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WETTABILITY OF SOLIDS

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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

								
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