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Surfaces, Interfaces and Colloids
• Introduction to colloidal science (2 h)• Thermodynamics of surfaces and interfaces (4 h) • Adsorption and monolayers (4 h)• Seminar 1. Protein adsorption (1 h)• Seminar 2. Monolayers and L-B films (1 h)• Surfactants (6 h)• Polymers in solution (8 h) • Seminar 3. Light scattering and SAXS (1 h)• Seminar 4. Neutron scattering (SANS) (1 h)• Student seminars (2 h)• Forces in colloidal systems (4 h)
• Colloidal stability (4 h)• Student seminars (4 h)• Electrokinetic phenomena (4 h)• Seminar 5. Imaging: SEM, TEM and AFM (1 h)• Seminar 6. Imaging: Confocal and multiphoton
microscopy. (1 h) • Student seminars (4 h)
Bibliography:D. Evans, H. Wennerström,The colloidal domain,Wiley 1999 P. Hiemenz e R. Rajagopalan, Principles of Colloid and
Surface Science, Marcel Dekker, 1987.Site: http://web.ist.utl.pt/~farinha/SIC/
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Evaluation
•1 report in english (3 pages+ref) on the state of the art of a chosen topic to be handed 1 week before the presentation- 40%
• 1 oral presentation in english (20 min) + discussion (10 min) on a specific theme of the chosen topic-30%
• final exam-30%
Important note:If student presence<80% final exam-100%
TOPICS
•Wetting of artificial tears •Biosensors•Water purification•Drug delivery•Surface modification•Polymer blends•Electroluminescent polymers•Porous polymers (covalent organic frameworks)•Smart polymers•Polymers in cosmetics•Stabilization of nanoparticles•Polymer colloids for coatings•Colloids in cooking
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Introduction to Colloid and Surface Science
Colloid - System of particles with diameters between 10 Å and 1 µm
Surface/Interface - Phase boundary
Colloids↔High surface area
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Classification of colloids
Reversible• Themodynamic stability
Irreversible
Lyophilic (hydrophilic)• Solvent interaction
Lyophobic (hydrophobic)
Examples of reversible colloids
• Solution of macromolecules (body fluids, fruit juices)
• Hydrophilic gels (gelatin-gel)
• Association colloids or self-assembled structures (detergents, microemulsions, vesicles and liposomes, biological membranes)
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Classification of irreversible colloidal dispersions
BASIC THERMODYNAMICS OF INTERFACES
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Interfacial Tension
• Increment of Gibbs or Helmholtz energy per unit area of interface extension:
• Force per unit lenght parallel to the interface which acts perpendicularand inward from the boundariesopposing an increase of the area
ii n,T,Vn,T,P A
F
A
G
∂∂=
∂∂=γ
l2/F=γ
Surface Energy
Surface energy - energy needed to generate the unit area of a surface:
¼ nA n ε
where:nA - number of molecules per unit arean - number of closest neighboursε - interaction energy of a pair of molecules
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Mechanical treatment
Euler´s theorem
where R1 and R2 are the principal radii of curvature.Projection of force γδl on the normal PN:
Projection of forces acting on elements δl at A, B, C and D:
Equilibrium between the total force and ∆P=PA-PB
Laplace equation
2121 R
1
R
1
b
1
b
1 +=+
1/sin bll ρδγφδγ =
+=
+
2121
112
22
RRl
bbl δγρρρδγ
+=
21
22
R
1
R
1P γπρπρ∆
+=
21 R
1
R
1P γ∆
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Thermodynamic treatment
• Gibbs model for the liquid/vapour interface
Real System Model
• Excess surface property - Difference between the value for the real system and that of a hypothetical system consisting of two uniform bulk phases separated by a mathematical dividing surface.
• Surface excess Gibbs energy:
Gs = G - Gα - Gβ
• Surface excess number of moles:
ns = n - nα - nβ
• Equimolar Gibbs surface: ns = 0
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Density profile
( )[ ] ( )[ ] 00
=∫ −+∫ −∞
dzzdzzze
vze
l ρρρρ
Multicomponent system with interfacial area A and Gibbs energy G(T, p, A, ni):
Gs = G - Gα - Gβ
dGs = dG - dGα - dGβ
where:
dG = - SdT + Vdp + γdA + ii
idn∑µ
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If and
dGs = -SsdT + γdA +
where γ = - liquid surface tension
If we keep constant the intensive variables,T,p and density ni/V, and duplicate the area A, then G duplicates which means it is an homogeneous function of first degree on V, S and ni.
