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J. Phys. Chem. 1991, 95, 7062-7064
Dlelectrk Constant Ettects on Water D)ssoclatlon and Electrical Conductlvity In Water-p-Dioxane Gdutlons J. E.Anderson Research Stafl, Ford Motor Company, Dearborn, Michigan 481 21 -2053 (Received: March I , 1991) We report 25 OC frequency domain impedance spectroscopy (FDIS) measurements as a function of composition in the water-p-dioxane system. This prototype liquid conductor-insulatorsystem exhibits a 10’ conductivity change between 0.0 and 0.1 weight fraction water. Fratiello and Douglass and then Clemett observed no corresponding concentration effect in previous self-diffusion measurements on water-p-dioxane. Their findings rule out any explanation of our conductivity data based on molecular mobility or percolation arguments: mobility changes would impact both conductivity and selfdiffusion in the same way. Rather, we interpret conductivity results in terms of the solution dielectric constant, e; and e effects on the H20-H+-OH- equilibrium. Specifically, we suggest that K for this equilibrium decreases by 10l6going from water where c = 78.5 to a 1% water in p-dioxane solution where c = 235. As p-dioxane content increases, there are many fewer charge carriers and conductivity demases. Critchfield, Gibson, and Hall and Clemett, Forest, and Smyth reported experimental dielectric constant-compositiondata. We used their results together with the Bjerrum-LarssOn theory to calculate (1) equilibrium constants and (2) solution conductivities as a function of composition. Calculated results agree with experimental data.
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Background We recently measured electrical conductivity, u, in several water-insulator systems.L-2 These systems include (a) water sorbed on the surface of solid insulators, (b) water dissolved in bulk insulators, and (c) binary liquid systems composed of water and a second, electrically insulating solvent. These s stems all exhibit enormous conductivity changes, of order 106-1 mho/cm, over a narrow range of water concentration (cf. Figure 1). At first, we attributed these conductivity changes to a percolation process involving topological constraints that restrict translational mobility of water molecules. In this, we followed percolation arguments advanced by previous researchers to explain conductivity-mposition relations in other systems.= Without question, percolation explains our conductivity results when they are viewed in isolation; Le., in the absence of ancillary experiments. Subsequently,we learned of other types of water transport data made on systems where we had conductivity measurement^.^*^ These transport parameters, e.g. selfdiffusion coefficients and water permeability, did not exhibit the strong concentration dependence seen in conductivity. Since topological constraints/ mobility arguments apply equally to all water-transportprocesses, this comparison rules out a percolation mechanism. The comparison also points up important differences among water-transport experiments. For example, selfdiffusionmeasures translational mobility of nonionized H 2 0 molecules. Owing to their low concentrations, H+ and OH- ions make no appreciable impact on selfdiffusion. In contrast, electrical conductivity reflects both mobility, cr,and concentration, n,of ionized charge carriers: u = C&(l)pC(i), where the sum runs over all charge carriers. In water, the chargecarriers are H+ and OH- ions, present in equal concentrations owing to electroneutrality, and related to the concentration of nonionized H20 through the relation K, = [H+][OH-]/[H20]. It follows that the conductivity can be expressed as u ([H+]p+ + [OH-]p-)F a= [H+](M++ P-)F (Kw[H201)‘”2’(r+ + r-)F (1)
d
~~
(1) Andmon, J. E.; Adam, K. M.; Troyk, P. R. J. Non-Crysr. Solids, in
press. (2) Andenon, J. E.; Adams, K. M.; Troyk, P. R.; Frankovic, R. IEEE Trow. Com urers, Hybrlds, Monul. Techno/. 1991, 14, 420-426. (3) Stauler, D.Introducrion lo Percolorlon Theory; Taylor d Francis: London, 1985. (4) Wong, P.-z. Phys. Today 1988, 41, (12), 24. ( 5 ) Eicke, H.-F.; Geiger, S.;Sauer, F. A,; Thomas, H.Err. Euwen-Ges. Phys. Chem. 1986,90,872-876. (6) Landauer, R. In Elecrrlcol Trowporr ond Oprlcal Propwries of Inhomogrnaow Medlo; Garland,J. C., Tanner, D. E.,Eds.;American Institute of Physia: N e w York, 1978; pp 2-43. (7) Fmtiello, A.; huglass, D. C. J. Mol. Spectmsc. 1%3* 11, 465-482. (8) Clemett. C. J. J . Chem. Soc., A 1969, 458-460.
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where F is Faraday’s constant. If the water dissociation constant, Kw,is a strong function of water concentration in the medium, it follows that u also exhibits a strong concentration dependenceeven when p+ and cc_ (the H+, OH- mobilities) are entirely concentration independent!
