II. LITERATURE SURVEY
2.8 Wettability and interfacial reactions
2.8.1 Fundamental of wetting theory
The Young's equation, which is related θto the surface energies σ of the three, interfaces [82]
LV SL
Cos SV
σ σ
θ =σ − (3)
WhereσSV ,σSL andσLV are the solid-vapor, solid-liquid and liquid-vapor interface energies, respectively. There are two major parameters to characterize the wettability of drop of liquid or glass on surface, such as degree of wetting (which indicated by the contact angle formed at the interface) and rate of wetting( which indicates that how fast the liquid or glass wets the surface and meantime spreads over the surface. Degree of wetting followed by surface and interfacial energies involved at interface and it is governed by law of thermodynamics. The value of σLV can be obtained from the sessile drop method by the following equation [83, 84]
⎥⎦
⎢ ⎤
⎣
⎡ − +
= f
f
Lgd
LV 0.0520 0.1227 0.0481
4 ρ 2
σ (4)
4142 . 2 ⎟−0
⎠
⎜ ⎞
⎝
=⎛ d
f h (5)
Η
⎟−
⎠
⎜ ⎞
⎝
=⎛ 2
h d (6)
Where ρLthe density of molten materials is, g is the gravitational acceleration, Η is the final height of the drop at a particular temperature and d is the drop base diameter. Rate of wetting is governed by various factors such as capillary forces, viscosity of the liquid, chemical reactions at interface and thermal conditions of the system.
Figure 2-14 illustrates an experimental approach used to measure equilibrium advancing and receding angles using the sessile drop method in high temperature systems [85, 86]. The sample is shaped either as a vertical piece or as a flat plate placed on the substrate. Because, the sample has a lower melting temperature than the substrate, it becomes liquid during heating whereas the substrate remains solid. If the sample is a vertical piece, the liquid advance across the surface of the substrate until the velocity of the liquid front becomes zero. The final angle in such a measurement is called “advancing contact angle” (Figure 2-14-A). When the initial sample is a flat plate (Figure 2-14-B), then the liquid retracts and the final angle is the “receding contact angle”.
Figure: 2-14 Schematic drawing of a sessile drop. Both (A) advancing and (B) receding angle are shown [34]
The dependence of θ on the velocity of the wetting line as shown in Figure 2-15. The contact angle varies with speed and direction of motion. In the advancing case, the angle
static advancing contact angle, θadv. In the receding case the angle decreases with increasing magnitude of velocity. For this case θ reaches the static receding contact angle θrec if the velocity is equal to zero. The difference between θadv and θrec can be quite large—as much as 50° for water on mineral surfaces. This is generally attributed to surface heterogeneity or surface roughness. The equilibrium angle θ0, which would occur if no surface roughness or chemical inhomogeneity on the substrate existed, lies in between these two values [87, 88].
Figure: 2-15 Schematic drawing of the advancing and receding contact angle versus. The spreading velocity (v) of the triple line is moving along two directions. The advancing angle exceeds the receding angle. This is called contact-angle hysteresis [87, 88].
2.8.1.1 Factors Influencing the Wettability
Different factors influencing the wettability at high temperature and the related applications are shown in Figure 2-16.
Figure: 2-16 Different factors influencing the wettability at high temperature.
¾ Absorption:
The adsorption of atoms (as for example, oxygen or carbon) on solid and liquid surfaces and at solid–liquid interfaces leads to a reduction in the surface and interface energies. The
activity of an active element are shown in Figure 2-17 [85, 88]. Since the equilibrium amount of adsorbate depends on the activity, it can be used as a measure of the amount of adsorbate on the surface. A critical activity acr exists where the surface interface energy decreases with increasing activity as shown in Figure 2-17. Depending on the amount of adsorbate the equilibrium contact angle decreases or increases. This can be derived from Young’s equation (1) by introducing activity dependent surface energies.
Figure: 2-17 Hypothetical variation of the interfacial energies (σSL, σSV, σLV) versus the activity a due to adsorption effects (for example oxygen or carbon adsorption) [85, 88].
¾ Ridge Formation
Young’s equation only applies to systems where the substrate (should be homogeneous) is perfectly rigid and insoluble, and where the triple line can only move in the direction parallel
to the substrate. The Young equation is derived by balancing the horizontal force components and vertical force components can be neglected. This approximation is valid for many low-temperature systems like organic liquids on hard, high-cohesive energy substrates such as most metals or ceramics [85, 89-91]. When liquids are in contact with soft solids pronounced local elastic deformation and formation of a triple line ridge on the substrate surface may occur. The ridges can be several tens of nanometers tall and they can affect the dynamics of wetting [92-96].
For most high-temperature systems (e.g., molten metals or oxides on ceramics or metals) the temperatures during the experiment are typically ≥0.5 Tm, and therefore, local atomic diffusion can occur. This provides a mechanism for ridge formation even for hard substrates. In the case of ridge formation, spreading requires motion of the triple line both horizontally and vertically, which leads to two independent relations:
Figure: 2.-18 Illustration of (a) contact angle between the solid and contact liquid (b) the dihedral angles in the case of ridge formation [85].
SL V SV
L S
σ φ σ
φ σ
φ sin sin
sin
LV
=
=
(7)
where øS, øL, øV are equilibrium dihedral angles in the solid, liquid and vapor respectively.
These dihedral angles are visualized in Figure 2-18.
