2.2.2. Surface Free Energy Calculation

The surface free energy is a kind of an attraction force of the surface which cannot be measure directly. Surface free energy determines how the solid behaves in contact with other materials. Contact angle measurement in different measurement liquids with different surface free energies are used in calculations according to several approaches [25]. In this study, three theories such as Owens–Wendt’s, van Oss–Chaudhury–Good’s or Zisman’s were used for surface free energy calculations.

The Owens–Wendt model considers the geometric mean of the dispersive and polar parts of the liquid’s surface tension and the solid’s surface energy [26]. This method assumes that surface free energy (γ_S) is a sum of two components: polar (γ_S^p) and dispersive (γ_S^d) (2):

To determine the polar and the dispersive components of the SFE, the measurements of the contact angle onto samples surface must be conducted with two measuring liquids. The SFE of the measuring liquids used in the test is known, including its polar and dispersive components. Typically, the tests are carried out with distilled water as the polar liquid and diiodomethane as the nonpolar liquid. Polar and dispersive component of solid’s SFE is calculated from the Formula (3) by creating a system of equations (one with data for a polar liquid and the second with data for a nonpolar liquid).

where γS-surface free energy of tested material, γSd-dispersive component of SFE of tested material, γSp-polar component of SFE of tested material, γL-surface free energy of measurement liquid, γLd-dispersive component of SFE of a liquid, γLp-polar component of SFE of a liquid and θ-measured contact angle.

The Owens–Wendt is one of the most common methods for surface free energy calculations.

According to the approach of the van Oss–Chaudhury–Good [27], the surface free energy of a solid (γ_S) is the sum of apolar Lifshitz–van der Waals (γ_S^LW) and polar acid-base interactions (γ_S^AB) (4):

where and γ_S⁺, γ_S^- represent the polar components (acid–base).

Different components of the solid, the liquid surface free energies, and the contact angle are related by this Equation (5):

In order to solve this equation, three unknown parameters γ_S^LW, γ+, γ− must be found. Thus, the contact angle measurement must be done with three different measurement liquids (one non-polar and two polar). This theory, sometimes also called acid–base theory, is the second most used surface free energy theory. It has especially been utilized to look at interactions of proteins (and other biopolymers) with hydrophobic solids [25].

The Zisman’s method is used to determine the so-called critical surface energy (γ_C), which is the surface tension of the liquid needed to completely wet the solid (in that case the contact angle of solid is zero). This critical surface tension value differs from the surface free energy of the solid and is not divided into dispersive and polar components. In a contact angle measurement, several liquids from a given homologous series are used. On the basis of contact angle values, a plot is generated having the surface tension of the liquid in x-axis and cosθ in y-axis. Straight line is fitted to these measurement points and extrapolated to point cosθ = 1 which will give the critical surface tension value for the surface [23]. An exemplary Zisman’s plot made on the base on the contact angle values measured with the use of several liquids for polytetrafluoroethylene (PTFE) was shown in Figure 3.

Zisman’s plot for PTFE with obtained value of critical surface free energy. Zones of surface energy were marked green according to [28,29].

The Equation (6) of the straight line can be determined in a defined coordinate system in which b is the directional coefficient of the line.

Using the Equations (1) and (6), for tested material, the relationship between surface free energy γS and critical surface free energy γC can be given as (7):

In the Zisman’s plot (Figure 3), the surface tension ranges corresponding to good and poor adhesion were shown. The zones were determined on the basis of research on interactions between polymer vascular implants and tissues reported by Baier [28]. In the late 1960s, Robert Baier investigated the role of surface energy of biomaterials in thrombogenesis and proposed the correlation of the degree of biological interactions with the critical value of surface free energy. The surface which indicated least retentive of depositing proteins was identified by the bioengineering criterion of having measured critical surface tension between 20 and 30 mN/m [28,29]. These studies showed that materials characterized by high values of the critical surface tension (above 40 mJ/m²) exhibit the best tissue adhesion. Poor tissue adhesion was observed for materials with low critical surface tension values (below 30 mJ/m²). Critical surface tension also influences the clotting time of blood surrounding the biomaterial [28,29].