TEMPERATURE DEPENDENCE OF TRANSPORT PROPERTIES OF IONIC LIQUIDS
3399
The Temperature Dependence of Transport Properties of Ionic Liquids. The Conductance and Viscosity of Calcium Nitrate Tetrahydrate and Sodium Thiosulfate Pentahydrate
by Cornelius T. Moynihan Department of Chemistry, California State colleoe at Lo8 Angelea, Lo8 Angele8, California 90098 (Received February 1, 1866)
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The conductivities, viscosities, and densities of liquid calcium nitrate tetrahydrate and sodium thiosulfate pentahydrate have been measured over the respective temperature ranges 5-70 and 5-50'. Equivalent conductance and viscosity data have been fitted by a computer to three-parameter equations of the forms, A = AT-"' exp[-kA/(T - To)] To). For both systems, the To parameter derived from conand g = BT"' exp[k7/(T ductance measurements has been found to be virtually identical with that derived from viscosity measurements. This furnishes good evidence that the To parameter can be given an unambiguous physical interpretation as the temperature at which molecular or ionic migration becomes impossible in the supercooled liquid.
-
I n a recent series of Angell has discussed the non-Arrhenius temperature dependence at low temperatures of the transport properties of ionic liquids. (Ionic liquids are considered here to be molten salts or highly concentrated solutions of salts in polar solvents, such that the solvent concentration is insufficient to satisfy more than the first coordination sphere of the ions.) I n particular, Angell has analyzed conductance data for such liquids in terms of a threeparameter equation originally derivede from a freevolume theory of liquid transport A
=:
AT-"' exp[-k.J(T
- TO)]
(1)
where A is the equivalent conductance, T is the absolute temperature, and A , kA, and To are the empirical parameters. The To parameter is interpreted as a theoretical glass transition temperature for the supercooled liquid, that is, the temperature at which molecular or ionic migration becomes impossible, the free volume disappears, and the configurational entropy of the liquid van is he^.^,^ To is expected to be somewhat lower than the experimental glass transition temperature, T,, determined by conventional means, because of the long relaxation times encountered in the measurement of the latter quantity.
If one assumes that the fluidity of an ionic liquid exhibits a temperature dependence similar to that of conductance, the viscosity expression corresponding to eq 1should be of the form5$* 71 =
BT"'exp[k,/(T
-
To)]
(2) where g is viscosity, and B, k,, and Toare again empirical parameters. Since conductance and viscous flow in ionic liquids should involve the migration of the same particles, it might be expected that the To parameters for the same system derived from conductance and viscosity data via eq 1and 2 would be identical. To test this conclusion, the conductance and viscosity of liquid calcium nitrate tetrahydrate (mp 42.7') and of liquid sodium thiosulfate pentahydrate (mp -50') were measured as a function of temperature. (1) C. A. Angell, J. Phys. Chem., 68, 1917 (1964). (2) C.A. Angell, ibid., 69, 2137 (1965). (3) C.A. Angell, J . Chem. Phys., 43, 2899 (1965). (4) C. A. Angell, J. Electrochem. Soc., 112, 1224 (1965). (5) C. A. Angell, J . Phya. Chem., 70, 2793 (1966). (6) M.H.Cohen and D. Turnbull, J . Chem. Phys., 31, 1164 (1959). (7)G.Adam and J. H. Gibbs, ibid., 43, 139 (1965). (8) P. B. Maoedo and T. A. Litovita, ibid., 42, 245 (1965).
Volume 70, Number 11
NovembeT 1966
3400
Since the non-Arrhenius behavior implicit in eq 1 and 2 appears most markedly in the metastable, supercooled state of a liquid, the choice of these two test systems was partially dictated by the fact that they are readily supercooled to well below their equilibrium freezing points. The non-Arrhenius temperature dependence of the conductance of calcium nitrate tetrahydrate2s4 and of the viscosity of sodium thiosulfate pentahydrateghave been reported previously.
