Langmuir 1989, 5, 1113-1115 consistent with the idea that molecular orientational effects are involved in this interaction. A question arises concerning the "hard-wall" type repulsion measured a t very small separations, especially between the untreated mica surfaces. Such short-range repulsive walls have also been recently measured in polymer melts.14J5 They are most likely due to the strong binding of the liquid molecules to the surfaces (the contact angle of 2-methyloctadecane on mica is zero or very small), which prevents the last few layers from being easily squeezed out. That the positions of these hard walls were closer with the surfactant-coated surfaces may therefore be due to the weaker adhesion of the liquid to these more inert surfaces. The progressive reduction in the strength of the adhesion forces as we go from untreated mica to surfactantcoated surfaces and-just within experimental error-from double-chained (Clz),DAB-coated surfaces to the singlechained CTAB-coated surfaces is likely to be related to the progressively increasing surface roughness of these surfaces.z3 Again, this observation is consistent with the notion that the attractive force is related to molecular orientation effects; viz., the ability of surfaces to align anisotropic molecules parallel to them must diminish as the surface roughness increases. Similar experiments have also been performed with other isoparaffins and mixtures of isoparaffins, resulting in force laws similar to those obtained here. Thus, the results presented here may well be generally applicable to other systems involving anisotropic flexible chain molecules or to certain tvpes of molecules havine: anisotropic interaction potentials (such as water, leading to the attractive hydrophobic interaction). In conclusion, it has been shown that, for certain anisotropic flexible chain liquid molecules between two (23)Christenson, H.K.J. Phys. Chem. 1986,90,4.
1113
surfaces, there exists a hitherto unsuspected attractive force that appears to be associated with entropic orientational (or alignment) effects. This type of attractive entropic force may be conceptually similar to the attractive entropic depletion forcez4associated with changes in the density of solute molecules between two surfaces as they approach each other. The latter interaction is described by a scalar order parameter (the density) while the former should be described by a vector (orientational) order parameter. Depending on the nature of the liquid and its interaction with the surfaces, repulsive entropic orientational forces could also arise, as they do in the case of repulsive hydration force^,^^^^^ though one would expect attractive forces whenever the surface-induced ordering lowers the entropy of the liquid adjacent to it, as occurs for polymer melts26and water.lsal0 There are also many obvious practical implications of these findings, e.g., for interparticle interactions in anisotropic media, for the stability of colloidal systems, for the action of lubricants, etc. Further investigation of this extra attractive force is under way, the results of which will be presented in a future publication. Acknowledgment. We thank the U.S. Department of Energy for financial support under DOE Grant DEFG03-87ER45331, although this support does not constitute an endorsement by the DOE of the views expressed in this article. Registry No. CTAB, 57-09-0;DTAB, 70755-47-4; 2-methyloctadecane, 1560-88-9. (24)Joanny, J. F.;Leibler, L.; de Gennes, P. G. J.Polym. Sci., Polym. Phys. 1979,17,1073. (25)Israelachvili, J. N.In Physics of Complex and Supermolecular Fluids; Safran, S. A., Clark, N. A. Eds.; Wiley: New York, 1987;pp 101-113. (26)Silberberg, A. J. Colloid Interface Sci. 1988,125,14.
Influence of Electric Field at the Electrode/Electrolyte Interface on EXAFS Results Mahesh G. Samant IBM Research Division, Almaden Research Center, K32l802, 650 Harry Road, San Jose, California 95120 Received December 12, 1988. I n Final Form: April 7, 1989 The effect of the electric field at an electrode/electrolyte interface on the structural parameters evaluated from the EXAFS measurements is considered. The apparent near neighbor distance evaluated by EXAFS is shifted. For an electric field of 5 X 10' V/cm, a near neighbor distance of 2.500 8, will appear shorter or larger by 0.012 8, depending on the direction of the electric field. The shift is larger for longer distances, 0.018 8, at 3.000 A. Introduction One of the recent advances in probing structures at electrode/electrolyte interfaces under in situ conditions has involved the successful application of fluorescencedetected surface extended X-ray absorption fine-structure spectroscopy (SEXAFS)1-3 and of surface X-ray diffrac(1)Blum, L.; Abruna, H.; White, J.; Gordon, J.; Borges, G.; Samant, M.; Melroy, 0. J. Chem. Phys. 1986,85,6732. (2)Samant, M. G.; Borges, G.; Gordon, J.; Blum, L.; Melroy, 0. J. Am. Chem. SOC.1987,109,5970.