Applying Euler‘s theorem we may integrate dG and dGs
inpTA
G
,,
∂∂
si
iidn∑µ
siii µµµ βα ==
ii
in∑µ
si
iin∑µ
G = γA +
Gs = γA +
If the dividing surface is chosen such that 0n sii =∑µ
AG s γ=
dT
dT
A
U s γγ −=
dT
d
A
S s γ−=
Differentiating we get:
Compared with the previous equation leads to:
Then the surface energy is
sss TSUG −=
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ii
si dn µ∑
si
iidn∑µ
ii
si dn µ∑
si
iidn∑µ
Diferenciating the full expression:
dGs = A dγ + γ dA +
Comparing with dGs
SsdT + A dγ +
Surface analogue of Gibbs-Duhem equation
=0
+
= -SsdT + γ dA +
System of two components:Component 1 – solvent Component 2 – solute
At constant T:
A dγ + n dµ1 + n dµ2 = 0 Gibbs adsorption equation
A
ns1
A
ns2dγ = - dµ1 - dµ2
being:
Γi = A
n si surface excess of component i
or adsorption of i
- dγ = Γ1 dµ1 + Γ2 dµ2
s1
s2
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How to choose the surface position?One possibility = n = 0
Then Γ = - adsorption of component 2relative to component 1
s1
12
T
∂∂
2µγ
As
12
2ln
1
ad
d
RT
γ
2
2
da
d
RT
a γΓ = -= -
If the solute decreases γ, it concentrates at the surface (Γ12>0)
Contact angles and wettability
Eq. of Young
Film pressure
αγγγ cosLVLSSV +=
SVS γγπ −=
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Lothus Leaf
Cohesion and adhesion
Work of cohesion Work of adhesion
AAAW γ2= ABBAABW γγγ −+=
AABBAAABBA WWS γγγ −−=−=/
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Goniometer
Wilhelmy balance
- is the liquid surface tension
- perimeter of the plate- contact angle- buoyant force
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- advancing contact angle
- receding contact angle- contact angle hystheresis
• Effect of roughness
Wensel eq.
- ratio between true area and projected area
- Wensel contact angle
- intrinsic contact angle
• Effect of chemical heterogeneities
Cassie eq.
- Cassie angle
- fraction of surface with contact angle
- fraction of surface with contact angle
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Hystheresis cycles for silanized glass in albumin saline solutions
Interfacial tension of a solid
Dupré eq.
Young-Dupré eq.
How can we get ?Rayleigh and Good assumed that forces across the interface are dispersive forces that obey the geometrical mean rule:
from Young-Dupré eq.
SLLVSVSLW γγγ −+=
( )θγ cos1W LVSL +=
SVγ
( ) ( ) 2/1LVSV
2/1LLSSSL 2WWW γγ==
( ) 2/1LVSV /21cos γγθ +−=
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Zisman plot
Contact angles of hydrocarbons on teflon
Critical surface tension
SLSVC γγγ −=
Additive approach
According to Fowkes:
But the interactions that contribute to the adhesion workare dispersive, then:
and
which allows calculation of from the contact angle and the surface tension of a purely dispersive liquid.
dSVγ
ndd γγγ +=
( ) 2/1dLV
dSVSL 2W γγ=
( ) 2/1dLV
dSV /21cos γγθ +−=
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Owens and Wendt extended Fowkes approach to polar interaction:
which substituted in Young-Dupré equation leads to:
from which the surface tension of the solid may be obtained using two testing liquids of known components of the surface tension.
( ) ( ) ( ) 2/12/122cos1 p
LVpSV
dLV
dSVLV γγγγθγ ⋅+⋅=+
( ) ( ) 2/1pLV
pSV
2/1dLV
dSVSL 22W γγγγ ⋅+⋅=
Non-additive approach
In contrast, van Oss considered two contributions, van derWaals and donor-acceptor:
where are the van der Waals parameters and , are the electron donor (-) and electron (+)
acceptor parameters.
Owens Wendt approach needs 2 testing liquids while van Oss approach needs 3.