Experimental Section Reagent grade Mallinckrodt calcium nitrate tetrahydrate was taken directly from a freshly opened bottle. Comparison of our density data with the precise composition os. density measurements of Ewing and l\llikovski10for calcium nitrate solutions indicates that the actual Ca(N0J2:Hz0 ratio of our salt was 4.04 =t 0.01. Reagent grade Baker and Adamson sodium thiosulfate pentahydrate was stored for several weeks in a hygrostat over a saturated aqueous solution of calcium chloride hexahydrate. Both salts formed clear liquids on fusion. Measurements were carried out in a 20-1. water bath whose temperature was regulated to +0.03" by a thermistor-activated temperature controller. Temperatures were measured with an NBS-calibrated precision thermometer. Conductivities were measured a t 1000 cps with a Leeds and Northrup Jones conductivity bridge. The conductivity cell was in the shape of a U-tube with the two arms connected by a 2-cm length of 2-mm i.d. capillary. Platinized platinum electrodes dipped into each arm of the cell; the arms were capped with ground-glass joints. The cell was calibrated with 0.1 demal KC1 solution at 25" and had a cell constant of 56.53 cm-l. T7iscosities were measured with two Cannon-Ubbelohde semimicro dilution viscometers of respective constants 2.871 and 0.2855 cstokes sec-l. The densities required for the viscosity and conductance calculations were measured with a dilatometer of approximately 26 cm3 capacity. The dilatometer was constructed by sealing a section of a volumetric pipet marked off in 0.1-ml divisions to the bulb of a 25-ml volumetric flask and was calibrated with distilled water. All measurements reported here were begun a t high temperatures and carried out on a descending temperature scale. I n a few cases, however, the samples were reheated following a run and a second series of measurements was carried out on an ascending temperature scale. I n all of these instances it was found that the results of the first series of measurements were reproducible. Calcium nitrate tetrahydrate samples were fused a t 50-60" in a tightly capped flask and poured The Journal of Physical Chemistry
CORNELIUS T. MOYNIHAN
rapidly into the conductivity cell, viscometer, and dilatometer just prior to the start of measurements. To avoid excessive loss of water on fusion, sodium thiosulfate pentahydrate samples were melted in sealed glass ampoules and were cooled to 50" before filling the various pieces of apparatus.
Results The conductivities K, viscosities 7, densities p , and equivalent conductances A of calcium nitrate tetrahydrate and sodium thiosulfate pentahydrate a t various temperatures are listed in Tables I and 11, respectively. Densities were linear functions of temperature within experimental error (0.05%) and are tabulated in equation form. The precision of both the conductivity and the viscosity measurements was of the order of 0.2%. Duplicate conductivity and viscosity runs agreed within 2% or less; the small discrepancy between runs is no doubt attributable to a small water loss a t high temperatures, since a t these high concentrations the transport properties are extremely sensitive to water composition. According to some recent measurements of Angelill on the conductances of calcium nitrate solutions a t O", the 2% discrepancy between our measurements on duplicate samples could be accounted for by a change of less than 0.2% in the mole fraction of water. For the purpose of assessing the temperature dependence of these transport properties, however, the internal precision of a given run is the important factor. The temperature dependence agreement between duplicate runs over the same temperature inTable I : Properties of Liquid Ca(NO& .4H205 -Conductivity--I,
'L
--Viscosity---
OC
ohm-' cm-1
cma ohm-' equiv -1
5.04 9.70 14.64 22.47 29.62 39.63 49.87 59.09 69.88
0.000983 0.001537 0.002339 0.004200 0.00658 0.01115 0,01742 0.02451 0.03453
0.0658 0.1031 0.1573 0.2835 0.4457 0.759 1.192 1.685 2.386
t,
' Density:
p
(g cm-9 = 1.768
t,
'I,
"C
CP
7.66 14.65 21.99 29.66 39.69 49.79 59.21 69.71
1489 715 370 208.2 111.2 66.2 43.8 29.72
- 0.00085t(OC).
