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Surfactant and Electric Field Strength Effects on Surface Tension at Liquid/Liquid/Solid Interfaces Johanna M. Santiago, David J. Keffer,* and Robert M. Counce Department of Chemical Engineering, UniVersity of Tennessee, KnoxVille, Tennessee 37996 ReceiVed October 28, 2005. In Final Form: February 15, 2006 We performed a series of experiments designed to elucidate the effects of the presence of sodium dodecyl sulfate (SDS) surfactant and an applied electrical field on the wetting behavior in a system containing a sessile droplet of phenylmethyl polysiloxane (PMPS) oil on a polished stainless steel surface submersed in aqueous solution. The voltage difference ranged from -3 to +3 V, which is at least 3 orders of magnitude smaller than from comparable recent work. We report the measured equilibrium contact angle of the droplet as a function of surfactant concentration and field strength. We then modeled the system. We solved the Laplace equation to obtain the 3D field within our system. We expanded the three surface tensions (oil droplet-aqueous solution (oa), oil droplet-metal surface (os), and aqueous solution-metal surface (as)) in a Taylor series with respect to surfactant concentration and local field strength. We use these three surface tensions in Young’s equation to obtain the theoretical contact angle of the organic droplet. We demonstrate that the large changes in contact angle due to the simultaneous presence of small concentrations of surfactant and small voltage differences can be accounted for by changes in the oa and as surface tensions.
I. Introduction Because environmental regulation limits the use of organic solvents, the use of more environmentally benign aqueous-based cleaning solutions has become the main focus for improving industrial cleaning and surface finishing processes. To maximize the treatment efficacy while minimizing the chemical additives, interest has turned toward the combined use of aqueous-based treatments in the presence of applied electrical potentials. Recently, Morton et al. reported a series of experiments in which they observed the droplet detachment of a sessile oil droplet from a stainless steel surface submersed in very dilute, less than 10 mM, aqueous solutions containing surfactant in the presence of very weak applied voltage differences in the range of -3 to +3 V.1 This work is of particular interest because these lowvoltage treatments have many advantages. They are less energy intensive (and thus both more environmentally benign and costeffective) and occupationally safer than high-voltage treatments. Also, these low voltages are not sufficient to split water molecules, which could otherwise lead to hydrogen damaging the metal surface. The study of Morton et al. was purely experimental in nature and provided the important demonstration that the simultaneous presence of dilute surfactant and weak electrical potential had a drastic effect on the wetting phenomena of the several oil/aqueous/metal systems that they studied. Although Morton et al. have developed a thermodynamic model to understand the contact angle in this system as a function of thermodynamic state, as characterized by surfactant concentration, temperature, and so forth,2,3 it has not been used to account for the presence of an electric field. In this work, we have designed a set of experiments to quantify the findings of Morton et al. Moreover, we complement the experimental work with a continuum-level theoretical model * To whom correspondence should be addressed. E-mail:
[email protected]. (1) Morton, S. A.; Keffer, D. J.; Counce, R. M.; DePaoli, D. W. Langmuir 2005, 21, 1758. (2) Morton, S. A.; Keffer, D. J.; Counce, R. M.; DePaoli, D. W.; Hu, M. Z. C. Sep. Sci. Technol. 2003, 38, 2815. (3) Morton, S. A.; Keffer, D. J.; Counce, R. M.; DePaoli, D. W.; Hu, M. Z. C. J. Colloid Interface Sci. 2004, 270, 229.
