Particles at Fluid Interfaces and Membranes

by Kralchevsky; Nagayama

• ISBN13: 9780444502346
• ISBN10: 0444502343
• Format: Hardcover
• Copyright: 2001-01-22
• Publisher: Elsevier Science

Summary

In the small world of micrometer to nanometer scale many natural and industrial processes include attachment of colloid particles (solid spheres, liquid droplets, gas bubbles or protein macromolecules) to fluid interfaces and their confinement in liquid films. This may lead to the appearance of lateral interactions between particles at interfaces, or between inclusions in phospholipid membranes, followed eventually by the formation of two-dimensional ordered arrays. The book is devoted to the description of such processes, their consecutive stages, and to the investigation of the underlying physico-chemical mechanisms. The first six chapters give a concise but informative introduction to the basic knowledge in surface and colloid science, which includes both traditional concepts and some recent results. Chapters 1 and 2 are devoted to the basic theory of capillarity, kinetics of surfactant adsorption, shapes of axisymmetric fluid interfaces, contact angles and line tension. Chapters 3 and 4 present a generalization of the theory of capillarity to the case, in which the variation of the interfacial (membrane) curvature contributes to the total energy of the system. The generalized Laplace equation is applied to determine the configurations of free and adherent biological cells. Chapters 5 and 6 are focused on the role of thin liquid films and hydrodynamic factors in the attachment of solid and fluid particles to an interface. Surface forces of various physical nature are presented and their relative importance is discussed. Hydrodynamic interactions of a colloidal particle with an interface (or another particle) are also considered. Chapters 7 to 10 are devoted to the theoretical foundation of various kinds of capillary forces. When two particles are attached to the same interface (membrane), capillary interactions, mediated by the interface or membrane, appear between them. Two major kinds of capillary interactions are described: (i) capillary immersion force related to the surface wettability (Chapter 7), (ii) capillary flotation force originating from interfacial deformations due to particle weight (Chapter 8). Special attention is paid to the theory of capillary immersion forces between particles entrapped in spherical liquid films (Chapter 9). A generalization of the theory of immersion forces allows one to describe membrane-mediated interactions between protein inclusions into a lipid bilayer (Chapter 10). Chapter 11 is devoted to the theory of the capillary bridges and the capillary-bridge forces, whose importance has been recognized in phenomena like consolidation of granules and soils, wetting of powders, capillary condensation, long-range hydrophobic attraction, etc. The nucleation of capillary bridges is also examined. Chapter 12 considers solid particles, which have an irregular wetting perimeter upon attachment to a fluid interface. The undulated contact line induces interfacial deformations, which engender a special lateral capillary force between the particles. The latter contributes to the dilatational and shear elastic moduli of particulate adsorption monolayers. Chapter 13 describes how lateral capillary forces, facilitated by convective flows and some specific and non-specific interactions, can lead to the aggregation and ordering of various particles at fluid interfaces or in thin liquid films. Recent results on fabricating two-dimensional (2D) arrays from micrometer and sub-micrometer latex particles, as well as 2D crystals from proteins and protein complexes, are reviewed. Chapter 14 presents applied aspects of the particle-surface interaction in antifoaming and defoaming. The mechanisms of antifoaming action involve as a necessary step the entering of an antifoam particle at the air-water interface. The considered mechanisms indicate the factors for control of foaminess.

