Electrically Controlled Membranes Exploiting Cassie-Wenzel Wetting Transitions

We report electrically controlled membranes which become permeable when an electrical field is exerted on a droplet deposited on the membrane. Micro-porous polycarbonate membranes are obtained with the breath-figures assembly technique, using micro-scaled stainless steel gauzes as supports. The membranes demonstrate pronounced Cassie-Baxter wetting. Air cushions trapped by the droplet prevent water penetration through the membrane. We demonstrate two possibilities for controlling the permeability of the membrane, namely contact and non-contact scenarios. When an electrical field is exerted on a droplet deposited on the membrane, the triple-line is de-pinned and the wetting transition occurs in the non-contact scheme. Thus, the membrane becomes permeable. The contact scheme of the permeability control is based on the electrowetting phenomenon.

PC membranes self-assembled with micro-porous stainless steel supports are depicted in Fig. 3. The average diameter of pores was about 5 mm.
Control of the permeability of membranes by electrowetting. We demonstrate the possibility to control the permeability of the membranes by exploiting the electrowetting effect 7 . When an aqueous electrolyte contacts a solid surface, a double electrical layer is formed [7][8][9][10][11] . The double layer works as a capacitor; thus the effective energy of the solid/liquid interface may be written as: where c 0 SL represents the solid/liquid interface tension at zero voltage, C is the capacitance per unit area of the substrate, and U is the voltage, applied between electrodes as shown in Fig. 1a. Substitution of Exp.
(1) into the Young Formula: cos h~c SA {c SL c , yields for the electrowetting of a flat surface a contact angle h el : Generalization of Exp. (2) for rough and chemically heterogeneous surfaces (and this is the case in our study) was reported in Ref. 11. When a droplet is deposited on PC-coated gauze as shown in Fig. 1a, we have a modification of the EWOD scheme with the gauze serving as an electrode. We established that voltages as high as 250 V are necessary for noticeable change of the apparent contact angle     Such high values of the voltage make the use of membranes problematic.
In order to decrease voltage, we performed hydrophilization of PC membranes with the cold air radiofrequency plasma, as described in detail in the Methods Section. The plasma treatment creates a complex mixture of surface functionalities which influence physical and chemical properties of the surface. In particular, it results in a dramatic change of wetting behavior, resulting in the hydrophilization of the surface [43][44][45][46][47] . The initial apparent contact angle of plasma treated membranes was of 70-80u. It should be emphasized that despite hydrophilization they remained impermeable for water.
After the treatment of membranes with the cold air radiofrequency plasma we succeeded in obtaining water penetration by applying a relatively low voltage of dozens of volts, as shown in Fig. 4. It could be seen from Fig. 5 that a sharp decrease in the contact angle was accompanied by an increase in the contact line radius occurring at 12 V. It is noteworthy that the decrease of the apparent contact angle, evidencing the wetting transition, was attended by the penetration of 5 ml of water through the membrane. Deformation of the droplet was accompanied by detachment (de-pinning) of the triple (three-phase) line of the droplet. The displacement of the triple line established with goniometer is illustrated in Fig. 5. The precise microscopic picture of the water penetration remained unknown, but it is reasonable to suggest that de-pinning of the triple line led to the wetting transition [19][20][21][22][36][37][38][39][40][41] . We established that the maximal displacement of the triple line DR max equaled approximately 0.1R 0 , 100 mm, hence the de-pinned triple line slipped over and filled a dozen lines of pores, as estimated very roughly.
Non-contact electrical control of the permeability of membranes. A uniform electric field of 0-10 kV/cm was applied to the droplet, as shown in Fig. 1b. The electric field sufficient for deformation of the droplet was 2.5 kV/cm as shown in Fig. 6. Deformation of droplets by an electric field results from the complex interplay of electrical, surface tension and gravity-related effects 48 . The free energy G of the droplet exposed to the electric field could be estimated as: where G S , G gr and G el are surface, gravitational and electrical fieldrelated contributions to the free energy respectively, G S > cS > c4pR 2 , G el > e 0 eE 2 V/2, G gr 5 rVgh > rVgR/2, where R, S, V and h are the characteristic dimension, surface, volume and the height of the center mass of the droplet respectively; c, r and e are surface tension, density and dielectric constant of a liquid respectively 48 . The dimensionless constants j and x could be introduced as:   The dimensionless constant j describes the interrelation of gravity and electrical field-induced effects, and the constant x describes the interrelation of surface tension-induced and electrical effects. Substituting R 5 1 mm, r 5 10 3 kg/m 3 , c 5 70?10 -3 J/m 2 , e 5 80 we obtain that when E , 1 kV/cm, j , 1, x , 0.1. It means that in our case the electrical energy is mainly spent as the counteraction to gravity. The deformation of a droplet was accompanied by the de-pinning of the triple line and water penetration through the membrane, as shown in Fig. 7. However, the displacement of the triple line was much less pronounced when compared to the electrowetting experiment. The maximal displacement of the triple line DR max was equal to approximately 0.02R 0 , 20 mm, hence in this case the de-pinned triple line slipped over and filled only a couple of the lines of pores (recall that the average size of the pore was of 5 mm).

