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Calculating Surface Free Energy from Contact Angle Values

Turkchem 09 Jun 2017 25 8 dk okuma

TURKCHEM

Calculating the surface free energy of any solid surface provides important and useful information on issues such as wetting of the material surface and adhesion between phases. In any chemical or physical process involving surface treatment, calculating the surface free energy plays an important role in process optimization. Understanding and correctly applying the methods used to measure surface free energy enables the effective and appropriate use of raw materials in sectors such as paints, inks and coatings.

Calculating surface free energy for any solid surface provides important and useful information on topics such as wetting of the material surface and adhesion between phases. In any chemical or physical process involving surface treatment, calculating surface free energy plays an important role in process optimization. Understanding and correctly applying the methods used to measure surface free energy enables effective and appropriate use of raw materials employed in sectors such as paints, inks, and coatings.

2. Surface Free Energy in Solids

Surface free energy can be defined as the work expended to increase the amount of any solid surface. Another definition describes surface free energy as the energy expended to transport molecules from inside a solid substance to the surface and create new surface [1,2].

Different surface free energy (σ) values for various solid examples are given in Table 1. Solids can generally be divided into two categories: those with high surface energy and those with low surface energy. Generally, metals, inorganic substances, oxides, silicas, diamond, and nitrides have high surface energy. These substances have surface free energies between 200-500 mN/m. Organic materials and polymers, conversely, have low surface energy and generally have energies below 100 mN/m [3].

Calculating surface free energy of solid surfaces is not done directly as it is in tensiometer measurements on liquids. This is because new surfaces cannot be created for measurement due to the rigid nature of solids. For this reason, various methods have been developed for measuring surface free energy on solid surfaces using the contact angle value measured at the interface and based on Young's equation. The ease of contact angle measurement and the ability to perform measurements with high precision make these methods based on contact angle measurement important. Figure 1 schematically shows the contact angle θ formed at the solid-liquid interface. Figure 1. Formation of contact angle at the solid-liquid interface [4]

The situation in Figure 1 is expressed mathematically by Young's equation. Young's equation is given in Equation 1.

Equation (1)

In this equation;

σs: Surface free energy of solid phase

σl: Surface free energy of liquid phase

θ: Contact angle

γsl: Solid-liquid interfacial tension

As can be understood from this, in Young's equation if the surface tension of the liquid is known and contact angle measurement is performed, the surface free energy and interfacial tension values of the solid remain as unknowns in the equation.

Various models have been developed by examining the relationship between surface free energy and interfacial tension. An important point to note here is that the surface free energy value measured on solid surfaces is not a single value.

The surface free energy value will vary depending on the method used and test liquids. For this reason, comparison of different sample solid surfaces should be performed using the same methods [5].

Most developed models use equations with the general form shown in Equation 2 [4].

Equation (2)

Among the developed models, commonly used ones include Zisman, Owen-Wendt-Rabel-Kaelbe (OWRK), Wu, Modified Fowkes, Wu, van Oss, and Good acid-base model, and the equation of state [6,7].

3.1. Zisman Method

In the Zisman plot, the cosine of the contact angle is plotted against the surface free energy of the liquid. The surface free energy is extrapolated at the point where the Cos(θ) value equals 1, meaning the contact angle is 0. An example Zisman plot is shown in Figure 2. As can be seen from the plot, the angle made by different test liquids on the surface is plotted against the surface tension value of the liquid. A line is drawn through these values and the surface tension value at the point where the cosine value equals 1 is accepted as the surface free energy. This value is called critical surface tension and according to Zisman, critical surface tension and surface free energy have the same value. In reality, this value is only the same for non-polar surfaces. Furthermore, as the difference between the surface tension of the test liquid used and the extrapolated critical value increases, the error in this method increases [6]. Test inks or pens with fixed surface tension used in the packaging sector, where corona treatment is applied, are applied according to the critical surface tension concept. Nevertheless, since the polar and dispersive components of test inks are unknown and the surface cannot be separated this way, measurement with test inks is less advantageous compared to the methods that will be explained later [6,7]. Figure 2. Zisman plot drawn for low-density polyethylene film

graph [5]

3.2. OWRK Method

In this method, it is assumed that surface free energy has dispersive and polar components. This is expressed by the mathematical equation in Equation 3.

Equation (3)

As can be seen in Equation 3, terms showing dispersive and polar components have been added for both liquid and solid surfaces. By using test liquids with known polar and dispersive components of surface tensions and performing contact angle measurement, the surface free energy of solids can be determined. In this two-component model, as interactions in polar-polar or dispersive sections increase, interfacial tension decreases and weaker wetting values are achieved, thus resulting in larger contact angles. Figure 3 demonstrates this:

Figure 3. Polar-Polar, Dispersive-Dispersive Interactions

As can be seen from the figure, an increase in polar-polar or dispersive interactions has resulted in lower contact angle values. For this reason, measuring surface free energy by separating it into its components is important in surface analysis. The OWRK method is frequently used in surface free energy measurements and produces good results [6].

3.3. Modified Fowkes Method

With this method, the term constituting the polar component in the OWRK equation used to calculate surface free energy has been separated into hydrogen bonding and dipole-dipole interaction terms. For this reason, application of this method requires at least 3 different test liquids. This method is generally not used in material testing. Nevertheless, it is important for seeing how hydrogen bonds have an effect and observing adhesion between two phases. Wetting of solid surfaces by water is largely related to hydrogen bonding [6].

