Supplementary Information

Supplementary Information Under-water Superoleophobic Glass: Unexplored role of the surfactant-rich solvent Authors: Prashant R. Waghmare, Siddhartha Das, Sushanta K. Mitra * Affiliation: Micro and Nano-scale Transport Laboratory, Department of Mechanical Engineering, University of Alberta, Edmonton, Canada, T6G 2G8. *Correspondence to: E-mail: sushanta.mitra@ualberta.ca This file includes: Supplementary Sections 15 Supplementary Figures S1S6 Supplementary Table S1 Supplementary Equations (S1S23) Supplementary References (110) 1

Figure S1: Schematic of the experimental setup used for the measurement of the contact angles. Inset (a): The drop of 2 µl is generated inside the cuvette and the needle holding this drop is retracted in the direction of the arrow. Inset (b): The moment the tip of the needle hits the air-water interface the oil drop detaches from the needle and falls down on the glass substrate. The hollow drop images show the intermediate positions whereas the filled images show the initial and the final positions. Inset (c): The image of the drop immediately after its deposition on the substrate. 2

Surfactant Equilibrium Standard Error in Spreading Standard Error in Concentration Contact Angle Equilibrium Contact time (s) Spreading time (µm) (degrees) Angle (± degrees) (± s) 10 134.5 0.5 1.04 0.06 30 131.9 0.5 1.15 0.06 50 128.8 0.5 1.16 0.08 60 121.7 0.5 1.58 0.06 80 126.2 0.5 3.20 0.26 100 144.7 0.9 10.34 0.72 200 Rolling NA NA 400 Rolling NA NA 800 Rolling NA NA Table S1: Variation of the equilibrium contact angle and spreading time (and the corresponding standard errors) as a function of the surfactant concentrations. Beyond c=100 µm, the oil drop does not spread; hence the corresponding spreading time is reported as Not Applicable (NA). 3

Supplementary Section 1: Estimation of the Weber number of the oil drop at the time of impact on the surfactant-covered glass surface To calculate the Weber number of the oil drop depositing on the glass substrate, we first need to obtain the speed at which the drop impacts the surface. The oil drop is deposited from the air-water interface and impacts the substrate after descending a height h, which is the height of the liquid column inside the cuvette. During its trajectory inside the water, the oil drop is subjected to the downward gravitational force and the upward buoyancy and the viscous drag forces. Therefore, one can express the oil drop velocity v (in the downward direction) as: m dv dt mg F B F D, (S1) where F B and F D are the buoyant and the drag forces on the oil droplet, m is the mass of the oil droplet and g is the acceleration due to gravity. Using F D =kv (where k~6r is the drag coefficient, is the dynamic viscosity of water and R is the radius of the oil drop), m=4r 3 oil /3 ( oil is the density of the oil) and F B =4R 3 w g/3 ( w is the density of the water), we can rewrite Eq. (S1) as: dv dt k 2 k 1 v, (S2) where k 2 =g(1 w / oil ) and k 1 =k/m~9/2r 2 oil. For our case, oil =1060 kg/m 3. Hence the oil is heavier than water, implying that k 2 is positive. Integrating Eq. (S2) in presence of the condition v(t=0)=v 0, we get: v v 0 k 2 exp k t 1 k 2. k 1 k 1 (S3) 4

Expressing v=dx/dt, we can integrate Eq. (S3) once more under the condition x(t=0)=0 to obtain: x 1 v k 0 k 2 1 1 exp k t 1 k t 2. k 1 k 1 (S4) For the present case the system parameters are x=h=25 mm, t~0.1 s (obtained from the experiment; for all the surfactant concentration this time scale remains more or less constant), R=0.78 mm (corresponding to a drop volume of 2 l), =0.001 Pa-s, w =1000 kg/m 3, oil =1060 kg/m 3 and g=9.8 m 2 /s. Therefore, from Eq. (S4), we can obtain v 0 =0.1134 m/s, which can be used in Eq. (S3) to obtain the velocity of the impacting drop as v(t~0.1s)=0.0964 m/s. Therefore, the corresponding Weber number of the impacting drop (with ow ~0.02 N/m, for c=30 M 1 ), is We= oil Rv 2 / ow ~0.38. Hence, the Weber number is substantially small to ensure that the drop does not bounce off. Another check to substantiate that the velocity of the impacting drop is small enough to ensure a composite interface 2 (or equivalently a CB state), is to ensure that the resulting dynamic pressure p d is less than the corresponding Laplace pressure 2, i.e., p d 1 2 oil v2 2 ow R v 32 ow H oil 2P D. (S5) 2 This critical velocity oil 32 ow H 2P D is the smallest for the case of the largest possible value 2 of P, i.e., P~1 m, and the least possible value of H, i.e., H~1 nm, and that value is 0.6 m/s. Therefore this critical value is much larger than the velocity of the impacting drop (~0.09 m/s), ensuring that there will indeed be a formation of the composite interface or a CB state 2. 5

