Surface energy

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Contact angle measurements can be used to determine the surface energy of a material. Contact angle measurement with Attension Theta.png
Contact angle measurements can be used to determine the surface energy of a material.

In surface science, surface energy (also interfacial free energy or surface free energy) quantifies the disruption of intermolecular bonds that occurs when a surface is created. In solid-state physics, surfaces must be intrinsically less energetically favorable than the bulk of the material (the atoms on the surface have more energy compared with the atoms in the bulk), otherwise there would be a driving force for surfaces to be created, removing the bulk of the material (see sublimation). The surface energy may therefore be defined as the excess energy at the surface of a material compared to the bulk, or it is the work required to build an area of a particular surface. Another way to view the surface energy is to relate it to the work required to cut a bulk sample, creating two surfaces. There is "excess energy" as a result of the now-incomplete, unrealized bonding between the two created surfaces.

Contents

Cutting a solid body into pieces disrupts its bonds and increases the surface area, and therefore increases surface energy. If the cutting is done reversibly, then conservation of energy means that the energy consumed by the cutting process will be equal to the energy inherent in the two new surfaces created. The unit surface energy of a material would therefore be half of its energy of cohesion, all other things being equal; in practice, this is true only for a surface freshly prepared in vacuum. Surfaces often change their form away from the simple "cleaved bond" model just implied above. They are found to be highly dynamic regions, which readily rearrange or react, so that energy is often reduced by such processes as passivation or adsorption.

Assessment

Measurement

Contact angle

The most common way to measure surface energy is through contact angle experiments. [1] In this method, the contact angle of the surface is measured with several liquids, usually water and diiodomethane. Based on the contact angle results and knowing the surface tension of the liquids, the surface energy can be calculated. In practice, this analysis is done automatically by a contact angle meter. [2]

There are several different models for calculating the surface energy based on the contact angle readings. [3] The most commonly used method is OWRK, which requires the use of two probe liquids and gives out as a result the total surface energy as well as divides it into polar and dispersive components.

Contact angle method is the standard surface energy measurement method due to its simplicity, applicability to a wide range of surfaces and quickness. The measurement can be fully automated and is standardized. [4]

In general, as surface energy increases, the contact angle decreases because more of the liquid is being "grabbed" by the surface. Conversely, as surface energy decreases, the contact angle increases, because the surface doesn't want to interact with the liquid.

Other methods

The surface energy of a liquid may be measured by stretching a liquid membrane (which increases the surface area and hence the surface energy). In that case, in order to increase the surface area of a mass of liquid by an amount, δA, a quantity of work, γ δA, is needed (where γ is the surface energy density of the liquid). However, such a method cannot be used to measure the surface energy of a solid because stretching of a solid membrane induces elastic energy in the bulk in addition to increasing the surface energy.

The surface energy of a solid is usually measured at high temperatures. At such temperatures the solid creeps and even though the surface area changes, the volume remains approximately constant. If γ is the surface energy density of a cylindrical rod of radius r and length l at high temperature and a constant uniaxial tension P, then at equilibrium, the variation of the total Helmholtz free energy vanishes and we have

where F is the Helmholtz free energy and A is the surface area of the rod:

Also, since the volume (V) of the rod remains constant, the variation (δV) of the volume is zero, that is,

Therefore, the surface energy density can be expressed as

The surface energy density of the solid can be computed by measuring P, r, and l at equilibrium.

This method is valid only if the solid is isotropic, meaning the surface energy is the same for all crystallographic orientations. While this is only strictly true for amorphous solids (glass) and liquids, isotropy is a good approximation for many other materials. In particular, if the sample is polygranular (most metals) or made by powder sintering (most ceramics) this is a good approximation.

In the case of single-crystal materials, such as natural gemstones, anisotropy in the surface energy leads to faceting. The shape of the crystal (assuming equilibrium growth conditions) is related to the surface energy by the Wulff construction. The surface energy of the facets can thus be found to within a scaling constant by measuring the relative sizes of the facets.

