Langmuir 2001, 17, 335-348
335
Spreading of Aqueous Trisiloxane Surfactant Solutions over Liquid Hydrophobic Substrates Tatiana F. Svitova,*,†,‡ Randal M. Hill,§ and Clayton J. Radke*,| Institute of Physical Chemistry, Russian Academy of Sciences, Moscow, Leninsky pr., 31, 117915, Russia, and Dow Corning Corporation, Midland, Michigan 48686, and Chemical Engineering Department, University of California at Berkeley, California 94720-1462 Received January 7, 2000. In Final Form: August 9, 2000 Systematic studies of trisiloxane surfactant aqueous solutions spreading over hydrophobic liquids are performed by videomicroscopy. Three trisiloxane nonionic surfactants M(D′E n)M with different ethoxychain lengths are investigated. In addition to surfactant concentration, the spreading rate strongly depends on surfactant solubility in the organic liquid substrate, even when the initial spreading coefficient is essentially constant. In contrast to previously studied DDAB solutions’ spreading (Svitova, T.; Hill, R.; Radke, C. Langmuir 1999, 15 (21), 7392), two different spreading regimes are found. At relatively low surfactant concentrations, the spreading rate is limited by surfactant mass transport toward stretching interfaces, as in the case of DDAB solutions. At concentrations greater than 0.5 wt %, however, the maximum rate increases to a level for which viscous dissipation by the substrate starts to play an important role, along with surfactant mass transport limitations. For all liquid substrates studied, the spreading lenses of the trisiloxane surfactant solutions retract after a maximum area is reached because of surfactant dissolution into the oil phase. Intensive surfactant dissolution into the substrate leads to fast lens retraction, and it overrides the gain due to less viscous drag when the substrate liquid is of lower viscosity. The presence of surface concentration gradients and the resulting Marangoni flow is established by monitoring the movement of Teflon particles at the upper surface of the spreading lens.
Introduction Spreading phenomena are important in nature and span applications from biological to physical and chemical technologies. The thermodynamic condition for complete wetting of a liquid 1 over the surface of a substrate 2 is that the initial spreading coefficient S has to be positive.1 S is defined as
S ) γ2 - (γ1 + γ12)
(1)
Here γ1 is the surface tension of liquid 1, γ2 is the surface tension of substrate 2, and γ12 is the interfacial tension between these two phases. The initial spreading coefficient appearing in eq 1 means that the tensions are taken for the pure phases which are not pre-equilibrated. The criterion of positive initial S for spreading proves to be rather general.1-16 * To whom correspondence should be addressed at the University of California, Berkeley. † Current address Chemical Engineering Department, University of California at Berkeley, CA 94720-1462. ‡ Russian Academy of Sciences. § Dow Corning Corporation. | University of California at Berkeley. (1) Harkins, W. D.; Feldman, A. J. Am. Chem. Soc. 1922, 44 (12), 2665. (2) Adamson, A. W.; Gast, A. P. Physical Chemistry of Surfaces; 6th ed.; Wiley-Interscience: 1997; pp 103-107. (3) Davies, J. T.; Rideal, E. K. Interfacial Phenomena; Academic Press: New York and London, 1963; pp 25-28. (4) Ellison, A. H.; Zisman, W. A. J. Phys. Chem. 1956, 60, 416. (5) Suciu, D. G.; Smigeschi, O.; Ruckenstein, E. J. Colloid Interface Sci. 1970, 33 (4), 520. (6) Ahmad, J.; Hansen, R. S. J. Colloid Interface Sci. 1972, 38, 601. (7) Foda, M.; Cox, R. G. J. Fluid Mech. 1980, 101 (1), 33. (8) Joos, P.; Pintens, J. J. Colloid Interface Sci. 1977, 60 (3), 507. (9) Joos, P.; Van Hunsel, J. J. Colloid Interface Sci. 1985, 106 (1), 161. (10) Fraaije, J. G. E. M.; Cazabat, A. M. J. Colloid Interface Sci. 1989, 133 (2), 452.
