Wetting on Regularly Structured Surfaces from “Core−Shell” Particles: Theoretical Predictions and Experimental Findings

Wetting on Regularly Structured Surfaces from “Core-Shell”Particles: Theoretical Predictions and Experimental Findings

Alla Synytska,*,† Leonid Ionov,‡ Victoria Dutschk,† Manfred Stamm,† and Karina Grundke†

Leibniz Institute of Polymer Research Dresden e.V., Hohe Strasse 6, D-01069 Dresden, Germany, andMax-Planck-Institute of Molecular Cell Biology and Genetics, Pfotenhauer Strasse 108,

01307 Dresden, Germany

ReceiVed April 7, 2008. ReVised Manuscript ReceiVed July 25, 2008

In this paper, we report on a systematic and thorough study of wetting phenomenon on regularly patterned surfacesfabricated from inorganic-organic hybrid “core-shell” particles of different radii (100 nm to 10 µm). Inorganic silicaparticles were modified through chemical anchoring of polymers and silanes with different hydrophobicities. Modified“core-shell” particles were assembled into regular hexagonally packed structures. The use of regular structuredsurfaces with specifically designed surface roughness allowed mathematic prediction of the wetting behavior accordingto existing models and its comparison with experimental observations. It was shown that the character of the wettingbehavior varies with the particles size and the chemical nature of the surface immobilized substance. For the regularparticle assemblies, an increase in the vertical roughness was achieved with increasing particle radius, but withoutchanging the Wenzel roughness factor.

IntroductionSurface wettability plays an important role in nature and

numerous industrial applications such as coatings, paintings,adhesives, microfluidic technology, microelectronics, etc.1-7 Oneof the factors influencing the wettability of solid surfaces is thesurface roughness. In many cases, rough surfaces possesscompletely different properties than flat ones made of the samematerial. The most brilliant natural example of the roughness-modulated wetting is the self-cleaning leaves of several plants.8,9

Despite significant progress achieved in the last few decades inengineering of rough self-cleaning surfaces and their charac-terization,4,8,10-22 the phenomenon of wetting on rough surfacesstill remains vague.

The first publications describing the wetting behavior of liquiddrops on rough surfaces appeared more than a half-century ago.Wenzel,23 Cassie and Baxter24 were the first who describedwetting on rough substrates. The Wenzel model describes a regimewhen a liquid completely penetrates into the roughness groovessa“homogeneous wetting regime”.18,23,25 The apparent contact angleon a rough surface in the homogeneous regime θW, is given bythe Wenzel equation (eq 1)

cos θW ) rs cos θY (1)

where θW and θY are the apparent contact angle on the roughsurface and the Young contact angle on the flat one, respectively.rs is the roughness factor, which was defined as the ratio of theactual area of the solid surface to the geometric/projected one.23

It was later shown by Johnson and Dettre that such surfacesoften have high contact angle hysteresis.26,27

The Cassie-Baxter model describes the wetting regime whenair is trapped in the microstructures of the surface and liquid sitson top of asperitiessthe “heterogeneous wetting regime”.18,24

The apparent contact angle in the heterogeneous wetting regime,θCB, is given by the Cassie-Baxter equation (eq 2)

cos θCB ) rf fcos θY + f- 1 (2)

where θCB and θY are the contact angle on rough surface accordingto Cassie and Baxter and the Young contact angle, respectively;f is the fraction of the projected area of the solid surface that iswetted by the liquid; and rf is the roughness ratio of the wettedarea. When f ) 1, and rf ) r, the Cassie–Baxter equation turnsinto the Wenzel equation. It should be noted that the wetting

* To whom correspondence should be addressed. Telephone:+49 (0351)4658 327. Fax: +49 (0351) 4658 474. E-mail: [email protected]

† Leibniz Institute of Polymer Research Dresden e.V.‡ Max-Planck-Institute of Molecular Cell Biology and Genetics.(1) Blossey, R. Nat. Mater. 2003, 2, 301–306.(2) Bico, J.; Quere, D. J. Fluid Mech. 2002, 467, 101–127.(3) Zhang, G.; Wang, D.; Gu, Z.-Z.; Mohwald, H. Langmuir 2005, 21(20),