Supplementary Section 2: Variation in the surfactant-mediated pillar -structure on account of interplay of the wettability of the solid and the wettabilities of the different segments of the Tween 20 molecule Tween 20 surfactant molecule consists of a hydrophobic alkyl tail and a hydrophilic head consisting of the ethylene-groups 3. Figure 1e, which depicts the proposed pillar -like structure formed by the interacting surfactant molecules, does not consider the possible interplay between the original wettability of the hydrophilic glass surface and the wettabilities of the different segments of the Tween 20 molecule. Glass being hydrophilic, it is necessarily the hydrophilic segment of the Tween 20 molecule that would get attached to it (by replacing the water molecules in contact with the hydrophilic surface, and this event occurs when the hydrophilic head of the surfactant molecule can form strong enough bond with the hydrophilic surface) and the hydrophobic tail will face the water. Such a behavior can be comprehended as follows: glass being very hydrophilic, it will always try to retain a layer of water molecules adsorbed to it. Therefore, in order for the Tween 20 molecule to get adsorbed on the glass, Tween 20 needs to replace the water molecules that are originally adsorbed on the glass. On a hydrophilic surface, it is only another hydrophilic component that can replace water. Hence, quite intuitively, it is the hydrophilic head of Tween 20, which would be stuck to the glass and the hydrophobic tail directed towards the bulk 4. However, at the oil water interface, the Tween 20 molecule will be so oriented that the hydrophilic head group faces the water. Hence the configuration of interacting surfactant molecules will be somewhat different as compared to Figure 1e in the main text. This altered configuration and the resulting pillar -like structure has been depicted in Figure S2. However, we think that the parameters characterizing the pillars in Figure 1e in the main text, 6

will be identical to those characterizing Figure S2. Therefore, Eq. (1) and Eq. (3) (see the main text) denoting the CB and Wn states, on the basis of the parameters pertaining to the pillars (in Figures 1e, S2), will remain unaltered. Figure S2: Orientation of the adsorbed surfactant molecules taking into consideration the interplay between the wettability of the different segments of the surfactant molecule (Tween 20 consists of a hydrophilic head and a hydrophobic tail) and the wettability of the solid such considerations invariably require the hydrophilic head of the Tween 20 molecule adhering to the solid (which is hydrophilic glass) and the hydrophobic tail of the Tween 20 molecule being directed towards the bulk 4. We also demonstrate the pillar formation due to interaction of the surfactants in this configuration. We would like to mention here an important issue regarding the configuration depicted in Fig. S2. In this figure, the hydrophobic tail (consisting of the alkyl chains) of the surfactant faces the water, whereas the hydrophilic head is adhering to the substrate. As explained above, such a 7

configuration stems from the fact that only the hydrophilic part of the surfactant molecule can replace (and therefore adsorb on the solid) the water molecules having strong affinity to the hydrophilic glass surface immersed in water. This configuration, on the other hand, creates a much greater carbon-water interaction area, since the hydrophobic tail consisting of the alkyl chains faces the water. Carbon-water interactions are energetically unfavored, which is very much understandable given the hydrophobic nature of the surfactant tail consisting of the alkyl chains. Therefore, whether the surfactant orientation would be as depicted in Fig. S2, or as that depicted in Fig. 1e (where hydrophilic head groups face the water) would be dictated by the net energy change as a combination of the two processes, namely the hydrophilic tail replacing the water molecule on the under-water hydrophilic glass surface and the hydrophobic tail facing the water. 8

Supplementary Section 3: Cassie-Baxter and Wenzel states caused by the interacting surfactant molecules: Role of the side chains of the Tween 20 molecule The analysis in the present paper is based on the hypothesis that the surfactant molecules adsorbed at the solid-liquid interface and at the oil-water interface would interact and form pillar -like structures (depicted in Figures 1e, S2), which ensure that the oil drop is at a Cassie- Baxter conformation, and depending on the pillar dimensions, the drop may or may not transit to the Wenzel state. In this section, we shall discuss the dependence of the contact angles in Cassie Baxter and Wenzel states of the drop as a function of the dimensions of the pillars, which in turn depends on the structure of the interacting Tween 20 molecules. The contact angle for a drop in Wenzel state is expressed as: cos Wn R f cos Y, (S6) where following Bhushan and Jung 5, we can state that R f is a roughness factor defined as R f =A SL /A, with A SL being the solid-liquid (liquid phase in the drop) contact area and A being the area projected on a flat plane. First, let us consider that the surfactant molecules form simple pillars, as shown in Figures 1e, S2. This structure does not take into account the effect of the 3 ethylene oxide side chains of the Tween 20 molecule. These simple pillars are considered to be cylindrical with height H, diameter D and pitch P, so that we get: A SL A N P DH, (S7) where N P is the total number of pillars expressed as N P =A/P 2. Hence, from Eq. (S6) we shall get the Wenzel drop contact angle as: 9

