Langmuir 2009, 25, 2907-2912
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Principles of Design of Superhydrophobic Coatings by Deposition from Dispersions Ludmila Boinovich* and Alexandre Emelyanenko A.N. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, Leninsky prospect 31, 119991 Moscow, Russia ReceiVed NoVember 17, 2008. ReVised Manuscript ReceiVed January 6, 2009 The analysis demonstrating the abilities of various types of ordered textures, constructed from spherical particles, to provide high water contact angles on the surface of the hydrophobic material is presented. For several ordered three-dimensional surface structures we have derived the equations, relating the contact angles, formed by water droplets on a textured coating, with the geometric parameters of the texture and the chemical properties of the coating. The conditions providing the thermodynamic stability of heterogeneous wetting regime on textured surfaces have been discussed. It was demonstrated that multimodal surface roughness facilitates essentially the attainment of the superhydrophobic state and the surface textures exhibiting the stable superhydrophobic properties may be effectively manufactured by controlled aggregation of particles. Based on the analysis of forces acting between the nanoparticles both in the bulk dispersions and in the deposited film, we discuss the correlation of the properties of dispersion with the surface textures formed.
1. Introduction The peculiarities of wetting of hydrophobic and superhydrophobic materials attracted the particular attention of researchers during the past decade and has been the subject of numerous studies.1-10 Such interest was initiated, on one hand, by the fundamental importance of wetting phenomena in various technological applications. On the other hand, the hydrophobic and superhydrophobic materials are widely used in design of self-cleaning panes, hydroprotection of reinforced concrete constructions, corrosion protection, biofouling protection, prevention of capillary condensation and icing, waterproof textile, proofing of surfaces against radioactive, organic, and inorganic contaminations, microfluidic devices, etc. The cost of such materials is the extremely important factor for the evaluation of their innovative potential. As a rule for bulk or consolidated materials, the cost is rather high. However, it is worth noting that the hydrophobicity is a surface feature of the material which is defined mainly by the structure and properties of a few nanometers of its superficial layer rather than by characteristics of the bulk material as a whole. Therefore, it is possible to replace the bulk material by a hydrophobic coating, the thickness of which varies in the range 10 to 104 nm, depending on the functional properties to be provided. With rare exceptions, such coatings are nanocomposite, allowing one not only to reduce significantly the cost of manufacture but also to provide the contact angles essentially exceeding 120°, due to creation of * To whom correspondence should be addressed. E-mail: boinovich@ mail.ru. (1) Sun, T.; Feng, L.; Gao, X.; Jiang, L. Acc. Chem. Res. 2005, 38, 644. (2) Quere, D. Rep. Prog. Phys. 2005, 68, 2495. (3) Li, X.-M.; Reinhoudt, D.; Crego-Calama, M. Chem. Soc. ReV. 2007, 36, 1350. (4) Nakajima, A.; Fujishima, A.; Hashimoto, K.; Watanabe, T. AdV. Mater. 1999, 16, 1365. (5) Genser, J.; Efimenko, K. Biofouling 2006, 22, 339. (6) Barbieri, L.; Wagner, E.; Hoffman, P. Langmuir 2007, 23, 1723. (7) Boinovich, L. B.; Emelyanenko, A. M. Uspekhi Khimii 2008, 77, 619. English translation: Russ. Chem. ReV. 2008, 77, 583. (8) Taurino, R.; Fabbri, E.; Messori, M.; Pilati, F.; Pospiech, D.; Synytska, A. J. Colloid Interface Sci. 2008, 325, 149. (9) Kim, S. H. J. Adhesion Sci. Technol. 2008, 22, 235. (10) Balu, B.; Breedveld, V.; Hess, D. W. Langmuir 2008, 24, 4785.
