Emergence of branched wetting states on a smooth surface

Emergence of branched wetting states on a smooth surface | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Physical Sciences - Article Emergence of branched wetting states on a smooth surface Mizuki Tenjimbayashi, Shunto Arai This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4493821/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract When the droplet is cast on the solid surfaces, part of the droplet/solid surface is replaced by their interface, and a wide variety of shapes and adhesion modes, from spreading1, sticky2, to super-repellent3, appears. In principle, droplets on a smooth surface exhibit a single wetting state. According to Young's law in 1805 4, the shape of a droplet, quantified with contact angle, is determined by the balance of substance-specific interfacial energies between three phases of a droplet, contacting solid surface and surrounding media4. Contact angles fluctuate due to external disturbance and the mobility of contact line 5, but the applicable range is generally fixed, which features the adhesion mode of the droplet. Here we show the emergence of branched wetting states with different contact angle ranges using the same droplet and surrounding media on a smooth, homogeneous surface. The applicable wetting states are high-contact angle droplet sticks to the surface or repellent, akin to the Wenzel 6 or Cassie 7 states observed on a nano/micro-textured surface, respectively. The phenomenon is commonly observed when site-specific molecular interactions trap the droplet metastable —the wettability branches when the interface formation order changes. This is because the molecular interactions at interfaces cause hysteresis in phase replacement under certain wettability conditions. Our experiment varied the combination and number of interaction molecules in phases, unravelling the design principles of the branched wettability. This work suggests that the site-specific molecular interaction can bifurcate macroscopic wetting modes, which advances the fundamental understanding of the molecular effect on macro-wettability. Physical sciences/Materials science/Soft materials/Wetting Physical sciences/Chemistry/Surface chemistry Figures Figure 1 Figure 2 Figure 3 Figure 4 Main Droplet static/dynamic shapes are quantified with contact angles. While the static contact angle θ s is obtained at the equilibrium of three-phase interfacial energies 4 , the maximum/minimum contact angle is observed when the contact line advances/recedes, namely advancing/receding contact angles θ a/r 5 . The mobility of the contact line depends on the degree of surface heterogeneity. Although most objects' surfaces are not perfectly homogeneous, at least on the molecular scale 8 , a surface with much smaller scale of heterogeneity than the radius of curvature of the droplet contact line can be regarded as a homogeneous surface 9 . A droplet on a homogeneous surface basically exhibits a single inherent contact angle range, namely a single wetting state. When the solid surface has nano- or micro-textured surfaces, on the other hands, the droplet follows two branched wetting states: (i) the droplet homogeneously infusing the texture (Wenzel state) 6 or (ii) limited contact to the texture's outermost surface (Cassie state) 7 . The difference between Wenzel and Cassie states is whether the texture is infused by droplet phase or surrounding media (Typically air or droplet immiscible liquids). Model equations of Wenzel and Cassie states explain that surface roughness increases the apparent contact angle θ * more than the angle on the smooth surface. In Wenzel state, surface roughness r is defined as the ratio of actual per projected surface area, and we obtain cos θ * = r cos θ s . In Cassie state, the area fraction of droplet texture contact area f s is defined, and we obtain cos θ * = −1+ f s (1+cos θ s ). Droplet adhesion property accessed by θ r is drastically different between these two states owing to their contacting behaviour 10 . In Wenzel state, the surface texture enhances the droplet−surface contact area, resulting in highly sticky droplets, and we observe θ * >> θ r . In Cassie state, the droplet adhesion area is negligibly small, which explains θ * ≈ θ r . Wenzel and Cassie states co-exist on the textured surface, one of which is energetically favoured. However, the energetic barrier in phase replacement between the droplet and surrounding media is formed by surface texture, which enables observation of the other metastable state 11 . Thus, the surface texture plays a significant role in the emergence of the branched wettability. According to the model equations, when the surface texture goes to smooth ( r and f s →1), model equations result in the same cos θ * = cos θ s , indicating that these wetting states are unified. Thus, droplets on a smooth surface are thought to exhibit a single wetting state when the surface texture is diminished. Here, we wonder whether site-specific molecular interactions at interfaces can regulate the energetic barrier in phase replacement without relying on the surface texture. In this work, we show that the two drastically different wetting states, which satisfy the wettability feature by Cassie and Wenzel, can co-exist on a smooth surface as the result of molecular scale wettability modulation. The static/dynamic wettability features of these states are experimentally confirmed, and the underlying mechanism is studied on a molecular scale interaction, thermodynamics, and force measurement. Finally, based on the proposed mechanism, we show that the branched wettability can be extended to different phase combinations. Two wetting states on a smooth surface Self-assembled silane monolayer can regulate the surface chemistry of the contacting substrate without texturing 12 . Here, the probe surface is the glass substrate containing a monolayer of phenylsilane. The surface has no texture ( Fig ure 1 a ), and the atomic force microscopy (AFM) measurement quantified the surface root-mean-square roughness of R q = 0.41 nm ( Figure 1b ). In addition to the hydrophobic phenyl group, the surface has a hydrophilic silanol group from the glass surface and hydrolysis of phenylsilane, confirmed from the infrared spectrum ( Extended Data Figure 1 ). The water contact angle in air is ( θ s , θ r ) = (79.4 ± 1.9°, 60.8 ± 1.3°). In changing the surrounding media from air to liquid state hydroxyl-terminated polydimethylsiloxane (PDMS−OH) with specific hydrophobic-hydrophilic balance HLB = 0.12 13 , the water droplet behaviour branched in sticky or repellent ( Fig ure 1 c , 1 d , and Movie 1 ). The applicable wetting states depend on the order of the interface formation (see Extended Data Figure 2 ). On the one hand, the droplet, cast on the probe surface after the PDMS−OH immersion (denote postcast droplet), has the water contact angle of ( θ * , θ r ) = (175.8 ± 0.5°, 173.0 ± 0.5°), exhibiting nearly perfect hydrophobicity but has observable small water adhesion (see Extended Data Figure 3 , Movie 2 ), which satisfies Cassie state feature θ * ≈ θ r . On the other hand, the droplet, cast before the immersion (denote precast droplet), exhibited ( θ * , θ r ) = (130.6 ± 3.8°, 107.4 ± 1.5°), follows Wenzel-like wetting behaviour θ * >> θ r . In both droplets, θ a reaches nearly 180°, which means PDMS−OH firmly adheres (that is equal to PDMS−OH receding angle being nearly 0°) to the probe surface and prevents contact line advance. Interfacial states Branched wetting states are observed at a specific HLB range. In Figure 2a , we pre/postcast water droplets on the probe surface under PDMS(−OH) with different HLB values. The probe PDMS (HLB = 0), PDMS−OH ( HLB = 0.12), and PDMS−OH ( HLB = 0.73) have a similar surface tension of γ o = 19.8 ± 0.3, 19.9 ± 0.2, and 21.4 ± 0.4 mN/m, and viscosity of η ≈ 50, 40, 35 mPa·s, respectively. Under PDMS ( HLB = 0), the two droplets exhibit similar contact angles of ( θ * , θ r ) = (124.8 ± 4.0°, 83.6 ± 3.8°) and (118.1 ± 4.4°, 83.0 ± 5.0°), which satisfies wetting feature of Wenzel state. In contrast, two droplets under PDMS−OH ( HLB = 0.73) exhibit contact angles of ( θ * , θ r ) = (169.7 ± 1.1°, 168.0 ± 3.9°) and (166.9 ± 2.0°, 146.2 ± 6.4°), both of which behave like Cassie-state droplets because of their high θ r . In HLB = 0.12, the branched repellent/sticky droplet behaviour is observed ( Figure 1c, 1d ). The possible interfacial states of Cassie-like (Configuration C) and Wenzel-like (Configuration W) droplets are illustrated in Figures 2b and 2c , respectively. In configuration C ( Figure 2b ), observed under PDMS−OH conditions, the droplet repellency is owing to the limited contact of the water−substrate, indicating that PDMS−OH is entrapped beneath the droplet. Since the postcast droplet under PDMS sticks to the substrate ( Figure 2a , left), the molecular interaction works to stabilise the PDMS−OH between the droplet and substrate works. We consider this interaction to be hydrogen bonding between water − PDMS−OH (HB Water-PDMS ) and the PDMS−OH – silanol interface (HB PDMS-Silanol ). Moreover, the oleophilic interactions between the PDMS−substrate phenyl group enhance entrapped PDMS−OH stability. In the absence of a phenyl group on the substrate, for example, on the unmodified glass substrate, the PDMS layer is replaced by water, and both pre/postcast droplets exhibit high wettability ( Extended Data Figure 4 ). In configuration W ( Figure 2c ), observed under PDMS or precast droplet under PDMS−OH ( HLB = 0.12) ( Figure 2a , left and middle), the droplet sticking property is owing to the direct contact between water and substrate. Water molecules have a higher affinity to the silanol than the phenyl group because of the possible hydrogen bonding with substrate silanol groups (HB Water-Silanol ). Hence, the applicable configuration depends on sticking the PDMS(−OH) onto the substrate beneath the water droplet by possibly forming HB PDMS-Silanol . To validate the HB PDMS-Silanol , we calculated intermolecular interaction energies based on density functional theory incorporating Grimme's dispersion correction 14 (see Methods for details). Figure 2d shows the interaction energy depending on the distance between PDMS (−OH) and the silanol. We optimised the rotation degree of freedom for these molecules around the molecular long