2486
J. Phys. Chem. 1982, 86, 2486-2490
Dlelectrlc Properties of Electrolyte Solutions. 1. Sodium Iodide in Seven Solvents at Various Temperatures Paul Winsor, I V , and Robert H. Cole’ Chemistry Department, Brown University, ProvMence, Rhode Island 029 12 (Received: September 23, 198 1; I n Final Form: Januaty 7, 1982)
We report results from time domain reflection measurements for complex permittivities of sodium iodide solutions in methanol, formamide, N-methylformamide, dimethylformamide, dimethylacetamide, propylene carbonate, and dimethyl sulfoxide at concentrations in the range 0.02-1 M. Most of these are at 25 “C with results for methanol and propylene carbonate at lower temperatures to -29 “C. The observed relaxation effects in the range from 100 MHz to 8 GHz were all very nearly of Debye form with relaxation time decreasing slightly with concentration for the hydrogen-bonding solvents, but significantly larger at the highest concentrations in the two aprotic solvents. The decreases in static permitivity with concentration are in all cases larger than predicted by the Hubbardansager theory of kinetic depolarizationand the differences correlate better with solvent molecule dipole moments than with static solvent permittivity.
Introduction Until recently, decreases in static permittivity and changes in relaxation properties of solutions with increasing concentrations of ions have been interpreted in terms of static effects of ion interactions with polar solvent molecules. Models which have been proposed include saturation of a solvent continuum near the ions, irrotational binding of solvent molecules to ions, and polarizable ion spheres in a polar continuum; these have been reviewed by Hastedl and by Lestrade, Badiali, and Cachet.2 In 1977, Hubbard and Onsager3 pointed out another effect as a result of changing electric fields of ions and solvent dipoles moving in applied electric fields, with counterpolarization of both from the finite dielectric relaxation time of the solvent molecules. The HubbardOnsager4v5(HO) theory of this kinetic depolarization effect for a continuum model predicts a decrease in solution permittivity proportional to the product of solution conductance and dielectric relaxation time 7D. The first experimental results to be compared with the HO theory, by Van Beek and Mandel: showed that most of the observed decrements for salts in methanol and an appreciable fraction of decrements in water were accounted for by the theory. A striking confirmation was found by Hall and Cole6for sulfuric acid solutions with dipolar ions produced by an excess of either H,O or SO3, as the very large decrements for given ion concentrations result in the kinetic theory from the very long relaxation time ( T =~ 340 ps as compared to 8 ps for water and 50 ps for methanol), while the static models either predict negligible effects or require ridiculuously large solvation numbers. The solvent systems just mentioned are all hydrogen bonded. The sulfuric acid system is the most highly structured, yet most closely follows the HO theory predictions even though the theory is based on the treatment of the solvent as a continuum fluid. Clearly further studies are in order to define the circumtances under which the HO theory is fully applicable or fails. (1) Hasted, J. C. “Aqueous Dielectrics”; Chapman and Hall: London, 1973. (2) Lestrade, J. C.; Badiali, J. P.; Cachet, H. “Dielectric and Related Molecular Processes”; Chemical Society: London, 1975; Chapter 3. (3) Hubbard, J.; Onssger, L.; Van Beck, W. M.; Mandel, M. Proc. Natl. Acad. Sci. U.S.A. 94, 401 1977, 401. (4) Hubbard, J.; Onsager, L. J. Chem. Phys. 67, 1977, 4850. (5) Hubbard, J. J. Chem. Phys. 68, 1978, 1649. (6) Hall, D. G.; Cole, R.H. J. Phys. Chem. 85, 1981, 1065.