Calculation

Deformed solid

In the deformation of solids, surface energy can be treated as the "energy required to create one unit of surface area", and is a function of the difference between the total energies of the system before and after the deformation:

.

Calculation of surface energy from first principles (for example, density functional theory) is an alternative approach to measurement. Surface energy is estimated from the following variables: width of the d-band, the number of valence d-electrons, and the coordination number of atoms at the surface and in the bulk of the solid. [5] [ page needed ]

Surface formation energy of a crystalline solid

In density functional theory, surface energy can be calculated from the following expression:

where

Eslab is the total energy of surface slab obtained using density functional theory.
N is the number of atoms in the surface slab.
Ebulk is the bulk energy per atom.
A is the surface area.

For a slab, we have two surfaces and they are of the same type, which is reflected by the number 2 in the denominator. To guarantee this, we need to create the slab carefully to make sure that the upper and lower surfaces are of the same type.

Strength of adhesive contacts is determined by the work of adhesion which is also called relative surface energy of two contacting bodies. [6] [ page needed ] The relative surface energy can be determined by detaching of bodies of well defined shape made of one material from the substrate made from the second material. [7] For example, the relative surface energy of the interface "acrylic glassgelatin" is equal to 0.03 N/m. Experimental setup for measuring relative surface energy and its function can be seen in the video. [8]

Estimation from the heat of sublimation

To estimate the surface energy of a pure, uniform material, an individual region of the material can be modeled as a cube. In order to move a cube from the bulk of a material to the surface, energy is required. This energy cost is incorporated into the surface energy of the material, which is quantified by:

Cube model. The cube model can be used to model pure, uniform materials or an individual molecular component to estimate their surface energy. Cubemodel.tif
Cube model. The cube model can be used to model pure, uniform materials or an individual molecular component to estimate their surface energy.

where zσ and zβ are coordination numbers corresponding to the surface and the bulk regions of the material, and are equal to 5 and 6, respectively; a0 is the surface area of an individual molecule, and WAA is the pairwise intermolecular energy.

Surface area can be determined by squaring the cube root of the volume of the molecule:

Here, corresponds to the molar mass of the molecule, ρ corresponds to the density, and NA is the Avogadro constant.

In order to determine the pairwise intermolecular energy, all intermolecular forces in the material must be broken. This allows thorough investigation of the interactions that occur for single molecules. During sublimation of a substance, intermolecular forces between molecules are broken, resulting in a change in the material from solid to gas. For this reason, considering the enthalpy of sublimation can be useful in determining the pairwise intermolecular energy. Enthalpy of sublimation can be calculated by the following equation:

Using empirically tabulated values for enthalpy of sublimation, it is possible to determine the pairwise intermolecular energy. Incorporating this value into the surface energy equation allows for the surface energy to be estimated.

The following equation can be used as a reasonable estimate for 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 Vα and Vβ and an infinitesimally thin boundary layer known as the Gibbs dividing plane (σ) separating these two volumes.

Guggenheim model. An extended interphase (s) divides the two phases a and b. Guggenheim takes into account the volume of the extended interfacial region, which is not as practical as the Gibbs model. Guggenheim Model.tif
Guggenheim model. An extended interphase (σ) divides the two phases α and β. Guggenheim takes into account the volume of the extended interfacial region, which is not as practical as the Gibbs model.
Gibbs model. The Gibbs model assumes the interface to be ideal (no volume) so that the total volume of the system comprises only the alpha and beta phases. Gibbs Model.tif
Gibbs model. The Gibbs model assumes the interface to be ideal (no volume) so that the total volume of the system comprises only the alpha and beta phases.

The total volume of the system is:

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 ni, and the entropy S.