that we use to explain the phenomena observed in the laboratory. We begin the article with a brief review of the pertinent literature. An applied electric field affects a droplet in two ways: droplet shape is distorted,4 and droplet wetting behavior is changed.5,6 Both types of droplet change can be attributed to a disturbance in the force balance around the droplet. The Young-Laplace equation is a force balance that is used to calculate the droplet shape change.7 Droplet wetting properties are described with Young’s equation, which is a force balance exclusively on points where three phases meet, also called the triple-line force balance.8 There are a number of ways to model droplet shape and droplet wetting in a three-phase system. In the work of Bateni et al.,4 droplet shape distortion under the influence of an electric field is modeled considering the change in surface tension. The Young-Laplace equation was used to model the system because it includes the surface tension term and an additional term for the field effect. Experimentally measuring the surface tension has been a problem. Bateni et al. created an algorithm where the surface tension changes were considered by fitting experimental data to the Young-Laplace equation. Our applied electric field is 5 orders of magnitude smaller than that used in Bateni’s experiments. Bateni did separate work on droplet wetting6 using contact angle measurements and employed Young’s equation into their model to determine surface tension changes. In contrast to Bateni’s work, a technique focusing on droplet wetting behavior called energy minimization is presented in the papers of Digilov9 and Shapiro.8 Shapiro et al. did not consider droplet shape distortion. The focus is on the change in droplet wetting behavior. Shapiro defined a system such that there was no droplet shape distortion when an electric field was applied. (4) Bateni, A.; Susnar, S. S.; Amirfazli, A.; Neumann, A. W. Langmuir 2004, 20, 7589. (5) Quilliet, C.; Berge, B. Curr. Opin. Colloid Interface Sci. 2001, 6, 34. (6) Bateni, A.; Laughton, S.; Tavana, H.; Susnar, S. S.; Amirfazli, A.; Neumann, A. W. J. Colloid Interface Sci. 2005, 283, 215. (7) Davis, H. T. Statistical Mechanics of Phases, Interfaces, and Thin Films; VCH Publishers: New York, 1996; p 366. (8) Shapiro, B.; Moon, H.; Garrell, R. L.; Kim, C. J. J. Appl. Phys. 2003, 93, 5794. (9) Digilov, R. Langmuir 2000, 16, 6719.
10.1021/la052903h CCC: $33.50 © 2006 American Chemical Society Published on Web 05/03/2006
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Figure 1. Modified experimental setup for the analysis of droplet shape in the presence of an applied voltage.
Their system is similar to ours in that we did not observe droplet shape distortion in our experiments. Shapiro used energy minimization with energy terms representing physical phenomena that have been affected by the electric field. Instead of force balance, they used energy balance to model droplet shape and wetting changes. They were able to reduce their equations to a Young-type equation where there are additional terms representing the different physical parameters that have been affected by the applied field. A complete review of electrowetting can be found in a paper recently published by Mugele.10 The systems that have previously been modeled are similar and yet have some differences with the system that we present in this article. In the systems that have been numerically modeled, a potential is applied directly to the droplet, and the magnitude of the voltage difference was at least 3 orders of magnitude greater than what we use here.4,6,8-10 Moreover, the droplet was an aqueous salt solution rather than oil, and the solutions surrounding the droplet were air or an immiscible liquid rather than a surfactant solution. Essentially, these papers were concerned with wetting phenomena. In our work, we focus on the improvement of benign aqueous surfactant solutions for metal surface treatment, thus we are interested in what may be called electro dewetting.1-3,11 In the remainder of this article, we present our Experimental Methods, Model Formulation, Results, Discussion, and Conclusions. II. Experimental Section Materials and Equipment. Because surface roughness can drastically affect the experimental reproducibility of contact angle measurements, great care was taken to use polished metal coupons. (10) Mugele, F.; Baret, J. C. J. Phys.: Condens. Matter 2005, 17, R705. (11) Davis, A. N.; Morton, S. A.; Counce, R. M.; DePaoli, D. W.; Hu, M. Z. C. Colloids Surf., A 2003, 221, 69.