special surface texture. Among such textured surfaces a particular place is occupied by superhydrophobic coatings characterized simultaneously by contact angles greater than 150°, and small slope angles at which water droplets slide from the surface. Since the slope angles are essentially determined by contact angle hysteresis (CAH), the smallness of the latter is crucial for providing the thermodynamically stable superhydrophobicity. The importance of accounting for CAH in the design of operationally durable superhydrophobic materials has been emphasized in numerous papers.2,3,7,11-14 In general, CAH is determined not only by the surface geometry but also by its chemical uniformity and the interaction of wetting liquid with underlying substrate. The latter property is characterized both by the thermodynamic characteristics such as the isotherm of disjoining pressure7 and by the kinetics of physicochemical interaction of water with molecules of hydrophobizing agent.15 The calculation of the hysteresis range for the textured surfaces considered below is beyond the scope of the present paper. At the same time, as it follows from many experimental results and theoretical estimations the heterogeneous wetting regime with small portions of solid area wetted by liquid provides the minimization of CAH. Thus, the problem of the design of superhydrophobic surfaces may be reformulated as the achievement of high (>150°) contact angles in the stable heterogeneous regime of wetting. With the above-mentioned, it becomes evident that the development of nanocomposite hydrophobic coatings requires, on one hand, the analysis of processes occurring in nanosize systems and, on the other hand, the study of the influence of both the chemical composition and the surface topography on the values of contact angles and sliding angles attainable at textured composite surfaces. (11) He, B.; Patankar, N. A.; Lee, J. Langmuir 2003, 19, 4999. (12) Li, W.; Amirfazli, A. AdV. Colloid Interface Sci. 2007, 132, 51. (13) Li, W.; Amirfazli, A. J. Colloid Interface Sci. 2005, 292, 195. (14) Gao, L.; McCarthy, T. J. Langmuir 2006, 22, 2966. (15) The numerous experiments performed in our laboratory indicate that the interaction between water and molecules of hydrophobizing agent related to chemical reactions or hydrogen bonding may be essential, and leads to the time dependence of receding contact angle. This issue will be discussed in more detail elsewhere.
10.1021/la803806w CCC: $40.75 2009 American Chemical Society Published on Web 02/10/2009
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In this paper we will discuss how the features of the texture composed by spherical particles influence the regime of wetting established on the textured surface. The wetting will be characterized by equilibrium contact angles, while the problem of quasiequilibrium advancing and receding contact angles as well as that of contact angle hysteresis will not be addressed. It will be shown that multimodality of surface roughness essentially promotes the achievement of superhydrophobic state. We will describe briefly the principles of formation of hydrophobic and superhydrophobic coatings by deposition from dispersions. The forces providing the design of required surface textures on the basis of purpose-oriented aggregation of nanoparticles will be analyzed.
2. Wetting of Surfaces with the Textures Based on Spherical Particles The abundant experimental data indicate that by modification of chemical composition of the substance or by application of various hydrophobic agents on the smooth surfaces one can achieve contact angles not exceeding 120°. The special efforts, providing the densely packed, defect-free surface structure of hydrophobizing monolayer, in some cases allow one to reach a contact angle close to 130°.5 To obtain surfaces characterized by higher contact angles, one needs to make use of combined action of chemical composition and surface roughness. Just the surface texture provides the possibility to achieve the superhydrophobic state.1-14,16-18 One of the most manufacturable approaches for formation of superhydrophobic coatings, which may be applied to almost all surfaces and is well-suited to cover large areas, is a method of deposition of particles from dispersions. In this method, the surface roughness of coating is affected by the packing density of precipitated particles, the character of their aggregation, the amount of hydrophobic agent, and the presence of binding agent. Following the approach proposed by Marmur,16,17 we have derived the relations for the basic parameters, characterizing the wettability of 3D surface structures for various packings of monodispersed spherical particles on the surfaces. Thus, for the dense packings of nonaggregating particles in the approximation of horizontality of liquid meniscus between the particles, the relations for effective roughness r and wetted portion of surface f in the heterogeneous wetting regime read as follows:
r) r)
2(1 + cos θ0) sin2 θ0 2(1 + cos θ0) sin2 θ0
π f ) sin2 θ0 4 for square packing π 2 for hexagonal packing f ) θ sin 0 , 2√3 ,
(1) We see that both the roughness and the wetted area portion do not depend on particle radii and are determined by Young contact angle θ0, characteristic of proper surface of particles. Note that in the case of use of the hydrophobizing agent the value θ0 is determined namely by its chemical structure. Deriving eq 1, we have taken into account the fact that for Young angles θ0 > 90° the liquid meniscus in the heterogeneous wetting regime is positioned above the equatorial diameter of the spherical particles. In the homogeneous wetting regime (f ) 1) the effective surface roughness is determined only by the type of packing independent of particle radii: (16) Marmur, A. Langmuir 2003, 19, 8343. (17) Marmur, A. Langmuir 2004, 20, 3517. (18) Patankar, N. A. Langmuir 2003, 19, 1249.
