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WETTABILITY OF SOLIDS Emil Chibowski Department of Physical Chemistry-Interfacial Phenomena, Faculty of Chemistry, Maria Curie- Skłodowska University, 20-031 Lublin, Poland OUTLINE Introduction Thermodynamics of wetting process The surface tension of pure liquids Types of wetting processes: spreading immersional adhesional. Wetting of solid surface in adsorption process Wetting contact angle Contact angle and the work of adhesion General problem of surface free energy formulation and determination Other approaches to the surface free energy determination Contact angle hysteresis Superhydrophobic surfaces Examples of practical application of solid surface wettability Summary Introduction Process of wetting of a solid by a liquid, usually by water, is often applied or it occures naturally. Some examples: • We wet our hands and body with water. • After having a meal we need to clean the dishes, thus wetting them. • Often we put dirt clothing into a washing machine adding some detergent. At first it is wetted. • The soil has to be wetted for plants to grow up. The plant leaves have to be wetted with appropriate solution, emulsion or suspension of chemical substances to protect them against insects or fungus. • Pharmaceutical and cosmetic products are needed to wet tissues or skin well. • Glues and adhesive tapes must also wet well a solid surface to strongly keep together the parts. • Painting of solid surfaces to protect them against corrosion, dyeing of fibres, lubrication, coatings. • One of most important industrial processes, which is totally based on the differences in wettability of the surfaces, is flotation process of mineral ores enrichment. Important: In all wetting processes the surface free energy of solid and liquid, and obviously the interfacial solid/liquid free energy, play a fundamental role. Therefore, to understand the wetting processes description of the interfacial interactions should be known too. Wetting process can be investigated as a static or dynamic one. The dynamics of wetting is of great importance in many practical processes. Here we will be mostly involved in description of the static wetting, that is, description of the process that has attended equilibrium. Thermodynamics of wetting process Wetting of a solid surface occurs when one fluid phase repel another (liquid or gas) being present on the surface. gas γl liquid γs γsl /////////////////////////////////////////////////////////// solid Fig.1. Scheme of wetting process of solid surface by a liquid. At T, p = const. the differential of Gibbs’ free energy ‘G ‘ for a pure liquid ‘l ’ wetting a solid surface ‘s’ determined by the changes in the surface area ‘ A’ equals: ∂G ∂G ∂G dG = dA s + dA sl + dA l (1) ∂A s ∂A sl ∂A l Where subscript ‘sl‘ means solid/liquid interfacial area. However, dA l = − dA s = dA sl (2) ∂G ∂G ∂G And; = γl = γs = γ sl (3) ∂A l ∂A s ∂A sl Sl/s = Ws = γs – γsl – γl (4) Sl/s is the spreading coefficient, Ws is the work of spreading wetting. The surface tension of pure liquids The surface tension (or surface free energy) of pure liquids, or surface free energy of solids, results from uncompensated forces acting between the molecules (atoms) in the surface layer being of a few molecular diameters thick. Fig.2. A scheme of intermolecular forces acting between molecules in bulk liquid and in the surface layer. The resulting net force is normal to the surface and directed toward the bulk; as well another force, tangential to the surface, is present. The surface tension γ is the force needed to enlarge a liquid surface by unit, or, it is the energy (work) needed to transport a unit area of the molecules from the bulk to the surface, i.e. to enlarge the surface area by a unit (numerically the same value). Surface of liquid Movable side Movable side Liquid (F)orce F/ l = γ [N/m] (W)ork W = γ ⋅ l⋅ dx = γ ⋅ dA [J/m2 ] Liquid film Fig.3. Mechanical analogy to the relationship between surface tension Fig.4. Illustration of surface and surface free energy. tension of a soup film stretched across a wire frame. (Figs. 3 and 4 are from A.W. Adamson and A.P. Gast, Physical Chemistry of Surfaces). Consider a hypothetical system shown in Fig.5. It consists of a pure liquid placed in a box with sliding cover made of a material that does not interact with the liquid (zero interfacial tension). If at T, p, n = const. the cover is slid back to create an uncovered surface dA, the reversible work done on this system equals, W = γdA, and it is just equal to the increase in free energy of this system: dG = γ ⋅ dA (6) dA W Fig.5. Model of the system for surface tension (Gibbs surface free energy) deter- mination (from A.W. Adamson and A.P. Gast, Physical Chemistry of Surfaces). Because the number of moles has not changed, the increase in the energy is in fact due to the dA increase. ∂G Gs = γ = (7) ∂A T ,p For the reversible process the accompanying heat gives the surface entropy ss (per the unit area). dq = T⋅ss ⋅dA (8) From a general thermodynamic relationship it results; ∂G s − Ss = = dγ (9) ∂T p dT Because Hs = Gs + TSs, where superscript s means ‘surface’, we have: s dγ H =γ−T (10) dT The surface enthalpy is usually larger than the surface free energy (surface tension). This is because the free energy is a decreasing function of temperature. Note: Surface tension of liquids can be measured by several more or less direct methods which are described in a handbook. Types of wetting processes Spreading wetting It occurs when a drop of liquid is settled on a solid surface and enlarges its contact perimeter (spreads) (Fig.1). The specific work of spreading (in J/m2) for this process describes Eq.(4). Ws = γs – γsl - γl (4) gas γl liquid γs γsl /////////////////////////////////////////////////////////// solid Fig.1. Scheme of wetting process of a solid surface by a liquid Its value can be positive or negative, depending on the surface free energy of the solid and the liquid used for the wetting. Ws > 0 if γs > (γsl + γl) Ws < 0 if γs < (γsl + γl) If the work of spreading is negative, the liquid drop will not spread but rest on the surface and form a definite wetting contact angle. Immersional wetting γs γl Immersional wetting process occurs, for example, when a γsl plate of a solid is in a reversible Fig.13. A scheme of process dipped into a liquid immersional wetting normally to the liquid surface process. (Fig.13). Then, because the The work of immersion liquid surface tension vector is equals: normal to the solid surface it does not contribute to the work WI = γs – γsl (11) of immersion WI. Adhesional wetting This is a process in which two unit areas are contacted in reversible way thus forming the interface of solid/liquid or liquid/liquid. The value of work of adhesion in solid/ liquid system equals: WA = γs + γl – γsl (12) Fig.14.An illustration of the adhesion wetting process between phases A and B (from A.W. Adamson and A.P. Gast, Physical Chemistry of Surfaces). If the process deals with the same phase (e.g. a column of liquid) this work is equal to the work of cohesion WC, and Eq.(12) reduces to Eq. (13). WC = 2γl (13) Comparison of the work of wetting in particular processes : WS = (γs – γsl) – γl It is clearly seen that:: WI = (γs – γsl) Ws < WI < WA WA = (γs– γsl) + γl Then: WS = (γs – γsl) – γl = WA {= (γs– γsl) + γl} – 2γl WS = WA – WC (14) Wetting of solid surface in adsorption process During the adsorption process the solid surface free energy is changed depending on the nature of adsorbing molecules. This change is termed as the surface pressure (or film pressure) π. In general it may be negative or positive. The resulting work of adsorption process may correspond to the work of spreading, immersional or even adhesional