Stainless steel 304 metal coupons, of approximate size 45 mm × 25 mm × 3 mm, underwent five levels of polishing on a variablespeed grinder and polisher (Buehler). At each level, a finer silicon carbide paper was used; grit sizes used were 250, 400, 600, 800, and 1200. Our ability to reproduce the contact angle improved greatly as a result of the polishing, not only across independent repetitions on the same coupon but also across different metal coupons. One type of oil, phenlymethyl polysiloxane (PMPS) (Fisher Scientific), was used in all experiments. This oil is denser than the aqueous solution in which it was submersed. One type of surfactant, sodium dodecyl sulfate (SDS), at a concentration of 8 mM was used. The maximum cleaning ability of a surfactant is observed when the concentration of the surfactant in solution is at or near its critical micelle concentration (cmc).12 At the cmc, the maximum droplet contact angle is observed. Increasing the surfactant concentration beyond the cmc would not enhance oil detachment.3 By applying low voltages to surfactant solutions at the cmc, we observe a further increase in the droplet contact angle. An ammeter was included in the circuit to give current readings up to a precision of 10-6 A. Contact angle measurements were made with a CAM 200 contact angle meter (KSV International). A constant voltage was applied from an HP E3632A dc power supply (HewlettPackard). Methods. Experiments were divided into two sets: with surfactant (set 1) and without surfactant (set 2). The range of voltages studied was from -3 to +3 V. In set 1, the voltages studied were +3, -3, +2, and -2 V. For experiments in set 2, +3, and -3 V were used. We used only two voltages in set 2 because it was observed that there was no change in the contact angle at either extreme of our range. For each combination of voltage and surfactant concentration, four different separation distances between the counter electrode and the metal coupon were studied and are as follows: 18, 22, 26, and 30 mm. In other words, we are presenting 24 data points. Sixteen of the data points had surfactant present, and 8 did not. The metal coupons were cleaned by immersing them in a petroleum ether bath for 12 to 24 h. Prior to conducting experiments, the metal (12) Mankowich, A. M. J. Am. Oil Chem. Soc. 1961, 38, 589.
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coupon was removed from the petroleum ether bath and allowed to dry for a period of 15 min. PMPS oil (5 µL) was placed on the metal coupon, where it was allowed to wet the metal surface for 5 min. The coupon with oil was then slowly immersed in the aqueous solution. The oil/aqueous/metal system was allowed to equilibrate for 15 min. After equilibration, a constant voltage was applied to the system for 15 min. Droplet shape was recorded at 10 s intervals during equilibration while the potential was applied to the system. In all cases, the droplet contact angle had reached an equilibrium value by the time 15 min had elapsed. The experimental apparatus is shown in Figure 1. The droplet contact angle was measured with software that fits a circle to a digital image of the droplet. Under all circumstances, droplets were observed to have maintained their spherical shape throughout the experiment. This is an important point, so we reiterate that we did not apply a sufficient voltage difference to distort the droplet from a spherical shape. Therefore, the only effect of the voltage difference is through changes in the surface tension. Our model will exploit this experimental observation.
III. Model Modeling Formulation. We begin with Young’s equation
cos θ )
γas - γso γoa
(1)
where θ is the contact angle, γoa is the surface tension at the oil-aqueous interface, γos is the surface tension at the oil-solid interface, and γas is the surface tension at the aqueous-solid interface. Young’s equation is based on a force balance parallel to the solid surface at the point where the three interfaces meet.7 Previous work has used the Young-Laplace equation as a starting point.4,6,10 The Young-Laplace equation is a force balance perpendicular to the surface.7 It can be generalized to account for nonspherical droplets, where the deviation from sphericity is due to gravitational and/or electric field effects. In our experimental system, we observed no deviation from sphericity. As such, the shape of the droplet is completely determined by the three surface tensions, which are accounted for in Young’s equation. We use a Taylor series expansion to express the three interfacial surface tensions as a function of the changes in electric field and surfactant concentration at the interface. For simplicity, we show a Taylor series expansion of one interfacial tension, aqueoussolid γas. The Taylor series expansion, truncated after the secondorder terms, is
γas(Eas, Cas) ) γas(0, 0) +
∂γas ∂γas |0,0∆Cas + | ∆E + ∂Cas ∂Eas 0,0 as
2 2 ∂γas 1 ∂ γas 1 ∂ γas 2 | ∆C + | ∆E 2 + | ∆C ∆E 2 ∂C 2 0,0 as 2 ∂E 2 0,0 as ∂Eas∂Cas 0,0 as as as
as
(2) where Cas is the local surfactant concentration at the as interface and Eas is the local electric field at the as interface. In the event that there is spatial variation in Cas and Eas, we use values averaged over the entire interfacial area. Equation 2 can be written for the oa and os interfaces as well. In eq 2, we have expanded the Taylor series about the (0, 0) point, which indicates no surfactant present and no applied voltage difference. However, even in the absence of an applied potential, a potential develops at the interface of a metal and an ionic solution, called a surface overpotential.13 Therefore, ∆Eas must include the effect of the surface overpotential, which is nonnegligible in these systems with small applied (13) Bockris, J. O. M.; Reddy, A. K. N.; Gamboa-Aldeco, M. Modern Electrochemistry, 2nd ed.; Plenum Press: New York, 1998; Vol 2A, p 777.
