Sandhya ch:

Your question seems quite broad to me, so let me comment as follows:

If you're talking about a liquid/solid interface you can solve for the interfacial energy using the classical Young's equation. But, you'll have to measure the liquid/vapor interfacial energy using methods like a Wilhelmy plate or Langmuir-Blodgett trough (or something similar, there are many methods). The surface tension of many liquids has been tabulated (See the CRC Handbook). The solid/vapor surface tension can also be measured directly using crack propagation or other techniques (e.g.: ab initio or creep measurements). There are many research papers on solid/vapor surface energies of many different solids. Given that, and an (also measured) contact angle, you can solve for the liquid/solid interfacial energy using simple algebra and Young's equation.

If you're talking about a liquid/liquid interface, you can measure the surface tension directly at the (buried) interface using a Langmuir-Blodgett trough. I'm sure there are other techniques, but this is a tough problem. Two liquids in intimate contact don't have a very 'sharp' interface like, say, a solid/air interface. So, there'll be many complicating factors. Obviously, if one liquid is partly or wholly soluble in the other, all bets are off.

If you're talking about a solid/solid interface you'll have to use such indirect methods as others have previously suggested. Of course, ab initio methods are always available. If a crack can actually propagate along the interface (for some reason), you can use crack propagation techniques to measure the solid/solid interfacial energy. Though, this situation is unlikely.

It's not actually possible to simply determine the solid/vapor surface energies of two different solids (same vapor), and then combine these measurements for the surface/surface interfacial energy. This is because the two materials will interact with each other differently than with the vapor. Note that simply placing the two solids in close contact is not the same thing as having two different solids in 'intimate' contact, i.e.: contact at the molecular level.

Another way you can get (relative) surface energies (if the material is crystalline) is to examine/analyze the Wolff shapes of nanoparticles grown from the vapor. The relative surface areas of the faces indicates relative surface energies. Then, with a crack propagation measurement along a particular plane, you can define absolute solid/vapor surface energies for the various crystalline faces.

Of course, nature often conspires against us in this matter. For example, if the solid does not propagate cracks well or is anisotropic or if the liquid has unusual properties (or very many other complicating factors) the problem is made more difficult and the results are less clear. Surface energy science is a broad topic and has wide applicability. There are many researchers in this and related areas and the body of research is quite large. If you have a specific example, try searching the literature. There's a good chance you'll find some research on exactly your topic, or something related.

I hope this helps!

Here is a possible answer (see the attached paper) based on a particular technique developed for the determination of solid-solid interfacial energy in metal-ceramic systems using alpha-Al2O3 as a ceramic phase and Au, Ag, Cu, Ni and gamma-Fe as metallic phases.

An indirect approach would be to measure heterogeneous nucleation rates of one material on the other (from solution). Then, if the interfacial energies with the solution are known, you can use classical nucleation theory to solve for the interfacial energy between the solids. This is an indirect way that needs a lot of a priori information, but it could be useful.

We recently published an example here:

http://dx.doi.org/10.1021/es3014826

Thank you Sergei and Alejandro. Could any one please suggest me interface energy between two surfaces interms of their surface energies/

Roughly speaking (and very approximately), such a formula for interface energy gamma_interface is given by equation on page 183 (in the above-attached paper) where gamma_substrate and gamma_particle stand for the surface energies of Al2O3 ceramic substrate and metal particle, respectively. The meaning of the two vectors r_1 and r_2 involved in this equation is explained in Fig.3(b). Read the text for more details.

Sandhya ch:

Your question seems quite broad to me, so let me comment as follows:

If you're talking about a liquid/solid interface you can solve for the interfacial energy using the classical Young's equation. But, you'll have to measure the liquid/vapor interfacial energy using methods like a Wilhelmy plate or Langmuir-Blodgett trough (or something similar, there are many methods). The surface tension of many liquids has been tabulated (See the CRC Handbook). The solid/vapor surface tension can also be measured directly using crack propagation or other techniques (e.g.: ab initio or creep measurements). There are many research papers on solid/vapor surface energies of many different solids. Given that, and an (also measured) contact angle, you can solve for the liquid/solid interfacial energy using simple algebra and Young's equation.

