Langmuir 1991, 7, 1000-1004
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Time-Resolved Measurement of Equilibrium Surface Tensions at the Electrified Mercury-Aqueous NaF Interphase by the Method of Wilhelmy Donald D. Montgomery? and Fred C. Anson* Arthur Amos Noyes Laboratories,t Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91 125 Received May 25,1990. I n Final Form: October 17, 1990 The Wilhelmy plate technique for measuring static and dynamic surface tensions was extended to the electrified mercury-aqueous electrolyte interphase. Several modifications to a conventional Wilhelmy plate are described,which were necessaryto implement the technique within an electrochemicalenvironment. Proper isolation of the Wilhelmy plate and associated instrument from vibration allowed sensitivities to be reached that were about 5 times greater than those attainable with maximum bubble pressure measurements. The surface tensions at the electrified mercury-aqueous NaF interphase measured with the modified Wilhelmy plate instrument agreed well with literature values. The capability of the instrument described for making rapid measurements of surface tensions was exploited to observe intrinsic fluctuations in the equilibrium surface tensions. The importance of intrinsic fluctuations and time-averaging for precise evaluation of the equilibrium surface tension are discussed.
Introduction Although several conventional techniques (e.g., sessile drop, capillary electrometer, and maximum bubble pressure) are available for directly measuring the equilibrium surface tension a t electrified interphases,' none has the capacity for measuring nonequilibrium or time-resolved surface tension^.^^^ One common technique for directly measuring both equilibrium and nonequilibrium surface tensions that has not been extended to the electrified interphase is the method of W i l h e l m ~ . Smitha ~ ~ ~ has employed this technique for measuring the surface tension at uncharged mercury-gas interphases and has outlined several technical problems inherent in the application of the Wilhelmy method with liquid metal substrates. In particular, Smith has stressed the critical role of effective vibration isolation and an inert ambient atmosphere. We have extended the seminal work of Smith to the electrified mercury-aqueous electrolyte interphase. This required modification of the conventional Wilhelmy plate to isolate it from the electrolyte solution and to insulate it electrically from the balance. The Wilhelmy instrument was contained within a stainless steel vacuum chamber to ensure an inert ambient atmosphere. The chamber was + Present address: Joint Institute for Laboratory Astrophysics, University of Colorado, Campus Box 440,Boulder, CO 80309-0440. Contribution No.8150. (1) (a) 'Interphase" is employed in the sense introduced by Gibbs and utilized previously by Parsons.lb (b) Parsons, R. In Comprehensive Treatise of Electrochemistry; Bockris, J.OM., Conway, B. E., Yeager, E., Eds.; Plenum Press: New York, 1980, Vol. 1. (2) (a) Mohilner, D. M. Electroanalytical Chemisrty, Vol. 1; Bard, A. J. Ed.; Marcel Dekker: New York, 1988. (b)Parsons, R. Modern Aspects ofElectrochemistry, Vol.1; Bockris,J.OM., Ed.; Buttersworth: London, 1954. (c) Delahay, P. Double Layer and Electrode Kinetics; Wiley-Interscience: New York, 1965; Chapter 2. (d) Conway, B. E. Theory and Principles of Electrode Processes; Ronald: New York, 1965; Chapters 4 and 5. (e) Bard, A. J.; Faulkner, L. R. ElectrochemicalMethods;J. Wiley and Sons: New York, 1980, Chapter 12. (3) Lawrence, J.; Mohilner, D. M. J.Electrochem. SOC.1971,118,259. (4) Wilhelmy, L. Ann. Phys. 1863, 119, 177. (5) Gaines, G. L. Insoluble Monolayers at the Liquid-Gas Interface; Wiley-Interscience: New York, lBgg, Chapter 2. (6) (a) Smith, T. Adu. Colloid Interface Sci. 1972,3,161. (b)Smith, T. J. Colloid Interface Sci. 1968,26,509. (c) Smith, T. J. Opt. SOC.Am.