∴
vWLV
vWSL γγ ⋅
−+LVSL γγ , +−
LVSL γγ ,
( ) ( ) ( ) 2/12/12/1222 +−−+ ⋅+⋅+⋅= LVSVLVSV
vWLV
vWSVSLW γγγγγγ
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Adsorption on the surface of aqueous solutions
1 – Organic, simple, non-ionized solutes2 – Inorganic electrolytes and hydrated organic species 3 – Amphiphilic species
Curves 1 e 3 may be described by a straight line when c→0
γ = γo – mc
mc = π film pressure (difference between the surface tension of pure water and that of the aqueous solution with adsorbed solute on the interface)For dilute solutions, we verify that:
Γ = π/RT or π A = n RT
similar to the ideal gas equation (2-D)
12
s2
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How can we measure ΓΓΓΓ ?
• Measures of γ as a function of ln c.
• Direct measures of Γ from isotopic labeling of the solute molecules with 3H, 14C or 35S.
• Calculation of Γ through ellipsometric measures of the thickness τ of the adsorbed layer: Γ = τ / V, where V is the molar volume.
12
12
12 1
2
Adsorption of sodium hyaluronate at the air-liquid interface
45
50
55
60
65
70
75
0 0.5 1 1.5 2 2.5 3 3.5 4
c / mg.mL-1
γ /
mN
.m-1
W. Ribeiro, J. L. Mata, B. Saramago Langmuir 2007, 23, 7014-7017
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0
2
4
6
8
10
12
14
0 0.5 1 1.5 2 2.5 3 3.5c / mg.ml-1
Γ x
104 /
mol
.m-2
Dilute Semi-dilute Semi- dilute non-entangled entangled
Adsorption on solid surfaces
The amount of solute adsorbed on a solid surface, atconstant T, per unit mass or per unit area of theadsorbent varies with the concentration of the solute insolution according to a function designated by:
adsorption isotherm
Chemical adsorption Physical adsorpti on
Chemical bonds Intermolecular forcesSpecific interactions Non-specific interactionsMonolayers Multilayers
-40 to -800kJ/mol -4 to -40 kJ/mol
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Langmuir model
Assumptions:
• Reversible process• Adsorbed molecules of Solvent (1) and Solute (2)
occupy similar areas (adsorption site), and a single molecule may be adsorbed in each site.
• Monolayer formation• There are no interactions between adsorbed molecules• Adsorbed molecules do not undergo conformational
changes
Equilibrium
Ads Solv. + Solut. in sol. ↔ Ads Solut.+ Solv. in sol.
K’ = = =21
12
aa
aas
s
21
12
ax
axs
s
22
12
)1( ax
axs
s
−
1/'
/')1('
12
12
1
222 +
=−=aaK
aaK
a
axKx ss
Dilute solutions K = K’/a1
12
22 +
=Ka
Kaxs Langmuir isotherm
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Molecules 1 and 2 ocupy the same area, then:
where and are the fractions of the surface occupied bymolecules 1 and 2.
or
• Infinite dilution a→0 = Ka• If Ka>> 1 = 1
11 θ=sx 22 θ=sx
12
22 +
=Ka
Kaθ
1θ 2θ
1+=
Ka
Kaθ
θθ
The shape of the isotherm is determined by the two limiting cases:
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Experimentally the number of moles of solute adsorbed per unit weight or per unit area of adsorbent is:
where is the specific area of the adsorbent.
NA- Avogadro´s numberσ0 - area occupied per molecule
sp
ss
wA
n
A
n 22 =
spA
== 02 σθ A
s
NA
n
sp
As
wA
Nn 02 σ
Saturation condition θ = 1
0
2
σA
sp
sat
s
N
A
w
n =
0
2 1
σAsat
s
NA
n =
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Brunauer-Teller-Emmet equation
Assumptions:• Same as Langmuir except multilayer formation
where:- V is the volume of gas adsorbed at pressure P- P* is saturation pressure- Vm is the adsorbed volume corresponding to the
monolayer- being the adsorption energy and
the vaporization energy
( ) *mm
* P
P
cV
1c
cV
1
PPV
P ⋅−+=−
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Adsorption of albumin onto TiN ( � ), TiNbN ( □ ) and TiCN
( ∆ ) coatings determined by QCM-D. The lines represent theoretical adsorption isotherms calculated according the Langmuir model (a) and the Freundlich model (b). The inserts represent the linearization data.