9143–9148.(4) Martines, E.; Seunarine, K.; Morgan, H.; Gadegaard, N.; Wilkinson,

C. D. W.; Riehle, M. O. Nano Lett. 2005, 5(10), 2097–2103.(5) Kwok, D. Y.; Neumann, A. W. AdV. Colloid Interface Sci. 1999, 81, 167–

249.(6) Lafuma, A.; Quere, D. Nat. Mater. 2003, 2(7), 457–460.(7) Israelachvili, J. N.; Gee, M. L. Langmuir 1989, 5, 288–289.(8) Barthlott, W.; Neinhuis, C. Planta 1997, 202, 1–8.(9) Furstner, R.; Barthlott, W.; Neinhuis, C.; Walzel, P. Langmuir 2005, 21(3),

956–961.(10) Furstner, R.; Barthlott, W. Langmuir 2005, 21(3), 956–961.(11) Ming, W.; Wu, D.; vanBenthem, R.; deWith, G. Nano Lett. 2005, 5(11),

2298–2301.(12) Yabu, H.; Takebayashi, M.; Tanaka, M.; Shimomura, M. Langmuir 2005,

21(8), 3235–3237.(13) Marmur, A. Langmuir 2006, 22(4), 1400–1402.(14) Quere, D.; Lafuma, A.; Bico, J. Nanotechnology 2003, 14(10), 1109–

1112.(15) Shibuichi, S.; Onda, T.; Satoh, N.; Tsujii, K. J. Phys. Chem. 1996, 100,

19512–19517.(16) Oner, D.; McCarthy, T. J. Langmuir 2000, 16, 7777–7782.(17) Takeshita, N.; Paradis, L. A.; Oner, D.; McCarthy, T. J.; Chen, W. Langmuir

2004, 20(19), 8131–8136.(18) Marmur, A. Langmuir 2003, 19(20), 8343–8348.(19) He, B.; Patankar, N. A.; Lee, J. Langmuir 2003, 19, 4999–5003.(20) Patankar, N. A. Langmuir 2003, 19, 1249–1253.(21) Jopp, J.; Gru, H.; Yerushalmi-Rozen, R. Langmuir 2004, 20(23), 10015–

10019.

(22) Han, W.; Wu, D.; Ming, W.; Niemantsverdriet, J. W.; Thune, P. C.Langmuir 2006, 22(19), 7956–7959.

(23) Wenzel, R. N. Ind. Eng. Chem. Res. 1936, 28, 988.(24) Cassie, A. B. D.; Baxter, S. Trans. Faraday Soc. 1944, 40, 546–551.(25) Marmur, A. Langmuir 2004, 20(9), 3517–3519.(26) Johnson, R. E.; Dettre, R. H. Contact Angle Hysteresis. I. Study of an

Idealized Rough Surfaces. In AdVances in Chemistry Series; Gould, R. F., Ed.;American Chemical Society: Washington, DC, 1964; Vol. 43, pp 112-135.

(27) Dettre, R. H.; Johnson, R. E. Contact Angle Hysteresis. II. Contact AngleMeasurements on Rough Surfaces. In AdVances in Chemistry Series; Gould, R. F.,Ed.; American Chemical Society: Washington, DC, 1964; Vol. 43, pp 136-144.

11895Langmuir 2008, 24, 11895-11901

10.1021/la8010585 CCC: $40.75 2008 American Chemical SocietyPublished on Web 09/18/2008

regime that yields the lowest contact angle is the more stable onefrom a thermodynamic point of view, since the Gibbs energyturns out to be a monotonically increasing function of the contactangle.18

Later on, Johnson and Dettre26,27 extended the Wenzel andCassie-Baxter models, arguing about a large number ofmetastable configurations of the liquid contact angle on roughsurfaces. Each metastable state is separated from an adjacent oneby the energetic barrier, and the probability of transition betweenmetastable states is inversely proportional to the height of theasperities. Moreover, they predicted and demonstrated experi-mentally a transition from homogeneous wetting regime toheterogeneous one with increase of surface roughness.

