contours for NaCIO, solutions.
Lorentzian and Gaussian bands. Band fitting was carried out interactively with Io, vo, X,,and X4 allowed to vary. The h a n bands in parallel and perpendicular polarization were convoluted to yield the isotropic and anisotropic band profiles. It is only for 4, 6, 8, and 10 M that there is an appreciable perpendicular component, and this information will be useful in later discussion. All bands had a low-energy asymmetry which is assigned to a combination of hot bands and 1 7 0 isotope components of the vibrational envelope. The contributions from these two sources may be described by a single broad component which moved slightly to higher energy at higher concentration. This is shown for solutions of LiC10, in Figure 3. Bands obtained from solutions of NH4C104were described at all concentrations by the weak, broad band described above and a single component which remained essentially invariant with concentration. For solutions of LiC10, the dominant components are again the broad, weak band (925 cm-') and a principal sharper band (933.7 cm-'1. This latter moved slightly to higher energy at high concentration, and there was evidence for a weak component at higher energy (938 cm-') which in a saturated solution amounted to some 8% of the total intensity. For the bands obtained for solutions of NaC10, in addition to the broad, weak, low-energy band two components separated by 5 cm-l are necessary to describe the profile from
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Ion-Pair Formation and Anion Relaxation
quite low concentration. The component of lower energy shows a behavior parallel to the major band for solutions of LiC104in that it broadens and moves slightly to higher energy as the concentration increases. The second band a t -938 cm-' grows in intensity as the concentration increases at the expense of the lower band. A t the highest concentrations there is a persistent residual at higher energy (-944 cm-'), and a third band was necessary in the fitting procedure to take account of this excess intensity. These results are collected in Table I1 and Figure 4. Ion-Ion-Solvent Interactions in Perchlorate Solutions. The solutions of sodium perchlorate give evidence of three species present in varying proportions at different concentrations. This behavior is similar to that observed for solutions of LiC104 in acetone2' where the dominant species isolated perchlorate ions, solvent-shared ion pairs, and contact ion pairs were identified. The assignment of band components to the three species in acetone was supported by evidence from infrared spectra, 3sCl NMR bandwidths, and chemical shifts for 'Li NMR and 13C NMR signals. The band components obtained for aqueous solutions of NaC104 are similar to those previously obtained in acetone solution, viz., 933.8 (933.8 cm-', isolated C104-), 937.8 (939.3 cm-', Li+, acetone, ClO,-), and 943.5 (947.7 cm-l, Li+C104-)cm-'. The two dominant bands in aqueous solution at 933.8 and 937.8 cm-' are assigned to the isolated, aquated perchlorate ion and the solventshared ion pair. The emergence of the 937.8 cm-'coincides with the appearance of an anisotropic contribution to the band profile, and this indicates that there is an appreciable symmetry perturbation of the C104- species. The movement of this anisotropic band to higher energies indicates that the weak, high-energy band has an even stronger symmetry perturbation, and this is tentatively assigned to a contact ion pair species. In solutions of LiC104 the spectral band is dominated by the component a t -933.5 cm-', which indicates that at all concentrations the separate ions are the major ionic Components. There is however a weak feature at -938 cm-' which we assign to a solvent-shared ion pair. If there is an anisotropic component to the band because of this associated species, it is too weak to be observed. This is to be expected as, for solutions of NaC104,the anisotropic band was not observed until the component intensity for the associated species was -40%. The bands observed for v1 in solutions of NH4C104,KClO,, and CsC104do not give evidence of additional high-energy bands and so it appears that ion pairing is not significant in these solutions. Previous studiesg have suggested that ion association does not occur in aqueous solution of alkali metal perchlorates. These conclusions were based on measurements made to a maximum concentration of 1 M. The NMR technique is not sensitive to the presence of solvent-shared ion pairs, and in view of the limited concentration range previously studied the conclusions drawn are not at variance with our observations. Studies of aqueous solutions of NaN03have shown that three nitrate ion environments can be identified,lg and these have been assigned to the isolated aquated nitrate ion (vl = 1047.6 cm-l), solvent-shared-ion-pair nitrate (vl = 1050.0 cm-l), and contact-ion-pair nitrate (vl = 1052 cm-l). Although the nitrate ion is more easily polarized (by a cation) than the perchlorate and shows a wide variation in values for vl, the changes observed on association are smaller than those observed in the case of sodium perchlorate. In addition, the bands do not show appreciable shift with concentration change in nitrate solutions, whereas in the perchlorate solutions there is a marked
The Journal of physical Chemistry, Vol. 86, No. 19, 1982 3043
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The Journal of Physical Chemistry, Vol. 86,No. 19, 1982
Frost et al.
