G. H. NANCOLLAS, D. S. REID,AND C. A. VINCENT
3300
YO, and Unfortunately, in the case of ScF the light was not filtered to allow the excitation of only one electronic transition a t a time. One wonders whether all excited states are equally effective in causing the shifts and whether an exceptionally large change of Ar (as in the C'Z +X'Z transition) might also be influential. Irradiating in the ultraviolet (-2400 to 4000 A) during fluorescence did appear to cause also a shift of the emission of the C + X system relative to the absorption by about 20 cm-l to the blue. The excellent agreement between Ar values for the C12 + X'Z and ElII + XI2 transitions obtained from the relative intensities of bands in the matrix spectra of ScF and those obtained from rotational analysis of the gas spectrum is gratifying (see Table VI). The conversion of relative intensities to Ar values involves the
assumption that Re, the electronic transition moment, is relatively independent of r . This is usually true but there can be large divergencies as discussed, for example, by H a l e ~ i . Our ~ ~ calculations indicate that the assumption is valid for ScF to within the accuracy of our observations. That accuracy does not allow anything to be said about the effect of the matrix on the Ar values, except that it cannot be large.
Acknowledgments. The authors thank Professor R. F. Barrow for his helpful correspondence concerning the gas phase spectroscopy and Professor K. D. Carlson for a discussion of his recent theoretical work on the ground state of ScF. (23) P. Halevi, Proc. Phys. SOC.(London), 86, 1051 (1965).
The Double Layer at the Mercury-Formamide Interface
by G.H. Nancollas, D. S . Reid, and C. A. Vincent' Department of Chemistry, State University of New York at Buffalo,Buffalo, New York, and, Department of Chemistry, The University, Glasgow, Scotland (Received May 23, 1966)
The differential capacitance of the electrical double layer at the interface between the dropping mercury electrode and solutions of potassium chloride (0.05, 0.071, 0.100, and 0.500 m), lithium chloride (0,100 m), cesium chloride (0.100 m), sodium chloride (0.100 m), and rubidium chloride (0.100 m) in formamide at 25" has been measured. Differential capacitance measurements have also been made on solutions of potassium chloride (0.100 7%) and cesium chloride (0,100m) in formamide at 5 and 45". Determinations of the interfacial tension have been carried out using a capillary electrometer. Relative surface excesses of chloride ion and potassium ion have been calculated from the results and evidence is advanced indicating specitic adsorption of potassium ions at the dropping mercury electrode-formamide interface. The capacitance-charge curves show a characteristic hump at more cathodic potentials than in aqueous solutions, and the shapes of these curves are discussed in terms of current theory.
Introduction The measurement of electrical capacitance offers one of the most sensitive methods for studying the structure of the double layer a t a metal-solution interface. Most of the work has been done with aqueous The Journal of Physical Chemistry
systems, and there is now a considerable body of pre-
cise capacitance and interfacial tension data for the dropping mercury electrode in aqueous solutions of (1) Visiting Lecturer, university of Illinois, Urbana, 111.
