Steric stabilization Dispersions in liquids: suspensions, emulsions, and foams ACS National Meeting April 9 – 10, 2008 New Orleans Ian Morrison© 2008
Rates of flocculation – Strength of interparticle forces
t1/ 2 =
The time for half the particles to flocculate is:
ηπ d 3W 8ΦkT
Since flocculation is a change in average particle size, the half life can be measured. And W, the stability ratio, be determined. ∞
The stability ratio depends on the interparticle forces:
Ian Morrison© 2008
⎛ U ⎞ dH W = d ∫ exp ⎜ 11 ⎟ 2 ⎝ kT ⎠ H 0
Lecture 4 - Steric stabilization
1
Hamaker model for the attraction between particles The intermolecular attraction is due to London (dispersion) energies:
3 U11 = − Λ11r −6 2
r Molecules in particle 1
Molecules in particle 2
H Ian Morrison© 2008
Lecture 4 - Steric stabilization
2
Hamaker equations for dispersion force attraction
For two spheres (per pair):
− A11d ΔG11 = 24 H For two flat plates (per unit area):
− A11 ΔG11 = 12π H 2 The A11 are the Hamaker constants. Ian Morrison© 2008
Lecture 4 - Steric stabilization
3
Hamaker constants for some materials Substance Graphite Gold Silicon carbide Rutile (TiO2) Silver Germanium Chromiun Copper Diamond Zirconia (n-ZrO2) Silicon Metals (Au, Ag, Cu) Iron oxide (Fe3O4) Selenium Aluminum Cadmium sulfide Tellurium Polyvinyl chloride Magnesia Polyisobutylene Mica Polyethylene Polystyrene
Ian Morrison© 2008
A11 (10-20 J) 47.0 45.3, 45.5, 37.6 44 43 39.8, 40.0 29.9, 30.0 29.2 28.4 28.4 27 25.5, 25.6 25 – 40 21 16.2, 16.2 15.4, 14, 15.5 15.3 14.0 10.82 10.5, 10.6 10.10 10, 10.8 10.0 9.80, 6.57, 6.5, 6.4, 7.81
Polyvinyl acetate Polyvinyl alcohol Natural rubber Polybutadiene Polybutene-1 Quartz Polyethylene oxide Polyvinyl chloride Hydrocarbon (crystal) CaF2 Potassium bromide Hexadecane Fused quartz Polymethylmethacryl ate Polydimethylsiloxane Potassium chloride Chlorobenzene Dodecane Decane Toluene 1,4-Dioxane n-Hexadecane Octane Benzene n-Tetradecane Cyclohexane Carbon tetrachloride
8.91 8.84 8.58 8.20 8.03 7.93 7.51 7.5 7.1 7 6.7 6.31 6.3 6.3
Methyl ethyl ketone Water Hexane Diethyl ether Acetone Ethanol Ethyl acetate Polypropylene oxide Pentane PTFE Liquid He
4.53 4.35, 3.7, 4.38 4.32 4.30 4.20, 4.1 4.2 4.17 3.95 3.94, 3.8 3.8 0.057
6.27 6.2 5.89 5.84, 5.0 5.45 5.40 5.26 5.1 5.02, 4.5 5.0 5.0 4.82, 5.2 4.78, 5.5
Lecture 4 - Steric stabilization
4
The affect of liquid between the particles The effect of an intervening medium calculated by the principle of Archimedean buoyancy:
A121 = A11 + A22 − 2 A12 Introducing the approximation:
A12
A121 = ( A
1/ 2 11
Which leads to:
[ A11 A22 ]
1/2
)
1/ 2 2 22
−A
and 1/ 2 A123 = ( A111/ 2 − A22 )( A331/ 2 − A221/ 2 )
Ian Morrison© 2008
Lecture 4 - Steric stabilization
5
Lifshitz theory Limitation of Hamaker theory: all molecules act independently Lifshitz theory: the attractions between particles are a result of the electronic fluctuations in the particle. What describes the electronic fluctuations in the particle? the absorption spectra: uv-vis-ir
Result:
nr ΔG123
nr A123 =− 12π H 2
The Lifshitz constant depends on the absorption spectra of the particles. Ian Morrison© 2008
Lecture 4 - Steric stabilization
6
Data for Lifshitz calculations The absorption spectra is measured. Often a single peak in the UV and an average IR is sufficient. That is two amplitudes and two wavelengths.
The dielectric spectrum is calculated from the absorption spectrum. The only additional information needed is the static dielectric constant.