axes. The potential depth near the interaction energy minimum is shallow for PDMS, whereas it is sufficiently large for PDMS−OH compared with the thermal fluctuation energy. The origin of this significant attractive interaction is explained based on the electrostatic interactions. Figure 2e shows the electrostatic potential map between the end of PDMS−OH and the silanol group. This colour map shows the O (or H) of the silanol attracts the H (or O) of the PDMS−OH, suggesting the formation of a hydrogen bond. Although the long-range interaction decays with a distance from the substrate, it is still large compared to the thermal effect with a distance of 5−6 Å This indicates that PDMS−OH forms sufficiently strong HBs even with silanol groups covered by phenyl groups (about 4 Å height), resulting in the formation of stable lubricant layer on the substrate surface compared with PDMS. Assuming the water−substrate contact is limited to HB Water-Silanol region and its interfacial energy is negligibly small, we can modify the classical Cassie equation to cos θ * = −1 + 2 f s , which is applicable for both configurations. From Figure 1c, we estimate f s = 0.17 ± 0.02 and 0.0014 ± 0.0003 for precast/postcast droplets under PDMS−OH ( HLB = 0.12). Since the precast droplet is in configuration W, we can quantify the silanol group fraction on the probe substrate as f silanol = f s = 0.17 ± 0.02. While this, the postcast droplet is in configuration C and ideally f silanol = 0. Overall, we obtain the contact angles of the branched droplets: cos θ * = −1 for configuration C, and cos θ * = −1+ 2 f silanol for configuration W. We then compared the total energies between the two configurations ( Figure 2f ). We assumed the unit area total interfacial energy γ total difference between two configurations to be Δγ = γ so + γ ow – γ sw , where γ so, ow, sw is unit interfacial energy and subscripts mean, s: substrate, o: PDMS (−OH), and w: water (see methods for calculation, Extended Data Figure 5 and Extended Data Table 1 ) 15 . We also confirmed that the PDMS−OH is not dissolved in the water layer, and water−PDMS interfacial energy is constant ( Extended Data Figure 6 ). Under PDMS ( HLB = 0) condition, Δγ = 28.2±2.8 mJ/m 2 >0, configuration W favoured thermodynamically. Thus, water droplet contact after immersion in PDMS transitioned from configuration C to configuration W ( Figure 2g(i) ). This transition time was 13 seconds, which reflected the viscosity-dependent rapture of the PDMS layer below the droplet 16 . Under PDMS−OH ( HLB = 0.12) conditions, still configuration W is thermodynamically stable as Δγ = 10.1 ± 1.9 mJ/m 2 ; however, the postcast droplet kept its shape ( Figure 2g(ii) ). This means a considerable energetic barrier prevents the transition, which should stem from HB Water-PDMS and HB PDMS-Silanol . In contrast, under PDMS−OH ( HLB = 0.73) conditions, configuration C is thermodynamically stable because of the negative Δγ = –3.3±0.9 mJ/m 2 . Despite the existence of the energetic barrier, the precast droplet immediately switched from a sticky to a repellent state, along with the transition from configuration W to C ( Figure 2g(iii) ). In this case, the precast droplet under PDMS−OH ( HLB = 0.12) was not switched because the droplet favours configuration W ( Figure 2g (iv) ). The energy level relationship ( Figure 2f ) of the configurations is similar to that of the Cassie and Wenzel states 17 . Droplet adhesion behaviour Droplets in configuration C(W) are mobile(sticky) under the PDMS−OH ( HLB = 0.12) condition; however, the quantification of the adhesion force is challenging because PDMS density is comparable to droplet one. Thus, we estimated the droplet adhesion by critical sliding angle α of PDMS-wrapped droplet ( Extended Data Figure 7 ) 18,19 , yielding F ≈ ρVg sin α , where ρ ≈ 0.997 g/mL is water density, V is droplet volume, and g ≈ 9.81 m 2 /s is gravitational acceleration constant ( Figure 3a ). Figures 3b and 3c show the sliding behaviour of PDMS−OH ( HLB = 0.12) wrapped droplets ( V = 5 μL) in different configurations. We observed the droplet in configuration C slide off at a constant speed of U = 36 ± 11 μm/s with tilting 1°, while the droplet in configuration W did not slide off on the 90° tilted surface. The apparent adhesion force difference depends on whether the droplet makes direct contact with the substrate or not. In configuration C, the droplet substrate direct contact is limited by PDMS−OH. Thus, the contact line friction is negligibly small, and adhesion force should mainly come from the viscous dissipation around the droplet 20 . In configuration W, the droplet makes direct contact with the substrate, and the adhesion force corresponds to the contact line friction 21 . In Figure 3d , we studied the HLB effect on the droplet adhesion force. In this experiment, the droplet volume is kept at V = 20 μL, which can get the sliding angle values for all test droplets. Additivity allows the fine HLB adjustment by varying the mixing ratio of the PDMS and PDMS−OH. Under PDMS ( HLB = 0) wrapped condition, in the absence of HB PDMS-Silanol , the adhesion force of pre/postcast droplets were F = 135.9 ± 18.2 / 110.2 ± 9.0 μN, respectively, not significantly different. However, the gap of adhesion force between precast/postcast droplets increased with HLB . Under HLB = 0.02, obtained by diluting PDMS−OH ( HLB = 0.12) with PDMS ( HLB = 0), pre/postcast droplets exhibited F = 27.2 ± 15.4 / 0.68 ± 0.34 μN, respectively. Here, the droplet in configuration C exhibited constant friction of hundreds nN. We find that both pre/postcast droplets transitioned from configuration W to configuration C, and the critical transition HLB was different between precast/postcast droplets. We defined the lower critical transition observed for postcast droplets at HLB ≈ 0.01−0.02 with HLB LC and upper critical transition HLB for precast droplets at HLB ≈ 0.5−0.7 with HLB UC , respectively. The branched wettability is observed between these critical HLB s (i.e., HLB LC < HLB < HLB UC ). We then discuss the physical meaning of these transition points. The transition of precast droplets near HLB UC is owing to the change in the thermodynamically favoured state of configurations, depending on the positive/negative sign of Δγ . The Δγ decreases with HLB ( Extended Data Figure 8 ) because γ ow decreases with the fraction of OH in PDMS by forming HB Water-PDMS . The critical HLB for Δγ = 0 is estimated to be HLB ≈ 0.62, which coincides with the value of experimentally obtained HLB UC . At HLB < HLB UC ( Δγ < 0), the interfacial state is in configuration W, and the contact line friction can be estimated from the Young-Dupré adhesion model F γ ~ γ ow (1+cos θ r ), which seems reasonable as the adhesion force decreases with HLB because of the decrease in γ ow . Here, slope fitting suggested F ~ HLB −0.5 , as shown in the black dashed line in Figure 3d . At HLB > HLB UC (that is Δγ > 0), the configuration C is favoured, and the adhesion force of the precast droplet drastically decreases. The transition point of postcast droplets at HLB LC depends on whether the OH group in PDMS can cover the substrate silanol that shields the HB Water-Silanol . The number of HB available molecules in PDMS should increase with increased HLB . We consider the HLB LC is the saturation point of HB PDMS-Silanol . At HLB < HLB LC , the amount of OH in PDMS is insufficient to cover substrate silanol. Thus, the uncovered silanol makes HB Water-silanol and droplets stick to the substrate. In this context, the configurations C and W co-exist beneath the postcast droplets, akin to a "partially Wenzel state" 22 , and the total adhesion force can be the sum of the HB Water-Silanol at the substrate−water contact area 23 . Under the assumption that the water-silanol interface has negligible interfacial tension and the Young-Dupré model is acceptable for molecular scale wetting, the unit adhesion force by HB Water-Silanol would be ~ F γ [ θ r →0]. Moreover, the number density of the HB Water-Silanol would be proportional to the number of the silanol that failed to cover with OH groups in PDMS. Thus, we expect F ~ F γ [ θ r →0] (1− f PDMS−OH / f silanol ) ~ HLB −0.5 (1− HLB / HLB LC ) where f PDMS−OH is the number density of OH bonding molecules in PDMS, which is approximately proportional to HLB . The model equations are fitted with the plot in Figure 3d by orange dash line, and we get HLB LC ≈ 0.019. At HLB > HLB LC , the postcast droplet favours configuration C and excess OH groups in PDMS, which does not play a significant role in droplet adhesion behaviour. Thus, we obtain F ≈ const (grey dash line). Extending wettability bifurcation to different phase combinations Based on the proposed mechanism, we show that the branched wettability can be extended to different phase combinations ( Figure 4 ). We observed branched wetting states using various surrounding media with different hydrogen bonding groups. For example, molecular interactions between amino-terminated PDMS (PDMS−NH 2 ) and silanol are similar to PDMS−OH ( Extended Data Figure 9 ). Thus, we first studied the effect of HLB on droplet adhesion force in replacing PDMS−NH 2 for PDMS−OH ( Figure 4a ). We observed the emergence of branched wettability at HLB from 0.0008 to 0.019. We did not observe bifurcation of droplet shape when we used various modified PDMS without hydrogen bonding species ( Extended Data Figure 10 ). The hydrophobic part of the surrounding media is not limited to PDMS as long as the media phase is water-immiscible and has a hydrogen-bonding group. We then studied the fatty acid system using a mixture of 1-octadecene (C 18 H 36 ) and oleic acid (C 17 H 33 COOH). Here, the carboxyl group in oleic acid is a hydrogen-bonding species. Figure 4b assessed the sliding angle of pre/postcast droplets ( V = 5 μL) with their different HLB . We also find that the branched wettability HLB region is from 0.3 to near 1.6. Notably, hydrogen bonding agents are not limited to liquids, but the branched wettability system is available by dissolving solute into the liquid. We dissolved 1 wt.