THEDOUBLELAYERAT
THE
MERCURY-FORMAMIDE INTERFACE
electrolytes, particularly those of the alkali halides and oxy anions.2 I n the presentation of the theories of electrocapillarity, it is usually assumed that among the inorganic ions, the anions with the possible exception of fluoride ions are capable of superequivalent or specific adsorption whjle the concentration of the cation at the interface is determined purely by its charge. The possibility of specific adsorption of cations, particularly cesium ions, has been suggested by some worker^,^ but as yet no firm conclusions have been reached. Another feature of the capacitance-potentia1 curves for the dropping mercury electrode in aqueous solutions which awaits satisfactory explanation is the appearance of the characteristic "hump," usually slightly to the anodic side of the potential of zero charge (pzc). Watts-Tobin4 and llacdonald and Barlows considered the influence of solvent dipole orientation on the dielectric constant of the inner region of the electrical double layer to be of basic importance in the explanation of this phenomenon. Because of their proximity to the metal surface, and because they may be subjected to very large electrical fields, solvent molecules near the interface behave differently from those in bulk; under certain conditions orientation polarization is almost complete, and hence the dielectric constant in this region may fall to a very low value. It was suggested4 that at the electrode surface there are two types of oriented water molecules, one with the oxygen toward the metal and the other with the hydrogen atoms directed toward the electrode. I n terms of these models, the appearance of the hump in the capacity curve is connected with the changing orientation polarization of the adsorbed water molecules at positive polarization. Hills and Payne,6 who measured the surface excess entropy and volume for 0.10 M aqueous solutions of electrolytes, also connected the appearance of the hump with solvent structure at the interface. They considered the two opposing effects which would accompany adsorption of excess solvent molecules into the compact double layer, namely (i) increase in the distortional component of the polarizability with increase in surface density of dipoles, and (ii) increase in the thickness of the compact double layer. Other workers have postulated that the capacitance hump is due to effects associated with specific adsorption of anions a t the mercury-solution interface. Thus, Damaskin, Schwartz, and Frumkin' considered polarization of solvent molecules by anions adsorbed into the inner Helmholtz plane, while Bockris, Devanathan, and hluller8 suggested lateral repulsion between such anions as the main factor.
3301
Study of the capacity hump in aqueous solution is sometimes made difficult since it may be obscured by strong specific adsorption of anions. Recently, 9-12 a similar maximum in the capacity-charge curve has been found for some alkali metal halides in nonaqueous solvents. I n formamide, an excellent polar solvent, this occurs at potentials considerably more negative than the potential of zero charge and it is thus less easily masked by anion specific adsorption. I n such solvents, quite different ion-solvent interactions are to be expected from those in aqueous solutions. I n the present work, the differential capacity of the dropping mercury electrode has been measured in formamide solutions of lithium, sodium, potassium, rubidium, and cesium chlorides as a function of concentration and temperature. Interfacial tension measurements have also been made using a capillary electrometer.
Experimental Section Formamide was first saturated with ammonia gas and filtered to remove any precipitated ammonium formate. It was then distilled six times under vacuum at temperatures below 60" to avoid decomposition, and stored under nitrogen. The pure formamide has a melting point of 2.5", close to the literature value of 2.55". Analar potassium, rubidium, cesium, and sodium chlorides were all recrystallized three times from conductivity water and dried a t 300" just prior to use. Lithium chloride was recrystallized three times from dry ethanol, and the ethanol was removed by gentle heating in a stream of dry nitrogen. The solid was heated to constant weight a t 120" and stored under nitrogen. Just before use it was heated again to 240". All solutions were made up by weight in a drybox filled with nitrogen, and their densities were found by using a pycnometer. Mercury was purified by triple distil(2) D. C. Grahame, Chem. Rev., 41,441 (1947); J . Electrochem. Soc., 98, 343 (1951); 99, 370C (1952); J . Am. Chem. Soc., 74, 4422 (1952); 76, 4819 (1954); 79, 2093 (1957). (3) B. B. Damaskin, N. V. Nikolaeva-Fedorovich, and A. N. Frumkin, Dokl. Akad. Nauk S S S R , 129, 121 (1958). (4) R. J. Watts-Tobin, Phil. Mag., 6, 113 (1961). (5) J. R. Macdonald and C. A. Barlow, Jr., J . Chem. Phys., 36, 3062 (1962). (6) G. J. Hills and R. Payne, Trans. Faraday Soc., 61, 316 (1965). (7) B. B. Damaskin, E. Schwarta, and A. N. Frumkin, Zh. Fiz. Khim., 36, 2419 (1962). (8) J. O'-M.Bockris, M. A. V. Devanathan, and K. Muller, Proc. Roy. Soc. (London), A274, 55 (1963). (9) C. A. Vincent, Ph.D. Thesis, Glasgow University, Scotland, 1963. (10) R. Payne, J. Chem. Phys., 42, 3371 (1965). (11) B. B. Damaskin and Yu. M.Povarov, Dokl. Akad. Nauk S S S R , 140, 394 (1961). (12) S. hlinc and hf. Breostowska, Roczniki Chem., 38, 301 (1964).
