DARWINJ. M E A DWITH RAYMOND M.
1720
[CONTRIBUTION FROM
THE
FUOSS
Vol. G2
RESEARCH LABORATORY OF THEGENERAL ELECTRIC Co. ]
Dependence of Conductance on Field Strength. 11. Tetrabutylammonium Bromide in Diphenyl Ether at 50’ Bk DARWINJ. MEADWITH RAYMOND M. Fuoss I. Introduction In the first paper of this series,‘ we showed that the Wien effect for tetrabutylammonium picrate in diphenyl ether a t 60 cycles was in agreement with Onsager’s theory.2 A dependence of the Wien coefficient on concentration and frequency also was observed. In this paper, further work on the frequency effect is reported. We find that the Wien coefficient decreases with frequency a t concentrations where the product of the Langevin time of relaxation into frequency is of the order unity. This time is defined by the equation2 7L =
1 -
€I
8 8 9 X 10”
K
where E’ is the dielectric constant and K is the specific conductance (in mho/cm. cube) of the solution. I t is a measure of the time required for establishment of equilibrium between charge distribution and external electrical field. For diphenyl ether, e’ = 3.53 a t 50°, so (1) becomes for this solvent TL =
15.6 X 10-14/~sec.
(2)
(The solutions to be considered are so dilute that the dielectric constant is not appreciably increased.) At N , tetrabutylammonium bromide in diphenyl ether a t 30’ has a conductance of 3.43 X so T L = 0.46 millisecond. Consequently frequencies of the order of kilocycles should show a dispersion of the Wien effect, as found in the data presented here.
11. Materials, Apparatus and Procedure Diphenyl ether was purified as before.’ Tetrabutylammonium bromide was that used in the low voltage work in chlorobenzene. Cells, bridges, and general procedure were the same as in the preceding work.’ For frequencies above 60 cycles, a variable speed alternator (480-1920 cycles a t 450-1800 r. p. m., 55-220 volts output) was used. For low voltages, the machine fed the bridge circuit directly. For the higher voltages, a 1-KVA transformer was used: it had 4480 turns in the secondary, and primary taps a t 100, 150 and 300 turns, giving output to input ratios of 15, 30 and 45. In order to get a good sine wave output from the generator-transformer circuit, 8pJ (Pyranol condensers) were connected (1) (a) Mead and Fuoss, THIS J O U R N A L , 61, 2047 (1939), (b) correction, tbrd , 61, 3589 (1939). (2) Onsager, J. Chem Phys., 2, 599 (1934). (3) McIntosh, Mead and Fuoss. THISJ O U R N A L , 62, 506 (1940).
across the primary and a load of 60,000 0 (“blue sticks”) across the secondary. One side each of primary and secondary were grounded: With this circuit, the output gave a very nearly circular Lissajou figure when fed into the vertical plates of an oscilloscope whose horizontal plates were connected to the output of a General Radio beat frequency oscillator set a t the same frequency. During the voltage runs on the solutions, the frequency was determined by beating against the above oscillator, which was in turn checked against the fundamental and harmonics of a 1000-cycle fork. Voltages were read on an electrostatic voltmeter, 0-5 KV range. The usual high series resistance protection in the meter was replaced by 75,000 il in order to make the readings independent of frequency in our working range; the capacity of the meter was 2 0 ~ ~ fThe . calibration was checked by measuring the current through our 100,000 il high voltage ~ t a n d a r d . ~In calibration the whole range of frequencies and voltages were covered; a typical calibration point is as follows: f = 2000 cps, i = 28.9 milliamperes, if? = 2.89 X lo3, E. S. voltmeter = 2.93 KV, i R / E = 0.986.
111. Experimental Results The low voltage data used to establish the conductance-concentration curve are given in Table I. These were determined in some cases a t 1000 cycles on the parallel bridge and in others on the resistance or Schering bridges a t GO cycles. In contrast to tetrabutylammonium picrate, the solutions of the bromide gave low voltage conductances independent of frequency. For example, for a 8.27 X N solution, K (60 -) = 3.822 X K (500 -) = 3.813 X and K (2000 = 3.818 x 10-9. The conductances a t both high and low voltages were independent of cell geometry when reduced to a field strength basis, so designation of the cells used is omitted in the tables. Typical voltage curves a t three frequencies, 60, 600, and 1000 cycles, are given in Table 11. Field strength, E , is given in average kilovolts per centimeter; it is determined from the root mean square voltage V, read on the electrostatic voltmeter by the relationshipl
->
E = 2 ~ ‘ ‘ i Z v ~ / ~-( rr,)~
(3)
where r l and r2 are the radii of the electrodes. The conductances are given as ratios to the low voltage conductance K ~ which, , by definition, is a (4) Fuoss, i b i d . , 60, 451 (1938).
voltage so low that doubling it makes no detectable change in conductance. TABLEI CONDUCTANCE OF TETRABUTYLAMMONIUM BROMIDEIN DIPHENYL ETHERAT 50 O AND Low VOLTAGE c
x
104
A
x
c
103
x
A X 108
104
3.48 4.62 1.504" 8.270 1.0024 3.43 4.57 7.840 0.887 3.52 7.180 4.45 ,865 3.53 5,009" 4.06 ,785 3.58 3.94 1.051 ,448 3.76 3.94 4.001" ,2867 4.20 3.88 3.587 4.56 3.70 ,1925 3.009' ,0964 5.78 2.558 3.68 ,0479 7.93 3.54 1,999" ,0240 11.28 3.59 1.782 a Voltage-frequency runs made on these solutions. Their low voltage values are shown as solid circles in Fig 1.
