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Surface Forces and Liquid Films

Surface Forces and Liquid Films. Peter A. Kralchevsky Department of Chemical Engineering, Faculty of Chemistry Sofia University, Sofia, Bulgaria Lecture at COST D43 School Fluids and Solid Interfaces Sofia University, Sofia , Bulgaria 12 – 15 April, 2011.

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Surface Forces and Liquid Films

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  1. Surface Forces and Liquid Films Peter A. Kralchevsky Department of Chemical Engineering, Faculty of Chemistry Sofia University, Sofia, Bulgaria Lecture at COST D43 School Fluids and Solid InterfacesSofia University, Sofia, Bulgaria 12 – 15 April,2011 Film of phase 3sandwiched between phases 1 and 2 Sofia University

  2. Surface Force, Disjoining Pressure and Interaction Energy gas  Π Example: Foam Film stabilized by ionic surfactant Disjoining pressure, Π= Surface force acting per unit area of each surface of a liquid film [1-4] h liquid Π Π > 0 – repulsion Π < 0 – attraction gas Π depends on the film thickness:Π = Π(h) At equilibrium, Π(h) = Pgas – Pliquid Interaction free energy (per unit area) f(h0)= Work to bring the two film surface from infinity to a given finite separation h0: Foam is composed of liquid films and Plateau borders

  3. DLVO Surface Forces (DLVO = Derjaguin, Landau, Verwey, Overbeek) Their combination leads to a barrier to coagulation (1) Electrostatic repulsion (2) Van der Waals attraction Non–DLVO Surface Forces (5) Hydrophobic attraction in water films between hydrophobic surfaces (4) Steric interaction due to adsorbed polymer chains (3) Oscillatory structuralforce(films with particles) (6) Hydration repulsion

  4. (1) Electrostatic (Double Layer) Surface Force Πel = excess osmotic pressure ofthe ions in the midplane of asymmetric film (Langmuir, 1938) [5-7]: n0 n1m, n2m n1m, n2m – concentrations of (1) counterions and (2) coions in the midplane. n0 – concentration of the ions in the bulk solution; ψmpotential in the midplane. Πel > 0  repulsion! For solution of a symmetric electrolyte: Z1 = Z2 = Z; Z is the valence of the coions.Boltzmann equation; Φm – dimensionless potential in the midplane (Φm << 1).

  5. Verwey – Overbeek Formula (1948) Π(h) = ? Near single interface, the electric potential of the double layer is [7]: Superposition approximation in the midplane: ψm = 2ψ1 [6]: More salt Greater κ Smaller Πel

  6. (2) Van der Waals surface force: AH – Hamaker constant (dipole-dipole attraction) Hamaker’s approach [8] The interaction energy is pair-wise additive: Summation over all couples of molecules.Result [8,9]: Symmetric film: phase 2 = phase 1 For symmetric films: always attraction! Asymmetric films, A11 > A33 > A22  repulsion!

  7. Lifshitz approach to the calculation of Hamaker constant E. M. Lifshitz (1915 – 1985) [10] took into account the collective effects in condensed phases (solids, liquids). (The total energy is not pair-wise additive over al pairs of molecules.) Lifshitz used the quantum field theory to derive accurate expressions in terms of: (i) Dielectric constants of the phases: ε1, ε2 and ε3; (ii) Refractive indexes of the phases: n1, n2 and n3: Zero-frequency term: orientation & inductioninteractions;kT – thermal energy. Dispersioninteraction term: νe = 3.0 x 1015 Hz – main electronic absorption frequency;hP = 6.6 x 10– 34 J.s – Planck’s const.

  8. Derjaguin’s Approximation (1934): The energy of interaction, U, between two bodies across a film of uneven thickness, h(x,y), is [11]: where f(h) is the interaction free energy per unit area of a plane-parallel film: This approximation is valid if the range of action of the surface force is much smaller than the surface curvature radius. For two spheres of radii R1 and R2, this yields: From planar films, f(h) to spherical particles, U(h0).

  9. DLVO Theory: The electrostatic barrier The secondary minimum could cause coagulation only for big (1 μm) particles. The primary minimum is the reason for coagulation in most cases [6,7]. Condition for coagulation: Umax = 0(zero height of the barrier to coagulation)

  10. The Critical Coagulation Concentration (ccc) [6,7]

  11. DLVO Theory [6,7]: Equilibrium states of a free liquid film Born repulsion Electrostatic component of disjoining pressure: Van der Waals component of disjoining pressure: (2) Secondary film (1) Primary film h – film thickness; AH – Hamaker constant; κ – Debye screening parameter

  12. Primary Film (0.01 M SDS solution) Secondary Film (0.002 M SDS + 0.3 M NaCl) Observations of free-standing foam films in reflected light. The Scheludko-Exerowa Cell [14,15] is used in these experiments.

