# Fileset

[Adv Materials Inter - 2026 - Tenjimbayashi - Bistable Wetting States on a Smooth Surface.pdf](https://mdr.nims.go.jp/filesets/b6b82dec-816a-47c5-a0cf-1d02c728d2f9/download)

## Creator

[Mizuki Tenjimbayashi](https://orcid.org/0000-0002-8107-8285), Shunto Arai

## Rights

[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Bistable Wetting States on a Smooth Surface](https://mdr.nims.go.jp/datasets/23253a8b-1d95-4bc5-a5fc-2b7ddfff97f4)

## Fulltext

Bistable Wetting States on a Smooth SurfaceAdvancedMaterials Interfaceswww.advmatinterfaces.deRESEARCH ARTICLEBistable Wetting States on a Smooth SurfaceMizuki Tenjimbayashi1 Shunto Arai21Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science, Tsukuba, Ibaraki, Japan 2Research Center forMacromolecules and Biomaterials, National Institute for Materials Science, Tsukuba, Ibaraki, JapanCorrespondence:Mizuki Tenjimbayashi (TENJIMBAYASHI.Mizuki@nims.go.jp)Received: 17 December 2025 Revised: 16 March 2026 Accepted: 25 March 2026Keywords: bistable wetting states | hydrophile–lipophile balance (HLB) | hydroxyl-terminated polydimethylsiloxane | non-textured surface | sticky/repellentstatesABSTRACTDroplets on a non-textured surface typically exhibit a monostable wetting state, as represented by Young state. Here, we showthat droplets can exhibit bistability without surface texture by tuning molecular interactions. We investigated the behavior ofwater droplets on a smooth substrate when immersed in oil. The oil contains hydrophilic interaction components, and theirhydrophobic–hydrophilic balance was systematically varied. For oils with a specific hydrophobic–hydrophilic balance, dropletstates bifurcate between repellent or sticky depending on the order of droplet casting and oil immersion. These states are neithertransient nor one-off, indicatingmolecular interactions can create an energetic barrier separating the two states rather than surfacetextures. Under other oil conditions, the droplet remains monostable, either repellent or sticky, regardless of the order. Thiswork advances the fundamental understanding of molecular effects on droplet behavior and expands surface design strategiesin functional materials without compromising mechanical durability.1WdvspAssdtaooacoTc©AhIntroductionhen a droplet is cast onto a solid surface, part of theroplet/solid surface is replaced by their interface, and a wideariety of shapes and adhesion modes, such as spreading [1],ticky [2], and super-repellent [3], can be obtained. In princi-le, droplets on smooth surfaces exhibit a single wetting state.ccording to Young’s law [4], droplet shape, quantified with atatic contact angle θs, depends on the balance of substance-pecific interfacial energies between the three phases of theroplet, contacting solid surface, and surrounding media unlesshe balance changes due to an external field [5–7]. Contactngles fluctuate due to external disturbances and the mobilityf the contact line. The maximum/minimum contact angle isbserved when the contact line advances/recedes, yielding thedvancing/receding contact angles θa/r [8]. The mobility of theontact line depends on the degree of surface heterogeneity. Mostbject surfaces are not perfectly homogeneous, at least on thehis is an open access article under the terms of the Creative Commons Attribution License, which permited.2026 The Author(s). Advanced Materials Interfaces published by Wiley-VCH GmbHdvanced Materials Interfaces, 2026; 13:e70495ttps://doi.org/10.1002/admi.70495molecular scale [9]. However, a surface with a much smallerdegree of heterogeneity than the droplet contact line length can beregarded as a non-patterned surfacewhenwemeasure the contactangles at droplet scale magnification [10].A droplet on a non-patterned surface exhibits a single inherentcontact angle range, that is, a monostable state. When thesurrounding media is air, the droplet shape follows Young’s law[4]. or completely spreads (θs ≈ 0◦) on the smooth substrate,depending on the signs of spreading coefficient S. When thesurrounding media is a droplet-immiscible liquid, the threephases follow Young’s law, or one of the liquids (droplet orsurrounding liquid) completely spreads on the smooth substrate.When the surrounding liquid completely spreads (that is, dropletspreading coefficient under surrounding liquid Sd is < 0), thedroplet becomes completely spherical and exhibits θs ≈ 180◦ [11].In these cases, these droplet states are monostable and can beobserved separately.its use, distribution and reproduction in any medium, provided the original work is properly1 of 9http://www.advmatinterfaces.dehttps://doi.org/10.1002/admi.70495https://orcid.org/0000-0002-8107-8285mailto:TENJIMBAYASHI.Mizuki@nims.go.jphttp://creativecommons.org/licenses/by/4.0/https://doi.org/10.1002/admi.70495http://crossmark.crossref.org/dialog/?doi=10.1002%2Fadmi.70495&domain=pdf&date_stamp=2026-04-02HtgdfdbtT[dwctrttotsiboIwcTeiamqabfTesacp22Aiwlmm2pgFwct2 21967350, 2026, 10, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/admi.70495 by National Institute For, Wiley Online