Surface energy

Interfacial energy

The presence of an interface influences generally all thermodynamic parameters of a system. There are two models that are commonly used to demonstrate interfacial phenomena: the Gibbs ideal interface model and the Guggenheim model. In order to demonstrate the thermodynamics of an interfacial system using the Gibbs model, the system can be divided into three parts: two immiscible liquids with volumes V_α and V_β and an infinitesimally thin boundary layer known as the Gibbs dividing plane (σ) separating these two volumes.

The total volume of the system is:

${\displaystyle V=V_{\alpha }+V_{\beta }}$

All extensive quantities of the system can be written as a sum of three components: bulk phase α, bulk phase β, and the interface σ. Some examples include internal energy U, the number of molecules of the ith substance n_i, and the entropy S.

${\displaystyle \begin{array}{cc}U& =U_{\alpha }+U_{\beta }+U_{\sigma }\\ N_i& =N_{i\alpha }+N_{i\beta }+N_{i\sigma }\\ S& =S_{\alpha }+S_{\beta }+S_{\sigma }\end{array}}$

While these quantities can vary between each component, the sum within the system remains constant. At the interface, these values may deviate from those present within the bulk phases. The concentration of molecules present at the interface can be defined as:

${\displaystyle N_{i\sigma }=N_i-c_{i\alpha }{V}_{\alpha }-c_{i\beta }{V}_{\beta }}$

where c_iα and c_iβ represent the concentration of substance i in bulk phase α and β, respectively.

It is beneficial to define a new term interfacial excess Γ_i which allows us to describe the number of molecules per unit area:

${\displaystyle {\mathrm{\Gamma }}_i=\frac{N_{i\alpha }}{A}}$

Wetting

Spreading parameter

Surface energy comes into play in wetting phenomena. To examine this, consider a drop of liquid on a solid substrate. If the surface energy of the substrate changes upon the addition of the drop, the substrate is said to be wetting. The spreading parameter can be used to mathematically determine this:

${\displaystyle S={\gamma }_{\text{s}}-{\gamma }_{\text{l}}-{\gamma }_{\text{s-l}}}$

where S is the spreading parameter, γ_s the surface energy of the substrate, γ_l the surface energy of the liquid, and γ_s-l the interfacial energy between the substrate and the liquid.

If S < 0, the liquid partially wets the substrate. If S > 0, the liquid completely wets the substrate.

Contact angle

A way to experimentally determine wetting is to look at the contact angle (θ), which is the angle connecting the solid–liquid interface and the liquid–gas interface (as in the figure).

If θ = 0°, the liquid completely wets the substrate.

If 0° < θ < 90°, high wetting occurs.

If 90° < θ < 180°, low wetting occurs.

If θ = 180°, the liquid does not wet the substrate at all.

The Young equation relates the contact angle to interfacial energy:

${\displaystyle {\gamma }_{\text{s-g}}={\gamma }_{\text{s-l}}+{\gamma }_{\text{l-g}}\cos \theta }$

where γ_s-g is the interfacial energy between the solid and gas phases, γ_s-l the interfacial energy between the substrate and the liquid, γ_l-g is the interfacial energy between the liquid and gas phases, and θ is the contact angle between the solid–liquid and the liquid–gas interface.

Wetting of high- and low-energy substrates

The energy of the bulk component of a solid substrate is determined by the types of interactions that hold the substrate together. High-energy substrates are held together by bonds, while low-energy substrates are held together by forces. Covalent, ionic, and metallic bonds are much stronger than forces such as van der Waals and hydrogen bonding. High-energy substrates are more easily wetted than low-energy substrates. In addition, more complete wetting will occur if the substrate has a much higher surface energy than the liquid.

Modification techniques

The most commonly used surface modification protocols are plasma activation, wet chemical treatment, including grafting, and thin-film coating. Surface energy mimicking is a technique that enables merging the device manufacturing and surface modifications, including patterning, into a single processing step using a single device material.