Discussion
The electrically controlled permeability of the membranes demonstrated in our study is based on the effect of the Cassie-Wenzel wetting transitions [19][20][21][22][36][37][38][39][40][41][42] . In our investigation wetting transitions were stimulated by exerting electric field on the liquid/porous solid system. One of the most debatable problems in the field of wetting is the problem of the "dimension" of the transitions, or, in other words: whether all pores underneath the droplet should be filled by liquid (the "2D scenario"), or perhaps only the pores adjacent to the threephase (triple) line are filled under external stimuli such as pressure, vibrations or impact (the "1D scenario") 34,20,37-42 . Our investigation does not supply an unambiguous answer to this question, but it demonstrates explicitly that the wetting transition is accompanied by a micro-metrically scaled displacement of the triple line depicted in Figs. 5, 7. It is plausible to suggest that the Cassie-Wenzel wetting transitions are mainly governed by wetting events occurring in the nearest vicinity of the triple line, as demonstrated in a series of recent investigations 34,[37][38][39][40][41][42] .
We conclude that electrically driven membranes obtained with breath-figures self-assembly allow a low voltage (,10 V) control of water penetration under conditions of electrowetting. The noncontact control of water penetration through membranes is also reported, however, it needs much higher voltage for the electrical deformation of a droplet. The permeability of membranes results from the Cassie-Wenzel wetting transitions, accompanied by the displacement of the triple line registered in both contact and non-contact schemes; however, the displacement of the triple line is more pronounced under conditions of the electrowetting experiment.

Methods
Membranes were manufactured with the fast dip-coating process. Stainless steel gauzes (depicted in Fig. 2) were used as carrying supports 23 . A 4 wt.% PC solution was prepared by dissolving the polymer in a mixture of chlorinated solvents (chloroform, CHCl 3 , 8 wt.% and dichloromethane CH 2 Cl 2 , 88 wt.%, were supplied by BIO-LAB Ltd, both solvents were of the chemical grade purity). Thoroughly cleaned stainless steel gauzes were pulled vertically at a high speed of v 5 40 cm?min -1 from the polymer solution and dried at room temperature and a rH of 50% in an environmental cell. Rapid evaporation of the solvent cooled the solution/humid air interface subsequently resulting in an intensive condensation of water droplets at the interface [24][25][26][27][28][29][30] . Water droplets then sank into the solution eventually forming microscaled pores typical for breath-figures self-assembly [24][25][26][27][28][29][30] . The topography of the membranes was studied with SEM (JEOL JSM 6510 LV, Japan).
Hydrophilization of membranes was achieved by exposure to an inductive cold air plasma discharge under the following parameters: the plasma frequency was on the order of 10 MHz, the power was 20 W, the pressure was P 5 6.7 ? 10 22 Pa, the volume of the discharge chamber was 45 cm 3 . The time span of irradiation was 10 s. After treatment, membranes were kept for 150 hours under ambient conditions (24uC and 50% rH) necessary for the hydrophobic recovery occurring after cold plasma treatment [44][45][46] . The apparent contact angle after completion of the hydrophobic recovery was approximately 90u (mean of 10 measurements).
Distilled water (pH 5 6; s 5 2.5 mS) was used for the electrowetting-driven water penetration study; a 98 wt.% water/ethanol solution was used for the non-contact scheme. Ethanol (chemical grade, 96% purity) was supplied by BioLab Ltd Israel.
Contact angles were established using a Ramé-Hart goniometer (model 500). Ten measurements were taken to calculate the mean apparent contact angle.