Bioinspired nanofilament coatings for scale reduction on steel

• Siad Dahir Ali,
• Mette Heidemann Rasmussen,
• Jacopo Catalano,
• Christian Husum Frederiksen and
• Tobias Weidner

Beilstein J. Nanotechnol. 2025, 16, 25–34, doi:10.3762/bjnano.16.3

• phenomenon, known as the Cassie state, results in the liquid being more in contact with air than with the solid surface, leading to high apparent contact angles [22]. The high contact angles also become apparent in Figure 1B, where a water droplet is resting on the Collembola surface. Here, we explore the

Hierarchically patterned polyurethane microgrooves featuring nanopillars or nanoholes for neurite elongation and alignment

• Lester Uy Vinzons,
• Guo-Chung Dong and
• Shu-Ping Lin

Beilstein J. Nanotechnol. 2023, 14, 1157–1168, doi:10.3762/bjnano.14.96

• increase in CA on the nanopillar and nanohole substrates may be due to either a Wenzel- or a Cassie-type of wetting [22]. To improve wetting on the substrates, we treated our samples with mild O2 plasma before laminin incubation. After plasma treatment, all samples became hydrophilic (CA < 80°), with the

Design of a biomimetic, small-scale artificial leaf surface for the study of environmental interactions

• Miriam Anna Huth,
• Axel Huth,
• Lukas Schreiber and
• Kerstin Koch

Beilstein J. Nanotechnol. 2022, 13, 944–957, doi:10.3762/bjnano.13.83

• homogeneous, smooth, non-deformable, and inert surface. Natural and technical surfaces hardly correspond to these ideal conditions. Wenzel [33] and Cassie and Baxter [34] studied CAs on rough surfaces, assuming that the liquid penetrates perfectly into the depressions of the surface (homogeneous wetting

• ). Cassie and Baxter [34] describe heterogeneous wetting in which the liquid does not penetrate the depressions of the surface. Air pockets form under the liquid, which reduce the contact between the solid surface and the liquid. In nature, ideal Wenzel or Cassie–Baxter wetting stages rarely occur. However

• completely fill the space between the anticlinal cell walls. Both observations suggest Cassie wetting or intermediate wetting. Cassie wetting was also assumed in a previous wettability study on wheat leaves [78]. In individual specimens, however, the water droplets remained attached to the surface and did

A review on slip boundary conditions at the nanoscale: recent development and applications

• Ruifei Wang,
• Jin Chai,
• Bobo Luo,
• Xiong Liu,
• Jianting Zhang,
• Min Wu,
• Mingdan Wei and
• Zhuanyue Ma

Beilstein J. Nanotechnol. 2021, 12, 1237–1251, doi:10.3762/bjnano.12.91

• by the Cassie state, where the liquid only wets the top surfaces of the roughness with the gas pockets maintained in between the surface structures, as shown in Figure 9. It is assumed that the no-slip boundary condition is still valid at the liquid–solid interface, while at the flat liquid–gas

• layer. Typically, for the case of water flow over air at room temperature, we can approximately take the value of the local slip length at the liquid–gas interface as 50t [93]. It should be noted that the above equation is only valid for shallow grooves associated with the Cassie state for

• superhydrophobic surfaces. For periodic deep grooves on superhydrophobic Cassie textures or even for more complex 2D textures, the classical “gas cushion” model does not apply. Instead, a general gas cushion model proposed by Nizkaya et al. can better evaluate the local slip length at the liquid–gas interface [115

A 3D-polyphenylalanine network inside porous alumina: Synthesis and characterization of an inorganic–organic composite membrane

• Jonathan Stott and
• Jörg J. Schneider

Beilstein J. Nanotechnol. 2020, 11, 938–951, doi:10.3762/bjnano.11.78

• rearrangement of the secondary, tertiary, or quaternary structure of the polypeptides. The reduction of the measured water contact angle can be explained by the established model of Cassie and Baxter, in which the wetting properties are affected by heterogeneous surfaces (inner surface is not wetted) and the

Biomimetic surface structures in steel fabricated with femtosecond laser pulses: influence of laser rescanning on morphology and wettability

• Camilo Florian Baron,
• Alexandros Mimidis,
• Daniel Puerto,
• Evangelos Skoulas,
• Emmanuel Stratakis,
• Javier Solis and
• Jan Siegel