1967,57,1207.
isolated from mechanical vibration by suspending it by elastomer fiber cords using a three-point suspension system. The electrocapillary response of the surface tension measured by the Wilhelmy method compared well with literature values when the electrobalance output was timeaveraged. The capacity of the Wilhelmy method for dynamic surface tension measurements also allowed observation of intrinsic fluctuations in the equilibrium surface tension. The importance of these intrinsic fluctuations for precise measurement of the equilibrium surface tension is discussed in this report.
Experimental Section Wilhelmy Plate. A 0.13 mm thick platinum plate was cut into a 0.7 cm by 2.5 cm rectangle and press fit into a 0.08-mm groove that had been machined into a tapered Kel-F support as illustrated in the inset of Figure 1. The press fit ensures a very tight seal between the Kel-F and the platinum, which excludes leakage of supporting electrolyte into this interstitial space. Approximately 4 mm of exposed platinum plate extends below the bottom lip of the Kel-F jacket on the assembled Wilhelmy plate. The exposed section of platinum was coated with mercury by dipping it into a fresh sodium-mercury amalgam (- 1:lO Na: Hg) until visual inspection indicated that the platinum surface had been completely covered (ca. 1 min). The mercury-coated Wilhelmy plate assembly was then cleaned by sonication (Bronstead 3200) for 30 min in methanol and then for another 30 min in l,l,l-trichloroethane. Whennot in use, theassemblywas stored by suspending it above a small mercury pool and adjusting the level of the pool such that the top of the meniscus abutted the edge of the Kel-F support. The Wilhelmy plate assembly was connected to a Cahn 2000 recording electrobalance for surface tension measurements by a stiff 5.5 mm diameter copper wire that was -80 cm in length. The electrobalancewas supported and encased within a modified glass bell jar and the wire ran down to the electrochemical cell via a feedthrough (Figures 1 and 2). The glass bell jar was suspended from a rigid frame by a brass threaded-rod and nut assembly, which allowed the vertical position of the electrobalance to be adjusted by rotation of the nut. This allowed the bottom edge of the Wilhelmy plate assembly to be positioned such that it just touched the surfaceof the mercury-pool electrode. Electrochemical Cell. The electrodeused here was acircular mercury pool with a surface area of 73.44cm2, which was formed by pouring mercury into the bottom of a crystallizationdish with
0743-7463/91/2407-10$02.50/0 0 1991 American Chemical Society
Surface Tensions at Mercury-Aqueous NaF Interphase
Langmuir, Vol. 7, No. 5,1991 1001
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,;lZEeohalance Support
-%.
I Electrohalance
Electrohalance Feedthmughs
,Reference Electmde Probe
Top Flange
Feedthmughs Vacuum Aspir
Inert Atmosphere
H Electrical Feedthrough
I
HgElectrode
CutawayKde-view of Wilhelmy Plate Assembly
I
Flange 1
Figure 1. Schematic illustration of the functional components of the Wilhelmy plate ap aratus employed in this study. The inset displaysa cutaway sile view of the Wilhelmy plate assembly, showingthe platinum plate press-fit into a Kel-Fjacket to isolate it from the supporting electrolyte. an internal diameter of 9.67 cm. Electrical contact was provided by a PTFE sheathed platinum wire, which clipped over the edge of the crystallizationdish. The counterelectrode was a largepiece of platinum wire that was formed into a nearly circular loop slightly larger in diameter than the inside of the crystallization dish. This allowed the counterelectrode to act as a spring when placed inside the crystallization dish and to hold itself tightly in placearound the perimeter of the cell. The cell was placed inside a large (ca. 55 cm diameter) stainless steel chamber (Figure 2) that provided both an inert atmosphere and vibration isolation. A saturated sodium chloride calomel (SSCE) reference electrode was located outside of the chamber and connected to the cell with a long glass probe. The tip of the probe that was in contact with the cell was sealed by a piece of Vycor glass, which provided a conductive and nearly ion-impermeable junction. The Vycor glass tip was allowed to equilibrate with the supporting electrolyte solution for several