% octadecyl amine (C 18 H 37 NH 2 ) as a hydrogen bonding additive, in 1-octadecene, and adjusted HLB = 0.012. We observed the branched wettability, as shown in Figure 4c . These results explained the potential expansion of branched wettability in various surrounding media. We also varied the substrate hydrophobic part from phenyl (C 6 H 5 −) to more hydrophobic alkyl (C 6 H 13 −, R q =0.82 nm) or perfluoroalkyl (C 4 F 9 C 2 H 4 −, R q = 1.14 nm) while keeping surface smoothness. With the increase of substrate hydrophobicity ( i.e. , increase γ sw ), the HLB UC should be decreased because of the decrease in Δγ . As expected, the branched wettability was observed for all probe surfaces. We find that the HLB UC is decreased with the increase of substrate hydrophobicity (which is high in the order of perfluoroalkyl, alkyl, and phenyl modification). ( Figure 4d ). This is because the Δγ decreases with the substrate hydrophobicity. Conclusion Molecular level tuning of the wettability balance enabled the observation of the branched wetting states. One droplet is in a metastable state owing to the energetic barrier by molecular interaction, and another droplet is in a thermodynamically favoured state. While this work mainly modulated the hydrogen bonding species of the surrounding media, which HLB quantifies, the concept can be expanded to modulation of droplets, substrate surface chemistry, and even molecular interactions different from HB. The observed droplet shape, adhesion behaviour, and energy level of configurations are analogous to those of Cassie and Wenzel droplets. Since the probe surface has molecular scale heterogeneity, we propose to term the observed droplet repellent/sticky state "Atomic Cassie/Wenzel state." We believe the atomic Cassie/Wenzel state would be a powerful tool for understanding the molecular effect on droplet mobility 8,24 , adaptivity 25 , micro-wetting 26 , and nanofluidics 27 . This finding will also guide the design of robust liquid-repellent or capturing surfaces since the surface nano/microscale texture typically suffers from low mechanical stability 28 . Methods Materials. All chemicals are used as received. We used phenyltriethoxysilane from Tokyo Chemical Industry Co., Ltd., Japan; hexyltriethoxysilane and nonafluorohexyltriethoxysilane from Fluorochem Ltd., UK; hexane from NACALAI TESQUE, INC., Japan; hydrochloric acid, acetone, oleic acid, and 1-octadecene from FUJIFILM Wako Pure Chemical Corporation, Japan; octadecyl amine from Sigma-Aldrich Co. LLC, USA; PDMS (DMS-T15) from Gelest Inc., USA. PDMS−OH with HLB = 0.12 (X-22-170BX), PDMS−OH with HLB = 0.73 (KF6000), PDMS−OH with HLB = 0.38 (KF6001), PDMS−NH 2 (X-22-161A), other modified PDMS: PDMS−Alkyl (KF414), PDMS−Ph (KF56), PDMS−Metacryl (KF2012), PDMS−Epoxy (X-22-173DX), PDMS−Mercapto (X-22-167B) were kindly provided from Shinetsu Co., Ltd., Japan. Ultrapure water with 18.2 MΩ/cm resistance was obtained using a Direct-Q UV3 system (Merck KGaA, Germany). Substrate modification. We modified the silane to a water-polished slide glass (Micro slides, MUTO PURE CHEMICALS CO., LTD., Japan). The glass surface was cleaned using plasma cleaner (PIB-10, Vacuum Device Inc., Japan). Then, the glass was immersed in a mixture of 1 mL silane, 20 mL hexane, and 1μL hydrochloric acid for 20 hours. After the immersion, the glass substrate was cleaned using acetone, hexane, and ultrapure water in this order. HLB modulation. We estimated the HLB of PDMS according to the Griffin method: HLB = 20 × [molecular mass of hydrophilic part] / [total molecular mass]. Moreover, additivity allowed the fine adjustment of HLB by varying the weight ratio of the mixture, which yields HLB = Σ w i HLB i , where w i and HLB i are the weight fraction and HLB of mixing component i = 1,2…. PDMS−OH with HLB from 0 to 0.12 was obtained by the varied mixing ratio of DMS-T15 and X-22-170BX. The mixture of KF6000 and KF6001 obtained PDMS−OH with HLB > 0.12. The mixing ratio of DMS-T15 and X-22-161A adjusted the HLB of PDMS−NH 2 . Wettability measurement. Contact angles, sliding angles, and interfacial tension were measured using a contact angle meter (Drop Master-SA-Cs1, Kyowa Interface Science Co., Ltd., Japan). The resolution of the sliding angle is 0.1 ± 0.05°. Interfacial tension was obtained using the pendant drop method. Dynamic contact angles were obtained from droplets just in contact line motion. We pushed the droplets using a Teflon needle tip (22 G). These measurements were repeated at least three times, and the results were reported as mean ± SD values. Calculation of interfacial energy difference. Equation Δγ = [total energy of configuration C] – [total energy of configuration W] = γ so + γ ow – γ sw obtained from Extended Data Figure 4 can be reduced to measurable quantities using Young’s equation, and we have Δγ = γ w cos θ w – γ o cos θ o + γ ow , where γ w and γ o are water and PDMS surface tensions, θ w and θ o are static water and PDMS contact angles on the probe surface in air, respectively 15 . The interfacial energies and contact angles are measured using a contact angle meter and summarized in Extended Data Table 1 . Surface analysis. The probe surface structure was observed using field-emission SEM (FE-SEM S-4800; Hitachi High-Technologies Co., Japan) and AFM (MFP-3D Origin AFM - Asylum Research, UK). Fourier transform infrared (FT-IR) attenuated total reflection (ATR) spectrum was measured using IRSpirit-L (Shimadzu Corp., Japan). Intermolecular interaction. We evaluated the intermolecular interaction energies between silanol and PDMS(−OH) using the Gaussian16 program 29 . The geometries of isolated molecules were optimized at the B3LYP/6-311G** level. We also obtained the electrostatic potential maps based on this computational level. To investigate the contribution of the terminal hydroxyl groups, the long axis of the PDMS molecule was aligned perpendicular to the substrate, and the PDMS(−OH) molecule was rotated along this axis to find the energy minima. We plotted the interaction energies at different distances between the molecule and the substrate while setting the optimized arrangement as the origin of the distance. The intermolecular interaction energies were calculated at the PBE/6-311G** level using Grimme’s D3BJ dispersion correction 14 . 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Gaussian 16. Wallingford, CT (2016). 30. Tsuzuki, S. & Uchimaru, T. Accuracy of intermolecular interaction energies, particularly those of hetero-atom containing molecules obtained by DFT calculations with Grimme’s D2, D3 and D3BJ dispersion corrections. Phys Chem Chem Phys 22 , 22508–22519 (2020). 31. Ransil, B. J. Studies in Molecular Structure. IV. Potential Curve for the Interaction of Two Helium Atoms in Single-Configuration LCAO MO SCF Approximation. J Chem Phys 34 , 2109–2118 (1961). 32. Boys, S. F. & Bernardi, F. The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors. Mol Phys 19 , 553–566 (1970). Additional Declarations There is NO Competing Interest. Supplementary Files ExtendedData.docx MovieS1.mp4 Movie S1 Pushing the precast water droplet induces a wetting transition under PDMS−OH ( HLB = 0.12). MovieS2.mp4 Movie S2 Vertical adhesion behaviour of the postcast water droplet under PDMS−OH ( HLB = 0.12). Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4493821","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Physical Sciences - Article","associatedPublications":[],"authors":[{"id":308104188,"identity":"f5ee3b8d-d3fc-4fef-8195-4b6412b88f41","order_by":0,"name":"Mizuki Tenjimbayashi","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0002-8107-8285","institution":"National Institute for Materials Science","correspondingAuthor":true,"prefix":"","firstName":"Mizuki","middleName":"","lastName":"Tenjimbayashi","suffix":""},{"id":308104189,"identity":"b21ac6ac-c38c-4a03-a4b2-57ae5a07a811","order_by":1,"name":"Shunto Arai","email":"","orcid":"https://orcid.org/0000-0002-0055-3006","institution":"National Institute for Materials Science","correspondingAuthor":false,"prefix":"","firstName":"Shunto","middleName":"","lastName":"Arai","suffix":""}],"badges":[],"createdAt":"2024-05-29 02:45:47","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4493821/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4493821/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":60689062,"identity":"fa540fa5-0b3f-4e50-b042-ad1e78fccf1b","added_by":"auto","created_at":"2024-07-19 14:35:27","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":395019,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTwo wetting states on a smooth surface.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e,\u003cstrong\u003eb,\u003c/strong\u003e Substrate surface images of phenyl silane modified glass substrate by field emission scanning electron microscopy (SEM) and AFM. \u003cstrong\u003ec\u003c/strong\u003e, A side view photograph of two 5 μL water droplets on the same substrate under PDMS−OH (\u003cem\u003eHLB \u003c/em\u003e= 0.12)condition. The left (right) droplet is cast after (before) immersing the substrate in PDMS−OH. \u003cstrong\u003ed\u003c/strong\u003e, The adhesion behaviour of the droplets just inmotion. Droplets are pushed with the Teflon needle parallel to the substrate(indicated by white arrows).\u003c/p\u003e","description":"","filename":"Fig1.png","url":"https://assets-eu.researchsquare.com/files/rs-4493821/v1/fd6d5cf078f62038c12ff021.png"},{"id":60689065,"identity":"b7fbefab-985d-46dc-8846-45f846ca3404","added_by":"auto","created_at":"2024-07-19 14:35:27","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":345235,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eInteracial states.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e, Pre/postcast water droplets under PDMS(−OH) with different \u003cem\u003eHLBs\u003c/em\u003e. \u003cstrong\u003eb\u003c/strong\u003e,\u003cstrong\u003ec\u003c/strong\u003e, Schematics of the two interfacial states: (\u003cstrong\u003eb\u003c/strong\u003e) PDMS−OH is entrapped beneath the droplet and minimise the droplet substrate contact, that is Configuration C; (\u003cstrong\u003ec\u003c/strong\u003e) The droplet adheres to the substrate −OH area, that is Configuration W. Possible hydrogen bondings decide the preference of two wetting states: hydrogen bonding between water and PDMS−OH (HB\u003csub\u003eWater-PDMS\u003c/sub\u003e), PDMS−OH and silanol from substrate and/or hydrolysed silane (HB\u003csub\u003ePDMS-Silanol\u003c/sub\u003e), or water and Silanol (HB\u003csub\u003eWater-Silanol\u003c/sub\u003e). \u003cstrong\u003ed\u003c/strong\u003e, Distance dependence of the intermolecular interaction energy between the −OH groups on the substrate surface and the molecular end group of PDMS(−OH). \u003cstrong\u003ee,\u003c/strong\u003e Electrostatic potential map of PDMS-OH in proximity to -OH groups on the substrate surface. \u003cstrong\u003ef\u003c/strong\u003e, Total interfacial energy levels of PDMS(−OH) entrapped beneath the water (Left) compared with the water-adhered state. \u003cstrong\u003eg\u003c/strong\u003e, Time-lapse photographs of the water droplet contact on the substrate under PDMS or PDMS−OH (bottom) condition. (i, ii) Postcast droplet under (i) PDMS (\u003cem\u003eHLB\u003c/em\u003e = 0) or (ii) PDMS−OH (\u003cem\u003eHLB \u003c/em\u003e= 0.12); (iii) Precast droplet through immersion in PDMS−OH (\u003cem\u003eHLB\u003c/em\u003e = 0.73).; and (iv) Precast droplet under PDMS−OH (\u003cem\u003eHLB\u003c/em\u003e = 0.12).