The kinetics of spreading, however, are more poorly understood. This work focuses on the dynamic of aqueous trisiloxane surfactant solutions spreading on hydrophobic liquids. Coupled with practical importance, this case is particularly interesting because without surfactant present in the water S is negative and spreading does not occur. Theoretical analysis of liquid-on-liquid spreading dynamics is complicated because of the complex fluid mechanics involved. Numerous attempts have been made to perform this analysis, based on approximations in which the spreading rate is determined by the balance of a driving force and an opposing viscous drag by the substrate liquid.5-15 These approaches typically lead to a power law for the distance which the spreading liquid front travels versus time, R ∼ Ctn,5-15 where R(t) is the distance traveled by the edge of a spreading liquid at time t and C is a parameter, accounting for the driving force of spreading and the viscosity and density of the substrate liquid. The driving force has been written in terms of the initial spreading coefficient5-9,14,15 or an effective surface tension γ-1 ) γ-12 + γ-112 (ref 12) or, for the case of an insoluble surfactant monolayer, the surface activity -dγ/dΓ multiplied by the total mass of surfactant M inside the spreading film.13 The exponent n varies depending on the model boundary conditions used and the substrate layer thickness. According to available theory,8,9,12-15 n is always less than 1, and thus, the rate of spreading dR/dt should smoothly decrease in time. A very useful relationship for the dynamics of a singlecomponent liquid drop spreading radially on the surface (11) Bergeron, V.; Langevin, D. Phys. Rev. Lett. 1996, 76 (17), 3152. (12) Joanny, J.-F. Physicochem. Hydrodyn. 1987, 9 (1-2), 183. (13) Jensen, O. E. J. Fluid Mech. 1995, 293, 349. (14) Dussaud, A. D.; Troian, S. M. Phys. Fluids 1998, 10 (1), 23. (15) Camp, D. W. Ph.D. Thesis, University of Washington, 1985. (16) Svitova, T.; Hill, R.; Radke, C. Langmuir 1999, 15 (21), 7392.
10.1021/la000019f CCC: $20.00 © 2001 American Chemical Society Published on Web 12/14/2000
336
Langmuir, Vol. 17, No. 2, 2001
Svitova et al.
of another liquid was derived by Foda and Cox7
S1/2 3/4 R(t) ) K t (µF)1/4
Table 1. Characteristics of Liquid Substrates and PDMS
(2)
where R is the radius of the precursor film, S is the initial spreading coefficient, µ and F are substrate liquid viscosity and density, respectively, and K is an empirical constant basically close to 0.75. Equation 2 rather accurately describes experimental observations for the spreading of drops of single-component liquids on a second immiscible liquid surface.10,11,14,15 Joos et al.8,9 proposed that the power law of eq 2 should also be valid for aqueous surfactant solutions spreading over liquid hydrophobic substrates. In our previous paper,16 we showed that eq 2 can, in principle, also be applied to the main drop of a surfactant solution spreading under Marangoni forces when thinfilm forces (i.e. disjoining pressures) are negligible. Despite practical importance, experimental data for aqueous solutions spreading over oils are quite limited.8,9,16-22 Svitova et al.17 established that for nonionic surfactant solution/hydrocarbon systems the rate of spreading correlates with the rate of surface/interfacial tension decrease. Stoebe et al.19 found that the rate of spreading of trisiloxane nonionic surfactant solutions over mineral oil strongly depends on surfactant concentration and ethoxy-chain length. They found that the area of the spreading lens is approximately linearly proportional to time. Unfortunately, their study was restricted to only mineral oil as the substrate, and the values of surface tension and viscosity of the particular mineral oil used were not reported. In a previous work, we