Superspreaders Versus Cousin Non-Superspreaders: Disjoining Pressure in Gravitational Film Drainage

Transcription

1 pubs.acs.org/langmuir Superspreaers Versus Cousin Non-Superspreaers: Disjoining Pressure in Gravitational Film Drainage S. Sett, R. P. Sahu, S. Sinha-Ray, an A. L. Yarin*,, Department of Mechanical an Inustrial Engineering, University of Illinois at Chicago, 84 West Taylor Street, Chicago Illinois , Unite States College of Engineering, Korea University, Seoul, South Korea *S Supporting Information ABSTRACT: Gravitational rainage of vertical films supporte on a wire frame of two superspreaers SILWET L-77 an BREAK-THRU S 78 an their respective cousin non-superspreaers SILWET L-7607 an BREAK-THRU S 33 reveale rastic ifferences. The superspreaer films showe complicate ynamic turbulent -like interferometric patterns in istinction from the orere color bans of the cousin non-superspreaers, which resemble those of the orinary surfactants. Nevertheless, the superspreaer films stabilize themselves at the thickness about 35 nm an reveale an orer of magnitue longer lifetime before bursting compare to that of the cousin non-superspreaers. Notably, the superspreaers reveale rastic ifferences from the non-superspreaers in aqueous solutions with no contact with any soli hyrophobic surface. The self-stabilization of the superspreaer films is attribute to significant isjoining pressure probably relate to long superspreaer bilayers hanging from the free surfaces. The scaling law for the isjoining pressure was foun as p isj (h) h m (with m 9 11) for the sufficiently concentrate superspreaer solutions, an as p isj (h) h s (with s 6) for more ilute solutions (in both cases, concentrations were above the critical micelle concentration). The non-superspreaers o not possess any significant isjoining pressure even in the films with thicknesses in the nm range. The results show that gravitational rainage of vertical films is a useful simple tool for measuring isjoining pressure. INTRODUCTION The aqueous solutions of trisiloxane-(poly)ethoxylate surfactants are wiely applie as agricultural ajuvants, soli moifiers, an cleaners. Such surfactants are commonly enote as M(D E n OMe)M, with M-D -M being the trisiloxane hyrophobe, E n - the ethylene oxie, Me - the methyl group, an O - oxygen. 1 Water rops with ae superspreaers easily sprea on hyrophobic surfaces such as polyethylene (PE) or polypropylene (PP). The superspreaing ability of trisiloxane- (poly)ethoxylate surfactants is etermine by the length of the (poly)ethylene oxie group. Two rastically ifferent cousin types of trisiloxane-(poly)ethoxylate surfactants with n = 7.5 (which is the superspreaer known uner the prouct name SILWET L-77; ref 1) an n = 16 [which is the nonsuperspreaer, enote as M(D E n )M uner the prouct name SILWET L-7607, ref ] are istinguishe. The superspreaer BREAK-THRU S 78 has a similar nominal structure as that of SILWET L-77 (ref 3). Its cousin non-superspreaer BREAK- THRU S 33 has an OH-terminate polyether group containing both ethylene oxie an propylene oxie. 3 The length of the poly(ethylene oxie) increases, thereby inicating a larger hyrophilic heagroup for the non-superspreaers SILWET L-7607 an BREAK-THRU S 33 than that of the superspreaers SILWET L-77 an BREAK-THRU S 78, respectively. The physicochemical origins of the superspreaing on hyrophobic surfaces are ebate. 1 3 Formation of bilayer structures was assume for superspreaers an argue to be the reason of the superspreaing effect on hyrophobic surfaces. 1 On the other han, the cousin non-superspreaers presumably o not form large-scale bilayer structures above the critical micelle concentration (cmc) but rather orinary micelles. 1 Superspreaing is frequently relate to the assume propensity of superspreaers to settle onto hyrophobic substrates close to the moving contact line, which presumably leas to an increase in surface tension there, the increase concentration-graientrelate Marangoni effect, an an enhance spreaing. 4,5 In the present work, gravitational rainage of vertical films of the aqueous solutions of the above-mentione superspreaers an their cousin non-superspreaers is stuie using the setup similar to the one escribe in our recent work. 6 Even though superspreaer solutions o not contact with any hyrophobic soli surfaces in the present case of gravitational rainage, their behavior is raically ifferent from that of the cousin nonsuperspreaers an the orinary surfactants. Namely, a ramatic eceleration of the rainage process at the later stage is observe, Receive: August 15, 013 Revise: February 1, 014 XXXX American Chemical Society A