days prior to use and was immersed in a 0.1 M solution of the appropriate supporting electrolyte when not in use. Prior toanexperiment, thechamberwas flushedwithavigorous flow of deoxygenated argon for severalhours. The crystallization dish was then placed into the chamber and connected to electrical leads, and mercury was added to form the pool electrode. The mercury surface was then cleaned by aspiration. After the electrode had been cleaned, the Wilhelmy plate was positioned near the center of the cell, and then lowered onto the surface of the mercury-pool electrode. Supporting electrolytethat had been deareated with deoxygenated argon was added until both the counter-electrode and the Wilhelmy plate were completely immersed (ca. 100 mL). The reference electrode probe was then introduced and positioned near the Wilhelmy plate. An electrostatic potential was applied to the electrochemical cell with a Princeton Applied Research 173-175 potentiostatprogrammer combination. Output from the electrobalance was collected by an IBM-AT microcomputer. Analog-to-digital conversion tasks were handled by 12-bit Analog Devices signal digitizing board (RTI-815). Data were acquired at 20 Hz. Experiments were conducted at ambient temperature. Potentials were all measured and are reported with respect to a saturated sodium chloride calomel electrode (SSCE). Vibration Isolation. The apparatus illustrated in Figure 2 was isolated from mechanical vibration by suspending the entire
Figure 2. Exploded view of the chamber that encased the functional components of the Wilhelmy plate apparatus, and provided an inert ambient environment. The electrobalance was housed within the modified bell jar near the top of the figure. Electrobalance feedthroughs and vacuum aspiration porta were attached to the lid of the chamber. Electrical connection to the electrochemical cell was made through a side port. The shelf attached to the lower portion of the chamber was used as a mass damper for effective vibration isolation. The entire assembled chamber was suspended from elastomer fiber cords, which were attached to eye-bolts on the lid.
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instrument from three elastomer fiber cords 1cm in diameter, which were attached to a wooden tripod assembly. The chamber was leveled by adjusting turnbuckles, which connected the cords to the tripod assembly. Prior to an experiment, the apparatus was supported from below by labjacks, which were lowered slowly to allow the chamber to hang freely during an experiment. No special precautions were taken to isolate the instrument from acoustic vibrations. Materials. Supporting electrolyte solutions were prepared from recrystallized analytical grade NaF. Laboratory distilled water was passed through a purification train (Barnstead-Nanopure). Triple-distilled instrument grade mercury (Bethlehem Apparatus Co.) was used for the pool electrodes.
Results and Discussion Description of the Technique. In 1863 Wilhelmy( introduced a method for measuring surface tension that is based on determining the force exerted by the meniscus of some fluid wetting the side of a thin plate that is positioned normal to and just touching the surface of the fluid. This technique is used most frequently for measuring the surface tension at liquid-gas interphases (e.g., Langmuir troughs), but can be adapted for studies of liquid-liquid interphases as well.& The basic elements of the physics of the technique applied to the electrified mercury-aqueous electrolyte interphase are illustrated in Figure 3. Fluid B, in this case mercury, is denser and has
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1002 Langmuir, Vol. 7, No. 5, 1991 \a
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pool electrode. Thus, the last four terms in eq 1 are constant. Because mercury was plated onto the surface of the platinum Wilhelmy plate, cos B = 1, and the differential form of eq 1 becomes
/
dF = L, dym
\Platinum
Plate
Fluid B Figure 3. Illustration of the basic elements of the physics of the Wilhelmy plate technique aa applied to the electrified mercuryaqueouselectrolyteinterphase. Fluid A is an aqueouselectrolyte solution and fluid B is the mercury electrode. The platinum and Kel-F Wilhelmy plate assembly is completely immersed in the supporting electrolyte solution.