  13. Oscillatory–Structural Surface Force A planar phase boundary (wall) induces ordering in the adjacent layer of a hard-sphere fluid. The overlap of the ordered zones near two walls enhances the ordering in the gap between the two walls and gives rise to the oscillatory-structural force. For details – see the book by Israelachvili [1]

  14. Oscillatory structural forces [1] were observed in liquid films containing colloidal particles, e.g. latex & surfactant micelles; Nikolov et al. [16,17]. The maxima of the oscillatory force could stabilize colloidal dispersions. The metastable states of the film correspond to the intersection points of the oscillatory curve with the horizontal line  = Pc. The stable branches of the oscillatory curve are those with /h < 0. Oscillatory-structuraldisjoiningpressure Depletion minimum

  15. Metastable states of foam films containing surfactant micelles Oscillatory-structuraldisjoiningpressure Foam film from a micellar SDS solution (movie): Four stepwise transitions in the film thickness are seen.

  16. Oscillatory–Structural Surface Force Due to Nonionic Micelles Ordering of micelles of the nonionic surfactant Tween 20 [19]. Methods:Mysels-Jones (MJ) porous plate cell[20],and Scheludko- Exerowa (SE) capillary cell [14]. Theoretical curve – formulas by Trokhimchuk et al. [18]. The micelle aggregation number, Nagg = 70, is determined [19].(the micelles are modeled as hard spheres)

  17. Steric interaction due to adsorbed polymer chains l– the length of a segment;N – number of segments in a chain;In a good solvent L > L0, whereas in a poor solvent L < L0. L depends on adsorption of chains,  [1,21].  Alexander – de Gennes theoryfor the case of good solvent [22,23]: The positive and the negative terms in the brackets in the above expression correspond to osmotic repulsion and elastic attraction. The validity of the Alexander  de Gennes theory was experimentally confirmed; see e.g. Ref. [1].

  18. Steric interaction – poor solvent Plot of experimental data for measured forces, F/R  2f vs. h, between two surfaces covered by adsorption monolayers of the nonionic surfactant C12E5 for various temperatures. The appearance of minima in the curves indicate that the water becomes a poor solvent for the polyoxyethylene chains with the increase of temperature; from Claesson et al. [24].

  19. Hydrophobic Attraction After Israelachvili et al. [25] Discuss. Faraday Soc. 146 (2010) 299. Force between two hydrophobic surfaces across water. (1) Short range Hphb force Due to surface-oriented H-bonding of water molecules (1–2 nm) w = 1050 mJ/m2 and  = 12 nm (2)Long-range Hphb force (h = 2 – 20 nm) proton-hopping polarizability of water (?): (3)Long-range Hphb force (h = 100 – 200 nm): electrostatic mosaic patches and/or bridging cavitation: +–+–+ –+–+ –

  20. Hydration Repulsion At Cel < 104 M NaCl, a typical DLVO maximum is observed. At Cel  103 M, a strong short-range repulsion is detected by the surface force apparatus – the hydration repulsion [1, 26]. Empirical expression [1] for the interaction free energy per unit area: Important: feldecreases, whereas fhydrincreases with the rise of electrolyte concentration! Different hypotheses: (1) Water-structuring models; (2) Discreteness of charges and dipoles; (3) Redu-ced screening of the electrostatic repulsion [27].

  21. Example: Data from [27] by the Mysels–Jones (MJ)Porous Plate Cell [20] SE cell: Π < 85 Pa(thickness h vs. time) MJ cell: Π > 6000 Pa (!) (Π vs. thickness h) (1) Electrostatic repulsion; (2) Hydration repulsion.

  22. The total energy of interactionbetween two particles , U(h), includes contributions from all surface forces: U(h) = Uvw(h) + Uel(h) + Uosc(h) + Ust(h) + Uhphb(h) + Uhydr + … DLVO forces Non-DLVO forces (The depletion force is included in the expression for the oscillatory-structural energy, Uosc)

