fundamentals of surface forces - unisa€¦ · surface work chemical work du tds pdv da dn...
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Fundamentals of Surface Forces
Surface Forces & Colloid Stability
Copyright © 2014 R. Sedev. All rights reserved.
by Rossen Sedev
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Length Scales
Surface Forces
Masliyah & Bhattacharjee (2006)
01 RA
V R
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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)
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Stability of Colloids
The stability of colloidal systems is intrinsically related to the
behaviour of thin liquid films.
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Thin Liquid Films
water
oil vapour
vapour
water
vapour
quartz
water
Emulsion Foam Flotation
oil
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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)
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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:
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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)]:
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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:
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Interfaces & Films
vapour
liquid
film
vapour
vapour
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A Liquid Film: Thick or Thin?
h
Independent interfaces = thick film Interacting interfaces = thin film
h
2f int2f f h
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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):
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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
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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
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Attraction & Repulsion
• Attraction and repulsion are different functions of the film thickness;
• The total curve may have a minimum.
h 0
attraction
repulsion
total
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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
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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:
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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.