2 which makes superspreaer films much more stable than their non-superspreaer counterparts. The reason of the unusual behavior of superspreaers in the case of gravitational rainage is trace to their isjoining pressure. Disjoining pressure is associate with the internal energy-relate part of the free energy, in istinction from the osmotic pressure, which is associate with the entropy-relate part of the free energy. 7 The isjoining pressure strongly epens on the film thickness h when h < 100 nm, an the epenence (the scaling or the oscillatory character) is etermine by the intersurface repulsion mechanisms in the film on the microscopic level For example, the electrostatic repulsion in the DLVO theory, the van er Waals attraction an repulsion, as well as the steric repulsion an micelle orering, result in rastically ifferent epenences of the isjoining pressure on the film thickness h. 7 1 Disjoining pressure was measure using Scheluko 13,14 an/or Mysels-Jones 10,15 cells for many orinary cationic, anionic, an nonionic surfactants. In the present work we introuce an alternative technique, gravitational film rainage, an apply it to superspreaers an their cousin non-superspreaers. The following section escribes the materials an the experimental setup an metho. Then, the experimental results are presente. After that, the theoretical section is given, which is followe by the comparison with the experimental ata an iscussion. Conclusions are rawn at the en. EXPERIMENTAL SECTION Materials. The following trisiloxane-(poly)ethoxylate surfactants were use in rainage experiments. SILWET L-77 (superspreaer) an SILWET L-7607 (the cousin non-superspreaer), both obtaine from Momentive, were use as receive. In aition, BREAK-THRU S 78 (superspreaer) an BREAK-THRU S 33 (the cousin nonsuperspreaer), obtaine from Evonik Inustries were use as receive. Solution Preparation. Trisiloxane surfactants SILWET L-77, SILWET L-7607, BREAK-THRU S 78, an BREAK-THRU S 33 were use to prepare solutions as follows. Using the superspreaer SILWET L-77, 0.1, 0., 0.5, an 1 ml of the surfactant was ae to 100 ml of eionize water (ASTM Type II). The resulting solutions were enote as L , L-77-0., L , an L , respectively. Using the cousin non-superspreaer SILWET L-7607, 0.1, 0., 0.5 an 1 ml of the surfactant was ae to 100 ml of eionize water (ASTM Type II), an the resulting solutions were enote as L , L , L , an L , respectively. Using the superspreaer BREAK-THRU S 78 an the cousin nonsuperspreaer BREAK-THRU S 33, solutions were prepare similarly. The BREAK-THRU S 78 solutions were enote as S , S 78-0., S , an S The BREAK-THRU S 33 solutions were enote as S , S 33-0., S , an S Experimental Setup an Metho. The experimental setup an metho use to stuy rainage of vertical plane surfactant films is escribe elsewhere. 6 In brief, Figure 1 epicts the schematic which shows how the container with a surfactant solution is raise using the linear actuator to create a film supporte by the fixe aluminum wire frame (4 cm 4 cm x cm). The container is then lowere, an the film that stays on the frame is photographe using a CCD camera (Phantom Miro 4), while the ata are store in the computer. It was foun that fully reliable an self-consistent ata can be acquire for film thicknesses above 30 nm. 6 The film thickness at the top was measure right below the top wire an cm from the left wire, so the sie wires i not have any effect on the film thickness. The local film thickness h was calculate using the interferometric formula. 6,16 0 EXPERIMENTAL RESULTS The cmc of each of the four surfactants was etermine by measuring the surface tension using the Wilhelmy plate Figure 1. Schematic of the experimental setup. apparatus (KRUSS Tensiometer K 1) 1, with the plate imensions of 0 mm 10 mm. The ata in Figure S1 of the Supporting Information (SI) show that at the concentration %v/v, for SILWET L-77, SILWET L-7607, BREAK- THRU S 78 an BREAK-THRU S 33 the surface tensions ha saturate. This value was consiere as the cmc value corresponing to these surfactants. The concentration of all the solutions use in the rainage experiments was above their cmc. Dynamic light scattering (DLS) was use to measure the aggregate sizes forme in solutions of SILWET L-77, SILWET L- 7607, BREAK-THRU S 78, an BREAK-THRU S 33 at concentration 0.5 %v/v above the cmc. The solutions prepare from the superspreaers SILWET L-77 an BREAK-THRU S 78 were turbi in appearance, an the turbiity was foun to increase with concentration. It is evient from Figure that the superspreaer solutions contain aggregates which are orers of magnitue larger than their counterpart non-superspreaers. The aggregate structures in the superspreaer solutions combine an form larger entities (Figure a,c) known as mesomorphic phases. 3 These are anisotropic structures causing solution turbiity an resulting in light scattering. Increasing surfactant concentration increases the number of such aggregates, an thus, turbiity. On the contrary, solutions prepare from the cousin non-superspreaers SILWET L-7607 an BREAK-THRU S 33 staye clear. They forme smaller aggregates/micelles (Figure b,) that are too small to cause any significant light scattering. 3 The size of aggregates forme in surfactant solutions epens on the critical packing parameter P 8,4 P = V a 0 c (1) where V is the chain volume, a 0 is the optimal aggregate water interfacial area (the hyrocarbon/water interfacial area), an c is the critical chain length. For surfactants with the hyrophilic heagroup larger than the hyrophobic part (P < 1), curve aggregates such as spherical or cylinrical micelles are forme. For comparable sizes of hyrophilic an hyrophobic parts, P = 1, surfactant bilayer aggregates are forme. 8,4 For trisiloxane surfactants, the length of poly(ethylene oxie) increases from 7.5 for SILWET L-77 to 16 for SILWET L A similar increase in the length of poly(ethylene oxie) is foun when BREAK-THRU S 78 an BREAK-THRU S 33 are compare. The small hyrophilic heagroup in the superspreaers SILWET L-77 an B