Table of Contents

Preface
Planar Fluid Interfaces	1	(63)
Mechanical properties of fluid interfaces	2	(10)
The Bakker equation for surface tension	2	(4)
Interfacial bending moment and surface of tension	6	(2)
Electrically charged interfaces	8	(3)
Work of interfacial dilatation	11	(1)
Thermodynamical properties of planar fluid interfaces	12	(25)
The Gibbs adsorption equation	12	(2)
Equimolecular dividing surface	14	(1)
Thermodynamics of adsorption of nonionic surfactants	15	(5)
Theory of the electric double layer	20	(5)
Thermodynamics of adsorption of ionic surfactants	25	(12)
Kinetics of surfactant adsorption	37	(19)
Adsorption under diffusion control	38	(3)
Adsorption under electro-diffusion control	41	(7)
Adsorption under barrier control	48	(5)
Adsorption from micellar surfactant solutions	53	(2)
Adsorption from solutions of proteins	55	(1)
Summary	56	(2)
References	58	(6)
Interfaces of Moderate Curvature: Theory of Capillarity	64	(41)
The Laplace equation of capillarity	65	(6)
Laplace equation for spherical interface	65	(1)
General form of Laplace equation	66	(5)
Axisymmetric fluid interfaces	71	(9)
Meniscus meeting the axis of revolution	72	(3)
Meniscus leveling off at infinity	75	(2)
Meniscus confined between two cylinders	77	(3)
Force balance at a three-phase-contact line	80	(18)
Equation of Young	80	(5)
Triangle of Neumann	85	(2)
The effect of line tension	87	(5)
Hysteresis of contact angle and line tension	92	(6)
Summary	98	(1)
References	99	(6)
Surface Bending Moment and Curvature Elastic Moduli	105	(32)
Basic thermodynamic equations for curved interfaces	106	(6)
Introduction	106	(1)
Mechanical work of interfacial deformation	106	(3)
Fundamental thermodynamic equation of a curved interface	109	(3)
Thermodynamics of spherical interfaces	112	(11)
Dependence of the bending moment on the choice of dividing surface	112	(3)
Equimolecular dividing surface and Tolman length	115	(2)
Micromechanical approach	117	(6)
Relations with the molecular theory and the experiment	123	(9)
Contributions due to various kinds of interactions	123	(6)
Bending moment effects on the interaction between drops in emulsions	129	(3)
Summary	132	(1)
References	133	(4)
General Curved Interfaces and Biomembranes	137	(46)
Theoretical approaches for description of curved interfaces	138	(2)
Mechanical approach to arbitrarily curved interfaces	140	(11)
Analogy with mechanics of three-dimensional continua	140	(2)
Basic equations from geometry and kinematics of a curved interface	142	(3)
Tensors of the surface stresses and moments	145	(2)
Surface balances of the linear and angular momentum	147	(4)
Connection between the mechanical and thermodynamical approaches	151	(11)
Generalized Laplace equation derived by minimization of the free energy	151	(3)
Work of deformation: thermodynamical and mechanical expressions	154	(3)
Versions of the generalized Laplace equation	157	(1)
Interfacial rheological constitutive relations	158	(4)
Axisymmetric shapes of biological cells	162	(6)
The generalized Laplace equation in parametric form	162	(2)
Boundary conditions and shape computation	164	(4)
Micromechanical expressions for the surface properties	168	(10)
Surface tensions, moments and curvature elastic moduli	168	(6)
Tensors of the surface stresses and moments	174	(4)
Summary	178	(1)
References	179	(4)
Liquid Films and Interactions Between Particle and Surface	183	(65)
Mechanical balances and thermodynamic relationships	184	(17)
Introduction	184	(2)
Disjoining pressure and transversal tension	186	(5)
Thermodynamics of thin liquid films	191	(6)
Derjaguin approximation for films of uneven thickness	197	(4)
Interactions in thin liquid films	201	(39)
Overview of the types of surface forces	201	(1)
Van der Waals surface forces	201	(10)
Long-range hydrophobic surface force	211	(1)
Electrostatic surface force	212	(4)
Repulsive hydration force	216	(4)
Ion-correlation surface force	220	(4)
Oscillatory structural and depletion forces	224	(7)
Steric interaction due to adsorbed molecular chains	231	(4)
Undulation and protrusion forces	235	(2)
Forces due to deformation of liquid drops	237	(3)
Summary	240	(1)
References	241	(7)
Particles at Interfaces: Deformations and Hydrodynamic Interactions	248	(39)
Deformation of fluid particles approaching an interface	249	(9)
Thermodynamic aspects of particle deformation	249	(5)
Dependence of the film area on the size of the drop/bubble	254	(4)