found16 that the rate of spreading of dimethyl didodecylammonium bromide (DDAB) solutions strongly depends on surfactant concentration even though the initial spreading coefficient is essentially constant at surfactant concentrations above the critical wetting concentration (CWC). It was also found that a simple power law such as in eq 2 does not describe the spreading dynamics of aqueous DDAB solutions. For these reasons we developed a new quantitative model20 that describes spreading of dilute surfactant solutions on the basis of the hypothesis that the rate of spreading is limited by surfactant adsorption kinetics and is independent of substrate bulk liquid properties. In this paper, we present the results for trisiloxane surfactant solutions spreading over hydrocarbon liquids. We choose these surfactants to extend our research to the case of high spreading rates, comparable with the rates of pure liquid-on-liquid spreading, and thus to ascertain whether eq 2, as was stipulated in refs 8, 9, and 16, provides an adequate description for the dynamics of surfactant solutions spreading under these conditions. Trisiloxane surfactants are known as “superspreaders”;22 they are very efficient in surface-tension reduction, typically giving a value of γ1 ∼ 21 mN/m against air. The interfacial tension of trisiloxane surfactant solutions against hydrocarbons γ12 can be lowered to a few tenths of a milliNewton per (17) Svitova, T. F.; Hoffmann, H.; Hill, R. M. Langmuir 1996, 12, 1712. (18) Svitova, T. F.; Hill, R. M.; Smirnova, Yu. P.; Stuermer A.; Yakubov, G. Langmuir 1998, 14 (18), 5023. (19) Stoebe, T.; Hill, R. M.; Ward, M. D.; Davis, H. T. Langmuir 1997, 13, 7276. (20) Chauhan, A.; Svitova, T. F.; Radke, C. J. J Colloid Interface Sci. 2000, 222 (2), 221. (21) Svitova, T. F.; Smirnova, Yu. P.; Yakubov, G. Colloids Surf., A 1995, 101, 251. (22) Zhu, S.; Miller, W. G.; Scriven, L. E.; Davis, H. T. Colloids Surf., A 1994, 90, 63.
hydrophobic liquid (HL) dodecane tetradecane hexadecane mineral oil (MO) PDMS
surface density, viscosity, tension, 3 F, g/cm µ, mPa‚s γ2, mN/m 0.7486 0.7628 0.7733 0.838 0.964
1.383 2.128 3.03 24.3 100
29.3 30.4 31.7 28.6 20.9
interfacial tension HL/H2O, γ12, mN/m 51.1 51.3 52.1 52.4 36.2 PMDS/MO ∼ 0
meter at concentrations greater than 0.1 wt %.17,18 Thus, the initial spreading coefficient for these solutions on hydrocarbons is positive and rather high. Another goal of this paper is to explore the role of surfactant solubility in the substrate liquids. In contrast to the earlier studied DDAB,16 which is practically insoluble in hydrocarbons, trisiloxane surfactants are substantially soluble in mineral oil (∼1 wt %) and almost completely miscible with dodecane at room temperature. A peculiarity of these surfactants is that they exhibit apparent35 bulk aqueous diffusion coefficients17 an order of magnitude higher than those of either DDAB20 or C12En17 at comparable concentrations. The mechanism of trisiloxane surfactant solutions spreading over hydrophobic liquid substrates is discussed on the basis of our experimental observations. Experimental Section Materials. The trisiloxane surfactants ((CH3)3SiO)2Si(CH3)(CH2)3(OCH2CH2)nOH are denoted as M(D′En)M, where M is a trimethyl end-cap unit, D′ ) CH3SiO(CH2)3, and E is an ethoxy group. We studied samples with average ethoxy group numbers of n ) 6, 8, and 12. Surfactant purity was 90%,36 from Dow Corning Corp., Midland, MI; they were used without purification. These surfactants, as with all commercial ethoxylated nonionics, consist of a broad distribution of ethoxy-chain lengths. Water, distilled and deionized by a Millipore system, was used for solution preparation. Spectroscopic grade purity hydrocarbons, from Fluka, were used as the subphases for the spreading-dynamics studies. The physical characteristics of the