Library on [21/05/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creatiowever, when the solid surface is nano- or microtextured,he droplet follows two branched states: (i) the droplet homo-eneously infuses the texture (Wenzel state) [12] or (ii) theroplet makes limited contact with the outermost textured sur-ace (Cassie state) [13]. While there have been suggestions toefine Wenzel/Cassie intermediate states [14–16], the distinctionetween the Wenzel and Cassie states is basically whether theexture is infused by the droplet phase or the surrounding media.hese states are observed not only in air but also in liquids17, 18]. In the Wenzel state, the surface texture enhances theroplet–surface contact area, resulting in highly sticky dropletsith θs >> θr [19]. In the Cassie state, the droplet–substrateontact area is smaller than the apparent contact area, andhe adhesion force is smaller than that in Wenzel state, whichesults in θs ≈ θr. The Wenzel and Cassie states coexisted on aextured surface, one of which is energetically favored. However,he energetic barrier for transitioning between two states existswing to surface texture, which enables the observation ofhe other metastable state [20]. Thus, surface texture plays aignificant role in the emergence of bistable states. Herein, wenvestigate whether molecular interactions at the interfaces cane substituted for surface texture in terms of the potential barrierf formation between the two states.n this study,we show that two apparently differentwetting states,hich satisfy the contact angle feature of θs ≈ θr and θs >> θr,an coexist on a smooth surface owing to molecular interactions.he observed states are neither transient, one-off, nor induced byxternal stimuli. We modulated the number of hydrogen bondsn three phases: a water droplet, a smooth silanized substrate,nd oil with a hydrogen bonding moiety as the surroundingedia. As a result of molecular-scale wettability modulation,uantified by the hydrophobic–hydrophilic balance (also knowns the Hydrophile–Lipophile Balance, or HLB), we found that theifurcation of the droplet states depends on the order of interfaceormation, that is, the order of droplet casting and oil immersion.he static and dynamic wettability features of these states werexperimentally confirmed, and the underlying mechanism wastudied on a molecular scale using interaction, thermodynamic,nd force measurements. We also confirmed that bistable statesan be extended to different substance combinations based on theroposed mechanism.Results and Discussion.1 Bistable States on One Smooth Surfaceself-assembled silane monolayer regulates the surface chem-stry of the substrate without texturing [21]. The probe surfaceas a glass substrate modified with a phenyl silane mono-ayer. The surface has no texture (Figure 1a), and atomic forceicroscopy (AFM) measurements quantified the surface root-ean-square roughness of Rq = 0.41 nm at the scan range of0 µm × 20 µm (Figure 1b). In addition to the hydrophobichenyl group, the surface had hydrophilic silanol groups fromlass and the hydrolysis of phenyl silane, as confirmed from theourier-transform infrared (FT-IR) spectrum (Figure S1). Theater contact angle in air is (θs, θr) = (80◦ ± 2◦, 61◦ ± 1◦). Byhanging the surroundingmedia from air to liquid state hydroxyl-erminated polydimethylsiloxane (PDMS–OH) with HLB = 0.12of 9[22], the water droplet behavior branched into sticky or repellent(Figure 1c,d). The applicablewetting states depend on the order ofinterface formation (Figure S2). On the one hand, the droplet caston the probe surface after immersion in PDMS–OH within 30 s(denoted as the post-cast droplet) has a water contact angle of (θs,θr) = (176◦ ± 1◦, 173◦ ± 1◦) (Figure 1c), exhibiting nearly perfecthydrophobicity but with observable “non-zero” water adhesion(Figure S3 andMovie S1). Here, a PDMS–OH layer was entrappedbeneath the resting post-cast droplet, similar to a Cassie state.The layer was too thin to be observed because it was squeezedby the droplet. During motion, the layer becomes sufficientlythick to allow side-view observation at the droplet scale. Thisis because the layer thickness increases with the droplet slidingvelocity, known as oleoplaning effect [11]. On the other hand,the droplet cast before the immersion (denoted as the precastdroplet) exhibited a water contact angle of (θs, θr) = (131◦ ±4◦, 107◦ ± 2◦) (Figure 1d; Movie S2). In both cases, θa reachesnearly 180◦, which means PDMS–OH spreads completely (thatis, equivalent to the PDMS–OH receding angle being nearly 0◦)to the probe surface as a liquid state and prevents contact lineadvance. Note that PDMS–OH is neither coated nor grafted tothe substrate, which is confirmed by the constant water contactangle in air regardless of the repeated PDMS–OH immersion andrinsing (Figure S4). Moreover, the droplets were not in a transientstate and maintained the observed wettability for a sufficientlylong time (discussed in Section 2.3 Interfacial stability).2.2 Interfacial StatesBranched wetting states are observed within a specific