r ) (1 + π) 2π r) 1+ √3
(
)
for square packing for hexagonal packing
(2)
Particular attention deserves to be paid to the case when the film of dispersion deposited on a substrate contains a considerable amount of hydrophobizing and/or binding agents. The texture of coating produced on the surface treated by such dispersion will contain truncated spheres depending on the level of particle incorporation into the composite matrix formed on the surface after evaporation of the solvent. For example, in the case of texture containing densely packed hemispheres, the effective roughness of the coating for the homogeneous wetting regime is determined by relations
π 4 π r) 1+ 2√3
(
r) 1+
(
)
)
for square packing (3) for hexagonal packing
Applying the Cassie-Baxter equation for a heterogeneous wetting regime and the Wenzel-Derjaguin equation for a homogeneous one jointly with eqs 1 and 2, it is straightforward to derive the expressions for water contact angles on substrates coated by densely packed monolayers of spherical particles. For the Cassie-Baxter regime we obtain
π cos θCB ) (1 + cos θ0)2 - 1 for square packing 4 π cos θCB ) (1 + cos θ0)2 - 1 for hexagonal packing 2√3 (4) while for the Wenzel-Derjaguin regime
cos θWD ) (1 + π)cos θ0 for square packing 2π cos θ0 for hexagonal packing (5) cos θWD ) 1 + √3
(
)
As clearly seen from eqs 3-5, the particle radius does not affect the value of the water contact angle on the surfaces textured by deposition of monodisperse spherical particles at packings, corresponding to direct contact of neighboring particles in a monolayer. This conclusion is substantiated by the experimental data of Shiu et al.,19 who studied the contact angles on the textures formed by hexagonal close packing of polysterene spherical particles. It was found that the variation of particle diameter from 270 to 690 nm did not affect the value of effective water contact angle θ ) 131 ( 2°. Note that the substitution of the Young angle θ0 ) 114°, experimentally determined for the above system,19 into the relation (4) for the hexagonal packing gives the contact angle θCB ) 132° coinciding well with the experiment. The effective values of the contact angles calculated according to eqs 3-5 as functions of the Young contact angle are presented in Figure 1. We see that at weakly hydrophobic surfaces (θ0 < 92° for hexagonal packing and θ0 < 96° for square packing) the homogeneous wetting regime is thermodynamically more stable (as a regime corresponding to a lower value of the effective contact angle16). The effective contact angle increases but very slightly under the influence of surface roughness. Further increasing of the Young angle causes the transition to the heterogeneous wetting regime. Note that less dense square packing provides higher effective contact angles than a hexagonal one. At the same time, if at the deposition of the coating the particles (19) Shiu, J. Y.; Kuo, C. W.; Chen, P.; Mou, C. Y. Chem. Mater. 2004, 16, 561.
Principles of Design of Superhydrophobic Coatings
Langmuir, Vol. 25, No. 5, 2009 2909
Figure 2. Value of spacing parameter, (R/D)t, at which the transition between the heterogeneous and the homogeneous wetting regimes takes place at a given value of the Young contact angle, θ0, for (1) hexagonal and (2) square lattices of loosely packed spherical particles.
Figure 1. Effective contact angles, θ, versus the Young angles, θ0, for textures formed by (a) the square (a) and (b) the hexagonal dense packings of spherical particles: 1, heterogeneous wetting regime; 2, homogeneous wetting regime, hemispherical particles; 3, homogeneous wetting regime, spherical particles.