hydrophobic liquids are listed in Table 1. Poly(dimethylsiloxane) (PDMS), SF99 from GE Silicones, was also used for spreading experiments on water and mineral oil. Apparatus and Procedures. A schematic of the apparatus for measuring spreading rates is presented in Figure 1. The apparatus and procedure are described in detail in ref 16. The oil substrate layer, 10-mm thick, was placed atop a water layer, 100-mm thick. Since the spreading liquid (an aqueous solution) is denser than the substrate (hydrocarbons), in order to avoid aqueous droplets sinking into substrate organic liquid, the aqueous drop must be less than about 3 mm3, to remain on the surface by capillary forces.12 We also performed several spreading experiments using a constant surfactant solution supply by an ISCO Model 1 syringe pump, similar to the procedure outlined by Suciu et al.5 and in ref 16. In this experiment, a constant flow of solution was supplied to the oil surface through a thin glass capillary, r ) 0.5 mm, connected to the pump. The capillary was fixed vertically about 1.0-1.5 mm above the substrate surface. Flow rates of 100 and 145 mm3/min were carefully chosen to provide a solution flow sufficient to sustain steady spreading. As illustrated in Figure 1, the entire apparatus, except for the VCR and TV monitor, is placed into an environmental chamber at room temperature, 22 ( 0.5 °C. Measurements were performed at ambient (35-55%) and saturated (>95%) relative humidity. Spreading experiments were repeated at least three times for each solution/substrate combination. We used the average of three diameter values for each captured lens image. The reproducibility of a transient lens diameter is (5%. Two positions of the video camera were employed for viewing of the lenses: straight vertical and under an angle of approximately 20-30°. Imaging at an oblique angle was adopted to provide better views
Aqueous Trisiloxane Surfactant Solutions
Langmuir, Vol. 17, No. 2, 2001 337 concentrations, the critical wetting concentrations (CWC). Svitova et al. showed that CWCs for the trisiloxane surfactants are independent of substrate physical state, solid or liquid, and surface energy.18 Interfacial tensions at expanding interfaces are generally higher than those at equilibrium because it takes some time for surfactant molecules to transport from the bulk and to adsorb at a freshly exposed interfacial area. The drop weight/volume method is used here for dynamic surface and interfacial tension measurements, as described elsewhere.21,25-28 We adopt the procedures proposed in refs 26 and 27 for the hydrodynamic correction to the drop volume. Using an asymptotic approach developed in ref 28, an effective or apparent diffusion coefficient D can be estimated from the slope of the interfacial tension γ versus t-1/2, at t f ∞, according to the following relation
( )
( )
RTΓ∞ π dγ ) -1/2 c0 4D dt
Figure 1. Schematic of experimental apparatus for spreading dynamics.
1/2
(3)
where Γ∞ is the equilibrium adsorption, corresponding to the bulk surfactant concentration c0, R is the universal gas constant, and T is the absolute temperature. Although this approach was developed for surfactant solutions below the critical aggregation concentration (CAC), it can be applied to calculate an effective or apparent diffusion coefficient in the presence of surfactant aggregates such as micelles or vesicles.20 More generally, D values obtained in this manner reflect, albeit qualitatively, the net rate of surfactant adsorption at the interface, including the combination of all different processes of monomer diffusion, aggregates diffusion, and dissociation, and the kinetics of transfer of monomer molecules from the sublayer to and through the interface. Apparent diffusion coefficients for aqueous trisiloxane surfactants used later have this meaning.