HLBrange. Figure 2a shows photographs of water droplets cast ontothe substrate before and after immersion in PDMS(─OH) withdifferent HLB values. PDMS (HLB= 0), PDMS–OH (HLB= 0.12),and PDMS–OH (HLB = 0.73) have similar surface tensions of γo≈ 19.8, 19.9, and 21.4 mN/m, respectively, and viscosities of η ≈50, 40, 35 mPa⋅s. Under PDMS, the post- and precast dropletsexhibit similar contact angles of (θs, θr) = (125◦ ± 4◦, 84◦ ± 4◦)and (118◦ ± 4◦, 83◦ ± 5◦), respectively. Under PDMS–OH (HLB =0.73), the post- and precast droplets exhibit contact angles of (θs,θr) = (170◦ ± 1◦, 168◦ ± 4◦) and (167◦ ± 2◦, 146◦ ± 4◦), respectively,with notably high θr values. In contrast, under PDMS–OH (HLB= 0.12), branched repellent/sticky droplet behavior was observed,as discussed above, with (θs, θr) = (176◦ ± 1◦, 173◦ ± 1◦) and (131◦± 4◦, 107◦ ± 2◦) for post- and precast droplets (Figure 1c,d).The possible interfacial states of the PDMS-entrapped regionand droplet–substrate contact region at the molecular scale areillustrated in Figure 2b,c, respectively. The former state is termedConfiguration R (repellent) because the entrapped PDMS layerlimits the droplet contact with the solid. The latter state istermed Configuration S (sticky) because the droplet forms directcontact with the substrate. We expected the composition of thetwo configurations under the droplet to differ depending onthe surrounding media. In Configuration R, droplet–substratecontact is not formed, thereby increasing the droplet repellency.Under PDMS−OH (HLB = 0.73), most of the region beneaththe droplet was in Configuration R, but not the entire regionbecause droplet adhesion was observed (Figure S3 and MovieS1). Under PDMS, most of the region beneath the droplet wasin Configuration S, and the droplet adhered to the substrateAdvanced Materials Interfaces, 2026ve Commons LicenseFIGURE 1 Bifurcated wetting states on one smooth surface. (a, b) Field emission scanning electron microscopy (FE-SEM; top) and AFM (bottom)images of the phenyl silane-modified glass substrate surface. Dust was included in the FE-SEM image to confirm that the focus is correct. (c) Side-viewphotographs of two 5 µL water droplets cast onto the one same substrate before (right) and after (left) immersing the substrate in PDMS–OH. (d) Theadhesion behavior of the droplets in motion. Droplets were pushed with a Teflon needle parallel to the substrate.FIGURE 2 Comparison of different interfacial states. (a) Photographs of pre-/post-cast water droplets under PDMS(─OH) with different HLBs.(b, c) Schematics of two interfacial states: (b) PDMS–OH is entrapped beneath the droplet and minimize the droplet substrate contact, denoted asConfiguration R; (c) the droplet adheres to the substrate –OH area, denoted as Configuration S. Possible hydrogen bonding determines the preferencebetween the twowetting states; hydrogen bonding betweenwater and PDMS–OH (HBWater–PDMS), PDMS–OHand silanol from the glass substrate and/orhydrolyzed silane (HBPDMS–Silanol), or water and Silanol (HBWater–Silanol). (d) Distance dependence of the intermolecular interaction energy between the–OH groups on the substrate surface silanol and the molecular end group of PDMS(─OH). (e) Electrostatic potential map of PDMS–OH in proximity to–OH groups on the substrate surface.Advanced Materials Interfaces, 2026 3 of 9 21967350, 2026, 10, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/admi.70495 by National Institute For, Wiley Online Library on [21/05/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License(tcatisItldhbgHAtsoio(iObmiesaowtOgrd2Ftadco(Ncdi=tatv[tB4 21967350, 2026, 10, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/admi.70495 by National Institute For, Wiley Online Library on [21/05/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable CreatiFigure 2a, left), indicating that molecular interaction stabilizedhe PDMS–OH layer between the droplet and substrate. Weonsider this interaction to be hydrogen bonding between waternd PDMS–OH (HBWater–PDMS) and between PDMS–OH andhe silanol interface (HBPDMS–Silanol). Moreover, the oleophilicnteractions between PDMS–OH and the substrate phenyl groupshould also enhance the stability of the entrapped PDMS–OH.n Configuration S (Figure 2c), observed under PDMS and forhe precast droplet under PDMS–OH (HLB = 0.12) (Figure 2a,eft and center), the sticking property of the droplet is due to theirect contact between water and the substrate. Water moleculesave a higher affinity for silanol groups than for phenyl groupsecause of possible hydrogen bonding with the substrate silanolroups (HBWater–Silanol). See Note S1 [23, 24] for estimation of theBWater–Silanol fraction in Configurations R and S.s shown above, the specific configuration of the region beneathhe droplet depends on the adhesion of PDMS(─OH) to the sub-trate beneath the water droplet through the possible formationf HBPDMS–Silanol. To investigate this further, we calculated thentermolecular interaction energies at the PBE/6-311G** levelf theory incorporating Grimme’s dispersion correction [25]see Methods