Chapter 11 Micro Macro Emulsions - kemi.lu.se

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Lund University / Physical Chemistry / Tommy Nylander

Colloidal Domain

Chapter 11: Micro and Macro Emulsions


Separating oil and water by a surfactant film

•  Surface free energy - surface tension

•  Area expansion modulus

r P

oil

water

!

" =#G#A$

% &

'

( ) T ,P

!

KA =" 2Gf

"A2#

$ %

&

' ( ns

A2

Stretching the film when the number of molecules in the interfacial layer constant KA is modulus

Radius of curvature

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Different modes of deformation of an interface

Bending Stretching Shearing

Splay or saddle like deformation


Concept of curvature The two curvatures 1/R1 and 1/R2 The mean radius of curvature H=1/2(1/R1 +1/R2) The Gaussian curvature is K= 1/R1x1/R2 Note positive curvature if surface is bend towards oil Genus describes the topology of the closed interface Sphere g=0 and a donut g=1, i.e. genus is number of holes or handles

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Spontaneous curvature of the film

•  Consider the free energy per unit area which for cylinder is

•  gf=Gf/(2πRL)

•  Free energy of a film depends on how curved it is, but due to packing restriction a global minima exist so that

at value of curvature defined as the spontaneous curvature

H0 = 1/R0 !

dgf

d 1R

= 0


In fact spontaneous curvature can be related to surfactant packing parameter

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The bending rigidity, κ

•  The bending rigidity or bending elastic modulus κ is obtained as the second derivative of the free energy per unit area, gf

•  Most convenient to evaluate derivative at 1/R =2H0

•  The bending plane is usually at the neutral surface where the area per molecule is the same as for a planar surface. !

" =d2gfd(1/R)2


The saddle splay modulus, κ

•  We will consider a saddle like deformation such that 1/R1=-1/R2 that is zero mean curvature or a minimal surface

!

" = #12

d2gfd(1/R1)

2

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Helfrich curvature (free) energy

•  Assuming that the area per molecule is constant when the film is bent (area expansion modulus is so large)

•  By integration

!

gf = " + 2#(H $H0)2 +# K

!

Gf = (gf " #)dA = 2$(H "H0)2 +$ K{ }%% dA


Estimating the elastic constants

•  Bending elasticity, κ, is 1-20kT •  κ for monolayer is half of that for a bilayer

•  The saddle splay, κ, is hard to measure but usually negative and in the order of kT

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κG or κ controls the topology, while κ controls bending rigidity and thereby fluctuations.


Bilayers can fold into intriguing structures forming structures with zero mean curvature

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Diamond type of cubic phase


Cubic phase can be both normal (curved towards oil) and reversed

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Different minimal surfaces (zero mean curvature) can describe different types of cubic phases.

A. Diamond (D) B. Gyroid (G) C. Primitive (P) surface


Curvature is important for life processes

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Cubic phases exist in nature (sea urchin (cidaris rugosa) calcite network)

Hyde et al The Language of Shape, Elsevier 1997


SARS-CoV-induced cubic membranes in Vero cells (Yuru Deng: Trends in Cell Biology

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Microemulsions are thermodynamically stable solution

•  Contains: –  Amphiphile –  Water –  Apolar compound

•  Can be both discrete or bicontinuous


Discrete microemulsions can be of both oil-in-water or water-in-oil type

Rc

RH

Rc is given by the ratio of the hydrocarbon volume, Vhc and the area of the core, Ahc:

Rc=3Vhc/Ahc Hydrocarbon volume = the oil volume and a fraction α of the surfactant volume Vhc=Vtot(Φ0 +αΦs) Surfactant are a0 => Ahc=(VtotΦsa0)/vs vs = surfactant molecular volume Rc=3(Φ0/Φs + α)(vs/a0) Rc depends solely on the volume fractions!!

1.5-2 nm

5-20 nm H0 ≈ Rc

-1, stable drop H0 >> Rc

-1=> smaller drops H0 << Rc

-1 => larger non-spherical drops H0 ≈ 0 => bicontinuous microemulsion

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Temperature controls the structure/stability of the nonionic surfactant microemulsion C12E5-water-tetradecane system

Low temperature (below PIT): more water in microemulsion (more oil in water) at even lower temperature L1 and microemulsion merges (Winsor I)

High temperature (above PIT): more oil in microemulsion (more water in oil) (Winsor II)

Medium temperature: At phase inversion temperature (PIT) microemulsion in three phase triangle contain as much water as oil (Winsor III)


Summarizing the temperature effect

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To illustrate the temperature dependence we can do different cuts χ-cut and fish-cut

χ-cut fish-cut


The χ-cut – surfactant concentration fixed at 16.6%- C12E5-water-tetradecane system