Volume 70, Number 10 October 1966
3302
lation under reduced pressure after standard chemical treatment, and was stored under nitrogen. Impedance measurements were made with the selftiming transformer ratio-arm bridge method described in a previous paper. l 3 The only modification made was the repositioning of the two 1000-kf blocking capacitors (see Figure 4 in ref 13) so that they were connected between the transformer ratio-arm bridge and the selector switch. Conversion from the measured parallel combination of impedances to the equivalent series combination was made with the aid of a K D F 9 computer (English Electric) using the method described previously. l 4 The cell and general experimental procedure were similar to that outlined in a previous paper,'* and precautions were taken to prevent moisture from entering the cell a t any time. Considerable attention was given to the choice of electrode for use as a reference in these nonaqueous solutions. Although many workers use an aqueous reference electrode necessitating an aqueous-nonaqueous liquid junction, it was felt to be undesirable to introduce an additional uncertainty from this source. The silver-silver chloride electrode has been shown to behave reversibly in formamide solutions,l5 and it was therefore used as the reference electrode dipping directly into the cell solution. The electrodes were prepared by the thermal electrolytic method,16 washed thoroughly with formamide containing a small quantity of potassium chloride, and allowed to age in the dark for several weeks in a similar solution. Electrocapillary maximum potentials were determined by method V described by Grahame and his cow o r k e r ~ using ~ ~ a streaming mercury electrode in deaerated cell solutions. The highest attainable potential was taken as that of the electrocapillary maximum. The capillary electrometer was enclosed in an air thermostat and was similar to that described by Parsons and Devanathan.'* It incorporated the same reference electrode system as for the capacity measurements, and all solutions were presaturated with nitrogen. The pressurizing system consisted of two large reservoirs containing mercury, one of which was connected to the mercury reservoir of the capillary and to a manometer. The pressure in the system could be sensitively controlled by raising and lowering the reservoir with a micrometer screw. The tip of the capillary was drawn by the method suggested by Conway and Barradas,lg and the illuminated mercury meniscus, viewed with a travelling microscope, was brought to a position 1.000 mm above the capillary tip each time. A drop of mercury was expelled between each measurement. The heights of the mercury columns were measured with an accuracy of 0.02% on a The Journal of Physical Chemistry
G. H. NANCOLLAS, D. S. REID,AND C. A. VINCENT
cathetometer, and the apparatus was calibrated by measuring interfacial tensions in 0.1 N potassium chloride aqueous solutions and comparing the results with those of Devanathan and Peries.20 The results of duplicate experiments in formamide solutions were reproducible to with 1 0 . 2 erg cm-* except at the most cathodic potentials, where the agreement was A0.5 erg cm-2.
Results The method used for applying back-pressure corrections has been described previou~ly.'~An approximate surface tension calculated from the drop weight is used to evaluate the equivalent constant rate of flow of mercury which would be obtained with the same mercury head in the absence of back-pressure. This is then used to calculate, by means of an iterative procedure on an electronic computer, the surface tension, the drop weight at any instant in the life of the drop, and the differential capacitance CO.l4 Differential capacitances a t different potentials, E, were determined for formamide solutions containing 0.l m lithium, sodium, rubidium, and cesium chlorides, and 0.05, 0.071, 0.1, and 0.5 m potassium chloride at 25". Some 0.1 ?n solutions of potassium chloride and cesium chloride in formamide were also studied a t 5 and 45". Each capacitance value is the averaged result of at least three runs under each set of conditions, the mean deviation being about 0.1%. Interfacial tensions at different potentials were determined for formamide solutions containing 0.05 and 0.10 m potassium chloride. I n Table I are listed the potentials of the electrocapillary maximum, and Table I1 includes the potential, interfacial tension, and capacity at the electrocapillary maximum for three of the potassium chloride solutions. I n 0.1 nz solutions of lithium, sodium, rubidium, and cesium chlorides, no significant difference in electrocapillary maximum potential (ecm) was observed from that for potassium chloride a t the same concentration and it is clear that the cation has (13) G. H. Nancollas and C. A. Vincent, J. Sci. Instr., 40, 306
(1963). (14)G. H. Nancollas and C. A. Vincent, Electrochim. Acta, 10, 97 (1965). (15) Y u . 51. Povorov, Yu. M. Kessler, A. I. Gorbanev, and I. V. Safonova, Dokl. Akad. Nauk SSSR, 155, 1411 (1964). (16) V. S. K. Nair and G. H. Nancollas, J . C h m . SOC.,4144 (1958). (17) D. C.Grahame, E. M. Coffin, J. I. Cummings, and M. A. Poth, J . Am. Chem. Sac., 74, 1207 (1952). (18) R.Parsons and M. A. V. Devanathan, Trans. Faraday Soc., 49, 673 (1953). (19) B. E. Conway and R. G. Barradas, Electrochim. Acta, 5, 319 (1961). (20) M. A. V. Devanathan and P. Peries, Trans. Faraday Soc., 50, 1236 (1954).
