Surface Forces and Liquid Films Sofia University Film of phase 3 sandwiched between phases 1 and 2

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

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

(1) Electrostatic (Double Layer) Surface Force n 1m, n 2m n0n0 Π el = excess osmotic pressure of the ions in the midplane of a symmetric film (Langmuir, 1938) [5-7]: n 1m, n 2m – concentrations of (1) counterions and (2) coions in the midplane. n 0 – concentration of the ions in the bulk solution; ψ m potential in the midplane.

Verwey – Overbeek Formula (1948) Superposition approximation in the midplane: ψ m = 2ψ 1 [6]: Π(h) = ?

(2) Van der Waals surface force: A H – 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, A 11 > A 33 > A 22  repulsion!

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: ε 1, ε 2 and ε 3 ; (ii) Refractive indexes of the phases: n 1, n 2 and n 3 : Zero-frequency term: orientation & induction interactions; kT – thermal energy. Dispersion interaction term: ν e = 3.0 x Hz – main electronic absorption frequency; h P = 6.6 x 10 – 34 J.s – Planck’s const.

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 R 1 and R 2, this yields: From planar films, f(h) to spherical particles, U(h 0 ).

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: U max = 0 (zero height of the barrier to coagulation)

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

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; A H – Hamaker constant; κ – Debye screening parameter

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

Oscillatory–Structural Surface Force For details – see the book by Israelachvili [1] 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.

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  = P c. The stable branches of the oscillatory curve are those with  /  h < 0. Depletion minimum Oscillatory structural forces [1] were observed in liquid films containing colloidal particles, e.g. latex & surfactant micelles; Nikolov et al. [16,17]. Oscillatory- structural disjoining pressure

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

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, N agg = 70, is determined [19]. (the micelles are modeled as hard spheres)

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 > L 0, whereas in a poor solvent L < L 0. L depends on adsorption of chains,  [1,21].  Alexander – de Gennes theory for 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].

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 C 12 E 5 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].

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) (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: + – + – ++ – + – + – + – + –

Hydration Repulsion Important: f el decreases, whereas f hydr increases 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].

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.

U(h) = U vw (h) + U el (h) + U osc (h) + U st (h) + U hphb (h) + U hydr + … DLVO forcesNon-DLVO forces (The depletion force is included in the expression for the oscillatory-structural energy, U osc )

Basic References 1. J.N. Israelachvili, Intermolecular and Surface Forces, Academic Press, London, P.A. Kralchevsky, K. Nagayama, Particles at Fluid Interfaces and Membranes, Elsevier, Amsterdam, 2001; Chapter 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 Additional References 4. B.V. Derjaguin, E.V. Obuhov, Acta Physicochim. URSS 5 (1936) 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) 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) E.J.W. Verwey, J.Th.G. Overbeek, Theory of Stability of Lyophobic Colloids, Elsevier, Amsterdam, 1948.