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:

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

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

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:

where S is the spreading parameter, γs the surface energy of the substrate, γl the surface energy of the liquid, and γs-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. [9]

Contact Angles: non-wetting, wetting, and perfect wetting. The contact angle is the angle that connects the solid-liquid interface and the liquid-gas interface. Diagrams.tif
Contact Angles: non-wetting, wetting, and perfect wetting. The contact angle is the angle that connects the solid–liquid interface and the liquid-gas interface.

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. [10]

The Young equation relates the contact angle to interfacial energy:

where γs-g is the interfacial energy between the solid and gas phases, γs-l the interfacial energy between the substrate and the liquid, γl-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. [11]

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. [12] In addition, more complete wetting will occur if the substrate has a much higher surface energy than the liquid. [13]

Modification techniques

The most commonly used surface modification protocols are plasma activation, wet chemical treatment, including grafting, and thin-film coating. [14] [15] [16] 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. [17]

Many techniques can be used to enhance wetting. Surface treatments, such as corona treatment, [18] plasma treatment and acid etching, [19] 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. [20]

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.

Vapor pressure of flat and curved surfaces. The vapor pressure of a curved surface is higher than the vapor pressure of a flat surface due to the Laplace pressure that increases the chemical potential of the droplet causing it to vaporize more than it normally would. Vapor Pressure.tif
Vapor pressure of flat and curved surfaces. The vapor pressure of a curved surface is higher than the vapor pressure of a flat surface due to the Laplace pressure that increases the chemical potential of the droplet causing it to vaporize more than it normally would.

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:

where PK
0
is the vapor pressure of the curved surface, P0 is the vapor pressure of the flat surface, γ is the surface tension, Vm 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. [21]

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. [21] 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. [22] 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. [21] 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. [22] 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. [23] 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.

Dispersion Stability Mechanisms: Charge Stabilization and Steric or Entropic Stabilization. Electrical repulsion forces are responsible for stabilization through charge while steric hindrance is responsible for stabilization through entropy. Charge and steric or entropic stabilizations.tif
Dispersion Stability Mechanisms: Charge Stabilization and Steric or Entropic Stabilization. Electrical repulsion forces are responsible for stabilization through charge while steric hindrance is responsible for stabilization through entropy.

Surface energies of common materials

MaterialOrientationSurface energy
(mJ/m2)
Polytetrafluoroethylene (PTFE)19 [24] [ page needed ]
Glass 83.4 [25]
Gypsum 370 [26]
Copper 1650 [27]
Magnesium oxide (100) plane1200 [28]
Calcium fluoride (111) plane450 [28]
Lithium fluoride (100) plane340 [28]
Calcium carbonate (1010) plane23 [28]
Sodium chloride (100) plane300 [29]
Sodium chloride (110) plane400 [30]
Potassium chloride (100) plane110 [29]
Barium fluoride (111) plane280 [28]
Silicon (111) plane1240 [28]

See also

Related Research Articles

<span class="mw-page-title-main">Hydrophobe</span> Molecule or surface that has no attraction to water

In chemistry, hydrophobicity is the physical property of a molecule that is seemingly repelled from a mass of water. In contrast, hydrophiles are attracted to water.

<span class="mw-page-title-main">Surface tension</span> Tendency of a liquid surface to shrink to reduce surface area

Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects to float on a water surface without becoming even partly submerged.

<span class="mw-page-title-main">Adhesion</span> Molecular property

Adhesion is the tendency of dissimilar particles or surfaces to cling to one another.

An artificial membrane, or synthetic membrane, is a synthetically created membrane which is usually intended for separation purposes in laboratory or in industry. Synthetic membranes have been successfully used for small and large-scale industrial processes since the middle of the twentieth century. A wide variety of synthetic membranes is known. They can be produced from organic materials such as polymers and liquids, as well as inorganic materials. Most commercially utilized synthetic membranes in industry are made of polymeric structures. They can be classified based on their surface chemistry, bulk structure, morphology, and production method. The chemical and physical properties of synthetic membranes and separated particles as well as separation driving force define a particular membrane separation process. The most commonly used driving forces of a membrane process in industry are pressure and concentration gradient. The respective membrane process is therefore known as filtration. Synthetic membranes utilized in a separation process can be of different geometry and flow configurations. They can also be categorized based on their application and separation regime. The best known synthetic membrane separation processes include water purification, reverse osmosis, dehydrogenation of natural gas, removal of cell particles by microfiltration and ultrafiltration, removal of microorganisms from dairy products, and dialysis.

