Sept., 1956
ADSORPTION FROM
1185
DIFFERENTIAL CAPACITANCE h ! f E A s U R E m N T S
THE INFERENCE OF ADSORPTION FROM DIFFERENTIAL DOUBLE LAYER CAPACITANCE MEASUREMENTS’S~ BY ROBERTS. HANSEN,ROBERT E. MINTURNAND DONALD A. HICKSON Institute for Atomic Research and Department of Chemistry, Iowa State College, Ames, Zmua Received February 94, la66
Frumkin’s theory of the dependence of surface tension on polarization and solute activity is modified and extended to establish the dependence of differential capacitance on polarization and adsorption. The resulting equation is applied to experimental capacitances in the system mercury-0.1 M perchloric acid-pentanoic acid. Variations of both actual and apparent adsorption with polarization are emphasized, and the relevance of these variations to the capacitance determination of adsorption is discussed.
Introduction A recent paper from this Laboratory emphasized the desirability of establishing methods for measurement of adsorption from solution a t low specific area metal surfaces, and surveyed the application of hydrogen overvoltage phenomena to this problem.a Preliminary work on inference of adsorption from double layer capacitance measurements was also included. Grahame4 has published an extensive review of work on the electrical double layer, including work on double layer capacitance. The large part of such work has involved the use of mercury electrodes, and Grahame and his co-workers have attained a high degree of reproducibility and precision in measurement of double layer capacity in systems involving mercury. Because of the availability of a considerable amount of information on the character of the mercury-aqueous electrolytic solution double layer, and especially because of the possibility of varying electrode polarizations over a considerable range, mercury was selected as well suited to a study of the effect of adsorbable components on the double layer capacitance. Barclay and Butler6 included a brief study of the effect of t-amyl alcohol concentration on the double layer capacitance a t the mercury surface in a general paper on double layer capacitance, but did not attempt to correlate observed effects quantitatively with adsorption, nor did they investigate the dependence of these effects on polarization. Frumkin6has published an extensive theoretical treatment of the effect of adsorbable components on the electrocapillary curve; we shall extend his results to differential Capacitance curves in the present work. The Russian physical chemists have maintained a n active interest in the application of differential capacitance measurements to adsorption problems; notable contributions include work by Frumkin and Melik-Gaikazyan’ on inference of adsorption kinetics from double layer capacitance frequency dependence and a
study by Melik-Gaikazyans in which formation of polymolecular layers adsorbed at the mercury surface was inferred from capacitance result^.^
Theoretical The dependence of boundary tension on boundary polarization and activity of a single adsorbable component is given by dy
--
-QdV
- RTrdlna
(1)
in which y is the boundary tension, Q the charge per unit area on the electrode side of the double layer, Y the potential of the electrode of interest with respect to a reference electrode (in the discussion to follow we shall for convenience refer V to the electrocapillary maximum) and l? is the surface excess of the adsorbable component per unit area. From eq. 1it follows that
If the functions Q(r, V) and r(a, V = 0) are known eq. 2 can be used to establish the function r(a, V ) . Frumkins assumes
Q (r,V)
=
QW
(1
- e)
+ C’(V - VN)e
(3)
and (4)
(1) Based in part upon a dissertation submitted by Robert E. Minturn to the Graduate School, Iowa State College, in partial fulhllment
in which e is the fraction of the surface covered by adsorbate (e = r S, where S is the molar area of the adsorbate), QWis the boundary charge per unit area at polarization V in absence of adsorbate, C‘ is the differential capacitance (assumed constant) of the double layer when e = 1, and V N is the potential (referred to the potential a t the electrocapillary maximum in the absence of adsorbate) at which there is no charge on the double layer when this double layer contains adsorbate at 0 = 1. Bo and CY are constants. The assumptions as to the character of the functions Q(0,V) and e(a, V = 0 ) contained in eq. 3 and 4 lead, using eq. 2, to the general dependence of e on V and a, thus e Bm-he = B o e - S * / R T m - h e
of the requirements for the degree of Doctor of Philosophy, 1955. (2) Work was performed in the Ames Laboratory of the Atomic
where
Energy Commission. (3) R. 9. Hansen and B. H. Clampitt. THIS J O U R N 41,, 68,908 (1954). (4) D. C. Grah.ame, Chem. Revs.. 41, 441 (1947). (5) I. M. Barclay and J. A. V. Butler, Trona. Faraday Soc., 36, 128 (1940). (6) A. Frumkin, Z. Physik, S6, 792 (1926). (7) (a) A. Frumkin and V. I. Melik-Gaikazyan, DokZody Akud. Nouk. U.S.S.R.,‘17, 855 (1951): (b) V. I. Melik-Gaikazyan, Zbur. p i a . him.. 16, 560 wx.2).
