2. 1 Day 1. Basics Structure of the course High-temperature interfacial forces, energies and phenomena by G.Kaptay Day 2. Forces Day 3. Energies Day 4. Phenomena Kaptay / Day 1 / 1

3. 2 Day 1. Basics of interfacial science George Kaptay kaptay@hotmail.com A 4-day short course Kaptay / Day 1 / 2

4. 3 Basics of thermodynamics (G = H - TS) The behaviour and properties of materials are dictated by their desire to minimize their energy, G (Gibbs energy). There are two desires: i. as strong as possible bonds (love) and ii. as high as possible freedom (at the same time). Strong bonds = negative enthalpy (H) (G ~ H) High freedom = positive entropy (S) (G ~ -S) Freedom has no sense without ability to move, what is proportional to T (K). Thus, (G ~ -T*S) G = H -T*S Kaptay / Day 1 /3

5. 4 Back to thermodynamics (G = H - TS) G = H -T*S = f(T, p, x i, r, fields) Heat capacity (C p ): H T = H To + C p *(T-T o ) (with increased T the bonds become weaker: H → +) At low T (low ability to move, i.e. winter, old age): negative H (strong love, strong bonds) is preferred At high T (high ability to move, i.e. summer, young age): positive S (high freedom) is preferred fcc  bcc  liquid  vapour Total mixing is preferred (no compounds, no segregation) Kaptay / Day 1 / 4

6. 5 Interfacial energy Kaptay / Day 1 / 5

7. 6 The average molar Gibbs energy (J/mol) of phases (with interfaces) and consequences There are 8 consequences of the existence of the interfaces and of the above equation. They are grouped according to the driving force: A/V  min,   min, G  min. Kaptay / Day 1 / 6

8. 7 Consequence #1. The equilibrium shape of phases Case i. Liquid in microgravity and free space A/V  min Kaptay / Day 1 / 7

9. 8 Case ii. Solids (Wulff’s theorem). Consequence #1. The equilibrium shape of phases Kaptay / Day 1 / 8

10. 9 Case iii. Liquid in contact with a flat solid surface. Consequence #1. The equilibrium shape of phases Kaptay / Day 1 / 9

11. 10 Possibility 1. If W > 2  l/g   = 0 o “the liquid perfectly wets the solid” Kaptay / Day 1 / 10

12. 11 If 2  l/g > W >  l/g  0 o <  < 90 o “the liquid wets the solid” Possibility 2. Kaptay / Day 1 / 11

13. 12 If  l/g > W > 0  90 o <  < 180 o “the liquid does not wet the solid” Possibility 3. Kaptay / Day 1 / 12

14. 13 If W = 0   = 180 o “the liquid does not wet the solid at all” but this situation exists only if gas = liquid2 Possibility 4. Kaptay / Day 1 / 13

15. 14 Case iv. Liquid in contact with solid, in gravity Consequence #1. The equilibrium shape of phases Kaptay / Day 1 / 14

16. 15 Case v. Liquid in contact with a capillary #1. The equilibrium shape/position of phases Non-wetting  No penetrationwetting  penetration Kaptay / Day 1 / 15

17. 16 Consequence #2. The equilibrium size of phases V = V A > A Not stable  Stable Many small phases One big phase Ostwald ripening. Smaller phases join together A/V  min Kaptay / Day 1 / 16

18. 17 The Kelvin equations (nano-equilibrium)   (small liquid in gas) (small solid in liquid) Kaptay / Day 1 / 17

19. 18 Consequence #3. Interface re-structuring Structured first layer Structured second layer Diffuse bulk liquid Gas phase   min Kaptay / Day 1 / 18

20. 19 Consequence #4. Adsorption of gases on the surface of solids and liquids   min Driving force:  is reduced due to adsorption  Reduces in row: metals – ionics – covalents with H-bond – covalents with van der Waals bond. In the same row the tendency of adsorption decreases. Covered surface area by adsorption increases with partial pressure of adsorbant, and decreases with temperature (entropy effect). Kaptay / Day 1 / 19

21. 20 Consequence #5. Inner adsorption of components from the solid or liquid solution   min Kaptay / Day 1 / 20 See P86

22. 21 Consequence #6. Marangoni convection   min Kaptay / Day 1 / 21

23. 22 Consequence #6. Marangoni convection   min Kaptay / Day 1 / 22

24. 23 Consequence #7. Surface phase transition G  min Kaptay / Day 1 / 23 See J99, J105

25. 24 High adsorption, invers T-dependence Kaptay / Day 1 / 24 Low adsorption, normal T- dependence

26. 25 Kaptay / Day 1 / 25

27. 26 Consequence #8. Supersaturation at nucleation G  min Kaptay / Day 1 / 26

28. 27 Consequence #8/2. Supersaturation at nucleation (with the Gibbs energy change of the parent phase) G  min Kaptay / Day 1 / 27 Stabilization of nano-nuclei See J106, J108

29. 28 8/2. Minimum on the nucleation curve The stabilization of nano-nuclei seems to be possible from oversaturated solutions Time is against it – Ostwald ripening. Very high cooling rates are requested to stabilze nano-nuclei Kaptay / Day 1 / 28

30. 29 Interfacial energiesInterfacial forces Interfacial phenomena Complex phenomena General modeling algorithm Kaptay / Day 1 / 29

31. 30 3 tasks: iii. Finally, we can deal with modeling of different interfacial phenomena, and based on that, even some complex phenomena (Day 4). ii. As the interfacial forces will turn out to be functions of different interfacial energies, we should also model the interfacial energies in different systems (Day 3), i.Classification and modeling of interfacial forces, acting on phases (Day 2), Kaptay / Day 1 / 30

32. 31 Thanks for your atention so far Kaptay / Day 1 / 32 And see you tomorrow….