wetting. The shape of adsorption isotherm depends on whether the liquid wets the surface completely or only partially, i.e. whether the liquid forms definite contact angle or not. For complete wetting the adsorption isotherm at p/po = 1 approaches to infinity and macroscopically thick layer is formed. In case of partial wetting the adsorbed amount is finite, and the film thickness is about few monolayers. Here, metastable and unstable regions may appear in the super- saturation regions and condensation of the vapor may also occur. Hence in a closed system at p/po = 1 the adsorbed film may be in equilibrium with the liquid droplet. Using the Gibbs adsorption equation thermodynamic relationship between vapor adsorption and wetting can be derived, assuming ideal behavior of the vapor. Γ π sv = RT ∫Γ =o Γd ln(p / p o ) (15) Where: πsv = γs – γsv is the adsorbed film pressure. The film pressure equals to the difference between the surface free energy of bare solid γs, and the solid surface free energy with adsorbed film γsv. The adsorbed amount is determined by the surface excess Γ. Wetting contact angle Fig.15. Schematic representation of liquid drop/solid/gas system showing contact angle θ. The equilibrium system corresponds to partial spreading wetting. Tomas Young described this system in 1805 and formulated (only in words) the relationship, which is now known as the Young equation. γs = γlcosθ + γsl (16) The original text “An Essay on the Cohesion of Fluids” published in Phil. Trans. Roy. Soc. in 1805 year by Young: “we may therefore inquire into conditions of equilibrium of the three forces acting on the angular particles, one in the direction of the surface of the fluid only, a second in that of the common surface of the solid and fluid, and the third in that of the exposed surface of the solid. Now supposing the angle of the fluid to be obtuse, the whole superficial cohesion of the fluid being represented by the radius, the part of which acts in the direction of the surface of the solid will be proportional to the cosine of the inclination; and this force, added to the force of the solid, will be equal to the force of the common surface of the solid and fluid, or to the difference of their forces… And the same result follows when the angle of the fluid is acute.” From Eq.(16) one would expect that for an insoluble in the liquid flat solid surface only one contact angle value should describe the liquid drop/solid/gas (vapor) system. Such contact angle is termed as the ‘equilibrium contact angle’ θe, or ‘Young’s contact angle’. If the solid surface behind the liquid droplet is bare, the contact angle is termed as the ‘advancing contact angle’ θa. Practically in all systems when the three-phase line has retreated, for example by sucking a volume of the liquid drop, the contact angle at this new equilibrium is smaller, and it is termed the ‘receding contact angle’ θr. The equilibrium contact angle value lies somewhere between the advancing and receding contact angle values. θa > θe < θr The difference between the advancing and receding contact angles is named ‘contact angle hysteresis’, H. H = θa - θr Contact angle and the work of adhesion In the Young equation: γs = γlcosθ + γsl contact angle θ liquid surface tension γl } - measurable solid surface free energy γs interfacial solid/liquid free energy γsl } - unknown However, the work of adhesion can be determined. γs = γlcosθ + γsl ⇒ γsl = γs – γlcosθ WA = γs + γl – γsl = γs + γl – γs + γlcosθ (17) WA = γl (1+ cosθ) Having determined WA then work of spreading WS can be calculated for such ‘contact angle system’. WS = WA – WC = WA - 2γl = γl (1+ cosθ) - 2γl WA = γl (1+ cosθ) WS = γl (cosθ -1) However, still the surface free energy of solids cannot be determined in this way. This is possible if the work of adhesion is formulated in such a way that it involves the solid surface free energy. This