Interest in wetting on rough surfaces was renewed again inthe last several years.18-20,25,28 Utilizing fundamental thermo-dynamic principles and applying methods for the minimizationof the free energy under the relevant constraints, the effects ofsurface topography on the wetting behavior of droplets wereaddressed. Patankar20 showed, on the basis of experimentalevidence, that there can be two contact angles (Cassie and Wenzelcontact angles) on the same rough surface, depending on howa drop is formed. A transition can occur between different statesby an external disturbance. Marmur has also discussed theoreti-cally equilibrium wetting on rough surfaces in terms of the“competition” between complete liquid penetration into the rough-ness grooves and entrapment of air bubbles inside the groovesunderneath the liquid.18 He placed the Wenzel and Cassie-Baxterequations into proper mathematical-thermodynamic perspectiveand defined the conditions for determining the transition betweenthe “homogeneous” and “heterogeneous” wetting regimes.

Oner and Extrand presented an alternative approach forconsideration of wetting on rough surfaces using a contact lineapproach.16,17,29,30 They argued that surfaces with completelydifferent topography can have the same values of fraction ofliquid area in contact with the material but completely differentcontact line structures.

Although there are plenty of publications reporting the influenceof surface topography on the contact angle, there are still manyantagonisms in the interpretation of wettability on rough surfaces:often the experimental observation cannot be explained by onlyone of these theories. We aim to compare the predictions based

on all theories for wetting on rough surfaces with the experimentalobservations.

Recently, it was demonstrated that layers made of regularlypacked spherical particles may provide a useful model for studyingthe influence of the surface geometry on the wettability.31-33

The peculiarity of particle layers is the independency of theroughness factor, which is a keynote roughness parameterdiscussed in the theories of Wenzel and Cassie, of the particlesize.31,33 Thereby, this study aims to elucidate the influence ofvertical surface roughness (particle size) on liquid contact angleon rough surfaces, keeping the roughness factor constant. Inparticular, we will systematically investigate the wetting behaviorof different model polar and nonpolar liquids and their mixtureson regular arrays from inorganic-organic hybrid “core-shell”particles and compare results with mathematical calculations.

Experimental SectionMaterials. Highly polished single-crystal silicon wafers with

native silicon oxide layers (Semiconductor Processing, Germany)were used as substrates. They were precleaned by rinsing three timesin dichloromethane in an ultrasonic bath for 5 min followed bywashing in a mixture of deionized water, ammonia solution (25%)and hydrogen peroxide (30%) in the 1:1:1 volume ratio at 60 °C for1 h. After washing, the substrates were thoroughly rinsed withdeionized reagent-grade water and then dried with nitrogen flux.

Carboxy-terminated polystyrene PS-COOH (Mn ) 45900 g/mol,PDI ) 1.05) synthesized by anionic polymerization was purchasedfrom Polymer Source (Germany). Random carboxy-terminatedcopolymer of polystyrene (Aldrich) and 2,3,4,5,6-pentafluoropoly-styrene (Aldrich), FPS-COOH (Mn ) 40000 g/mol, PDI) 2.4), wasprepared by free radical polymerization in toluene with the ratio80:20. Toluene (Aldrich) was distilled after drying over sodium.(Tridecafluoro-1,1,2,2-tetrahydrooctyl) dimethylchlorosilane (FSI)from Gelest (Germany) and 3-glycidoxypropyl trimethoxysilane(GPS) from ABCR (Germany) were used as received. Silica particlesof different radius varying from 0.1 to 10 µm were purchased in drystate from Geltech (Germany), Microparticles (Germany), and DukeScientific Corporation (USA) (Table 1).

Millipore grade water, methanol, n-alkanes CnH2n+2, with n )6, 7, 8, and 10-13, formamide, methlylene iodide, and benzyl

(28) Jopp, J.; Grull, H.; Yerushalmi-Rozen, R. Langmuir 2004, 20(23), 10015–10019.

