I would like to calculate the surface free energy of solid by using contact angle measurement of liquid by the relation of Young's equation.
ϒs=ϒsl+ϒl Cos θ
where, the inter-facial tension of the solid-liquid (ϒsl) is unknown.
So, anyone can suggest me to calculate interfacial tension of solid-liquid
You can calculate the work of solid-liquid adhesion according to the Dupre-Young equation
Wa/ϒl = 1+ cos θ
For Teflon θ = 1080 , H2O 250 C ϒl = 72,0х10 -3 J/ m2 , Wa = 50,3x10-3 J/ m2
Dear Sir,
Thank You for reply
I have calculated the work of adhesion using Young-Drupe equation
Wa=ϒl(1+Cos θ)
But, I want to know whether work of adhesion equal to surface free energy of solid/substrate??
Who are you applying to? If to me, then I have a name, a surname. If you know the Young–Dupré equation, then substitute the Antonov equation in it and calculate what you need.
The solid -liquid surface Gibbs enery is not easily available. With contact angle measurements one needs to make an additional assumption regarding the type of interactions that prevail in the SL interface. Several classical (simple) models are available in literature that make such an assumption. In general they apply best for low energy (polymeric type) solids. The rule of Antonov is one of them. Other classilacl models are the Fowkes model, the model of Good and Girifalco (worked out by Wu et al) and the model of Van Oss which is an extention of the Fowkes model.The Antonov and classicla Fowkes model don't take polar interactions into account. The Good and Girifalco model formally also considers polar interactions but involve an additional parameter that is not easily available in practice. The Van Oss method explicitly adds the polar interactions but a series of contact angle measurements has to be carried out with different standard liquids. See for more detail and references: L.K. Koopal / Advances in Colloid and Interface Science 179–182 (2012) 29–42 and L.K. Koopal, Interface Science, chapters 3 and 13. These refs are available through Research Gate.
Article Wetting of Solid Surfaces: Fundamentals and Charge effects
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The work of adhesion is different from the surface free energy of a substrate γS.
You can calculate the surface free energy by measuring obtained contact angles of different reference liquids (at equilibrium) on the substrat. Reference liquids are : water, ethylene glycol, diiodomethane, formamide, glycerol..These reference liquids have known polar and dispersive components. Then, you can use the experimental Owens-Wendt model to determine your surface free energy
At final, you plot a graph which gives the polar and dispersive parts of γS
Sabine is right that the work of adhsion is different from th urface free energy of a solid. The adhesion is by definition between two different materials. The surface free energy is directly related to the work of cohesion (in vacuo).
Sabine and tMirgorod are not right in stating that the surface free energy can be measured using contact angle measurements. Only with contact angle measurements PLUS an assumption about the nature of the mutual interactions the surface free energy of the solid substrate can be obtained. In Sabine's case the assumption is implicit in the Owens-Went model, with Mirgorod the assumtion is the Antonov rule.
Possibly the analysis article mentioned later might help you? You may find the article to contain too much information, so to summarize - measure contact angles with water, formamide and methylene iodide or Bromonapthalene and then use the Lifshitz van der Waals Acid Base (LWAB) approach to convert the values to surface energies.
Analysis of different approaches for evaluation of surface energy of microbial cells by contact angle goniometry
PK Sharma, KH Rao
Advances in colloid and interface science 98 (3), 341-463
2liquids (1 polar-water, 2nd nonpolar alkane) are used-giving contact angles and on basis of OWRK method-SE(mJ/m2) is calculated yielding polar and dispersive parts.
BTW
interfacial tension or energy of solid-liquid or liquid-liquid can be measured by Girifalco and Good equation
[IFT1,2= (Surface tension or energy of 1-γ1)+ (surface tension or energy of 2-γ2) - 2*chi*(Surface tension or energy of 1-γ1* surface tension or energy of 2-γ2)^0.5 ]
where chi is assumed 1.
2nd option is applicable if someone knows polar and dispersive components of phases (solid-liquid or liquid-liquid)
[γ1,2 =γl+γ2-2*[(γ1d*γ2d)^0.5+(γ1p*γ2p)^0.5]
Work of adhesion is Wa=2*[(γ1d*γ2d)^0.5+(γ1p*γ2p)^0.5]
Reference https://www.kruss-scientific.com/en/know-how/glossary/surface-free-energy
and many other papers
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