problem is not fully solved yet. Intermolecular forces have to be considered, which are: dispersion, dipole-dipole, π-electrons, hydrogen bonding, or generally Lewis acid-base, i.e. electron-donor and electron-acceptor. F.M. Fowkes in 1960 took into account that between paraffin hydrocarbon molecules only dispersion forces interacted and assumed that the same was true for n-alkane/water molecules interactions. Applying the Berthelot’s rule (u11u22)1/2 = u12 for the interfacial dispersion interactions between two phases Fowkes expressed the work of adhesion for hydrocarbon/water as: WA = 2(γHd γWd)1/2 (18) Because: WA = γH + γW – γHW Hence: γHW = γH + γW – 2(γHd γWd)1/2 (19) Where: H - hydrocarbon (n-alkane); W - water - For n-alkanes: γH = γHd - The interfacial tension n-alkane/water γHW can be measured. - Fowkes determined in this way contribution of the dispersion interactions to water surface tension, i.e. the dispersion component of water surface tension γWd = 21.8 ± 0.7 mN/m. - The total surface tension of water equals 72.8 mN/m at 20oC. - The difference between the two γWn = 51 mN/m results from the presence of nondispersion forces originating from water molecules. - These nondispersion forces are dipole-dipole and hydrogen bonding. Fowkes (and later others) considered that surface tension (surface free energy) of a liquid or solid can be expressed as a sum of several components, of which not necessarily all are present at a surface. d p i h π da e γ=γ +γ +γ +γ +γ +γ +γ (20) The superscripts mean interactions: d – dispersion, p – dipole- dipole, i – dipole-induced dipole, h – hydrogen bonding, π – π- electrons, da – donor-acceptor, e – electrostatic. General problem of surface free energy formulation and determination Recently Lyklema has revisited fundamental aspects of phenomenological thermodynamics of surface excess energy and entropy in relation to the surface and interfacial tensions of liquids and arrived at some important conclusions. According to Lyklema the work of adhesion WA = 2(γ1d γ2d)1/2 expressed by geometric mean of dispersion interactions has a weak thermodynamic background, because it is formulated like the energy u12 (Berthelot’s rule (u11u22)1/2 = u12) . He states that thermodynamic quantities, here the surface tensions, are mixed up with mechanical ones, i.e. internal energy. The description of thermodynamic parameters involves temperature, while the mechanical quantity does not. The term (γ1d γ2d)1/2 is formulated as temperature independent, because the Helmholtz energy (U-TS) is actually considered as the energy (U), which is obviously not true. However, for many systems γHW = γH + γW – 2(γHd γWd)1/2 well describes wetting and adhesion processes in conjunction with contact angles. Lyklema considers two reasons for such behavior: 1 - the same type of approximation made for two coupled phenomena, i.e. surface tension and contact angle, which may lead to compensation of the errors and thus pointing to the consistency, 2 - for most liquids the surface entropy is a generic property (i.e. remains practically the same within the range of experimental errors).and combination of different pair of liquids give the same error. His final statement is that there is a reason to continue using equation the equation, but the data should be reconsidered. However, over-interpretation of this equation, by adding extra terms (like acid-base interactions), or combination of γ values with contact angle data, by introducing an additional empirical terms to obtain solid-liquid interfacial tensions is not justified. A correct equation describing the interfacial tension γ12 should be following: γ12 = γ1+ γ2 – 2(U1,aσ,d U2,aσ,d)1/2 + T∆adhSaσ (21) From Eq.