THE DOUBLELAYERAT
THE
MERCURY-FORMAMIDE INTERFACE
3303
Table I : Potentials of the Electrocapillary Maximum 25 0.050 -0.467
Temp, "C Molality of KCI
Eem, va
25 0.071 -0.465
25 0.100 -0.462
25 0.500 -0.457
45 0.100 -0.442
5 0.100 -0.477
E is the potential of the cell AgIAgCllKCl in formamide (m)lHg.
Table I1 : Electrocapillary Maximum Data for Potassium Chloride Solutions in Formamide a t 25' C,
Concn,
E,
Y,
m
v
ergs cm-2
0.050 0.071 0.100
-0.467 -0.465 -0.462
382.7
16.69 17.52
381.5
18.36
pf
40
om-¶
30
only a very small effect on the potential of the ecm as is the case in aqueous solution.21 The charge on the dropping mercury electrode, q, given by
t
&
0'
W
20
E
=
\-
SEec?U
a
was obtained by integration of the capacitance-potential curves. An electronic computer was used to fit the data to a polynomial of any chosen degree, and the closeness of fit was verified by comparing a plot of the polynomial with the experimental points; polynomials of degree six or eight were normally sufficient. The necessary integration constants were taken from the ecm potentials, and the integration was carried out by the computer. Plots of differential capacitance against charge at 25" are shown in Figures 1 and 2; the capacitance-charge curves for potassium and cesium chloride solutions a t 5 , 2 5 , and 45" are given in Figure 3. It was found that the maximum cathodic polarization which could be achieved before decomposition of the formamide, and accompanying current flow, depended markedly upon the purity of the solvent. With each successive fractional distillation at reduced pressure and a temperature below 60°, this cathodic region could be extended. I n the present work the dropping mercury electrode was studied at charges beyond -20 kcoulombs/cm2 in contrast to the maximum value of - 14 pcoulombs/cm2 achieved by Payne.'O
Discussion It is seen in Figures 1, 2, and 3 that the capacitance curves have a well-defined hump a t considerably more cathodic potentials than in aqueous solutions, and similar observations have been made for potassium iodidelo and fluoride12solutions in formamide. I n the
10
0
10
0 q,
- 10 woulombs/cm*.
- 20
Figure 1. Differential capacitance of the electrical double layer a t a mercury electrode in 0.1 m solutions of the alkali metal chlorides in formamide a t 25'. For clarity, successive curves are displaced upward by 2 fif/cm*. 0, LiCl; A, NaCl; 0, KCl; V, RbCl; 0,CsC1.
case of potassium chloride (Figure a), the specific adsorption of chloride ion does not begin to seriously obscure the hump until quite high concentrations are reached (0.5 m). I n aqueous solution this occurs a t about 0.1 M . If the maximum in the curve is due to solvent dipole reorientation, this suggests that the formamide molecule has its most stable orientation with the positive pole of the solvent dipole directed away from the mercury surface. This is consistent with the expected most favorable orientation of the formamide molecule in which the oxygen atom is directed toward the mercury surface. (21) D. C . Grahame,
J. Electrochem. SOC.,98, 343 (1951).
Volume 70,Number 10 October 1966
3304
G. H. NANCOLLAS, D. S. REID,AND C . A. VINCENT
40
30
e%
*
G
20
10
0
0 ~
10
- 10
0 q,
- 20
rcoulombslcma.