voltages. Equation 3 illustrates the prior statement in equation form:
∆Eas ) |E Bas + B EOP| - |E BOP|
(3)
We use absolute values because we assume that the field gradient is normal to the surface, thus we are interested in the difference in field magnitudes. It is known that potential developed at the surface is on the order of magnitude of 109 V/m.13 The largest value of the imposed field Eas obtained in the experiment is 58 V/m, which is significantly smaller than EOP; therefore, eq 3 reduces to
∆Eas ) Eas
(4)
which can be either positive or negative. We will discuss shortly how we obtain values of Eas, Eoa, and Eos. Equation 2 is also a function of the local surfactant concentration at the as interface, Cas. In our experimental work, we know the bulk surfactant concentration, Cbulk. We require an adsorption isotherm to obtain the relationship between Cas and Cbulk. In the absence of these adsorption isotherms, we can linearize the relationship for dilute concentrations:
Cas ) Cas(Cbulk ) 0) +
∂Cas ∂Cas |C ) |C (5) ∂Cbulk 0 bulk ∂Cbulk 0 bulk
We can substitute this expression into eq 2 so that the contact angle is in terms of the bulk concentration, which we do know from the experiment.
γas(Eas, Cbulk) ) γas(0, 0) +
∂γas ∂Cas | |C + ∂Cas 0,0∂Cbulk 0 bulk
( |)
2 ∂Cas ∂γas 1 ∂ γas |0,0∆Eas + |0,0 2 ∂Eas 2 ∂C ∂Cbulk as
2
0
Cbulk2 +
2
∂γas ∂Cas 1 ∂ γas | ∆E 2 + | | C ∆E (6) 2 ∂E 2 0,0 as ∂Eas∂Cas 0,0∂Cbulk 0 bulk as as
At this point, we have a model that will allow us to calculate the surface tension if we know the bulk concentration of surfactant and the local electric field. This expression represents the averaged surface tension. We will obtain the local electric field through the numerical solution of the Laplace equation, as discussed shortly. We also have six terms on the right-hand side of eq 6, each with a constant. Because we can write eq 6 for each of three averaged surface tensions (as, os, oa), we have 18 constants that must be determined. We now proceed to justify the elimination of 13 of these 18 constants from the model. Morton et al. has already shown that the presence of surfactant (in the absence of applied voltage) changes the contact angle.2,3 Therefore, we know that ∂γas/∂Cas|0,0 is nonzero. However, we will show experimental evidence in this work that demonstrates that the applied voltage in the range we are using and in the absence of surfactant does not change the contact angle. Therefore, we have experimental evidence that ∂γas/∂Eas|0,0 and consequently ∂2γas/∂Eas2|0,0 are zero for all three interfaces. Thus, we have eliminated six constants in the model. We can choose to keep only the lowest-order nonzero term for each effect, which allows us to drop the term that is quadratic in concentration, setting ∂2γas/∂Cas2|0,0 equal to zero for all three interfaces and eliminating three more constants. This reduces the model to
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γas(Eas, Cbulk) ) γas(0, 0) +
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∂γas ∂Cas | |C + ∂Cas 0,0∂Cbulk 0 bulk ∂Cas ∂γas |0,0 | C E (7) ∂Eas∂Cas ∂Cbulk 0 bulk as
We will use an equation of this form for the as and oa interfaces. For the os interface, there is no reason to believe that the polar surfactant can penetrate into the os interfacial region, allowing us to eliminate ∂γos/∂Cos|0,0. Finally, our oil droplet is not conductive, allowing us to eliminate any effect of the field on the os surface tension, thus reducing eq 7 for the os interface to a constant.