(29) Extrandt, C. W. Langmuir 2002, 18, 7991–7999.(30) Extrand, C. W. Langmui 2006, 22, 1711–1714.

(31) Nakae, H.; Inui, R.; Hirata, Y.; Saito, H. Acta Mater. 1998, 46(7), 2313–2318.

(32) Shiu, J. Y.; Kuo, C. W.; Chen, P. L.; Mou, C. Y. Chem. Mater. 2004,16(4), 561–564.

(33) Synytska, A.; Ionov, L.; Dutschk, V.; Minko, S.; Eichhorn, K.-J.; Stamm,M.; Grundke, K. Prog. Colloid Polym. Sci. 2006, 132, 72–81.

Table 1. Surface Tensions of Used Liquids (T ) 23 °C)

individual liquids

surfacetension,

γLV

(mN/m) mixturesmass %

methanol

surfacetension,

γLV

(mN/m)

n-hexane 19.0 methanol 100 22.3n-heptane 19.7 water/methanol 77.0 25.2n-octane 22.1 water/methanol 70.4 28.9methanol 22.3 water/methanol 60.2 31.8n-decane 23.4 water/methanol 50.2 34.5n-dodecane 25.1 water/methanol 40.0 37.8n-hexadecane 27.6 water/methanol 30.6 41.4benzyl alcohol 40.0 water/methanol 25.0 44.1methylene iodide 50.8 water/methanol 20.0 47.7formamide 58.2 water/methanol 14.8 51.3water 71.8 water/methanol 10.4 55.03 M CaCl2 in water 78.7 water/methanol 6.0 59.7

water/methanol 5.4 62.5water/methanol 3.8 62.9water/methanol 1.8 67.8water 0 71.8

Scheme 1. Scheme of “Grafting to” Approach ofCarboxy-Terminated Polymer onto an Anchored Layer of

3-Glycidoxypropyltrimethoxysilane

11896 Langmuir, Vol. 24, No. 20, 2008 Synytska et al.

alcohol for contact angle measurements were used as receivedfrom Fluka and Aldrich (Germany). We also have prepared a 3M solution of CaCl2 (Merck) for additional contact anglemeasurements.

Particle Modification and Surface Characterization. Detailsof the particle modification, deposition, and characterization by FTIR-ATR/diffuse reflection IR spectroscopy, capillary penetrationexperiments, surface topography by scanning electron microscopy(SFM), and optical sensor (MicroGlider) are given elsewhere.33,34

Briefly, the “grafting to” approach was used to anchor polymerchains (carboxy-terminated polystyrene and random carboxy-terminated copolymer of polystyrene and 2,3,4,5,6-pentafluoropoly-styrene) onto the surface of silica particles (Scheme 1). The syntheticprocedure starts with covalent grafting of 3-glycidoxypropyltrimethoxysilane (GPS) onto the surface. The next step of the syntheticprocedure consists in grafting of the carboxy-terminated polymers(PS-COOH or FPS-COOH) onto the surface of the GPS-modifiedparticles.

The modified silica particles were deposited onto supported silicawafers using a vertical deposition technique.33-35 The quality of theprepared layers was controlled by scanning force (SFM) scanningelectron (SEM) microscopies and an optical imaging instrument(MicroGlider).33 Scanning force microscopy (SFM) studies wereperformed on a Dimension IV (Digital Instruments, USA) micro-scope. The tapping mode was used to map the surface morphologyat ambient conditions. Standard silicon tips with radii of about 10-30nm, apex angle 65°, and frequency of about 300 kHz as well asultrasharp ones with tip radius <10 nm and apex angle 12° for thehighest resolution imaging were used.

An imaging measuring instrument for the optical analysis ofroughness (MicroGlider, Germany) was used as a complementarymethod because of its large-scale vertical resolution from 10 nmto 300 µm and the possibility to investigate samples with a maximalsize area of 100 × 100 mm2. The lateral resolution is, however,determined by the size of the reflected light on the sample,1-2 µm.

Scanning electron microscopy (SEM) studies were performed ona DSM 982 Gemini (ZEISS, Germany) microscope.