Research Hypothesis a d Objectives We explain the large concentration dependence of u in water-insulator systems in terms of dielectric constant, e, effects on water dissociation. Electrostatic arguments (vide infra) show that e variations produce major shifts in the equilibrium between ionized and nonionized species. The dielectric constant/dissociation explanation,which involves charge-carrier concentrations instead of mobility, is consistent with both (a) strongly concentration-dependent conductivitiesand (b) concentration-insensitive self-diffusion coefficients. We initiated this research to test this hypothesis. Our objective was to measure conductivity in a well-characterid binary solvent system, and to correlate the concentration dependenceof u with variations in solution dielectricconstant. We chose a binary solvent system to exclude percolation effects. previous Studies 011
Water-p-Dioxane We selected the water-dioxane system for two reasons. First, Fratiello and Douglass7and Clemett8 determined self-diffusion coefficients for both components as a function of composition. While water-p-dioxane exhibits certain interesting transport characteristics resulting from molecular association between its .component species,’P8 this ,association has minimal impact on self-diffusion. Water-pdioxane behaves as an entirely normal binary liquid system, whose self-diffusion coeficients change by less than an order of magnitude over the entire composition range. Hartmanng and Lind and F u o ~ s reported ’~ other pertinent transport measurements on this system. Second, there is a wealth of dielectric data available: For over sixty years, water-pdioxane has been the prototype system used to study e effects on molecular association. Water and pdioxane are miscible in all proportions. At 25 ‘C, they have dielectric constants of 78 and 2.2, respectively,” and corres nding liquid-phase conductivities of lod and mho/cm.lP Conductivity data have been reportedi0 over the limited composition range extending from 0.20 to 1.0 weight fraction water (cf. Figure 1). Critchfield, Gibson, and Hall” and (9) Hartmann, H. 2.Phys. Chem. 1942, A191, 197-226. (IO) Lind, Jr., J. E.; F u w , R. M.J . Phys. Chem. 1961, 6S,999-1004. (1 1) Critchfield, F. E.; Gibson, Jr., J. A.; Hall, J. L. J . Am. Chem. Soc. 1953, 75, 1991-1992. ( 12) D o b , D. Electmhemical &tu; Ekvier: Amsterdam, 1975; Table 62.
Ca 1991 American Chemical Society
The Journal of Physical ChemisttynVol. 95, No. 18#1991 7063
Dielectric Constant Effects on Water Dissociation -4
14
1
1
-6 -7 s
-8
:
-9
c .L,
-10
0
-11 0
-12
."
0.0
0.2
0.4
0.6
0.8
1 .o
- 3 - 2 - 1
Weight Fraction Water
Clemett, Forest,and SmythI3 reported dielectric constant-composition data over the entire composition range. For use in subsequent data analysis, we treated their results by regression analysis to yield 78.5
- 7 2 . 6 ~- 50.W + 48.9$
(2)
In this expression, c, is the solution dielectricconstant measured at 25 OC, and w is the weight fraction p-dioxane. A long and distinguished history surrounds studies of dielectric constant effects upon chemical equilibria. In 1894, Nemst" and Thomson15established that the underlying relation had the form
Kq = A exp(-B/c)
(3)
where A and B are constants. In 1920, Bom16 computed the electrostatic energy, Ed, of a spherical particle of radius 6 and charge 1291 in a medium of dielectric constant e:
Eel =
1
2
3
4
5
6
Log Frequency (Hz)
Figare 1. Electrical conductivity of water-pdioxane solutions as a function of comptxition: (0)present results; (0)data of Lind and Fuoss (ref 10). The solid curve was calculated following the procedure described in the text.
4
0
(s)2/(w
(4)
In this expression, 9 is the unit elcctmtatic charge. Then in 1927, Bjerrum and Larsson17 combined the previous results1c16 to compute an equilibrium constant for the AB =A+ E reaction:
+
Kq = A expl-[(~9)~/(2(6)kT)l(l/c)) (5) In this expression (6)is the mean ionic radius and kT has its usual meaning. The Bjerrum-Larsson paper prompted a plethora of research directed at ionic association in media of varying e. Kirkwood, Onsager, and Fuoss added theoretical refinements to the Bjermm-Larsson analysis." Fuoss, Kraus, Hamed, Owen, and their students r y r t e d numerous experiments on ion pairing as a function of t.I8*l For reasons noted above, water-pdioxane emerged as the system of choice in many of these studies. These experiments concerned dissolving a third component, such as HCl in various water-pdioxane solutions. Changes in HCl association were monitored as a function of solution dielectric constant. Oddly (1 3) Clcmctt, C.J.; Forest, E.; Smyth, C. P. J. Chem. Phys. 1964,40, 2123-2128. (14)Nernrt, W. P h p . 2.1094, I3,531-536. (15) Thomson, J. J. Phil. Mag. 1893,36,320-325. (16)Born, M.2.Phys. 192Q, I,45-48. (17)Bjer", N.: Lamon, E. 2.Phys. Chem. 1927, 127,358-384. (18) Fuom, R. M.:Aocaacina, F. Electrolytic conducrancr;Interscience: New York, 1959. (1 9) Hatncd, H.S.;Owen, B. B. Physicul Chemistryo/€lecfrolytk Solutions; ACS Monograph Series; Reinhold New York, 1958.