γos(Eos, Cbulk) ) γos(0, 0)
(8)
As a result, our model has seven constants: γas(0,0), ∂γas/ ∂Cas|0,0∂Cas/∂Cbulk|0, ∂γas/∂Eas∂Cas|0,0∂Cas/∂Cbulk|0, γoa(0, 0), ∂γoa/ ∂Coa|0,0∂Coa/∂Cbulk|0, ∂γoa/∂Eoa∂Coa|0,0∂Coa/∂Cbulk|0, and γos(0, 0). However, the number of independent constants can be further reduced because we must substitute the three surface tensions into Young’s equation, which yields cos θ ) ∂Cas ∂γas ∂Cas ∂γas | |C + | | C E - γos(0, 0) ∂Cas 0,0∂Cbulk 0 bulk ∂Eas∂Cas 0,0∂Cbulk 0 bulk as ∂Coa ∂γoa ∂Coa ∂γoa γoa(0, 0) + |0,0 |0Cbulk + |0,0 |C E ∂Coa ∂Cbulk ∂Eoa∂Coa ∂Cbulk 0 bulk oa
γas(0, 0) +
(9) Equation 9 can be rearranged as
cos θ )
1 + λ1Cbulk + λ2CbulkEas λ3 + λ4Cbulk + λ5CbulkEoa
(10)
Figure 2. Three-dimensional geometry of the modeled system (FEMLAB).
the effect of any remaining imperfections in the surface, we have chosen to model ∆θ rather than θ itself, where ∆θ represents the change in the contact angle observed with the application of the voltage difference. Thus, if a droplet was sitting in an imperfection on the surface, then it is there both before and after the application of the voltage, reducing the impact of the imperfection on the data. Using eq 10, we can express ∆θ as
∆θ ) a cos
(
)
1 + λ1Cbulk + λ2CbulkEas λ3 + λ4Cbulk + λ5CbulkEoa a cos
where we have five parameters defined as
λ1 )
λ2 ) λ3 )
λ4 )
λ5 )
∂γas ∂Cas | | ∂Cas 0,0∂Cbulk 0 γas(0, 0) - γos(0, 0) ∂Cas ∂γas | | ∂Eas∂Cas 0,0∂Cbulk 0 γas(0, 0) - γos(0, 0) γoa(0, 0) γas(0, 0) - γos(0, 0) ∂γoa ∂Coa | | ∂Coa 0,0∂Cbulk 0 γas(0, 0) - γos(0, 0) ∂Coa ∂γoa |0,0 | ∂Eoa∂Coa ∂Cbulk 0 γas(0, 0) - γos(0, 0)
(11a)
(11b)
(11c)
(11d)
(11e)
The third parameter is simply the reciprocal of the contact angle in the absence of any surfactant or applied voltage difference. This we know from experiment. The other four parameters represent the effects of the surfactant and electric field on the surface tensions of the oa and as interfaces. They are not known and will be fit to the experimental data. As mentioned above, polishing the surface improved the experimental reproducibility of our results greatly. To minimize
(
)
1 + λ1Cbulk (12) λ3 + λ4Cbulk
In our modeling work, we will use eq 12 to generate theoretical estimates of the change in contact angle to compare with our experimental work. Solution for the Electric Field. The electric field at every point in the system is obtained by solving the Laplacian of the electrostatic potential and then solving the gradient of the electrostatic potential.
∇2V ) 0
(13a)
-∇V ) Efield
(13b)
Finite element analysis in a 3D system in FEMLAB was used to solve the Laplace equation. The 3D geometry of our modeled system is shown in Figure 2. We now discuss the boundary conditions. At the front, back, sides, and top of the rectangular box and at the droplet surface, we imposed a no-flux condition, n‚∇V ) 0, because the electric field has no normal component at these surfaces. These surfaces act as an electrical insulator. At the counter electrode, V ) 0. At the coupon surface and the rod attached to the coupon, we set V ) +3, -3, +2, -2. In FEMLAB, we solve for the electric field at any point within our system. Figure 3 shows a plot of constant electric potential surfaces. We then calculated the average electric field at the solid-aqueous interface and the aqueous-oil interface to obtain the values required in eq 12. We repeated this solution for every experimental data point. In each case, we used the experimental value of the contact angle to define the droplet shape.