Beilstein J. Nanotechnol. 2018, 9, 2802–2812, doi:10.3762/bjnano.9.262

• , also termed Wenzel and Cassie-Baxter regimes, respectively, wetting can in principle be described by taking into account the interfacial tension between substrate, liquid, and vapor and the surface geometry. Yet, the sole presence of one or another regime is a matter of debate [45]. While this

Preparation and morphology-dependent wettability of porous alumina membranes

• Dmitry L. Shimanovich,
• Alla I. Vorobjova,
• Daria I. Tishkevich,
• Alex V. Trukhanov,
• Maxim V. Zdorovets and
• Artem L. Kozlovskiy

Beilstein J. Nanotechnol. 2018, 9, 1423–1436, doi:10.3762/bjnano.9.135

• altered from the Wenzel to the Cassie state. The main aim of this study is preparation and investigation of the wetting properties of porous membranes with an ordered structure based on anodic alumina (PAMs) with different pore lengths and diameters. For this purpose we carry out a comparative analysis of

• possible to make membranes with hydrophilic properties, combining different methods of barrier layer etching. With the assistance of plasma treatment, the contact angle could be reduced by three times from 93.97° to 31.15° (see Table 2). According to our results, it is possible to assume that the Cassie

• ) after etching of the barrier layer. Schematic representation of the different models for pore wetting: A – Cassie–Baxter model [38], B – Wenzel model [38], C, D – schemes to explain wetting in our study. Contact angle as a function of surface topology (middle column images (B, E, H) are outer surfaces

Interface conditions of roughness-induced superoleophilic and superoleophobic surfaces immersed in hexadecane and ethylene glycol

• Yifan Li,
• Yunlu Pan and
• Xuezeng Zhao

Beilstein J. Nanotechnol. 2017, 8, 2504–2514, doi:10.3762/bjnano.8.250

• significantly inhibit the degree of boundary slip on both superoleophilic surfaces in Wenzel state and superoleophobic surfaces in Cassie state immersed in oil. The oleic systems were likely to enhance boundary slip and resulted in a corresponding reduction in drag with decreasing roughness on the solid–oil

• using an AFM with a colloidal probe in contact mode. Reference surface of superoleophilic and superoleophobic samples were defined and the effective slip lengths were obtained. The situation of superoleophilic surfaces in Wenzel state and superoleophobic surfaces in Cassie state were discussed in this

• Cassie state remains an open question. It can be different in different applications. When the hydrodynamic force on the surface immersed in liquids is calculated, the reference surface should be localized at the contact line of the liquid and the air between liquid and solid. When we calculate the

Surfactant-induced enhancement of droplet adhesion in superhydrophobic soybean (Glycine max L.) leaves

• Oliver Hagedorn,
• Ingo Fleute-Schlachter,
• Hans Georg Mainx,
• Viktoria Zeisler-Diehl and
• Kerstin Koch

Beilstein J. Nanotechnol. 2017, 8, 2345–2356, doi:10.3762/bjnano.8.234

• reduction of the epicuticular wax structures and a change from Cassie–Baxter wetting to an intermediate wetting regime with an increase of droplet adhesion. Keywords: droplet adhesion; epicuticular wax; Glycine max L; superhydrophobic; surfactants; Introduction The cuticle, as the outermost layer of

• applied liquid also depends on the wetting mode. In the Wenzel mode [26] an applied water droplet penetrates into cavities formed by the surface structures, increasing the contact area, and resulting in high hysteresis of the applied liquid. In Cassie–Baxter mode [27] air remains in the surface cavities

• becomes visible. The SEM figure shows (see the right bottom area of the droplet) imprints within the droplet surface caused by the epicuticular wax, indicating that the droplet in a Cassie–Baxter state on the epicuticular wax layer. Discussion Chemical analysis The isolation kinetics has been performed to

Collembola cuticles and the three-phase line tension

• Håkon Gundersen,
• Hans Petter Leinaas and
• Christian Thaulow

Beilstein J. Nanotechnol. 2017, 8, 1714–1722, doi:10.3762/bjnano.8.172

• scale [5]; this makes Collembola cuticle structures easily reproducible, as well as more resilient against mechanical wear [7]. While the water repellency of Collembola has long been described in general, macroscopic terms, a specific mechanical explanation has been lacking. Cassie and Baxter described

