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Spontaneous Spreading of Surfactant Solutions on Hydrophilic Surfaces: CnEm in Ethylene and Diethylene Glycol M. Cachile† and A. M. Cazabat*,‡ Colle` ge de France, Physique de la Matie` re Condense´ e, 11 place M. Berthelot, 75231 Paris Cedex 05, France, and Grupo de Medios Porosos, Facultad de Ingenieria-UBA, Paseo Colon 850 (1063), Buenos Aires, Argentina Received July 8, 1998. In Final Form: October 16, 1998 The spontaneous spreading of solutions of nonionic CnEm surfactants in ethylene and diethylene glycol on hydrophilic surfaces is investigated. The parameters of the study are the relative concentration of surfactant, defined as being the ratio between the bulk concentration and the critical micellar concentration, and the relative humidity (RH) of the surrounding atmosphere. At low RH, RH < 30%, normal spreading is observed, i.e., the radius R of the drops scales like t1/10, t being the time. For RH > 40%, an acceleration of spreading rate and the emergence of contact-line instabilities are observed in an increasing range around the cmc. A systematic study of these spreading laws and instabilities is reported. We propose a qualitative model of the processes, where the mobility of the surfactant on the solid surface controls the start of a Marangoni flow at the free liquid surface. Once started, this flow dominates the spreading.
Introduction Because of its obvious technical relevance, the spreading of surfactant solutions has been the subject of many experimental1-9 and theoretical10-14 studies. The complexity of the problem arises from a delicate interplay between spreading, surfactant diffusion, and adsorption processes at interfaces. Surface-tension gradients may develop at free liquid surfaces, leading to Marangoni flows. On the other hand, the very high speading rates observed not only on hydrophilic but also on hydrophobic surfaces suggest the presence of precursor films with hydrodynamic mobility.1,3-9 We report experiments on the systems C12E4 and C12E10 in ethylene and diethylene glycol. The surfactants have been chosen to differ only by the hydrophilic part, which is expected to be of some relevance on hydrophilic surfaces. The spreading of aqueous solutions of these surfactants on hydrophobic substrates has been extensively studied by Stoebe et al.7 Contact-line instabilities on hydrophilic substrates have been reported by Frank and Garoff.5 Here, the substrates are also hydrophilic, but replacing water † ‡
Grupo de Medios Porosos, Facultad de Ingenieria-UBA. Colle`ge de France.
(1) Marmur, A.; Lelah, M. D. Chem. Eng. Commun. 1981, 13, 133. (2) Princen, H. M.; Cazabat, A. M.; Cohen Stuart, M. A.; Heslot, F.; Nicolet, S. J. Colloid Interface Sci. 1988, 126, 84. (3) Troian, S. M.; Wu, X. L.; Safran, S. A. Phys. Rev. Lett. 1989, 62, 1496. (4) Lin, Z.; Hill, R. M.; Davis, H. T.; Ward, M. D. Langmuir 1994, 10, 4060. (5) Frank, B.; Garoff, S. Langmuir 1995, 11, 87. (6) Stoebe, T.; Lin, Z.; Hill, R. M.; Ward, M. D.; Davis, H. T. Langmuir 1996, 12, 337. (7) Stoebe, T.; Lin, Z.; Hill, R. M.; Ward, M. D.; Davis, H. T. Langmuir 1997, 13, 7270. (8) Stoebe, T.; Hill, R. M.; Ward, M. D.; Davis, H. T. Langmuir 1997, 13, 7276. (9) Stoebe, T.; Lin, Z.; Hill, R. M.; Ward, M. D.; Davis, H. T. Langmuir 1997, 13, 7282. (10) Borgas, M. S.; Grotberg, J. B. J. Fluid Mech. 1988, 193, 151. (11) Gaver, P. D.; Grotberg, J. B. J. Fluid Mech. 1990, 213, 127. (12) Troian, S. M.; Herbolzheimer, E.; Safran, S. A. Phys. Rev. Lett. 1990, 65, 333. (13) Jensen, O. E.; Grotberg, J. B. J. Fluid Mech. 1992, 240, 259. (14) Jensen, O. E. J. Fluid Mech. 1995, 240, 349.