became partially embedded into the polymer matrix of binding and/or hydrophobizing agent and the surface topography is formed by truncated spheres, the transition from the homogeneous to the heterogeneous wetting regime takes place at higher Young angles. Thus, the comparison of data presented in Figures 1a and 1b leads to the conclusion that the greater hydrophobicity for densely packed textures, obtained by deposition of monodisperse particles, is achieved for a less dense square arrangement of particles and for a lower degree of particle embedding into the polymer matrix of the coating. However, one has to keep in mind that such texture is less persistent to mechanical impacts. Another important result of the above analysis is a conclusion that, for dense packing of monodisperse particles, irrespective of their diameter, the superhydrophobic state of the surfaces cannot be achieved. An additional characteristic parameter of surface texture, D, associated with the spacing between centers of neighboring particles appears for loose arrangements of spherical particles with radius R < D/2. Then for the heterogeneous wetting regime effective contact angles on such textures are described by relations
( DR ) (1 + cos θ ) - 1 2π R ) ( ) (1 + cos θ ) - 1 √3 D 2
cos θCB ) π cos θCB
2
0
2
2
0
for square packing for hexagonal packing (6)
For the homogeneous wetting regime
( DR ) )cos θ 8π R ) (1 + ( ) )cos θ √3 D (
cos θWD ) 1 + 4π cos θWD
2
for square packing
0
2
0
for hexagonal packing (7)
As follows from eqs 6 and 7, the decreasing of the R/D ratio leads to the increasing of the effective contact angle for the
heterogeneous wetting regime and to its decreasing for the homogeneous one. However, as was shown in ref 16, the thermodynamically stable regime will correspond to the lowest of the two angles associated with homogeneous and heterogeneous wetting regimes. The analysis of eqs 6 and 7 shows that at the increase of spacing between centers of neighboring particles the equilibrium effective contact angle will grow at the beginning, being determined by the heterogeneous wetting regime, then will achieve some maximum value, corresponding to equal probability of two wetting regimes, and will decrease at further growth of spacing, because the homogeneous wetting regime will have become a stable one. It is straightforward to derive from eqs 6 and 7 the relation for the value (R/D)t, at which the transition between the heterogeneous and the homogeneous wetting regimes (at a given value of the Young contact angle) takes place:
(
(1 + cos θ0) R 1 ) D t (1 - cos θ0) π
)
1/2
() √3(1 + cos θ ) 1 ) ( DR ) ) (1 - cos θ )( 2π 0
t
for square packing 1/2
for hexagonal packing
0
(8)
The substitution of the (R/D)t value, calculated from eq 8, into either of the eqs (6) or (7) allows evaluating the maximal attainable hydrophobicity of the surface texture by tuning the particle spacing at the given Young angle (that is, for a given hydrophobizing agent). The calculations show that the introduction of two characteristic lengths, associated with the particle size and separation, allows achieving superhydrophobic state with textures formed by both the square and the hexagonal packing of monodisperse particles (see Figures 2 and 3). Important point here is related to the fact, that the maximal hydrophobicity, attainable on loosely packed monolayers is the same for both packings (Figure 3). However the constraints, imposed on the Young contact angle (θ0 > 113°) and on the particles spacing (R/D) < 0.3 are rather severe and require special technological methods to create the desired surface texture. The situation becomes essentially different if one considers the formation of a texture with the multimodal roughness.20-23 (20) Hikita, M.; Tanaka, K.; Nakamura, T.; Kajiyama, T.; Takahara, A. Langmuir 2005, 21, 7299. (21) Zhang, G.; Wang, D.; Gu, Z.-Z.; Mohwald, H. Langmuir 2005, 21, 9143. (22) Ferrari, M.; Ravera, F.; Liggieri, L. Appl. Phys. Lett. 2006, 88, 203125. (23) Boinovich, L. B.; Emelyanenko, A. M.; Muzafarov, A. M.; Myshkovskii, A. M.; Pashinin, A. S.; Tsivadze, A.Yu.; Yarova, D. I. Nanotechnol. Russ. 2008, 3, 587.
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BoinoVich and Emelyanenko
( ( DR ) + 1)cos θ 2
cos θWD ) 16π
(11)
0
From eqs 9-11 by simple algebra one can deduce the value of the packing parameter, (R/D)t, for which at a given value of the Young contact angle the transition between the homogeneous and the heterogeneous wetting regime takes place. For state B we obtain
(
1 + cos θ0 R B ) Dt π(1 - 14 cos θ0 + cos2 θ0)
()
while for state C
Figure 3. Maximal value of the thermodynamically stable effctive contact angle, θt, attainable on loosely packed monolayers of spherical particles for both the square and the hexagonal packings as a function of the Young contact angle, θ0.
Figure 4. (a) Texture formed by square lattice of four-particle pyramids and (b) the scheme illustrating the positions of line of three phase contact, pinned on top (state B) and lower (state C) layers of particles.
