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

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

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

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

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

INHOMOGENEOUS SYSTEMS: The Interfacial Tension The key equations:

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

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

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

With density gradient contributions: or

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

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:

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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) )

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

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

Process Design and Development: Processing Polymeric Materials with Supercritical Fluids

Pressure Quench: A Process for Porous-Structure Formation

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

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 :

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

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

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

Critical radius for nucleus formation in PS-CO 2

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

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

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