Spreading Observations
Figure 2. Initial spreading coefficient of aqueous M(D′E8)M solutions on different hydrocarbons as a function of concentration. The critical wetting concentration is identified at S ) 0. of possible rims at the leading edge of a spreading lens. In certain experiments, we employed small Teflon particles, 0.05-0.1 mm in the large dimension, to detect the spreading-lens edge and to check whether a thin precursor film moves ahead of the visible lens edge.10,11,14 Interfacial Tension Measurement. Equilibrium surface and interfacial tension measurements against mineral oil and hexadecane were made with the pendant-drop method using NIH image processing software and a numerical solution to the Young-Laplace equation.23,24 Some measurements for concentrated M(D′En)M solutions against hexadecane were performed by the spinning-drop method. The initial spreading coefficient on tetradecane, hexadecane, and mineral oil as a function of M(D′E8)M concentration is presented in Figure 2. The initial spreading coefficient at the M(D′En)M solution/oil interface becomes positive at a concentration of 0.03 wt % (5.52 × 10-4 M) for M(D′E6)M, 0.05 wt % (7.9 × 10-4 M) for M(D′E8)M, and 0.1 wt % (1.24 × 10-3 M) for M(D′E12)M. Droplets of the solutions spread on the hydrophobic substrates only above these specific (23) Padday, J. In Surface and Colloid Science; Matijevic, E., Ed.; Wiley-Interscience: New York, Vol. 1, 1969. (24) Beverung, C. J. M.S. thesis, University of California at Berkeley, 1996.
In the following sections, we first present images of surfactant solution lenses spreading on different substrates. Then we present the quantitative results, derived from the image analyses, for spreading-lens radii versus time histories under varying conditions. Precursor Film. In all experimental observations performed for single-component liquid-on-liquid spreading, a microscopically thin precursor film is observed moving ahead of the macroscopic lens edges.10,11,14,16 Indeed, eq 2 is based on a precursor-film mechanism for single-component liquid-on-liquid spreading. We found previously16 that spreading of a PDMS precursor film on water does obey an R ∼ t3/4 dependence, in agreement with refs 10, 11, and 14. Here we studied PDMS spreading on mineral oil. A precursor film was again detected from the motion of Teflon particles sprinkled onto the oil surface. These particles were rapidly pushed to the sides of the dish before the main lens reached that area. We confirmed that the radius of a PDMS precursor film on mineral oil sustains the 3/4-power scaling with time for several seconds, but at longer times spreading decelerates more rapidly than dR/dt ∼ t-1/4, likely because of PDMS dissolution into the substrate. Conversely, we found that no precursor film forms during DDAB solutions spreading on hydrophobic liquids.16 The question of a precursor film forming (or not forming) ahead of trisiloxane surfactant solutions placed on a hydrophobic liquid substrate is addressed in Figure 3. A 0.5-mm3 drop of 1 wt % M(D′E8)M solution at ambient (25) Jho, C.; Burke, R. J. Colloid Interface Sci. 1983, 95, 61. (26) Miller, R.; Hofman, A.; Hartman, R.; Shano, K. H.; Halbig, A. Adv. Mater. 1992, 5 (4), 370. (27) Miller, R.; Shano, K. H.; Hofman, A. Colloids Surf., A 1994, 92, 189. (28) Fainerman, V. B.; Makievski, A. V.; Miller, R. Colloids Surf., A 1994, 87, 61.
338 Langmuir, Vol. 17, No. 2, 2001 Svitova et al.
Figure 3. Images of 0.5-mm3 volume drops of 1 wt % M(D′E8)M solutions spreading on mineral oil at ambient relative humidity.
Aqueous Trisiloxane Surfactant Solutions
relative humidity forms the aqueous lens, which is viewed from above. Teflon particles, seen as black speckles, remain immobile until the outer edge of the spreading lens reaches them. Then they move in concert with the spreading-lens front, thus demonstrating that there is no significant precursor film moving ahead faster than the main lens. Due to trisiloxane surfactant dissolution into the substrate, the aqueous lens retracts at a later time.1 For all cases studied, trisiloxane solution lenses shrink to a final size that is close to the initial size of the lens at the very first moment of drop/substrate contact. The Teflon particles also retract together with the lens edge after the maximum area is reached. The spreading lenses in Figure 3 have an almost perfect circular shape and are slightly iridescently colored, although colorless “holes” appear at later times. These colorless spots are characteristic of experiments at ambient humidity and do not appear at saturated humidity. We suppose that these spots reveal local regions where, due to water evaporation, some parts of the relatively thick, >100 nm, lens collapse to a thinner film with a thickness