1 - e
I
=
sov
(5)
[Qw
- c’(v -
VN)]dV
(6)
The preceding development is a slight modification (to account for the known variation of the dfler(8) V. I. Melik-Gaikazyan, ibid.. 46, 1184 (1952). (9) We are indebted to Dr. David C. Grahame for making available to ua translations of references 7 and 8.
R. S. HANSEN,R. E. MINTURN AND D. A. HICKSON
118G
u,
60
VOl.
TO POSITIVE SIDE OF POTENTIOMETER ADSORBATE IN
MERCURY SEAL
I
(TO MERCURY BUBBLER)
P
Fig. 1.-Circuit
diagram for capacitance bridge.
en tial capacitance CW of the mercury-aqueous electrolytic solution double layer with polarization (2)) of one given in detail by Frumkin,O who also emphasizes that the physical significance of eq. 5 and 6 is that, a t high polarizations and hence, a t high fields in the double layer, material of low dielectric constant will be displaced by material of high dielectric constant in a manner analogous t o the “salting out” effect. The depression of boundary tension a t coverage e and polarization V is given by
Since the differential capacitances must satisfy
Equation 7 implies the dependence of differential double layer capacitance C on polarization and adsorbate activity; the result, after moderate algebraic manipulation, can be expressed in the form
c
=
cw - 8 S
’i
RT 1-2
(CW
1
- C!)
-e
a 8 (1
- 0)
[Qw
- C’(V - V r i ) l Z j
(9)
The terms CW - e(& - C’) represent the capacitance of an adsorbate-filled capacitor of area e and a water filled capacitor of area (1 - e) connected in parallel, and would be the total differential capacitance according to eq. 3, if e did not change with V ; the remaining terms on the right side of eq. 9 arise from the change in e with V , and could be considered a pseudo-capacitance in the sense that no set of invariant capacitors could be arranged t o give rise to such a term. An apparent fractional surface coverage Bapp can now be defined by @SPP
=
cw=c c w - C’ =
i
@1 -
ING
Ag-AgCI REFERENCE ELECTRODE PLATINUM GAUZE ELECT MERCURY ELECTRODE
I
TJ OSCILLATOR, BRIDCE, HELIUM GAS IN
-
Fig. 2.--Adso!ption-citpacitance
a POTENTIOMETER
cell.
This is the quantity measured hy Hanseri a i d Clanipitt; the term C’ was neglected by them. In eq. 10, C and Cw are measurable, C’ is in principle best obtninetl by estjrapolation of C ( a , V = VN) to iiifiiiite a from low activity results, since its inference from measurements in pure liquid solute would involve tenuous assumptions as to similarity of orientation in the compact double layer and character of the diffuse double layer in the pure solute case, BO,XIRT, a and VN remain as adjustable parameters; VN is best established by setting Q w = C’(V - VN) a t the average maximum in several plots of Oapp against V a t several activities, Bo and (Y are best established from dependence of 0 on V a t the potential of maximum espp, and X/RT is then chosen for best representation of the dependence of eappon V . The following reservations as to the validity of eq. 10 should be made explicit. (1) Equation 3 is probably most nearly valid if the diffuse double layer contribution t o capacitance can be ignored, and hence eq. 10 should be applied to solutions with a t least moderate electrolyte concentrations. (2) Equation 4 limits application to unimolecular adsorption. Modification to permit application to multimolecular adsorption would involve introduction of an isotherm equation valid for such adsorption at this point, and probably a more complex variation of ey. 3. (3) C’ and T/“ are here treated as constants; since Cw varies with polarization C’ may also vary; further J7:q would change if the orientation of a dipolar adsorbate changes, and hence might be expected to change somewhat with coverage.
Sept., 1956 Experimental
ADSORPTION:FROM DIFFERENTIAL CAPACITANCE MEASUREMENTS 4.0
The impedance bridge used for capacitance measurements is shown I O in Fig. 1, and is similar to one designed by C:rahame.lo R1and Rzare small temperature coefficient wire-wound Nobleloy resistors of resistance 1004.5 ohms ‘ 0 each. R, is a Leeds and Northrup a.c.-d.c. decade resistor, catalogue No. 4755, with resistance variable in 0.10 ohm steps from 0 to 11,000 ohms. C,. is a Freed Transformer 3.0 Co. Decade Capacitor Model 1350 with capacitance continuously variable from 0 to 11 +rofarads. It was calibrated against a Beco Model 250-C impedance bridge. C, p f , The power source 0, a HulettPackard wide-range oscillator model 200 CI), fed a 1000 cycle a.c. current into the 1 O : l transformer T and was adjusted to maintain an a c. signal of approximately 4 millivolts, as measured 2.0 by the meter V, across the cell terminals. The unbalanced signal across the bridge was amplified by the 1000 cycle high gain amplifier AMP and detected on the ,Du Mont type 323 cathode rag osc~lloscope CRQ. The potentiometer P was adjusted t o apply the desired polarizing voltage to the test electrode using the Ag-AgC1 electrode E as reference. The microammeter A measured d.c. current through the cell. AC signal was I. 0 eliminated from the potcntiometer circuit by the 3 henry inductance I, and direct current was eliminated from the transformer circuit by the 2 pf. coiidenser C. The Pyrex adsorption cell is shown in Fig. 2. Helium, purified by passage through an activated uranium train st 240” and a charcoal trap inainhained a t liquid nitrogen temperature, stirred the solution and provided an inert atniosphere. The mercury bubbler and mercury seals prevented contamiI 3 nating gases from entering the cell
1
I
I
I
I
1187 I
c/co
LEGEND 0
0.m
A
0.023
1
0.042 0.080 0.162
I
x
0,320
I
2
I
4
I
6
I
a
I
.