• a composite wetting state, where water wets only the tops of surface features, without wetting the substrate in between [15]. The composite wetting state assumed by Cassie and Baxter is well known in a range of other natural superhydrophobic surfaces [9]. The stability of the composite wetting state

• overhanging surface features does not affect the apparent contact angles predicted by the Cassie–Baxter equation for a system in the composite wetting state, but does affect the stability of the composite wetting state. The apparent contact angle of a composite wetting state is predicted by the Cassie–Baxter

Air–water interface of submerged superhydrophobic surfaces imaged by atomic force microscopy

• Markus Moosmann,
• Thomas Schimmel,
• Wilhelm Barthlott and
• Matthias Mail

Beilstein J. Nanotechnol. 2017, 8, 1671–1679, doi:10.3762/bjnano.8.167

• cantilevers on the right-hand side marked in grey. Below the lower cantilever the sample is already wetted (Wenzel state), as marked with white crosses. The rest of the sample shows air retention (Cassie–Baxter state). Figure 4b was taken after three minutes. In the upper left area, the air layer has

Measuring adhesion on rough surfaces using atomic force microscopy with a liquid probe

• Juan V. Escobar,
• Cristina Garza and
• Rolando Castillo

Beilstein J. Nanotechnol. 2017, 8, 813–825, doi:10.3762/bjnano.8.84

• adhesion force: 1) An array of silicon structures with nanometer-scale peaks (test grating TGT1 from NT-MDT Co., Russia; Figure 1) normally used for determining the radius of curvature of the AFM tip. A macroscopic mercury drop wets this surface following the Cassie–Baxter model [13] (θc ≈ 150°). The

Three-gradient regular solution model for simple liquids wetting complex surface topologies

• Sabine Akerboom,
• Marleen Kamperman and
• Frans A. M. Leermakers

Beilstein J. Nanotechnol. 2016, 7, 1377–1396, doi:10.3762/bjnano.7.129

• (contact angle on a smooth surface θY < 90°) to hydrophobic (effective advancing contact angle θ > 90°). Both the Wenzel wetting state, that is cavities under the liquid are filled, as well as the Cassie–Baxter wetting state, that is air entrapment in the cavities under the liquid, were observed using our

• -called Cassie–Baxter state is then given by [16] with Φs the fraction under the droplet that is in contact with the solid and (1 − Φs) the fraction under the droplet in contact with air. This approach thus defines the solid as a new material with a different effective surface energy on a macroscopic

Nanostructured superhydrophobic films synthesized by electrodeposition of fluorinated polyindoles

• Gabriela Ramos Chagas,
• Thierry Darmanin and
• Frédéric Guittard

Beilstein J. Nanotechnol. 2015, 6, 2078–2087, doi:10.3762/bjnano.6.212

• C6F13 fluorinated chains have also the highest oleophobicity even if the oil contact angles are relatively low. Indeed, two equations (the Wenzel and the Cassie–Baxter equation) [36][37] depending on θY are very often used to explain the effect of the surface roughness on the wetting properties. In the

• interface and thereby, increasing the adhesion between the water drop and the surface. Only the Cassie–Baxter equation [37] (cos θ = rf·f·cos θY + f − 1, where rf is the roughness ratio of the substrate wetted by the liquid, f the solid fraction and (1 − f) the air fraction) can predict the

Applications of three-dimensional carbon nanotube networks

• Manuela Scarselli,
• Paola Castrucci,
• Francesco De Nicola,
• Ilaria Cacciotti,
• Francesca Nanni,
• Emanuela Gatto,
• Mariano Venanzi and
• Maurizio De Crescenzi

Beilstein J. Nanotechnol. 2015, 6, 792–798, doi:10.3762/bjnano.6.82

• wettability is well described by a Cassie–Baxter model [20] for which a quite rough surface allows air trapping and ensures the high contact angle measured. In particular, in such a system pores in the random network (i.e., void fraction) favor air trapping due to the strong capillary force that the surface

• exerts on the liquid. The water drop can be viewed as sitting on a composite surface consisting of solid and air. Therefore, one can describe the wetting properties of the sponge surface in the super-hydrophobic regime using the Cassie-Baxter equation [20]: where and are the fractions of solid and air

Exploiting the hierarchical morphology of single-walled and multi-walled carbon nanotube films for highly hydrophobic coatings

• Francesco De Nicola,
• Paola Castrucci,
• Manuela Scarselli,
• Francesca Nanni,
• Ilaria Cacciotti and
• Maurizio De Crescenzi