MONOLAYERS AT FLUID INTERFACES
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Surfactants
O S O
O
ONa
NBr
Sodium Dodecyl Sulphate (SDS)
cetyl trimethylammonium bromide (CTAB)
single “tail” ionic amphiphiles
CMC = 0.9M
CMC = 8.1M
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Amphiphiles at surfaces
Reaction of an amphiphile to a surface or interface will depend on the nature of the surface. Hydrophobic surfaces will associate with hydrophobic tails while hydrophilic surfaces will associate with hydrophilic head groups.
What will happen at an air water interface?
• Adsorbed or Gibbs monolayers (soluble)
• Spread or Langmuir monolayers (insoluble)
• Interfacial pressure
Gibbs and Langmuir Monolayers
Integration of the Gibbs equation, at constant T, keeping constant components j≠i :
For an ideal solution:
For an ideal diluted monolayer:
Langmuir monolayers follow this behaviour, although the Gibbs eq does not apply
i
x
0x idi
i
µΓγ∆ ∫ =−=
∫ Γ=c
cdcRT0
ln)(π
RTnA s2=π
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Formation of Langmuir monolayers
Full spreading if ( ) 0>−−≡ βγαγαβγαβ γγγS
LANGMUIR TROUGH
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Amphiphiles organize upon compression (freeze)
Pressure-area isotherm of a spread monolayer
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Fluorescence micrograph of DMPA monolayer (dimyristoylphosphatidic acid) containing a 1% fluorescent
dye in the gel+fluid region
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Interfacial pressure-area isotherms as a function of temperature
• The transitions in monolayers may be treated thermodynamically as 3D systems:
Clapeyron eq.
isobaric expantion coef.
isothermal compressibilitycoef.
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Monolayer will adhere to a hydrophobic surface upon immersion
hydrophobicsurface
Multiple layers can be deposited by multiple passes
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Layers can be inverted by using a hydrophilic surface
Y Type Deposition
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X-Type and Z-Type transfer
Self-assembled monolayers
Alkane thiols (R-SH) on gold
Silanization
Polymer brushes
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Applications of MONOLAYERS and LB films
• Molecular electronics
• Electron-beam microlithography
• Piezoelectric films
• Optical devices
• Semiconductor devices
• Chemical and biological sensors
• Highly selective membranes
Optical switch based on LB films
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Water treatment
• Functionalised SAMs on silica quartz sand are used to remove natural organic mater,NOM, Escherichia coli bacteria, and MS2 bacteriophage virus from water.
• 3-Aminopropyltrimethoxysilane (NH2(CH2)3Si(OCH3)3 ) (NH2-SAM) was used providing a NH2-functionality.
• Trimethoxysilane (Si(OCH3)3)forms tightly covalent Si-O-Si-bonds to the surface atoms of silica.
• Head groups like NH2 form, depending on pH, negatively or positively charged surfaces which attach to NOM.
Size exclusion cromatography of NOM vs. molecular weight after 1 h of treatment of the water sample from the Hope Valley Reservoir, South Australia, with SAMs coated silica powder. Insert right: ToF-SIMS analysis of particle surface. Insert left: Dissolved organic carbon (DOC) content in mg/l after a treatment of 1 h.
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Cholesterol biosensor based on self-assembled monolayers
• The covalent immobilization of cholesterol oxidase (ChOx) onto SAM of poly-(3-hexylthiophene) using 1-fluoro-2-nitro-4-azidobenzene (FNAB) as a bridge (cross linker) between CH3 group of SAM and NH2 group of ChOx is achieved for the estimation of cholesterol.
• Surface plasmon resonance technique can be used to estimate cholesterol using ChOx/FANB/P3HT/Au electrode, up to a detection limit of 50 mg/dl.
(a) Gold plate, (b) gold surface having terminal C–H group of P3HT SAM, (c) 1-fluoro-2-nitro-4-azido-benzene modified SAM using nitrene reaction and (d) immobilized ChOx on SAM by displacing labile fluoro group at 37 ◦C.
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SELF-ASSEMBLED STRUCTURES
Critical Micelle Concentration
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Surfactant distribution
0
0.5
1
1.5
2
0 0.5 1 1.5 2 2.5 3
monomermicelle
total concentration
SELF-ASSEMBLY AS PHASE SEPARATION
Volume fraction of oil
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For ideal mixture the entropy of mixing is:
and the Gibbs energy of mixing:
Taking into account the different interactions AA, BB, AB,and a random distribution of the molecules:
where
and gives the difference between nonidentical and identical contacts.