All details about the roughness evaluation on prepared structuredrough layers and discussion of those surface roughness parameterswere given elsewhere.33 Some representative SEM and AFM imagesand their profiles are shown in Figures 1 and 2.

Contact Angle Measurements. Apparent advancing and recedingcontact angles were measured by the sessile drop method using aconventional drop shape analysis technique (Kruss DSA 10,Hamburg, Germany). For high measuring accuracy, the optical devicewas calibrated with a certified calibration kit obtained from FibroSystem (Sweden). This tool has a steel ball with well-defined shapeparameters. The tolerance of(5 µm will give the following maximumerror margins: height ( 0.01 mm, base ( 0.01 mm, volume ( 0.01mL, and contact angle ( 0.3 degree.

High purity deionized reagent grade water, methanol, andwater-methanol mixtures, n-alkanes CnH2n+2, with n ) 6, 7, 8, and10-13, formamide, methlylene iodide, and benzyl alcohol (Table1) were chosen as model liquids to investigate the wettability ofstructured rough layers prepared from polymer modified particles.

The advancing contact angle θA was measured by supplying theliquid into the drop at constant velocity. When the pump was reversed,the drop volume started to decrease linearly and the receding contactangle θR was measured.

Liquid droplets (10 µL) were dropped carefully onto the samplesurface, and the average value of ten measurements, made at differentpositions of the same sample, was adopted as the average value ofthe contact angles of the substrates. The error of the mean contactangle values, calculated as the standard deviation, did not exceed2 and 3° for advancing and receding contact angles, respectively.All contact angle measurements were carried out at 24 ( 0.5 °C anda relative humidity of 40 ( 3%, which were kept constant. It shouldbe noted that additional contact angle measurements on severalsamples were performed in a closed chamber where the relativehumidity was about 80%. No noticeable effect between wettingbehavior on designed structured surfaces obtained under relativehumidities of 40 and 80% was detected.

Surface Tension Measurements. The equilibrium surface tensionof the liquids and solutions used was evaluated by the pendant dropmethod using a cell integrated into a FibroDAT 1100 device (FibroSystems, Sweden). The instrument was located in a temperature-controlled laboratory maintained at 3 ( 1 °C. The relative humidityof 40 ( 2% was kept constant. This device equipped with a videocamera, which collects up to 50 images per second, and anelectromagnet, which releases the drop from the tip, allows precisemeasurements of the contact angle and equilibrium surface tension.The experimentally determined values of the surface tension liquidsused are presented in Table 1.

Results and Discussion

WettingonRegularlyStructuredSurfacesfrom“Core-Shell”Particles: Theoretical Calculations. We begin the discussionfrom the overview of the wetting behavior predicted by severaldifferent theoretic models: equilibrium contact angle (Wenzeland Cassie-Baxter theories, maximal and minimal contact angles,and Extrand model). Relying on theories mentioned above, wewill made an effort at the mathematic prediction of wettingproperties of fabricated regular arrays and its comparison withexperimentally observed findings.

Note, if the liquid droplet is small, the influence of thegravitation factor on the contact angle can be excluded. Inthis case, only surface forces determine the shape of thedrop.

Wenzel and Cassie-Baxter Contact Angles. According tothe Wenzel wetting model (homogeneous wetting regime), theactual contact angle is proportional to the roughness factor rs andthe cosine of the contact angle on the flat surface (Young contactangle), cos θW ) rs cos θY,23 where rs is a roughness factor thatis rs ≈ 1.9 for a regular particle array and is independent ofparticle size.31,33 The results of our calculations are representedby the blue solid line in Figure 6.

The contact angle according to the Cassie-Baxter model(heterogeneous wetting regime) (cos θflat < 0) is determined by

(34) Synytska, A. Ph.D. Thesis, TU Dresden, 2005.(35) Goldenberg, L. M.; Wagner, J.; Stumpe, J.; Paulke, B.-R.; Gornitz, E.

Langmuir 2002, 18(8), 3319–3323.

