ANALYSIS OF
THE
IONIC COMPOSITION OF THE DIFFUSE DOUBLELAYER
reaction similas to eq 14 militating against the hole migration. AEIa result, very little solute cation is formed, while the mion is produced to the extent of the yield of scavengeable electrons. In contrast to primary and secondary amines, tertiary amines conduct positive holes, apparently because of the lack of protonation reaction. Corresponding to the difference, the esr results for DTBPO solutions in sec-butylamine or diisopropylamine were similar to those of MTHF solution, while triethyla,mine, tri-n-butylamine, and dimethylcyclohexylamine solutions gave analogous results to those of 3MP rgolution. Even in the protic amines or MTHF, a limited amount of DTBPO cation may be produced at a high solute concentration. The slight amount of methyl radical appearing on photobleaching the MTHF solution (Figure 3, right) is thus explained in the framework discussed above. In methanol solutions not a trace of methyl radicals was detected in esr measurements, while about twice as much of the methanol radical, CH20H,was produced as in pure methanol glasses which substantiates reactions 9 and 10.
727
Esr Studies of Irradiated Hydroperoxide and Hypochlorite Solutions. Reactions 10 and 13 are also supported by the following result. y irradiation of t-butyl hydroperoxide or t-butyl hypochlorite in methanol, MTHF, and 3MP solutions at -196” did not produce any color center nor the solvent-trapped electron band, and no new esr spectrum due to the additives appeared. The result is readily accounted for by the reactions
t-BuOC1
+ e- -+t-BuO. + C1-
(20)
followed by an H atom abstraction from the matrix molecule by the butoxy radical. The fact that the hydroperoxide anion decomposes into fragments while DTBPO anion exists stably is also explained in terms of the higher electron affinity of OH than that of t-BuO and the higher solvation energy of OH- than that of t-BuO-.
Analysis of the Ionic Composition of the Diffuse Double Layer in Mixed Electrolytes by Charge-Step Chronocoulometry by Fred C. Anson Contribution No. 8666 from the Gates and Crellin Laboratories of Chemistry, California Institute of Technology, Pasadena, California 91 109 (Received August 31, 1967)
A new, faradaic method for determining the ionic composition of the diffuse double layer at electrodes is described. The method is simpler and faster to use than the standard electrocapillary method although not as accurate. Application of the method to solutions of zinc nitrate in lithium, sodium, potassium, cesium, and magnesium nitrate supporting electrolytes produced results which were in good agreement with the predictions of the Gouy-Chapman theory for mixed electrolytes. The ionic composition of the electrical double layer at mercury electrodes has been determined for about two dozen aqueous electrolytes by means of classical electrocapillary measurements. This procedure has the attractiveness of thermodynamic rigor but the disadvantage that the necessary data are tedious to gather and require lengthy analysis to obtain accurate values of the surface excesses. The relative paucity of doublelayer data, in spite of their indispensability for accurate
interpretation of electrochemical kinetic measurements, can be largely attributed to the considerable experimental effort required to obtain and analyze them by the classical procedure. In this paper an alternative method for determining the ionic composition of the double layer is described. (1) P. Delahay, “Double Layer and Electrode Kinetics,” Interscience Publishers, Inc., New York, N. Y., 1965, Chapter 2.