(9) 5. S. Urazovskii and P. A. Chernyavskii, Dokl. Akad. Nauk SSSR, 111, 640 (1956). (10) W. W. Ewing and R. J. Mikovski, J . Am. Chem. Soc., 7 2 , 1390 (1950).
(11) C. A. Angell, private communication.
TEMPERATURE DEPENDENCE OF TRANSPORT PROPERTIES OF IONIC LIQUIDS
TOwas considered acceptable if the average per cent deviation, given by
Table 11: Properties of Liquid NazS203.5H~0a -----Conductivity----
OC
ohm-1 em-1
& om2 o h m - ] equiv-1
5.04 9.74 17.43 24.98 33.73 42.61 50.15
0.00951 0.01388 0.02351 0.03638 0.0551 0.0787 0.1016
0.700 1.023 1.738 2.698 4.102 5.88 7.62
x,
t.
a
Density:
p (g
cm-9 = 1.691
-
av
-Viscosityt,
r),
O C
CP
5.23 9.59 17.53 25.00 33.61 42.74 49.91
331 218.4 114.1 68.3 41.8 26.94 19.99
0.00071t('C).
terval, as determined by the computer curve-fitting procedure described below, was exact. Equivalent conductances were calculated from the expression A
=
KE/P
where E is the equivalent weight of the salt hydrate (118.08 g equiv-' for Ca(NOa)2.4H20 and 124.09 g 5H20). The Arrhenius plots of equiv-1 for IYa2Sz03. log A and log ( l / ~vs. ) 1/T exhibited the expected deviations from linearity. The conductance and viscosity data for the two systems were fitted to equations of the form of (1) and (2) by the IBM 1401 computer in the following fashion. The computer was programmed to select To values at 1" intervals over a specified temperature range. For each Tovalue a least-squares fit of the experimental data to the logarithmic form of eq 1 or 2 was performed, and the values of A or B and kh or k, corresponding to that TO were printed out. For each To value the computer also calculated and printed out the sum of the absolute values of the per cent deviations of the experimental data points from the least-squares curve, where per cent deviation is defined = 100(Aexpti -
&alcd)/&xptl
or
% deviation
= lOO(Vexpt1
- ?osled)/Vexptl
AexPtl and qexptl are the measured values of conductance and viscosity, and Acalcd and Vcalod are the values calculated from the least-squares curve for a given value of TO. Such sums of the absolute values of the per cent deviations were observed to pass through a fairly sharp minimum as the value of To was varied. The fit of the experimental data achieved with a given
1%
1 devl = n
n
1%
devl
where n is the number of data points, was less than or equal to the experimental precision. The empirical parameters of eq 1 and 2 evaluated in this fashion for the data in Tables I and I1 are given in Table 111, along with the average per cent deviation of the experimental points from the calculated curve for a given To. To illustrate the precision of the curve-fitting procedure, some parameters which do not fit the data within experimental error are included for the conductance of calcium nitrate tetrahydrate. Likewise, Figure 1 shows a plot of % deviation us. temperature for the conductance of calcium nitrate tetrahydrate for three values of To. It is evident from this figure that the least-squares curves for the To values of 196 and 206 show systematic deviations from the experimental data, while the deviations of the curve for To = 201 from the experimental data are much smaller
Table 111: Parameters for Empirical Equations for Conductance and Viscosity of Calcium Nitrate Tetrahydrate and Sodium Thiosulfate Pentahydrate. Parameters in Rows Marked with an Asterisk ( * ) Do Not Fit Data within Experimental Precision
A or B
kA or k,
To
a v / % devl
Conductance of Ca(N0&.4H~0
4846 3859 3620 3402 2668
689 639 626 613 664
196 200 201 202 206
0.8 * 0.3 0 . 2 Best fit 0.2 0.9 *
Viscosity of Ca(N03)2.4H20
0.01100 0.01192 0.01275
691 676 662
204 205 206
0.3 0 . 2 Bestfit 0.3
Conductance of Nap( SZO~)5Hz0
8858 7970 7141
505 484 464
202 204 206
0.3 0 . 2 Best fit 0.2
609 583 559
201 203 205
0.3 0 . 1 Best fit 0.2
3
% deviation
3401
Viscosity of 0.007552 Na~(S203)-5H~0 0.008657 0.009820
and random in direction. Plots of this sort for all other series of measurements of conductance and viscosity on other samples are similar in appearance. In particular, the deviations of the least-squares curves from the experimental data points for the best-fit values of Toare always random and nonsystematic. Volume YO, Number 11
November 1966
CORNELIUS T. MOYNIHAN
340'2
2.0
1.0
i *
.e
0.0 -e
8 - 1.0
- 2.0
1
I
1
1
20
0
40
I
I
1
60
80
t , "C.
