Chap. 3. Colloids

3.1. Introduction

- Simple definition of a colloid: a macroscopically heterogeneous system where one component has dimensions in between molecules and macroscopic particles like sand (1 nm to 1 um). -> high surface-to-volume ratio: surface chemistry is very important! - Colloids in porous rocks, clays, mists, and smoke.

*blood and bones contain colloids. *milk is a good example of a colloidal dispersion.

- Colloids in industries: synthetic paints, foams, pastes

- Stabilized dispersion of solid colloidal particles in liquid: charging the surface or adsorbing molecules.

-> modification of the steric interactions between the particles. -> a balance between the repulsive forces and van der Waals forces.

- Aggregation: 1) flocculation: the process of reversible aggregation 2) coagulation: irreversible process (sedimentation)

- Surfactants in solution: 'association colloids'

3.1. Types of Colloids

- Two-phase dispersions in a continuous medium.

- Sols: 'lyophobic (solvent hating) solids' <-> lyophilic (solvent loving)

cf. poor solvent and good solvent for polymers.

3.3. Forces between Colloidal Particles

3.3.1. Van der Waals Forces

- Attractions between the electric dipoles of the molecules

-> Dispersion interactions between the molecules on each particle.

- For flat infinite surfaces separated in vacuum by a distance h,

the potential per area with AH = the Hamaker constant

- For two spherical particles of radius R where the interparticle separation

is small ( ≪ ), the Derjaguin approximation:

- Medium: vacuum -> liquid (dielectric)

For a system of particle 1 and particle 2 are in medium 3,

1) Particles are far apart -> each interacts with medium 3 independently and the total AH is a sum of two particle-medium terms.

2) Particle 1 is close to particle 2 -> the particle1 interacts with a similar body (particle 2) and the effective AH is a sum of particle-particle and medium-medium contributions.

- In the Hamaker approach, multi-body interactions are neglected.

- The correct theory involves QM calculations of the dielectric permittivity of the continuous media (instantaneous fluctuations of the induced dipolar interactions): very complex!

3.3.2. Electrical Double-Layer Forces

- The electrical potential around a charged colloid particle in solution:

-> counterions: an ionic atmosphere is formed around it.

- The diffusive double layer: described by the Gouy-Chapman equation

<- a solution of Poisson-Boltzmann equation for a planar double layer.

At a point where the electrical potential is ,

and

where is the number density (molar concentration = ) of each ionic species of valance z.

The excess charge density -> into Poisson's equation:

- In the case that ≪ (for the surface potential at x=0 is much smaller than and/or the electrolyte is weakly charged),

with the Debye screening length

3.4. Characterization of Colloids

3.4.1. Rheology: The flow behavior of colloids

3.4.2. Particle Shape and Size

- Colloidal sols: solid particles are dispersed in a liquid.

particle shapes of 3-D spherical, 2-D plate-like, 1-D rod-like forms.

3.4.3. Electrokinetic Effects

- For charged colloid particles, the effect of an electric field on the flow behavior of the dispersion.

- In electrophoresis measurements, the mobility in a stationary liquid.

- Zeta potential: the potential at the surface between a stationary solution and a moving charged colloidal particle. (a moving particle will have a certain number of counterions attached to it)

- Huckel and Smoluchowski equation :

1) Huckel : a charged colloid particle is small enough to be treated as a point charge. (≪ )

2) Smoluchowski : the particle radius is large, being as a planar charged surface. (the double layer thickness << 1 -> ≫ )

- In the Huckel approximation,

<-> (Stokes' law)

When the particle moves steadily,

Using the Debye-Huckel theory, the zeta potential

-> In the limit that ≪ , ≈

- In the Smoluchowski approximation (the double layer in thin enough or R >>1), The double layer can be considered to be uniform and parallel to a flat surface.