<span class="mw-page-title-main">Wetting</span> Ability of a liquid to maintain contact with a solid surface

Wetting is the ability of a liquid to maintain contact with a solid surface, resulting from intermolecular interactions when the two are brought together. This happens in presence of a gaseous phase or another liquid phase not miscible with the first one. The degree of wetting (wettability) is determined by a force balance between adhesive and cohesive forces. There are two types of wetting: non-reactive wetting and reactive wetting.

<span class="mw-page-title-main">Dewetting</span> Retraction of a fluid from a surface it was forced to cover

In fluid mechanics, dewetting is one of the processes that can occur at a solid–liquid, solid–solid or liquid–liquid interface. Generally, dewetting describes the process of retraction of a fluid from a non-wettable surface it was forced to cover. The opposite process—spreading of a liquid on a substrate—is called wetting. The factor determining the spontaneous spreading and dewetting for a drop of liquid placed on a solid substrate with ambient gas, is the so-called spreading coefficient S:

<span class="mw-page-title-main">Contact angle</span> The angle between a liquid–vapor interface and a solid surface

The contact angle is the angle between a liquid surface and a solid surface where they meet. More specifically, it is the angle between the surface tangent on the liquid–vapor interface and the tangent on the solid–liquid interface at their intersection. It quantifies the wettability of a solid surface by a liquid via the Young equation.

<span class="mw-page-title-main">Cassie's law</span>

Cassie's law, or the Cassie equation, describes the effective contact angle θc for a liquid on a chemically heterogeneous surface, i.e. the surface of a composite material consisting of different chemistries, that is non uniform throughout. Contact angles are important as they quantify a surface's wettability, the nature of solid-fluid intermolecular interactions. Cassie's law is reserved for when a liquid completely covers both smooth and rough heterogeneous surfaces.

The Kelvin equation describes the change in vapour pressure due to a curved liquid–vapor interface, such as the surface of a droplet. The vapor pressure at a convex curved surface is higher than that at a flat surface. The Kelvin equation is dependent upon thermodynamic principles and does not allude to special properties of materials. It is also used for determination of pore size distribution of a porous medium using adsorption porosimetry. The equation is named in honor of William Thomson, also known as Lord Kelvin.

<span class="mw-page-title-main">Capillary length</span>

The capillary length or capillary constant, is a length scaling factor that relates gravity and surface tension. It is a fundamental physical property that governs the behavior of menisci, and is found when body forces (gravity) and surface forces are in equilibrium.

Mucoadhesion describes the attractive forces between a biological material and mucus or mucous membrane. Mucous membranes adhere to epithelial surfaces such as the gastrointestinal tract (GI-tract), the vagina, the lung, the eye, etc. They are generally hydrophilic as they contain many hydrogen macromolecules due to the large amount of water within its composition. However, mucin also contains glycoproteins that enable the formation of a gel-like substance. Understanding the hydrophilic bonding and adhesion mechanisms of mucus to biological material is of utmost importance in order to produce the most efficient applications. For example, in drug delivery systems, the mucus layer must be penetrated in order to effectively transport micro- or nanosized drug particles into the body. Bioadhesion is the mechanism by which two biological materials are held together by interfacial forces. The mucoadhesive properties of polymers can be evaluated via rheological synergism studies with freshly isolated mucus, tensile studies and mucosal residence time studies. Results obtained with these in vitro methods show a high correlation with results obtained in humans.