Such texture can easily be created either by aggregation of particles directly at the surface or by deposition of aggregates already formed in dispersion. The advantages of the multimodal roughness in design of the superhydrophobic textures can be demonstrated by an example of a texture formed by square packing of aggregates, each consisting of four particles as shown in Figure 4a. On further analysis we will suppose that particles in the aggregates are large enough to neglect the capillary effects and therefore in the homogeneous wetting regime water penetrates the internal pores of the aggregates. The free energy of a system consisting of water droplet on the surface with the texture described will exhibit several local minima corresponding to the pinning of the interface on the upper (state B) or lower (state C) layer of particles in aggregates (Figure 4b). Taking into account the effective roughness and the relative portion of area encompassed by the three phase contact line, it is easy to derive the relations for the effective contact angles of water droplets on textured surfaces in various wetting regimes. The heterogeneous wetting regime in state B will be charaterized by relation
( DR ) (1 + cos θ ) - 1
(9)
( DR ) (3 cos θ + 10 cos θ + 3) - 1
(10)
B cos θCB )π
2
2
0
(
1 + cos θ0 R C 1 ) D t 1 - cos θ0 3π
()
)
)
1/2
(12)
1/2
(13)
As follows from eqs 12 and 13, the higher the value of the Young contact angle for the particles, the lower the surface density of aggregates required to achieve maximum possible hydrophobicity of the textured surface, as illustrated in Figure 5. By equating the right-hand sides of eqs 9 and 10, we find that the value of the Young contact angle θ0 ) cos-1(-2 + 3) ≈ 105.5° corresponds to the thermodynamic equilibrium of states B and C. That is, at weak hydrophobicity of particle surfaces the maximum of attainable effective contact angle will correspond to the heterogeneous wetting regime in state C, whereas state B will be characteristic for highly hydrophobic particles. Substituting eq 12 to eq 9 (or, respectively, eq 13 to eq 10), we obtain the relations for maximum achievable for the given texture value of effective contact angle as a function of the Young contact angle characteristic of a particle surface:
(cos θCB)tB )
(1 + cos θ0)3 (1 - 14 cos θ0 + cos2 θ0)
-1
(14)
4 cos θ0(1 + cos θ0) 3 (cos θCB)tC ) + -1 (1 - cos θ0)2 (1 - cos θ0)2 (15) (1 + cos θ0)3
The dependencies of effective contact angles for aggregatetextured surfaces versus the Young contact angles, described by eqs 14 and 15, are plotted in Figure 6. The analysis of results obtained (cf. also data presented in Figures 1, 3, and 6) shows that for surface textures with multimodal roughness the superhydrophobic state can be reached at essentially lower hydrophobicity of the particles surface than in cases of mono- or
while in state C C cos θCB )π
2
2
0
0
In the homogeneous wetting regime the effective contact angle will be described by the equation
Figure 5. Value of spacing parameter, (R/D)t, at which the transition between the heterogeneous (for states B and C, respectively) and the homogeneous wetting regimes takes place at a given value of the Young contact angle, θ0.
Principles of Design of Superhydrophobic Coatings
Langmuir, Vol. 25, No. 5, 2009 2911 Table 1. Character of the Dependence of the Energy of the van der Waals Interaction on Separation, h, for Various Systems in Nonretarded and Retarded Limits system
Figure 6. Dependencies of maximal value of the thermodynamically stable effective contact angle, θt, attainable (for the states B and C, respectively) on texture formed by square lattice of four-particle pyramids, on the Young contact angle, θ0.
bimodal roughness. This circumstance is especially important for the technological applications because it allows a considerable broadening of the range of hydrophobizing agents, including the cheaper reagents as well. Besides, it is known that disordering of hydrophobic agents on the treated surface leads to the noticeable lowering of the Young contact angle compared to the ordered structure. Exploiting the advantages of the multimodal roughness texture allows one to relax the requirements for the quality of deposition of hydrophobic agent without detriment to the superhydrophobic properties of the surface with the textured coating. It is worth noting that the multimodal roughness is characteristic of the majority of superhydrophobic surfaces, both the natural textures and the textures (either ordered or disordered) created artificially. In the next section we will discuss briefly the physical nature of forces, determining the peculiarities of particles aggregation in both the bulk dispersion and the wetting film deposited on the surface from the dispersion.