( )BBAAm XlnXXlnXRS +−=∆
( )BBAAconfigm XlnXXlnXRTG +=∆
ermconfigmm GGG int∆+∆=∆
BAerm XXRTG χ=∆ int
( )( )[ ]RT
gg21g BBAAAB +−
=χ
(a) (b)
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spinodalbinodal
NN
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
Spherical Micelles
CTAB: Cetyltrimethylammonium Bromide
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Cylindrical Micelles
NN
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
Vescicles (liposomes)
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Phase diagram for a solution of surfactants
Spherical Micelles
Interior is disordered and liquid like.
Headgroups are not in fixed position, but are mobile.
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Effective length of chain in the liquid state ≤ lmax
Optimal head group area
Hydrophobic interactions
• Atractions between non-polar chains to avoid contact with water.
• Entropy-driven process due to the increase in entropy of water molecules that form the walls of the cavities where the non-polar chains were located.
• A large negative value of:
which justifies negative and relatively temperature--independent 000 sThg trtrtr ∆−∆=∆
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Gibbs energy of associationComprises two terms:
• Volume contribution- accounting for promotion of aggregation (more important for large particles)
• Surface contribution- disfavours aggregation due to the energy needed for creating an interface (more important for small particles)
If there was no repulsion between
head groups, ∆assg is similar to ∆nucleig
of a liquid drop in a vapour:
Gibbs energy of association as a function of number of monomers in the aggregate
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Gibbs energy of association as a function of average area available per head group
Prediction of Assembly
“critical packing parameter”
v / aolcv = volume of amphiphileao = area of head grouplc = length of apolar part
can be approximated as the angle of the amphiphile cone or inverse cone
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MASS ACTION MODEL FOR MICELLIZATION
• Consider a solution of the amphiphilic A where the molecules are present as monomers and i-mers (dimers, trimers, etc) in the molar fractions:
• Micelles are formed when
monAX
2
monAi
X ( )iXX monAA ii
/=1AX
The chemical potential of the free molecule A equals that of A in the agglomerate:
iAmeriAAaqA Xi
RTXRT lnln 0
)(0
)( 111+=+ −µµ
cmcX1A >
The standard Gibbs energy for the transfer of a monomerfrom solution into an i-mer:
The standard Gibbs energy of the formation of a micelle:
as
or
i
Xln
i
RTXlnRTG
monA
A0Atr
i
11−=∆
00
1Atrmicel GiG ∆=∆
iAiA ↔1
( ) ( ) iA
monA
iA
A
micel X
iX
X
XK ii
11
/==
( )
i
A
miceli
A
cmc
X
Kcmc
Xi
= 1
0≈iAX
sharplyincreasesXiA
bellow cmc:
above cmc:
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Mole fraction of micelles as a function of mole fraction of monomers in solution
As i amounts a few tens:
cmcRTG Atr ln0
1=∆
000
1 partapolartrpartpolartrAtr GGG ∆+∆=∆
RT
G
RT
Gcmc partapolartrpartpolartr
00
ln∆
+∆
=
For a homologous series of surfactants with the same polar head and different number, n, of -CH2 - groups:
bnacmcln ×+=
RT
Ga
0partpolartr∆
=RT
Gb
0CHtr 2 −−=
∆
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CMC vs number of C-atoms in the hydrocarbon chain
Ionic surfactants
Non-ionic surfactants
Effect of temperature on cmc
( )T
TG
RdT
cmcd Atr
∂∆∂
=/1ln
0
1
∆=
Td
R
Hcmcd Atr 1
ln0
1
For most surfactants cmc is independent of temperature. Exceptions are nonionic surfactants based on oxyethylene where cmc decreases with increasing temperature and ionic surfactants where cmc first decreases but then increases.
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Temperature dependence of micellization of SDS
Micelles of ionic amphiphiles
• Due to high charge density, there is counterion (M) condensation. The micelle is and the mass action model yields:
• At cmc, and ascmcXX1AM =≈
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Lamellae
monolayer bilayer
Lamellae
Multilayers
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Vesicle
O
O
O
OO P
O
O
O
O
ONH3
Dipalmitoyl phosphatidyl serine
O
O
O
OO P
O
O
O
NH3Dipstearoyl phosphatidyl ethanolamine
Bilayer forming amphiphiles
phospholipids
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Bilayer forming amphiphiles
Gel-Liquid transition
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NanoSorb is a Biopharma trademark for delivery systems. In this case it Is used as a food supplement carrier.