Figure 1. Representative topography images of the particle arrays: (a)SEM image for 0.1 µm; (b) SFM image for 0.5 µm; (c) MicroGliderimage for 1.2 µm s; (d) MicroGlider image for a 2.5 µm particle layer;(e) MicroGlider image for 2.5 µm large particles in radius (larger scale).Reprinted from ref 33 with permission from Springer.

Wetting of Core-Shell Particle Surfaces Langmuir, Vol. 24, No. 20, 2008 11897

the roughness factor (rs) and the fraction of air entrapped in thepores (1 - fs).

cos θrough ) rs fs cos θflat + 1- fs (3)

Both the roughness factor and the fraction of air entrapped inthe pores in the Cassie-Baxter model are adjustable parametersand can be expressed as a function of the depth of penetrationof liquid into the particle layer (Figure 3). On the other hand,the depth of penetration (h) is determined by the minimum ofthe Gibbs energy on the liquid/particle layer interface, which isa sum of free pairs of interaction: liquid/solid (γLS), liquid/vapor(γLV), and solid/vapor (γSV).

Hence, the roughness factor rs and fraction of solid/liquidinterface fs expressed as a function of depth of penetration ofliquid into the particle layer (h) are the following:

fS(h)) [2(h/R)- (h/R)2] π

2√3(4)

rS(h)) 1+ (h/R)2 π

2√3(5)

where

h)R(cos θflat + 1) (6)

Introducing eqs 4-6 into eq 3, one can obtain the expressionswhich describe the wetting behavior on the particle layercorresponding to the global minimum of the free surface energy(blue dashed line in Figure 6, cos θflat < 0).

Maximal and Minimal (Nonequilibrium) Contact Angles.The contact angles discussed above correspond to the equilibriumstate. Shuttleworth and Bailey36,37 first introduced nonequilibrium

contact angles called the maximal and minimal possible contactangles, which were further discussed by Johnson and Dettre.26,27

The maximal contact angle (θmax) is a sum of the intrinsic contactangle (θA,flat or (θR,flat) and the angle of the asperity inclination(R). The minimal contact angle (θmax) is a difference betweenthe two (Figure 4). For densely packed particle layers, the angleof asperities inclination depends on the penetration depth of aliquid inside the pores, and it is a function of the intrinsic contactangle, similar to the models of Cassie-Baxter and Extrand. Themaximal and minimal contact angles for the particle geometryare calculated using MathCAD software and represented by blacksolid and dashed lines in Figure 6, respectively.

Extrand Model. The model suggested by Extrand29 based onthe contact line approach was also used to predict the wettingbehavior of different liquids on well-ordered “core-shell” particlelayers. This model suggests that, for suspended drops, bothadvancing and receding contact angles should increase with

(36) Shuttleworth, R.; Bailey, G. L. J. J. Colloid Sci. 1948, 14, 584.(37) Shuttleworth, R.; Bailey, G. L. J. Disc. Faraday Soc. 1948, 3, 16.

Figure 2. Representative SFM images and corresponding height profiles along the [100] direction for 0.1 µm (a) and 1.2 µm (b) particles in radius.Reprinted from ref 33 with permission from Springer.

Figure 3. 2D projection of the geometry used for calculation of theminimum of the Gibbs energy on the liquid/solid/air interfaces (SSL, SSV,and SLV). The depth of penetration of liquid into a layer of particles withradius R is h.

11898 Langmuir, Vol. 24, No. 20, 2008 Synytska et al.

increasing surface roughness (in our case particle radii). Fordrops collapsed over surface asperities, advancing contact anglesshould increase, whereas receding ones should decrease. In hismodel, the linear fraction of the contact line on the asperities λP

is connected with the linear fraction of the contact line betweenthe asperities λB:

λP + λB ) 1 (7a)

Many possible contact lines can be drawn on the particleslayer, and two of them are presented in Figure 5a. Based on theassumption that the contact of liquid with the solid surface ismore energetically favorable than that with air, the most probablecontact line connecting the tops of adjacent particles is L1. Forthis case, the linear fraction of the contact line on the asperitiesis expressed as a function of contact angle on a flat surface(Figure 5b)

λP )π

π+ 2( 1sin θflat

- 1)(7b)

ω)π- θflat (7c)

The summary of calculated contact angles of collapsed andsuspended drops according to the Extrand model is given inTable 2 as well as represented in Figure 6 by green and red lines.

