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**Lecture 9: Surface Energy, Surface tension and Adhesion energy**

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**In the last lecture… Optical tweezers The wave nature of light**

Optical trapping A point dipole in a field revisited Using lasers to trap particles Applications of optical trapping F F

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**In this lecture… Surface energy and interfacial energy Surface tension**

Calculating Surface energy of materials Adhesion energy of simple materials Wetting interactions Contact angles Further reading P and p in

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**Cohesive Energy of bulk materials**

In the bulk of a material, atoms and molecules are surrounded by NBulk nearest neighbours. If each interaction with the central atom/molecule has an energy, -u, the total interaction energy becomes UBulk = -NBulku Bulk atom neighbours

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**Cohesive Energy near a surface**

When we create a surface in material and expose it to vacuum each surface atom/molecule has fewer nearest neighbours Nsurf < NBulk The interaction energy per atom/molecule is then Usurf = -Nsurfu There is therefore an excess amount of energy DU = Usurf -UBulk = (NBulk - Nsurf ) u associated with each surface atom/molecule

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Surface Energy Surface energy is the excess energy required per unit area to create a surface in vacuum (or air) The energy required to create two new surfaces in a material, each having area S is Area, S where g is the surface energy of the material in Jm-2

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Interfacial Energy Interfacial energy is the excess energy per unit area required to create an interface between two different materials. The interfacial energy between materials 1 and 2 is represented by g12 Area, S

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**Surface and Interfacial Tensions**

Surface/interfacial tension is the force required per unit length to extend a surface/interface (measured in Nm-1) The surface energy and surface tension are identical. They act to prevent a surface from increasing in area. Consider… The same reasoning applies to interfacial tension and interfacial energy Barrier F L Surface Barrier Nm-1 = Jm-2 See notes dx

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**Typical values Many materials have surface energies of ~10-50 mJm-2**

Metals typically have higher surface energies of 1-3 Jm-2 (see page 205, Israelachvili) Interfacial energies are of the same order of magnitude as surface energies P315 Intermolecular and Surface Forces, J. N. Israelachvili

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**Calculating the surface energy of materials**

The surface energy of a material can be described in terms of unsatisfied bonds or missing interactions at the surface. Each atom/molecule at the surface can be thought of as having approximately half as many neighbours as one in the bulk material. Excess surface energy Energy required to break half the bonds around an individual atom/molecule (See OHP)

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**Calculations based upon latent heat of vapourisation**

The energy required to break all the bonds in a mole of material and separate all the atoms and molecules is equal to the Latent heat of vapourisation Lv The surface energy should be equal to half the energy required to break all the bonds around an atom/molecule. This gives the result that r=density (kgm-3) NA=Avogadro’s number (mol-1) M=molar mass (kgmol-1)

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**Calculating surface energies from dispersion potentials**

The surface energy is the energy required to separate two surfaces from their inter-atomic/molecular distance and remove them to infinity Recall from lectures 5 and 6 that inter-surface potential energy, U is Surface Area, S Do Surface energy is half this energy (there are two surfaces) per unit area A= Hamaker constant (J)

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**Do these simplistic approaches work?**

Material Measured g (mJm-2) (mJm-2) A/(24pDo2) (Do=0.165nm) A (x10-20J ) Liquid Helium - 0.28 0.057 Polystyrene 33 32.1 6.6 Benzene 28.8 110 24.4 5 Ethanol 22.8 20.5 4.2 Mercury 600 630 Nitrogen 10.5 11 Liquid Argon 13 14

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Problem A conical AFM tip with a half angle of a=26.56o and height , l, is placed at a flat interface between two immiscible liquids (liquids 1 and 2) such that the tip protrudes a distance, D, into liquid 1. If the interfacial energies between the tip material and the liquids are g1 and g2 respectively and g12 is the interfacial energy between the two liquids; Derive an expression for the total surface energy of the tip as a function of the distance D b) Hence derive an expression for the force on the tip c) If g1=0.99 Jm-2 , g2=1Jm-2 and g12=50mJm-2 calculate the magnitude and direction of the force on the tip if it protrudes 10nm into liquid 1

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Work of Adhesion The energy required per unit area to separate two surfaces of materials 1 and 2 in a third medium (medium 3) is called the work of adhesion (W) It is the energy required to break the interface between two materials and form two new interfaces g13 g23 g12

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Wetting interactions Surface and interfacial energies determine the shape of macroscopic liquid droplets when they are placed on a surface Partially wetting films Wetting film (q=0)

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Contact Angles The contact angle made between a droplet and a surface is determined by a subtle balance of the interfacial energies/tensions. We can derive the expression for the contact angle by considering the balance of forces/interfacial tensions at the 3 phase contact line. Resolving horizontally we have Huang et al., Science , 650 (2007) Material 3 Mat. 2 Material 1

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**Unbalanced vertical components**

The assumption of a planar surface results in unresolved vertical forces due to interfacial tension of the droplet. Clearly this can not happen otherwise the droplet would accelerate upwards! The flat interface must deform to compensate for these unresolved components

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**Summary of key concepts**

Surface/Interfacial Energy is the energy per unit area associated with the creation of a surface/interface (Jm-2) Surface tension (Nm-1) = Surface energy (Jm-2) Surface energies can be calculated using the latent heat of vapourisation of a material or from the inter-atomic/molecular potentials A subtle balance of interfacial energies determines the adhesive properties of simple materials and the shape of droplets on surfaces

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