\u003c/p\u003e","description":"","filename":"Fig2.png","url":"https://assets-eu.researchsquare.com/files/rs-4493821/v1/1e3b5954bc628d601abddda2.png"},{"id":60689067,"identity":"2bd3c99e-37f7-4ea4-86cd-26fb2090301e","added_by":"auto","created_at":"2024-07-19 14:35:27","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":152661,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDroplet adhesion behaviour.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e, An experimental setup used to estimate the droplet adhesion force under PDMS conditions. The water droplet is cast on the PDMS or PDMS−OH lubricated substrate and tilted till the droplet starts sliding. The adhesion force is quantified with the critical sliding angle \u003cem\u003eα\u003c/em\u003e. \u003cstrong\u003eb,c,\u003c/strong\u003e A 5 μL water droplet wrapped with PDMS−OH (\u003cem\u003eHLB\u003c/em\u003e = 0.12) in (\u003cstrong\u003eb\u003c/strong\u003e) configuration C and (\u003cstrong\u003ec\u003c/strong\u003e) configuration W. \u003cstrong\u003ed\u003c/strong\u003e, Adhesion force evolution of the wrapped 20 μL water droplets as a function of \u003cem\u003eHLB\u003c/em\u003e. Dash lines are fitting from our estimation: \u003cem\u003eF\u003c/em\u003e~ \u003cem\u003eHLB\u003c/em\u003e\u003csup\u003e−0.5\u003c/sup\u003e (black), \u003cem\u003eF\u003c/em\u003e~ \u003cem\u003eHLB\u003c/em\u003e\u003csup\u003e−0.5\u003c/sup\u003e(1−\u003cem\u003eHLB\u003c/em\u003e/\u003cem\u003eHLB\u003c/em\u003e\u003csub\u003eLC\u003c/sub\u003e) (orange), \u003cem\u003eF \u003c/em\u003e≈ const. (grey).\u003c/p\u003e","description":"","filename":"Fig3.png","url":"https://assets-eu.researchsquare.com/files/rs-4493821/v1/53417138c3bb001f12d1f213.png"},{"id":60690159,"identity":"38908adc-c5ef-41b2-8815-2d04f6092d3e","added_by":"auto","created_at":"2024-07-19 14:51:27","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":161822,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExtending wettability bifurcation to different phase combinations.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e, Adhesion force evolution of the wrapped 20 μL water droplets as a function of \u003cem\u003eHLB\u003c/em\u003e of a mixture of PDMS and PDMS−NH\u003csub\u003e2\u003c/sub\u003e \u003cstrong\u003eb\u003c/strong\u003e, Sliding angle of 5 μL water droplets under the mixture of oleic acid and 1-octadecene. \u003cstrong\u003ec\u003c/strong\u003e, Branched wettability of water droplet under a mixture of 1 wt.% octadecyl amine and oleic acid. \u003cstrong\u003ed\u003c/strong\u003e, Sliding angle of pre/postcast 5μL water droplets on substrates with different hydrophobic parts under a mixture of PDMS and PDMS−OH.\u003c/p\u003e","description":"","filename":"Fig4.png","url":"https://assets-eu.researchsquare.com/files/rs-4493821/v1/a2ebc050a96bc4300a3a326b.png"},{"id":66087190,"identity":"5c0cab26-2ec7-452c-8fd6-b975b7596627","added_by":"auto","created_at":"2024-10-07 14:35:30","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1828569,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4493821/v1/9d4af71e-453c-4415-9644-66114e588365.pdf"},{"id":60689063,"identity":"dcc0b584-4553-4bef-b928-dfceba0f5591","added_by":"auto","created_at":"2024-07-19 14:35:27","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":1254458,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"ExtendedData.docx","url":"https://assets-eu.researchsquare.com/files/rs-4493821/v1/f83bddc61cd73acc1ec4c584.docx"},{"id":60689069,"identity":"43aa5584-3521-4c76-89ad-c35fc9dca401","added_by":"auto","created_at":"2024-07-19 14:35:27","extension":"mp4","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":6748587,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eMovie S1\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003ePushing the precast water droplet induces a wetting transition under PDMS−OH (\u003cem\u003eHLB\u003c/em\u003e = 0.12).\u003c/p\u003e","description":"","filename":"MovieS1.mp4","url":"https://assets-eu.researchsquare.com/files/rs-4493821/v1/e66a45d7e586c6a54f7b5f1b.mp4"},{"id":60689754,"identity":"45bb0fcf-e7af-44c3-bcd5-ae8b4142a277","added_by":"auto","created_at":"2024-07-19 14:43:27","extension":"mp4","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":303205,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eMovie S2\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eVertical adhesion behaviour of the postcast water droplet under PDMS−OH (\u003cem\u003eHLB\u003c/em\u003e= 0.12).\u003c/p\u003e","description":"","filename":"MovieS2.mp4","url":"https://assets-eu.researchsquare.com/files/rs-4493821/v1/cc8072ace95e40d10ef41653.mp4"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Emergence of branched wetting states on a smooth surface","fulltext":[{"header":"Main","content":"\u003cp\u003eDroplet static/dynamic shapes are quantified with contact angles. While the static contact angle \u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e is obtained at the equilibrium of three-phase interfacial energies\u003cstrong\u003e\u003csup\u003e\u0026nbsp;\u003c/sup\u003e\u003c/strong\u003e\u003csup\u003e4\u003c/sup\u003e, the maximum/minimum contact angle is observed when the contact line advances/recedes, namely advancing/receding contact angles \u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003ea/r\u003c/sub\u003e \u003csup\u003e5\u003c/sup\u003e. The mobility of the contact line depends on the degree of surface heterogeneity. Although most objects\u0026apos; surfaces are not perfectly homogeneous, at least on the molecular scale \u003csup\u003e8\u003c/sup\u003e, a surface with much smaller scale of heterogeneity than the radius of curvature of the droplet contact line can be regarded as a homogeneous surface \u003csup\u003e9\u003c/sup\u003e. A droplet on a homogeneous surface basically exhibits a single inherent contact angle range, namely a single wetting state.\u003c/p\u003e\n\u003cp\u003eWhen the solid surface has nano- or micro-textured surfaces, on the other hands, the droplet follows two branched wetting states: (i) the droplet homogeneously infusing the texture (Wenzel state) \u003csup\u003e6\u003c/sup\u003e or (ii) limited contact to the texture\u0026apos;s outermost surface (Cassie state)\u0026nbsp;\u003csup\u003e7\u003c/sup\u003e. The difference between Wenzel and Cassie states is whether the texture is infused by droplet phase or surrounding media (Typically air or droplet immiscible liquids). Model equations of Wenzel and Cassie states explain that surface roughness increases the apparent contact angle \u003cem\u003e\u0026theta;\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e more than the angle on the smooth surface. In Wenzel state, surface roughness \u003cem\u003er\u003c/em\u003e is defined as the ratio of actual per projected surface area, and we obtain cos\u003cem\u003e\u0026theta;\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e = \u003cem\u003er\u003c/em\u003ecos\u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e. In Cassie state, the area fraction of droplet texture contact area \u003cem\u003ef\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e is defined, and we obtain cos\u003cem\u003e\u0026theta;\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e = \u0026minus;1+\u003cem\u003e\u0026nbsp;f\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e(1+cos\u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e).\u003csup\u003e\u0026nbsp;\u003c/sup\u003eDroplet adhesion property accessed by \u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e is drastically different between these two states owing to their contacting behaviour \u003csup\u003e10\u003c/sup\u003e. In Wenzel state, the surface texture enhances the droplet\u0026minus;surface contact area, resulting in highly sticky droplets, and we observe \u003cem\u003e\u0026theta;\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e \u0026gt;\u0026gt; \u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e. In Cassie state, the droplet adhesion area is negligibly small, which explains \u003cem\u003e\u0026theta;\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e \u0026asymp; \u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e. Wenzel and Cassie states co-exist on the textured surface, one of which is energetically favoured. However, the energetic barrier in phase replacement between the droplet and surrounding media is formed by surface texture, which enables observation of the other metastable state\u003csup\u003e\u0026nbsp;11\u003c/sup\u003e. Thus, the surface texture plays a significant role in the emergence of the branched wettability. According to the model equations, when the surface texture goes to smooth (\u003cem\u003er\u003c/em\u003e and \u003cem\u003ef\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e \u0026rarr;1), model equations result in the same cos\u003cem\u003e\u0026theta;\u003c/em\u003e* = cos\u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e, indicating that these wetting states are unified. Thus, droplets on a smooth surface are thought to exhibit a single wetting state when the surface texture is diminished. Here, we wonder whether site-specific molecular interactions at interfaces can regulate the energetic barrier in phase replacement without relying on the surface texture.