section for details [26–29]). Figure 2d shows thenteraction energy as a function of the distance between PDMS–H and the silanol group. The potential well is shallow for PDMSut sufficiently large for PDMS–OH compared with the ther-al fluctuation energy. The origin of this significant attractiventeraction can be explained by electrostatic interactions. Thelectrostatic potentialmap between the end of PDMS–OHand theilanol group (Figure 2e) shows that the O (or H) of the silanolttracts the H (or O) of PDMS–OH, suggesting the formationf a hydrogen bond. Although the long-range interaction decaysith distance from the substrate, it is still large compared to thehermal effect with a distance of 5–6Å. This indicates that PDMS–Hcan form sufficiently strong hydrogen bonds evenwith silanolroups covered by phenyl groups (approximately 4 Å in height),esulting in the formation of a stable PDMS–OH layer below theroplet, which is absent in the case of PDMS..3 Interfacial Stabilityigure 3a–c shows a comparison of the total energies of thewo configurations under PDMS, PDMS–OH (HLB = 0.12),nd PDMS–OH (HLB = 0.73), respectively. We calculated theifference in the unit area total interfacial energy γtotal of twoonfigurations using Δγ = γso + γow – γsw, where the subscripts s,, and w denote substrate, PDMS(─OH), and water, respectivelysee Methods section for details [30], Figure S5, and Table S1).ote that this value is intrinsically equivalent to the spreadingoefficient Sd. We also confirmed that PDMS(─OH) does notissolve in the water layer, and that the water–PDMS(─OH)nterfacial energy is constant (Figure S6). Under PDMS, Δγ28.2 ± 2.8 mJ/m2, indicating that Configuration S favoredhermodynamically (Figure 3a). Thus, the water droplet contactsfter immersion in PDMS transitioned from Configuration Ro S, and the transition time was 13 s, which reflects theiscosity-dependent rupture of the PDMS layer below the droplet31]. Under PDMS–OH (HLB = 0.12), Configuration S still ishermodynamically stable with Δγ= 10.1± 1.9 mJ/m2 (Figure 3c).ecause the viscosity of PDMS–OH (HLB= 0.12) is similar to thatof 9of PDMS, the transition time is expected to be similar; however,the post-cast droplet maintained its shape for significantly longer.This implies that a considerable energetic barrier prevents thetransition, which should mainly arise from the work required todetach PDMS–OH (HLB = 0.12) from the substrate underwater(that is, advance the contact line of water). Despite the difficultyin comparing the detachment force from the θa ≈ 180◦ (thatis, PDMS receding contact angle ≈ 0◦) for the precast droplets,we consider that the detachment work is higher for PDMS–OH (HLB = 0.12) than for PDMS owing to the HBPDMS–Silanol.In contrast, under PDMS–OH (HLB = 0.73), Configuration Ris thermodynamically stable, as indicated by Δγ = −3.3 ± 0.9mJ/m2 (Figure 3b). Despite the existence of an energetic barrierby HBWater–Silanol, the precast droplet immediately switched froma sticky to a repellent state. This means the energetic barrier istoo small to prevent the transition. In this case, the energeticbarrier arises from the work required to detach (recede thecontact line of) water from the substrate. Owing to the hydropho-bicity (oleophilicity) of the substrate phenyl group, the waterdetachment is easier than the PDMS–OH detachment despitethe existence of the HBWater–Silanol. That is apparent from the θa>> θr for droplets in Configuration S. While this, the precastdroplet under PDMS–OH (HLB = 0.12) did not switch becausethe droplet favors Configuration S (Figure 3c). The energy-levelrelationships of the configurations in Figure 3c were similarto those of the Cassie and Wenzel states observed in texturedsurfaces [32]. Notably, the energetic barriers to transitioning fromconfiguration R to S should not differ significantly across thesePDMS–OH systems, as HB sites in PDMS are sufficient to coverthe silanol group on the substrate (see the discussion in the nextsection). Rather than that, the transition difficulty is dominatedby the plus or minus sign of the Δγ. In the HLB = 0.12 case, toexhibit bistability, HBPDMS–Silanol shouldwork to prevent transitionfrom Configuration R to S. In this case, the HBPDMS–Silanol shouldbe large enough to prevent the receding (advancing) of the PDMS(water). In theHLB= 0.73 case, to exhibit bistability, HBWater–Silanolshould work to prevent transition from Configuration S to R. Inthis case, the HBWater–Silanol should be large enough to preventthe receding (advancing) of water (PDMS). This difference arisesfrom the presence of a hydrophobic/oleophilic part.2.4 Droplet Adhesion BehaviorAlthough droplets in Configuration R (S) are repellent (sticky)under PDMS–OH (HLB = 0.12), the quantification of theadhesion force is challenging because the density of PDMS iscomparable to that of the droplet. Thus, we estimated the dropletadhesion by measuring the critical sliding angle α of a PDMS-wrapped droplet (Figure S7) [33, 34], yielding F≈ ρVg sinα, whereρ≈ 0.997 g/mL is the density ofwater,V is the droplet volume, andg≈ 9.81m2/s is