The purpose of the work reported here is to explore such questions by a systematic study of the dielectric behavior of electrolyte solutions employing a single salt, NaI, in several solvents with varying molecular weight, molecular dipole moment, and macroscopic dielectric behavior. The choice of NaI was made on the basis of solubility in a variety of solvents and amount of other relevant data in the literature for the solutions. The dielectric behavior of the aprotic polar solvents selected, as modified by the addition of conductive salts, had been studied only at frequencies above 1.6 GHz and at excessively high increments of salt concentration (0.5-2 M).’ Because of recent improvements in time domain reflectometry (TDR)8over the methods described in ref 6, it has become possible to study with reasonable precision systems with high static permittivities and relaxation times greater than 30 ps. The solvents used in this study are, in order of increasing molecular weight, methanol (MeOH), formamide (F), N-methylformamide (NMF), dimethyl sulfoxide (Me2SO), dimethylacetamide (DMA),and propylene carbonate (PC). Of these, only the first three are “associated” by hydrogen bonding, while the amides differ only by the successive addition of methyl groups and have nearly the same dipole moments (3.7-3.8 D). In addition, measurements over the range from 25 to -29 “C were made for the two solvents with the most widely differing characteristics: PC, which is the largest (mol wt = 102),most polar (p = 4.98 D), and aprotic; and MeOH (mol wt = 32), the least polar GL = 1.70 D), and hydrogen bonded. In a companion paper we report a study of several alkali halides in methanol to test the molecular theory of kinetic depolarization developed by Hubbard, Colonomos, and W ~ l y n e s . ~ Experimental Method
The arrangement employed here for TDR measurements is open circuit sample termination, where the sample is placed at the end of a 50-ohm coaxial line. The incident pulse Vo(t)at the input of the empty cell is reflected unchanged as V ( t )= Vo(t- 2d/c), where d is the effective electrical length of the cell inner conductor (actual length plus apparent length due to the inner conductor end ca(7) Barthel, J.; Behret, H.; Schmithals; F. Ber. Bunsenges. Phys. Chem. 75, 1971, 305. (8)Cole, R. H.; Winsor, P.; Mashimo, S. J.Phys. Chem. 84, 1980,786. (9) Hubbard, J.; Colonomos, P.; Wolynes; P. G. J. Chem. Phys. 71, 1979, 2652.
0022-3654182f2086-2486$01.25/0 0 1982 American Chemical Society
Dielectric Properties of Electrolyte Solutions
The Journal of Physical Chemistry, Vol. 86, No. 13, 1982 2487
pacitance). Denoting the reflection from the cell fded with sample by R(t),the total permittivity tt* of the sample is given by the simple relation6
- 40
I I I
0.10 M NaI in Methanol,
25'C
d
I I I
- 30 where uo and r are the Laplace transforms of Vo(t)and R(t),respectively. The effects of propagation and multiple
I
reflections in the finite sample length are given by the factor f ( 2 ) N 1- az2,where 2 = (wd/c)tt*1/2, for the short sample cell (d = 0.7 mm) used here. The V ( t )and R ( t ) records are obtained by sampling oscilloscope and signal-averaging techniques; these, as well as the numerical methods used to evaluate the transforms uo + r and uo r are described in detail elsewhere.8J0 Since the total permittivity of a solution with dc conductance diverges as (iw)-l in the limit of low frequency, w 0, it is useful to calculate a sample permittivity t* that is the total permittivity minus the permittivity attributable to dc conductance. Thus, we have
-
e*
4TUo
-iw
=
(2)
where uo is the dc specific conductance in esu. The "static" permittivity e8 for conducting solutions is then simply the limit E*(W 0). The specific conductance is proportional to P,/Q- where P, and Q m are the limits of Po@)= Vo(t) - R ( t ) and QO(t)= Vo(t) R(t) as t m. For a cell constant d defined in terms of a sample cell with the same inner to outer conductor diameter ratio m the 50-ohm line, the specific conductance (esu) is simply
-
+
5
20
30
Flgure 1. Complex permittivities for 0.10 M NaI in metanoi at 25 "C. Open and filled clrcles are values before and after subtracting dc conductance contribution to t"(w). Solld curve is a "Debye semicircle".
-
The cell constants d and a were found by calibration with water (to = 78.6 at 25 "C) as the standard of known permittivity; this gave d = 0.694 mm and a = 1.5. The f ( 2 ) correction fails when 121I0.4, which corresponds to 3.9 GHz for water and 8 GHz for methanol at 25 "C. The sample cell arrangement was similar to that described by Hall and Cole: the principal differences being in the arrangements for temperature measurement and control. The temperatures 25 and 1 "C were maintained by water and water/crushed ice baths. Below 0 "C, temperature was maintained by dry ice slushes in both the cell bath and a cooling jacket surrounding the coaxial line below the bath, using 1-octanol for -15 "C and 2 -octanol for -29 "C. The temperature was monitored by a twothermister probe and resistor network combination which gave a direct digital readout down to 0 "C, below which calibration with the melting points of known standards wm necessary. Temperature precision was within 0.3 "C over the whole temperature range and within 0.1 "C at room temperature. Since the purpose of this work was to measure relative changes in permittivity on addition of electrolytes to solvents rather than exact values, no special effort was made to purify the commerically obtained solvents. However, the solvents were assayed for water by Karl Fisher Titration. The solvents used in the preparation of the NaI solutions were methanol, Fisher certified ACS (