a larger intrinsic surface tension than fluid A. Fluid B wets the surface of the Wilhelmy plate, forming a meniscus with a contact angle that depends on the degree of wetting. The plate is suspended above the surface of the mercury pool, and the position of the bottom edge of the plate is adjusted so that it is just at, or slightly below, the level of the mercury surface. Because the plate is immersed completely in fluid A, there are two surface tensions that can contribute to the observed force on the plate. One is the surface tension a t the interphase between the mercury electrode and fluid A, ym, and the other is the surface tension a t the interphase between fluid A and the plate, YAP. Fluid A in this case was a 0.1 M NaF supporting electrolyte solution. Because both surface tensions can depend upon the applied electrostatic potential, it was necessary t o isolate the platinum plate from the supporting electrolyte by encasing the portion of the plate that gives rise to TAP in a Kel-F jacket. The interphase between fluid A and the Kel-F jacket is not electrified, so the only potential-dependent surface tension that is observable with the Wilhelmy plate assembly illustrated in Figures 2 and 3 is TAB. The net force exerted on the balance by the Wilhelmy plate assembly employed here was
F = ymLp COS B + y&,
COS
8’ + m g - PAVAg - pBVeg (1)
whereg is the acceleration of gravity, mpis the mass of the plate, P A and PB are the densities of fluids A and B, respectively, L, is the perimeter of the plate, cos B and cos 8’ are the cosines of the contact angles of the meniscus a t the platinum-mercury interphase and the supporting electrolyte-Kel-F interphase, respectively, and VAand VB are the volumes of the plate assembly in fluid A and in fluid B, respectively. The Wilhelmy plate technique is not regarded favorably as a technique for measuring absolute values of the surface tension5 because of uncertainty in evaluating the last two buoyancy terms on the right-hand side of eq 1. However, if a recording electrobalance is used, it is a fast and accurate method for measuring differential and dynamic surface tensions because the buoyancy terms drop out of the expression for dF. The recording electrobalance measured the force exerted on it by applying an equal and opposite force to a torque motor and therefore always maintained the plate at a constant vertical position relative to the surface of the mercury
(2)
Thus, d y m is directly proportional to the observable quantity dF. The proportionality constant, L,, can be determined by direct measurement or evaluated independently if absolute values of y m are known. The value of L, employed here was evaluated empirically by comparing values of F obtained with the Wilhelmy plate technique with values of ym reported in the literature. Sensitivity of t h e Wilhelmy Plate Technique. The primary limit to the sensitivity of the Wilhelmy plate ,technique is either the lowest mass unit the electrobalance can resolve ( k 5 x g) or noise in the electrobalance signal due to mechanical vibrations. For the instrument employed here, mechanical vibration proved to be the sensitivity limiting factor. To determine the sensitivity, the electrobalance output was monitored for a 5-min period as it measured the force on the Wilhelmy plate assembly, which was suspended a t the interphase of the mercury-pool electrode and a 0.1 M NaF supporting electrolyte solution. The sensitivity obtained in this fashion was f 5 X g, a number 2 orders of magnitude larger than the lower limit for mass detection of the electrobalance. The surface tension sensitivity can be related in a simple fashion to the mass sensitivity by replacing dF in eq 2 with gdm, e.g. dym = L,-’gdm = Kdm
(3)
where m is the mass of the meniscus. The value of K for the Wilhelmy plate assembly used here was 497.8 s - ~ ,and this gave a surface tension sensitivity of f 5 X dyn cm-l. The high sensitivity of the Wilhelmy plate apparatus described here is a direct result of an efficient vibration isolation scheme. Although wood and elastomer fiber cords might be expected to damp mechanical vibrations efficiently a t high and medium frequencies, the effective vibration isolation observed a t low frequencies is probably not ascribable directly to the dissipation characteristics of these materials. Rather, it was the three-point suspension system that was responsible for the good lowfrequency behavior of the vibration isolation system. A tripod suspension system will give rise to low-frequency normal modes that are torsional, whereas the lowfrequency modes of most buildings are translational. As a result, the coupling between the low frequency modes of the building and the instrument was inefficient and good vibration isolation was achieved over a wide effective bandwidth. Intrinsic Fluctuations i n t h e Equilibrium S u r f a c e Tension. The response time of the Wilhelmy plate technique for modern recording electrobalances is of the order of 0.05 s, allowing an effective sampling rate of about 20 Hz.’ This response time is about 2 orders of magnitude shorter than that associated with the maximum bubble pressure technique (the fastest conventional technique for measuring surface tension a t electrified interphases).293 Comparing the measurements of equilibrium surface tensions obtained with our apparatus to literature values (7) (a) Mann, J. A., Jr. Techniques of Surface Chemistry and Physics, Vol. 1; Good, R. J., et al., Eds.; Marcel Dekker: New York, 1972. (b) Boonman, A,; Gieles, P.; Massen, C. H.; Egberta, J. Thermochim. Acta 1986,103,107. (c) van dem Tempel, M.; Lucassen-Renders, E. H. Adu. Colloid Interface Sci. 1983, 18, 281.