3. Mechanisms of Aggregation and Self-organization of Particles on the Surface at Deposition of Coatings from Dispersions As was mentioned above, the method of nanoparticles deposition from dispersions is one of the most promising and manufacturable methods of coating formation on large area surfaces. The texture of such deposited coating is determined, on one hand, by the processes of particles aggregation and selforganization and, on the other hand, by adsorption and aggregation of molecules of hydrophobic agent. The polarity of the dispersion medium is one of the key factors, determining all the abovementioned processes. For instance, in nonpolar media it is reasonable to neglect the effects of charging of the interfaces (both particle/dispersion medium and substrate/dispersion) associated with the dissociation of components of the dispersion. At the same time, if the particles get charged before dispergation, say, due to triboelectrization, the nonpolarity of the dispersion medium promotes the prolongated conservation of charge at their surfaces. In this case the electrostatic repulsion is insignificantly weakened in the medium with low dielectric permittivity and prevails over the van der Waals attraction between the nanoparticles, thus providing the stabilization of nanodispersion. When such dispersion is deposited on a surface, the charged particles polarize the substrate. Depending on the relation between the dielectric permittivities of the dispersion medium ε1 and the substrate ε2, the induced electrostatic image forces between the particles and the substrate surface can be either attractive (when
crossed nanowires parallel nanowires (per unit length) nanoparticle/half-space nanoparticle/nanoparticle foil/foil (per unit area) parallel macrocylinders (per unit length), for h , R′ where R is the cylinders radius large (compared to separation h) spherical particle/large spherical particle large spherical particle/half-space half-space/half-space
nonretarded limit retarded limit 1/h4 1/h5
1/h5 1/h6
1/h3 1/h6 1/h5/2 1/h3/2
1/h4 1/h7 1/h3 1/h5/2
1/h
1/h2
1/h 1/h2
1/h2 1/h3
ε1 < ε2) or repulsive (ε1 < ε2). As a rule, nonpolar liquids possess lower dielectric permittivity than condensed media, serving as substrates, and therefore polarization effects usually cause the attraction of particles to the substrate. The self-organization of particles in the deposited film in the process of evaporation of volatile components of the dispersion will be determined by combined action of an electrostatic repulsion of charged particles, a capillary attraction of neighbor particles joined with a liquid meniscus, and the van der Waals forces. As a result, the deposition of films from dispersions of charged particles in nonpolar solvent leads to the formation of a coating, containing a monolayer of nanoparticles embedded in a matrix of the binding hydrophobizing agent. The density of particles in the monolayer depends first of all on their concentration in bulk dispersion and the thickness of the deposited dispersion film. Thus, the coating formed in the case under consideration will be characterized either by the bimodal roughness, if the bulk concentration of nanoparticles in dispersion is small, or by the unimodal one if the concentration is large. As follows from the analysis presented in the previous section, in both cases the texture formed is not one favorable for the attaining of the superhydrophobic state. In the absence of free charges on surfaces the van der Waals forces represent the main mechanism of interaction of particles with each other and with the substrate. For coarse colloid particles at large separations (between the two particles or between the particle and the substrate) the van der Waals forces can readily be calculated on the basis of the Dzyaloshinsky, Lifshitz, and Pitaevsky (DLP) approach24 in the so-called retarded limit. In this case the forces between two colloid particles or between the particle and the substrate can be recalculated based on the Derjaguin method25 from the interaction, computed within the DLP theory for two half-spaces separated by a flat fluid interlayer. In the nonretarded limit, the analytical expressions were derived for the dispersion interactions between large colloid particles for sphere-sphere and crossed cylinders geometries by methods of continuous media electrodynamics within the DLP approach. To date, several relations were obtained by various methods for systems with different geometries (Table 1). However, it should be mentioned that analytical expressions were derived only as asymptotic solutions for the energy and/or forces of interaction, valid in the limits of particle sizes either essentially higher or much lower than the separation between two particles or a particle and a substrate. (24) Dzyaloshinsky, I. E.; Lifshitz, E. M.; Pitaevsky, L. P. SoV. Phys. Uspekhi 1961, 4, 153. (25) Derjaguin, B. V. Kolloid Z. 1934, 69, 155.