Figure 2. Differential capacitance of the electrical double layer a t a mercury electrode in solutions of potassium chloride in formamide a t 25". For clarity successive curves are displaced upwards by 2 pf/cmz. 0, 0.050m; A, 0.071 m; 0, 0.100m; V, 0.500m.
I n the far-cathodic region (Figures 1 and 3) there is a very noticeable effect of cation: the capacitance values in formamide fall in the order E(+ < Na+ < Li+ < Rb+ < Csf. It is interesting that in every case a minimum in the capacity curve at large cathodic polarizations could be observed before the onset of solvent decomposition. The capacitance of cesium chloride and rubidium chloride rises much more rapidly than that of Iithium chloride, whereas the rise in capacitance has barely begun for sodium chloride and potassium chloride. This difference is in marked contrast to the results in aqueous solution, and cannot be explained simply on the basis of compressional forces and size of solvated cation. It is of interest to note that a similar behavior has been observed in N-methylformamide I n formamide solution of potassium iodide, Payne'o did not take the applied potential to sufficiently negative values to observe the capacitance rise. The expected greater specific adsorption of iodide ions m compared with chloride ions, however, causes masking of the capacitance hump in the former soluThe Journal of Physical Chemistry
10
0
- 10
- 20
q, rcoulombs/cm?
Figure 3. Differential capacitance of the electrical double layer a t a mercury electrode in 0.1 m solutions of potassium chloride and cesium chloride in formamide as a function of temperature. The left ordinate scale refers to the curves for potassium chloride, that on the right to cesium chloride: a, 0.1 mCsC1, 5'; b, 0.1 m CsCl, 25'; c, 0.1 m CsCl, 45"; d, 0.1 m KCl, 5'; e, 0.1 m KCl, 25"; f, 0.1 m KCl, 45".
tions a t very much lower electrolyte concentrations (about 0.05 m KI as compared with 0.5 772 I(C1). The effect of temperature on the capacity curves for potassium chloride and cesium chloride is seen in Figure 3. The general lowering of the hump with increasing temperature is similar to that observed in aqueous solutions and has been explained qualitatively by attributing the phenomenon to the orientation of solvent molecules a t the interface.22 A feature of the curves in Figure 3 is that at the higher temperatures the curves intersect twice. At cathodic polarization, the curve at 25" is uniformly lower than a t 5", as would be expected on the basis of the higher specific adsorption of cation (discussed below) a t the lower temperature. On the negative side of the hump, however, the 45" curve crosses that at 25", as is consistent with the temperature dependence of the solvent orientation polarization term of the Watts-Tobin theory. It is very interesting to note that similar temperature-in(22) D. C. Grahame, J . Am. Chem. SOC.,7 9 , 2093 (1957).
THEDOUBLE LAYERAT
THE
MERCURY-FORMAMIDE INTERFACE
-6
3305
I -0.1
- 1.0
-0.5
- 1.5
E-, v. 0
- 0.5
- 1.0
- 1.5
E - , v.
Figure 4. Contribution of anions (C-) and cations (C+) to the differential capacitance of the electrical double layer at a mercury electrode in 0.071 m potassium chloride in formamide a t 25'.
duced double intersection of capacity-charge curves have recently been reported for aqueous 1 N solution of perchlorates; the effect in very concentrated solutions (9.3N ) was even more marked.23 The relative surface excess of anion, r-, and cation, r+,in potassium chloride solution at a concentration of 0.071 m was calculated by the method of Grahame and S ~ d e r b e r g . The ~ ~ part of the differential capacitance attributable to the cations, C+, was obtained by integration of (ACo/AIog ai)E- with respect to Eusing the mean activities given by Povarov, Kessler, and GorbanevZ5for the evaluation of the mean activity ai. The integration constant was based on the calculated value of C+ a t the electrocapillary maximum.