Figure 1. Plot of per cent deviations of experimental values of the conductance of calcium nitrate tetrahydrate from the least-squares curve for various values of TO. AJ TO= 196; 0,To= 201; 0, TO= 206; % ' deviation = 100(&xptl
- AwlcdAexptl).
This method of data treatment has thus allowed an evaluation of the Toparameters with an uncertainty of only 1 or 2". As was stated previously, the discrepancies between duplicate runs showed up entirely in the preexponential A or B parameters. The bestfit Toparameters for duplicate runs never differed by more than lo, and values of k, or k, corresponding to the same value of Towere identical within 0.5%. The conductivities for calcium nitrate tetrahydrate previously reported by Angel14are from 5 to 25% lower than the conductivities determined in the present work, the discrepancies being largest at low temperatures. The fact that the relative differences are not constant suggests that the source of the discrepancies may lie in Angell's temperature measurements, especially since his conductivity measurements were performed on a sample which was being cooled continuously at a slow rate rather than on a thermostated sample. Slight differences in melt composition may also explain the discrepancies, since the conductivity is extremely sensitive to water content in this composition range." Computer fitting of Angell's data to eq 1 yields k, = 638 and To = 203. These values are in fairly good agreement with those listed in Table 111, showing that small errors in temperature measurement or composition do not have any drastic effect on the temperature-dependence parameters derived by the curve-fitting procedure used here.
Discussion As the data in Table I11 indicate, the agreement between the To parameters for conductance and viscosity is excellent for both calcium nitrate tetrahydrate (201°K vs. 205°K) and sodium thiosulfate pentahydrate (204°K vs. 203°K). This constitutes strong evidence for an unambiguous physical interpretation of To as the previously discussed theoretical glassThe Journul of Physical Chemktry
transition temperature for the supercooled liquid. An experimental glass-transition temperature, T,, of 231 OK, determined by expansivity measurements, has been reported for sodium thiosulfate pentahydrate;12 as expected, the value of To for this system lies below that of the measured T g . For both systems studied here k, is larger than kA. This is a manifestation of the (often much larger) differences in Arrhenius activation energies for conductance and viscosity generally observed for molten salts13 and for concentrated aqueous solution^.'^ An explanation often accorded this phenomenon is that one of the ions of the ionic liquid is more mobile than the others. Electrical conduction is presumed to occur chiefly by the migration of the more mobile ion. In viscous flow, however, the ions are constrained to move along together, and the ease of such flow is determined primarily by the resistance afforded to the motion of the less mobile ion. This resistance to ionic migration may be considered to arise from a conventional activation e n e r g ~ ' ~or J ~from the requirement that some critical free volume be available to an ion before migration becomes possible.6 The fact, however, that self-diffusion measurements in molten salts show that the Arrhenius activation energies are very nearly the same for cations and anions and that mobility differences arise primarily from differences in preexponential terms15 seems to argue against this point of view. An alternative (and considerably more attractive) picture of liquid transport, which avoids dissection of the transport properties into contributions from the individual ions, postulates that migration involves the cooperative rearrangement of a group of ions of a certain minimal size, and that