TABLEI1 WIEN EFFECTFOR TETRABUTYLAMMONIUM BROMIDE IN DIPHENYL ETHERAT 50" AND VARIABLE FREQUENCY E
x(~O)/KO
E
x(600)/xo
E
c = 5.009 X 0.74 1.86 3.71 B.57 7.43 9.25 10.81 12.70 15.41 16.03 18.00
1.002 1.011 1.036 1.061 1.102 1.130 1.164 1.220 1.261 1.292 1.289
0.92 1.37 1.83 2.75 3 87 4.17 5.57 6.74 7.48 8.15 8.98
1.004 1.007 1.014 1.026 1.043 1.051 1.071 1.087 1.100 1.114 1.128
0.74 1.86 3.71 5.50 7.43 9.25 11.03 13.11 14.74 16.71 18.08
1.003 1.015 1.043 1.064 1.102 1.125 1.172 1.214 1.243 1.298 1.322
121
DEPENDENCE OF CONDUCTANCE ON FIELD STRENGTH
July, 1940
0.37 2.78 3.79 5.61 7.43 9.36 11.14 13.07
1.002 1.023 1.037 1.061 1.088 1.125 1.157 1.196
14.85 16.71
1.246 1.288
c = 4.001 X 0.24 1.001 1.36 1.008 1.83 1,013 2.75 1.023 3.74 1.035 4.58 1.047 5.50 1.063 6.32 1.073 7.31 1.091 8.24 1.108 9.16 1.124 c = 3.009 X 10W4 0.48 1.003 3.79 1.039 5.57 1.063 7.43 1.089 9.28 1.112 11.14 1.141 13.07 1.170
0.64 5.64 7.54 9.28 11.14 13.11 14.85 16.71
0.36 2.42 2.75 3.66 4.58 5.50 6.60 7.38 8.24 9.20
0.74 5.68 7.50 9.28 11.18 13.03 15.11 16.71
c = 1.999
5.57 7.28 9.28 11.00 12.96 14.85 16.50 18.38
1.079 1.098 1.138 1.168 1.216 1.246 1.275 1.310
1.86 3.71 5.57 7.46 9.36 10.84 13.00 14.85
1.018 1.048 1.076 1.111 1.141 1.175 1.210 1.249
0.48 3.71 5.57 7.43 9.32 11.21 12.96 14.96 16.71
x
10-4
1.002 1.038 1.082 1.087 1.116 1.140 1.172 1.208 1.234
c = 1.504 x 10-4 5.61 1.060 7.54 1.088 9.36 1.108 11.25 1.136 13.03 1.168 14.93 1.183 16.79 1.227 18.27 1.267
0.87 5.57 7.43 9.36 11.25 13.26 14.85 16.86 18.49
1.002 1.059 1.082 1.114 1.133 1.166 1.197 1.219 1.237
5.57 7.46 9.36 11.14 12.85 15.04 16.89
1.053 1.081 1.105 1.130 1.148 1.183 1.204
c = 1.002 x 10-4 1.37 1.011 1.83 1,015 2.75 1.026 3.65 1.038 4.62 1,050 5.48 1.061 6.41 1.075 7.31 1.088 8.21 1.101 9.16 1.114
2 . 38 1.017 0.92 1.007 1.024 1.83 1.021 2. 77 ~(1000)/~0 2.76 3 . 68 1.035 1.037 1.046 4. 58 3.66 1.053 1,059 5. 50 4.58 1.065 1.003 1.073 6 . 45 5.50 1.081 1.057 7 . 29 1.086 6.41 1.100 1.082 8. 24 7.33 1.114 1.098 1,112 8.28 1.133 9 . 16 1.109 1.161 9.09 1.147 1.200 1.215 c = 0.601 x 10-4 1.251 1.062 1.86 1.019 2.78 1.021 5.64 1.086 3.71 1.034 7.50 3.71 1.049 1.110 5.57 1.080 5.68 1.060 9.32 1.138 7.50 1.082 11.21 7.43 1.108 1.165 9.32 1.106 13.03 9.25 1.138 1,001 11.14 1.172 1.185 11.25 1.132 14.63 1.018 1.218 13.03 1.158 16.93 13.00 1.206 1.021 14.85 1.243 14.96 1.189 1.031 16.78 1.202 16.71 1.268 1.045 18.38 1.212 1.057 1.069 IV. Discussion 1.082 The conductance-koncentration curve (Fig. 1.096 1.113 1) is typical for electrolytes in solvents of low
1.003 1.060 1.085 1.103 1.128 1.159 1.196 1.222
dielectric constant: i t comprises a linear section with slope ( - '/2) a t low concentrations on a log A - log c plot, followed by a minimum a t lo-* N . Assuming Aov = 0.484, we estimate A. = 23.1. From a plot5 of h+g(c) against c, we find (5) Fuoss and Kraus, THISJOURNAL, 55, 1019 (1933). An approximation for g ( c ) was used here, which is much simpler to handle than the original formula. I t is -(2.303A;fl ..)a login g(c) e -0.4343 d l 0 0 0
a0"2
where p is the Debye-Hiickel coefficient for activity, a is the Onsager coefficient for conductance and K is the specific conductance. For diphenyl ether at SO", log g(