Volume 78, Number 2 February 1968
728 The method, charge-step chronocoulometry,2 is based on measurements of diff usion-limited faradaic reactions a t electrodes rather than thermodynamics. It is thus less rigorous than the classical electrocapillary method but offers advantages in speed and simplicity. It has been applied here to a study of mixed electrolytes in which the ionic reactant is a significant component of the diffuse double layer. Good agreement was found between the experimental results and the predictions of the Gouy-Chapman theory.3 The technique of potential-step chronocoulometry has been thoroughly described4J and widely applied to the measurement of specifically adsorbed reactants at elect r o d e ~ . ~ -For ~ charged reactants, the value of the amount adsorbed provided by the chronocoulometric method includes the surface excess of reactant contained in the diffuse double layer as well as that specifically adsorbed on the electrode surface. All previous chronocoulometric measurements were carried out in solutions containing much larger concentrations of supporting electrolyte than of reactant so that the diffuse layer was composed essentially entirely of the supporting electrolyte ions and only specifically adsorbed reactant contributed to the measured adsorption. However, by employing amore dilute supporting electrolyte and multiply charged reactants, the amount of reactant in the diffuse layer is increased to readily measurable values. For cases where no specific adsorption of the reactant occurs, the diffuse layer is the only source of the measured adsorption and an analysis for one component of the diffuse layer is obtained. Potential-step chronocoulometry is not well suited to experiments in dilute electrolyte solutions because of the severe difficulty in maintaining true potential control in the presence of the larger uncompensated resistances present. Charge-step chronocoulometry is immune to this problem and i t was therefore the method of choice in the present experiments. Charge-step chronocoulometry consists of the rapid injection into an electrode of an amount of charge great enough to bring the electrode potential well beyond the polarographic half-wave potential of the reactant being studied. The subsequent open-circuit potential-time transient is determined by the diff usion-limited rate a t which reactant reaching the electrode consumes the injected charge by means of a faradaic reaction. The potential-time transient is recorded oscilloscopically and analyzed by conversion into the corresponding charge-time transient with the aid of appropriate charge-potential data obtained in reactant-free supporting electrolyte. The usual chronocoulometric plot6 of charge vs. square root of time is then made and the amount of adsorbed reactant, if any, is determined by comparing the charge-axis intercept of this plot with the amount of injected charge. The charge-time behavior is given by The Journal of Physical Chemistry
FREDC. ANSON
where AQ is the change in the charge density on the electrode produced by the injection of charge, Qinj ; C and D are, respectively, the bulk concentration and diffusion coefficient of the reactant, I’ is the total amount of adsorbed reactant in mo1es/cm2, and the other symbols have their usual significance. Thus, a plot of Qinj AQ VS. t”* will pass through the origin when there is no reactant adsorption and will have a positive intercept equal to nFr in the presence of adsorption. A schematic presentation of these properties is in Figure 1. The fact that the charge-step chronocoulometric technique involves an open-circuit measurement of the electrode potential makes it far superior to potentialstep chronocoulometry for investigations of the more dilute electrolyte solutions necessary to obtain measurable incorporation of reactant into the diffuse layer. Attempts to employ potential-step chronocoulometry in solutions having ionic strengths much below 0.1 were thwarted by the severe degradation of the real rise time of the potential steps introduced by the larger uncompensated resistances.’O
-
u
( T I ME 1’2
Figure 1. Schematic charge-step chronocoulometric plots: A, no reactant adsorption; B, with nFr moles/cm2 of adsorbed reactant.
(2) F. C. Anson, Anal. Chem., 38, 1924 (1966). 1, Chapter 3. (4) F. C. Anson, Anal. Chem., 38, 54 (1966). (5) J. H. Christie, R. A. Osteryoung, and F. C. Anson, J . Electroanal. Chem., 13, 236 (1967). (6) F. C. Anson, Anal. Chem., 36, 932 (1964). (7) F. C. Anson and D. A. Payne, J . Electroanal. Chem., 13, 36 (1967). (8) F. C. Anson, J. H. Christie, and R. A. Osteryoung, ibid., 13, 343 (1967). (9) B. Case and F. C. Anson, J . Phys. Chem., 71,402 (1967). (10) 0.Lauer and R. A. Osteryoung, Anal. Chem., 38, 1106 (19661.
(a) Reference
ANALYSIS OF
THE
IONIC COMPOSITION OF
THE
DIFFUSEDOUBLE LAYER
The charge-potential characteristics needed to convert the measured potential-time transients into the corresponding oharge-time transients were obtained by adjusting the electrode potential to -900 mV us. sce in pure supporting electrolyte, injecting small increments of charge, and measuring the resulting step-change in potential. Plots of the resulting data were used to convert potentials to charges in the experiments with reactant present. The potential measurements in the chronocoulometric experiments were confined to the range from - 1.25 to - 1.60 V us. sce in order to maintain diffusion control of the reduction of zinc ion and to avoid any reduction of the supporting electrolyte. I n order to calculate the theoretical values of the surface excess of zinc, the total electronic charges on the electrode at the initial potentials were needed. They