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Figure 3. Constant electric potential surfaces within the modeled system (FEMLAB).
Parametrization of the Model. We are fitting experimental data points with our five-parameter model. The method we used to obtain mean values for the parameters is nonlinear least squares. The objective function was defined as the error between the theoretical and experimental values of ∆θ
Fobj )
1
Ndata
(∆θtheory(Eoa, Eas, Cbulk) - ∆θ expt)2 ∑ 2 i)1
(14)
The theoretical value of ∆θ is solved using eq 12. The inputs required are a set of initial guesses for the parameters λ and experimental data for Eoa, Eas, Cbulk. The objective function is minimized with the help of an optimization procedure imbedded in the MATLAB least-squares function.14 A good initial guess is required for the nonlinear least squares. We surveyed a range of initial guesses to confirm that we had located the global minimum in parameter space. The solution algorithm is shown in Figure 4.
IV. Results Experimental Results. The mathematical model was fit to 24 data points. In Figure 5, we plot the experimental data for the change in contact angle as a function of the applied voltage and the separation distance between the two electrodes. We have remarked that we have polished the surface in order to improve the experimental reproducibility. However, one can still see some noise in the data, with a standard deviation of (4° for the change in the contact angle (based on experimental repetition), but the noise is small, relative to the effect of the presence of surfactant and applied voltage that we are seeking to understand. Representative error bars on the change in contact angle are shown on -3 V of experiment set 1 in Figures 5 and 6. The magnitude of the change in the contact angle ranged from 0 to 57°. When we have no surfactant in the experiment, we see that there is virtually no change in the contact angle due to the (14) Coleman, T. F.; Li, Y. Y. SIAM J. Control Opt. 1996, 6, 418.
Figure 4. Solution algorithm from the collection of experimental data, followed by the calculation of the electric field at the interfaces and finally optimization of the five parameters in eq 14. The boldframed boxes represent inputs into the nonlinear least-squares parameter optimization routine.
application of voltage. We have already used this information to eliminate several terms in our model. When we do have surfactant present in the experimental system, we see that the negative voltages have a much stronger effect on the contact angle than do the positive voltages. Similar effects were shown previously by Morton et al.1 This illustrates the correlated effect of surfactant and applied voltage on the contact angle. The simultaneous presence of surfactant and applied voltage causes a much greater change in contact angle than does either one alone. For a given applied voltage, we see that in general the change in contact angle increases as we decrease the separation between the electrodes. This is expected behavior because the field strength increases with decreasing separation. Theoretical Results. The mean values of the five parameters used in eq 10 are given in Table 1. As we noted before, the third parameter is the inverse of the cosine of the contact angle for the system in the absence of surfactant and applied voltage. As such, the model yields a value of 78.78°, which can be compared to an experimental value of 66.19°. As such, we see that because of the (i) remaining statistical noise in the experimental data and (ii) the approximate nature of the Taylor series expansion that we are not generating quantitative absolute numbers for the contact angles. Rather, this model is allowing us determine the relative
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Figure 5. Experimental data for the change in contact angle as a function of the applied voltage and the separation distance between the two electrodes.
Figure 6. Experimental data and the theoretical estimates for the change in contact angle as a function of the theoretically obtained field strength at the as interface. Table 1. Mean Values of the Model Parameters parameter
value (dimensionless)
λ1 λ2 λ3 λ4 λ5
6.0183 0.039597 5.1399 6.1772 0.042336
effects of the surfactant, the applied potential difference, and their combination. In Figure 6, we plot both the experimental data and the theoretical estimates for the change in contact angle as a function of the theoretically obtained field strength at the as interface. We see that the theoretical model is capable of reproducing several important features of the experimental data: (1) In the absence of surfactant, there is no effect of applied voltage on the contact angle. (2) In a system with surfactant, the negative voltage causes a greater change in contact angle than does the positive voltage. (3) In a system with surfactant, an increase in the magnitude
of the voltage (for both positive and negative voltages) results in an increase in the change in the contact angle. (4) As we decrease the separation between the electrodes, the change in the contact angle increases. The principle weakness of the model is the fact that it describes the combined effect of surfactant and applied voltage in a nonquantitative manner. This is a result of the simplicity of our Taylor series expansion and will be discussed further.