\u003cs\u003e\u0026nbsp;\u003c/s\u003e\u003c/p\u003e\n\u003cp\u003eIn this work, we show that the two drastically different wetting states, which satisfy the wettability feature by Cassie and Wenzel, can co-exist on a smooth surface as the result of molecular scale wettability modulation. The static/dynamic wettability features of these states are experimentally confirmed, and the underlying mechanism is studied on a molecular scale interaction, thermodynamics, and force measurement. Finally, based on the proposed mechanism, we show that the branched wettability can be extended to different phase combinations.\u003c/p\u003e"},{"header":"Two wetting states on a smooth surface","content":"\u003cp\u003eSelf-assembled silane monolayer can regulate the surface chemistry of the contacting substrate without texturing\u003csup\u003e12\u003c/sup\u003e. Here, the probe surface is\u0026nbsp;the glass\u0026nbsp;substrate containing a monolayer of\u0026nbsp;phenylsilane. The surface has no texture (\u003cstrong\u003eFig\u003c/strong\u003e\u003cstrong\u003eure\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;1\u003c/strong\u003e\u003cstrong\u003ea\u003c/strong\u003e), and the\u0026nbsp;atomic force microscopy (AFM)\u0026nbsp;measurement\u0026nbsp;quantified\u0026nbsp;the surface root-mean-square roughness of \u003cem\u003eR\u003c/em\u003e\u003csub\u003eq\u003c/sub\u003e =\u0026nbsp;0.41 nm\u0026nbsp;(\u003cstrong\u003eFigure 1b\u003c/strong\u003e).\u0026nbsp;In addition to the hydrophobic phenyl group, the surface has a\u0026nbsp;hydrophilic\u0026nbsp;silanol group from the glass surface and hydrolysis of phenylsilane, confirmed\u0026nbsp;from the infrared spectrum\u0026nbsp;(\u003cstrong\u003eExtended Data Figure\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e1\u003c/strong\u003e). The water contact angle in air is (\u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e, \u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e) = (79.4\u0026nbsp;\u0026plusmn;\u0026nbsp;1.9\u0026deg;, 60.8\u0026nbsp;\u0026plusmn;\u0026nbsp;1.3\u0026deg;).\u0026nbsp;In changing\u0026nbsp;the surrounding media from air to\u0026nbsp;liquid state hydroxyl-terminated polydimethylsiloxane (PDMS\u0026minus;OH) with specific hydrophobic-hydrophilic balance \u003cem\u003eHLB\u003c/em\u003e = 0.12 \u0026nbsp;\u003csup\u003e13\u003c/sup\u003e, the water\u0026nbsp;droplet behaviour\u0026nbsp;branched\u0026nbsp;in\u0026nbsp;sticky or repellent\u0026nbsp;(\u003cstrong\u003eFig\u003c/strong\u003e\u003cstrong\u003eure\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;1\u003c/strong\u003e\u003cstrong\u003ec\u003c/strong\u003e, \u003cstrong\u003e1\u003c/strong\u003e\u003cstrong\u003ed\u003c/strong\u003e, and \u003cstrong\u003eMovie 1\u003c/strong\u003e). The applicable wetting states depend on the order of the interface formation (see \u003cstrong\u003eExtended Data Figure 2\u003c/strong\u003e).\u0026nbsp;On the one hand, the droplet, cast on the probe surface after the PDMS\u0026minus;OH\u0026nbsp;immersion (denote postcast droplet), has the water contact angle of (\u003cem\u003e\u0026theta;\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e, \u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e) = (175.8 \u0026plusmn; 0.5\u0026deg;, 173.0 \u0026plusmn; 0.5\u0026deg;), exhibiting nearly perfect hydrophobicity but has observable small water adhesion (see \u003cstrong\u003eExtended Data Figure 3\u003c/strong\u003e, \u003cstrong\u003eMovie 2\u003c/strong\u003e), which satisfies Cassie state feature \u003cem\u003e\u0026theta;\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e \u0026asymp; \u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e. On the other hand, the droplet, cast before the immersion (denote precast droplet), exhibited (\u003cem\u003e\u0026theta;\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e, \u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e) = (130.6 \u0026plusmn; 3.8\u0026deg;, 107.4 \u0026plusmn; 1.5\u0026deg;), follows Wenzel-like wetting behaviour \u003cem\u003e\u0026theta;\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e \u0026gt;\u0026gt; \u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e. In both droplets, \u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003e reaches nearly 180\u0026deg;, which means PDMS\u0026minus;OH firmly adheres (that is equal to PDMS\u0026minus;OH receding angle being nearly 0\u0026deg;) to the probe surface and prevents contact line advance.\u003c/p\u003e"},{"header":"Interfacial states","content":"\u003cp\u003eBranched wetting states\u0026nbsp;are\u0026nbsp;observed at a specific \u003cem\u003eHLB\u003c/em\u003e range.\u0026nbsp;In \u003cstrong\u003eFigure 2a\u003c/strong\u003e, we pre/postcast water droplets on the probe surface under PDMS(\u0026minus;OH) with different \u003cem\u003eHLB\u0026nbsp;\u003c/em\u003evalues. The probe PDMS (HLB = 0), PDMS\u0026minus;OH\u0026nbsp;(\u003cem\u003eHLB\u003c/em\u003e = 0.12), and PDMS\u0026minus;OH\u0026nbsp;(\u003cem\u003eHLB\u003c/em\u003e = 0.73) have a similar surface tension of \u003cem\u003e\u0026gamma;\u003c/em\u003e\u003csub\u003eo\u003c/sub\u003e = 19.8 \u0026plusmn; 0.3, 19.9 \u0026plusmn; 0.2, and 21.4 \u0026plusmn; 0.4 mN/m, and viscosity\u0026nbsp;of\u0026nbsp;\u003cem\u003e\u0026eta;\u003c/em\u003e \u0026asymp;\u0026nbsp;50, 40, 35\u0026nbsp;mPa\u0026middot;s, respectively. Under PDMS (\u003cem\u003eHLB\u003c/em\u003e = 0), the two droplets exhibit similar contact angles of (\u003cem\u003e\u0026theta;\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e, \u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e) = (124.8\u0026nbsp;\u0026plusmn;\u0026nbsp;4.0\u0026deg;,\u0026nbsp;83.6\u0026nbsp;\u0026plusmn;\u0026nbsp;3.8\u0026deg;) and (118.1\u0026nbsp;\u0026plusmn;\u0026nbsp;4.4\u0026deg;,\u0026nbsp;83.0\u0026nbsp;\u0026plusmn;\u0026nbsp;5.0\u0026deg;), which satisfies wetting feature of Wenzel state. In contrast, two droplets under PDMS\u0026minus;OH\u0026nbsp;(\u003cem\u003eHLB\u003c/em\u003e = 0.73) exhibit contact angles of (\u003cem\u003e\u0026theta;\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e, \u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e) = (169.7\u0026nbsp;\u0026plusmn;\u0026nbsp;1.1\u0026deg;,\u0026nbsp;168.0\u0026nbsp;\u0026plusmn;\u0026nbsp;3.9\u0026deg;) and (166.9\u0026nbsp;\u0026plusmn;\u0026nbsp;2.0\u0026deg;,\u0026nbsp;146.2\u0026nbsp;\u0026plusmn;\u0026nbsp;6.4\u0026deg;), both of which behave like Cassie-state droplets because of their high\u0026nbsp;\u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e. In \u003cem\u003eHLB\u003c/em\u003e = 0.12, the branched repellent/sticky droplet behaviour is observed (\u003cstrong\u003eFigure 1c, 1d\u003c/strong\u003e).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u0026nbsp; \u0026nbsp;\u0026nbsp;\u003c/strong\u003eThe possible interfacial states of Cassie-like (Configuration C) and Wenzel-like (Configuration W) droplets are illustrated in \u003cstrong\u003eFigures 2b\u003c/strong\u003e and \u003cstrong\u003e2c\u003c/strong\u003e, respectively. In configuration C (\u003cstrong\u003eFigure 2b\u003c/strong\u003e), observed under PDMS\u0026minus;OH\u0026nbsp;conditions, the droplet repellency is owing to the limited contact of the water\u0026minus;substrate, indicating that PDMS\u0026minus;OH\u0026nbsp;is entrapped beneath the droplet. Since the postcast droplet under PDMS sticks to the substrate (\u003cstrong\u003eFigure 2a\u003c/strong\u003e, left), the molecular interaction works to stabilise the PDMS\u0026minus;OH\u0026nbsp;between the droplet and substrate works. We consider this interaction to be hydrogen bonding between water \u0026minus; PDMS\u0026minus;OH (HB\u003csub\u003eWater-PDMS\u003c/sub\u003e) and the PDMS\u0026minus;OH \u0026ndash; silanol interface (HB\u003csub\u003ePDMS-Silanol\u003c/sub\u003e).\u003csup\u003e\u0026nbsp;\u003c/sup\u003eMoreover, the oleophilic interactions between the PDMS\u0026minus;substrate phenyl group enhance entrapped PDMS\u0026minus;OH stability. In the absence of a phenyl group on the substrate, for example, on the unmodified glass substrate, the PDMS layer is replaced by water, and both pre/postcast droplets exhibit high wettability (\u003cstrong\u003eExtended Data Figure\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e4\u003c/strong\u003e). In configuration W (\u003cstrong\u003eFigure 2c\u003c/strong\u003e), observed under PDMS or precast droplet under PDMS\u0026minus;OH (\u003cem\u003eHLB\u003c/em\u003e = 0.12) (\u003cstrong\u003eFigure 2a\u003c/strong\u003e, left and middle), the droplet sticking property is owing to the direct contact between water and substrate. Water molecules have a higher affinity to the silanol than the phenyl group because of the possible hydrogen bonding with substrate silanol groups (HB\u003csub\u003eWater-Silanol\u003c/sub\u003e).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eHence, the applicable configuration depends on sticking the PDMS(\u0026minus;OH) onto the substrate beneath the water droplet by possibly forming HB\u003csub\u003ePDMS-Silanol\u003c/sub\u003e. \u0026nbsp;To validate the HB\u003csub\u003ePDMS-Silanol\u003c/sub\u003e, we calculated intermolecular interaction energies based on density functional theory incorporating Grimme\u0026apos;s dispersion correction \u003csup\u003e14\u003c/sup\u003e (see Methods for details). \u003cstrong\u003eFigure 2d\u003c/strong\u003e shows the interaction energy depending on the distance between PDMS (\u0026minus;OH) and the silanol. We optimised the rotation degree of freedom for these molecules around the molecular long axes. The potential depth near the interaction energy minimum is shallow for PDMS, whereas it is sufficiently large for PDMS\u0026minus;OH compared with the thermal fluctuation energy. The origin of this significant attractive interaction is explained based on the electrostatic interactions. \u003cstrong\u003eFigure 2e\u003c/strong\u003e shows the electrostatic potential map between the end of PDMS\u0026minus;OH and the silanol group. This colour map shows the O (or H) of the silanol attracts the H (or O) of the PDMS\u0026minus;OH, suggesting the formation of a hydrogen bond. Although the long-range interaction decays with a distance from the substrate, it is still large compared to the thermal effect with a distance of 5\u0026minus;6 \u0026Aring; This indicates that PDMS\u0026minus;OH forms sufficiently strong HBs even with silanol groups covered by phenyl groups (about 4 \u0026Aring; height), resulting in the formation of stable lubricant layer on the substrate surface compared with PDMS.