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Dynamics of Spontaneous Spreading under Electrowetting Conditions C. Decamps and J. De Coninck* Centre de Recherche en Mode´ lisation Mole´ culaire, Universite´ de Mons-Hainaut, Place du Parc 20, B-7000 Mons, Belgium Received April 19, 2000. In Final Form: September 21, 2000 The dynamics of spontaneous spreading of drops is well described by the molecular kinetic theory. We show that it is also the case under electrowetting conditions for drops of glycerol on PTFE substrate. The associated friction between the liquid and the solid surface is independent of the applied voltage between 0 and 700 V.
1. Introduction Electrowetting or the use of electric fields to improve the wetting of a surface already has several practical applications, yet many open questions remain concerning our fundamental understanding of the phenomenon. As a starting point, let us consider here the simplest case: a liquid drop A in equilibrium with a gas phase B is applied from a syringe needle to dielectric a substrate S as shown in Figure 1. From its initial configuration, the droplet will spread on S to reach its equilibrium shape. The associated dynamics of the three-phase line A/B/S characterize the spreading process and have been the subject of many recent studies from both experimental and theoretical points of view.1-3 If we now apply a potential difference between the needle and the substrate, we induce an electric field which changes the wetting characteristics of the system, effectively increasing the wettability of the substrate S. In 1969, Blake and Haynes4 proposed a molecular kinetic (MK) description of spreading in which the principal energy dissipation is that due to the molecular displacements that occur within the three-phase zone, that is within the immediate vicinity of the three-phase line. This dissipation can be viewed effectively as friction between the liquid molecules and the solid surface. Provided the dissipation is not too great, this leads to a simple linear relationship of the form
dR 1 ) γLV(cos θ0 - cos θ) dt ξ
(1)
where R (m) is the base radius of the drop, ξ (N s/m2) the coefficient of friction between the solid and the liquid molecules per unit length of the wetting line, γLV (N/m) the liquid-vapor interfacial tension, θ0 the equilibrium contact angle, and θ the contact angle at time t. In classical terms, ξ ) F/ν, where F ) γLV(cos θ0 - cos θ) is the driving force for spreading at velocity v. In molecular kinetic terms, ξ ) kT/κ0λ3, where λ and κ0 are respectively the characteristic length and equilibrium frequency of molecular displacements within the three-phase zone, k is Boltzmann’s constant, and T is the absolute temperature. (1) Blake, T. D.; Clarke, A.; De Coninck, J.; de Ruijter, M. J. Langmuir 1997, 13, 2164-2166. (2) de Ruijter, M. J.; Blake, T. D.; De Coninck, J. Langmuir 1999, 15, 7836-7847. (3) Blake, T. D.; Decamps, C.; De Coninck, J.; de Ruijter, M. J.; Voue´, M. Colloids Surf., A 1999, 154, 5-11. (4) Blake, T. D.; Haynes, J. M. J. Colloid Interface Sci. 1969, 30, 421.
Figure 1. Schematic drawing of the apparatus used to study the electrowetting effect. A droplet of a conductive liquid is deposed on an insulating layer of PTFE which is in contact with a copper plate.
A number of recent papers have established the underlying validity of this theory, even at microscopic scales.2 Here, our aim is to study how, under electrowetting conditions, an electric field affects not only the equilibrium contact angle θ0 but also the coefficient of friction ξ during spreading. This work complements other studies of electrowetting on a variety of substrates (polyester film, glass covered by Parylene C or polyimide): static contact angles by Berge5,6 and Welters and Fokkink7 and Verheijen and Prins;8,9 and static and dynamic contact angles under forced wetting conditions by Blake, Clarke, and Stattersfield.10 Here, we examine these phenomena under conditions of spontaneous wetting on another type of substrate, PTFE. The paper is organized as follows. Section 2 is devoted to the presentation of our experiments, the results are discussed in section 3, and concluding remarks are given in section 4. 2. Experimental Section 2.1. Materials. The liquid used was glycerol (glycerin: ACS reagent assay 99.8%, SIGMA) to which was added 25% of MilliQ water and 4 g/L NaCl to increase the solution conductivity. The (5) Vallet, M. Etude des phe´nome`nes limitant l’e´talement de solutions aqueuses sur des films de polyme`res par e´lectromouillage. Ph.D. thesis, Unversite´ Joseph Fourier- Grenoble1, France, 1997. (6) Vallet, M.; Vallade, M.; Berge, B. Submitted, 1999. (7) Welters, W. J. J.; Fokkink, L. G. J. Langmuir 1998, 14, 15351538. (8) Verheijen, H. J. J.; Prins, M. J. W. Submitted to Langmuir, 1999. (9) Verheijen, H. J. J.; Prins, M. J. W. Submitted to Rev. Sci. Instrum., 1999. (10) Blake, T. D.; Clarke, A.; Statterfield, E. H. Langmuir 2000, 16, 2928-2935.