increase with increasing concentration. We feel that both at least qualitatively reasonable by looking at the molar intensity of the complete band relative to the ul band of of these differences may be explained in terms of the aquation of the anion. For the nitrate ion, which is relaCH3CN. The association quotients for NaC10, solutions tively strongly hydrated, the polarization by the cation is can be represented by mediated by the solvent sheath, whereas for the perchlorate for which the solvation is very weak the polarization by the cation remains quite directional and causes a stronger directional perturbation than in the case of the nitrate. For solutions of NH4C104the position of the perchlorate vibration does not increase with concentration, whereas for solutions of LiC104 an increase is observed. This rewhere M is the molar concentration and flects the strong polarization by the Li+ ion as opposed to U s 4 4 / CI) the very weak polarization or neutral interaction of the Qz = NH4+ ionsz7 This also indicates that, although solventshared ion pairs are not readily formed in solutions of LiC104,there is a longer-range polarization, which could perhaps be described as a solvent-separated-ion-pair inThe association quotients are listed in Table 11, and it is teraction, which both shifts and broadens the band. It is evident that, except at high NaC104 concentration, the because of the very weak hydration of the anion that this values for Q1are small. For LiC104 solutions the values influence can be observed. are not strongly concentration dependent while for NaC10, The breadth of the %C1NMR resonance has been exthe values increase with increasing concentration. The tensively used as a criterion for contact-ion-pair formation. values for LiC104 solutions are smaller than those for Early studies of HC104 in concentrated HCl yielded NaC10, solutions, which is probably a reflection of the 35C1(C104-)line widths of -60 H Z . ~Dilute ~ solutions of strength of the hydration of the cation. LiC104in nonaqueous solvents yielded line widths of 10 Perchlorate Relaxation. Previous studies of anion Hz, but this line width increased with increasing concensolvation, in particular of perchlorate ions in methanol and tration until widths of up to 4000 Hz were r e c ~ r d e d . ~ * ~water, ~ have been able to distinguish the solvent molecules The appearance of an electric field asymmetry at the 35Cl which are bound to the a n i 0 n . ~ 3 In ~ ~solutions of NaC104 nucleus caused by the formation of a contact ion pair has we have related component bands to associated species been related to this broadening. The line widths which and, although the components are subject to the uncerwe measure in dilute solutions of both LiC104and NaC104 tainty inherent in the component analysis, the changes in in water are comparable to previous reportss and are very band parameters can be considered in terms of energy narrow (1-2 Hz). In saturated aqueous LiC104 this has relaxation processes. Based on a Lorentzian approximaincreased slightly to -3 Hz, which is in accord with the t i ~ n vibrational , ~ ~ relaxation times of 1.33 (isolated dominance of separate ions in solution. For solutions of (ClOJ ) 1.06 ((Na+(H20)C10-),), and 1.21 ((Na+CIO,)Bs) NaC104the appearance of an anisotropic band component ps mayye calculated. The value for (c104-),is compaabove 4 M indicates that there is an appreciable symmetry rable with that obtained for (NO;)a29 and indicates that perturbation of the C10, ion, and in the most concentrated the relaxation process for the two aquated anions is solution contact ion pairs are identified. The 35Cl line probably similar. The relaxation is much shorter than that width in saturated solution has only increased to 11 Hz. for the solvated perchlorate in acetone (7, = 3.8 ps) and In saturated aqueous Ca(C104)zwhere contact ion pairs thus the increased anion solvation by water leads to a more predominate the band has broadened to -60 H Z . ~These efficient dephasing process. The component band correwidths are not viscosity corrected and so they overestimate sponding to the (C104-)wspecies is almost pure Lorentzian the increase in bandwidth. in shape, which indicates that the damping by the solvent On the basis of the NMR evidence alone it might be sheath is small. For the (Na+(HzO)C104-),,species the concluded that even in solutions of NaC104 ion pairing is relaxation is much faster, and this is what is expected on of little significance. However, there is strong symmetry the basis of more efficient dephasing by the unsymmetric perturbation evident from the Raman