\u003c/p\u003e\n\u003cp\u003eAssuming the water\u0026minus;substrate contact is limited to HB\u003csub\u003eWater-Silanol\u003c/sub\u003e region and its interfacial energy is negligibly small, we can modify the classical Cassie equation to cos\u003cem\u003e\u0026theta;\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e = \u0026minus;1 +\u003cem\u003e\u0026nbsp;\u003c/em\u003e2\u003cem\u003ef\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e, which is applicable for both configurations. From Figure 1c, we estimate \u003cem\u003ef\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e = 0.17 \u0026plusmn; 0.02 and 0.0014 \u0026plusmn; 0.0003 for precast/postcast droplets under PDMS\u0026minus;OH\u0026nbsp;(\u003cem\u003eHLB\u003c/em\u003e = 0.12). Since the precast droplet is in configuration W, we can quantify the silanol group fraction on the probe substrate as \u003cem\u003ef\u003c/em\u003e\u003csub\u003esilanol\u003c/sub\u003e = \u003cem\u003ef\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e = 0.17 \u0026plusmn; 0.02. While this, the postcast droplet is in configuration C and ideally \u003cem\u003ef\u003c/em\u003e\u003csub\u003esilanol\u003c/sub\u003e = 0. Overall, we obtain the contact angles of the branched droplets: cos\u003cem\u003e\u0026theta;\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e = \u0026minus;1 for configuration C, and cos\u003cem\u003e\u0026theta;\u003c/em\u003e\u003csup\u003e*\u003c/sup\u003e = \u0026minus;1+\u003cem\u003e\u0026nbsp;\u003c/em\u003e2\u003cem\u003ef\u003c/em\u003e\u003csub\u003esilanol\u003c/sub\u003e for configuration W.\u003c/p\u003e\n\u003cp\u003eWe\u0026nbsp;then\u0026nbsp;compared the total energies between\u0026nbsp;the two configurations (\u003cstrong\u003eFigure 2f\u003c/strong\u003e). We assumed the unit area\u0026nbsp;total interfacial\u0026nbsp;energy\u0026nbsp;\u003cem\u003e\u0026gamma;\u003c/em\u003e\u003csub\u003etotal\u003c/sub\u003e\u003cem\u003e\u0026nbsp;\u003c/em\u003edifference\u0026nbsp;between two configurations to be \u003cem\u003e\u0026Delta;\u0026gamma;\u003c/em\u003e =\u0026nbsp;\u003cem\u003e\u0026gamma;\u003c/em\u003e\u003csub\u003eso\u003c/sub\u003e + \u003cem\u003e\u0026gamma;\u003c/em\u003e\u003csub\u003eow\u003c/sub\u003e \u0026ndash; \u003cem\u003e\u0026gamma;\u003c/em\u003e\u003csub\u003esw\u003c/sub\u003e, where \u003cem\u003e\u0026gamma;\u003c/em\u003e\u003csub\u003eso, ow, sw\u003c/sub\u003e is unit interfacial energy\u0026nbsp;and\u0026nbsp;subscripts\u0026nbsp;mean,\u0026nbsp;s: substrate, o: PDMS\u0026nbsp;(\u0026minus;OH), and w: water\u0026nbsp;(see\u003cstrong\u003e\u0026nbsp;methods\u003c/strong\u003e for calculation,\u0026nbsp;\u003cstrong\u003eExtended Data Figure\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e5\u003c/strong\u003e and\u0026nbsp;\u003cstrong\u003eExtended Data\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003eTable 1\u003c/strong\u003e)\u0026nbsp;\u003csup\u003e15\u003c/sup\u003e.\u0026nbsp;We\u0026nbsp;also\u0026nbsp;confirmed that the PDMS\u0026minus;OH is not dissolved in the water layer, and water\u0026minus;PDMS interfacial energy is constant\u0026nbsp;(\u003cstrong\u003eExtended Data Figure\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e6\u003c/strong\u003e).\u0026nbsp;Under PDMS (\u003cem\u003eHLB\u003c/em\u003e = 0) condition, \u003cem\u003e\u0026Delta;\u0026gamma;\u003c/em\u003e = 28.2\u0026plusmn;2.8 mJ/m\u003csup\u003e2\u003c/sup\u003e \u0026gt;0, configuration W favoured thermodynamically. Thus, water droplet contact after immersion in PDMS transitioned from configuration C to configuration W (\u003cstrong\u003eFigure 2g(i)\u003c/strong\u003e). This transition time was 13 seconds, which reflected the viscosity-dependent rapture of the PDMS layer below the droplet \u003csup\u003e16\u003c/sup\u003e. Under\u0026nbsp;PDMS\u0026minus;OH (\u003cem\u003eHLB\u003c/em\u003e = 0.12) conditions, still configuration W is thermodynamically stable as \u003cem\u003e\u0026Delta;\u0026gamma;\u003c/em\u003e = 10.1 \u0026plusmn; 1.9 mJ/m\u003csup\u003e2\u003c/sup\u003e; however, the postcast droplet kept its shape (\u003cstrong\u003eFigure 2g(ii)\u003c/strong\u003e). This means a considerable energetic barrier prevents the transition, which should stem from HB\u003csub\u003eWater-PDMS\u003c/sub\u003e and HB\u003csub\u003ePDMS-Silanol\u003c/sub\u003e.\u003c/p\u003e\n\u003cp\u003eIn contrast, under\u0026nbsp;PDMS\u0026minus;OH (\u003cem\u003eHLB\u003c/em\u003e = 0.73) conditions, configuration C is thermodynamically stable because of the negative \u003cem\u003e\u0026Delta;\u0026gamma;\u003c/em\u003e =\u0026nbsp;\u0026ndash;3.3\u0026plusmn;0.9 mJ/m\u003csup\u003e2\u003c/sup\u003e. Despite the existence of the energetic barrier, the precast droplet immediately switched from a sticky to a repellent state, along with the transition from configuration W to C (\u003cstrong\u003eFigure 2g(iii)\u003c/strong\u003e). In this case, the precast droplet under PDMS\u0026minus;OH (\u003cem\u003eHLB\u003c/em\u003e = 0.12) was not switched because the droplet favours configuration W (\u003cstrong\u003eFigure 2g (iv)\u003c/strong\u003e). The energy level relationship (\u003cstrong\u003eFigure 2f\u003c/strong\u003e) of the configurations is similar to that of the Cassie and Wenzel states \u003csup\u003e17\u003c/sup\u003e.\u003c/p\u003e"},{"header":"Droplet adhesion behaviour","content":"\u003cp\u003eDroplets in configuration C(W) are mobile(sticky) under the PDMS\u0026minus;OH (\u003cem\u003eHLB\u003c/em\u003e = 0.12) condition; however, the quantification of the adhesion force is challenging because PDMS density is comparable to droplet one. Thus, we estimated the droplet adhesion by critical sliding angle \u003cem\u003e\u0026alpha;\u003c/em\u003e of PDMS-wrapped droplet (\u003cstrong\u003eExtended Data Figure 7\u003c/strong\u003e)\u0026nbsp;\u003csup\u003e18,19\u003c/sup\u003e, yielding \u003cem\u003eF\u003c/em\u003e \u0026asymp; \u003cem\u003e\u0026rho;Vg\u003c/em\u003e sin\u003cem\u003e\u0026alpha;\u003c/em\u003e, where \u003cem\u003e\u0026rho;\u003c/em\u003e \u0026asymp; 0.997 g/mL is water density, \u003cem\u003eV\u003c/em\u003e is droplet volume, and \u003cem\u003eg\u003c/em\u003e \u0026asymp; 9.81 m\u003csup\u003e2\u003c/sup\u003e/s is gravitational acceleration constant (\u003cstrong\u003eFigure 3a\u003c/strong\u003e).\u003cstrong\u003e\u0026nbsp;Figures 3b\u003c/strong\u003e and \u003cstrong\u003e3c\u003c/strong\u003e show the sliding behaviour of PDMS\u0026minus;OH (\u003cem\u003eHLB\u003c/em\u003e = 0.12) wrapped droplets (\u003cem\u003eV\u003c/em\u003e = 5 \u0026mu;L) in different configurations. We observed the droplet in configuration C slide off at a constant speed of \u003cem\u003eU\u003c/em\u003e = 36 \u0026plusmn; 11 \u0026mu;m/s with tilting 1\u0026deg;, while the droplet in configuration W did not slide off on the 90\u0026deg; tilted surface. The apparent adhesion force difference depends on whether the droplet makes direct contact with the substrate or not. In configuration C, the droplet substrate direct contact is limited by PDMS\u0026minus;OH. Thus, the contact line friction is negligibly small, and adhesion force should mainly come from the viscous dissipation around the droplet \u003csup\u003e20\u003c/sup\u003e. In configuration W, the droplet makes direct contact with the substrate, and the adhesion force corresponds to the contact line friction \u003csup\u003e21\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eIn \u003cstrong\u003eFigure 3d\u003c/strong\u003e, we studied the \u003cem\u003eHLB\u003c/em\u003e effect on the droplet adhesion force. In this experiment, the droplet volume is kept at \u003cem\u003eV\u003c/em\u003e = 20 \u0026mu;L, which can get the sliding angle values for all test droplets. Additivity allows the fine \u003cem\u003eHLB\u003c/em\u003e adjustment by varying the mixing ratio of the PDMS and PDMS\u0026minus;OH. Under PDMS (\u003cem\u003eHLB\u0026nbsp;\u003c/em\u003e= 0) wrapped condition, in the absence of HB\u003csub\u003ePDMS-Silanol\u003c/sub\u003e, the adhesion force of pre/postcast droplets were \u003cem\u003eF\u003c/em\u003e = 135.9 \u0026plusmn; 18.2 / 110.2 \u0026plusmn; 9.0 \u0026mu;N, respectively, not significantly different. However, the gap of adhesion force between precast/postcast droplets increased with \u003cem\u003eHLB\u003c/em\u003e. Under \u003cem\u003eHLB\u0026nbsp;\u003c/em\u003e= 0.02, obtained by diluting PDMS\u0026minus;OH (\u003cem\u003eHLB\u0026nbsp;\u003c/em\u003e= 0.12) with PDMS (\u003cem\u003eHLB\u0026nbsp;\u003c/em\u003e= 0), pre/postcast droplets exhibited \u003cem\u003eF\u003c/em\u003e = 27.2 \u0026plusmn; 15.4 / 0.68 \u0026plusmn; 0.34 \u0026mu;N, respectively. Here, the droplet in configuration C exhibited constant friction of hundreds nN. We find that both pre/postcast droplets transitioned from configuration W to configuration C, and the critical transition\u003cem\u003e\u0026nbsp;HLB\u003c/em\u003e was different between precast/postcast droplets. We defined the lower critical transition observed for postcast droplets at \u003cem\u003eHLB\u003c/em\u003e \u0026asymp; 0.01\u0026minus;0.02 with \u003cem\u003eHLB\u003c/em\u003e\u003csub\u003eLC\u003c/sub\u003e and upper critical transition \u003cem\u003eHLB\u003c/em\u003e for precast droplets at \u003cem\u003eHLB\u003c/em\u003e \u0026asymp; 0.5\u0026minus;0.7 with \u003cem\u003eHLB\u003c/em\u003e\u003csub\u003eUC\u003c/sub\u003e, respectively. The branched wettability is observed between these critical \u003cem\u003eHLB\u003c/em\u003es (i.e., \u003cem\u003eHLB\u003c/em\u003e\u003csub\u003eLC\u003c/sub\u003e \u0026lt;\u003cem\u003e\u0026nbsp;HLB\u0026nbsp;\u003c/em\u003e\u0026lt; \u003cem\u003eHLB\u003c/em\u003e\u003csub\u003eUC\u003c/sub\u003e).