3 Figure. Aggregate size istribution for 0.5 %v/v solutions of (a) SILWET L-77, (b) SILWET L-7607, (c) BREAK-THRU S 78, an () BREAK- THRU S 33. %P stans for the percentage of polyispersity which is a measure of stanar eviation an is inicative of the istribution of each peak. %Mass is the percentage of mass of aggregates of a particular size present in the solution. BREAK-THRU S 78 results in formation of larger aggregates (vesicles an bilayers) an turbi solutions as compare to the smaller micellar aggregates of the non-superspreaers SILWET L-7607 an BREAK-THRU S 33, an their clear solutions. This is in agreement with a well-establishe fact that surfactants having shorter hyrophilic chains form large aggregates, while those with longer chains form smaller aggregates. 1,5 Solutions with ifferent concentrations of the superspreaers SILWET L-77 an BREAK-THRU S 78, an their nonsuperspreaer counterparts SILWET L-7607 an BREAK- THRU S 33, respectively, were use in the gravitational rainage experiments. For SILWET L-77 solution L , it was observe that initially the interference color bans were forme. These color bans were not uniform horizontally, an each color strip was of uneven thickness. With time, the visible colors in the upper part of the wire frame mixe with one another, inicating nonuniform film thickness in the horizontal irection. Towar the bottom of the wire frame, the film became turbi with time, an no istinct colors coul be seen in a while. After 55 s from the formation of the film, the topmost part of the film turne black, where the measure thickness was 50 nm (Figure 3a). The top part of the film remaine black for the remaining time. The black omain was confine to the topmost part an i not sprea ownwar with time. The color intermittency over the entire film further increase graually till the film burst after 105 s (Figure 3a, the inset image). It is emphasize that the abstract color patterns in all the superspreaer solutions as shown in Figure 3 (the inset images) are ramatically ifferent from the regular horizontal color bans observe before for the orinary cationic, anionic an nonionic surfactants. 6 As it is shown below, the abstract color patterns of the superspreaer solutions are also very ifferent from those of the cousin non-superspreaers. For SILWET L-77 solution L-77-0., similar observations were one. The black film ha been forme at the film top after 65 s (Figure 3b). It escene own with time an a consierable part of the film at the top was black when the film burst after 118 s (Figure 3b, the inset image). For SILWET L-77 solution L , after the initial color intermittency le to an uneven color istribution, plumes were seen to rise from the bottom, inicating that the thickness istribution is uneven an highly transient. The plumes mae the bottom part of the film blurre an no istinct colors were seen in these regions. The top part of the film turne black after 7 s (Figure 3c) an the black omain avance ownwar with time. The black film occupie at about one-half of the film length along the wire frame at the time of bursting after 150 s (Figure 3c, the inset image). It shoul be emphasize that the color intermittency in the horizontal irection over the superspreaer films in Figure 3 accoring to the interferometric formula 6,1 5 correspons to the film thickness variation in the horizontal irection Δh on the scale of Δh = Δλ/(πn), with Δλ being the wavelength ifference between the two colors, an n being the refractive inex (n = 1.333). In the worst case of re color replace by blue color or vice versa, Δh 3.8 nm, which woul result in variance close to ±10 nm about the mean. In reality, the color intermittency is less than in the worst case, an the results shown in Figure 3 reveal the following accuracies corresponing to the thinnest films C

4 Figure 3. Drainage of the plane films of the superspreaer SILWET L-77 solutions: (a) L , (b) L-77-0., (c) L , an () L The ata correspon to the film top. The experimental results are shown by symbols. The incline straight lines correspon to the theoretical preiction of ref 6, eq 16 in the present work. The inset images show the interference patterns just prior to the film bursting. Figure 4. Drainage of the superspreaer SILWET L film at: (a) t = 0 s, (b) t = 5 s, (c) t = 50 s, () t = 70 s, (e) t = 90 s, (f) t = 110 s, (g) t = 130 s, an (h) t = 155 s. stabilize by the superspreaer: Figure 3a: 36 ± 4 nm (L ), Figure 3b: 35 ± 3 nm (L-77-0.), Figure 3c: 36 ± 3 nm (L ), an Figure 3: 35 ± 3 nm (L ). This shows that the accuracy is sufficient even at the lowest ata branches for the highly intermittent films of superspreaer solutions. Note also that measurements were one only when istinct colors were fully recognizable, whereas turbi areas near the bottom of the wire frame were never use. The time evolution of the film of the superspreaer SILWET L-77 solution L is illustrate in Figure 4. In such a film, the number of rising plumes increase an eventually coul be seen covering the entire film. Turbulent -like patterns seen on the film were also much larger compare to the lower concentration films. The black film forme at the top after 78 s (Figure 3, the inset image, an Figure 4e), increase with time an covere the entire film at the moment of bursting (Figure 3, the inset image, an Figure 4h). Even though the superspreaer films looke pretty agitate an transient (Figure 3, the inset images, an Figure 4), they showe a remarkable stabilization at the latter stage of their existence, as is seen in Figure 3. They were stabilize at thicknesses 35 nm, where they stoppe thinning linearly in time, 6 an their thinning was practically arreste for a long