I .o
I
I .2
PO LA R I ZATl ON, V O L T S ~ ~ ~ i Fig. 3.--Dependence ~ ~ of differential ~ capacitance ~ on polarization v ~and adsorbate ~ activity,~ \,,hen adsorb&e was added through system tnercury-0.lOOM aqueous perchloric acid-pentanoic acid. C/Co is reduced concen~l~~ mer- tration of pentanoic acid. Capacitances can be convertpd to capacitances per unit the curyappropriate surface was taper. renem,ed ,$,hende- area by division by the electrode area of approximately 0.074 Potentials are returlling the thumb Screw ferred to Ag-AgC1 electrode in 0.001 KCl. sired controliing the-plunger in the mercury metering syringe, used was redistilled from alkaline permanganate solution. causing the mercury to overflow and the niercury surface Eastman Kodak Co. best grade n-valeric acid was distilled to renew. There was no contact between solution or vapor in a 30-plate Oldershaw column a t reflux ratio 10 to 1; the fraction used had a boiling range of 186.5 to 186.8’ corand stopcock grease. The reference electrode was a Agrected to 760 mm. AgCl electrode prepared liy the thermal-electric method of The electrolytic solution was 0.100 M HCIOa and 0.0010 M Harried." The mercury electrode was formed i n a 2.5 Inm. i.d. KCI; approximately 400 ml. of this solution was added to Pyrex tube section, so that the top of the mercury meniscus the adsoFption cell.- An anode compartment with a fine was approximately tangent to the plane of the top of the pore fritted glass plate was inserted through the standard tube. A jilatinuin screen cylinder surrounded the mercury taper joint provided by the “ground” exit in Fig. 2, and the amp. with a electrode, and was in series with the mercury electrode solution pre-electrolyzed 12 hours a t 5 X in the a x . circuit; its area, and hence its capacitance, was stream of hydrogen bubbling through the solution, using a 1:trge compared to that of the mercury drop, so that its platinum flag electrode inserted through the central standard taper joint as cathode. effecton cell impedance should have been negligible. The anode compartment and flag electrode were then reDry, clean n.ir was bubbled through Goldsmith Bros. triple-distilled mei.cury for two days, after u~hiclithe mer- placed by platinum screen electrode and Ag-AgC1 electrode cury \vas filtered, washed thoroughly with 509; concentrated as shown in Fig. 2 . The hydrogen stream wae replaced by a nit,ric acid by volume, followed by washing with distilled purified helium stream which was allowed to bubble through water, dried and distilled three times in uucuo. Water the solution for a t least two hours to remove any dissolved non-inert gas. Adsorbate was added through the “adsorbate in” standard taper joint using a pipet or micropipet depend(10) D. C. Graliame, J . A m . Chem. Soc., 71, 2075 (1949); (b) R e c . Chem. f r o g . , 11, 93 (1950). ing on amount, helium being passed through the solution (11) H. S. Harmd, J . A m . Chem. Soc., 61, 416 (1929). for a t least one hour after each addition.