If you're talking about a liquid/liquid interface, you can measure the surface tension directly at the (buried) interface using a Langmuir-Blodgett trough. I'm sure there are other techniques, but this is a tough problem. Two liquids in intimate contact don't have a very 'sharp' interface like, say, a solid/air interface. So, there'll be many complicating factors. Obviously, if one liquid is partly or wholly soluble in the other, all bets are off.

If you're talking about a solid/solid interface you'll have to use such indirect methods as others have previously suggested. Of course, ab initio methods are always available. If a crack can actually propagate along the interface (for some reason), you can use crack propagation techniques to measure the solid/solid interfacial energy. Though, this situation is unlikely.

It's not actually possible to simply determine the solid/vapor surface energies of two different solids (same vapor), and then combine these measurements for the surface/surface interfacial energy. This is because the two materials will interact with each other differently than with the vapor. Note that simply placing the two solids in close contact is not the same thing as having two different solids in 'intimate' contact, i.e.: contact at the molecular level.

Another way you can get (relative) surface energies (if the material is crystalline) is to examine/analyze the Wolff shapes of nanoparticles grown from the vapor. The relative surface areas of the faces indicates relative surface energies. Then, with a crack propagation measurement along a particular plane, you can define absolute solid/vapor surface energies for the various crystalline faces.

Of course, nature often conspires against us in this matter. For example, if the solid does not propagate cracks well or is anisotropic or if the liquid has unusual properties (or very many other complicating factors) the problem is made more difficult and the results are less clear. Surface energy science is a broad topic and has wide applicability. There are many researchers in this and related areas and the body of research is quite large. If you have a specific example, try searching the literature. There's a good chance you'll find some research on exactly your topic, or something related.

I hope this helps!

The interfacial energy is the difference of the surface energies of the two materials forming an interface.

Dear Sandhya,

                                   if you are interested to calculate the interface energy between two faces of  two different "crystalline" materials, the Dupré's formula rules this simple problem:

-first the surface energy of each surface is needed

- secondly, their adhesion energy is needed as well.

If you are interested in, we developed a nice program to do that , and I should send you some papers about it.

Hoping this helps,

Dino

Dear Sandhya,

                                    let's consider to condensed phases (A,B) and a planar interface between A and B. The specific surface energy of the interface is gamma(AB); the specific surface energy of the A phase  is gamma(A), while the specific surface energy of the phase B is gamma(B);  the specific energy recovered when the two surface come in contact is beta (AB). Then, the Dupré formula says that:

gamma(AB)= gamma(A)+ gamma(B) - beta (AB).

As I said in the previous answer, I' ll send you some interesting papers, if you are interested in, of course

Sincerely yours

Dino

Calculating Inter facial energy by using Therno-Calc.

How about interfacial energy in biological tissues?

Very good question! Do we (RG community) have experts in this field?

Hamidreza:

could you be more specific about the kind of applications you intended for ?

Let's say, you have two different type of biological cells sitting next to each other. what is the interfacial energy then? How to measure it?

Dear Sandhya,

                                     in the attached file you will find all you need to calculate the interface energy between two different  surfaces (of different materials, in general). The same formulas (Dupré and Young) can be used also for twins (or polytypes).

If you are interested to the calculation of other quantities ( surface and adhesion energy, for instance), don't hesitate to contact me.

All the best !

Dino

Dear Dino,

Thanks so much for your reply. Therefore If we know the cohesion energies of phases A and B separately and the contact angle as well, we can compute the cohesion energy between phases, right? 

Dear Hamidreza, 

                                         you are right. But, don't forget that the cohesion energy  (k) of a phase is 2 times its surface energy (gamma) ,i.e. k=2 gamma. From the two fundamental formulas you can compute the final term, i.e. the interface energy between two condensed phases.

Regards !

Dino

For the interface between Au and MgO/Mo(100), how we can get the interfacial energy? Actually, we can not get the MgO(100) surface energy when it is deposited on Mo(100) surface. And more important, the lattice mismatch in some cases will be serous, how we deal with it?

It would be better to enter in the details of the problem. Please, make a drawing of the interfaces. How many interfaces are interested? What is the orientation of Au on the complex MgO/Mo(100) ?

It is the Au(111) surface that contacts with MgO/Mo(100) because the potential 5.7% lattice mismatch between Au(100) and MgO/Mo(100). On MgO/Ag(100) surface, perfect lattice match (