1 Institute of Biocolloid Chemistry of National Academy of Sciences of Ukraine, Kiev, Ukraine Dilatational rheology of complex fluid-fluid interfaces V.I. Kovalchuk

2 Scope Diffusion and mixed relaxation kinetics in adsorption layers Dilatational rheology of complex fluid-fluid interfaces Dilatational rheology of thin liquid films Summary and conclusions V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011 Effect of equilibrium thermodynamic properties Particles at interfaces Relaxation in mixed adsorption layers

3 Interfacial rheology V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011 Expansion / Compression Shear Elasticity Viscosity

4 Surface dilational modulus E - characterizes the response of the surface tension   against relative surface area change  A: V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011 where  A(t) can be arbitrary function of time - surface dalational elasticity - surface dalational viscosity

5 Purely diffusion relaxation of adsorption layers V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011 Diffusion in the bulk phase: Boundary conditions: Initial condition: Additional conditions – surface tension and adsorption isotherms:

6 Purely diffusion relaxation of adsorption layers V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011 Diffusion in the bulk phase: Boundary conditions: Initial condition: Additional conditions – surface tension and adsorption isotherms:

7 Purely diffusion relaxation of adsorption layers V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011 Diffusion in the bulk phase: Boundary conditions: Initial condition: Additional conditions – surface tension and adsorption isotherms: Dilational elasticity modulus: or: where: J. Lucassen and M. van den Tempel, Chem. Eng. Sci., 27 (1972) 1283; J. Colloid Interface Sci., 41 (1972) 491

8 Lucassen – van den Tempel model: V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011 Maxwell model: Kelvin-Voigt model: - limiting elasticity - characteristic frequency of diffusion relaxation

9 Lucassen – van den Tempel model: V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011 Maxwell model: Cole-Cole plot:

10 Microgravity experiments during the STS-107 space shuttle mission Real part of complex surface dilatational modulus vs. frequency for different C 12 DMPO concentrations. V.I. Kovalchuk et al. / Journal of Colloid and Interface Science 280 (2004) 498–505 V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011

11 Microgravity experiments during the STS-107 space shuttle mission Imaginary part of complex surface dilatational modulus vs frequency for different C 12 DMPO concentrations. V.I. Kovalchuk et al. / Journal of Colloid and Interface Science 280 (2004) 498–505 V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011

12 Microgravity experiments during the STS-107 space shuttle mission Cole-Cole diagram for complex surface dilatational modulus for different C 12 DMPO concentrations. V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011

13 Diffusion from two adjacent phases V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011 Effective diffusion coefficient: Surfactant distribution coefficient:

14 Mixed adsorption kinetics V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011 Diffusion in the bulk phase: B.A. Noskov, Adv. Colloid Interface Sci., 69 (1996) no equilibrium at the interface Relaxation time:

15 Micellar solutions – Lucassen equation V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011 J. Lucassen, Faraday Discuss. Chem. Soc., 59 (1975) 76. disturbance time is much larger than the characteristic time of the “slow process” - for ordinary surfactants of the order of milliseconds and characterizes the change in the number of micelles - the ratio of micelles to monomers diffusion coefficients m - the aggregation number, C K = CMC (critical micelle concentration) Effective diffusion coefficient:

16 Effect of equilibrium thermodynamic properties - limiting elasticity - characteristic frequency of diffusion relaxation Equilibrium surface tension and adsorption isotherms: V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011

17 Frumkin adsorption model V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011  =  0  - the surface coverage  0 - the molar area - surface pressure isotherm (equation of state) - adsorption isotherm a - the interaction constant b - the adsorption equilibrium constant

18 V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011 Frumkin model: Γ  = const, Ω = 1/Γ  = const Intrinsic compressibility model: Ω = 1/Γ  = Ω 0 (1 – εΠ) (ε – intrinsic 2D monolayer compressibility) C 12 DMPO V.I. Kovalchuk et al. / Journal of Colloid and Interface Science 280 (2004) 498–505 Intrinsic 2D monolayer compressibility Theory: Experiment: Theory:

19  =  0 (1 – εΠ) ε – intrinsic 2D monolayer compressibility,  – surface pressure The area occupied by a molecule on the interface can continuously change with the surface pressure. V.I. Kovalchuk, R. Miller, V.B. Fainerman and G. Loglio / Advances in Colloid and Interface Science, (2005) 303. V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011 Intrinsic 2D monolayer compressibility

20 V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011 Intrinsic 2D monolayer compressibility Frumkin model: Γ  = const, Ω = 1/Γ  = const Intrinsic compressibility model: Ω = 1/Γ  = Ω 0 (1 – εΠ) V.I. Kovalchuk et al. / Journal of Colloid and Interface Science 280 (2004) 498–505 The surface rheological characteristics are much more sensitive to the state and interaction of molecules in the adsorption layer than equilibrium isotherms!

21 V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011 Dependence of C 14 TAB adsorption  on activity c*: neutron reflection data ( ) and calculations according to Frumkin and compressibility model. Intrinsic 2D monolayer compressibility - C 14 TAB adsorption V.I. Kovalchuk, R. Miller, V.B. Fainerman and G. Loglio / Advances in Colloid and Interface Science, (2005) 303.

22 Reorientation model Adsorbed molecules can acquire two (or more) orientation states with respect to the interface. V.B. Fainerman, S.A. Zholob, E.H. Lucassen-Reynders and R. Miller, J. Colloid Interface Sci., 261 (2003) 180. V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011

23 Protein Adsorption Layers V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden the total surface coverage - the molar area in state i ( ) with and V.B. Fainerman, E.H. Lucassen-Reynders and R. Miller, Adv. Colloid Interface Sci., 106 (2003) 237.