(21) it would result that for water the dispersion component of its surface tension, γwd = 21.8 mN/m (as determined by Fowkes) is probably underestimated by ca. 8%. Other approaches to the surface free energy determination Despite Lyklema’s criticizm there are several different equations in which geometric mean of polar (dipole-dipole) or hydrogen bonds interactions have been added. They are still used sometimes. Often an equation like (21) was used in which all non-dispersion interactions (polar) γp were expressed by the geometric mean. γ12 = γ1 + γ2 – 2(γ1d γ2d)1/2 -2(γ1p γ2p)1/2 (21a) In the late 80th of past century van Oss, Good and Chaudhury introduced a new formulation of the surface and interfacial free energy. γi = γiLW + γiAB = γiLW +2(γi– γi+)1/2 (22) γiLW – apolar Lifshitz-van der Waals component a phase ‘i ‘ γiAB - polar Lewis acid-base interactions (hydrogen bonding). γi– - electron-donor γi+ - electron-acceptor }– mostly hydrogen bonding Note that the polar interactions are expressed by the geometric mean. H γ1– Fig.16. A scheme of hydrogen bonding •x •• • • • • γ1+ between two water molecules. The ‘free’ • O• −H O H x x electron-donor γ1– and electron-acceptor •x •• γ1+ interactions are also shown. H Interfacial solid/liquid free energy is derived basing on Eq.(22) . γSL = γS + γ L − WA = γS + γ L − 2 (LW LW 1 / 2 γS γ L ) ( −2 ) + − 1/ 2 γS γ L −2 ( ) − + 1/ 2 γS γ L (24) And the work of adhesion reads: WA = γl (1+ cosθ) =2 (LW LW 1 / 2 γS γ L ) +2 (+ − 1/ 2 γS γ L ) +2 (− + 1/ 2 γS γ L ) (25) If one has measured contact angles of three liquids, whose surface tension components are known, then three equations of type (25) can be solved simultaneously and the surface free energy components of the solid can be determined. Van Oss et al. assumed for water at room temperature equal electron-donor and electron-acceptor interactions. Because: γwAB = 2(γw– γw+)1/2 = 51 mN/m, Hence: γ1– = γ1+ = 25.5 mN/m. Basing on this value the relative values for other liquids have been determined. Table 1. Surface tension and its components, in mN/m, of some liquids, usually used as the probe liquids for solid surface free energy determination. Liquid γlTOT γlLW γl+ γl- Diiodomethane 50.8 50.8 0 (0.4-0.7) 0 α-Bromonaphthalene 44.4 43.6 0.4 0.4 Decane 23.8 23.8 0 0 Water 72.8 21.8 25.5 25.5 Formamide 58.0 39.0 2.28 39.0 Ethylene glycol 48.0 29.0 1.92 47.0 Glycerol 64.0 34.0 3.92 57.4 Dimethylsulfoxide 44 44 0 30 In the literature there are several other ‘scales’ of the liquid tension components, more or less justified, which are based on the assumption that for water γ1– ≠ γ1+. In general, this approach is controversial one. It always gives large γ1– and small γ1+ values. The authors explain it as a generic nature of surfaces. Thus determined solid surface free energy components depend to some extent on the kind of three probe liquids used. Such values should be considered as relative ones, but they are useful to observe changes of the surface free energy. To obtain reasonable and comparable results, one of the three probe liquids should be apolar, e.g. diiodomethane, and the two polar, usually water and formamide, or ethylene glycol. Contact angle hysteresis The difference between advancing contact angle θa and receding con- tact angle θr is termed ‘contact Fig.17. Illustration of advancing and angle hysteresis. receding contact angle measurements H = θa - θr • The hysteresis was explained (and still it is) by roughness of real surfaces and/or their chemical heterogeneity. • Later it appeared that even on molecularly flat surfaces and on self-assembled monolayer the hysteresis also appears. • This author considered that contact angle hysteresis may also result from the liquid film left behind the droplet during retreat of its three-phase contact line. Basing on this assumption an equation for calculation of total surface free energy of a solid from three measurable parame- ters, i.e. advancing and receding contact angles and the liquid surface tension, has been derived. Using the Young equation it can be written: γs = γsl + γl cosθa (16) γsf = γsl + γl cosθr (26) Where γsf is free energy of the solid surface on which the liquid film is present. γsf = γs + π Combining Eqs.