Inverted Micelles
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Surfactants for reverse micelles
Microemulsions
• The size of particles in microemulsions is in the range of tens of nanometers whereas in emulsions this is in order of micrometers.
• Microemulsions form spontaneously while emulsions meed an energy input and are thermodynamically unstable.
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MONOLAYERS AT FLUID INTERFACES
MICROEMULSIONS
(a) am,o>v/l (b) am,o<v/l (c) am,o≈v/l
Phase diagrams
• Gas
Isotropic• Liquid Smetic
Liquid Crystal NematicCholesteric
Crystal• Solid Plastic crystal
Amorphous
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Liquid crystals
Molecular order in LC phases
smetic nematic
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Ternary diagrams
Ternary diagrams
Higher temperature
or→
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Complex phase diagrams
Ternary phase diagram: water (W), hexanoic acid (A), sodium dodecyl sulfate (S)
Two liquids- two phase region where two solutions exist as distinct layers or as an emulsion where droplets of one phase are dispersed in the second.
L1 and L2- isotropic liquid solutions where the acid is solubilized in aqueous micelles (L1) and water is solubilized in reverse micelles (L2).
Liquid crystal-
→ incresase of surfactant concentration
Solid- the surfactant precipitates.
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L1-micellar and L2-reversed micellar solutionH1-normal hexagonal and H2-reversed hexagonal liquid crystalline phaseLα-lamellar phase
Phase diagram of water-dodecyltrimethylammonium chloride:Cubic phase (left)-contains rodlike aggregates in cubic arrayCubic phase (right)- bicontinuous phase
Neat phase
Middle phase
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Cubic phases
Effect of temperature on phase equilibria of nonionic surfactants
Phase diagram of the systemwater-C12H25(OC2H4)5OH:L1, L2 are normal and reversed micellar solutionsH1,V1,Lα are hexagonal, cubic and lamellar liquid crystalsL3 is isotropic solution containing bilayersS is solid surfactant
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Determining phase diagrams
• Direct observation with polarizing microscope.
• Calorimetry to determine the temperatures of phase transitions.
• Light, x-ray or neutron scattering to determine the phase structure.
• NMR spectroscopy.
Calculating phase diagrams
According to the regular solution model:
• The mixture is random
• The enthalpy of mixture ≠0
where w, the effective interaction parameter, is positive forunfavourable A-B interactions.
( )BBAAm XlnXXlnXRS +−=∆
( )BBAAm XXXXRTG lnln +=∆ BA XwX+
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2* ln BAAA wXXRT ++= µµ2AB
*BB wXXlnRT ++= µµ
22 )1(ln)1(ln ββααAAAA XwXRTXwXRT −+=−+
2AA
2AA )X(w)X1ln(RT)X(w)X1ln(RT ββαα +−=+−
βαAA X X ≠
If the system separates into two liquid phases α and β:
For what w/RT can we obtain a solution where ?
As
Plots of µA vs µB
No phase separation
Critical point at kink
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The chemical potentials are equal at XA=0.93 and XA= 0.07. Between these compositions, there is phase separation.Between the kinks the liquid is unstable.
Phase diagram calculated with regular solution theory
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Surfactant applications
• From anti-aging creams to make-up, surfactants play a key role as delivery systems for skin care and decorative cosmetic products. Surfactants in Personal Care Products and Decorative Cosmetics, Third Edition, 2007
• Subjects like solubilization of drugs in micellar systems, triggered drug-release from liposome formulations, microemulsions in oral and topical administration, are described in Surfactants and Polymers in Drug Delivery, 2002.
Detergent molecular structures consist of a long hydrocarbon chain and a water soluble ionic group. Most detergents have a negative ionic group and are called anionic detergents.
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Another class of detergents have a positive ionic charge and are called "cationic" detergents. In addition to being good cleansing agents, they also possess germicidal properties which makes them useful in hospitals. Most of these detergents are derivatives of ammonia.A cationic detergent is most likely to be found in a shampoo or clothes "rinse". The purpose is to neutralize the static electrical charges from residual anionic (negative ions) detergent molecules. Since the negative charges repel each other, the positive cationic detergent neutralizes this charge.It may be surprising that it even works because the ammonium (+1) nitrogen is buried under the methyl groups as can be seen in the space filling model.