Beilstein J. Nanotechnol. 2015, 6, 353–360, doi:10.3762/bjnano.6.34

• wettability. It is indeed well-established [12][13] that on composite rough surfaces a hierarchical morphology may induce a wetting transition from Wenzel [1] to Cassie–Baxter [9] state owing to air trapping. Moreover, this transition may occur by passing through thermodynamically metastable states [13][14

• range of stability of the Cassie–Baxter state [14][17]. Conversely, a negative consequence of metastability is that it might prevent or slow down the transition between Wenzel and Cassie–Baxter states [14][17]. Moreover, biomimetics [18][19] may be exploited in order to realize cutting edge artificial

• petals [2] in which micropapillae are made of nanopapillae, improves the hydrophobic behavior of carbon nanotube coatings compared to bare SWCNT and MWCNT films. Moreover, we report for the first time the experimental Wenzel/Cassie–Baxter phase diagram [8][12][17] for a carbon nanotube surface, showing

Measuring air layer volumes retained by submerged floating-ferns Salvinia and biomimetic superhydrophobic surfaces

• Matthias J. Mayser,
• Holger F. Bohn,
• Meike Reker and
• Wilhelm Barthlott

Beilstein J. Nanotechnol. 2014, 5, 812–821, doi:10.3762/bjnano.5.93

• of the surface structures (Cassie–Baxter wetting state) [13]. The contact angle of water droplets can be equally high in both wetting states [14][15]. However, in the Wenzel wetting state the water is in full contact with the surface and individual droplets adhere firmly [16]. In contrast to this in

• the Cassie wetting state the solid–water interface is strongly reduced while the majority of the interface is between water and air, thereby trapping an air layer between water and surface. As a result the adhesion of the water to the surface is minimised and individual droplets often roll off at very

• low tilting angles. However for true and persisting superhydrophobicity the Cassie wetting state has to be stable, i.e., no wetting transitions should occur [17][18]. One effective solution to prevent wetting transitions are surfaces with multiscale roughness [19][20][21]. Recently potential

The surface microstructure of cusps and leaflets in rabbit and mouse heart valves

• Xia Ye,
• Bharat Bhushan,
• Ming Zhou and
• Weining Lei

Beilstein J. Nanotechnol. 2014, 5, 622–629, doi:10.3762/bjnano.5.73

• , the roughness coefficient r will be given by the following Equation 5: In this formula, two surface characteristic values, i.e., periodic space A (A = b/a) and aspect ratio B (B = h/a) are defined. When a droplet is at Cassie status, the bottom of it partially contacts with the top of the mastoid and

• the periodic space, A, and the aspect ratio, B. The apparent contact angle increases with the increasing of B and decreases with the increasing of A. While the apparent contact angle of a droplet in Cassie state decreases with the increasing of A, but also relates to the steepness, k, of the mastoid

• mastoid, b is the space between two mastoids and h is the height of the mastoid. A droplet in Cassie state on the mastoid microstructure surface. Acknowledgements This research is supported by the Natural Science foundation of Jiangsu Province (BK2010203) and the Key Laboratory Opening foundation of

Micro to nano: Surface size scale and superhydrophobicity

• Christian Dorrer and
• Jürgen Rühe

Beilstein J. Nanotechnol. 2011, 2, 327–332, doi:10.3762/bjnano.2.38

• from a wetting situation (referred to as Cassie or composite wetting) where liquids no longer penetrate, but rest on top of the roughness features [1][2][11]. Air remains enclosed underneath, and drops are therefore supported by a “composite surface” that consists of solid and air (Figure 1a and 1b

Hierarchically structured superhydrophobic flowers with low hysteresis of the wild pansy (Viola tricolor) – new design principles for biomimetic materials

• Anna J. Schulte,
• Damian M. Droste,
• Kerstin Koch and
• Wilhelm Barthlott

Beilstein J. Nanotechnol. 2011, 2, 228–236, doi:10.3762/bjnano.2.27

• leaves (petals) of many plants are superhydrophobic, but water droplets do not roll-off when the surfaces are tilted. On such surfaces water droplets are in the “Cassie impregnating wetting state”, which is also known as the “petal effect”. By analyzing the petal surfaces of different species, we