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Surface Tensions at Mercury-Aqueous NaF Interphase proved problematic because we observed small and relatively long-lived fluctuations in the electrobalance output signal with the interphase a t equilibrium. Evidence of these fluctuations has not been reported previously, probably because of the slower sampling rates of conventional techniques. The time-resolved values of any observable for a system at thermodynamic equilibrium that is coupled to a heat bath will fluctuate about some time-average value.8 These intrinsic fluctuations are generated by random, thermally driven molecular events, which cause the system to drift about on the hypersurface in phase space that describes the set of states available to the system. Experimental detection of intrinsic fluctuations in an observable requires the sampling rate of the measurement technique to be at least as fast as the Nyquist limit for the fluctuation^.^ The response time of the Wilhelmy technique as implemented in the apparatus described is adequate to allow these intrinsic fluctuations in the surface tension at electrified interphase to be observed. The possibility that the observed fluctuations in the surface tension were due to mechanical noise was eliminated by measuring the autocorrelation function, c ( T ) , for the fluctuations and comparing it to the autocorrelation function for the mechanical noise in the instrument. The autocorrelation function is definedbb in eq 4
4 7 ) = lim t--
t-'llY(t) - ( y ( t ) ) ) * b (+t 7 ) - ( y ( t ) ) l )dt
(4)
where ( y ( t ) )is the time-average of the observable y ( t ) . In Figure 4A the autocorrelation function calculated for the electrobalance output with the Wilhelmy plate assembly hanging freely in a 0.1 M aqueous solution of NaF is displayed. The data were acquired a t 20 Hz,and 50 OOO data points were used to evaluate c ( 7 ) because accurate evaluation of the integral in eq 4 using discrete time data requires very large data sets.& The autocorrelation function in Figure 4A drops rapidly to zero as expected for uncorrelated white noise. When the Wilhelmy plate assembly is positioned a t the electrified mercury-aqueous NaF interphase, 4 7 ) assumes an entirely different form as displayed in Figure 4B. The autocorrelation function of the mechanical noise displayed in Figure 4A is still present in Figure 4B,but additional processes must also be present that serve to lengthen the correlation time by several orders of magnitude. The autocorrelation function in Figure 4B requires nearly 3.5 s to decay to zero. Thus, the observed fluctuations in the measured surface tensions are not ascribable to the perturbations produced by lowfrequency mechanical noise. The shape of C ( T ) in Figure 4B is not: what would be expected for a simple linear system where fluctuations are driven by processes that are Markovian, Gaussian, and ergodic.8 However, the electrified interphase is a highly nonlinear system in the sense that the ratio of the charge density to the electrostatic potential is not independent of that potential. The unusual form of the C ( T ) curve in Figure 4B is presumably a result of this fact. Comparison with Literature Values. To compare the surface tension values measured by the Wilhelmy plate assembly described here with literature values obtained, (8) (a) Kubo, R.;Toda, M.; Haehibume, N. Statistical Physics ZZ. Nonequilibium Statistical Mechanics; Cardona, M., Ed.;Springer-Verhg: Berlii! 1983. (b)Yourgrau,W.; van der Merwe, A.; Raw, G. Treatise on Irreversrbleand Statistical Thermophysics. AnZntroduction to Nonclassical Thermodynamics; Dover, New York, 1982. (c) Grandy, W.T., Jr. Foundation8 of Statistical Mechanics, Val. ZI Nonequilibrium Phenomenu; van der Merwe,A., Ed.;Reidel: Dordrecht, 1987. (9) Nyquist, H. Phys. Reu. 1928, 92, 110.