Figure 2. Representative FDIS results for water-pdioxane. From top to bottom, the data represent 0.03,0.075, and 1 .OO weight percent water. The solid curves correspond to equivalent parallel RC circuits.
enough, little of the early work considered c effects on water dissociation itself. Even this researchmwas limited to the range 19 < c < 78; Le., to 0.30-1.0 weight fraction water.
Experimental Results In the present study, frequency domain impedances p e c t m q y (FDIS) measurements were made over the entire composition range. Experiments were performed at 25 OC at frequencies between and 106 Hz. Representative results are shown in Figure 2 as Bode plots; viz., log (impedance magnitude) versus log frequency. Solutions containing 0.05-1 .O weight fraction water exhibit impedance spectra that are well-represented by an equivalent parallel RC circuit. This circuit corresponds to a low-frequency resistive impedance governed by solution conductivity and a high-frequency capacitive impedance govemed by solution dielectric constant. As concentration decreases below 0.05 weight fraction water, FDIS data deviate progressively from equivalent parallel RC circuits. Noise-generated artifacts may cause these deviations since the solutions exhibit conductivities, of order IWI3 mho@, which approach the noise floor of our instrumentation. An equivalent parallel RC circuit was assumed in analyzing all FDIS data. Solution conductivities, a,, were determined from a, = (c&)'I, where R and co are the experimental resistance and cell constant, respectively. Low-frequency data were given high statistical weight in determining experimental conductivities. Figure 1 shows a semilogarithmic plot of a, as a function of compition. It is noteworthy that a, exhibits an overall change of IO9 mho/cm and that the largest proportion of this change, IO' mho/cm, occurs between 0.0 and 0.1 weight fraction water. Equations 1,2, and 5 were used to compute a, as a function of composition. The parameters A and ( 6 ) were chosen to fit a, = IO4 mho/cm and a, = lW15 mho/cm at 0.0 and 1.0 weight fraction water respectively. The resulting cuwe, shown in Figure 1, gives a reasonable fit to experimental conductivitydata. The experimental parameter ( 6 ) was 3.0 X lv cm. The physical significance of this quantity is admittedly uncertain, but it is reassuring to obtain a value of molecular dimensions and not, for or 1o-" cm. example, 1 K, values derived from conductivitydata ranged between 1.8 X (mol/cm3) for liquid water (e = 78.5) and 2.0 X (mol/C") for 1% water in dioxane (e = 2.7). Plots of calculated Kwvalues versus compition have the same general fm as Figure 1 and are not shown. It is important to note the somewhat unusual definition of Kw used in these calculations: K, = (H+][OH']/
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(20) Hamcd, H.S.;Owen, B. 8.Chem. Rco. 1939,31,3144.
J. Phys. Chem. 1991, 95, 7064-7067
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[H20]in units of (m01/cm3). Because total water content changes in our experiments, we cannot follow custom and include [H20] in the equilibrium constant.
Discussion Percolation phenomena have attracted considerable recent attention.= Both theory and computer-simulationexperiments on conducto~insulatorsystems show that percolation always leads to an enormous conductivity change over a narrow composition range. This research shows that the converse of this statement cannot be true. Specifically, our experiments demonstrate that conductor-insulator systems may exhibit huge conductivity changes for reasons having nothing to do with percolation. Dielectric constant effects on solvent dissociation represent a general phenomenon that should affect conductivity in other systems. Indeed, we have observed large conductivity increases with increasing solvent content in binary water-polymer systems.lJ The polymers used in these experiments were elastomers, whose facile segmental motions do little to impede self-diffusion or permeation of small molecules. Additional details of this work will be published separately. Similar effects may occur in measurements of surface conductivity, u,. It is well known that us is extremely sensitive to relative humidity, RH: T pica1 usvalues increase by 106-108, going from 0 to 100%RH%e2I The relation u, = a exp(oRH"), where a, 6, and n are experimental parameters, fits a great deal of surface conductivity data. The physicochemical basis of this relation remains obscure. On the basis of Born's electrostatic calculation, vide eq 4, a number of researcher^^^-^^ computed exclusion of ions from water-(solid insulator) and from waterair interfaces. (n.b., the dielectric constant of air is unity.) These arguments can be extended to show that proximity to a low-dielectric-constant interface shifts the H@-H+-OHequilibrium in favor of nonionized H20. It follows that thin water layers should exhibit anomolously low conductivity and that surface conductivity should increase dramatically with increasing thickness, i.e. with increasing RH.