time. This is ramatically ifferent from the observations of rainage of the orinary cationic, anionic an nonionic surfactants (refs 6 an 6 an references therein, an the cousin non-superspreaers iscusse below). For the secon superspreaer stuie in this work, BREAK- THRU S 78, similar trens were observe to those in Figure 3 for the superspreaer SILWET L-77. The corresponing results for solutions S to S are presente in Figure S of the SI. With the increase in the surfactant concentration, the length of the black section at the film top at the time of bursting increases an reaches the maximum for S (Figure S, the inset images). Even for BREAK-THRU S 78 solution S (Figure S, the inset image), the black film i not sprea over the entire film length, in istinction from the superspreaer SILWET L-77 in Figure 3 (the inset image). Also, plumes D

5 Figure 5. Drainage of the non-superspreaer SILWET L-7607 solution films: (a) L , (b) L , (c) L , an () L The ata correspon to the film top. The experimental results are shown by symbols. The films burst in about 5 10 s. The incline straight lines correspon to the theoretical preiction of ref 6, eq 16 in the present work. The inset images show the interference patterns just prior to the film bursting. were seen to rise from the bottom of the wire frame for BREAK- THRU S 78 solution S (Figure Sb, the inset image) an the intensity of these plumes increase for S (Figure Sc, the inset image) an S (Figure S, the inset image). Figure 5 shows that the experimental ata for the nonsuperspreaer SILWET L-7607 is in goo agreement with eq 16 (see the theoretical part below), which reveals a linear ecrease in the film thickness uring the gravitational rainage near the film top. This is similar to the cationic, anionic, an nonionic surfactants stuie earlier, 6,6 an is rastically ifferent from the results for the cousin superspreaer SILWET L-77 shown in Figure 3. For the non-superspreaer SILWET L-7607 solution L , the films burst just after the top part turne black (Figure 5a, the inset image). The length of the black film part on top of the film increase only slightly with the increase in the surfactant concentration, in istinction from the cousin superspreaer SILWET L-77 (cf. Figure 3, the inset images, an Figure 4). In fact, only for SILWET L-7607 solution L was there a noticeable increase in the black film length at the time of bursting (Figure 5, the inset image). Gravitational rainage of plane vertical films of the nonsuperspreaer BREAK-THRU S 33 solutions S , S 33-0., S , an S reveale a linear ecrease in the film thickness (Figure S3 of SI) with no stabilization characteristic of the superspreaer counterpart BREAK-THRU S 78 (Figure S of SI). Solutions of the non-superspreaer BREAK-THRU S 33 reveale similar regular horizontal interference color strips like those of the non-superspreaer SILWET L-7607 solutions (Figure 5, the inset images) or the solutions of the orinary cationic, anionic, an nonionic surfactants stuie in refs 6 an 6 an references therein. On the other han, such film patterns are rastically ifferent from those for both superspreaers SILWET L-77 (Figure 3, the inset images, an Figure 4) an BREAK- THRU S 78 (Figure S, the inset images, of the SI). Only the small top parts of the non-superspreaer BREAK-THRU S 33 films turne black before the bursting (Figures S3, the inset images). Overall, the thin films forme from the superspreaer solutions were stable for a much longer time in comparison with the cousin non-superspreaers an the orinary surfactants, 6,6 albeit also much more vigorous (Figures 3, 4, an S, the inset images, versus Figures 5 an S3, the inset images). The thinning of the superspreaer films was practically arreste at the latter stage, whereas the cousin non-superspreaer films continue to rain (Figures 3 an S versus Figures 5 an S3). The thin films forme by the superspreaers (cf. Parts 1 an of the vieo in the SI, an Figures 6a,c) reveale a turbulent - like motion (a pretty stable motion) visibly ifferent from the marginal regeneration, 7 3 which is a estabilizing effect. On the other han, the non-superspreaer films (cf. Parts 3 an 4 of the vieo in the SI an Figure 6b,) reveale the orere rainage pattern characteristic of the orinary surfactants (refs 6 an 6 an references therein). THEORETICAL Effect of Disjoining Pressure on Drainage Rate. Gravitational rainage of a vertical plane film of surfactant solution suspene on a wie rectangular wire frame sketche in Figure 7 was theoretically stuie in ref 6 for the cases where the films were sufficiently thick for the isjoining pressure to be neglecte. The theory accounts for the surfactant concentration graient-riven Marangoni flow associate with the surface elasticity an irecte upwar, which ecelerates the gravityriven rainage. In aition, in the present work, a generalization for the case where the isjoining pressure is important is propose. The nee for such generalization is motivate by the experimental ata for the superspreaers, which reveale ramatic stabilization of the rainage process at the latter stages in Figures 4 (for SILWET L-77) an S (in the SI, for BREAK- THRU S 78). In Figure 7 the coorinate reckone in the rainage irection is enote as x an the coorinate normal to it as y. E