\u003c/p\u003e\n\u003cp\u003eWe then discuss the physical meaning of these transition points. The transition of precast droplets near \u003cem\u003eHLB\u003c/em\u003e\u003csub\u003eUC\u003c/sub\u003e is owing to the change in the thermodynamically favoured state of configurations, depending on the positive/negative sign of \u003cem\u003e\u0026Delta;\u0026gamma;\u003c/em\u003e. The \u003cem\u003e\u0026Delta;\u0026gamma;\u003c/em\u003e decreases with \u003cem\u003eHLB\u003c/em\u003e (\u003cstrong\u003eExtended Data Figure 8\u003c/strong\u003e) because \u003cem\u003e\u0026gamma;\u003c/em\u003e\u003csub\u003eow\u003c/sub\u003e decreases with the fraction of OH in PDMS by forming HB\u003csub\u003eWater-PDMS\u003c/sub\u003e. The critical \u003cem\u003eHLB\u003c/em\u003e for \u003cem\u003e\u0026Delta;\u0026gamma;\u0026nbsp;\u003c/em\u003e= 0 is estimated to be \u003cem\u003eHLB\u003c/em\u003e \u0026asymp; 0.62, which coincides with the value of experimentally obtained \u003cem\u003eHLB\u003c/em\u003e\u003csub\u003eUC\u003c/sub\u003e. At \u003cem\u003eHLB\u003c/em\u003e \u0026lt; \u003cem\u003eHLB\u003c/em\u003e\u003csub\u003eUC\u003c/sub\u003e (\u003cem\u003e\u0026Delta;\u0026gamma;\u0026nbsp;\u003c/em\u003e\u0026lt; 0), the interfacial state is in configuration W, and the contact line friction can be estimated from the Young-Dupr\u0026eacute; adhesion model\u003cem\u003e\u0026nbsp;F\u003c/em\u003e\u003csub\u003e\u0026gamma;\u003c/sub\u003e ~ \u003cem\u003e\u0026gamma;\u003c/em\u003e\u003csub\u003eow\u003c/sub\u003e(1+cos\u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e), which seems reasonable as the adhesion force decreases with HLB because of the decrease in \u003cem\u003e\u0026gamma;\u003c/em\u003e\u003csub\u003eow\u003c/sub\u003e. Here, slope fitting suggested \u003cem\u003eF\u003c/em\u003e ~ \u003cem\u003eHLB\u003c/em\u003e\u003csup\u003e\u0026minus;0.5\u003c/sup\u003e, as shown in the black dashed line in \u003cstrong\u003eFigure 3d\u003c/strong\u003e. At \u003cem\u003eHLB\u003c/em\u003e \u0026gt; \u003cem\u003eHLB\u003c/em\u003e\u003csub\u003eUC\u003c/sub\u003e (that is \u003cem\u003e\u0026Delta;\u0026gamma;\u0026nbsp;\u003c/em\u003e\u0026gt; 0), the configuration C is favoured, and the adhesion force of the precast droplet drastically decreases.\u003c/p\u003e\n\u003cp\u003eThe transition point of postcast droplets at \u003cem\u003eHLB\u003c/em\u003e\u003csub\u003eLC\u003c/sub\u003e depends on whether the OH group in PDMS can cover the substrate silanol that shields the HB\u003csub\u003eWater-Silanol\u003c/sub\u003e. The number of HB available molecules in PDMS should increase with increased \u003cem\u003eHLB\u003c/em\u003e. We consider the \u003cem\u003eHLB\u003c/em\u003e\u003csub\u003eLC\u003c/sub\u003e is the saturation point of HB\u003csub\u003ePDMS-Silanol\u003c/sub\u003e. At \u003cem\u003eHLB\u003c/em\u003e \u0026lt; \u003cem\u003eHLB\u003c/em\u003e\u003csub\u003eLC\u003c/sub\u003e, the amount of OH in PDMS is insufficient to cover substrate silanol. Thus, the uncovered silanol makes HB\u003csub\u003eWater-silanol\u003c/sub\u003e and droplets stick to the substrate. In this context, the configurations C and W co-exist beneath the postcast droplets, akin to a \u0026quot;partially Wenzel state\u0026quot; \u003csup\u003e22\u003c/sup\u003e, \u0026nbsp;and the total adhesion force can be the sum of the HB\u003csub\u003eWater-Silanol\u003c/sub\u003e at the substrate\u0026minus;water contact area \u003csup\u003e23\u003c/sup\u003e. Under the assumption that the water-silanol interface has negligible interfacial tension and the Young-Dupr\u0026eacute; model is acceptable for molecular scale wetting, the unit adhesion force by HB\u003csub\u003eWater-Silanol\u003c/sub\u003e would be ~ \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u0026gamma;\u003c/sub\u003e [\u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e\u0026rarr;0]. Moreover, the number density of the HB\u003csub\u003eWater-Silanol\u003c/sub\u003e would be proportional to the number of the silanol that failed to cover with OH groups in PDMS. Thus, we expect \u003cem\u003eF\u003c/em\u003e ~ \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u0026gamma;\u003c/sub\u003e [\u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e\u0026rarr;0] (1\u0026minus;\u003cem\u003e\u0026nbsp;f\u003c/em\u003e\u003csub\u003ePDMS\u0026minus;OH\u003c/sub\u003e/\u003cem\u003ef\u003c/em\u003e\u003csub\u003esilanol\u003c/sub\u003e) ~ \u003cem\u003eHLB\u003c/em\u003e\u003csup\u003e\u0026minus;0.5\u003c/sup\u003e(1\u0026minus;\u003cem\u003eHLB\u003c/em\u003e/\u003cem\u003eHLB\u003c/em\u003e\u003csub\u003eLC\u003c/sub\u003e) where \u003cem\u003ef\u003c/em\u003e\u003csub\u003ePDMS\u0026minus;OH\u003c/sub\u003e is the number density of OH bonding molecules in PDMS, which is approximately proportional to \u003cem\u003eHLB\u003c/em\u003e. The model equations are fitted with the plot in \u003cstrong\u003eFigure 3d\u003c/strong\u003e by orange dash line, and we get \u003cem\u003eHLB\u003c/em\u003e\u003csub\u003eLC\u003c/sub\u003e \u0026asymp; 0.019. At \u003cem\u003eHLB\u003c/em\u003e \u0026gt; \u003cem\u003eHLB\u003c/em\u003e\u003csub\u003eLC\u003c/sub\u003e, the postcast droplet favours configuration C and excess OH groups in PDMS, which does not play a significant role in droplet adhesion behaviour. Thus, we obtain \u003cem\u003eF\u003c/em\u003e \u0026asymp; const (grey dash line).\u003c/p\u003e"},{"header":"Extending wettability bifurcation to different phase combinations","content":"\u003cp\u003eBased on the proposed mechanism, we show that the branched wettability can be extended to different phase combinations (\u003cstrong\u003eFigure 4\u003c/strong\u003e). We observed branched wetting states using various surrounding media with different hydrogen bonding groups. For example, molecular interactions between amino-terminated PDMS (PDMS\u0026minus;NH\u003csub\u003e2\u003c/sub\u003e) and silanol are similar to PDMS\u0026minus;OH (\u003cstrong\u003eExtended Data Figure\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e9\u003c/strong\u003e).\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003eThus, we first studied the effect of \u003cem\u003eHLB\u003c/em\u003e on droplet adhesion force in replacing\u0026nbsp;PDMS\u0026minus;NH\u003csub\u003e2\u003c/sub\u003e for\u0026nbsp;PDMS\u0026minus;OH\u0026nbsp;(\u003cstrong\u003eFigure 4a\u003c/strong\u003e). We observed the emergence of branched wettability at\u0026nbsp;\u003cem\u003eHLB\u0026nbsp;\u003c/em\u003efrom 0.0008\u0026nbsp;to 0.019. We did not observe bifurcation of droplet shape when we used various modified PDMS without hydrogen bonding species (\u003cstrong\u003eExtended Data Figure\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e10\u003c/strong\u003e).\u003c/p\u003e\n\u003cp\u003eThe hydrophobic part of the surrounding media is not limited to PDMS as long as the media phase is water-immiscible and has a hydrogen-bonding group. We then studied the fatty acid system using a mixture of 1-octadecene (C\u003csub\u003e18\u003c/sub\u003eH\u003csub\u003e36\u003c/sub\u003e) and oleic acid (C\u003csub\u003e17\u003c/sub\u003eH\u003csub\u003e33\u003c/sub\u003eCOOH). Here, the carboxyl group in oleic acid is a hydrogen-bonding species. \u003cstrong\u003eFigure 4b\u003c/strong\u003e assessed the sliding angle of pre/postcast droplets (\u003cem\u003eV\u003c/em\u003e = 5 \u0026mu;L) with their different \u003cem\u003eHLB\u003c/em\u003e. We also find that the branched wettability HLB region is from 0.3 to near 1.6.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eNotably, hydrogen bonding agents are not limited to liquids, but the branched wettability system is available by dissolving solute into the liquid. We dissolved 1 wt.% octadecyl amine (C\u003csub\u003e18\u003c/sub\u003eH\u003csub\u003e37\u003c/sub\u003eNH\u003csub\u003e2\u003c/sub\u003e) as a hydrogen bonding additive, in 1-octadecene, and adjusted \u003cem\u003eHLB\u003c/em\u003e = 0.012. We observed the branched wettability, as shown in \u003cstrong\u003eFigure 4c\u003c/strong\u003e. These results explained the potential expansion of branched wettability in various surrounding media.\u003c/p\u003e\n\u003cp\u003eWe also varied the substrate hydrophobic part from phenyl (C\u003csub\u003e6\u003c/sub\u003eH\u003csub\u003e5\u003c/sub\u003e\u0026minus;) to more hydrophobic alkyl (C\u003csub\u003e6\u003c/sub\u003eH\u003csub\u003e13\u003c/sub\u003e\u0026minus;, \u003cem\u003eR\u003c/em\u003e\u003csub\u003eq\u003c/sub\u003e=0.82 nm) or perfluoroalkyl (C\u003csub\u003e4\u003c/sub\u003eF\u003csub\u003e9\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eH\u003csub\u003e4\u003c/sub\u003e\u0026minus;, \u003cem\u003eR\u003c/em\u003e\u003csub\u003eq\u003c/sub\u003e = 1.14 nm)\u0026nbsp;while keeping surface smoothness. With the increase of substrate hydrophobicity (\u003cem\u003ei.e.\u003c/em\u003e, increase \u003cem\u003e\u0026gamma;\u003c/em\u003e\u003csub\u003esw\u003c/sub\u003e), the \u003cem\u003eHLB\u003c/em\u003e\u003csub\u003eUC\u003c/sub\u003e should be decreased because of the decrease in \u003cem\u003e\u0026Delta;\u0026gamma;\u003c/em\u003e. As expected, the branched wettability was observed for all probe surfaces. We find that the \u003cem\u003eHLB\u003c/em\u003e\u003csub\u003eUC\u003c/sub\u003e is decreased with the increase of substrate hydrophobicity (which is high in the order of perfluoroalkyl, alkyl, and phenyl modification). (\u003cstrong\u003eFigure 4d\u003c/strong\u003e). This is because the \u003cem\u003e\u0026Delta;\u0026gamma;\u003c/em\u003e decreases with the substrate hydrophobicity.\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eMolecular level tuning of the wettability balance enabled the observation of the branched wetting states. One droplet is in a metastable state owing to the energetic barrier by molecular interaction, and another droplet is in a thermodynamically favoured state. While this work mainly modulated the hydrogen bonding species of the surrounding media, which \u003cem\u003eHLB\u003c/em\u003e quantifies, the concept can be expanded to modulation of droplets, substrate surface chemistry, and even molecular interactions different from HB. The observed droplet shape, adhesion behaviour, and energy level of configurations are analogous to those of Cassie and Wenzel droplets. Since the probe surface has molecular scale heterogeneity, we propose to term the observed droplet repellent/sticky state \u0026quot;Atomic Cassie/Wenzel state.\u0026quot; We believe the atomic Cassie/Wenzel state would be a powerful tool for understanding\u0026nbsp;the molecular effect on droplet\u0026nbsp;mobility \u003csup\u003e8,24\u003c/sup\u003e, adaptivity \u003csup\u003e25\u003c/sup\u003e, micro-wetting \u003csup\u003e26\u003c/sup\u003e, and nanofluidics \u003csup\u003e27\u003c/sup\u003e.\u0026nbsp;This finding will also guide the design of robust\u0026nbsp;liquid-repellent or capturing surfaces\u0026nbsp;since the surface nano/microscale texture typically suffers from low mechanical stability\u0026nbsp;\u003csup\u003e28\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003e\u003cu\u003eMaterials.