V. Discussion It is clear from the results section, that our model has qualitatively captured the combined effect of (i) surfactant, (ii) applied voltage, and (iii) separation between electrodes on the change in contact angle of an oil droplet on a metal surface submersed in aqueous solution. We have chosen to represent the presence of the surfactant in our model through the bulk surfactant concentration (due to the absence of an adsorption isotherm). We have chosen to represent the effect of the applied voltage and the separation between electrodes through the local field
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strengths at the oa and as interfaces. Moreover, we have done so using a Taylor series expansion that allows for direct changes in the contact angle by the surfactant and correlated (secondorder) changes in the contact angle through the combined presence of the surfactant and the applied voltage. As such, it becomes clear that the role of the applied potential is not to change the surface tension directly. If that was the case, then we would have observed a change in the contact angle in the absence of surfactant. Rather, the applied voltage changes the interaction between the surfactant and the oa and as interfaces, thus changing the adsorption isotherms at those two interfaces. It is not surprising that the adsorption isotherm of surfactant at the as interface is strongly affected by the applied voltage because the Coulombic forces dominate the interaction between the electrified surface and the ionic surfactant. The change in the surfactant concentration causes a change in the surface tension, which then changes the contact angle. In other words, if one had adsorption isotherms for surfactants at these two interfaces, which incorporated field strength, then one should be able to observe the same behavior. The model assumes that the changes in the contact angle are due to changes in the oa and as surface tensions and that the os surface tension is unchanged. Certainly, there is no reason to believe that a polar surfactant will penetrate into the interface between the oil and the metal. Also, because the oil is nonconductive, the effect of the applied potential on the interaction between an oil molecule and the metal surface is also negligible. However, from our model, we can examine the relative effects of the surfactant and the applied voltage on the oa and as interfaces. First, we examine the effect of the surfactant. Considering the λ1/λ4 ratio, we have
∂γas ∂Cas | | λ1 ∂Cas 0,0∂Cbulk 0 ) λ4 ∂γoa ∂Coa | | ∂Coa 0,0∂Cbulk 0
(14a)
which has a numerical value of 0.97, indicating that the relative change in surface tension due to the presence of surfactant is the same at both the oa and as interfaces. This is an interesting point because there has been previous argument in the literature that the changes in contact angle due to the presence of the surfactant were due primarily to changes in the oa surface tension.5,15-20 Morton et al. have argued that the changes in the as surface tension due to the presence of surfactants are important as well.21 Here the calculated ratio suggests that they are roughly equivalent in terms of importance. We can also examine the λ2/λ5 ratio
∂Cas ∂γas |0,0 | λ2 ∂Eas∂Cas ∂Cbulk 0 ) λ5 ∂γoa ∂Coa |0,0 | ∂Eoa∂Coa ∂Cbulk 0
(14b)
which has a numerical value of 0.94, again indicating that the relative change in the surface tension due to the combined presence (15) Bienia, M.; Quilliet, C.; Vallade, M. Langmuir 2003, 19, 9328. (16) Tsekov, R.; Kovac, S.; Zutic, V. Langmuir 1999, 15, 5649. (17) Ivosevic, N.; Tomaic, J.; Zutic, V. Langmuir 1994, 10, 2415. (18) Ivosevic, N.; Zutic, V. Langmuir 1998, 14, 231. (19) Ivosevic, N.; Zutic, V.; Tomaic, J. Langmuir 1999, 15, 7063. (20) Janocha, B.; Bauser, H.; Oehr, C.; Brunner, H.; Gopel, W. Langmuir 2000, 16, 3349. (21) Morton, S. A. Ph.D. Dissertation, The University of Tennessee, Knoxville, TN, 2004.
