Fundamentals of Surface Forces

Surface Forces & Colloid Stability

Copyright © 2014 R. Sedev. All rights reserved.

by Rossen Sedev

Length Scales

Surface Forces

Masliyah & Bhattacharjee (2006)

01 RA

V R

Classification of Colloids

Suspension: solid particles in a liquid

Emulsion: liquid droplets in a liquid

• oil droplets in water (O/W)

• water droplets in oil (W/O)

Foam: gas bubbles in a liquid, solid or gel

Froth = Foam + Particles

Aerosol:

• Smoke: solid particles in gas

• Fog: droplets in gas

Dispersed phase

Dispersion medium (continuous phase)

Stability of Colloids

The stability of colloidal systems is intrinsically related to the

behaviour of thin liquid films.

Thin Liquid Films

water

oil vapour

vapour

water

vapour

quartz

water

Emulsion Foam Flotation

oil

Phases & Components

Water + Ice in a thermos:

• 3 phases (solid, liquid, vapour)

• 1 component (H2O)

Seawater:

• 1 phase (liquid)

• n components (H2O, Cl-, Na+, SO42-, Mg2+, Ca2+,…)

Water:

• 1 phases (liquid)

• 1 component (H2O)

Emulsion:

• 2 phases (liquid-liquid)

• 3 component (H2O, C12H26, surfactant)

Thermodynamic Description

Heat Bulk Work Surface Work Chemical Work

dU TdS PdV dA dN

Generalized Forces (intensive parameters):

T – temperature, K

P – pressure, Pa

– surface tension, J/m²

µ – chemical potential, J/mol

Generalized Coordinates (extensive parameters):

S – entropy, J/K

V – volume, m³

A – surface area, m²

N – number of moles, mol

Internal Energy, U:

• The system is uniquely represented by its internal energy, U;

• The absolute value of U is difficult/impossible to obtain;

• A process will occur only if the energy decreases, i.e. ΔU <0;

• The fundamental equation is for U is:

Free Energy

dU TdS PdV

F U TS

G H TS

dF SdT PdV

dG SdT VdP

max

max

T

T

dF PdV dW

dG VdP dW

F – Helmholtz Free Energy G – Gibbs Free Energy

The change in free energy change is the maximum work obtainable from the system:

The internal energy is often practically inconvenient because U = U(S,V):

Alternative thermodynamic potentials can be defined:

The fundamental equation is then modified [F = F(T,V) and G = G(T,P)]:

Conditions for Equilibrium

F(x)

x

Global minimum of F = stable equilibrium

Local minimum of F = metastable equilibrium

stable

metastable

Energy barrier

0dF

dx

The thermodynamically stable state is the one with the lowest free energy.

The equilibrium condition is:

Interfaces & Films

vapour

liquid

film

vapour

vapour

A Liquid Film: Thick or Thin?

h

Independent interfaces = thick film Interacting interfaces = thin film

h

2f int2f f h

Disjoining Pressure (Surface Force)

The interaction between the two interfaces is given by the disjoining pressure, Π:

P h P

, , iT V

h

f

h

f dh

The interaction between the two interfaces can be discussed in terms of disjoining

pressure Π (force per unit area, N/m²) or, alternatively, free energy f (energy per

unit area, J/m²):

Repulsion

• As the interfaces approach each other they experience an

increasingly repulsive force (disjoining pressure);

• A stable film of thickness h0 is established at pressure Π = P0.

P0

h h0

0

Attraction

• As the interfaces approach each other they experience an

increasingly attractive force (disjoining pressure);

• The film is unstable at any thickness.

P0

h 0

Attraction & Repulsion

• Attraction and repulsion are different functions of the film thickness;

• The total curve may have a minimum.

h 0

attraction

repulsion

total

Disjoining Pressure Isotherm

Realistic force profile:

• Films of thickness h1 will be metastable

• Films of thickness h2 will be stable.

PM – primary minimum

SM – secondary minimum

FB – Force barrier

0 h

PM

SM

FB

h1 h2

Disjoining Pressure Components

Components:

• van der Waals (VW): interaction between permanent

and/or induced dipoles.

• Electrostatic (EL): interaction between the electrical

double layers.

• Steric (ΠST): interactions between large molecules

adsorbed on the surfaces.

VW EL ST

The total disjoining pressure, Π, is made up of different types of interactions.

These can be considered as independent:

References

• Israelachvili, J.N. (2011) Intermolecular & Surface Forces, 3rd Edition, Academic Press/Elsevier.

• Butt, H.-J. & Kappl, M. (2010) Surface & Interfacial Forces, Wiley-VCH.

• Everett, D.H. (1988) Basic Principles of Colloid Science, Royal Society of Chemistry, Cambridge.

• Everett, D.H. (1971) An Introduction to the Study of Chemical Thermodynamics, Harlow, Longman.