\u003c/u\u003e All chemicals are used as received. We used phenyltriethoxysilane from Tokyo Chemical Industry Co., Ltd., Japan; hexyltriethoxysilane and nonafluorohexyltriethoxysilane from Fluorochem Ltd., UK; hexane from NACALAI TESQUE, INC., Japan; hydrochloric acid, acetone, oleic acid, and 1-octadecene from FUJIFILM Wako Pure Chemical Corporation, Japan; octadecyl amine from Sigma-Aldrich Co. LLC, USA; PDMS (DMS-T15) from Gelest Inc., USA. PDMS\u0026minus;OH with \u003cem\u003eHLB\u003c/em\u003e = 0.12 (X-22-170BX), PDMS\u0026minus;OH with \u003cem\u003eHLB\u003c/em\u003e = 0.73 (KF6000), PDMS\u0026minus;OH with \u003cem\u003eHLB\u003c/em\u003e = 0.38 (KF6001), PDMS\u0026minus;NH\u003csub\u003e2\u003c/sub\u003e (X-22-161A), other modified PDMS: PDMS\u0026minus;Alkyl (KF414), PDMS\u0026minus;Ph (KF56), PDMS\u0026minus;Metacryl (KF2012), PDMS\u0026minus;Epoxy (X-22-173DX), PDMS\u0026minus;Mercapto (X-22-167B) were kindly provided from Shinetsu Co., Ltd., Japan. Ultrapure water with 18.2 MΩ/cm resistance was obtained using a Direct-Q UV3 system (Merck KGaA, Germany).\u003c/p\u003e\n\u003cp\u003e\u003cu\u003eSubstrate modification.\u003c/u\u003e We modified the silane to a water-polished slide glass (Micro slides, MUTO PURE CHEMICALS CO., LTD., Japan). The glass surface was cleaned using plasma cleaner (PIB-10, Vacuum Device Inc., Japan). Then, the glass was immersed in a mixture of 1 mL silane, 20 mL hexane, and 1\u0026mu;L hydrochloric acid for 20 hours. After the immersion, the glass substrate was cleaned using acetone, hexane, and ultrapure water in this order.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e\u003cu\u003eHLB\u003c/u\u003e\u003c/em\u003e\u003cu\u003e\u0026nbsp;modulation.\u003c/u\u003e We estimated the \u003cem\u003eHLB\u003c/em\u003e of PDMS according to the Griffin method: \u003cem\u003eHLB\u003c/em\u003e = 20 \u0026times; [molecular mass of hydrophilic part] / [total molecular mass]. Moreover, additivity allowed the fine adjustment of \u003cem\u003eHLB\u003c/em\u003e by varying the weight ratio of the mixture, which yields \u003cem\u003eHLB\u003c/em\u003e = \u0026Sigma;\u003cem\u003ew\u003csub\u003ei\u003c/sub\u003eHLB\u003csub\u003ei\u003c/sub\u003e\u003c/em\u003e, where \u003cem\u003ew\u003csub\u003ei\u003c/sub\u003e\u003c/em\u003e and \u003cem\u003eHLB\u003csub\u003ei\u003c/sub\u003e\u003c/em\u003e\u003csub\u003e\u0026nbsp;\u003c/sub\u003eare the weight fraction and HLB of mixing component \u003cem\u003ei\u003c/em\u003e = 1,2\u0026hellip;. PDMS\u0026minus;OH with \u003cem\u003eHLB\u003c/em\u003e from 0 to 0.12 was obtained by the varied mixing ratio of DMS-T15 and X-22-170BX. The mixture of KF6000 and KF6001 obtained PDMS\u0026minus;OH with \u003cem\u003eHLB\u003c/em\u003e \u0026gt; 0.12. The mixing ratio of DMS-T15 and X-22-161A adjusted the \u003cem\u003eHLB\u003c/em\u003e of PDMS\u0026minus;NH\u003csub\u003e2\u003c/sub\u003e.\u003c/p\u003e\n\u003cp\u003e\u003cu\u003eWettability measurement.\u003c/u\u003e\u003cem\u003e\u0026nbsp;\u003c/em\u003eContact angles, sliding angles, and interfacial tension were measured using a contact angle meter (Drop Master-SA-Cs1, Kyowa Interface Science Co., Ltd., Japan). The resolution of the sliding angle is 0.1\u0026nbsp;\u0026plusmn;\u0026nbsp;0.05\u0026deg;. Interfacial tension was obtained using the pendant drop method. Dynamic contact angles were obtained from droplets just in contact line motion. We pushed the droplets using a Teflon needle tip (22 G). These measurements were repeated at least three times, and the results were reported as mean \u0026plusmn; SD values.\u003c/p\u003e\n\u003cp\u003e\u003cu\u003eCalculation of interfacial energy difference.\u003c/u\u003e Equation \u003cem\u003e\u0026Delta;\u0026gamma;\u003c/em\u003e = [total energy of configuration C]\u0026nbsp;\u0026ndash;\u0026nbsp;\u0026nbsp;[total energy of configuration W] =\u0026nbsp;\u003cem\u003e\u0026gamma;\u003c/em\u003e\u003csub\u003eso\u003c/sub\u003e + \u003cem\u003e\u0026gamma;\u003c/em\u003e\u003csub\u003eow\u003c/sub\u003e \u0026ndash; \u003cem\u003e\u0026gamma;\u003c/em\u003e\u003csub\u003esw\u003c/sub\u003e obtained from \u003cstrong\u003eExtended Data Figure 4\u003c/strong\u003e can be reduced to measurable quantities using Young\u0026rsquo;s equation, and we have \u003cem\u003e\u0026Delta;\u0026gamma;\u003c/em\u003e =\u0026nbsp;\u003cem\u003e\u0026gamma;\u003c/em\u003e\u003csub\u003ew\u003c/sub\u003ecos\u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003ew\u003c/sub\u003e \u0026ndash;\u0026nbsp;\u003cem\u003e\u0026gamma;\u003c/em\u003e\u003csub\u003eo\u003c/sub\u003ecos\u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003eo\u003c/sub\u003e + \u003cem\u003e\u0026gamma;\u003c/em\u003e\u003csub\u003eow\u003c/sub\u003e, where\u0026nbsp;\u003cem\u003e\u0026gamma;\u003c/em\u003e\u003csub\u003ew\u003c/sub\u003e and\u0026nbsp;\u003cem\u003e\u0026gamma;\u003c/em\u003e\u003csub\u003eo\u003c/sub\u003e are water and PDMS surface tensions, \u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003ew\u003c/sub\u003e and \u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003eo\u003c/sub\u003e are static water and PDMS contact angles on the probe surface in air, respectively \u003csup\u003e15\u003c/sup\u003e. The interfacial energies and contact angles are measured using a contact angle meter and summarized in \u003cstrong\u003eExtended Data Table 1\u003c/strong\u003e.\u003c/p\u003e\n\u003cp\u003e\u003cu\u003eSurface analysis.\u003c/u\u003e\u003cem\u003e\u0026nbsp;\u003c/em\u003eThe probe surface structure was observed using field-emission SEM (FE-SEM S-4800; Hitachi High-Technologies Co., Japan) and AFM (MFP-3D Origin AFM - Asylum Research, UK).\u0026nbsp;Fourier transform infrared (FT-IR) attenuated total reflection (ATR) spectrum was measured using IRSpirit-L (Shimadzu Corp., Japan).\u003c/p\u003e\n\u003cp\u003e\u003cu\u003eIntermolecular interaction.\u003c/u\u003e We evaluated the intermolecular interaction energies between silanol and PDMS(\u0026minus;OH) using the Gaussian16 program\u003csup\u003e\u0026nbsp;29\u003c/sup\u003e. The geometries of isolated molecules were optimized at the B3LYP/6-311G** level. We also obtained the electrostatic potential maps based on this computational level.\u0026nbsp;To investigate the contribution of the terminal\u0026nbsp;hydroxyl\u0026nbsp;groups, the long axis of the PDMS molecule was aligned perpendicular to the substrate, and the PDMS(\u0026minus;OH) molecule was rotated along this axis to find the energy minima. We plotted the interaction energies at different distances between the molecule and the substrate while setting the optimized arrangement as the origin of the distance.\u0026nbsp;The intermolecular interaction energies were calculated at the PBE/6-311G** level using Grimme\u0026rsquo;s D3BJ dispersion correction\u0026nbsp;\u003csup\u003e14\u003c/sup\u003e. Note that it has been demonstrated that this level of calculation provides reasonable estimations for the interaction energies of hydrocarbon molecules and molecules, including hetero atoms\u0026nbsp;\u003csup\u003e30\u003c/sup\u003e. Basis set superposition error (BSSE)\u0026nbsp;\u003csup\u003e31\u003c/sup\u003e was corrected using the counterpoise method\u0026nbsp;\u003csup\u003e32\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003cp\u003e1.\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;Kalliadasis, S. \u0026amp; Chang, H. Dynamics of Liquid Spreading on Solid Surfaces. \u003cem\u003eInd Eng Chem Res\u003c/em\u003e \u003cstrong\u003e35\u003c/strong\u003e, 2860\u0026ndash;2874 (1996).\u003c/p\u003e\n\u003cp\u003e2.\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;Feng, L. \u003cem\u003eet al.\u003c/em\u003e Petal Effect : A Superhydrophobic State with High Adhesive Force. \u003cem\u003eLangmuir\u003c/em\u003e \u003cstrong\u003e24\u003c/strong\u003e, 4114\u0026ndash;4119 (2008).\u003c/p\u003e\n\u003cp\u003e3.\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;T. Onda, S. Shibuichi, N. Satoh, and K. T. 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In principle, droplets on a smooth surface exhibit a single wetting state. According to Young's law in 1805 4, the shape of a droplet, quantified with contact angle, is determined by the balance of substance-specific interfacial energies between three phases of a droplet, contacting solid surface and surrounding media4. Contact angles fluctuate due to external disturbance and the mobility of contact line 5, but the applicable range is generally fixed, which features the adhesion mode of the droplet. Here we show the emergence of branched wetting states with different contact angle ranges using the same droplet and surrounding media on a smooth, homogeneous surface. The applicable wetting states are high-contact angle droplet sticks to the surface or repellent, akin to the Wenzel 6 or Cassie 7 states observed on a nano/micro-textured surface, respectively. The phenomenon is commonly observed when site-specific molecular interactions trap the droplet metastable —the wettability branches when the interface formation order changes. This is because the molecular interactions at interfaces cause hysteresis in phase replacement under certain wettability conditions. Our experiment varied the combination and number of interaction molecules in phases, unravelling the design principles of the branched wettability. This work suggests that the site-specific molecular interaction can bifurcate macroscopic wetting modes, which advances the fundamental understanding of the molecular effect on macro-wettability.","manuscriptTitle":"Emergence of branched wetting states on a smooth surface","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-07-19 14:35:22","doi":"10.21203/rs.3.rs-4493821/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"4eea4a47-617f-40c7-ba81-cf6d348ff0d6","owner":[],"postedDate":"July 19th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":32544616,"name":"Physical sciences/Materials science/Soft materials/Wetting"},{"id":32544617,"name":"Physical sciences/Chemistry/Surface chemistry"}],"tags":[],"updatedAt":"2024-11-22T06:35:19+00:00","versionOfRecord":[],"versionCreatedAt":"2024-07-19 14:35:22","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4493821","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4493821","identity":"rs-4493821","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}