3.4. Wu Method

This method gives better results at low surface free energy values. Calculations are performed using an equation created by taking the harmonic mean of the polar and dispersive components of the surface tension value. Best results are obtained in the 30-40 mJ/m² range [5,6].

3.5. van Oss and Good acid-base model

According to this method, the OWRK method is the basis; however, the polar component is divided into two as electron-accepting and electron-donating. An example of this approach: Lewis base components only interact with acid components, not with basic components. The van Oss and Good model is generally used on inorganic, organometallic, and ion-containing surfaces and gives good results. There are certain limitations in applying this method. First, knowledge of the basic and acidic components of test liquids is very limited. Moreover, Wu and OWRK methods are frequently and successfully applied [6].

3.6. Equation of state

The equation of state approach differs from the methods explained above by adopting a thermodynamic approach to explain surface free energy. The free energy is not separated into different components to determine it. For this reason, only a single test liquid is sufficient for this method. Studies conducted with this method have generally been performed with non-polar liquids, so this method can be applied on solid surfaces with low polarity [6,8].

4. Equipment, Test Liquids Used in Calculations, and Sample Preparation

When using the methods mentioned above, contact angle measurement is performed as the most important parameter. Contact angle measurement for solid surfaces is generally carried out using optical systems. These systems are called "optical goniometer devices." An example of such a system is shown in Figure 4

Figure 4. Contact Angle Measurement Device. The operating method of the system is the recognition of the shape of a droplet placed on a solid surface with the aid of a camera and its conversion into mathematical data. This work can be accessed [9].

After contact angle measurement is performed, this value is used in the model equations mentioned above. Selection of a liquid with known surface tension is equally important as contact angle measurement. Additionally, as the number of test liquids used increases, the accuracy of the method used increases.

For Zisman, OWRK, Fowkes, and modified Fowkes methods, this means more points in the linear regression to be performed.

For other methods, calculations mean more equations. In both cases, the use of a larger number of test liquids increases measurement accuracy [6]. The selection of test liquids also varies according to the method. In equations with multiple components, the surface tensions of the test liquids selected should not be close to each other. This way, the linear regression used during calculation is performed more appropriately. For the Fowkes and OWRK methods, liquids to be used should be selected as a pair with very high and very low polar fractions. The pair of distilled water and diiodomethane is quite suitable for this purpose and is frequently used. This is because the high surface tension of diiodomethane creates contact angles that are easy to measure. Additionally, its low polarity is a preference for its use. On the other hand, liquids with high polarity (Example: n-hexane) will spread immediately on the surface to be applied and contact angle measurement will become difficult [6].

The number of liquids that can be used in the modified Fowkes and acid-base methods is very limited. This is because the components needed to be used in the methods are known for very few liquids. Nevertheless, water as a first choice can always be used as a test liquid.

This is because it forms distinctive hydrogen bonds and is suitable for these models with its amphoteric character.

Finally, mixtures should not be preferred in test liquid selection. This is because the interactions of liquids forming the mixture and their effect on the solid surface cannot be predicted [6]. When measuring on solid surfaces using the methods explained in this article, in addition to selecting the test liquid, knowing the properties of the sample surface is also important. Surface free energy of solid surfaces is generally greater than that of liquids. For this reason, solid surfaces encounter oxidation, gas or vapor adsorption on the surface, and similar conditions.

This affects surface free energy measurement. For this reason, working under the same temperature and humidity conditions for all samples during measurements will increase measurement precision. Furthermore, the test liquids to be used to prevent vapor formation on solid surfaces should be selected from liquids with low vapor pressures under measurement conditions. Otherwise, the surroundings of the solid surface on which measurement will be performed becomes contaminated with vapors of the test liquid. Additionally, due to the roughness and heterogeneity formed on the surface of solid surfaces, it should be considered that different results may be obtained at different points of the solid sample. For this reason, taking measurements at different points on solid surfaces and using average values would be a more accurate approach [6].

Conclusion

Surface free energy is one of the most common quantities that must be used and calculated in paints, coatings sectors, and processes where surface treatment is performed. How the surface will interact with the liquid it comes into contact with can be predicted by determining this value. In this article, some of the commonly used models for calculating surface free energy have been discussed. Understanding the theory behind a value that is not measured directly but measured using different models and calculating the surface free energy value frequently encountered in surface treatment processes is of great importance.

Yusuf Tanuğur - Product Manager - Alptek Kimya Laboratory Equipment and Consulting Foreign Trade Ltd. Co. References

[1] http://www.kruss.de/services/education-theory/glossary/surface-free-energy/ Retrieved on 8 December 2014.

[2] H. Y. Erbil, 2006, Surface Chemistry Of Solid and LiquidInterfaces, p. 5.

[3] S. Ebnesajjad, 2008. Adhesives Technology Handbook, p. 24.

[4] http://www.kruss.de/services/education-theory/glossary/contact-angle/ Retrieved on 6 December 2014.

[5] So you want to measure surface energy, 1999, KrussApplication Note TN306CR, Krüss Gbmh.

[6] Custom-made models: from contact angle to surface free energy,2008, Kruss Application Note TN315e, Krüss Gmbh.

[7] Why Test Inks cannot tell the full truth about surface free energy, 2014, Kruss Application Note AR272, Krüss Gmbh.

[8] M. Żenkiewicz, 2007, Methods for the calculation of surface free energy of solids, Journal of Achievements in Materials and Manufacturing Engineering Volume 24 Issue 1.

[9] Practical Contact Angle Measurement (4), 2008, Kruss Application Note TN314e, Krüss Gmbh