Experimental Methods We prepared solutions by weight from spectral-quality p-dioxane and 1 MCkm conductivitywater. Subsequently,we stored Curtis, H. L.US.Bureau of StandardsScience Paper No.234,1915, Yager, W. A.; Morgan, S . 0.J. Phys. Chem. 1931,35,2026-2030. Wagner, C. Phys. Z . 1924, 25,414-411. Onsager, L.;Samaras, N.T.J. Chem. Phys. 1934, 528-536. ( 2 5 ) Glueckauf, E.Proc. Inr. Symp. Water DcsrrNn., 1st 1965, 143-145. (26) Anderson, J. E.;Jackson, H.W. J. Phys. Chem. 1974.78,2259-2262.
(21) (22) (23) (24)
the solutions in sealed containersto minimize C02absorption from the air; viz., to prevent conductivity changes due to dissolved carbonic acid. A Yellow Springs Instrument Co. Model 3403 conductivity cell was used. It was housed within a Faraday-shielded enclosure. This cell was optimized by its manufacturer for conductivity studies; it proved less than ideal for capacitance measurements. We modified cell cable connections to minimize stray capacitance, but the modified design still exhibited -1-pF capacitance in parallel with the solution capacitance. This 1 pF introduced considerable uncertainty into solution capacitancevalues, C,, which ranged between 4 and 100 pF. Solution dielectric constants, e,, were obtained from the relation cs = KocOCswhere co is the cell constant and KO = 11.3 cm/pF. Experimental % values were of reasonable magnitude (1 < cs < 100); they increased, as expected, with weight fraction water in the solutions. We believe that 4 values derived from the present data are less precise than those reported by previous investigators."*" For this reason, our results are not reported herein. FDIS measurements were made with a Solartron Model 1260 frequency response analyzer. Water-p-dioxane solutions containing more than 0.10 weight fraction water have conductivities greater than 1@lo mho/cm: the frequency-dependentimpedance of these solutions was measured by connecting the conductivity cell directly to the current input of the Solartron. This arrangement was used for all measurements made at frequencies above 10 Hz. Solutions containing less than 0.10 weight fraction mho/cm. To measure water have conductivities less than these solutions, a Keithley Model 427 current-to-voltage converter/amplitier was placed in the circuit between the Conductivity cell and the voltage input of the Solartron. The Keithley, an inverting amplifier, produced a 180° phase shift in Solartron output. At frequencies below 1 kHz, there were no other distortions either in impedance magnitude or in phase angle. Above 1 kHz, filtering circuits in the Keithley produced inescapable distortion. FDIS measurements were made with air in the conductivity cell in order to establish experimental limits. This yielded a low-frequency conductivity of order lO-" mho/cm, which we take as the noise floor of our equipment. Experimentswere performed with minimum modulation voltage consistent with useable S/N ratios. In practice, modulation amplitudes were 0.01, 0.10, or 1.0 V. FDIS measurements were made on a limited number of solutions at all three modulation amplitudes and gave indistinguishable results. Water electrolysis was a persistent threat, particularly at low frequencies and 1-V modulation amplitude. However, we saw no evidence for this electrochemical process. R e g t r y No. p-Dioxane, 123-91-1; water, 7732-18-5.
A Study of the HlgkPressure Phase Transhion in Lithium Hydroxide by Infrared and Raman Spectroscopy David M. Adams* and Julirn H a i m Department of Chemistry, University of Leicester, Leicester LE1 7RH, England (Received: February 25, 1991) The infrared and Raman spcctra of lithium hydroxide have been obtained up to pressures of 126 and 82 kbar, respectively. A phase transition, involving the formation of weak hydrogen bonds, was found to begin at close to 7 kbar upon compression. The spectra indicate that the high-pressure phase belongs to a centrosymmetric space group. A model is proposed in which hydrogen-bondedchain8 are formed within the layers containing the hydroxide ions, leading to the formation of an orthorhombic structure with cell doubling.
Introduction Crystals containing molecular anions commonly exhibit polymorphism. The simplest cases are those containing linear anions such as the alkali-metal cyanides, thiocyanates, and hydroxides. 0022-3654/91/2095-7064$02.50/0
The phase transitions in these systems usually involve a change in anion orientation. LiOH is unique among alkali-metal hydroxides in adopting the tetragonal anti-PbO (litharge) structure at STP (P4/nmm = DG', 0 1991 American Chemical Society