The mobility has a form of (or ≈

)

- Henry equation: with (Huckel and Smoluchowski)

3.5. Charge Stabilization

3.5.1. Charged colloids

- Electrostatic interactions in stabilizing many colloidal systems:

ionization of surface acid or base groups in aqueous solution preferential ion adsorption/desorption, ionic surfactants selective dissolution (silver iodide crystals dissolved in water + Ag+ ions), etc variations of concentration and nature of an electrolyte

=> the balance bet the electrostatic (repulsive) forces and vdW (attractive) forces

3.5.2. Derjaguin-Landau-Verwey-Overbe다 (DLVO) Theory

- Forces between electrical double layers and long-range vdW forces:

->

Stability of the colloid suspension (dispersion or association)

1) Primary minimum and possibly a secondary minimum

2) Potential barrier vs thermal fluctuations

- For two spherical colloid particles (R >>1) in an electrolyte of bulk concentration of co,

the electric potential from a charged plane

with

3.5.3. Critical Coagulation Concentration

- Coagulation can occur at an electrolyte concentration such that the repulsive double-layer interaction is reduced significantly to enable the attractive interactions to predominate.

- At the ccc (V=0 and F=0), the interparticle separation is .

into the total potential -> ccc (moles/unit vol) =

×

∝

3.6. Steric Stabilization

- Attachment of long chain molecules to colloid particles.

- Steric stabilization,

1) the interparticle repulsion is indep of the electrolyte concentration. 2) effective in both non-aqueous and aqueous media 3) applicable for a wide range of colloid concentrations

- Matching the properties of the adsorbed layers on the particles with

1) the dispersion medium or 2) the particle core

-> interparticle interactions can be manipulated or tailored!

[Reading Assignment]

3.7 - 3. 11 (p. 133 - p. 139)

3.12. Foams

- Liquid (solid) foams: a coarse dispersion of a gas in a liquid (solid) where the volume fraction of the gas is greater than that of the liquid (solid).

- Foams are not thermodynamically stable due to large interfacial area (surface energy)

- Some foams are metastable by the addition of small amount of soaps or surfactants. by retardation of drainage of liquid from the foam and prevention of rupture.

Drainage of liquid under gravity: thinning of the liquid film Rupture from random disturbances (mechanical, thermal, evaporation, impurities)

- The development of a form structure: dynamic process

Drainage of liquid throughout the liquid film -> polyhedral cellular structure Curvature at vertices of polyhedra (plateau borders) -> lower pressure built up -> pressure drop ( > surface tension) -> flow generation -> film rupture -> foam collapse

3.13. Emulsions

- Dispersion of immiscible or partially miscible liquids.

The free energy to disperse a liquid of volume V into drops of radius R

with the interfacial tension

- Emulsions: foods, pharmaceutical products, cosmetics, and agricultural products.

- Emulsions (macroemulsions: 0.1-10 um -> scattering of light) are thermodynamically unstable whereas microemulsions (1-100 nm -> clear and optically isotropic) are stable.

The kinetics of exchange of molecules in and out of the stabilizing film are much greater in microemulsions.

3.13.1. Emulsions

- Most common examples: water-in-oil (w/o) and oil-in-water (o/w) milk : fat droplets in a continuous aqueous phase, in fresh unskimmed cow's milk, 86% water, 5% lactose, 4% fat, 4% protein, and 1% salts.

mayonnaise: dispersion of vegetable oil in vinegar or lemon juice, stabilized by natural lecithin surfactant molecules.

margarine: a water-in-oil emulsion.

- The spontaneous formation of emulsions is rather uncommon.

- The thermodynamic stability of emulsions: the free energy difference bet dispersed and undispersed systems.

≈

with A = the interface area, and = the interfacial tension.

The configurational entropy

with = the vol fraction of liquid b and N = the number of droplets

-> The limiting value of for which emulsification occurs is defined by .

where with r = the average droplet radius.

- In emulsions stabilized by surfactant, the interfacial tension is reduced compared to that between pure liquids -> reduction in the free energy required to break up the emulsion.

3.13.2. microemulsions

- Two types: dispersed (droplets) and bicontinuous (networks)

Spontaneous curvature of the surfactant interface Ho -> 0 for droplets *Ho ≠ 0 for bicont networks [positive or negative depending on whether the interface is curved toward oil (o/w) or water (w/o)]

- Ternary (oil+water+surfactant) phase diagram in a triangular representation

- Winsor microemulsions: excess water (I) or oil (II), both (III)

[Reading Assignment]

3.14 (p. 149 - p. 155)

3.15. Concentrated Colloid Dispersions

- Liquid, solid (crystalline), glass phases: Hard sphere model

vol fraction : liquid freezing to a crystalline solid at crystal melting into liquid at coexistence between them. *glass transition occurs at ≈