0743-7463/89/2405-1113$01,50/0
tion.4~~ These techniques utilized hard X-rays, which have significant penetration depth in a condensed phase such as the electrolyte and have Provided direct information on the atomic di&nces and C r y s a o P P h i c s h ~ ~ t u r In e . the case of both of these techniques, surface sensitivity was (3)Melroy, 0.; Samant, M. G.; Borges, G.; Gordon, J.; Blum, L.; White, J.; Albarelli, M.; McMillan, M.; Abruna, H. Langmuir 1988,4 , 728. (4)Samant, M. G.; Toney, M.; Borges, G.; Blum, L.; Melroy, 0. J. Phys. Chem. 1988,92,220. ( 5 ) Samant, M. G.; Toney, M.; Borges, G.; Blum, L.; Melroy, 0. Surf. Sci. 1988,193,L29.
0 1989 American Chemical Society
1114 Langmuir, Vol. 5 , No. 4, 1989
Letters
achieved by having X-rays incident a t grazing angles (angles typically less than 0.5') and by depositing a monolayer of material with a different chemical identity than the substrate. Surface X-ray diffraction was used to determine lattice spacing, atomic spacing, epitaxy between deposit and substrate, and the size of domains of deposits. The SEXAFS probed the local environment of the absorbing element and gave information on the type of near neighbor, near neighbor distance, coordination number, and Debye-Waller type factor. An interesting result of the SEXAFS measurements was the observation of a well-defined near neighbor distance corresponding to a metal-oxygen atomic pair. Oxide formation was precluded by maintaining a proper control of the electrode potential. This was confirmed by the edge position of the deposited metal, which was identical with that of a reference metal foil. Hence, this metal-oxygen distance was assigned to adsorption of an electrolyte species onto the electrode surface. The species which were thought to be adsorbed were either water molecules or anions of sulfate or acetate, and these were argued to form a well-ordered structure on the surface. Furthermore, in the particular case of a P b monolayer underpotentially deposited on a A g ( l l 1 ) electrode, it was noted that the Pb-0 near neighbor distance showed a variation with the electrode potential: it was 2.33 and 2.38 A for electrode potentials of -0.53 and -1.0 V versus Ag/AgCl reference electrode,2 respectively. This was explained on the basis that as the electrode potential is made more negative the species which is adsorbed via its electronegative end (i.e., via an oxygen atom) will be repelled away from the electrode surface. The effect of change in the electric field at the electrode on the EXAFS itself was not considered and as yet has not been discussed in any of the papers which are concerned with SEXAFS of structures a t an electrochemical interface. It is the contention of this paper that the presence of a sufficiently strong electric field a t the electrode surface can cause the apparent near neighbor distances from SEXAFS measurements to differ from the actual value. Furthermore, it is possible that a change in electric field at the electrode surface as a result of change in the electrode potential can alter the distance determined from SEXAFS data even though the real distance may still be unchanged. Theory The EXAFS function, x ( h ) ,is defined as
x ( k ) = (P - Po)/Po
(1)