by ethylene glycol or diethylene glycol, which have a lower surface tension, allows us to achieve more easily a complete wetting situation with very regular and reproducible patterns. Moreover, as the viscosity is larger, the processes are slower and do not require very fast recorders. Finally, the role of the solvent viscosity can be investigated. In the first part of the paper, we report the experimental observations and measurements. Some interpretation follows in the second part. Experimental Section The surfactants are the nonionics C12E4 and C12E10 purchased from Sigma and used without further purification. Ethylene and diethylene glycol are commercial samples from Prolabo, purity > 99%. The surface tension γ(c) of the solutions has been measured as a function of the surfactant molar concentration using a ring method. As expected, the cmc’s of the two surfactants, mainly controlled by their hydrophobic part, are fairly close for a given solvent. Figure 1a-d summarizes the results. The plots give γ(c) vs Log10 c, as usual. In the following, we shall also use the relative concentration c* ) c/cmc. The substrates are bare, oxidized silicon wafers, cleaned by UV illumination in the presence of an oxygen flow.15 After the UV lamp was switched off and before the cleaning cell was opened, a flow of oxygen saturated with water sweeps the substrate for a few minutes. The cleaned wafers are kept in controlled humidity chambers before and during experiments. These surfaces are water-wettable but not very hydrophilic. They have been characterized by the ellipsometric measurement of the adsorption isotherm of water at room temperature.16 The adsorbed amounts are low: at RH ≈ 80%, the average thickness of the adsorbed water film is only 3-4 Å.16 From complementary data,17 we believe that below 80% RH the water is adsorbed on the isolated silanol groups and forms patches, which become connected above 80% RH. However, even at the highest RH used here (85%, film thickness ≈ 5 Å), we do not expect the water to be mobile on the surface. At time t ) 0, a drop with an initial radius R(0) e 1 mm is deposited on the substrate. The spreading is observed with a (15) Vig, J. R. J. Vac. Sci. Technol. A 1985, 3, 1027. (16) Tiberg, F.; Cazabat, A. M. Langmuir 1994, 10, 2301. (17) Villette, S.; Valignat, M. P.; Cazabat, A. M.; Jullien, L.; Tiberg, F. Langmuir 1996, 12, 825.
10.1021/la980840f CCC: $18.00 © 1999 American Chemical Society Published on Web 01/08/1999
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Figure 1. Surface tension γ (mN m-1) as a function of Log10 c, where c is the surfactant concentration (mol/L), obtained for the systems (a) C12E4 and (b) C12E10, both in EG, and (c) C12E4 and (d) C12E10, both in DiEG. The continuous lines are the best fit with a Boltzmann curve shape. CCD camera through a binocular, and the images are recorded on videotapes. The image analysis is performed afterward. The sequence of behavior is summarized in Figure 2a,b as a function of both the concentration and the relative humidity. At low RH, a normal spreading is observed regardless of the concentration. The contact line of the drop is a perfect circle, with a radius R scaling like t1/10. With increasing RH, an acceleration of the spreading rate and dendritic contact-line instabilities take place in an increasing range around the cmc. Typical pictures of this case are given in Figure 3a-c. Now the characterization of the dynamics is more complex. We measure the radius Rc(t) of the central part of the drop, the overall length L(t) of the dendritic film, and, using image processing, the total area A(t) covered by the liquid. As only trends are investigated, the radius and the film length were written as power laws: Rc(t) ∝ ta and L(t) ∝ tb. The exponents a and b for C12E10 in ethylene glycol are plotted versus c* in Figure 4, both in the dry case (open symbols, RH < 30%), where only a exists and is around 0.1, and at intermediate relative humidity (filled symbols, RH ≈ 60%). The data at RH ≈ 60% were