cos Wn A A P 2 DH A cos Y cos Wn 1 DH cos Y, P 2 (S8) which is Eq. (3) in the main paper. In case we consider the effect of the structure (presence of 3 ethylene oxide side chains) of the Tween 20 surfactant molecule in affecting these pillar -like structures, these pillars will attain a hierarchical structure as shown in Figure S3. The concept of such configuration of the Tween 20 molecule, accounting for ethylene oxide side chains, has been reported elsewhere 6. For the pillar structure shown in Figure S3, we can write A SL A N P DH 2 n sc d sc h sc, (S9) where n sc is the number of side chains (for each Tween 20 molecules) and d sc and h sc are the dimensions of the hierarchical structures (of the hypothetical pillars) formed by these side chains (please see Figure S3). Therefore, using N P =A/P 2, we shall get: cos Wn 1 DH P 2 2 n sc d sc h sc P 2 cos Y, (S10) which is Eq. (4) in the main paper. For a drop in Cassie-Baxter state, we can express the contact angle as: cos CB R f f SL1 cos Y f L1 L 2, (S11) where (using L 1 to denote the liquid inside the drop and L 2 to denote the liquid surrounding the drop; L 2 is air, if the surrounding medium is air), where f SL1 and f L1 L 2 are fractional flat geometrical areas of the solid liquid (drop) and liquid (drop)-liquid(surrounding medium) interfaces below the drop. For simple (non-hierarchical) cylindrical pillars (i.e., if we do not consider the effect of the structure of the Tween 20 molecules), we have: 10

f SL1 1 f L1 L 2 D 2 N P 4 A. (S12) Using N P =A/P 2, we shall get: f SL1 1 f L1 L 2 D2 4P 2. (S13) Also the pillars being assumed to have flat tops (i.e., the drop is in contact with flat tops), we have R f =1. Consequently, the contact angle for the drop in CB state becomes: cos CB D2 cos 4P 2 Y 1 1, (S14) which is Eq. (1) in the main paper. When the pillars have hierarchical structures (i.e., we account for the 3 ethylene oxide side chains of the Tween 20 molecule, see Figure S3), as has been conjectured here, we shall have (with N P =A/P 2 ): f SL1 D2 4P 2, (S15) f L1 L 2 A 1 N P D2 4 2n sc d sc h sc A 1 D2 4P 2 2n sc d sc h sc P 2. (S16) Hence, we have (with R f =1, since the drop is in contact with flat tops). cos CB D2 cos 4P 2 Y 1 1 2 n sc d sc h sc which is Eq. (2) in the main paper. P 2, (S17) 11

Figure S3: Hierarchical pillar -like structure formed by the interacting Tween 20 molecule with ethylene oxide side chains (such representation of the Tween 20 molecule with ethylene oxide side chains has been reported elsewhere 6 ). These hierarchical pillars are characterized by a large cylinder (analogous to Figures 1e and S2) with height H and diameter D, whereas the hierarchical structures are characterized by smaller cylinders (having axis perpendicular to the axis of the larger cylinder) with height h sc and diameter d sc. As a closing remark of this subsection, it is important to mention here that chances are that at c=400 M, surfactants adsorb on the glass as hemi-micelles 7. This is particularly relevant given the hydrophilic nature of the glass surface, which would require that the adsorbing surfactant molecules have lesser contact area with the glass hence the surfactants which form micelles in the bulk solution (for c=400 M, i.e., c>>c CMC ) would adsorb and remain on the solid as hemi-micelles, without showing any tendency to spread further (such spreading would have happened in case the solid was hydrophobic). In case surfactants have formed such hemimicelles at the solid, the quantification of the Wenzel and Cassie-Baxter angles would not be the 12

same as that expressed in Eqs. (1-4) in the main paper. These equations need to be modified based on wetted solid-liquid areas. However, the qualitative dependences of the Wenzel and the Cassie-Baxter angles on the parameters (such as the pitch or the other dimensions of the hypothetical pillars ) would remain unaltered, so that our theoretical hypothesis remains perfectly valid. 13