(16) and (26): π = γl (cosθr – cosθa) (27) The work of adhesion for both advancing (A) and receding (R) modes can be expressed: WAA = γl (1+ cosθa) (28) WAR = γl (1+cosθr) (29) Hence: WAR – WAA = γl (cosθr - cosθa) = π (30) The work of adhesion can also be expressed with a help of so called Good’s parameter: WA = 2Φ γ s γ l A (31) WA = 2Φ γ sf γ l R (32) Taking ratio of the works of adhesion and the relationships expressed by Eqs.(27)-(29) one obtains. tot (1 + cos θa ) 2 γ s = γ l (cos θr − cos θa ) (34) 2 2 (1 + cos θr ) − (1 + cos θa ) Or: tot γ l (1 + cos θa ) 2 γs = (35) (2 + cos θr + cos θa ) In Table 2 and 3 are shown the surface free energy values of glass surface determined from van Oss et al.’s and hysteresis appro-aches . The average values from both methods agree very well, and standard deviation from the contact angle hysteresis is even less than from the components. Table 2. Total surface fee energy of the glass surface calculated from Eq.35. Liquid surface Adv. contact angle Rec. contact angle Total surface free Liquid tension, mN/m θa , deg θr, deg. energy, mJ/m2 Water 72.8 42.14 ± 3.25 37.40 ± 2.54 62.4 Glycerol 64 42.36 ± 1.46 36.50 ± 0 54.6 Formamide 58 36.94 ± 2.23 33.33 ± 2.38 51.7 Diiodomethane 50.8 48.13 ± 0.74 34.37 ± 0.74 40.4 Ethylene glycol 48 31.83 ± 2.48 26.67 ± 2.05 43.9 Average: from the components 50.9 ± 9.1 mJ/m2 (Table 3) 50.6 ± 7.8 Table 3. Total surface free energy and its components (mJ/m2) of glass calculated from Eq.(25), using θa, and surface tension of probe liquids listed in Table 1, in mJ/m2. Probe Liquid Triads Energy D-W-F D-W-G D-W-EG W- G – F W-F-EG γsLW 35.3 ± 0.4 35.3 ± 0.4 35.3 ± 0.4 23.4 ± 1.7 58.3 ± 1.4 γs+ 0.85 ± 0.04 1.57 ± 0.06 0.23 ± 0.01 4.2 ± 0.52 0.63 ± 0.6 γs- 37.6 ± 2.7 33.7 ± 3.1 43.3 ± 3.1 36.4 ± 2.8 39.5 ± 2.9 γstot 46.6 ± 1.1 49.9 ± 1.3 41.6 ± 0.7 48.1 ± 4.3 68.3 ± 2.3 Av. γstot 50.9 ± 9.1 mJ/m2 Key: D- diiodomethane, W –water, F – formamide, G –glycerol, EG – ethylene glycol Other examples of the hysteresis approach application for surface free energy determination (Eq.35) show Figs.18 and 19. 80 70 60 50 Silicon grafted with (CH3)3Si-//// 1. After 6-min, γstot = 33.5 2 mJ/m2 , 54 % reduction Surface free energy, γs , mJ/m 1 34 tot 32 2. After 1-2.5 h, γstot = 29 2 mJ/m2, 60% reduction 30 3 28 3. After 48 h - 196 h (8 26 days), γstot = 24.5 mJ/m2, 66% reduction 24 0 1 2 3 4 5 24 48 72 96 120 144 168 192 Reaction time, h Fig. 18. Total surface free energy, γstot , of silicon surface grafted at room temperature with (CH3)3Si– in toluene solution depending on the reaction time as determined form water contact angle hysteresis (A.Y. Fadeev, T.J. McCarthy, Langmuir, 15 (1999) 375). Wettability of trialkylchloro–, dialkyldichloro– and alkyltrichloro– silane layers 40 Silicon grafted with the silanes 1. For methylsilanes monolayers 38 - R(CH3)2SiCl γstot in mJ/m2 : 2 Surface free energy, γs , mJ/m 36 - R CH3 SiCl2 (CH3)3Si– 23 34 (CH3)2Si= 33 - RSiCl3 tot 32 CH3Si≡ 39 30 28 2. For R = –C6H11 to –C18H35 26 γstot practically the same. 24 These alkyl chains shield the 22 silicon surface to similar degree. 20 Methylene groups determine 0 2 4 6 8 10 12 14 16 18 20 the free energy giving 22–24 Number of carbon atoms in R chain mJ/m2. Fig. 19. Total surface free energy, γstot , of the silyl layers versus the number of carbon atoms in the alkyl chain (R) determined from water contact angle hysteresis (A.Y. Fadeev and T. McCarthy, Langmuir, 16,7268(2000)). . 