taken at very short time, typically the range illustrated in Figure 3a-c where, in principle, Rc(t) and L(t) are approximately independent (at least, the conservation of drop volume does not play a role in the film dynamics). The exponent a is approximately independent of c*, while b decreases significantly; the film grows faster at low c*. Note that the pictures in Figure 3 are taken at different times, in order to have similar film lengths. The area A(t) covered by the liquid obviously scales like t2/10 in the dry case. The moist case RH ≈ 60% is more complex: we find that A(t) increases linearly with time, a behavior first reported by Davis and co-workers,4 but in the absence of contactline instabilities. This time dependence was observed at RH ≈ 60% for the four systems investigated. Such an A(t) record is shown in Figure 5. Now the dynamics is characterized by the slope S(c*) of this linear dependence. Typical S(c*) vs Log10 c* curves are plotted in Figure 6a,b. The spreading rate goes through a maximum, and the shape of S(c*) is rather similar to the one of the derivative - dγ/d(Log10 c*), which is represented as the continuous line in the figures. At very high RH, RH ≈ 85%, the drop pictures are not qualitatively different, but now the area A(t) increases faster
Figure 2. Behavior of the system C12E10 in EG as a function of the concentration c* relative to cmc and RH. Normal spreading, with a stable contact line, is obtained at RH < 35%, regardless of the concentration. At larger RH, there is a range of concentration where fast spreading and contact-line instabilities are observed. For C12E10 in EG, this range is around c* ) 1. (a) Same figure as Figure 1b; the concentrations where unstable spreading has been observed are indicated as filled symbols. (b) Corresponding “phase diagram”, where the instability domain is represented. than linear, as shown in Figure 7. In the cases where a quadratic fit A(t) ≈ A(0) + C(c*)t2 is acceptable, the trend is that C has a maximum in the same range of concentrations as before, see Figure 8. When a linear term must be included in the fit, the physical meaning of the fitted parameters becomes poor.
Data Analysis and Qualitative Discussion As already mentioned, the use of ethylene and diethylene glycol as the solvent allows us to work easily in the complete-wetting case regardless of the surfactant concentration. The counterpart is the hygroscopic character of these liquids: pure ethylene and diethylene glycol may exhibit Marangoni effects due to the penetration of atmospheric water vapor, which builds up a surfacetension gradient at the edge of the drop. A very typical drop shape results, with a dip in the center and a circular bump of liquid spreading out. This effect has been investigated by Bardon.18 The result relevant for the present study is that the initial size of the drop is very critical. Drops with initial radii less than 1.5 mm do not (18) Bardon, S. 1997 report in ESPCI, Paris. The results have been submitted to Colloids Surf. (Cachile et al.).
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Figure 4. Exponents of C12E10-EG drops for very short times (pictures like the ones in Figure 3). Filled symbols are the exponents obtained at RH ≈ 60% for Rc(t) (circles) and L(t) (squares). Triangles represent stable drops (without dendrites) in the dry case (RH < 30%, open) and at RH ≈ 60% (filled). Instability domain 0.06 e c* e 2.
Figure 5. Typical A(t) record obtained from an unstable C12E10-EG drop at normal humidity.
Figure 3. Pictures of C12E10-EG drops at RH ≈ 60% with c* equal to (a) 2, (b) 1, and (c) 0.2. The pictures are taken at different times, increasing from bottom to top, in order to have comparable film lengths. The times printed have no immediate meaning, the initial times being different.
show a significant Marangoni flow, probably because they are thin enough for the water to equilibrate rapidly in the bulk. The drops here are small, with initial radii e 1 mm, and no suspicious effect was ever detected.