Supplementary Section 4: Scaling estimate of the time t required for the oil drop to spread after it has impacted the glass surface As the drop undergoes a transition from the CB state to the Wn state, it is subjected to different forces that eventually decide the scaling of t. The oil drop transits from the CB to Wn state under the influence of the deforming Laplace pressure 2. This force can be expressed as, under the condition that the area of the deforming oil drop scales as R: F L ~ ow R R ~ ow. (S18) As the surfactant-laden oil-water interface of the oil drop approaches the surfactant-covered glass substrate, there are several other interaction effects between the surfactant molecules at these two interfaces. These interaction effects eventually ensure a net force on the oil drop (since there is a layer of surfactant molecules adsorbed at the oil-water interface). Here we express the scaling behavior of these interactions. First is the attractive van der Waals (vdw) interaction force between the interacting surfactant molecules, and can be expressed as: F vdw ~ N S k B T, (S19) where N S is the total number of interacting surfactant molecules. The other important interaction between the surfactant molecules is the entropic interaction, which gets manifested as the Steric interactions 8. These interactions are repulsive in nature and outweigh the attractive influences vdw forces. These entropic Steric interactions can be triggered once two layers of non-ionic polymeric surfactant molecules inter-penetrate or compress each other. Hence they are made up of two contributions, namely the force due to 14

interpenetration effect F St Ip (Fig. 1f, top) and the force due to the elastic deformation of the surfactant molecules F St E (Fig. 1f, bottom), and can be expressed as 8 : F St F St IP F St E ~ N S k B T. (S20) Therefore, it is of the same order as the vdw attractive influence; however it would be necessarily larger (in magnitude) than the vdw effect, or else there will be no existence of any inhomogeneous wetting state like the CB state. Therefore, the interaction force would scales as: F I ~ F vdw F St ~ N S k B T ~103 cr 2 N A k B T. (S21) Please note that in the above discussions, we have only considered scaling estimates of the entropic Steric interactions, and have not considered modifications on account of effects such as regimes of conformations of the polymer chains constituting the surfactant molecules 8, concentration dependence of the interpenetration effect 8,9, surfactant-solvent interaction parameter 8,10, surfactant segment density distribution dependence of the elastic effect 8, etc. Before using Eq. (S18) and Eq. (S21) to obtain the scaling of t, we compare the magnitude of the forces F L and F I. For c =100 M, ow ~0.01 N/m 1 and ~1 nm, so that we get [using Eq. (S18)] F L ~10 11 N and [using Eq. (S21)], F 1 ~10 11 N (with R~1 mm). For smaller surfactant concentration, the retardation force is smaller (due to smaller c) and the driving pressure force is higher (due to larger ow ), leading to a faster spreading dynamics (or smaller t) justifying the observations of Figure 1c. Also to obtain this t we can write the force balance as: 15

oil V oil d 2 x dt 2 F L F I. (S22) Using d 2 x/dt 2 ~R/(t) 2, we can use equations. (S18), (S21), (S22), to obtain the scaling of t as: t ~ oil V oil R ow 10 3 N A k B TcR 2, (S23) which is Eq. (7) in the main paper. 16

Supplementary Section 5: Methodology to choose the pillar parameters from the AFM results and other observations AFM results corresponding to a scan area of 1m1m and different surfactant concentrations have been provided in Figure 2 in the main paper. There is an interesting observation corresponding to Figure 2c. We observe distinct periodic horizontal lines on the substrate. We perform experiments by rotating the glass substrate (about a vertical axis) and these periodic lines get rotated. Therefore, we conclude that these lines are caused by the adsorption of surfactants, and are not any artifact. The most important part of the AFM roughness data (Figure 2) is that they allow us to obtain the parmeters P, D and H that characterize the pillars formed by the surfactants. The diameter D is obtained from the approximate estimate of the thickness of the surfactant molecules, which is more or less independent of the concentration. We do not have appropriate estimate of this diameter D; however, this does not affect our analysis, as long as we can assume D<<P, which is invariably the case for any concentration (even if the surfactant adsorb as halfmicelles, see later for more explanation). Secondly, we can obtain H value directly from the scale bars of the AFM data: we can clearly see that for small to intermediate surfactant concentration, we have H~1 nm or H<1 nm, whereas for larger surfactant concentration, we have H>1 nm. Another key parameter is the pitch P. To obtain P we analyze the surface height data at different locations. For large or intermediate surfactant concentrations (e.g., c=400m or 100 M), we can characterize the pitch as the distance between two successive maxima (in height), as illustrated in Figs. S4,S5. Here, we first provide analysis for the case of 400 M (Fig. S4) and 100 M (Fig. S5). Through this analysis, it is demonstrated that for c=400 M, P~10 nm and H~3-4 nm, whereas for c=100 M, P~50 nm and H~1 nm. Therefore these results establish our 17

