Figure 1. Contact angle as a function of the three surface energies.
Contact Angle
Young gave the mathematical expression of this relationship as
γSV = γSL + γLVCOSθ
In some samples where the solid substrate has a surface energy much higher than the liquid, cosθ approaches 1 as the contact angle approaching 0, denoting that the liquid spreads on the substrate’s surface. When the solid has a much lower surface energy than the liquid, cosθ approaches -1 as the contact angle approaches 180° and the liquid is nearly completely non-wetting, as shown in Figure 2.
Figure 2. Contact angle of poorly wetting liquid (left) and well wetting liquid (right). Assuming the same liquid, the substrate on the left has a much lower surface energy than the substrate on the left.
Experimental Parameters
Other experimental parameters can be obtained directly from surface tension and contact angle results. Some examples are as follows:
Work of Adhesion
It is defined as the work needed to isolate the liquid and solid phases, or the negative free energy related to the adhesion of the liquid and solid phases. Work of Adhesion is utilized to express the strength of the interaction between the liquid and solid phases. It is given by the Young-Dupre equation as:
Wa =γ (1 + COSθ)
Work of Cohesion
It is defined as the work needed to isolate a liquid into two parts, and is a measure of the strength of molecular interactions within the liquid. It is given as:
Wc = 2γ
Work of Spreading
Work of Spreading, also called as Spreading Coefficient, is the negative free energy related to spreading of liquid over solid surface. It is given as:
Ws = γ (COSθ - 1)
Wetting Tension
It is a measurement of force/length and is defined as:
τ = Fw/p = γLVCOSθ
This value also denotes the product of the cosine of the surface tension and the contact angle. It enables the characterization of the strength of the wetting interaction sans separate measurement of surface tension. This latter equation can be utilized in a separate approach to measure the contact angle by means of the strength of interaction between the substrate and the wetted meniscus. In this configuration, a flat plate is immersed into a liquid and the ensuing meniscus produces the force Fw, enabling extraction of the contact angle (Figure 3).
θ = atan(-ET/2)
Figure 3. Schematic of forces arising from wetted interface in a flat plate configuration.
Direct Optical Measurement of Contact Angle
The most optimal approach for ascertaining contact angle is direct optical measurement of the contact angle using a high resolution camera or microscope. While the contact angle can be determined directly, it is often measured geometrically using the observed diameter and height of the drop on the surface (Figure 4). This method not only eliminates uncertainties regarding the precise angle at the interface, but also results in an average contact angle and does not handle receding and advancing contact angles quite well.
Figure 4. Representative image of a sessile drop with construction lines shown.
A different approach can also be used by applying techniques which are not defined in ASTM standards. This approach utilizes direct measurement of the wetting force and hence enables simple measurement of receding and advancing contact angles and is inherently not at equilibrium. It is often called as "Dynamic Contact Angle". In this technique, forces that are directly measured are utilized to calculate contact angle. First, the liquid’s surface tension must be determined. A de Nouy ring, which is a thin platinum wire of perimeter ρ, must determine the surface tension (Figure 5). The force needed to pull the ring clear of the water is directly related to the surface tension through:
γL = Fmax / ρ
Figure 5. Image of a de Noüy ring at point where meniscus is stretched to almost breaking point.
After the surface tension is known, an experiment can be conducted where a known geometry is impeded into the liquid and the ensuing wetting force generates the contact angle from the equation above. This method enables simple measurement of receding and advancing contact angles when the surface is dry and already wetted. The equipment can also be utilized to ascertain other wetting phenomena such as wicking.
In order to distinguish the wetting behavior of a specific solid/liquid pair, it is important to quantify and report the contact angle.surface energy, it is essential to employ a range of liquids of known surface energy. Tiny drops are placed on the substrate’s surface, and the contact angle is determined optically, as illustrated in ASTM D5946.
The calculations based on these measurements create a parameter with the units of force/unit length. The two common techniques used to determine this parameter are critical surface tension and free surface energy.
Figure 6. Critical surface energy for polyethylene determined from the Zisman plot.
A technique was developed by Zisman to estimate the surface energy of solid substrates. Using a range of homologous liquids of varying surface tensions, the contact angle θ is measured for each liquid. Based on these measurements, a graph of cosθ 8 vs γLV is drawn, where γ represents the liquids’ surface energy. The line is extrapolated to cosθ = 1; the value of the surface energy where the line crosses 1 is called the critical surface tension, and indicates the maximum surface tension of a liquid that may completely wet the substrate (Figure 6).
Free Surface Energy
Another approach to differentiate a solid surface is by measuring free surface energy, also called as solid surface tension. In this method, the solid is tested against a range of wetting liquids that are well characterized. The liquids utilized must be characterized in such a way that the dispersive and polar components of their surface tensions are known. The related equation is given by Owens and Wendt as:
γ1 (1+ cos θ) / (γld)1/2 = (γsp)1/2 [(γlp)1/2 /(γld)1/2] + (γsd)1/2
where θ represents the contact angle, γ 1 is liquid surface tension and γ s is the solid surface tension. The addition of d and p refer to the dispersive and polar components of each. The relationship of (γld)1/2 /(γld)1/2 vs Y I (1+ cos θ ) / (γld)1/2 can be plotted; the slope will be (γsp)1/2 and the γ-intercept will be (γsd)1/2. The overall free surface energy is just the sum of its two component forces.
This article described the analysis of surface energy of solid substrates using either the force-rebalance method or the sessile drop technique. These methods give compatible values, but offer different tools for assessing the materials’ surface properties.
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