the gravitational acceleration constant (Figure 4a).Figure 4b,c shows the sliding behavior of post- and precastdroplets wrapped in PDMS–OH (HLB = 0.12) (V = 5 µL). Ata 1◦ tilt, the post-cast droplet in Configuration R slid off at aconstant speed of U = 36 ± 11 µm/s, while the precast dropletin Configuration S did not slide off with the surface tilted at 90◦.The apparent adhesion force difference depends on whether thedroplet makes direct contact with the substrate. In ConfigurationR, the droplet–substrate contact is limited by PDMS(─OH);therefore, the contact line friction is negligible, and the adhesionAdvanced Materials Interfaces, 2026ve Commons LicenseFIGURE 3 Interfacial stability. Interfacial energy diagram and possible wetting transition of water droplet under (a) PDMS, (b) PDMS–OH (HLB= 0.73), and (c) PDMS–OH (HLB = 0.12). In (a)/(b), the post-/pre-cast droplet transitioned from repellent/sticky to sticky/repellent owing to theirmonostability. However, the pre-/post-cast droplet keeps sticky/repellent under PDMS–OH (HLB = 0.12) owing to the bistability.fdwc≈FIaFPwprticPaeFfdt0atNTiA 21967350, 2026, 10, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/admi.70495 by National Institute For, Wiley Online Library on [21/05/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creatiorce mainly originates from the viscous dissipation around theroplet [35]. In Configuration S, the droplet makes direct contactith the substrate, and the adhesion force corresponds to theontact line friction [36], especially on the rear side (note that θa180◦).igure 4d shows the HLB effect on the droplet adhesion force.n this experiment, the droplet volume was V = 20 µL, whichllowed us tomeasure the sliding angle values for all test droplets.ine HLB adjustment was achieved by varying themixing ratio ofDMS to PDMS–OH. In the PDMS (HLB= 0)-wrapped condition,ith HBPDMS–Silanol absent, the adhesion force of the pre- andost-cast droplets was F = 135.9 ± 18.2 and 110.2 ± 9.0 µN,espectively, not significantly different.However, the difference inhe adhesion force between pre-/post-cast droplets increasedwithncreasing HLB. Under the PDMS–OH (HLB = 0.02)-wrappedondition, obtained by diluting PDMS–OH (HLB = 0.12) withDMS, the pre- and post-cast droplets exhibited F = 27.2 ± 15.4nd 0.68 ± 0.34 µN, respectively. The droplet in Configuration Rxhibited a mostly constant friction values of hundreds of nN.urthermore, both the pre- and post-cast droplets transitionedrom Configuration S to R, and the critical transition HLBiffered for pre-/post-cast droplets. We defined the lower criticalransition HLB observed for post-cast droplets as HLBLC = 0.01–.02 and the upper critical transition HLB for precast dropletss HLBUC = 0.5–0.7. Branched wettability was observed betweenhese critical HLBs, that is, HLBLC < HLB < HLBUC.ext, we discuss the physical meaning of these transition points.he transition of precast droplets nearHLBUC is due to the changen the thermodynamically favored configuration, depending ondvanced Materials Interfaces, 2026vwhether Δγ is positive or negative. Δγ decreases with increasingHLB (Figure S8) because γow decreases with the increasingfraction of PDMS–OH by forming HBWater–PDMS. The critical HLBfor Δγ = 0 is estimated to be HLB ≈ 0.62, which coincides withthe experimentally obtained value of HLBUC (= 0.5–0.7). At HLB<HLBUC (that is, Δγ > 0), the interfacial state is in configurationS, and the contact line friction can be estimated using the Young–Dupré adhesion model Fγ ∼ γow(1 + cosθr). This is reasonablebecause the adhesion force decreases with increasing HLB owingto the decrease in γow. Here, slope fitting suggested F ∼ HLB−0.5,as shown by the black dashed line in Figure 4d. At HLB >HLBUC(that is, Δγ < 0), Configuration R is favored, and the adhesionforce of the precast droplet drastically decreases.The transition point of the post-cast droplets atHLBLC depends onwhether the OH groups in the PDMS can cap the substrate silanolgroups, that is, to replace the HBWater–Silanol with HBWater–PDMS. Thenumber of hydrogen bonds available in PDMS(─OH) increaseswith increasing HLB. We considered HLBLC to be the saturationpoint for HBPDMS–Silanol. At HLB < HLBLC, the amount of OHgroups in the PDMS was insufficient to cover the substratesilanol groups; thus, the uncovered silanol groups result in theformation of HBWater–silanol, and the droplets stick to the substrate.In this context, configurations R and S coexist beneath the post-cast droplets, akin to a “partial Wenzel state [37] or transitionalstate [16, 37],” and the total adhesion force is the sum of theHBWater–Silanol at the substrate–water contact region [38]. Underthe assumption that (i) the water–silanol interface has negligibleinterfacial tension and (ii) that the Young–Dupré model isappropriate for molecular scale wetting, the unit adhesion forceby HBWater–Silanol is ∼Fγ [θr→0]. Moreover, the number density of5 of 9e Commons LicenseFIGURE 4 Droplet adhesion behavior. (a) The experimental setup used to estimate the droplet adhesion force under PDMS(─OH). The waterdroplet was post-cast on the PDMS(─OH) lubricated substrate and tilted until the droplet started sliding. The adhesion force was quantifiedusing the critical sliding angle α. A 5 µL water droplet wrapped with PDMS–OH (HLB = 0.12) in (b) Configuration R and (c) Configuration S.