were obtained by measuring the amount of injected charge needed to change the electrode potential from the point of zero charge (taken as -518 mV us. sce in these solutions on the basis of Payne's datal') to the various initial potentials used in the chronocoulometric experiments (-500, -600, -700, -800, and -900 mV us. sce). Solutions containing the zinc ion were used for making these measurements because of the dependence of the double-layer capacity on the concentration of zinc ion when substantial nonspecific adsorption of zinc occurs. This procedure, in which zinc ion is present during the measurements of the initial charges on the electrode but absent during the measurement of the charge-potential characteristic that is used to analyze the experimental potential-time traces, is entirely appropriate because the diffuse layer is free of zinc ion at potentials negative of -1.25 V us. sce whether or not zinc ion is present in the bulk of the solution. Note that the possible ambig~ities~ in~the s~~ true charge-potential characteristic for the electrode in the vicinity of the standard potential of the zinc ion-zinc amalgam couple are avoided with the procedure described because all of the data with zinc solutions are taken while the electrode is a t potentials far from the standard potential. I n more dilute solutions, some adjustment may be necessary in the concentration of the pure supporting electrolyte usedl to measure the charge-potential characteristic because of the significant changes in the concentration of supporting electrolyte a t the electrode surface that can be produced by the faradaic consumption of the reactant. For example, suppose one intended to study a solution containing 1 mM potassium nitrate as supporting electrolyte and 1 mM thallous nitrate as reactant (these particular salts were selected because the three ions involved, K+, T1+, NOa-, all have essentially identical diffusion coefficients and ionic mobilities). During the course of a charge-step chronocoulometric experiment with this solution the thallous ion concentration at the electrode surface would be zero and the diffuse double layer would be in equilibrium
729
with a potassium nitrate solution having a concentration of 1.5 mM (assuming that the transference numbers of potassium and nitrate are exactly equal in this solution and independent of Concentration), Therefore, the charge-potential characteristic needed to analyze the experimental potential-time data should be determined in a 1.5 mM rather than a 1.0 mM solution of potassium nitrate. In the experiments reported in this paper7the concentration of the supporting electrolytes was 0.01 M and the concentration of the reactant, zinc ion, was ca. 0.2 mM so the change in ionic strength a t the electrode surface produced by the charge injection was very small and was neglected in the analysis of the data. The charge-potential characteristics were determined in 0.01 M solutions of lithium, sodium, potassium, cesium, and magnesium nitrates.
Experimental Section Apparatus. A conventional cell was employed with a commercially available (Brinkman Instruments, Inc.) hanging mercury drop electrode, a platinum wire counterelectrode, and a saturated calomel reference electrode separated from the main body of the solution by a salt bridge composed of an aliquot of the test solution. With 0.01 M electrolyte solutions the total resistance of the cell amounted to several thousand ohms. In order to inject the rather large charges (up to 20 pC/cm2) required in times short enough (1-10 psec) to be negligible on the experimental time scale (0.5-4 msec), it was necessary to use small injection capacitors (500-1000 pF) charged with relatively high voltages (200-700 V). The coulostatic injection circuits described by Delahay and Aramata14 were found to be unsatisfactory for our purposes because the charge tended to leak from the injection capacitor at the higher voltages and because switching transients were difficult to eliminate. The injection circuit employed is shown in Figure 2. It has the advantage that any leakage from the injection capacitor is continuously replenished until the instant of charge injection. The circuit has functioned entirely satisfactorily with injection voltages up to 800 V. The potential of the reference electrode was monitored with respect to the grounded working electrode by means of a fast-response cathode ray oscilloscope (Tektronix Type 531) equipped with a vertical plug-in amplifier (Tektronix Type W) designed for very rapid recovery from overload. The reference electrode was connected to the oscilloscope input by means of an attenuating probe with an input resistance of 10 megohms (Tektronix P6006). The potential-time transients were photographed with a Polaroid camera (Tektronix (11) R. Payne, J. Phys. Chem., 69, 4113 (1965). (12) P. Delahay, K. Holub, G . Susbielles, and G . Tessari, ibid., 71, 779 (1967). (13) K. Holub, G . Tessari, and P. Delahay, ibid., 71, 2612 (1967). (14) P. Delahay and A. Aramata, ibid., 66, 2208 (1962). V o l u m e 78, N u m b e r P February 1068
FREDC.ANSON
730 +IJvolt
I
e
/E
1 Lt
1
L -
Figure 2. Charge injection circuit. LI, L2, the activating coils for relay 1 and relay 2, respectively; RLY 1, DPDT mercury-wetted relay, C. P. Clare & Co., Type HG 2A 1072; RLY 2, SPDT mercury-wetted relay, C. P. Clare & Co., Type HGS 5008; P, 1.5-V biasing potentiometer; V. M., digital voltmeter; CI, precision adjustable capacitor, Electro Scientific Industries, Portland, Ore., Model DC 57; delayed trigger circuit, an operational amplifier-based timing circuit that provides a 15-V triggering pulse at an adjustable time following activation of relay 1.