WettingonRegularlyStructuredSurfacesfrom“Core-Shell”Particles: Experimental Findings. We turn to consider ex-perimental results for wetting properties of PS-, FPS-, and FSi-modified silica particles and compare them with calculations.

We found the experimental results do not completely followany of the theoretical models. The wetting behavior of lesshydrophobic FPS- and PS-coated particles is “localized” betweenequilibrium contact angle (“Cassie-Baxter” and “Wenzel”contact angles) and maximal (for advancing contact angle) orminimal (for receding contact angle, Figure 7) ones. The wettingbehavior of more hydrophobic layers of FSI-coated 200 nm and1 µm large particles is close to the equilibrium contact angledescribed by the Wenzel and Cassie-Baxter models. The wettingbehavior of FSI-coated particles approaches maximal and minimalcontact angles as the size of the particles increases. Moreover,the deviation from equilibrium behavior for FSI-modified particlesincreases with the decrease of advancing (θA,flat) and receding(θR,flat) contact angles on flat substrates (Figure 7). Thus, it canbe concluded that both particle size (height of the features) andintrinsic hydrophobicity of the polymer “shell” (surface freeenergy) influence an overall wetting behavior and deviationsfrom equilibrium contact angles on prepared structured surfaces.

Different wetting properties are observed for layers preparedfrom FSI coated particles. The wetting behavior of liquids on thelayer of small (100 nm and 0.5 µm in radius) FSI coated particlesat high values of advancing (θA,flat) and receding (θR,flat) contactangles is very close to the equilibrium wetting behavior predictedby the Cassie-Baxter and Wenzel models. The deviation fromequilibrium behavior for FSI-modified particles increases withthe decrease of advancing (θA,flat) and receding (θR,flat) contactangles on flat substrates and with the increase of particle size(Figure 7).

It should be noted that a pronounced deviation from wettingproperties based on the contact line approach suggested by Extrandis found for all systems investigated (Figure 7, green and redlines).

Johnson and Dettre26,27 did show that the values of advancingand receding contact angles experimentally measured on roughsubstrates could differ from the equilibrium ones predicted bythe Cassie and Wenzel models. Johnson and Dettre26,27 suggestedthat there are many metastable configurations of the contact angleof liquid on rough surface. Each metastable state is separatedfrom an adjacent one by the energetic barrier, and the probabilityof transition between metastable states is inversely proportionalto the height of asperities. The height of the energy barrier isapproximately directly proportional to the height of the part ofasperities which is in contact with liquid and almost independentof the distance between the asperities.26,27 At the same time, theheight of the energy barrier is related to the hydrophobicity ofthe grafted substance as well as the particles size and increaseswith increasing θflat and particle size (see eq 6). On the otherhand, the drop is unable to jump to the next equilibrium statewhen the vibration energy is less than the height of the energy

Figure 4. Calculation scheme for minimal (a) and maximal (b) contact angles.

Figure 5. Possible contact lines (L1 and L2) on the hexagonally packedparticle layer (a). Schematic representation of the geometry used forcalculation of the contact angles of collapsed and suspended dropsaccording to the Extrand approach (b).

Table 2. Advancing and Receding Contact Angles of Collapsedand Suspended Drops Calculated for Densely Packed Particle

Layers According to the Extrand Model

suspended drop θA,rough ) πθR,rough ) λPθR,flat + (1 - λP)θair

collapsed drop θA,rough ) πλP + (1 - λP)θA,flat

θR,rough ) λP(2θR,flat - π) + (1 - λP)θR,flat

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barrier. Assuming that the vibration energy in the experimentsis constant, the probability to jump to the equilibrium state isinversely proportional to the height of the wetted part of theasperities. In other words, the state corresponding to the global

minimum of energy can be reached easier for more hydrophobicpolymeric “shells” and smaller particles. Indeed, we observedthat the contact angle of liquids with high surface tension on thelayers of smallest particles (100 nm in radius) coated with themost hydrophobic shell (FSI) is very close to the contact anglecorresponding to thermodynamic equilibriumsregimes Cassie-Baxter. On the other hand, deviations from the equilibrium contactangle increase upon increase of the size of the asperities anddecrease of the intrinsic hydrophobicity of the substrate.