Inverse gas chromatography is a physical characterization analytical technique that is used in the analysis of the surfaces of solids.

Adsorption is the adhesion of ions or molecules onto the surface of another phase. Adsorption may occur via physisorption and chemisorption. Ions and molecules can adsorb to many types of surfaces including polymer surfaces. A polymer is a large molecule composed of repeating subunits bound together by covalent bonds. In dilute solution, polymers form globule structures. When a polymer adsorbs to a surface that it interacts favorably with, the globule is essentially squashed, and the polymer has a pancake structure.

Polymeric materials have widespread application due to their versatile characteristics, cost-effectiveness, and highly tailored production. The science of polymer synthesis allows for excellent control over the properties of a bulk polymer sample. However, surface interactions of polymer substrates are an essential area of study in biotechnology, nanotechnology, and in all forms of coating applications. In these cases, the surface characteristics of the polymer and material, and the resulting forces between them largely determine its utility and reliability. In biomedical applications for example, the bodily response to foreign material, and thus biocompatibility, is governed by surface interactions. In addition, surface science is integral part of the formulation, manufacturing, and application of coatings.

Biomaterials exhibit various degrees of compatibility with the harsh environment within a living organism. They need to be nonreactive chemically and physically with the body, as well as integrate when deposited into tissue. The extent of compatibility varies based on the application and material required. Often modifications to the surface of a biomaterial system are required to maximize performance. The surface can be modified in many ways, including plasma modification and applying coatings to the substrate. Surface modifications can be used to affect surface energy, adhesion, biocompatibility, chemical inertness, lubricity, sterility, asepsis, thrombogenicity, susceptibility to corrosion, degradation, and hydrophilicity.

The surface chemistry of paper is responsible for many important paper properties, such as gloss, waterproofing, and printability. Many components are used in the paper-making process that affect the surface.

<span class="mw-page-title-main">Elasto-capillarity</span> Physical phenomenon

Elasto-capillarity is the ability of capillary force to deform an elastic material. From the viewpoint of mechanics, elastocapillarity phenomena essentially involve competition between the elastic strain energy in the bulk and the energy on the surfaces/interfaces. In the modeling of these phenomena, some challenging issues are, among others, the exact characterization of energies at the micro scale, the solution of strongly nonlinear problems of structures with large deformation and moving boundary conditions, and instability of either solid structures or droplets/films.The capillary forces are generally negligible in the analysis of macroscopic structures but often play a significant role in many phenomena at small scales.

Rheological weldability (RW) of thermoplastics considers the materials flow characteristics in determining the weldability of the given material. The process of welding thermal plastics requires three general steps, first is surface preparation. The second step is the application of heat and pressure to create intimate contact between the components being joined and initiate inter-molecular diffusion across the joint and the third step is cooling. RW can be used to determine the effectiveness of the second step of the process for given materials.

<span class="mw-page-title-main">Ideal surface</span>

An ideal solid surface is flat, rigid, perfectly smooth, and chemically homogeneous, and has zero contact angle hysteresis. Zero hysteresis implies the advancing and receding contact angles are equal.

Liquid phase sintering is a sintering technique that uses a liquid phase to accelerate the interparticle bonding of the solid phase. In addition to rapid initial particle rearrangement due to capillary forces, mass transport through liquid is generally orders of magnitude faster than through solid, enhancing the diffusional mechanisms that drive densification. The liquid phase can be obtained either through mixing different powders—melting one component or forming a eutectic—or by sintering at a temperature between the liquidus and solidus. Additionally, since the softer phase is generally the first to melt, the resulting microstructure typically consists of hard particles in a ductile matrix, increasing the toughness of an otherwise brittle component. However, liquid phase sintering is inherently less predictable than solid phase sintering due to the complexity added by the presence of additional phases and rapid solidification rates. Activated sintering is the solid-state analog to the process of liquid phase sintering.

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