I
0
0.5
I 1
I
I
1.5
2
I
Figure 3. Charge-step chronocoulometric plots for a
Type C-12) and the data were read directly from the photographs. To eliminate noise from ac pickup-an especially troublesome problem with dilute solutionsl~all electrical power except that for the oscilloscope was supplied by batteries. The high voltage to charge the injection capacitor was obtained by connecting sets of 300-V batteries (Burgess Model U200) in series. The cell was mounted inside a hollow copper cylinder for shielding. Reagents. Solutions were prepared from triply distilled water; the second distillation was from alkaline permanganate. Reagent grade chemicals were used without further purification. The sodium, potassium, and cesium nitrate solutions were prepared determinately. The zinc and magnesium nitrate solutions were standardized with EDTA. The lithium nitrate solution was analyzed by adding 1 ml of 18 M HzS04to a 10-ml aliquot, evaporating to dryness, igniting, and weighing as LizS04. The pH of all experimental solutions was between 5.5 and 7.5, the temperature was not controlled but was within 2" of 25". The prepurified nitrogen used to deoxygenate the solutions was further purified by passage through hot copper turnings and a Dry Ice trap.
Results and Discussion Values of nFI'Zn2+for 0.253 mM solutions of zinc nitrate in 10 mM solutions of sodium, potassium, lithium, cesium, and magnesium nitrates were obtained from the intercepts of the chronocoulometric plots of Qinj - AQ vs. t/'. The dependence of the intercepts on the initial potential (and the initial charge, amo) was The Journal of Phyakal Chemistry
K+-Znz+ mixture. All solutions were 10.00 mM in KNOa and 0.253 mM in Zn( NO&. The initial electrode potentials were: A, - 100 to -500; B, -600; C, -700; D, -800; E, -900 mV us. sce.
determined for potentials on both sides of the point of zero charge (pzc). A typical set of plots for potassiumzinc mixtures is presented in Figure 3. The expected qualitative behavior is observed: the intercept is essentially zero when the electrode is a t or positive of the pzc; as the charge of the electrode becomes increasingly negative, the intercept increases. Note that the slopes of all of the lines in Figure 3 are the same and equal to 2nFCD1Iz/l/?r according to eq 1. This slope is also observed in solutions with less supporting electrolyte (where the transference number of the reactant becomes significant) because the measurements are made a t open circuit which eliminates any contribution from migration of the reactant in an electric field. I n order to compare the results obtained with the predictions of the simple Gouy-Chapman theory, the procedure given by Joshi and Parsons*ewas followed: for each electrolyte mixture the theoretical diffuse layer composition was determined by numerical integration of eq 2 with the aid of a digital computer. At 25"
(16) P. Delahay, R. delevie, and A,-M. Guiliani, Electrochim. Acta, 11, 1141 (1966). (16) K,M. Joshi and R. Parsons, ibid., 4, 129 (1961).
ANALYSIS OF
THE
IONIC COMPOSITION OF THE DIFFUSEDOUBLE LAYER I
731 1
I
I
A
+6
+4
+2
0
I
I
I
I
-2
-4
-6
-8
q m , pc/cm2 Figure 4. Experimental and theoretical values of nFI'Znz+.Solid curve wae calculated from eq 1 for [Zn2+] = 0.253 mM, [NOs-] = 0.010486 M , and 0,0100 M univalent cation. The experimental points are for Li+ (O), Na+ (A), K + (O), and Cs+ (A)supporting electrolytes. The ordinate scale is expanded tenfold for negative values of rznz+.
The summation in the denominator is over all the ionic constituents of the solution having charges Zi and bulk concentrations Ci moles per liter; u = exp( -0.038924) at 25", where 4 is the potential at any point within the diffuse layer, and uz = exp( -0.03892$2), where $2 is the potential at the outer Helmholtz plane. The integration was performed for various values of $2, and the corresponding values of qm, the charge on the electrode, were calculated from qm = *11.74[Eci(~2'i
- l]"s
(3)
The accuracy of the numerical integration was confirmed by comparison with the results of Joshi and Parsons16and by making sure that the sum of the ionic charges in the diffuse layer calculated from eq 2 matched the values of the charge on the electrode calculated from eq 3. (Agreement to better than 0.01 pC/cm2 was obtained.) The solid curve in Figure 4 gives the values of n F r z n z +calculated from eq 2 as a function of the electrode charge. 'The absence of specific adsorption of all ions was assumed at the concentrations employed. The points plotted in the same figure are the experimental values for nFI'znz+ obtained from the chronocoulometric plots. The agreement between the simple diffuse layer theory and experiment is well within the experimental uncertainty of ca. *0.5 pC/cm2 except in