foundation of hypothesis based on the fact that the increase in the surfactant concentration decreaeses the pitch and increases the height of the hypothetical surfactant-mediated pillars. Please note that for larger concentrations (e.g., c=400 M), the surfactants may adsorb on the solid as hemi-micelles (also see end of section S3) 7. For such a case the maximum height values are located at the top of the hemi-micelles, and hence in this proposed method the pitch is quantified as the distance between the top of the adjacent adsorbed hemi-micelles (or the centerto-center distance between the hemi-micelles). However, in case one argues to represent the pitch as the space between the adsorbed hemi-micelles, then the pitch would be different than that described above. This difference would be less significant provided P>>R hm (where R hm is the radius of the hemi-micelles). In the present case the approximation P>>R hm is very much valid, as evident from Fig. S4, which shows P20 nm and R hm H3-4 nm. 18

Figure S4: (a) AFM height trace image of glass substrate for 400 μm surfactant concentration. (b) Roughness height variations in the indicated zone along the horizontal section AA identified in (a). In (b), we obtain the pitch P (always expressed in nanometers) as the distance between the adjacent maxima. 19

Figure S5: (a) AFM height trace image of glass substrate for 100 μm surfactant concentration. (b) Roughness height variations in the indicated zone along the horizontal section AA identified in (a). In (b), we obtain the pitch P (always expressed in nanometers) as the distance between the adjacent maxima. Getting the pillar -parameters for c=30 M are much less obvious. Here the adsorption of surfactant molecules on the surface is very minimal, and the peaks in the roughness profile are 20

often representative of the water molecules adsorbed (or layered) on the hydrophilic glass surface. Hence the pitch here cannot be quantified by obtaining the distance between the adjacent peaks. Rather, we first need to determine which one of the peaks represents an adsorbed surfactant and not a water molecule. This can be easily determined from the peak value that would be substantially higher than the peak values corresponding to the layering of the water molecules. In Fig. S6, we get such a peak value (~0.5 nm), which represents a height that is much larger than the adsorbed water molecule, and such a peak value is obtained only over a distance of 400-500 nm [we have done line section analysis at locations other than that depicted in Fig. S6a, and the spatial frequency of arriving at such peaks (representing adsorbed surfactants) is pretty similar]. Therefore, for c=30 M, we indeed get P~1 m. 21

Figure S6: (a) AFM height trace image of glass substrate for 30 μm surfactant concentration. (b) Roughness height variations in the indicated zone along the horizontal section AA identified in (a). Here the pitch is calculated by the spatial frequency of occurrence of maxima values that are substantially larger than the values corresponding to water molecular dimensions. 22

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Supplementary Movie 1: We generate a silicone oil drop (volume: 2 l) at the tip of a needle, which is inserted inside the solution (containing 30 M Tween 20 surfactant). Then we attempt to deposit the drop on the glass substrate. The oil drop does not form any contact with the substrate and simply lifts off from the substrate adhering to the needle. This is a major difficulty associated with the drop deposition with the conventional technique in the present case. (QuickTime format; 67 KB) Supplementary Movie 2: We generate a silicone oil drop (volume: 2 l) at the tip of a needle, which is inserted inside the solution (containing 30 M Tween 20 surfactant). Then we attempt to deposit the drop on the glass substrate. Contrary to the previous case (Supplementary Movie 1), the oil drop forms a finite contact with the substrate as we bring the needle close to the substrate. However, as the needle is lifted the drop gets detached from the substrate and lifts off with the needle. This is another type of difficulty associated with the drop deposition in the present case. (QuickTime format; 71 KB) Supplementary Movie 3: A silicone oil drop (volume: 2 l) is deposited from the air-water interface inside the solution (containing 100 M Tween 20 surfactant). It gets deposited on the glass substrate (thereby forming a CB state), and does not bounce off (since the Weber number is substantially small, see the Supplementary Section 1). Then after a finite time gap, the drop spreads (CB-to-Wn transition) and attains an equilibrium state (contact angle 144.78 0 ). 24

(QuickTime format; 63 KB) Supplementary Movie 4: A silicone oil drop (volume: 2 l) deposited on the glass substrate inside the solution (containing 200 M Tween 20 surfactant) rolls with an inclination (roll off angle) of 1/12 th of a degree (~ 5 minutes). (QuickTime format; 79 KB) 25