• ) leaf. However, the surface of the wild pansy petal does not possess the wax crystals of the lotus leaf. Its petals exhibit high cone-shaped cells (average size 40 µm) with a high aspect ratio (2.1) and a very fine cuticular folding (width 260 nm) on top. The applied water droplets are in the Cassie

• geometrically enhances its hydrophobicity. In the Cassie–Baxter model [12] air remains trapped below the droplet in the surface cavities, which also leads to a superhydrophobic behavior, because the droplet sits partially on air [13]. The Wenzel model describes homogeneous wetting by the following equation

Sorting of droplets by migration on structured surfaces

• Wilfried Konrad and
• Anita Roth-Nebelsick

Beilstein J. Nanotechnol. 2011, 2, 215–221, doi:10.3762/bjnano.2.25

• Figure 4. Droplets coming in contact with these structures should experience a Cassie state, leading also to very high effective contact angles [8]. Notice that the mechanisms depicted in Figure 4 and Figure 5 predict droplet migration in opposite directions. Concentrating on Figure 4, a possible

Moisture harvesting and water transport through specialized micro-structures on the integument of lizards

• Philipp Comanns,
• Christian Effertz,
• Florian Hischen,
• Konrad Staudt,
• Wolfgang Böhme and
• Werner Baumgartner

Beilstein J. Nanotechnol. 2011, 2, 204–214, doi:10.3762/bjnano.2.24

• (r ≈ 2.3) or Phrynocephalus arabicus (r ≈ 1.4) as estimated from the above mentioned dimensions of the honeycomb structures. So the reduction of the contact angle for these animals cannot simply be explained by increased roughness alone. Thus it is tempting to assume the Cassie-model for liquid

• impregnating [18] to be valid, i.e., that the honeycombs and dimples respectively, allow for the formation of a stable thin water film within a dimple so that even with a contact angle of about 60–70° as given by the scale's material, an outspread water-scale-contact is stable. The Cassie-formula for the

Superhydrophobicity in perfection: the outstanding properties of the lotus leaf

• Hans J. Ensikat,
• Petra Ditsche-Kuru,
• Christoph Neinhuis and
• Wilhelm Barthlott

Beilstein J. Nanotechnol. 2011, 2, 152–161, doi:10.3762/bjnano.2.19

• contact with water [20] and to prove the theories such as those of Wenzel or Cassie and Baxter. For precise modelling of the behaviour of natural water repellent surfaces, an exact knowledge of the chemical composition and molecular structure are essential. Resistance against environmental stress The

• retention of the Cassie state with only partial contact between surface and water – an intrusion of water between the surface structures must be avoided. When the air layer is displaced by water, the water repellency is lost and the surface becomes wet (Wenzel state). The pressure which is necessary to

Capillary origami: superhydrophobic ribbon surfaces and liquid marbles

• Glen McHale,
• Michael I. Newton,
• Neil J. Shirtcliffe and
• Nicasio R. Geraldi

Beilstein J. Nanotechnol. 2011, 2, 145–151, doi:10.3762/bjnano.2.18

• origami or droplet wrapping. In this work, we consider how the conditions for the spontaneous, capillary induced, folding of a thin ribbon substrate might be altered by a rigid surface structure that, for a rigid substrate, would be expected to create Cassie–Baxter and Wenzel effects. For smooth thin

• case) or it can bridge between the asperities of the structure (the Cassie–Baxter case). In this report, we show theoretically that droplet wrapping should occur with both types of solid–liquid contact. We also derive a condition for the transition between the Cassie–Baxter and Wenzel type droplet

• wrapping and relate it to the same transition condition known to apply to superhydrophobic surfaces. The results are given for both droplets being wrapped by thin ribbons and for solid grains encapsulating droplets to form liquid marbles. Keywords: capillary origami; Cassie; contact angle

Superhydrophobic surfaces of the water bug Notonecta glauca: a model for friction reduction and air retention

• Petra Ditsche-Kuru,
• Erik S. Schneider,
• Jan-Erik Melskotte,
• Martin Brede,
• Alfred Leder and
• Wilhelm Barthlott

Beilstein J. Nanotechnol. 2011, 2, 137–144, doi:10.3762/bjnano.2.17

• all cases a Cassie–Baxter regime [29] can be assumed so that the applied drop rests on an air layer in between the cover of surface protuberances. These hydrophobic structures enable the animal to trap an air film between the bottom surface and the tips of the surface protuberances. Air film