spectra. The confield. The band shape has also become more Gaussian, flicting observations indicate that the electric field gradient showing that damping by the unsymmetrical environment produced in ion-pair formation can be strongly influenced is stronger than for the isolated ion. The interpretation by the solvation of the separate ions and the associated of relaxation parameters for component bands must be species. The composition which we determine in 10 M regarded as qualitative at best as there are a large number NaC104 in water is very similar to that previously deterof factors contributing to the relaxation process and the mined for a 4 M solution of LiC104in acetone.21 The 35Cl shape of the calculated component bands. line width in the acetone solution is 550 Hz, which comThe appearance of an anisotropic component in the pares with 11 Hz reported above. The use of the line width measured band profile allows the calculation of a reoriof a quadrupolar nucleus as a criterion of ion association entational relaxation time for the Clod- species. This TOR must therefore be considered carefully if no corroborating is 1.26 ps, which is markedly smaller than that obtained evidence is produced. for the nitrate ion in solutions of NaN03 (>2.2 ps).I6 The Association quotients may be calculated for the assosmall TOR shows that the constraint on the rotational ciation equilibria if it is assumed that the molar intensity motion of the perchlorate ion is small, reflecting the weak of the perchlorate ion in different environments is not solvation of the anion. appreciably different. This assumption was found to be
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(27)P.M.Volmer, J. Chem. Phys., 39,2236 (1963). (28)K.J. Johnson, J. P. Hund, and H. W. Dodgen, J. Chem. Phys., 51,4993 (1969). (29)D. W. James, P. Cutler, and R. L. Frost, unpublished.
(30)M.C. R. Symons and D. Waddington, J. Chem. SOC.,Faraday Trans. 2, 71, 22 (1975). (31) D. M . Adams, M. J. Blandemer, M. C. R. Symons, and D. Waddington, Trans. Faraday SOC.,67, 611 (1971). (32)W. G. Rothschild, J. Chem. Phys., 65, 455 (1976).
J. Phys. Chem. 1082, 86,3045-3052
Conclusion Studies of the perchlorate anion Raman profiles have proved to be useful in the study of ion+lvent interactions. The use of the perchlorate anion in a ternary system of water and a second electrolyte has often been used to promote ion pairing of the second e l e ~ t r o l y t e . ~How,~~ ever, the assumption that the perchlorate anion is not also involved in ion pairing is not strictly true. The perchlorate anion has also been used as a "noninteracting" anion in (33)T.G. Chang and D. E. Irish, J. Solution Chem., 3, 161 (1974). (34)B.Balaeubrabmanyan and G. J. Janz, J. Am. Chem. SOC.,92,4189 (1970).
3845
the study of ligand-metal e q ~ i l i b r i a . It ~ ~is assumed that the perchlorate anion does not form metal-anion association. Such interactions cannot be neglected, and the perchlorate anion may play a greater role in the study of metal-ligand equilibria than has been previously considered. Certainly our component analysis indicates that association of the perchlorate anion to the group 1metals is small but significant. Acknowledgment. The ARGC are thanked for grants enabling the purchase and maintenance of the Raman spectrometer and for a fellowship for R.A. (35)L. Johansson, Coord. Chem. Rev., 12,241 (1974).
Test of the Entropy Basis of the Vogel-Tammann-Fulcher Equation. Dielectric Relaxation of Polyalcohols Near T, C. A. Angell" and D. L. Smlth Department of Chemisby, furdue University, West Lafeyette, Indiana 47907 (Received: October 13, 1981; I n Flnal Fwm: May 18, 1982)
We describe a family of hydrogen-bonded molecular liquids in which transport processes all appear to be strongly coupled and which exhibit relaxation times conforming to the Vogel-Tammann-Fulcher (VTF) equation 7 = T~ exp(B/ [ T - To]) over as much as 12 orders of magnitude in 7. For such systems a stringent test of the identity of the VTF equation Toand the Kauzmann isoentropy temperature TK can be made. New data on dielectric relaxation times extending into the glass transformation range are presented for three polyalcohols, and heat capacity data for crystallineand liquid ethylene glycol are also reported. Estimates of the Kauwnann temperature, TK,at which the internally equilibrated supercooled liquid would have the same entropy as the crystal, are made. Despite a threefold variation in TK,these are found to be close to the best-fit VTF equation Toparameter and even closer to the Tovalue obtained by adding the constraint B = 12.7T0to the analysis.