6 Figure 6. Drainage of (a) the superspreaer SILWET L-77, an (b) its cousin non-superspreaer SILWET L Drainage of the superspreaer (c) BREAK-THRU S 78, an () its cousin non-superspreaer BREAK-THRU S 33. Figure 7. Sketch of a plane vertical surfactant film on a wire frame. The quasi-one-imensional mass balance equation for the film rainage 6 can be written as h = h + u h = h u t t () with h being the film thickness, u being the longituinal velocity component, t being time, an h/t being the material time erivative. The normal stresses in viscous liqui in the film rea u v σxx = p + μ, σ yy = p + μ y with p being pressure, v being the transversal velocity component, an μ being the viscosity. In the quasi-one-imensional approximation, the stress σ yy is constant across the film, an thus, σ yy = p γ p isj where p γ an p isj are the capillary an isjoining pressure. Then, pressure in the film is foun as u p = p + p μ γ (3) isj (4) where use is mae of the fact that ue to the continuity equation v/ y = u/. F

7 Table 1. Superspreaer SILWET L-77 Solution Films a solution t (s) t b (s) x (cm) h i = h 0 (nm) T (s) ε (g/s ) L L L L a The film lifetime is enote t; t b enotes the time at which black film sets in at the top of the wire frame. The x column correspons to the position at the film center (reckone from the top) to which the black film reache at the moment of bursting. The initial film thickness at the top is enote h i = h 0 ; the characteristic rainage time is enote as T. The values of the surface elasticity ε were foun from T using eq 17. Combining the first eq 3 an eq 4 yiels u σxx = 4μ p p γ isj (5) an, corresponingly, the total normal force in the film crosssection reas σ h + γ = μh u xx 4 ph p h+ γ γ isj (6) with γ being the surface tension. In the inertialess approximation the quasi-one-imensional momentum balance equation reas σ h γ + xx 0 + σ + ρgh = 0 yx,surf where, γ 0 represents an invariable part of the surface tension (if any) an, as usual, 6,33,34 the variable part of the surface tension associate with the concentration Marangoni effect etermines the shear stress acting at the film surface σ yx,surf. In aition, ρ enotes the liqui ensity an g is the gravity acceleration. In the almost uniform films of low viscosity aqueous surfactant solutions the contribution of the first term on the left in eq 7 is negligibly small, 6,6,33 the capillary pressure is absent, also γ 0 / 0, an eq 7 reuces to the following form σ yx,surf ρgh 1 p h isj = + which generalizes eq 3 of ref 6, or eq 1 of ref 6, or eq 3 of ref 33 on the cases where the isjoining pressure is important. It shoul be emphasize that the theoretical approach to gravitational rainage of surfactant films evelope in refs 6 an 33 fully accounts for the surfactant concentration graient-riven (7) (8) Figure 8. The epenences of M an p isj on the film thickness h for the superspreaer SILWET L-77 solutions. L solution: (a) Function M, (b) the imensional isjoining pressure, (c) the imensionless isjoining pressure, () scaling of the isjoining pressure: the experimental ata is shown in re, the straight line use to etermine the exponent in the scaling law is black. The epenences of M an p isj on the film thickness h for the superspreaer SILWET L solution, L solution, an L solution are shown similarly in panels e h, i l, an m p, respectively. G

8 Figure 9. Disjoining pressure versus the film thickness for SILWET L-77 solutions of ifferent concentration: (a) L , (b) L-77-0., (c) L , an () L The experimental ata is shown with symbols spanne with lines an fitte by continuous straight lines of the corresponing color to etermine the exponent in the scaling law. The ifferent colors represent ifferent experimental trials where the initial film thickness varie. The ata from Figure 8,h,l,p is shown in re. The insets show the straight lines corresponing to the scaling laws separately. Table. Scaling Exponents for the Disjoining Pressure of the Superspreaer SILWET L-77 Solutions Foun Using the Slope of the Scaling Laws Shown in Figure 9a solution trial 1 trial trial 3 trial 4 trial 5 average exponent L ± 0.1 L ± 0. L ± 0.1 L ± 0.19 Marangoni effect an the associate surface elasticity of such films. Taking the material time erivative /t of eq 8 an accounting for the relation of σ yx,surf with the surface elasticity (the Gibbs elasticity corresponing to the Marangoni effect) ε = Γ( γ/ Γ), one arrives at the following expression: ρg h = u ε t 1 p h isj ε t where ε is associate with the epenence of the surface tension γ on the istribution of surfactant concentration Γ at the surface. (9) Using the mass balance eq, we rearrange eq 9 to the following form u ε 1 h = u ρg ρg [ ( p h) / ] isj t u (10) This equation generalizes eq 9 of ref 6 in the cases where the isjoining pressure is important. Note that p h = t p h h = h t isj isj isj p h h u h x (11) H