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The analysis of the effect of nanosize state on the magnitude and the character of dispersion interactions allowed both the considerable weakening and the faster decaying of interaction with the decreasing of particles size to be deduced. For symmetric systems, that is, for similar particles, the dispersion interactions are always attractive, like in the case of macroscopic bodies. Such an attraction promotes the squeezing of liquid from the interlayer between the particles and their aggregation, both in the bulk dispersion and in the deposited film. The equilibrium particle separation within the aggregate is determined by competition between the van der Waals forces, depletion forces, induced by the nonuniformity of distribution of nonadsorbed hydrophobizator molecules around the particles, and steric repulsion, associated with the adsorption of hydrophobic agent on particles surface.26 The analysis26 of experimental data shows that the equilibrium separation just slightly exceeds the doubled thickness of adsorption layer. With regard to the aggregates themselves, their sizes in bulk dispersion are determined by the particles concentration and the kinetic factors. At the same time, the size of aggregates on the substrate will also be dependent on the thickness of deposited film of dispersion, being larger for thicker films. Therefore, one can effectively control the multimodal roughness of the texture, formed at the substrate surface, by adjusting the particle concentration in the bulk dispersion and the thickness of deposited film. The characteristic scales of this roughness are determined, on one hand, by the size of aggregates and their lateral distribution at the surface and, on the other hand, by the size of initially dispersed particles. Importantly, the latter not only decorates the surface of aggregates but also changes, upon the solvent evaporation, the topography of the film of the binding agent between the aggregates. Thus, the conditions, providing the superhydrophobic properties of the coatings, can be easily met in the process of coating formation from the dispersions of uncharged particles in nonpolar solvents. At last, let us consider the case more complicated for the analysis, when the coating is deposited from dispersions in polar solvents. On one hand, in this case one has to take into account the charging of the particles surface due to the dissociation of surface moieties and the ions adsorption from the solution. On the other hand, the extent of the double electric layers formed around the particles and at the substrate surface is also very important. At small concentration of ions in the dispersion medium and significant surface charge the stabilization of dispersion due to electrostatic forces will induce the formation of coating, containing the monolayer of particles embedded in a matrix of the binding hydrophobizing agent, similar to the first case considered above in this section. At higher ion concentrations the aggregative stability of the dispersion will be determined by the entire set of forces acting between the particles.26,27 Predominantly, it is necessary to take into account the van der Waals attraction, the depletion attraction, ion-electrostatic (26) Boinovich, L. B. Uspekhi Khim. 2007, 76, 510. English translation: Russ. Chem. ReV. 2007, 76, 471. (27) Derjaguin, B. V.; Churaev, N. V.; Muller, V. M. Surface Forces; Consultants Bureau; Plenum Press: New York, 1987.
BoinoVich and Emelyanenko
repulsion, and finally, the image-charge forces and the structural forces, the sign and the magnitude of which are dependent on the peculiarities of the given system. The character of interaction of the particles (and their aggregates) with the substrate is an important factor, affecting the operational durability of the coatings formed by the deposition from dispersions with polar solvent. Thus, at similar charges of particles and substrate surfaces the double electric layers prevent the close enough approach of particles to the substrate suface. The loose coating formed in this case can be unsatisfactory not only because of its failure to provide the texture necessary for superhydrophobic features but also because of its weak binding of particles to the surface and, consequently, weak adhesion of the coating to the substrate. To summarize this section, we would like to emphasize that the final texture of deposited coating can be effectively manipulated by variation of dispersion medium polarity and viscosity, particle concentration and charges, solvent volatility, dispersion aging, deposition rate, etc. The appropriate choice of above parameters allows one to obtain either bimodal or multimodal (due to particle aggregation) surface texture, providing the stable superhydrophobic properties.
4. Conclusions In this paper we have considered the principles of formation of nanocomposite superhydrophobic coatings by deposition from dispersions. It is shown that the manufacturing of such coatings presumes the combination of chemical hydrophobization with the creation of a surface texture, characterized by a multimodal roughness. The analysis presented in this paper demonstrates the abilities of various types of ordered textures to meet the conditions necessary to provide high water contact angles on the surface of the hydrophobic material. For several ordered structures we have derived the equations, relating the contact angles, formed by water droplets on a textured coating, with the geometric parameters of the texture and the chemical properties of the coating, the latter being characterized by the Young angle. The conditions providing the thermodynamic stability of heterogeneous wetting regime on textured surfaces have been discussed. It is shown that multimodality of surface roughness facilitates essentially the attainment of the superhydrophobic state. The analysis of forces, acting between the nanoparticles and their aggregates both in the bulk dispersions and in the deposited films, has allowed us to conclude that the desired surface texture may be effectively manufactured by controlled aggregation of particles. The coatings produced by deposition from dispersions of uncharged nanoparticles in nonpolar solvents seem to be one of the most promising for manufacture of superhydrophobic coatings at large area surfaces. Acknowledgment. This research was supported by the programs P-18 and P-27 of the Presidium of Russian Academy of Sciences and by the grant 08-08-12130 of the Russian Foundation for Basic Research. LA803806W