1 ///-Si 45 2 ///-Si As determined from water contact angle hysteresis 3 ///-Si 40 4 ///-Si 2 Surface free energy, mJ/m 35 5 ///-Si 30 6 ///-Si 25 7 ///-Si 8 ///-Si 20 9 ///-Si 15 10 ///-Si 10 1 2 3 4 5 6 7 8 9 10 11 12 11 ///-Si C18H37 Type of sylane monolayer 12 ///-Si C8H17 From: A.Y. Fadaeev and T.J. McCarthy, Langmuir, 15, 3759 (1999), Tabl.6 Superhydrophobic surfaces If one takes water contact angle as a measure of surface hydrophobicity, then ‘Superhydrophobic’ means that the surface becomes abnormally more hydrophobic. For example, on a hydrophobic surface water contact angle is, say, 100-120o, so on the superhydrophobic surface the contact angle increases up to 150o and more. This is possible if micro- or nano- size roughness are produced on the surface. Therefore, a water droplet rests on it like on a brash, and in fact, the droplet contact with the surface is much smaller than on the same flat surface. There are several natural superhydrophobic surfaces, and the most known is that of lotus leaf on which θ equals up to 170o. A B Fig.19. A). A water droplet on a lotus leaf. (From: http://www.botanik. unibonn.de/ system/lotus/en/ prinzip.html.html). B) SEM-image of lotus leaf. The micro structural epidermal cells are covered with nanoscopic wax crystals. Bar: 20 µm. (from W. Barthlott and C. Neinhuis, Planta 202, 1(1997). The air trapped between the wax roughness on the leaf surface minimizes the contact area of the water droplet. For suchs system description, instead the Young equation often Wenzel or Cassie equation is applied. Young equation γs – γsl = γlcosθ Wenzel equation r>1 r (γs – γsl) cosθ’= r cosθ real ⋅ surface ⋅ area r= apparent ⋅ surface ⋅ area Cassie equation f cosθ’= f cosθ + (1-f) cos180o = f cosθ’= f (1+ cosθ) –1 Fig.20. Illustration of Young, Wenzel and f = area fraction of solid surface Cassie equations. From A. Nakajima et al., Monatshefte fur Chemie, 132, 31 (2001) Wenzel - roughness factor r > 1 the surface roughness increases apparent hydrophobicity of a hydropho- bic surface, but also hydrophilicity of a hydrophilic surface. Cassie - contact angle θ’ – the surface consists of solid and air The solid fraction under the droplet is described by the factor f. On the fraction occupied by air the contact angle is180o. For superhydrophobic surfaces the apparent surface free energy can be calculated from contact angle hysteresis Such values delivers interesting information about properties of the surface. Some examples of model superhydrophobic surfaces, produced by photolithography method, are shown in Figs.21 and 22 30 25 1 Surface free energy, mJ/m2 20 15 2 10 3 5 0,4 0,3 1- ODMCS 0,2 2- DMDCS 0,1 3- FDDCS 0,0 0 20 40 60 80 100 120 Size of square post, µm Fig.2. SEM images of surface containing 8 µm × 8 µm Fig.22. Changes in apparent surface square posts with different free energy of silicon wafer roughed spacings. surfaces treated with dimethyl- (DMDCS), n-octyl- (ODMCS), or heptadecafluoro-1,1,2,2-tetrahydro- decyl- (FDDCS) dimethylchlorosilane. From: D. Öner and T.J. McCarthy, Langmuir ,16 (2000) 7777. For the surfaces shown in Figs.21and 22: The advancing water contact angles were: θa = 166-173o, The receding contact angles were: θr = 131-138o. The free energy of smooth silicone surfaces covered with the silane depending on its kind was: 16-26 mJ/m2. The apparent free energy of the rough surfaces was less than 0.2 mJ/m2. Up to ca. 40µm of the square post size the energy increased only a little. If the post size was larger than 120 µm the surfaces behaved as flat ones. x 0.18 ODMCS surface 1- 16x16 µm x 0.16 2- 32x32 µm 2x 2 0.14 Surface free energy, mJ/m 0.12 0.10 0.08 2 0.06 0.04 0.02 1 0.00 20 40 60 80 100 120 140 Post height, µm Post Advancin Receding Advancin Receding height g contact contact g contact contact angle, θa, angle, θr, angle, θa, angle, θr, µm deg deg deg deg 20 173 138 170 137 40 174 134 170 132 60 169 138 168 139 From: D. Öner and T.J. McCarthy, Langmuir 16 80 169 136 167 134 (2000) 7777 100 173 138 173 134 140 168 136 166 131 Examples of practical application of solid surface wettability One of very important applications of wetting process is flotation method