where k is the magnitude of the photoelectron wave vector ((2m(E - Eo))1/2)/h,m is the rest mass of the electron, E - Eo is the kinetic energy of the photoelectron, h is Planck's constant, h = (h/27r),1-1is the mass absorption coefficient of the atom in the sample, and po is the mass absorption coefficient of a free atom. Here, the kinetic energy ( E Eo) of the photoelectron is determined by the difference in energy of the incident X-ray beam and the absorption edge position E, of the core electron. In an electrochemical system, this photoelectron travels along a very strong electric field both in forward scattered and backscattered directions. Thus, the value of the wave vector k will be altered as the ejected photoelectron undergoes acceleration and deceleration depending on the direction of travel relative to the electric field, yet upon return to the absorbing atom the value of k will be identical with its initial value. This effect can be accounted for by simple electrostatic relationship, which gives the acceleration, a, of the photoelectron in an electric field, Ef, as follows: a = eEf/m
(2)
where e is the charge of the electron and m is the rest mass of the electron. Since this acceleration occurs between the metal surface and the closest atom belonging to the solution layer, the effective dielectric constant can be assumed to be identical with that of a vacuum, which is 1. This photoelectron travels a distance equivalent to the near neighbor distance, R, which is being probed before it undergoes scattering. Assuming that a and R lie along the same direction, they are related by the following expression:
R = ( h k / m ) t + '/zat2
(3)
where hklm is the initial velocity of the photoelectron and t is the time required to travel distance R. Then t can be explicitly evaluated as
t = [ - ( h h / m )+ ( ( h k / m ) 2+ ~uR)'/']/u
(4)
The value of the wave vector a t the backscattering atom, k b , is kb
=k
+ (m/h)at
(5)
and the average value of the wave vector along the atomatom vector, k,, is ha = h
+ '/z(m/h)at
(6)
The effect of these modifications of the wave vector on the EXAFS equation can now be considered. The EXAFS equation for the first coordination shell, based on the assumptions of one electron propagating as a plane wave and point scattering, is x(k) =
C,(~,/kR,2)f,e-2ui2k2e-2R~/'J sin (2hR, + 4])
(7)
where the summation is over different types of atoms in the first coordination shell. N, is the coordination number, R, is the nearest-neighbor distance, f, is the backscattering amplitude, a, is the Debye-Waller-type factor, A, is the mean free path of the photoelectron, and 4, is the phase shift. The functions f, X, and 4 are also dependent on k . In this paper, the dependence of X on k has been neglected. The k dependence off and 4 was obtained from the work of Teo and Lee.6 The following strategy is used to generate the experimental EXAFS function in presence of the electric field Ef. For a set of values of h in the range from 3 to 12 .kl, both ha and kb are evaluated. x ( k ) is determined by replacing k only on the right-hand side of eq 7 by ha. The correct value o f f is f(kb). The phase shift function is obtained by adding the central atom phase at h and the backscattering atom phase at kb according to the relationship given by Teo and Lee.6 The x(k) thus generated is considered representative of the experimental ~ ( h ) .The structural parameters are then obtained by using well-established fitting procedures.' For a flat electrode, the electric field extends from the metal surface in a direction perpendicular to the surface. Since the oxygen-bearing species adsorbed on the electrode is on the solution side of the interface, it is expected that the electric field will most strongly affect determination of the metal-oxygen distance. To understand the magnitude of this effect, the x(k) functions were generated for the case of oxygen-bearing species adsorbed on the atop sites by considering the system comprising the Ag-0 atomic pair. Various distances between these near neighbors and various values of the electric field were assumed during (6) Teo, B.-K.; Lee, P. A. J . Am. Chem. Soc. 1987, 101, 2815. (7) Lee, P. A.; Citrin, P. H.; Eisenberger, P.; Kincaid, B. M. Reu. Mod. Phys. 1981, 53, 769.