this rearrangement is opposed by a potential energy barrier.5,' In this case, the fact that kA > k, implies that this barrier opposing the cooperative rearrangement is greater for the shearing stresses encountered in viscous flow than for the linear free-energy gradient (electrical potential gradient) stresses encountered in electrical conduction. Why this should be the case, however, is not obvious at this time. Angel14 has previously claimed that the value of kA was very nearly the same for the systems C S ~ ( N O ~ ) ~ KN03, Ca (N03)2-KN03-H~0, and Mg(NO3)2-Hz0 and equal to 675 f 15. Our value of k, for the Ca(N03)2.4Hz0system (626 f 13) is slightly lower (12) M. Samsoen, Ann. Phys., 9, 35 (1928). (13) J. P. Frame, E. Rhodes, and -4. R. Ubbelohde, Trans. Faraday SOC.,55, 2039 (1959). (14) M. L. Miller, J . Am. C h m . SOC.,60, 189 (1956). (15) B. R. Sundheim, Ed., "Fused Salts," McGraw-Hill Book Co., Inc., New York, N. Y., 1964, pp 224-227.
BIPHASIC OXIDATION-REDUCTION WITH
A
3403
LIQUIDELECTRON EXCHANGER
than this. Part of the discrepancy is undoubtedly assignable to the different method of curve fitting employed by Angell. It remains true, however, that the values of k A for the above systems are remarkably similar. The value of k A for the sodium thiosulfate pentahydrate system ia considerably smaller than k.,, for the nitrate systems. This difference is not surprising in view of the difyerences between the ionic components of the two types of systems. The almost exact agreement between the To values for the calcium nitrate tetrahydrate and the sodium thiosulfate pentahydrate
systems is undoubtedly fortuitous, although according to the arguments of Angelll1s4in which concentrated aqueous solutions are compared to fused salts with large, weak field ions, Tovalues of about this magnitude are to be expected.
Acknowledgment. The assistance of M. Jaro, who performed the computer calculations, and of C. A. Angell, who provided several valuable comments on this work, is gratefully acknowledged. This work was supported in part by a National Science Foundation Institutional Grant.
Biphasic Oxidation-Reduction Reaction with a Liquid Electron Exchanger
of the Hydroquinone-Quinone Type
by G. Scibona, P. R. Danesi, and F. Orlandini Centro Studi Nucleari, Casaccia, Rome, Italy
(Received February 7, 1966)
The electron exchange at ct liquid-liquid .interface between tetrachlorohydroquinone in a suitable organic solvent and an aqueous solution of metal ions, able to change valence state, has been studied. The aim of this work is the investigation of the physical properties of this organic system which behaves like a liquid electron exchanger. The standard oxidation-reduction potential Eo' of the organic electron exchanger has been measured by means of a two-phase potentiometric titration technique carried out in 1 N HCIOI and 1 N H2S04. The dependence of the oxidation-reduction potential E on the pH also has been studied. A slope of (5.5 i 0.5) X was found, supporting a two-electron mechanism. An independent evaluation of Eo' was carried out by determining the equilibrium constant of the reaction 2Fe+3 R(0H)zcorg) = 2Fe2+ RO2corg) 2H+. Some efforts were also made in order to study the reaction rate of the oxidation-reduction between tetrachlorohydroquinone and Fe3+.
+
Introduction The heterogeneous electron exchange between an aqueous solution of an appropriate oxidation-reduction couple and an organic solution of a liquid electron exchanger, hydroquinone-quinone type, hm been studied by us with the aim of obtaining qirantitative
+
+
information about the potentials of the electrode reaction at the oil-water interface. The few data existing in the literature' on liquid(1) C. F. Coleman, U. S. Atomic Energy Commission Report ORNL CF-61-5-74, M~~ 1961.
Volume 70, Number 11
November 1966