24 V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011 Relaxation in mixed adsorption layers

25 V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011 where: and, Viscoelasticity of mixed adsorption layers This expression includes 6 parameters determined from surface tension and adsorption isotherms: Jiang Q, Valentini JE, Chiew YC. J. Colloid Interface Sci. 174 (1995) 268.

26 V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011 Viscoelasticity of mixed adsorption layers P. Joos, Dynamic Surface Phenomena, 1999 where: and, This expression also includes 6 parameters determined from surface tension and adsorption isotherms:

27 V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011 E.V. Aksenenko, V.I. Kovalchuk, V.B. Fainerman and R. Miller / J. Phys. Chem. C, 111 (2007) Dilational elasticity of mixed adsorption layers: Mixture of C 10 DMPO and C 14 DMPO C 14 DMPO/C 10 DMPO concentrations in µmol/l

28 Mixtures of proteins and surfactants Protein/ non-ionic surfactant Protein/ ionic surfactant Cs. Kotsmar, et al. / Advances in Colloid and Interface Science 150 (2009) 41–54 V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011

29 V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011 where:  S =  S   S - surface coverage by surfactant molecules;  P =  P   P - total surface coverage by protein molecules; Adsorption isotherms: These tree equations allow one to calculate the necessary 6 partial derivatives Equation of state for protein/non-ionic surfactant mixtures E.V. Aksenenko et al. / Advances in Colloid and Interface Science 122 (2006) 57–66

30 Dilational elasticity modulus |E| vs. frequency f at various C 10 DMPO concentrations (in mmol/l) in the β-LG/C 10 DMPO mixtures. Experimental data from R. Miller et al., Tens. Surf. Deterg. 40 (2003) 256. V.I. Kovalchuk et al., in Progress in Colloid and Interface Science, Vol.1, Brill, Leiden-Boston, 2009, p Dilational rheology of mixed adsorption layers: Mixture of C 10 DMPO and β-lactoglobulin V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011

31 V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011 Particles at interfaces Position of a spherical particle at the water/air interface (top) and modification of particles via adsorption of ionic surfactants (bottom). R. Miller et al: Project Proposal for the Investigation of Particle-Stabilised Emulsions and Foams by Microgravity Experiments, Microgravity sci. technol. XVIII-3/4 (2006)

32 Particles at the interface V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011  0 - the molar area of solvent molecules A - the available surface area per particle  - the molar area of particles  coh - the cohesion pressure V.B. Fainerman, V.I. Kovalchuk, D.O. Grigoriev, M.E. Leser and R. Miller / NATO Science Series, Vol. 228, 2006, P

33 Dependence of surface pressure on the monolayer coverage for polymeric particles 113 nm in diameter without dispersant (▲) and with dispersant (■). Experimental data according to E. Wolert et al., Langmuir 17 (2001) V.B. Fainerman, V.I. Kovalchuk, D.O. Grigoriev, M.E. Leser and R. Miller / NATO Science Series, Vol. 228, 2006, P Surface pressure in a monolayer of polymeric particles V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011

34 Particles at the interface V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011 J. Lucassen, Colloids Surfaces, 65(1992) 139 Apparent dilatation modulus of composite monolayers: X i is the surface fraction having the dilatational modulus E i. Corresponds to the case of particles which do not interact and do not move but are characterized by a certain internal compressibility. For incompressible particles:  P is the surface coverage for particles, E s is the local elasticity of interparticle space (e.g. covered by surfactants). - excluded area effect

35 Particles at the interface V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011 R. Miller et al., Adv. Colloid Interface Sci., 128–130 (2006) 17–26 Alternatively, for a mixed particle-surfactant layers the surface elasticity can be obtained by considering the surface pressure as a function of two variables: where θ P and θ S is the surface coverage by particles and surfactant. For insoluble surfactant molecules and particles: and

36 Particles at the interface V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011 R. Miller et al., Adv. Colloid Interface Sci., 128–130 (2006) 17–26 For a mixed particle-surfactant layers described by the surface pressure isotherm: the partial elasticities are: with For fast oscillations: For slow oscillations:

37 Dilatational rheology of thin liquid films V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011

38 Dilatational rheology of thin liquid films FF F F Δγ f γ f = 2γ Film elasticity: Δγ f ≠ 2Δγ E f ≠ 2E V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011

39 Film elasticity vs. thickness dependencies for normal alcohols: n-hexanol, n-octanol, n-decanol; films with initial surface pressure  0 = 42 mN/m and initial thickness h 0 = 10  m V.I. Kovalchuk et al., in Progress in Colloid and Interface Science, Vol.1, Brill, Leiden-Boston, 2009, p Dilatational rheology of thin liquid films h cr h0h0 V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011

40 Effect of characteristic disturbance time on film elasticity modulus (full lines) and its imaginary part E i (dotted lines). Frumkin isotherm with the parameters for C8 (octanol), h 0 = 10  m,  0 = 42 mN/m. V.I. Kovalchuk et al., in Progress in Colloid and Interface Science, Vol.1, Brill, Leiden-Boston, 2009, p Film elasticity – time effect of disturbances h cr h0h0 V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011

41 Summary and conclusions Surface tension studies provide general information about the formation of adsorption layers. However, interfacial rheology gives more insight into the details of single and mixed adsorption layers. The study of interfacial rheological properties represents a versatile and very sensitive experimental tool to investigate the adsorption layer properties. This techniques requires, however, quantitative theories combining interfacial dynamics and mass transfer aspects. V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011

42 Acknowledgements Financial support by Max-Planck-Institute of Colloids and Interfaces and COST D-43 Action is gratefully acknowledged. V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011 August 2008