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.? 'rime.
3
4
5
YCC.
Figure 4. Autocorrelation functions for the steady-state electrobalance output signal: (A) Wilhelmy plate assembly fully immersed and hanging freely within a 0.1 M aqueous NaF solution. (B) Wilhelmy plate assembly positioned at the electrified mercury-0.1 M aqueous NaF interphase. Applied electrostatic potential was -0.550 V vs SSCE.
for example, by the maximum bubble pressure technique, it was necessary to perform a 5-s time-average over the intrinsic fluctuations after the data were acquired by the computer. The curve denoted by the solid line in Figure 5 displays the equilibrium electrocapillary curve for the electrified mercury-0.1 M aqueous NaF interphase obtained by using the Wilhelmy plate technique. The data were acquired by stepping the applied electrostatic potential in 5-mV increments, allowing the system to settle for 10 s, and then recording the electrobalance output over a 10-s period. Time-averages were performed over 5-s segments of the electrobalance output and the resulting values used to construct the electrocapillary curve in Figure 5. The data agree very well with electrocapillary data for the same interphase obtained by Mohilner6 using the maximum bubble pressure technique. These data are plotted in a dashed line in Figure 5. The agreement is so close that the latter line is barely visible. Thus, the Wilhelmy plate technique provides a reliable method for measuring the equilibrium surface tension a t electrified interphases. Effect of Intrinsic Fluctuations on Equilibrium SurfaceTensionMeasurements. The value of theequilibrium surface tension acquired from conventional techniques is usually an average over a set of independent measurements, which is not necessarily equivalent to the maximum value because of intrinsic fluctuations. This
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1004 Langmuir, Vol. 7, No.5, 1991 r
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0550 0450 Potential [mV vs SSCE]
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Figure 5. Equilibrium electrocapillarycurves for the mercury0.01 M aqueous NaF interphase. Solid line corresponds to values obtained in this study by performing a 5-8 time average. Dashed line corresponds to values obtained by Mohilner using a maximum bubble pressure i n ~ t r u m e n t . ~
Figure 6. Equilibrium electrocapillary curves for the mercury0.01 M aqueous NaF interphase. Solid line corresponds to maximum values of intrinsic fluctuations in the time-resolved surface tension data. Dashed line correspondstovalues obtained by performing a 5-8 time average over the time-resolved data.
effect is demonstrated in Figure 6 where an electrocapillary curve (solid line) obtained by taking maximum values of the surface tension from the time-resolved data obtained by using the Wilhelmy technique is compared to the curve (dashed line) obtained by using time-averaged values. Although the effect illustrated in Figure 6 is small, it is well within the previously indicated * 5 X dyn cm-' sensitivity limit of the Wilhelmy plate technique and demonstrates the need to account for the type of fluctuations described here when surface tension measurements of very high precision are sought. It is interesting to note that the amplitude of the intrinsic fluctuations depends upon the applied electrostatic potential and reaches a maximum a t the electrocapillary maximum (ECM). Thus, the effect of intrinsic fluctuations on the measurement of the surface tension is apparently greatest a t the ECM.
sensitivity method for measuring the surface tensions a t electrified mercury-electrolyte interphases. The electrocapillary curve obtained for the mercury-0.1 M aqueous NaF interphase by using the Wilhelmy plate assembly described here compared well with values obtained for the same interphase by the maximum bubble pressure technique, if the Wilhelmy data are time-averaged. The need for time-averaging was imposed by the presence of long-lived intrinsic fluctuations in the equilibrium surface tension, which were detected in this study but have not been observed by conventional methods. The capability of the Wilhelmy plate technique for performing dynamic surface tension measurementa was demonstrated by the observation of these intrinsic fluctuations in the surface tension. This capability provides new possibilities for fundamental studies of the dynamical properties of the electrified interphase.
Summary The Wilhelmy plate technique as implemented in the apparatus described in this study offers a new, high-
Acknowledgment. This work was supported by the National Science Foundation and the US.Army Research Office.