9 where use was mae of eq. Then, eq 10 takes the form u ε p h = 1 isj h 1 ρ ρ u g g h x x (1) The characteristic length scale along the film is ε/(ρgh) [note that it is of the orer of 1 cm in the present case]. Using this length scale, the following approximation is mae p h ρgh p h isj isj h ε h (13) Table 3. Superspreaer BREAK-THRU S 78 Solution Films a solution t (s) t b (s) x (cm) h i = h 0 (nm) T (s) ε (g/s ) S S S S a The film lifetime is enote t; t b enotes the time at which black film sets in at the top of the wire frame. The x column correspons to the position at the film center (reckone from the top) to which the black film reache at the moment of bursting. The initial film thickness at the top is enote h i = h 0 ; the characteristic rainage time is T. The values of the surface elasticity ε were foun from T using eq whereas eq 1 approximately takes the following form: u ε x Fh () h = ρ 1 u g ε with Fh () = h p h h [ ()] h (14) isj (15) The first multiplier on the right-han sie in eq 14 escribes gravitational rainage without accounting for the effect of the isjoining pressure, 6 whereas the secon one is the correction associate with the isjoining pressure. Without the effect of the isjoining pressure, the film thickness at the top of the film linearly iminishes in time as t hx (, t) = h 0 1 T (16) where h 0 is the initial film thickness at the top, an the characteristic time scale T is given by ε T = ρ( gh ) (17) 0 3/ Figure 10. The epenences of M an p isj on the film thickness h for the superspreaer BREAK-THRU S 78 solutions. S solution: (a) Function M, (b) the imensional isjoining pressure, (c) the imensionless isjoining pressure, () scaling of the isjoining pressure: the experimental ata is shown in re, the straight line use to etermine the exponent in the scaling law is black. The epenences of M an p isj on the film thickness h for the superspreaer BREAK-THRU S solution, S solution, an S solution are shown similarly in panels e h, i l, an m p, respectively. I

10 Langmuir Figure 11. Disjoining pressure versus the film thickness for BREAK-THRU S 78 solutions of ifferent concentration: (a) S , (b) S 78-0., (c) S , an () S The experimental ata is shown with symbols spanne with lines an fitte by continuous straight lines of the corresponing color to etermine the exponent in the scaling law. The ifferent colors represent ifferent experimental trials where the initial film thickness varie. The ata from Figure 10,h,l,p is shown in re. The insets show the straight lines corresponing to the scaling laws separately. Accounting for the effect of the isjoining pressure, we obtain from eqs 14 an 16 the following expression for the film thickness at the top: h = (1 t ) M( h ) (18) where the imensionless film thickness h = h/h 0, the imensionless time t = t/t, an the imensionless function M(h ) is foun using eq 15 as M( h ) = 1 h p h h [ ( ) ] h isj (19) In the latter equation, the isjoining pressure is renere imensionless by ε/h 0. It is emphasize that the function M(h ) can be calculate from the eviation of the experimental ata for the film thicknesses of the superspreaer solutions from the linear re lines in Figures 3 an S (the latter in the SI), i.e., plotting M(h ) =h /(1 t ) versus h. Then, the isjoining pressure responsible for the rastic eceleration of the gravitational film rainage is foun as 1 1 [ Mh ( ) 1] p ( h ) = h isj h h h (0) which implies that the initial film thickness is large enough to have a negligible isjoining pressure, i.e. p isj(1) = 0. Note that evaluating the integral in eq 0, we account for the fact that h <1. DISCUSSION: EXPERIMENTS VERSUS THEORY The ata in Figure 3 for the film thickness of the superspreaer SILWET L-77 solutions uring gravitational rainage was use to fin the characteristic time T of the process before the isjoining pressure becomes significant (cf. eqs 16 an 17). Then, using the ifference between the measure ata an the linear ecrease in the film thickness, the function M (cf. eq 18) is establishe as M(h ) =h /(1 t ). After that, the isjoining pressure is foun from eq 0. The results for the superspreaer SILWET L-77 solutions are summarize in Table 1. The corresponing istributions of M(h ) an the isjoining pressure are shown in Figure 8a p, for the superspreaer SILWET L , L-77-0., L , an L solutions, respectively. In aition, the log log plots of the measure isjoining pressure versus the film thickness for these superspreaer solutions are shown in Figure 9a to emonstrate the repeatability of the results an evaluate the variance. J

11 Table 4. Scaling Exponents for the Disjoining Pressure of the Superspreaer BREAK-THRU S 78 Solutions Foun Using the Slope of the Scaling Laws Shown in Figures 11a solution trial 1 trial trial 3 trial 4 trial 5 average exponent S ± 0.18 S ± 0. S ± 0.15 S ± 0.19 The scaling exponents foun using Figures 9a are liste in Table. The ata for the superspreaer BREAK-THRU S 78 in Figure S of the SI was processe similarly to those for the superspreaer SILWET L-77. The results for the linear rainage time T an the corresponing surface elasticity ε of BREAK- THRU S 78 are summarize in Table 3. The istributions of M(h ) an the isjoining pressure foun using the ata in Figure S of the SI are shown in Figures 10a p for the superspreaer solutions BREAK-THRU S , S 78-0., S an S , respectively. In aition, the log log plots of the measure isjoining pressure versus the film thickness for these superspreaer solutions are shown in Figures 11a 11 to emonstrate the repeatability of the results an evaluate the variance. The scaling exponents foun using Figures 11a 11 are liste in Table 4. It is emphasize that the values of the isjoining pressure foun in Figures 8 an 10 are in the range up to yn/cm, which is to be compare to the values up to yn/cm measure for the micellar solutions of two nonionic surfactants Brij 35 an Tween 0 using the Scheluko capillary cell or the Mysels Jones porous-plate cell. 10 The results in Table show that for the sufficiently concentrate %v/v superspreaer SILWET L-77 solutions the measure scaling exponents are close to 9 or 10. On the other han, for the most ilute solution of 1.0 %v/v, the measure exponent is 6.39 ± 0.1. The results in Table 4 show