Introduction The temperature dependence of liquid transport properties,' particularly in the case of viscous liquids, is complex and at this time poorly understood. An empirical equation which has been given much attention is that first proposed for viscosity by Voge12and later applied in simplified form to various liquids by Tammann and Heme3 and, independently to molten oxides, by F ~ l c h e r . ~The VogelTammann-Fulcher (VTF) equation has the simple form 7 = A exp[B/(T - To)] log 7 = A ' + B ' / ( T - To)= A ' + ( B / 2 . 3 0 3 ) / ( T - To) (1) and is transformable into the Williams-Landel-Ferry (WLF) equation, well-known for its ability to describe It has also been successfully applied polymer fl~idities.~ to molecular liquids! ionic salts and solutions,' and metallic glasses.8 Davidson and Colegpointed out that Toin (1) J. R. Partington, 'An Advanced Treatise on Physical Chemistry", Longmans, Green and Co., London, 1951. (2)H.Vogel, Phys. Z., 22,645 (1921). (3)G.Tammann and G. Hesse, Z. Amrg. A&. Chem., 166,245(1926). (4)G. S.Fulcher, J. Am. Chem. SOC.,8,339 (1925). (5)M. L. Williams, R. F. Landel, and J. D. Ferry, J. Am. Chem. SOC., 77,3701 (1955). (6) . . (a) . . R. C. Makhiia and R. A. Stairs. Can. J. Chem.. 48.1214(1970): (b) M. P. Carpenter, D.B. Davies, and A. J. Matheson,'J. &em. Phys.; 46,2451 (1967). (7)(a) C. A. Angell, J.Phys. Chem., 68,1917(1964);70,2793(1966); (b) C. T.Moynihan, ibid., 70,3399 (1966).
alcohols and glycerol had the same value for dielectric relaxation and viscosity and that this value was close to the value of the Debye temperature OD determined from velocity of sound measurements. A more challenging correlation was emphasized by Adam and GibbslOJ' and, indirectly through the WLF equation, by Bestul and Chang.12 These authors noted that in several cases the temperature Toalmost coincided with a temperature (which we denote here TK)at which the liquid entropy curve extrapolated below the glass transition temperature would intersect the crystal entropy curve. That this alarming intersection would occur quite generally in supercooling liquids were it not for the timely intervention of the (nonequilibrium) glass transition (at which (dS/BT), for the liquid changes to much lower values) was first pointed out by Kauzmann13-hence, our choice of subscript for the extrapolated isoentropy temperature, TW Since Gibbs and Dimarzio14had earlier formulated an equilibrium theory for polymers (recently challenged by Gujrati and Gold~tein'~) which predicted an equilibrium (8) H.S. Chen and D. Turnbull, J. Chem. Phys., 48, 2560 (1968). (9)D. W.Davidson and R. H.Cole, J. Chem. Phys., 19,1484 (1951). (10)G. Adam and J. H.Gibbs, J. Chem. Phys., 43,139 (1965). (11)References 10 and 12 actually compare T,/To with T /TK.Direct comparisons of Toand TK are given in C. A. Angell and J. Rao, J. Chem. Phys., 57,470 (1972). (12)A. B. Bestul and S. S. Chang, J. Chem. Phys., 40,3731 (1964). (13) (a) W.Kauzmann, Chem. Reu., 43,219 (1948);(b) C. A. Angell, J. Chem. Educ., 47,583 (1970). (14)J. H.Gibbs and E. A. Dimarzio, J. Chem. Phys., 28,373 (1958).
0022-3654l82l2086-3845$0 1.2510 0 1982 American Chemical Society
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