1. 1 Fall, 2013 Ch 3. Surface & Interfacial Energies Instructor: J.-W. John Cheng Mech. Engr. Dept., Nat ’ l Chung Cheng Univ. Interfacial Physics and Thin-Film Processing

2. JCheng201311 2 Outline 3.1 Interaction between Macroscopic Bodies 3.2 Definitions of Cohesion/Adhesion Work and Surface/Interfacial Free Energy 3.3 Cohesion Work/Adhesion Work and Intermolecular Energy 3.4 Contact-Angle Approach to Estimation of Surface Free Energy

3. 3 3.1 Interactions between Macroscopic Bodies Molecule – surface interaction Surface – surface interaction

4. JCheng201311 4 Some Notations & Facts w(r) = -c/r n The interaction energy between two molecules of interest E.g. n = 6 for van der Waals interaction  Diameter of a molecule of interest  The number density of molecules of an aggregate of molecules For FCC and HCP (see Appendix 4):

5. JCheng201311 5 Additivity Assumption Pair potentials are additive i.e., pair potential is not affected by existence of third molecule nearby

6. JCheng201311 6 Molecule – Surface Interaction Consider a small molecule p situated at a distance D above a solid S with planar surface p Molecule-surface interaction potential w(D): D S Making surface a well-defined concept in particle- surface & surface-surface interactions because W(D) does not depend on where the molecule sits upon the surface

7. JCheng201311 7 Molecule – Surface Interaction Consider a small molecule at contact with a solid S with planar surface p Molecule-surface interaction potential at contact: D=  /2 +  /2 S This is of the same order as –C/  6 of two small molecules in contact. contd

8. JCheng201311 8 Surface – Surface Interaction Consider a solid S 1 with unit-area surface situated at a distance D above a solid S 0 with infinite planar surface Sphere-surface interaction potential w(D): D S0S0 S1S1

9. JCheng201311 9 Surface – Surface Interaction When 2 surfaces are in contact, assuming the van der Waals potential HCP or FCC closely packed d =  (not necessarily always true) contd

10. JCheng201311 10 Summary For van der Waals interaction (n = 6) at distance d interactionpotential at distance dPotential at contact with HCP or FCC pack molecule – surface surface – surface