fundamentals of surface forces - university of south · pdf filefroth = foam + particles ......
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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.