the case of the lithium solution where there appears to be a slight deficit of zinc ion in the diffuse layer which is presumably made up by an excess of lithium ion. The data for 0.01 M magnesium nitrate supporting electrolyte also agreed with the diffuse layer theory in that essentially no zinc ion was found in the diffuse layer: for the 0.0100 M Mg(N03)2-0.253 mM Zn(NO& mixture the predicted values for n F r z n z +at potentials of -600, -700, -800, and -900 mV vs. sce are 0.05, 0.09, 0.1, and 0.2 pC/cm2, respectively. The observed values of n F r z n z +were 0 0.5 pC/cm2 at all potentials. Data for pot,assium-zinc mixtures were obtained for potentials on both sides of the pzc (see Figure 4). As expected, essentially no zinc ion was found in the diffuse layer until the initial potential was negative of the pzc. The small negative theoretical values of nFrZn,+ at positive electrode charges would not be expected to contribute a detectable effect in these experiments. The relatively good agreement between the experimental results in Figure 4 and the simple diffuse-layer theory contrasts with the larger discrepancies between theory and experiment found by Joshi and Parsons for more concentrated solutions of barium and hydrogen ions.I6 These authors showed that differences in the planes of closest approach of the two cations could account for their results if the difference were in excess of 2 b. Because a much lower ionic strength was employed
*
Volume 76,Number 6 February 1068
732 in the present experiments (0.01 M vs. 0.35 M ) , differences of even several Angstroms in the planes of closest approach of the cation pairs would not have produced detectable deviations from the simple diffuse-layer theory. The better agreement between theory and experiment obtained in these experiments is, therefore, not an indication that both cations in the mixtures approach the electrode equally closely. The data in Figure 4 do show that, with the possible exception of lithium ion, simple diffuse-layer theory can yield satisfactory results for mixtures of cations which differ greatly in size as well as charge. Although the experimental accuracy presently achievable with the chronocoulometric method (ca. *0.5 pC/cm2) is not as high as is possible with electrocapillary measurements (ca. *O.l pC/cm2), it provides a much faster route to the determination of the amount of reactant contained in the diffuse double layer. Application of the procedure to cases in which a nonelectroactive component of a mixed electrolyte is specifically adsorbed, e.g., halide anions, should be particularly interesting because of the independent test it would provide of diff use-layer theory in the presence of specific adsorption. This technique may also prove useful with solid electrodes for which it would provide a convenient means for measuring the potential of zero charge.
Appendix Perturbations Produced by Charge Injection
Additional Reactant Incorporation. I n the absence of specific adsorption, the nFr term in eq 1 represents the amount of reactant present in the diffuse layer a t the initial value of the charge on the electrode, qmo, plus whatever additional amount of reactant is incorporated into the new double layer created by the charge injection. When the charge injection is accomplished in vanishingly short times, it seems likely that the additional reactant instantaneously introduced into the diffuse layer will not be the equilibrium value described by eq 1 but will be given for catonic reactants by
where f r is the fractional contribution of the reactant to that part of the solution conductivity due to cations, i.e.
The Journal of Physical Chemistry
FREDC. ANSON
where A, C, and x are the equivalent conductance, bulk concentration, and ionic charge of the cationic components of the solution, and (dq+/dqm)measures the fraction of a change in electronic charge on the electrode, qm, that is matched by a change in the cationic charge, p+, in the diffuse layer. (In the absence of specific adsorption, (dq+/bqm)will vary from zero to one-half to unity as the charge on the electrode varies from positive values, to zero, to negative values, respe~tively.'~) I n the experiments reported here, the concentration of zinc ion was only 1/40 as large as the concentration of supporting electrolyte so that f r in eq 2 was quite small (it ranged from 0.05 in the case of lithium nitrate supporting electrolyte to 0.03 for cesium nitrate) and AI? was neglected in the analysis of the data. With more dilute solutions of supporting electrolyte it would be necessary to take this factor into account. Time-Dependent Double-Layer Capacity. When charge is suddenly injected into an electrode in dilute electrolyte solutions, the differential double-layer capacity a t constant potential is time dependent because of the transient concentration gradients produced by the creation of the new diffuse double layer.'" This effect gives rise to transient potential changes which perturb the initial part of the measured potential-time curves. In solutions containing 0.01 M electrolyte these perturbing potentials are quite small and short-lived.'* They were neglected in the analysis of the experiments reported here for which data points were taken in the interval from 0.5 to 4 msec following the charge injection. In more dilute solutions these transient potential changes could degrade the accuracy of the technique.
Acknowledgments. The charge injection circuit in Figure 2 was devised by George Lauer. Helpful preliminary experiments were performed by Peter Lingane and Brian Case. The numerical integration program employed was written by Roger Abel. This work was supported in part by the U. S. Army Research Office (Durham). The author is an Alfred P. Sloan Foundation Research Fellow. (17) R. Parsons, Proc. Intern. Congr. Surface Activity, dnd, London, 1967, 38 (1967); cf. ref 1, Chapter 4. (18) F. C . Anson, J . Phys. Chem., 71, 3605 (1967).