that for the superspreaer BREAK-THRU S 78 only 1.0 %v/v solution reveale the scaling exponent of a high magnitue ± 0.19, the other solutions of the superspreaer BREAK-THRU S 78 ( %v/v) reveale the measure exponent close to 6. The DLS results in Figure imply that in the films forme from the superspreaer solutions of sufficient concentration (efinitely above the cmc) there are bilayer aggregates of sizes larger than the film thickness h. This can be viewe as the presence of multiple sections of bilayer aggregates hanging from the free surface 1 an forming fluffy surfaces of the film as sketche in Figure 1. Steric repulsions of the entropic origin can certainly ecelerate thinning of such films. However, the scaling exponents in Tables an 4 iffer from the preictions for any of the entropic steric repulsions, e.g., those iscusse in refs 7 an 8. It shoul be emphasize that in the present case of solutions of nonionic superspreaers in eionize water formation of ouble layers characteristic of electrolytes is exclue, an thus there is no stabilizing electric forces. In istinction from the superspreaers, the corresponing non-superspreaers SILWET L-7607 an BREAK-THRU S 33 reveale the linear rainage pattern (Figure 5 an Figure S3 of the SI, respectively) an regular horizontal interferometric color bans (Figure 6 an Figure S3 of the SI) with practically no stabilization associate with the isjoining pressure. Such horizontal uniformity of color bans was neither seen for the plane films of the superspreaer SILWET L-77 (Figure 3, the Figure 1. Sketch of fluffy surfaces of the film forme by long hanging superspreaer bilayers. inset images, an Figure 4) solutions, nor for the superspreaer BREAK-THRU S 78 (Figure S, the inset images, of the SI) solutions. Therefore, for the non-superspreaers the only parameter of interest to be eluciate from the present measurements is the surface elasticity ε, which is foun from the measure values of the characteristic time T using the ata in Figures 5 an S3 of the SI, similarly to ref 6. The results for the non-superspreaer SILWET L-7607 solutions are summarize in Table 5, an for the non-superspreaer BREAK-THRU S 33 in Table 6. Table 5. Non-superspreaer SILWET L-7607 Solution Films a solution t (s) t b (s) x (cm) h i = h 0 (nm) T (s) ε (g/s ) L L L L a The film lifetime is enote t; t b enotes the time at which black film sets in at the top of the wire frame. The x column correspons to the position at the film center (reckone from the top) to which the black film reache at the moment of bursting. The initial film thickness at the top is enote h i = h 0 ; the characteristic rainage time is T. The values of the surface elasticity ε were foun from T using eq 17. The ifference between the superspreaers an the cousin non-superspreaers is only in the length of the poly(ethylene oxie) group. Yet, they show raically ifferent rainage behavior, both morphologically an by uration. For example, the rainage of the superspreaer SILWET L-77 an BREAK-THRU S 78 films is by an orer of magnitue longer than the rainage of their non-superspreaer counterparts SILWET L-7607 an BREAK- THRU S 33. The thinning of the superspreaer films was practically arreste by the isjoining pressure at the latter stages of gravitational rainage, whereas the cousin non-superspreaer K

12 Table 6. Non-superspreaer BREAK-THRU S 33 Solution Films a solution t (s) t b (s) x (cm) h i = h 0 (nm) T (s) ε (g/s ) S S S S a The film lifetime is enote t; t b enotes the time at which black film sets in at the top of the wire frame. The x column correspons to the position at the film center (reckone from the top) to which the black film reache at the moment of bursting. The initial film thickness at the top is enote h i = h 0 ; the characteristic rainage time is T. The values of the surface elasticity ε were foun from T using eq 17. films raine without any visible inhibition an laste for only a short time. Morphologically, the interferometric patters of the superspreaer films uring the rainage reveale a turbulent -like motion. On the contrary, the cousin non-superspreaer films showe horizontal interference bans, inicating orere rainage pattern characteristic of the orinary surfactants (refs 6 an 6 an references therein). CONCLUSIONS Gravitational rainage of vertical films suspene on a rectangular wire frame is establishe as a relatively simple metho of measurement of isjoining pressure. The effect of the isjoining pressure is in rastic eceleration of the later stage of the rainage process where the film thickness eviates (at about h < 100 nm) from the linear ecrease sustaine by the interplay of gravity an surface elasticity, an practically stabilizes at about 35 nm. Gravitational rainage of two superspreaers SILWET L-77 an BREAK-THRU S 78 was ramatically stabilize in this manner, even though their interferometric patterns were highly ynamic an turbulent -like. The significant isjoining pressure reveale by the superspreaers is associate with the fluffy surfaces of the film forme by long superspreaer bilayers hanging from the free surfaces (sketche in Figure 1). The ability to form long bilayer elements was attribute in the literature to the shorter length of poly(ethylene oxie) group in superspreaers compare to their non-superspreaer cousin non-superspreaers SILWET L-7607 an BREAK-THRU S 33. The present work showe that these non-superspreaers o not possess any significant isjoining pressure in the nm