of mineral ores enrichment. It is based on the differences in wettability of the mineral grains and those of gangue. In this case the mineral surface is needed to be hydrophobic. From the work of spreading, WS = WA – WC = γl (cosθ -1), it results that Ws > 0 (hydrophobic surface), if a water droplet forms defined contact angle on the mineral grain surface. Generally, mineral surfaces are rather hydrophilic. Therefore to convert them into hydrophobic ones the use of appropriate surfactant is needed. It adsorbs from the solution of flotation pulp onto the mineral surface with its polar head to the surface and the hydrophobic tail directed toward the liquid phase, thus lowering the solid surface free energy γs, as well as the interfacial mineral-water free energy γsl. In this way the surfactant can reverse the work of spreading from positive to negative. The surfactants used in the flotation process are called ‘collectors’. Fig.23 shows how flotation recovery of several minerals depends on the value of the work of spreading. Fig.24 presents flotation activity of barite samples precovered with different amounts of anionic sodium dodecyl sulfate (SDS) or cationic tetradecyl ammonium chloride surfactant. Volume of nitrogen, cm3 110 10 Marble/0.62 TDACl 100 1.06 Sulfur 20 0.53 Barite/1.0 SDS 90 30 0.265 80 Quartz/DDACl 40 70 Barite/0.4 SDS 80 Recovery, % 60 Recovery, % 60 1 2 50 Coal 33 40 40 Barite/1.0 TDACl Marble 20 30 0 20 Barite/0.25 TDACl 0 1 2 3 4 Chalcocite 10 Barite Quartz Statistical monolayers: SDS - 1 or TDACl - 2 Quartz/1.0 SDS 0 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 120 Work of water spreading, WS, mJ/m 2 Fig.24. Dependence of the flotation recovery of barite on the number of Fig.23. Dependence of the flotation statistical monolayers of SDS or recovery of mineral on the value of TDACl (upper part shows the nitrogen work of spreading of water. volumes needed for 100% flotation of the sample). Fig.24 - more effective is cationic TDACl than anionic SDS collector. The complete flotation of the sample with TDACl is achieved even below coverage of one calculated monolayer. An example of the surface free energy changes of mineral as a function of its surface coverage with a collector is shown in Fig. 25 for apatite. The decrease in its surface free energy due to the adsorption of oleic acid is shown at different temperatures and pH values. The energy values were calculated from water contact angle hysteresis. The minimum energy of fluorite occurs at about monolayer coverage of the surface, assuming vertical orientation of the molecules. 65 60 Apatite/Oleate pH=8, 20 C o 55 o pH=9.5, 20 C 2 Surface frre enrgy, mJ/m 50 o pH=9.5, 65 C 45 40 35 2 30 21.3 A /molec. 25 O 20 15 2 25A /molec. 10 0 1 2 3 4 5 6 7 8 9 10 11 12 2 Adsorption, µmol/m J. Drelich et al, J. Colloid Interface Sci., 202, 462-476 (1996) Fig.25.Total surface free energy for apatite as a function of oleate adsorption calculated at two different temperatures and pHs. The contact angles data were from Y. Lu, J. Drelich and J.D. Miller, J. Colloid Interface Sci. 202, 462 (1998). The arrow shows monolayer coverage suggested by the authors (25 Å2/molec.), and the vertical dotted line shows the monolayer coverage assuming 21.3 Å2/molec. Summary The presented examples show an important role of wetting in everyday life and industrial processes. Understanding of wetting processes is based on the knowledge of solid and liquid surface free energy. Knowing the energies and their components prediction whether the solid surface will be wetted, and to which extent, is possible. Note: There are solids that occur only in a powdered state, e.g.: soils, clays, pigments. For such solids real contact angle cannot be measured directly. There are methods based on measurements of penetration rates of a liquid into porous layer or column of the tested solid. One more way of wetting