of the surfactant and the local electric field is the same at both the oa and as interfaces. We can also examine the relative effects of the surfactant alone to the combined effect of the surfactant and applied voltage by examining the dimensionless ratios
∂γas | λ1 ∂Cas 0,0 ) λ2Eas ∂γas | E ∂Eas∂Cas 0,0 as
(14c)
∂γoa | ∂Coa 0,0 λ4 ) λ5Eoa ∂γoa | E ∂Eoa∂Coa 0,0 oa
(14d)
These ratios have numerical values that vary with local field strength. For the work in this article, the first ratio ranges from 2.62 to 7.27, and the second ratio varies from 1.70 to 5.35 units. These ratios indicate that the combined effect of the surfactant and applied voltage can be a significant fraction of the effect due to surfactant alone for both the oa and as interfaces. An interesting observation from both the experimental data and the theoretical model is the fact that the change in contact angle is greater for negative voltages than it is for positive voltages. We now suggest a molecular-level mechanism responsible for this behavior. At this point, the mechanism is speculation, but it could be confirmed or invalidated through molecular dynamics simulations of the charged oa and as interfaces. We begin with the experimental fact that as the magnitude of the voltage increases, the contact angle increases, leading to dewetting of the solid surface. For contact angles of less than 90°, an increase in θ corresponds to a decrease in cos θ, which through Young’s equation corresponds to either a decrease in the as surface tension or an increase in the oa surface tension, assuming as we have throughout the article the constancy of the os surface tension. We focus first on the as interface. A decrease in the as surface tension corresponds to an increase in the amount of surfactant adsorbed at the interface. In other words, the application of voltage results in enhanced SDS adsorption at the as interface, resulting in dewetting of the oil droplet. Now, we can address the finer point that the degree of dewetting is greater for negative voltages than for positive voltages. This behavior can be attributed to one of two mechanisms. First, the application of a negative voltage creates a negative surface charge at the as interface, whereas a positive surface charge results from a positive voltage. Because the local electrostatic environment is different, certainly the adsorption of an anionic surfactant will reflect the difference in the strong Coulombic interactions. The precise nature of the effect of the local electrostatic field at the interface on the nanostructure of the adsorbed surfactant phase is beyond the scope of this work but could be investigated through molecular dynamics simulations. A second cause of the difference in dewetting due to positive and negative voltages could come from analogous changes in the surfactant adsorption isotherm at the oa interface. We have simplified the Taylor series expansion by including the second-order terms of the expansion. We have demonstrated that we are able to simplify our model further because of the nature of our experimental system. The most probable cause of the quantitative discrepancy between the theoretical prediction and the experimental data is that the Taylor expansion is not able to capture the nonlinearity of the surfactant adsorption isotherm.
Surface Tension at Liquid/Liquid/Solid Interfaces
VI. Conclusions In this work, we have performed a coordinated experimental and theoretical investigation of the simultaneous effect of surfactant and applied voltage difference on the contact angle of an oil droplet on a metal surface submersed in aqueous solution. We have verified that the experimental result of Morton et al.,1 involving applied voltages in the range of -3 to +3 V, are sufficient in the presence of millimolar quantities of surfactant to cause drastic changes in the wetting behavior of the system. In the absence of surfactant, no change in contact angle is observed. We used a theoretical model that employed the Laplace and Young equations. We expanded the surface tensions in surfactant concentration and local electric field and kept the lowest nonzero terms. Our model qualitatively predicts all of the features of the experimental data. The model shows that the surfactant affects the oa and as interfaces, potentially to a similar degree. We also
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have shown that the surfactant and local field effect are both important. Future work that would look into improving the model where the real adsorption isotherm for the system is known and incorporated into the model would probably quantitatively capture the behavior of the contact angle as a function of surfactant concentration and electric field strength. One avenue to developing an adsorption isotherm for the present system is to conduct molecular dynamics simulations of the oa and as interfaces. Employing a small electric potential in the presence of dilute surfactant aqueous solution to drastically change the wetting behavior of an oil droplet on a metal surface can be exploited to enhance environmentally benign industrial metal treatment processes. Acknowledgment. We thank Venkat Subramanian at the Tennessee Technological University for valuable discussions. LA052903H