(d) Adhesion force evolution of wrapped 20 µL water droplets as a function of HLB. Dashed lines correspond to the fitment of F ∼ HLB−0.5 (black),F ∼ HLB−0.5(1−HLB/HLBLC) (orange), and F = const. (gray) to the experimental data.HfFfsFo>ir(2DBw(P6 21967350, 2026, 10, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/admi.70495 by National Institute For, Wiley Online Library on [21/05/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable CreatiBWater–Silanol is proportional to the number of silanol groups thatailed to be covered by OH groups in PDMS. Thus, we expect F ∼γ [θr→0] (1− fPDMS–OH/fsilanol)∼HLB−0.5(1−HLB/HLBLC), wherePDMS–OH (fsilanol) is the number density ofOHgroups in PDMS (theubstrate), which is approximately proportional to HLB (HLBLC).itment of this model to the experimental data is shown by therange dashed line in Figure 4d, affordingHLBLC ≈ 0.019. AtHLBHLBLC, the post-cast droplet favors Configuration R, and theres an excess of OH groups in PDMS that do not play a significantole in the droplet adhesion behavior. Thus, we obtain F ≈ constgray dashed line)..5 ExtendingWettability Bifurcation toifferent Material Combinationsased on the proposed mechanism, we show that branchedettability can be extended to different material combinationsFigure 5). Branched wetting states were observed in variousDMSmedia containing different hydrogen-bonding terminatingof 9groups. For example, molecular interactions between amino-terminated PDMS (PDMS–NH2) and silanol are similar to those ofPDMS–OH (Figure S9). Thus,we first studied the effect ofHLBonthe droplet adhesion force by substituting PDMS–NH2 for PDMS–OH (Figure 5a). Branched wettability emerged at HLB = 0.0008–0.019. Notably, bifurcation of the droplet shape was not observedwhen we used PDMS modified with non-hydrogen-bondinggroups (Figure S10). The hydrophobic part of the surroundingmedium is not limited to PDMS as long as the medium phase iswater-immiscible and has a hydrogen-bonding group.We studieda fatty acid system using a mixture of 1-octadecene (C18H36) andoleic acid (C17H33COOH). Figure 5b shows the sliding angle ofpre-/post-cast droplets (V = 5 µL) as a function of different HLBachieved by varying the mixing ratio of 1-octadecene to oleicacid. Branched wettability was observed in the region of HLB =0.3–1.6. Furthermore, hydrogen-bonding agents are not limitedto liquids; a branched wettability system can be achieved bydissolving a solute in the liquid medium. We dissolved 1 wt.%octadecyl amine (C18H37NH2) as a hydrogen bonding additive in1-octadecene. After the dissolution, the HLB of the 1-octadeceneAdvanced Materials Interfaces, 2026ve Commons LicenseFIGURE 5 Extending wettability bifurcation to different material combinations. (a) Adhesion force evolution of the wrapped 20-µL water dropletsas a function of HLB for a mixture of PDMS and PDMS–NH2. (b) Sliding angle of 5-µL water droplets under different mixtures of 1-octadecene and oleicacid. (c) Branched wettability of a water droplet under a mixture of 1 wt.% octadecyl amine and oleic acid. (d) Sliding angle of pre-/post-cast 5-µL waterdroplets on substrates with different hydrophobic moieties under a mixture of PDMS and PDMS–OH.bobW(omhdwtA 21967350, 2026, 10, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/admi.70495 by National Institute For, Wiley Online Library on [21/05/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creatiecomes 0.012. As shown in Figure 5c, branched wettability wasbserved. These results demonstrate the potential expansion ofranched wettability to various surrounding media.e also varied the hydrophobic part of the substrate from phenylC6H5−) to more hydrophobic alkyl (C6H13−, Rq = 0.82 nm)r perfluoroalkyl (C4F9C2H4−, Rq = 1.14 nm) groups whileaintaining surface smoothness. With the increase of substrateydrophobicity (that is, an increase in γsw), HLBUC shouldecrease because of the decrease in Δγ. As expected, branchedettability was observed on all the probe surfaces. We foundhat HLBUC decreased with increasing substrate hydrophobicitydvanced Materials Interfaces, 2026in the order of perfluoroalkyl, alkyl, and phenyl modification(Figure 5d).3 ConclusionThe molecular-level tuning of the wettability balance enabledthe observation of branched wetting states. Depending on thesubstrate and surrounding medium, a water droplet can be ina metastable state owing to the energetic barrier formed bymolecular interactions, while another droplet is in a thermody-namically favored state. While this study mainly modulated the7 of 9ve Commons LicensehdtmduraeiotdHtiawialmwWtt[aotAWMsFJNJ(CNDTsRS22W3F8 21967350, 2026, 10, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/admi.70495 by National Institute For, Wiley Online Library on [21/05/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creatiydrogen-bonding