Let us try to list the processes occurring during the spreading of the drop. The surfactant in the drop may adsorb either at the liquid-solid interface, which is hydrophilic, or at the liquid-air interface, which is hydrophobic. Adsorption processes of the CnEm surfactants at hydrophilic and hydrophobic interfaces have been investigated by Tiberg.19,20 At the liquid-solid interface, the adsorption is achieved in a narrow concentration range around the cmc. Below, there is no adsorption; above, the interface is saturated. At the liquid-air interface, the adsorption proceeds in a very progressive way, being already significant at 10-2 cmc, to saturate above the cmc. The bare solid surface is hydrophilic, with some water adsorbed, very probably bound to the silanol sites. If some surfactant tries to diffuse from the drop onto the surface, the relative humidity, which controls the surfactant mobility on the surface,21 will therefore control the flux of surfactant on the solid. This diffusion process also builds up a hydrophobic barrier on the substrate at the edge of the drop. The following sequences can be proposed: (i) At low RH, the surfactant diffusion on the dry surface is negligible because the diffusion coefficient Ds of the surfactant on the solid is too low. For c < cmc, the liquid-solid interface is free of surfactant. Some surfactant is adsorbed at the liquid-air interface. As no significant surfactant flow is possible onto the dry solid, no concentration gradient at the liquid-air interface resulting from surfactants passing from that interface to the solid can develop at the drop edge. However, spreading is observed with normal spreading laws. This means that the spreading parameter is positive and that no surface-tension gradient is present at the liquid-air interface. We conclude that, in the absence of (19) Tiberg, F. J. Chem. Soc., Faraday Trans. 1996, 92, 531. (20) Brinck, J.; Jo¨nsson, B.; Tiberg, F. Langmuir 1998, 14, 1058. (21) Bardon, S.; Cachile, M.; Cazabat, A. M.; Fanton, X.; Valignat, M. P.; Villette, S. Faraday Discuss. 1996, 104, 307.
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Figure 8. Comparison between S(c*) (normal humidity) and C(c*) (high humidity) for the system C12E4-DiEG. The maximum is at the same relative concentration c*.
Figure 6. Fits of S as a function of Log10 c*, fitted with a function of the form dγ/d(Log10 c*); the surface tension and its derivative are showed for clarity for both systems (a) C12E10EG and (b) C12E4-EG. The derivatives are calculated from the Boltzmann curve shape.
Figure 7. Typical A(t) record obtained from an unstable drop at high humidity. The fit is a second-degree polynomial.
surfactant mobility on the solid, the normal spreading is not fast enough to generate a surfactant gradient at the free liquid interface. For c > cmc, the situation is the same, except that now the solid-liquid surface is saturated with surfactant. (ii) At moderate or high RH, the surfactant diffusion on the solid is no longer negligible. For c < cmc, the liquid-solid interface is free of surfactant. Some surfactant is adsorbed at the liquid-air interface. As the surfactant can go onto the solid, an
outwardly directed surface-tension gradient develops at the drop edge. This gradient gives rise to a Marangoni flow. The flow in turn increases the concentration gradient at the liquid interface. The characteristic velocities are much higher than the ones associated with surfactant diffusion on the solid21 and also with the ones in normal spreading. We conclude that the surfactant diffusion on the solid controls the start of the process by allowing a surface-tension gradient to develop at the free liquid interface. Then the spreading is controlled by the Marangoni flow. For c > cmc, surfactant is present both at the liquidsolid and liquid-air surfaces. The surfactants diffusing on the solid come from both interfaces. A Marangoni flow takes place if a concentration gradient is produced at the liquid-air interface. On the contrary, the surfactants coming from the liquid-solid interface only build up the hydrophobic barrier. (a) In the presence of micelles, the adsorption at the liquid-solid interface is relatively slow,19,20 and we cannot be sure that the interface is saturated. Anyway, with or without micelles, the