10.1021/la000590e CCC: $19.00 © 2000 American Chemical Society Published on Web 12/01/2000
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Figure 2. Schematic drawing of the apparatus used to apply the high voltage and to measure the contact angle. We have represented the following elements: (1) microscope, (2) camera, (3) video recorder, (4) computer, (5) image of the drop on the computer, (6) oscilloscope, (7) TREK supply/amplifier/controller, and (8) frequency meter. associated surface tension was 64 mN/m, and the viscosity is 10 mPa s at the temperature of the experiments (22 ( 1 °C). The viscosity was measured with a Brookfield cone/plate Viscosimeter RVDVII+. The substrate was cut from a 100 µm thick sheet of poly(tetrafluoroethylene): PTFE (Teflon). This material has a critical surface tension of 19 mN/m, as determined using n-alkanes (C6C11). The principal reasons for using PTFE were that it has a chemically inert surface, low water absorption (100), these sets turn out to be normally distributed, providing us with the mean value and the standard deviation for the parameter.
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Table 1. Values of a and b (Eq 10) Obtained by Fitting the Data of Figure 5 for Each Voltage with the Modified Molecular Kinetic Theory Uampl (V) 400 500 600 700 1/a ) 3.55 ( 0.6 5.0 ( 0.65 4.41 ( 0.40 4.26 ( 0.42 1/ξ [1/(Pa‚s)] b ) 1/4a 0.29 ( 0.02 0.25 ( 0.01 0.27( 0.02 0.25 ( 0.01 a The coefficient b in eq 10 is compatible with the predicted value of 1/4 (see eq 9).
Figure 7. Contact angle versus the applied ac potential (Uampl): (f) advancing contact angle; (b) receding contact angle. The system used is aqueous glycerol (75%) put on top of a plate of PTFE (100 µm thick). This graph shows that the hysteresis is rather constant with the applied ac potential.
Figure 6. Friction (1/a) versus applied ac potential (Uampl). The friction is obtained by fitting the data of Figure 5 for each voltage with the modified molecular kinetic theory (see eq 9).
From the fit we can extract the value of a ) 1/ξ [1/(Pa‚ s)] for each voltage and the value of the parameter b to check if the coefficient 1/4 is valid. These results are presented in Table 1. That this coefficient b is always equal to 1/4 is not so obvious. Indeed, in the presence of electrical charges on the solid surface, we may expect some pining phenomena for the liquid molecules which could strongly influence the dynamics of the process. This is obviously not the case in our experiments. Concerning the first factor a, we have plotted the friction versus Uampl in Figure 6. For voltages below 700 V, the parameter ξ is sensibly constant, but above 700 V, where the substrate is altered by the electrical discharges, then ξ changes also. To check for the existence of a precursor film in front of the three-phase line, we have used spectroscopic ellipsometry.16 No significant layer was detected in front of the drop with a spot resolution of about 30 µm. To have a better understanding of the electrowetting phenomenon, we also measured the amplitude of the
contact angle hysteresis ∆θ ) θadv - θrec as a function of the applied voltage Uampl. Although there is considerable scatter in the results, it appears that ∆θ is rather constant for Uampl less than 700 V, showing that there is no significant degradation of the substrate due to the electrical charges (see Figure 7). 4. Conclusion These experiments show that, under electrowetting conditions, the wetting dynamics in this system are satisfactorily explained by the MK theory. In addition, the wetting friction on the PTFE remains constant over a large range of potential. We have also shown by ellipsometry that there is no associated precursor film. If we calculate the density of charges induced by the electric field, we get an estimate of one charge every 223 Å2. We can conclude that while there are evidently sufficient charges on the surface of the substrate to change the static contact angle, there are not enough charges to influence the friction significantly. That this property is always constant remains, however, an intriguing result. Acknowledgment. The authors thank T. Blake, A. Clarke, and E. Statterfield for many simulating discussions. They also thank M.Voue´ for his help with the spectroscopic ellipsometry experiments. LA000590E