Langmuir, Vol. 5, No. 4 , 1989 1115
Letters Table I. Evaluated Near Neighbor Distance R (in A) versus Electric Field (in lo' V/cm)
R V
2.000
-5.0 -2.5 2.5 5.0
2.008 2.004 1.996 1.992
2.500 2.512 2.506 2.494 2.487
3.000 3.018 3.009 2.991 2.981
these calculations. The choice of Ag as the absorbing atom was arbitrary; however, it should be noted that for these calculations the Ag atom contributes only through the central atom phase shift, which is evaluated a t k. Hence these results are quite general and applicable for most metal-oxygen pairs. Results and Discussion The near neighbor distance evaluated by a standard curve-fitting analysis procedure from the generated EXAFS data is included in Table I. The actual distances are varied from 2.000 to 3.000 8, so as to cover the range of possible near neighbor distances which could potentially be observed. The value of the electric field which is typical of the electrode/electrolyte interface is of the order of (2.5-5.0) X lo7 V/cm.8 Thus, the field variation is also considered in this range. The results show that the positive electric field causes the evaluated R to be smaller than the actual R, whereas the negative electric field causes a higher value to be assigned to R. As expected, the magnitude of this effect depends primarily on the strength of the electric field. The positive electric field represents the electrode potential on the positive side of the potential for zero charge (pzc), and likewise a negative electric field is indicative of potentials lower than the pzc of the electrode. Thus change in the electrode potential from the positive side of pzc to the negative side of pzc will lead to observation of distance elongation even for a near neighbor distance which remains unchanged. In the case of the Ag-0 pair at a distance of 2.500 A, the variation of electric field from 5 X lo7 to -5 X lo7 V/cm can the cause the distance to appear 0.025 8, longer. This variation is larger than the error bar associated with the distance obtained from EXAFS measurements, which is approximately *0.01 The major contribution to this variation in R arises from the 2kR term in the sine part of the EXAFS function. The change in the backscattering phase shift function caused by the electric field is small and accounts for only a small fraction of the total change. The adjustment of the edge position E, done during the normal curve-fitting analysis procedure should adequately compensate for a slight change in the phase shift function. The coordination number and change in the Debye-Waller-type factor were also evaluated during the course of this analysis. The coordination number showed a systematic dependence on the electric field and decreased as the strength of the electric field decreased. However, this variation was less than 2% of the expected value. Since the error bars associated with the measured coordination number from the (8) Bockria, J. O.'M.; Reddy, A. K . N . Modern Electrochemistry; Plenum Press: New York, 1973; Vol. 2.
EXAFS data are in the range of 10-20% of the measured value, this slight dependence of coordination number on strength of the electric field can be neglected. The effect of the strength of the electric field on the Debye-Waller-type factor was quite small, within the range 10-5-104, and hence can be considered negligible, as it will have little bearing on the interpretation of the EXAFS results. In an electrochemical system, the electric field at the electrode can be modified at a given value of the electrode potential by changing the nature of cations present in the supporting electrolyte. The effective size of the cation, which is the sum of its size and that of the solvent sheath, determines the distance of the outer Helmoltz plane (OHP) from the electrode. This OHP distance increases as the effective size of the cation increases,8 which reduces the magnitude of the electric field present at the electrode surface. The metal-oxygen distance being probed lies in the inner layer and should see the variance in the potential drop caused by change in the cation size. The effect of the cation size on the electric field has not only been postulated theoretically but recently has been invoked to explain the dependence on the nature of cations in the supporting electrolyte of the vibrational frequencies of adsorbed thiocyanate ions on a polycrystalline platinum ele~trode.~ The anion adsorption at the electrode determines the distance of the inner Helmoltz plane (IHP) from the electrode surface. Thus adsorption of anions of different sizes but identical charge and electrosorption vaIence will move the position of the IHP relative to the electrode surface. The metal-oxygen linkage will be subjected to an electric field whose strength depends only on the size of these anions. The determination of the cation size effect or the anion size effect on the near neighbor distance evaluated from EXAFS should provide a more detailed understanding of the electrode/electrolyte interface, as the strength of the electric field can be obtained directly. Conclusions A simple method based on electrostatics has been presented to describe the effect of the electric field on the structural parameters determined from EXAFS data. The magnitude of the effect of the electric field depends on the near neighbor distance probed and the strength of the electric field. At a near neighbor distance of 2.500 8, and an electric field of 5 X lo7 V/cm, the near neighbor distance will appear as 2.487 or as 2.512 8, depending on the sense of the electric field. If a near neighbor distance shows a variation with the electrode potential, then Table I can be used to determine whether the chemical effect or the electric field effect is dominant. The modification of electric field by the cation size effect or the anion size effect provides a way to experimentally determine typical values of the electric fields at the electrode/electrolyte interface by using EXAFS measurements. Acknowledgment. I acknowledge useful discussions with Dr. Joseph G. Gordon 11. Registry No. Ag, 7440-22-4. (9) Ashley, K.; Samant, M. G.; Seki, H.; Philpott, M . R. J.Electroanal. Chem. Interfacial Electrochem., in press.