Ian Morrison© 2008
Lecture 4 - Steric stabilization
7
Lifshitz calculations The Lifshitz constant is a double summation of products of dielectric functions: The dielectric functions are differences in dielectric constants over a series of frequencies:
The frequencies are:
Δ12 =
A123
3kT = 2
∞
∞
∑´∑ n = 0 m =1
( Δ12 Δ32 )
m
m3
ε1 ( iξ n ) − ε 2 ( iξ n ) ε ( iξ ) − ε 2 ( iξ n ) and Δ 32 = 3 n ε1 ( iξ n ) + ε 2 ( iξ n ) ε3 ( iξ n ) + ε 2 ( iξ n )
4π2 kT ξn = n h
where k is the Boltzmann constant, T is the absolute temperature, h is Planck's constant, and the prime on the summation indicates that the n = 0 term is given half weight. At 21°C, ξ1 is 2.4 × 1014 rad/s, a frequency corresponding to a wavelength of light of about 1.2 µm. As n increases, the value of ξ increases and the corresponding wavelength decreases, hence ξ takes on more values in the ultraviolet than in the infrared or visible. Ian Morrison© 2008
Lecture 4 - Steric stabilization
8
Lifshitz calculation vs measurement Force - separation for TiO2 at the PZC 100
50
F/R (μN/m)
0
-50
-100
-150
-200 -10
0
10
20
30
40
50
60
Separation (nm)
direction perpendicular parallel
Ian Morrison© 2008
ε(0) 86 170
ωIR(rad/s) 14
1 x 10 14 1 x 10
CIR 80 163
ωUV(rad/s) 15
7.49 x 10 15 7.24 x 10
CUV 4.77 6.01
Lecture 4 - Steric stabilization
Larson, I.; et al JACS, 1993, 115,11885-11890.
9
Colloidal stability requires a repulsion force:
Electrostatically stabilized
Ian Morrison© 2008
Sterically stabilized
Lecture 4 - Steric stabilization
10
Steric stabilization
H Work is required to push polymer layers into each other.
When H < 2t then ΔG Ian Morrison© 2008
0
Lecture 4 - Steric stabilization
11
Dispersion attraction between spheres
− A121d ΔG121 = 24 H
kT
2t
Ian Morrison© 2008
Lecture 4 - Steric stabilization
12
Criterion for Steric Stabilization (1st order) The kinetic energy must be greater than the attractive energy:
A121d kT > 24 H
kT >
Especially when the polymer layers just touch: or
t>
A121 d 48kT
A121d 48t
For example:
Oil-water Polystyrene-water Carbon-oil TiO2 – water
Ian Morrison© 2008
A121 (x 1020) J 0.5 1.05 2.8 7.0
Lecture 4 - Steric stabilization
A121/48kT 0.025 0.05 0.14 0.35
13
Polymer thickness for steric stabilization t ita n ia / w a t e r
c a r b o n / o il p o ly s t y r e n e / w a t e r
o il/ w a t e r
Ian Morrison© 2008
Lecture 4 - Steric stabilization
14
A simple theory for polymer “thickness” A reasonable assumption is that the surface coating has a thickness equal to the radius of gyration.
Radius of gyration for linear polymers:
r
2
1/ 2
Molecular weight
∼ 0.06 MW 1/ 2
"Length" (nm) r2
1,000 10,000 100,000 1,000,000
Ian Morrison© 2008
Lecture 4 - Steric stabilization
1/ 2
2 6 20 60 15
The Size of polymers in solution A polymer forms a random coil in solution. The polymer increases the viscosity of the solution in a manner approximately dependent on molecular size. This polymer size can be calculated from the intrinsic viscosity: r
2 1/ 2
⎛ 2 MW ⎞ =⎜ η [ ]⎟ 5 N 0 ⎝ ⎠
1/ 3
The intrinsic viscosity is gotten by:
[η ] =
or
or
Rg =
Ian Morrison© 2008
1 c*
l n 6
Where MW is molecular weight and N0 is Avogadro’s number.
[η ] = lim c →0
1 ⎛ ηsolution ⎞ − 1⎟ ⎜ c ⎝ ηsolvent ⎠
where c* is the concentration where the viscosity is not linear in concentration.
where l is the “Kuhn” length. Lecture 4 - Steric stabilization
16
Steric stabilization – a better model +
Steric repulsion
ΔGT
H Coil diameter
-
Ian Morrison© 2008
Dispersion attraction
Lecture 4 - Steric stabilization
17
Configurations of adsorbed polymers Homopolymers Time
Random copolymers Brush Anchor
Block copolymers Two or three segments are common.
Grafted polymers Polymers may be attached to or grown from the surface.
Ian Morrison© 2008
Lecture 4 - Steric stabilization
18
Polymers in solution - Phase Diagrams
Temperature
Two phase region ΘL
One phase region
ΘU Two phase region
Concentration Sterically stabilized dispersions are stable when the polymer is soluble – the one phase regions. Ian Morrison© 2008
Lecture 4 - Steric stabilization
19
Steric stabilization!
Ethylacetate Aqueous
141 nm silica particles- with grafted polymer. Pictures were taken at 0 C and 60 C. The particles phase-transfer with the change in polymer solubility.
Ian Morrison© 2008
Lecture 4 - Steric stabilization
20