Conclusions

We performed a thorough study of wetting phenomenon onregularly structured surfaces fabricated from inorganic-organichybrid “core-shell” particles of different radii (100 nm to 10µm). Inorganic silica particles were modified through chemicalanchoring of polymers and silanes possessing different hydro-phobicities (surface free energy). Modified particles wereassembled into regular hexagonally packed structures.

Relying on all existing theories on rough structured surfaces,we made an effort for the mathematic prediction of wettingproperties of fabricated regular arrays and its comparison withexperimentally observed findings. It was shown that the characterof wetting behavior varies with the particles size and the chemicalnature of a surface immobilized substance.

The wetting properties on regular layers were predictedaccording to the Wenzel, Cassie-Baxter (contact area approach),and Extrand (structure of contact line approach) models as wellas minimal and maximal possible contact angles introduced byShuttleworth and Bailey. It has been shown that deviations fromthe equilibrium contact angle (Wenzel and Cassie-Baxtermodels) increase with increasing particle radius, decreasingintrinsic contact angle, and increasing solid free energy of theparticle “shell” on the layers fabricated from particles modifiedby PS, FPS, and FSI. This provides experimental evidence forthe theory proposed by Johnson and Dettre for metastableconfigurations of contact angles. Similar to this theory, the heightof the energetic barrier has been found to be proportional to thecosine of the intrinsic contact angle and the height of the asperities(particle radii in the present case) and approximately independentof the lateral distance between them. Large deviations fromequilibrium contact angles were found for polystyrene PS and

Figure 6. Summary of wetting behavior on a well-ordered particle layer predicted by different models.

Figure 7. Wetting behavior of the water/methanol mixtures on the regularlayers prepared from PS (a, b), FSP (c, d), and FSI (e, f) coated particles.The point with the minimal cos θA,flat and cos θR,flat (maximal values ofcontact angles) was obtained for a 3 M water solution of CaCl2: (9) 200nm; (b) 1 µm; (2) 2.37 µm; (0) 5 µm; (O) 10 µm; (4) 20 µm. The lineson the plots correspond to the minimum of the global energy and tominimum and maximal contact angles.

11900 Langmuir, Vol. 24, No. 20, 2008 Synytska et al.

fluoropolystyrene FPS modified particles for all radii (100 nmto 10 µm). Their wetting properties correspond to the metastablecontact angles.

On the other hand, wetting behavior of model liquids on regulararrays made from 100 nm large particles in radius modified bymore hydrophobic material (tridecafluoro-1,1,2,2-tetrahydrooctyl)dimethylchlorosilane FSI was found to be in reasonable agreementwith theoretical predictions according to the Wenzel andCassie-Baxter theories. This wetting behavior corresponds tothe equilibrium wetting regime.

We believe that our study can contribute to a deeperunderstanding of the wetting phenomenon on rough structuredsurfaces. Moreover, obtained knowledge could be helpful forthe prediction/control of the wettability for real coating materials.

In the next part of our work, we will report on results forwetting behavior on irregular arrays fabricated from the similar“core-shell” particles, since random rough surfaces are muchmore relevant from a practical perspective.

Acknowledgment. The authors thank Prof. A. Marmur forhelpful comments on the manuscript. For financial support wegratefully acknowledge the German Ministry of Education andResearch (BMBF) (Project 01 RC 0040) and Leibniz Instituteof Polymer Research Dresden.

Supporting Information Available: Wetting behavior of theindividual liquids on the regular structured surfaces prepared from PS,FSP, and FSI coated particles. This material is available free of chargevia the Internet at http://pubs.acs.org.

LA8010585

Wetting of Core-Shell Particle Surfaces Langmuir, Vol. 24, No. 20, 2008 11901