Hydrodynamic interactions	258	(10)
Taylor regime of particle approach	259	(1)
Inversion thickness for fluid particles	260	(1)
Reynolds regime of particle approach	261	(1)
Transition from Taylor to Reynolds regime	261	(2)
Fluid particles of completely mobile surfaces (no surfactant)	263	(1)
Fluid particles with partially mobile surfaces (surfactant in continuous phase)	264	(1)
Critical thickness of a liquid film	265	(3)
Detachment of oil drops from a solid surface	268	(14)
Detachment of drops exposed to shear flow	268	(8)
Detachment of oil drops protruding from pores	276	(4)
Physicochemical factors influencing the detachment of oil drops	280	(2)
Summary	282	(2)
References	284	(3)
Lateral Capillary Forces Between Partially Immersed Bodies	287	(64)
Physical origin of the lateral capillary forces	288	(20)
Types of capillary forces and related studies	288	(6)
Linearized Laplace equation for slightly deformed liquid interfaces and films	294	(2)
Immersion force: theoretical expression in superposition approximation	296	(3)
Measurement of lateral immersion forces	299	(4)
Energy and force approaches to the lateral capillary interactions	303	(5)
Shape of the capillary meniscus around two axisymmetric bodies	308	(8)
Solution of the linearized Laplace equation in bipolar coordinates	308	(4)
Mean capillary elevation of the particle contact line	312	(2)
Expressions for the shape of the contact line	314	(2)
Energy approach to the lateral capillary interactions	316	(18)
Capillary immersion force between two vertical cylinders	316	(5)
Capillary immersion force between two spherical particles	321	(6)
Capillary immersion force between spherical particle and vertical cylinder	327	(1)
Capillary interactions at fixed elevation of the contact line	328	(6)
Force approach to the lateral capillary interactions	334	(11)
Capillary immersion force between two cylinders or two spheres	334	(7)
Asymptotic expression for the capillary force between two particles	341	(2)
Capillary immersion force between spherical particle and wall	343	(2)
Summary	345	(2)
References	347	(4)
Lateral Capillary Forces Between Floating Particles	351	(45)
Interaction between two floating particles	352	(15)
Flotation force: theoretical expression in superposition approximation	352	(2)
``Capillary charge'' of floating particles	354	(2)
Comparison between the lateral flotation and immersion forces	356	(2)
More accurate calculation of the capillary interaction energy	358	(3)
Numerical results and discussion	361	(6)
Particle-wall interaction: capillary image forces	367	(25)
Attractive and repulsive capillary image forces	367	(2)
The case of inclined meniscus at the wall	369	(5)
Elevation of the contact line on the surface of the floating particle	374	(2)
Energy of capillary interaction	376	(3)
Application of the force approach to quantify the particle-wall interaction	379	(3)
Numerical predictions of the theory and discussion	382	(4)
Experimental measurements with floating particles	386	(6)
Summary	392	(2)
References	394	(2)
Capillary Forces Between Particles Bound to a Spherical Interface	396	(30)
Origin of the ``capillary charge'' in the case of spherical interface	397	(4)
Interfacial shape around inclusions in a spherical film	401	(11)
Linearization of Laplace equation for small deviations from spherical shape	401	(3)
``Capillary charge'' and reference pressure	404	(2)
Introduction of spherical bipolar coordinates	406	(3)
Procedure of calculations and numerical results	409	(3)
Calculation of the lateral capillary force	412	(10)
Boundary condition of fixed contact line	413	(1)
Boundary condition of fixed contact angle	414	(3)
Calculation procedure for capillary force between spherical particles	417	(3)
Numerical results for the force and energy of capillary interaction	420	(2)
Summary	422	(2)
References	424	(2)
Mechanics of Lipid Membranes and Interaction Between Inclusions	426	(43)
Deformations in a lipid membrane due to the presence of inclusions	427	(3)
``Sandwich'' model of a lipid bilayer	430	(14)
Definition of the model; stress balances in a lipid bilayer at equilibrium	430	(5)
Stretching mode of deformation and stretching elastic modulus	435	(3)
Bending mode of deformation and curvature elastic moduli	438	(6)
Description of membrane deformations caused by inclusions	444	(10)
Squeezing (peristaltic) mode of deformation: rheological model	444	(2)
