1. Interfacial Tension and Interfacial profiles: The essentials of the microscopic approach Costas Panayiotou University of Thessaloniki, Greece

2. Macro-porous to nano-porous structures Supercritical Fluid - Polymer Interactions Aerogel

3. Production of porous materials: Phase inversion with antisolvent (scCO2)

4. Production of porous membranes: 3. Phase inversion using supercritical CO 2 as antisolvent

5. The concentration profiles through an interface in a binary system H z

6. INHOMOGENEOUS SYSTEMS: The Interfacial Tension The key equations:

7. INHOMOGENEOUS SYSTEMS : The Interfacial Tension Alternative Formulation The key equations: Apply Euler relation: where: G intf : free-energy of the system WITH interface : G e : free-energy of the system WITHOUT interface

8. Using ρ i (z) and ψ i (z) or, density gradient is considered

9. As a consequence, γ is given by where No contribution from density gradients yet

10. With density gradient contributions: or

11. Density gradient in mixtures Quadr. truncation Δψ 0 : no dens. gradients Applying Euler-Lagrange minimization (calc. var.) Multiplying these equations by dρ i /dz, summing over all components i, and integrating, we obtain: or

12. Density gradient in mixtures II With last equation go from z-space to ρ-space This equation when inte- grated gives the inter- facial profile z(ρ) or ρ(z) Combining with eq. for γ we obtain:

13. Density gradient in mixtures III From Euler-Lagrange eq.: For binaries they are: Assuming c ij = c ii c jj we get which upon differentiation gives

14. Density gradient / calculations Influence parameters κ ii dimensionless adjustable In hydrogen-bonded: For multimers we may write φ is the segment fraction Local point thermodynamics Requires in quadr. truncation β=2/3 universal ! which upon differentiation gives

15. Is the above truncation adequate? Requirement for internal consistency: All four alternative ways of calculating γ should give equivalent results. In general, then: or

16. by setting: From the general equation: we obtain: And without truncation? β has a universal value of 2 !

17. Figure 1: Experimental28 (symbols) and calculated (lines) surface tensions of normal alkanes as a function of temperature. Numbers near the curves indicate the number of carbons of the n-alkane.

18. Experimental 28 (symbols) and calculated (lines) surface tensions of pure fluids as a function of temperature.

19. The calculated interfacial layer thickness as a function of temperature for n-Hexane.

20. Experimental 28 (symbols) and calculated (lines) surface tensions of Methanol as a function of temperature.

21. Experimental 28 (symbols) and calculated (lines) surface tensions of Ethanol as a function of temperature.

22. Experimental 1 (symbols) and calculated (solid lines) surface tensions of pure polymers.

23. Experimental 29,30 (symbols) and predicted (lines) surface tensions of Cyclohexane(1) + n-Hexane(2) mixture at 293.15 K as a function of composition.

24. The calculated interfacial layer thickness as a function of composition for Cyclohexane(1) + n-Hexane(2) mixture at 293.15 K.

25. Experimental (symbols)[PWN] and predicted VLE data for Ethanol + Hexane.

26. Experimental (symbols) 30-32 and predicted (lines) surface tensions of Ethanol(1) + n-Hexane(2) mixture at 298.15 K as a function of composition.

27. VLE predictions of the model for the system: 1-Propanol+Hexane

28. Methanol(1) – Toluene(2) at 308.15 K: The evolution of composition profiles across the interface, as predicted by the present model.

29. 1-Propanol(1) – n-Hexane(2) at 298.15 K: The evolution with liquid phase composition of the interfacial composition profiles as predicted by the present model.

30. Experimental (symbols) and calculated (lines) surface tensions of pure fluids as a function of temperature. Inhomogeneous Systems / Interfaces (Langmuir, 2002, 18, 8841, IEC Res. 2004, 43, 6592) )

31. Experimental (symbols) and calculated (solid lines) surface tensions of pure polymers.

32. Experimental (symbols) and predicted (lines) surface tensions of Cyclohexane(1) + n-Hexane(2) mixture at 293.15 K as a function of composition.

33. Process Design and Development: Processing Polymeric Materials with Supercritical Fluids

34. Pressure Quench: A Process for Porous-Structure Formation

35. Figure : Porous structures of polystyrene, 80 ο C, (α) 180 bar, (β) 230 bar, (γ) 280 bar, (δ) 330 bar, (ε) 380 bar

36. The Nucleation Theory According to the nucleation theory, in a closed isothermal system in chemical equilibrium the difference of the free energy per unit volume related to the formation of new phase cluster is given by the following equation :

37. Activation energy for homogeneous nucleation: Nucleation rate: Total number of nuclei: Modeling the foaming of polymers with scCO 2 : Nucleation Theory

38. Figure: Sorption of CO 2 in polystyrene. Experimental data: (o) 100 ο C, (  ) 120 ο C, (—) NRHB Figure: Glass transition temperature for the system polystyrene-CO 2, (  ) experimental data, (----) CO 2 vapor pressure, (—) NRHB

39. Surface tension of polystyrene versus temperature, (  ) experimental data, (—) NRHB System CO 2 – polystyrene: γ mix r = (1-w CO2 ) γ pol r

40. Critical radius for nucleus formation in PS-CO 2

41. Activation energy for homogeneous nucleation (polystyrene-CO 2 ) ΝRΗΒ combined with nucleation theory

42. Figure: Observed cell density, (  ), and calculated nuclei density, (—), versus pressure for the system polystyrene-CO 2 at 80 o C ΝRΗΒ combined with nucleation theory

43. Observed cell density, (  ), and calculated nuclei density, (—), versus temperature for the system polystyrene-CO 2 at 330 bar ΝRΗΒ combined with nucleation theory