PIT is the temperature where H0=0

From L1 (normal) to L2 (reversed)

Connecting L3 phases

Weight fraction of oil

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Self-diffusion coefficient as a function oil content (C12E5-water-tetradecane system)

Weight fraction of oil

water

oil

Bicontinuous phase (highest surfactant mobility)


The fish-cut at oil weight ration 0.5 (C12E5-water-tetradecane system)

PIT

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Packing parameter is unfavorable for ionic surfactant to form microemulsion: Adding electrolyte or cosurfactant or double chain surfactant gives a microemulsion

microemulsion

AOT =di(ethyhexyl)sulfosuccinate


The χ-cut – surfactant concentration fixed at 5% Water-isocotane-AOT-NaCl

Note that in the ionic system in presence of salt the electrostatic free increases with temperature as the electrostatic free energy is dominantly entropic so the curvature is expected to increase. It is also true that the tail becomes more bulky and thus the curvature should decrease, however the electrostatic contribution is larger. Thus the curvature increases with temperature.

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The fish-cut at oil weight ratio 0.5: Different concentration of NaCl

(water-decane-AOT-NaCl)

•  Increase in salt content => decrease in H0

•  H0 can thus be found by increasing temperature

•  The tail of the fish tilts with lower ionic strength as the counterions to the surfactant becomes more important


Macroemulsions are thermodynamically unstable

•  The ultimate fate of macroemulsion is separation into two or more equilibrium phase

•  Mechanical energy is needed to form them •  Free energy needed is ΔGem to disperse a liquid of volume V with

drops of radius R and the interfacial tension γ is

•  For water in oil (γ = 50 mN/m) to form drops of R=100 nm needs a free energy of 27 J/mol and lowering this values by adding a emulsifier that decreases γ

!

"Gem = #3VR

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Turbulent flow governs the size of the droplet –averaged droplet size as a function of energy input

A spherical drop exhibits a Laplace pressure Pressure gradient to tear such a drop in two parts:

!

p(Laplace) =2"r

!

"p"x

#2$r2


Destabilisation of an emulsion

+ Ostwald ripening: if dispersed substance is slightly soluble in solvent the diffusion and merge with larger droplets.

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Emulsions can be stabilised by emulsions by adding particle* or polymers

*Pickering emulsion


Protein and lipids can stabilize lipids can stabilize emulsions

Globular proteins (e. g. whey proteins) as well as flexible proteins (caseins) can stabilize emulsions Surfactants and lipids can stabilize emulsions. Larsson, Krog and Friberg should that a multi-lamellar phase can form at the interface

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The Marangoni effect- deformation causes a gradient in surface tension


Two droplets in contact will deform

Thickness of water layer determined determined by force between interfaces (disjoining pressure)

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Concentration fluctuation can destabilize film that prevents coalescence

The effect can be simulated by estimating the increase in surface free energy ΔG=(γ0-γ)A


Rupture of the liquid film between to emulsion droplets leads to the formation of the neck of the dispersed liquid that connects the two drops

Free energy: Gf=W1+W2+W3+W4

Decreasing flat part of film: W1=-2πγ(a+b)2

Creating the new curved part of film: W2=2πγ[π(a+b)-2b2]

!

W3 = 2" H #H0( )2 #H02{ }dA$

W3 = 2%" 2%H0a +2 a + b( )2

b a a + 2b( )[ ]1/ 2arctan 1+ 2b /a( )1/ 2 + 2 % # 4( )bH0 # 4

& ' (

) (

* + (

, (

W4 = #4%"

Bending term

Splay term

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Calculated free energy as function of neck radius a for O/W or W/O emulsions stabilised by C12E5, different curves are deviation from balance temperature T0

!

V (a) =Gf (a,b0)with"G(a,b)"b

= 0

atb = b0


FOAM Forms tetrahedral connecting points

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Foams integrate by Ostwald Ripening and Film Rapture


Experimentally determined bulk osmotic pressure and film thickness for 0.1 mM KBr β-octylglucoside (CMC 20 mM)

3 mM

10 mM 21 mM 25 mM

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Stabilisation – destabilisation of foams with surfactants/lipids and/or proteins

•  Gibbs-Marangoni effect: the high lateral mobility of the surfactant makes it possible to quickly restore the surface tension gradient, which arises from thinning of the film.

•  In the protein stabilised foam the thinning is counteracted by strong intermolecular interactions, which give a viscoelastic film. Adopted from: Clark, D.C., Coke, M., Wilde, P.J. and Wilson, D.R. In 'Food, Polymers, Gels and Colloids' (E. Dickinson, ed) Royal Society of Chemistry, London (1991) pp 272-278.

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Chapter 11 Micro Macro Emulsions - kemi.lu.se