The ridge will evolve until complete equilibrium is reached. If a ridge is present one has to differentiate between microscopic and macroscopic angles. The microscopic angles are the aforementioned dihedral angles øS, øL, øV. The macroscopic angle is the angle between the tangent of the liquid/vapor interface at the triple line and the unperturbed substrate surface. The presence of a ridge can strongly influence the spreading kinetics and the equilibrium angle. The observed spreading rates can be orders of magnitudes lower than for liquids, where the flow is just controlled by capillarity and viscosity Saiz et al [85, 91].
The spreading process divided into four stages, depending on the degree of ridge growth Saiz et al [85]. In the first stage, the deformation which occurs at the triple line is due to elastic strains in the solid and capillary forces drive the contact angle towards the one defined by Young’s equation. In the case of metallic or ceramic substrates this distortion was calculated and found sufficiently small such that no plastic deformation is expected. This stage is found at short times when the liquid spreads very fast with a high driving force so that a triple line ridge would be unstable Saiz et al [85, 91]. In the second stage some diffusion processes or solution precipitation is allowed to occur. The substrate will deform at the triple line and capillary forces will drive θ towards a value close to Young’s angle but spreading kinetics will be dictated by the velocity at which the attached ridge moves. There exists a certain time where the ridge will be small compared to the radius of curvature of the liquid. A ridge can form, depending on the ratio of the height of the ridge compared to the curvature of the liquid one differentiates between second and third stage (as shown in Figure2-19). The fourth stage describes complete equilibrium, which means macroscopic 2D equilibrium and constant curvature. To reach full 2D equilibrium, times much longer than the experimental ones might be necessary in many practical systems.
Figure 2-19 The geometry of a liquid drop on a substrate depends on time. In Regime 1 (A) the spreading velocity of the liquid is faster than the ridge formation. The liquid spreads on a flat surface. Regime 2+3 (B): a ridge can form, depending on the ratio of the height of the ridge
compared to the curvature of the liquid one differentiates between Regime 2 and 3. Regime 4 (C):
full equilibrium is obtained. The curvature of the drop is constant [85, 88, 91].
2.8.1.2 Reactive and Non-Reactive Wetting: Thermodynamic Point of View
¾ Non-Reactive Wetting:
Spreading of liquid or glass on surface without local reaction /adsorption at interface is known as non-reactive wetting. In case of non-reactive wetting higher contact angles can be obtained and for this type of wetting, only thermodynamic principle of energy reduction of system should be under considerations. The change in surface free energy ( ) following a small displacement of liquid is [97-100].
= ΔA (σSL – σSV) + ΔA σLV Cos (θ – Δθ) (8)
Where change in area of surface covered by liquid. At equilibrium condition, and values are unity and surface free energy becomes zero at uniform temperature and chemical potentials. Therefore Eq. (5) obeys young’s equation:
σSL – σSV + σLV Cosθ = 0 (9)
¾ Reactive Wetting:
In reactive wetting, uncertain stabilize conditions exist at interfaces. It means a new solid compound formation at interface due to the mainly chemical reactions or mass transports between the liquid or glass and substrate. The wettability and reactivity is determined by the
for reactive wetting is more sensitive and many deviations exhibits to analysis the unique concept. On the other hand the concept of thermodynamics of wetting is limited only to non-reactive systems [88, 98]. From Gibbs free energy of wetting; wetting is still enhancing in systems, where bulk reactions are occurred between the phases even may not be thermodynamically feasible.
In reactive systems, the strength of chemical bonding between mating surfaces can be assessed by determining the work of adhesionW . The thermodynamic work of adhesion a W a
defined as follows by Dupré: [85, 88, 91-98]
Wa = σSV + σLV - σSL (10)
W is the work per unit area that must be performed to separate a solid- liquid interface to obtain a
a solid/vapor and a liquid/vapor interfaces. Combing equations (1) and (10), the Young-Dupré equation can be obtained: [85, 88, 91-98]
( θ)
σ 1+cos
= LV
Wa (11)
Hence, the condition for complete wetting in a reactive system is at contact angle is 0 .
2.8.1.3 Dynamic Wetting: Effects of Surface Roughness
In dynamic wetting process, the dynamic contact angle increase with the increasing wetting velocity, the stress should increase . It was reversed in dewetting process. The change of the solid-liquid interfacial tension is proportional to the viscous shear stress at triple line from below mentioned equation [101]
(12)
(13)
Where is solid-liquid interfacial tension in the dynamic wetting process, c proportional constant having dimension of length and is viscous shear stress in N.m-2.
In generally, capillarity (θd) and gravity (drop weight) aretwo forces that drive spreading (W).
For drop volume V, viscosity η, density ρ and surface tension σ, the radius of the wetted spot grows as [101]
1/10 (14)
For small drops and as for large drops follows:
1/8 (15)
For a drop of maximum height H, the viscous force is proportional to ηUR/H, where U=dR/dt is the velocity of the contact line. However, there is no involvement of spreading parameters (for example, spreading coefficient) in above laws and not well -defined value of R of the triple line formation at interface.
Surface roughness improves the surface energy value by providing an additional interfacial area for the spreading liquid over on it. Wenzel theory [101] discusses the effect of roughness on the equilibrium contact angle and apparent contact angle on a rough surface as
Cos = r Cosθ (16)
Where is Wenzel angle (also called as apparent contact angle on rough surface), is the equilibrium contact angle and is the average roughness ratio (i.e. ratio of actual wetted surface area to projected or geometric surface area). - Value always greater than unity and equal to unity for smooth surfaces.