  23. Basic References 1. J.N. Israelachvili, Intermolecular and Surface Forces, Academic Press, London, 1992. 2. P.A. Kralchevsky, K. Nagayama, Particles at Fluid Interfaces and Membranes, Elsevier, Amsterdam, 2001; Chapter 5. 3. P.A. Kralchevsky, K.D. Danov, N.D. Denkov. Chemical physics of colloid systems and Interfaces,Chapter 7 in Handbook of Surface and Colloid Chemistry", (Third Edition; K. S. Birdi, Ed.). CRC Press, Boca Raton, 2008; pp. 197-377. Additional References 4. B.V. Derjaguin, E.V. Obuhov, Acta Physicochim. URSS 5 (1936) 1-22. 5. I. Langmuir, The Role of Attractive and Repulsive Forces in the Formation of Tactoids, Thixotropic Gels, Protein Crystals and Coacervates. J. Chem. Phys. 6 (1938) 873-896. 6. B.V. Derjaguin, L.D. Landau, Theory of Stability of Strongly Charged Lyophobic Sols and Adhesion of Strongly Charged Particles in Solutions of Electrolytes, Acta Physicochim. URSS 14 (1941) 633-662. 7. E.J.W. Verwey, J.Th.G. Overbeek, Theory of Stability of Lyophobic Colloids, Elsevier, Amsterdam, 1948.

  24. 8. H.C. Hamaker, The London – Van der Waals Attraction Between Spherical ParticlesPhysica 4(10) (1937) 1058-1072. 9. B.V. Derjaguin, Theory of Stability of Colloids and Thin Liquid Films,Plenum Press: Consultants Bureau, New York, 1989. 10. E.M. Lifshitz, The Theory of Molecular Attractive Forces between Solids, Soviet Phys. JETP (English Translation) 2 (1956) 73-83. 11. B.V. Derjaguin, Friction and Adhesion. IV. The Theory of Adhesion of Small Particles,Kolloid Zeits.69 (1934) 155-164. 12. H. Schulze, Schwefelarsen im wässeriger Losung, J. Prakt. Chem. 25 (1882) 431-452. 13. W.B. Hardy, A Preliminary Investigation of the Conditions, Which Determine the Stability of Irreversible Hydrosols, Proc. Roy. Soc. London 66 (1900) 110-125. 14. A. Scheludko, D. Exerowa. Instrument for Interferometric Measuring of the Thickness of Microscopic Foam Films. C.R. Acad. Bulg. Sci. 7 (1959) 123-132. 15. A. Scheludko, Thin Liquid Films, Adv. Colloid Interface Sci. 1 (1967) 391-464. 16. A.D. Nikolov, D.T. Wasan, P.A. Kralchevsky, I.B. Ivanov. Ordered Structures in Thinning Micellar and Latex Foam Films. In: Ordering and Organisation in Ionic Solutions (N. Ise & I. Sogami, Eds.), World Scientific, Singapore, 1988, pp. 302-314.

  25. 17. A. D. Nikolov, D. T. Wasan, et. al. Ordered Micelle Structuring in Thin Films Formed from Anionic Surfactant Solutions, J. Colloid Interface Sci. 133 (1989) 1-12 & 13-22. 18. A. Trokhymchuk, D. Henderson, A. Nikolov, D.T. Wasan, A Simple Calculation of Structural and Depletion Forces for Fluids/Suspensions Confined in a Film, Langmuir 17 (2001) 4940-4947. 19. E.S. Basheva, P.A. Kralchevsky, K.D. Danov, K.P. Ananthapadmanabhan, A. Lips, The Colloid Structural Forces as a Tool for Particle Characterization and Control of Dispersion Stability, Phys. Chem. Chem. Phys. 9 (2007) 5183-5198. 20. Mysels, K. J.; Jones, M. N. Direct Measurement of the Variation of Double-Layer Repulsion with Distance.Discuss. Faraday Soc. 42 (1966) 42-50. 21.W.B. Russel, D.A. Saville, W.R. Schowalter, Colloidal Dispersions,Cambridge Univ. Press, Cambridge, 1989. 22. S.J. Alexander, Adsorption of Chain Molecules with a Polar Head: a Scaling Description, J. Phys. (Paris) 38 (1977) 983-987 23. P.G. de Gennes, Polymers at an Interface: a Simplified View, Adv. Colloid Interface Sci. 27 (1987) 189-209.

  26. 24.P.M. Claesson, R. Kjellander, P. Stenius, H.K. Christenson,  Direct Measurement of Temperature-Dependent Interactions between Non-ionic Surfactant Layers, J. Chem. Soc., Faraday Trans. 1, 82 (1986), 2735-2746. 25. M.U. Hammer, T.H. Anderson, A. Chaimovich,M.S. Shell, J. Israelachvili, The search for the Hydrophobic Force Law. Faraday Discuss. 2010, 146, 299–308. 26. R.M. Pashley, J.N. Israelachvili, Molecular layering of water in thin films between mica surfaces and its relation to hydration forces. J. Colloid Interface Sci. 1984, 101, 511–22. 27. P.A. Kralchevsky,K.D. Danov, E.S. Basheva, Hydration force due to the reduced screening of the electrostatic repulsion in few-nanometer-thick films. Curr. Opin. Colloid Interface Sci. (2011) – in press.

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