diffusion of surfactant from that interface is expected to be slow. (b) The adsorption at the air-liquid interface is faster, which means that concentration gradients hardly develop above the cmc, as the interface, even extending, is rapidly saturated. (c) It is clear that the driving term for spreading decreases above the cmc and that the barrier increases. Therefore, the Marangoni flow will ultimately fade out. One may note that as soon as this flow has started, the barrier plays little role, because once overcome, it has no time to be rebuilt at a fast-moving contact line. This remark is of some relevance for the dendritic fingers because the velocity is large at the finger tip but not on the sides. In summary, we assume that (i) the mobility of the surfactant on the solid surface controls the start of the Marangoni flow and (ii) once started, this flow is controlled by the gradient at the liquid-air interface, and the hydrophobic barrier plays little role if the film velocity is large. This barrier increases with surfactant concentration and might play a role in the lateral extension of the dendrites. Semiquantitative Approach at Moderate RH for the Marangoni Flow. Let us try to discuss the time dependence of the wetted area A(t), assuming that this
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time dependence does not basically change in the presence of dendritic instabilities. This is a strong assumption, yet acceptable as long the aim of the analysis is only to give support to the conclusion above, i.e., that the driving term for spreading in the unstable cases is the surface-tension gradient at the liquid-air interface. We restrict ourselves to relatively short times, when the volume conservation does not have too much effect, i.e., when the central part of the drop contains most of the liquid and acts as a reservoir for the film. This means that the thickness e of this film does not depend on the drop total radius R. Let us assume that the driving term for spreading is the surface-tension gradient at the free-liquid surface. This gradient results from a concentration gradient at the surface,
∇γ b)
dγ ∇c b dcs s
(1)
where cs is the local surface concentration, lower than the bulk value c. If ∇cs is proportional to cs, which is a plausible assumption, ∇γ is proportional to dγ/d(Log cs). The velocity of the drop “edge” is
e dγ dR e ≈ ∇γ ) ∇c dt η η dcs s
(2)
where η is the bulk viscosity of the solution, and e is the thickness of the film. The gradient is unknown. As the surfactant is soluble, the bulk is a reservoir, and the case differs from the ones of the insoluble surfactants discussed by Jensen.13,14 In particular, the local surfactant concentration cs is not fixed by the area of the free interface. A plausible assumption in this case is that the gradient scales like 1/R because it is induced by the stretching of the interface in contact with a reservoir. This leads to a linear behavior for the area A(t), as it was observed for RH ≈ 60%. More specifically, if ∇cs ≈ cs/R, one obtains
dγ e dR ≈ dt d(Log cs) η
(3)
dγ e S ≈ 2π η d(Log cs)
(4)
R and
Let us compare these predictions with the experiments at RH ≈ 60%. First, the fit of S with the shape of the derivatives is fairly good. However, there is usually a shift of the S curve to higher c* compared to the derivative. The data in Figure 6 are fitted as
S(c*) )
dA(t) dγ dγ )B )B (5) dt d(Log10 c*) d(Log10 c)
For diethylene glycol, the viscosity is η ) 30 mPa‚s at 25 °C, and for ethylene glycol 16 mPa‚s. The viscosity ratio is 1.8, acceptably close to the ratios of the B values obtained on ethylene glycol and diethylene glycol, respectively (1.5 for C12E10 and 1.7 for C12E4 ). This agrees with eq 4 if the film thickness e is the same, which seems to be approximately the case close to the maximum. The shift of S(c*) to the right with respect to the derivative might be due to the difference between c and cs. As a matter of fact, the S values have been plotted
Figure 9. Pictures of C12E4-DiEG drops at high humidity (≈85%). Lines of nonwettable ink stop the precursor film; as it becomes thicker, the spreading is faster on that side. Frame c shows a configuration in which one half of the film is faster than the other. Configurations shown in frames a and b have more evident effects.
