Experimental determination of surface energy for high-energy surface: A review

The knowledge of surface energy is of theoretical importance and application for both researchers in basic research and engineers in engineering applications. The magnitude of the surface energy reflects the magnitude of the internal bonding force of a solid [1,2]. At the same time, surface energy externally affects the adsorption on the surface of the solid, which is essential for enhancing biocompatibility in medical devices [3,4]. Surface energy likewise affects the behavior of dispersions of colloids, adhesion and friction [5]. A deeper understanding based on surface phenomena even dominates manufacturing processes, such as the preparation of micro and nano structures in integrated circuits, the control of crystal growth and morphology in optical devices, and the preparation of metal matrix composites [[6], [7], [8]].

The formation of new surfaces is necessarily accompanied by changes in the energy of the system, as defined by Gibbs in 1961 as the work required to form additional surfaces [9].γ=∂F∂SaT,v,p,niwhere F is the total free energy of the system, Sa is the surface area, T is the temperature (in K), v is the volume, p is the pressure, ni is the number of moles of component i, and γ is the energy per unit area. As indicated in this case, the Helmholtz free surface energy that represents the change in free energy when a new surface per unit area is formed under constant temperature and volume conditions, is equal to the Gibbs free surface energy that represents the change in free energy when a new surface per unit area is formed under constant temperature and pressure conditions. From a thermodynamic point of view, for solid materials, the formation of new surfaces can be formed by elastic deformation and plastic deformation. The former corresponds to an increase in surface area dependent on mechanical stretching, which leads to an increase in the inter-atomic distance between the nearest neighbors of the surface but not in the number of atoms; the latter corresponds to an increase in surface area dependent on a proportional increase in the number of atoms on the surface, a situation that often corresponds to an increase in the surface area of liquids [10]. Thus, the solid surface energy (or surface stress) is different from the liquid surface tension. The former is usually a vector quantity, representing the formation or disappearance of a new surface; the latter is usually a scalar quantity, representing a force directed from the surface to the interior of the liquid. Surface tension can be used as an intrinsic property to distinguish substances, yet surface energy is disturbed by many factors (e.g., crystal orientation [11], surface contamination [12]) to the extent that accurate experimental (or intrinsic) values are difficult to obtain. The surface energy of a solid can be expressed as,γs=dεpdεtot∙γp+dεedεtot∙γs0where γs is the generalized surface energy, εp is the plastic strain, εe is the elastic strain, εtot is the elastic strain, γp is the surface tension (corresponding to the change in energy per unit area caused by plastic deformation), and γ0 s is the surface energy (corresponding to the change in energy per unit area caused by elastic deformation) [[13], [14], [15]]. The difficulty in the experimental empirical determination process is to distinguish whether the formation of a new surface is elastic or plastic deformation and to quantify it. Therefore, the methods to obtain experimental surface energies are rather limited.

Solids with high cohesion energy in general (metals, ceramics, glass, etc.) usually have surfaces with high surface energy (hundreds to thousands of mJ/m2) and the composition of these substances is usually dominated by chemical bonds (covalent, ionic, metallic bonds) [16]. Due to the requirement that the surface tension of solids must be equal to or slightly greater than that of liquids, it is almost impossible to determine the solid surface tension using contact angle measurements. This is the basis for direct calculation of surface tension of solids using methods such as Zisman, Wu model, Owens model, Fowkes theory, Acid/Base theory, and Equation of State, which all need to satisfy this condition. Selecting an appropriate auxiliary liquid becomes crucial for most high-energy surfaces, but it should be noted that the high-energy surface can absorb the vapor of the auxiliary liquid, leading to a reduction in the surface tension of the solid. Surprisingly, although water droplets should obtain perfect wetting on high-energy surfaces (i.e., the contact angle should be close to zero degrees according to Young's equilibrium equation), in fact non-zero contact angles are obtained in most cases. This is obviously related to the extremely strong affinity of the high-energy surface, which is more likely to adsorb low-energy substances under the atmosphere to balance the unsaturated chemical bonds on the surface. Contact angles of zero or near zero can only be obtained when some extreme conditions are taken, such as heating and annealing under ultra-high vacuum and then cooling to room temperature. This suggests that it is almost impossible to obtain surface energies close to the theoretical values for high-energy surfaces measured in atmospheric environments [17,18].

Before further research, we must first distinguish these concepts. Surface tension is the energy per unit length of surface and is usually used to describe the resistance of liquid surface. Surface energy is the total interaction force between liquid molecules and air or solid molecules, and is usually used to describe the interaction forces that liquid molecule experience at the surface. The Helmholtz surface free energy is the free energy of liquid molecules formed in small areas of the surface. It is the work required to remove unit surface area of liquid molecules from the liquid surface at constant temperature and pressure, and therefore reflects the strength and stability of surface molecule interaction. The Gibbs surface free energy is the total interaction force between liquid molecules and air or solid molecules during the formation of a liquid surface. It is the work required to remove unit surface area of liquid molecules from the liquid surface and compress it to a certain pressure at constant temperature and pressure, and therefore reflects the strength and stability of surface molecule interaction, while also taking into account the volume change of liquid molecules. Compared with the Helmholtz surface free energy, the Gibbs surface free energy considers the compression effect and is therefore more practical in the formation and stability of liquid surface and droplets.

Based on the above, most researchers in this field are well aware that experimental measurement of surface energy is not an easy task, and in some cases, it is not even a pleasant one. Even so, the significance of experimental measurements is not limited to obtaining values close to theoretical ones, but more importantly to obtaining apparent values under specific conditions, which can be used to explain experimental phenomena and guide the actual production process. In order to obtain surface energy values, indirect or direct measurements are usually used, despite the presence of many interfering factors and known measurement difficulties. In this work, we reviewed the current measurement methods and their respective drawbacks.

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