~
~
1H8
R. S. HANSEN,R. E. MINTURN AND D. A. HICKSON e ODD
LEGEND
of electrode area will lead to the same relative error in the parameter S and in the same direction but will not affect values of other parameters used in the treatment of apparent adsorption. I n Fig. 4 experimental values of eappare compared with curves calculated for the corresponding activities using the following values of parameters
‘40 A = ,023
1.0
Vol. 60
V = ,042
Bo = 10.5 C‘ = 5.21 pf./cm.P VN = 0.24 volt
soy
i
Fig. 4.-De endence of apparent fractional surface coverage on porarization and adsorbate reduced concentration. Points are experimental, curves are calculated from eq. 10. Potentials are referred to the electrocapillary maximum, taken as -0.6 volt relative to N/1000 Ag-AgCl electrode. If the mercury meniscus had been accurately hemispherical, ita area, computed from the diameter of the tube in which it waa formed, would have been 0.098 cm.* Actually, the drop diameter is rather large for the meniscus to be considered a spherical segment and the interfacial contact angle is somewhat less than 180’ and depends somewhat on the manner of formation. Both of these effects tend to cause an electrode area less than 2 ~ 2 and , the latter effect causes this area to be imperfectly reproducible. Therefore, when the electrode was renewed it was adjusted to give the same capacitance aa the previous electrode at the polartation at which formed; with this adjustment the capacitance- otential curve could be reproduced to within a fraction o r a per cent. at all but the most anodic polarizations investigated.
Results Results in the form of differential capacitancepotential data for six different reduced concentrations (concentration divided by saturation concentration) of pentanoic acid varying from 0.02 to 1.00 are presented graphically in Fig. 3. Observed capacitances can be converted to capacitances per unit area by division by electrode area; as previously indicated, this area should be rather less was used than 0.098 cm.2, and an area of 0.074 in calculations as leading to capacitances per unit area closely parallel t o those reported for a similar electrolyte by Grahame.4 An error in assignment
a = 1.00 = 0.81 cm.*/bj.
S/RT
sov
Integrals QW = Cw dV and QW dV needed for calculations were evaluated graphically. It will be seen that eq. 10 gives an excellent representation of the general dependence of espp on V, differences between theory and experiment certainly being of such an order of magnitude as to be ascribed to minor variations in C‘ and VN not accounted for in the theory. Values of parameters are physically reasonable. A value of 0.810cm.2/ pj. corresponds to a molecular area of 33.5 A.2 approximately sufficient to accommodate a methyl and two methylene groups but not the entire molecule in a “lying down” configuration. The parameter a accounts for attractive interaction between adsorbed molecules, and it should be possible to estimate its magnitude from comparable interactions in solution. The quantity R T Info represents the change in interaction free energy per mole when pentanoic acid is transferred from pure pentanoic acid to a state of infinite dilution in water. fo is the activity coefficient of pentanoic acid a t infinite dilution in water. The corresponding interaction free energy change in the adsorbed layer is represented by 2aRT, except that molecules in the film are always bounded on one side by the adsorbent, on the other side by (essentially) water. Hence, we should expect 2 CY = l/z Info. The value of 2a thus estimated from solution activity coefficient is 2.5 compared t o 2.0 used. The value of e.s.u., coupled with VN, 0.24 volt o,r 0.805 X the value of 33 A.2for S, is interpretable tentatively as Corresponding t o an oriented dipole layer with normal component of the dipole moment 0.21 E debye units, where E is the effective dielectric constant within the dipole. One might expect 1 < E < 2, so that the normal component of the dipole would be small. This is in the order of magnitude t o be expected if part of the alkyl chain were adsorbed and the carboxyl group extended away from the surface into the aqueous medium. An important conclusion illustrated by Fig. 4 and eq. 10 is that actual and apparent surface coverages coincide only in the neighborhood of the maximum in the eappus. V curve, so that, in estimating adsorption from double layer capacitance measurements, it is essential that the variation of capacitance with potential be sufficiently investigated to establish the polarization a t this maximum, and that isotherms be determined a t this polarization. More extensive conclusions can be reached from fairly complete capacitance-polarization-activity data. I n this case, not only fractional coverage but actual amounts adsorbed can be established, since molecular areas (S) can be obtained from curvatures of the BaPP us. V plots. Finally, it
Sept., 1956
ADSORPTION FROM DIFFERENTIAL CAPACITANCE MEASUREMENTS
is t o be emphasized that the actual adsorption of a solute by a metal depends on its polarization. Dipolar molecules normally adsorbed with positive end of the dipole toward the metal will be most strongly adsorbed somewhat on the cathodic side of the electrocapillary maximum. Those adsorbed with negative end of the dipole toward the metal will be most strongly adsorbed somewhat on the anodic side of the electrocapillary maximum, and that a t sufficient polarizations, either anodic or cathodic, organic molecules will be almost completely desorbed in the presence of aqueous electrolytes.
1189
The dependence of capacitance on polarization in 0.100 M HCIOa saturated with pentanoic acid is shown in Fig. 3, but no corresponding curve is shown in Fig. 4 because this curve illustrates the effect of multimolecular adsorption on capacitance, as was first shown by Melik-Gaikazyan.8b The pronounced dip below the apparent convergence limit is interpreted by Melik-Gaikazyan as due to an increase in thickness of the compact double layer accompanying multi-molecular adsorption, and the stepwise rise above this limit due t o a “pseudocapacitance” accompanying the desorption of the second layer.