range of the film thickness. Therefore, the non-superspreaer gravitational rainage procees uninhibite, the thickness ecrease is fully controlle by gravity an surface elasticity, an is not ifferent from the orinary surfactants. The scaling law for the isjoining pressure of the sufficiently concentrate superspreaer solutions are p isj (h) h m (with m 9 11), as well as p isj (h) h s (with s 6) for more ilute solutions (in both cases concentrations were above the cmc). These scaling laws iffer from those known for the entropic steric repulsions. ASSOCIATED CONTENT *S Supporting Information The Supporting Information inclues figures relate to the surface tension measurements using the Wilhelmy plate technique, rainage of the superspreaer BREAK-THRU S 78, an of the non-superspreaer BREAK-THRU S 33, as well as vieos of rainage processes corresponing to those in Figure 6. This information is available free of charge via the Internet at L AUTHOR INFORMATION Corresponing Author *To whom corresponence shoul be aresse. ayarin@uic.eu. Phone: +1(31) Fax: +1(31) Notes The authors eclare no competing financial interest. ACKNOWLEDGMENTS This work was partially supporte by The U.S. Gypsum Corporation (USG). REFERENCES (1) Venzmer, J. Superspreaing-0 years of physicochemical research. Curr. Opin. Colloi Interface Sci. 011, 16, () Walerhaug, H.; Knusen, K. D. Microstructures in aqueous solutions of a polyoxyethylene trisiloxane surfactant an a cosurfactant stuie by SANS an NMR self-iffusion. Langmuir 008, 4, (3) Venzmer, J. (personal communication). (4) Karapetsas, G.; Craster, R. V.; Matar, O. On surfactant-enhance spreaing an superspreaing of liqui rops on soli surfaces. J. Flui Mech. 011, 670, (5) Malarelli, C. On the microhyroynamics of superspreaing. J. Flui Mech. 011, 670, 1 4. (6) Sett, S.; Sinha-Ray, S.; Yarin, A. L. Gravitational rainage of foam films. Langmuir 013, 9, (7) Derjaguin, B. V.; Churaev, V. N.; Muller, V. M. Surface Forces; Plenum Press: New York, (8) Israelachvili, J. Interfacial an Surface Forces; Acaemic Press: Lonon, 199. (9) Nikolov, A. D.; Kralchevsky, P. A.; Ivanov, I. B.; Wasan, D. T. Orere micelle structuring in thin films forme from anionic surfactant solutions. J. Colloi Interface Sci. 1989, 133, 13. (10) Basheva, E. S.; Kralchevsky, P. A.; Danov, K. D.; Ananthapamanabhan, K. P.; Lips, A. The colloi structural forces as a tool for particle characterization an control of ispersion stability. Phys. Chem. Chem. Phys. 007, 9, (11) Alexaner, S. Asorption of chain molecules with a polar hea. A scaling escription. Physique 1977, 38, (1) e Gennes, P. G. Polymers at an interface: A simplifie view. Av. Colloi Interface Sci. 1987, 7, (13) Scheluko, A. Thin liqui films. Av. Colloi Interface Sci. 1967, 4, (14) Exerova, D.; Kruglyakov, P. M. Foam an Foam Films. Theory, Experiment, Application; Elsevier: Amsteram, (15) Mysels, K. J.; Jones, M. N. Direct measurement of the variation of ouble-layer repulsion with istance. Discuss. Faraay Soc. 1966, 4,4 50. (16) Karakashev, S. I.; Nguyen, A. V.; Manev, E. D.; Phan, C. M. Surface foam film waves stuie with high-spee linescan camera. Collois Surf., A 005, 6, 3 3. (17) Karakashev, S. I.; Nguyen, A. V. Do liqui films rupture ue to the so-calle hyrophobic force or migration of issolve gases? Langmuir 009, 5, (18) Karakashev, S. I.; Ivanova, D. S. Thin film rainage: Ionic vs. nonionic surfactants. J. Colloi Interface Sci. 010, 343, (19) Karakashev, S. I.; Stockelhuber, K. W.; Tsekov, R. Wetting films on chemically patterne surfaces. J. Colloi Interface Sci. 011, 363, (0) Karakashev, S. I.; Manev, E. D.; Nguyen, A. V. Effect of oublelayer repulsion on foam rainage. Collois Surf., A 008, 319, (1) Rao, A. A.; Wasan, D. T.; Manev, E. D. Foam stability Effect of surfactant composition on the rainage of microscopic aqueous films. Chem. Eng. Commun. 198, 15, () Danov, K. D.; Kralchevska, S. D.; Kralchevsky, P. A.; Ananthapamanabhan, K. P.; Lips, A. Mixe solutions of anionic an

13 zwitterionic surfactant (Betaine): Surface-tension isotherms, asorption, an relaxation kinetics. Langmuir 004, 0, (3) Phase Behavior of Surface-Active Solutes. Particle Sciences, Drug Development Services, Technical Brief, 01, Vol. 6. (4) Venzmer, J.; Wilkowski, S. P. Trisiloxane surfactants-mechanisms of spreaing an wetting. ASTM Spec. Tech. Publ. 1998, 1347, (5) Hill, R. M. Silicone Surfactants; Marcel Dekker: New York, (6) Lucassen, J. Dynamic properties of free liqui films an foams. In Anionic Surfactants. Physical Chemistry of Surfactant Action; Lucassen- Reyners, E. H., E.; Marcel Dekker: New York, 1981; (7) Berg, S.; Aelizzi, E. A.; Troian, S. M. Experimental stuy of entrainment an rainage flows in microscale soap films. Langmuir 005, 1, (8) Mysels, K. J. Dynamic processes in soap films. J. Gen. Physiol. 1968, 5, (9) Mysels, K. J.; Shinoa, K.; Frankel, S. Soap Films. Stuies of Their Thinning an a Bibliography; Pergamon Press: Lonon, (30) Nierstrasz, V. A.; Frens, G. Marginal regeneration an the Marangoni effect. J. Colloi Interface Sci. 1999, 15, (31) Nierstrasz, V. A.; Frens, G. Marangoni flow riven instabilities an marginal regeneration. J. Colloi Interface Sci. 001, 34, (3) Berg, S.; Aelizzi, E. A.; Troian, S. M. Images of the floating worl: Patterns in thinning soap films. Phys. Fluis 004, 16, S6. (33) e Gennes, P. G. Young soap films. Langmuir 001, 17, (34) Levich, V. G. Physicochemical Hyroynamics; Prentice Hall: Englewoo Cliffs, 196. M