RTB In a since it was not possible t o assume the absence of specific adsorption of cation at the most negative potential attainable, C- was obtained from the relationship
c, = c++ cand plot of C+ and C- against E- are shown in Figure 4. r+was evaluated by integration of the C+ vs. E- curve, the integration constant being obtained from the rela-
Figure 5 . Relative surface excess of anions (2-Fr-) and cations (z+Fr+ in the electrical double layer a t a mercury electrode in 0.071 m potmsium chloride in formamide a t 25".
tionship between the interfacial tension and the chemical potential at the electrocapillary maximum
(for a 1:1 electrolyte)
r- was obtained from the relationship -Q
=
z+FF+
+ z-Fr-
where zi is the valence of the ion, with the sign of its charge. The values of the surface excess agreed with those calculated from interfacial tension measurements to within the experimental error. Plots of r+and r- as a function of E- are given in Figure 5, and their shapes suggest superequivalent adsorption of the cation, although to a smaller extent than adsorption of the anion under the corresponding anodic conditions. I n the case of cesium chloride, the marked rise in capacitance at cathodic potentials may reflect even more extensive superequivalent adsorption of the cation. It is of interest to note that FrumkinZ6 (23) V. F. Ivanov, B. B. Damaskin, A. N. Frumkin, A. A. Ivashchenko, and N. I. Peshkova, Electrokhimiya, 1, 279 (1965). (24) D. C. Grahame and B. A. Soderberg, J . Chem. Phys., 22, 449 (1954). (25) Yu. M. Povarov, Yu. M. Kessler, and A . I. Gorbanev, Izv. A M . Nauk SSSR, Ser. Khim., 1895 (1964). (26) A. N. Frumkin, B. B. Damaskin, and N. V. Nikolaeva-Fedorovich, Dokl. Akad. Nauk SSSR, 115, 751 (1957); 121, 129 (1958).
Volume 70,Number 10 October 1966
G. H. NANCOLLAS, D. S. REID, AND C. A. VINCENT
3306
has interpreted the results of electrocapillary and differential capacitance measurements in aqueous cesium halide solutions in terms of similar cationic adsorption. In an attempt to obtain a more quantitative explanation of the capacitance maximum in formamide, the Watts-Tobin theory for a mercury-water interface has been extended by taking into account the possibility of nonequivalent orientations of the solvent molecule a t the mercury interface. The solvent contribution term in the Watts-Tobin theory
reduces to the Watts-Tobin expression when sin e = sin q = l/@. Substitution of this extended Csolvent term into the Watts-Tobin expression for water was found to be insufficient to explain the results obtained for formamide. ilccordingly, a fourth term of the ( C I / C ~ ) ~ V~)/dkTf form ( + N ~ z ~ / c ~ ~ ~ T )exp(-p2(p was added to allow for the contribution of superequivalent adsorbed cation to the capacitance. The final capacitance equation
+
+ in which the symbols have the same meaning as in ref
4, was recomputed assuming that the solvent dipole had the possible orientations e and q with respect to the surface of the mercury. The resulting expression for Csolvent Csolvent
=
+
Np2(sin e sin q ) 2 X d2kT
+
exp{ (V - cp)p(sin 0 sin q)/dkT) [1 exp{ (V - cp)p(sin e sin q)ldkT]l2
+
The Journal of P h y s h l Chemistry
+
+ sin
Np2(sin 9 d2kT[1
+
+
exp(V - q)p(sin e sin q)/dkT expf(V - cp)p(sin 0 sin q ) / d k T ) ] 2 ~ ) 2
+
was found to fit the results quite closely, but a final choice between this theory and that of Hills and Payne6 cannot be made on the basis of the present data. Acknowledgments. We thank the Carnegie Trust for the Universities of Scotland for a grant to D. S. Reid.