versus bulk concentrations which are larger than the ones at the surface. Let us recall the assumptions of the model above. We
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found A to scale linearly with time because we assumed (i) e to be independent of R and (ii) the gradient to scale like 1/R, i.e., to be controlled by the whole drop. This seems plausible in our case. The first assumption would need further discussion for flatter drops, like the ones obtained with aqueous solutions of superspreaders.4 Note that the presence of a preexisting thick water film on the substrate would also lead to a linear A(t) dependence, because the dissipation would take place in the water film and be independent of R. However, this is not the case here, first because we know that no preexisting film exists on our surfaces, and also because the solvent viscosity would play no role, contrary to the experimental observations. High Humidity Results. If one wants to account for the high humidity results, RH ≈ 85%, where A(t) is quadratic, one must assume the gradient to be independent of R. One might argue that the part of the interface where the gradient is induced by stretching becomes independent of R at high velocities. This is obviously an ad hoc argument which would have to be supported by complementary measurements. We know that there is no thick preexisting water film on our substrates, neither at RH ≈ 60% nor at RH ) 85%. However, the growth of a rapid precursor film ahead of the visible part of the drop and thick enough to play a hydrodynamic role is very probable. This film comes from the drop and has the same viscosity. An indirect way to give evidence of its presence is to stop it with a line of nonwettable ink. This is done on the pictures taken at RH ≈ 85%, Figure 9. The visible spreading is faster on the side where the film, being stopped, has become thicker. The presence of such a film has previously been assumed by many authors.1,3-9 A direct observation has been reported by Frank and Garoff5 for an aqueous SDS solution spreading on surfaces similar to those used in the present study. Such a film may contain surfactant and exist on hydrophobic as well as hydrophilic surfaces.22 The Dendritic Patterns. The growth of the center of the drop and of the observable film is also far from being understood. At very short times, where the volume in the film is negligible (see typical pictures in Figure 3), the radius Rc of the center of the drop scales like ta, with a ≈ 0.2. If τ is the gradient at Rc and Ω the drop volume, one may write
dRc e Ω ≈ τ ≈ 2τ dt η R
(8)
c
A plausible assumption is to assume the gradient to scale like 1/Rc, in which case a ) 0.25, reasonably close to 0.2, although somewhat larger. To find a ) 0.2, one should assume the gradient to scale like 1/Rc2. Such a dependence is found for nonsoluble surfactants because the amount of surfactant at the surface is fixed, and the surface concentration inversely proportional to the interface area.13,14 This is not the case here, and we shall refrain from making this assumption. The value of b decreases when c* increases, and the amount of liquid in the dendritic film decreases. This is a monotonic behavior, in contrast with the spreading rate. The interpretation for this behavior is the increasing role of the hydrophobic barrier, because the flow is large only in the thick center of the dendrites, but not on the lateral sides, where the barrier becomes effective. This explains (22) Hill, R. M. Curr. Opin. Colloid Interface Sci. 1998, 247.
Figure 10. Pictures of C12E4-EG drops at RH ≈ 60% with c* equal to (a) 2, (b) 1, and (c) 0.2; same values as in Figure 3 for C12E10-EG.
why the dendrites are increasingly thin when the concentration increases above the cmc and also when the diffusion coefficient Ds of the surfactant on the solid is smaller. We chose the two surfactants in order to show the role of Ds: C12E10 has a larger hydrophilic part and is larger than C12E4. Therefore, Ds is much less for C12E10
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on a hydrophilic surface,18 and the barrier is more effective. This is illustrated by the comparison between Figure 10 for C12E4 and Figure 3 for C12E10. The dendritic patterns are rather similar below the cmc and increasingly different above, the fingers with C12E10 being much thinner. Note that values of b larger than 1 have been obtained, see Figure 4, in contrast with the ones found on the system water/CTAB by Troian.3 To say more, a theoretical model of the dynamics of the dendritic pattern would be needed. Conclusion We propose a qualitative discussion of the behavior of surfactant solutions spreading on a hydrophilic surface as a function of surfactant concentration and atmospheric relative humidity. We chose the systems in order to achieve complete wetting and to be able to investigate the role of parameters such as solvent viscosity and surfactant
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diffusion coefficient on the solid. We believe that the mobility of the surfactant on the solid controls the emergence of a surface-tension gradient at the free liquid surface. Once born, this gradient gives rise to a Marangoni flow which dominates the spreading process. The surfactant barrier at the contact line increases with surfactant concentration and is effective at very low velocities, especially on the sides of the dendritic fingers. Acknowledgment. The present study was initiated during a stay of Adel Elyousfi in our group. We gratefully thank Raymond Ober for his kind help in surface-tension measurements and Fredrik Tiberg for enlightening discussions. Randy Hill and Steve Garoff kindly made helpful comments on the manuscript. M.C. was supported by the program ECOS A97E03. LA980840F