Deformations in the hydrocarbon-chain region	446	(1)
Deformation of the bilayer surfaces	447	(3)
The generalized Laplace equation for the bilayer surfaces	450	(2)
Solution of the equations describing the deformation	452	(2)
Lateral interaction between two identical inclusions	454	(6)
Direct calculation of the force	454	(3)
The energy approach	457	(3)
Numerical results for membrane proteins	460	(3)
Summary	463	(2)
References	465	(4)
Capillary Bridges and Capillary Bridge Forces	469	(34)
Role of the capillary bridges in various processes and phenomena	470	(2)
Definition and magnitude of the capillary bridge force	472	(5)
Definition	472	(2)
Capillary bridge in toroid (circle) approximation	474	(3)
Geometrical and physical properties of capillary bridges	477	(15)
Types of capillary bridges and expressions for their shape	477	(3)
Relations between the geometrical parameters	480	(3)
Symmetric nodoid-shaped bridge with neck	483	(3)
Geometrical and physical limits for the length of a capillary bridge	486	(6)
Nucleation of capillary bridges	492	(6)
Thermodynamic basis	492	(4)
Critical nucleus and equilibrium bridge	496	(2)
Summary	498	(1)
References	499	(4)
Capillary Forces Between Particles of Irregular Contact Line	503	(14)
Surface corrugations and interaction between two particles	505	(7)
Interfacial deformation due to irregular contact line	505	(3)
Energy and force of capillary interaction	508	(4)
Elastic properties of particulate adsorption monolayers	512	(3)
Surface dilatational elasticity	513	(1)
Surface shear elasticity	514	(1)
Summary	515	(1)
References	516	(1)
Two-Dimensional Crystallization of Particulates and Proteins	517	(74)
Methods for obtaining 2D arrays from microscopic particles	518	(12)
Formation of particle 2D arrays in evaporating liquid films	518	(4)
Particle ordering due to u Kirkwood-Alder type phase transition	522	(2)
Self-assembly of particles floating on a liquid interface	524	(3)
Formation of particle 2D arrays in electric, magnetic and optical fields	527	(2)
2D arrays obtained by adsorption and/or Langmuir-Blodgett method	529	(1)
2D crystallization of proteins on the surface of mercury	530	(5)
The mercury trough method	530	(2)
Experimental procedure and results	532	(3)
Dynamics of 2D crystallization in evaporating liquid films	535	(15)
Mechanism of two-dimensional crystallization	535	(7)
Kinetics of two-dimensional crystallization in convective regime	542	(8)
Liquid substrates for 2D array formation	550	(6)
Fluorinated oil as a substrate for two-dimensional crystallization	550	(4)
Mercury as a substrate for two-dimensional crystallization	554	(2)
Size separation of colloidal particles during 2D crystallization	556	(5)
Methods for obtaining large 2D-crystalline coatings	561	(5)
Withdrawal of a plate from suspension	561	(3)
Deposition of ordered coatings with a ``brush''	564	(2)
2D crystallization of particles in free foam films	566	(6)
Arrays from micrometer-sized particles in foam films	566	(2)
Arrays from sub-micrometer particles studied by electron cryomicroscopy	568	(4)
Application of 2D arrays from colloid particles and proteins	572	(8)
Application of colloid 2D arrays in optics and optoelectronics	572	(1)
Nano-lithography, microcontact printing, nanostructured surfaces	573	(4)
Protein 2D arrays in applications	577	(3)
Summary	580	(2)
References	582	(9)
Effect of Oil Drops and Particulates on the Stability of Foams	591	(42)
Foam-breaking action of microscopic particles	592	(10)
Control of foam stability; Antifoaming vs. defoaming	592	(2)
Studies with separate foam films	594	(6)
Hydrodynamics of drainage of foam films	600	(2)
Mechanisms of foam-breaking action of oil drops and particles	602	(15)
Scheme of the consecutive stages	602	(4)
Entering, spreading and bridging coefficients	606	(5)
Spreading mechanism	611	(2)
Bridging-dewetting mechanism	613	(2)
Bridging-stretching mechanism	615	(2)
Stability of asymmetric films: the key for control of foaminess	617	(9)
Thermodynamic and kinetic stabilizing factors	617	(3)
Mechanisms of film rupture	620	(3)
Overcoming the barrier to drop entry	623	(3)
Summary and conclusions	626	(2)
References	628	(5)
Appendix 1A: Equivalence of the two forms of the Gibbs adsorption equation	633	(2)
Appendix 8A: Derivation of equation (8.31)	635	(1)
Appendix 10A: Connections between two models of lipid membranes	636	(5)
Index	641	(10)
Notation	651