Nonionic detergents are used in dish washing liquids. Since the detergent does not have any ionic groups, it does not react with hard water ions. In addition, nonionic detergents foam less than ionic detergents. The detergent molecules must have some polar parts to provide the necessary water solubility.In the graphic on the left, the polar part of the molecule consists of three alcohol groups and an ester group. The non-polar part is the usual long hydrocarbon chain.
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Bile acids are produced in the liver and secreted in the intestine via the gall bladder. Bile acids are oxidation products of cholesterol. First the cholesterol is converted to the trihydroxy derivative containing three alcohol groups. The end of the alkane chain at C # 17 is converted into an acid, and finally the amino acid, glycine is bonded through an amide bond. The acid group on the glycine is converted to a salt. The bile salt is called sodiumglycoholate. The main function of bile salts is to act as a soap or detergent in the digestive processes. The major action of a bile salt is to emulsify fats and oils into smaller droplets. The various enzymes can then break down the fats and oils.
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Electrokinetic Phenomena
• Electrophoresis - charged particle moves relative to a stationary liquid.
• Electroosmosis – electrolyte moves relative to a stationary, charged surface.
• Steaming potential-results from the electric field generated when the electrolyte is forced to flow past a charged surface.
• Sedimentation potential- results from the electric field generated when charged particles sedimente.
Mobility of ions and macroions• IonsThe force of the electric field is compensated by the forcedue to viscous resistance:
where the friction coefficient may be given by Stokes´s lawfor a spherical particle of radius Rs and a liquid of
viscosity η.Mobility, u, is the velocity, v, per unit field:
where ze is the charge of the particle.
EqFel = vfFvis =
SR6f ηπ=
SR6
ezu
ηπ=
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• MacroionsIn this case, u, is called electrophoretic mobility which isreadly measured but difficult to interpret.
Alternatively, the friction coefficient may be related with thediffusion coefficient
and u is given by
which yields the particle charge only when the colloidalparticle is isolated from the other ions. In fact, the charged
particle is surrounded by an electric double layer.
D
Tkf =
Tk
eDzu =
What is the size of an ion?
• The Debye lenght k-1 is the distance parameter which may be considered an estimative of the double layer thickness.
• It quantifies the electrical potential distribution near a charged surface. For a spherical surface with radius Rs, the electric potential at a distance r:
• Definition of k is:
where Mi is the molar concentration of ions and ε = εr.ε0
with εr the dielectric constant of the medium.
( ) ( )[ ]ss0 Rrkexpr/R −−=ψψ
2/1
ii
2i
B
A2
MzTk
Ne1000k
= ∑ε
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• Small ions
small
• Large ions
large
1S
kR
−1
S
kR
−
1S
kR
−
Zeta potential:Thick electrical double layer• How does electrical potential vary with distance from a
charged surface?
• Poisson eq
• Debye-Hückel aproximation, assuming the probability of finding an ion given by the Boltzmann factor
if
where is the bulk concentration of ions i
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• In spherical coordinates and assuming spherical symmetry, Poisson eq. is:
where is the Debye length.This is the basic relationship of the Debye-Hückel theory which may be integrated using: Thus
and
Then and
And substituting by its definition:
As when should be
In the limit of infinite dilution and the potential around the charged particle is given by the potential of anisolated charge:
and
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Then the general expression for the potential around a
spherical particle at low potential is:
Now, if at
We recover:
( ) ( )[ ]ss0 Rrkexpr/R −−=ψψ
Schematic illustration of the variation of the potential with distance from a charged wall
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For thick double layers ( large), the surface of shear may be regarded as coinciding with the surface of the particle:
If k is small, the exponential may be expanded:
or
Which may be decomposed as the sum of two potentials:
This is the net potential between two concentric sphereswith equal, opposite charges and differing in radius by
The second term is negligible ( is large) and we may keep only the first which combined with:
leads to Hückel equationsmall particles
That enables the calculation of zeta potential ξ once theelectrophoretic mobility is known
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Electrophoresis cell
Zeta potential:Thin electrical double layers
• Thickness of double layer is negligible compared with R:flat or slightly curved surface or concentrated electrolyte( small)
• Consider a volume element of solution of area A at distance from the charged surface, where is the relative velocity
beteween the surface and the surrounding liquid
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Net viscous force
If is small:
• Under stationary conditions, an equal, opposite force by the electrical field acting on the ions inside the volume element:
• Applying the Poisson eq for a planar surface:
• Equating both forces:
• Assuming and as constants, this eq. may be integrated:
as at large distances =0
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• The eq. may be integrated using the limits:
at the surface of shear at the outside edge electrophoretic velocity
The same equation is valid in electro-osmosis.