species in the surrounding medium, whichetermined the HLB, the insights gained can be expanded tohe modulation of droplets, substrate surface chemistry, andolecular interactions other than hydrogen bonds. The observedroplet shape, adhesion behavior, and energy level of the config-rations were analogous to those of Cassie and Wenzel droplets,egardless of the use of a smooth surface. In a Cassie-like state,PDMS–OH (HLB = 0.12) layer too thin to be observed isntrapped beneath the resting droplet, whereas PDMS (HLB = 0)s squeezed out by a post-castwater droplet. In contrast to classicalbservations (that is, the case of Δγ< 0), it is energetically favoredhat PDMS–OH (HLB = 0.12) is squeezed out by the post-castroplet. Therefore, HBWater–PDMS and/orHBPDMS–Silanol outcompeteBWater–Silanol to achieve surrounding media entrapment beneathhe water droplet. In a Wenzel-like state, HBWater–Silanol formnstead of HBPDMS–Silanol. It is difficult to distinguish betweenWenzel-like state and a classical Young state in macroscopicettability; however, the apparent difference is that the dropletn aWenzel-like state exhibits θa ≈ 180◦, resulting in large contactngle hysteresis. Overall, this study found that a Cassie/Wenzel-ike heterogeneous interfacial configuration appeared at theolecular scale, and themolecular effect resulted inmacroscopicettability features akin to those of Cassie/Wenzel droplets.e believe that a molecular-scale model interface analogous tohe Cassie/Wenzel states is a powerful tool for understandinghe molecular effects on droplet mobility [12, 39], adaptivity40], micro-wetting [41], and nanofluidics [42]. These findingslso provide guidance for the design of robust liquid repellentsr capturing surfaces because surface nano/microscale texturesypically suffer from low mechanical stability [43].cknowledgementse acknowledge Dr. Gen Hayase for the FT-IR measurements, Ms.akiko Yabune for the interfacial tension measurements, and generalupport fromWPI-MANA.undingapan Society for the Promotion of Science (JSPS) KAKENHI (Granto. 23K21042) (M.T.), 21H05234 (S.A.), 23K23201 (S.A.), LEADER (M.T.),apan Science and TechnologyAgency (JST), FOREST grant JPMJFR223VM.T.), PRESTO (Grant No. JPMJPR23N1) (S.A.).onflicts of Interestone of the authors have a conflicts of interest to disclose.ata Availability Statementhe data that supports the findings of this study are available in theupplementary material of this article.eferences1. S. Kalliadasis and H.-C. Chang, “Dynamics of Liquid Spreading onolid Surfaces,” Industrial & Engineering Chemistry Research 35 (1996):860–2874.. L. Feng, Y. Zhang, J. Xi, et al., “Petal Effect: A Superhydrophobic Stateith High Adhesive Force,” Langmuir 24 (2008): 4114–4119.. T. Onda, S. Shibuichi, N. Satoh, and K. Tsujii, “Super-Water-Repellentractal Surfaces,” Langmuir 12 (1996): 2125–2127.of 94. T. Young, “An Essay on the Cohesion of Fluids,” PhilosophicalTransaction of the Royal Society London 95 (1805): 65–87.5. A. A. Papaderakis,M. Leketas, Z.Wei, et al., “Electrowetting of Carbon-Based Materials for Advanced Electrochemical Technologies,” ChemElectro Chem 11 (2024): 202400143.6. J. Li, N. S. Ha, T. L. Liu, R. M. Dam, and C. J. Kim, “Ionic-Surfactant-Mediated Electro-Dewetting for Digital Microfluidics,” Nature 572 (2019):507–510.7. S. Kumar, P. Kumar, S. DasGupta, and S. Chakraborty, “Electrowettingof a Nano-Suspension on a Soft Solid,” Applied Physics Letters 114 (2019):073702.8. H.-J. Butt, J. Liu, K. Koynov, et al., “Contact Angle Hysteresis,” CurrentOpinion in Colloid & Interface Science 59 (2022): 101574.9. S. Lepikko, Y.M. Jaques,M. Junaid, et al., “Droplet SlipperinessDespiteSurface Heterogeneity at Molecular Scale,” Nature Chemistry 16 (2024):506–513.10. J. Drelich, J. L. Wilbur, J. D. Miller, and G. M. Whitesides, “ContactAngles for Liquid Drops at a Model Heterogeneous Surface Consisting ofAlternating and Parallel Hydrophobic/Hydrophilic Strips,” Langmuir 12(1996): 1913–1922.11. D. Daniel, J. V. I. Timonen, R. Li, S. J. Velling, and J. Aizenberg,“Oleoplaning Droplets on Lubricated Surfaces,” Nature Physics 13 (2017):1020–1025.12. R. N. Wenzel, “Resistance of Solid Surfaces to Wetting by Water,”Industrial & Engineering Chemistry 28 (1936): 988–994.13. A. B. D. Cassie and S. Baxter, “Wettability of Porous Surfaces,”Transactions of the Faraday Society 40 (1944): 546.14. S. Wang and L. Jiang, “Definition of Superhydrophobic States,”Advanced Materials 19 (2007): 3423–3424.15. K. Mądry and W. Nowicki, “Wetting Between Cassie–Baxter andWenzel Regimes: A Cellular Model Approach,” The European PhysicalJournal E 44 (2021): 138.16. A. Giacomello, M. Chinappi, S. Meloni, and C. M. Casciola,“Metastable Wetting on Superhydrophobic Surfaces: Continuum andAtomisticViews of theCassie-Baxter–Wenzel Transition,”Physical ReviewLetters 109 (2012): 226102.17. W. Ren, Z. Lian, J. Wang, J. Xu, and H. Yu, “Fabrication of DurableUnderoil Superhydrophobic Surfaces With Self-Cleaning and Oil–WaterSeparation Properties,” RSC Advances 12 (2022): 