Many techniques can be used to enhance wetting. Surface treatments, such as corona treatment, plasma treatment and acid etching, can be used to increase the surface energy of the substrate. Additives can also be added to the liquid to decrease its surface tension. This technique is employed often in paint formulations to ensure that they will be evenly spread on a surface.

The Kelvin equation

As a result of the surface tension inherent to liquids, curved surfaces are formed in order to minimize the area. This phenomenon arises from the energetic cost of forming a surface. As such the Gibbs free energy of the system is minimized when the surface is curved.

The Kelvin equation is based on thermodynamic principles and is used to describe changes in vapor pressure caused by liquids with curved surfaces. The cause for this change in vapor pressure is the Laplace pressure. The vapor pressure of a drop is higher than that of a planar surface because the increased Laplace pressure causes the molecules to evaporate more easily. Conversely, in liquids surrounding a bubble, the pressure with respect to the inner part of the bubble is reduced, thus making it more difficult for molecules to evaporate. The Kelvin equation can be stated as:

${\displaystyle RT\ln \frac{P_0^K}{P_0}=\gamma V_m\left(\frac{1}{R_1}+\frac{1}{R_2}\right)}$

where P^K
₀ is the vapor pressure of the curved surface, P₀ is the vapor pressure of the flat surface, γ is the surface tension, V_m is the molar volume of the liquid, R is the universal gas constant, T is temperature (in kelvin), and R₁ and R₂ are the principal radii of curvature of the surface.

Surface modified pigments for coatings

Pigments offer great potential in modifying the application properties of a coating. Due to their fine particle size and inherently high surface energy, they often require a surface treatment in order to enhance their ease of dispersion in a liquid medium. A wide variety of surface treatments have been previously used, including the adsorption on the surface of a molecule in the presence of polar groups, monolayers of polymers, and layers of inorganic oxides on the surface of organic pigments.

New surfaces are constantly being created as larger pigment particles get broken down into smaller subparticles. These newly-formed surfaces consequently contribute to larger surface energies, whereby the resulting particles often become cemented together into aggregates. Because particles dispersed in liquid media are in constant thermal or Brownian motion, they exhibit a strong affinity for other pigment particles nearby as they move through the medium and collide. This natural attraction is largely attributed to the powerful short-range van der Waals forces, as an effect of their surface energies.

The chief purpose of pigment dispersion is to break down aggregates and form stable dispersions of optimally sized pigment particles. This process generally involves three distinct stages: wetting, deaggregation, and stabilization. A surface that is easy to wet is desirable when formulating a coating that requires good adhesion and appearance. This also minimizes the risks of surface tension related defects, such as crawling, cratering, and orange peel. This is an essential requirement for pigment dispersions; for wetting to be effective, the surface tension of the pigment's vehicle must be lower than the surface free energy of the pigment. This allows the vehicle to penetrate into the interstices of the pigment aggregates, thus ensuring complete wetting. Finally, the particles are subjected to a repulsive force in order to keep them separated from one another and lowers the likelihood of flocculation.

Dispersions may become stable through two different phenomena: charge repulsion and steric or entropic repulsion. In charge repulsion, particles that possess the same like electrostatic charges repel each other. Alternatively, steric or entropic repulsion is a phenomenon used to describe the repelling effect when adsorbed layers of material (such as polymer molecules swollen with solvent) are present on the surface of the pigment particles in dispersion. Only certain portions (anchors) of the polymer molecules are adsorbed, with their corresponding loops and tails extending out into the solution. As the particles approach each other their adsorbed layers become crowded; this provides an effective steric barrier that prevents flocculation. This crowding effect is accompanied by a decrease in entropy, whereby the number of conformations possible for the polymer molecules is reduced in the adsorbed layer. As a result, energy is increased and often gives rise to repulsive forces that aid in keeping the particles separated from each other.

Surface energies of common materials