3838–3846.18. X. Tian, V. Jokinen, J. Li, J. Sainio, and R. H. A. Ras, “Unusual DualSuperlyophobic Surfaces in Oil–Water Systems: The Design Principles,”Advanced Materials 28 (2016): 10652–10658.19. A. Lafuma andD.Quéré, “Superhydrophobic States,”NatureMaterials2 (2003): 457–460.20. G. Manukyan, J. M. Oh, D. van den Ende, R. G. H. Lammertink, andF. Mugele, “Electrical Switching of Wetting States on SuperhydrophobicSurfaces: A Route Towards Reversible Cassie-to-Wenzel Transitions,”Physical Review Letters 106 (2011): 014501.21. M. Wang, K. M. Liechti, Q. Wang, and J. M. White, “Self-AssembledSilane Monolayers: Fabrication With Nanoscale Uniformity,” Langmuir21 (2005): 1848–1857.22. W. C. Griffin, “Classification of Surface-Active Agents by ′HLB,”Journal of Cosmetic Science 1 (1949): 311–325.23. J. N. Israelachvili and M. L. Gee, “Contact Angles on ChemicallyHeterogeneous Surfaces,” Langmuir 5 (1989): 288–289.24. X. Zhao, B. Khatir, K. Mirshahidi, K. Yu, J. N. Kizhakkedathu, and K.Golovin, “Macroscopic Evidence of the Liquidlike Nature of NanoscalePolydimethylsiloxane Brushes,” ACS Nano 15 (2021): 13559–13567.25. S. Grimme, S. Ehrlich, and L. Goerigk, “Effect of the DampingFunction in Dispersion Corrected Density Functional Theory,” Journalof Computational Chemistry 32 (2011): 1456–1465.Advanced Materials Interfaces, 2026ve Commons License2W2tOp22IA2aW3(3lC3FS3L3S(3F(3D3SA3H3G4“14A6424SSAISSSSA 21967350, 2026, 10, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/admi.70495 by National Institute For, Wiley Online Library on [21/05/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed6. M. J. Frisch, G. W. Trucks, H. B. Schlegel, et al., Gaussian, Inc.,allingford CT 16 (2016).7. S. Tsuzuki and T. Uchimaru, “Accuracy of Intermolecular Interac-ion Energies, Particularly Those of Hetero-Atom Containing Moleculesbtained by DFT Calculations With Grimme’s D2, D3 and D3BJ Dis-ersion Corrections,” Physical Chemistry Chemical Physics 22 (2020):2508–22519.8. B. J. Ransil, “Studies inMolecular Structure. IV. Potential Curve for thenteraction of TwoHeliumAtoms in Single-ConfigurationLCAOMOSCFpproximation,” The Journal of Chemical Physics 34 (1961): 2109–2118.9. S. F. Boys and F. Bernardi, “The Calculation of Small Molecular Inter-ctions by the Differences of Separate Total Energies. Some Proceduresith Reduced Errors,”Molecular Physics 19 (1970): 553–566.0. A. Lafuma and D. Quéré, “Slippery Pre-Suffused Surfaces,” EPLEurophysics Letters) 96 (2011): 56001.1. H. Xu, Y. Zhou, D. Daniel, et al., “Droplet Attraction and Coa-escence Mechanism on Textured Oil-Impregnated Surfaces,” Natureommunications 14 (2023): 4901.2. D. Murakami, H. Jinnai, and A. Takahara, “Wetting Transitionrom the Cassie–Baxter State to the Wenzel State on Textured Polymerurfaces,” Langmuir 30 (2014): 2061–2067.3. J. D. Smith, R. Dhiman, S. Anand, et al., “Droplet Mobility onubricant-Impregnated Surfaces,” Soft Matter 9 (2013): 1772–1780.4. T.-S.Wong, S. H. Kang, S. K. Y. Tang, et al., “Bioinspired Self-Repairinglippery Surfaces With Pressure-Stable Omniphobicity,” Nature 4772011): 443–447.5. A. Keiser, P. Baumli, D. Vollmer, and D. Quéré, “Universality ofriction Laws on Liquid-Infused Materials,” Physical Review Fluids 52020): 014005.6. G. H. McKinley, “Quantifying Contact Line Friction via Oscillatingroplet Dynamics,” Droplet 1, (2022): 2–4.7. K. A. Wier and T. J. McCarthy, “Condensation on Ultrahydrophobicurfaces and Its Effect on Droplet Mobility: Ultrahydrophobic Surfacesre Not Always Water Repellant,” Langmuir 22 (2006): 2433–2436.8. J. F. Joanny and P. G. de Gennes, “A Model for Contact Angleysteresis,” The Journal of Chemical Physics 81 (1984): 552–562.9. J. Zhang, K. Jia, Y. Huang, et al., “Intrinsic Wettability in Pristineraphene,” Advanced Materials 34 (2022): 2103620.0. H.-J. Butt, R. Berger, W. Steffen, D. Vollmer, and S. A. L. Weber,Adaptive Wetting—Adaptation in Wetting,” Langmuir 34 (2018): 11292–1304.1. D. Daniel,M. Vuckovac,M. Backholm, et al., “Probing SurfaceWettingcrossMultiple Force, Length andTime Scales,”Communications Physics(2023): 152.2. L. Bocquet, “Nanofluidics Coming ofAge,”NatureMaterials 19 (2020):54–256.3. X. Tian, T. Verho, and R. H. A. Ras, “Moving Superhydrophobicurfaces Toward Real-World Applications,” Science 352 (2016): 142–143.upporting Informationdditional supporting information can be found online in the Supportingnformation section.upportingFile: admi70495-sup-0001-SuppMat.docx.upportingMovie 1: admi70495-sup-0002-MovieS1.mp4.upportingMovie 2: admi70495-sup-0003-MovieS2.mp4.upportingData: admi70495-sup-0004-DataFile.xlsx.dvanced Materials Interfaces, 2026 9 of 9 by the applicable Creative Commons License Bistable Wetting States on a Smooth Surface 1 | Introduction 2 | Results and Discussion 2.1 | Bistable States on One Smooth Surface 2.2 | Interfacial States 2.3 | Interfacial Stability 2.4 | Droplet Adhesion Behavior 2.5 | Extending Wettability Bifurcation to Different Material Combinations 3 | Conclusion Acknowledgements Funding Conflicts of Interest Data Availability Statement References Supporting Information