As
the Helmholtz-Smoluchowski eq. for big particles
where u stands for both the electro-osmotic or the electrophoretic mobility.
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A domain of particle size/electrolyte concentration exists for which neither the H-S nor the Hückel eqs are valid.
General formulation of electrophoresis for spherical particles:Henry’s equation
• Assuming that the external field deformed by the presence of the colloidal particle and the field of the double layer are additive, Henry derived the equation for the mobility:
where is the radial distance from the center of the particle
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• To solve this eq. the dependence must be simple
• We return to the solution of the Poisson-Boltzmann eq for a spherical particle
• A is evaluated by recalling that when (considering the diffuse part of the layer)
• Combining this eq with the Henry eq. and integrating:
with two limiting results for <1 and >1 which are
known as Henry’s equations
Two assumptions for derivation of Henry’s equation• The ion atmosphere is undistorted by the external field• The potential is low enough to consider that
Hückel eq if • Henry’s eq
Helmholtz-Smoluchowski eq. if
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• If we consider and represent C as a function offor spherical colloidal particles in 1:1 electrolyte
solutions at various zeta potentials:
Electrophoretic Relaxation Effect
The centers of charges do not coincide when the particleis in motion:
.This effect depends on particle size, zeta potencial andionic strenght.
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• The relationship between and under conditions of intermediate values is complex.
• This relation is simple for the Hückel and the Helmholtz-Smoluchowski limits.
• The Hückel limit demands spherical, small particles and is not specially useful for aqueous colloids.
• The Helmholtz-Smoluchowski limit is independent of particle shape.
• If and are known and is known to be small, it can be evaluated from mobility measurements and Henry’s eq.
Other methods to measure zeta potentials
The electrolyte solution moves past a charged stationary wall due to an applied:
Potential Pressurein in
Electroosmosis Streaming potential
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Electroosmosis cell
• Helmholtz-Smoluchowski eq. is valid because there is also displacement of one part of the double layer relative to the other.
• The condition is applicable to capillaries of macroscopic radius of curvature .
• This eq. does not depend on the shape of particles and can be applied to cylindrical capillaries.
• The volume of liquid displaced per unit time is the velocity of the liquid x cross-sectional area:
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Ohm’s law
where
because resistance per unit lenghtbeing the conductivity
then:
Zeta potential may be evaluated from measurements of the rate of volume flow through the capillary
Effect of surface conductivity on electroosmosis
The current carried by the ions in the double layer mustbe added to the bulk current
Then
because is the cross area of the capilary andis the perimeter, while and are the bulk and thesurface conductivities.
Thus and
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Streaming potential
Potentiometer
• The velocity of the fluid at radius in a capillary of radius and lenght is:
• The volume flow rate through na elemental area
• The current associated with this flow rate is:
where is the charge density
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• Now we make a change of variable
• Near the capillary wall
• Substituting the charge density by
• The total current is obtained by integrating by parts:
since at and at
is the streaming current which is due to the displacement of the mobile part of the double layer relative to the stationary part
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• The field associated with this current is:
• Multiplying both sides by the capillary lenght , the potential difference between the two measuring electrodes is the streaming potential:
• In the limit of large , the two electrokinetic ratiosbecome equal:
streaming electroosmosis
Flow profiles in a capillary tube
• Streaming potential – solution moves due to an applied pressure and a potential is induced
• Electroosmosis – the applied electric field causes the counterions of the double layer to move and they carry the solution. A stationary state occurs when =
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• Electrophoresis – a moving charged particle in a fixed solvent. The closed capillary causes a return flow with maximum velocity in the center which added to electroosmosis flow leads to a parabolic distribution.True electrophoretic velocity must be measured at 0.71 R.
Comparison of zeta potentials from different methods
• The effects of relaxation and surface conductivity must be either negligible or taken into account
• The surface of shear must divide comparable double layers
• Electroosmosis and streaming potentials are comparable in what concerns the second limitation
• Electrophoresis is more difficult because it deals with particle surfaces not capillaries. Coating with protein may be a solution
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Applications
• Electrophoresis is used to investigate systems where colloid stability is involved ( clay suspensions, water purification, paper making), to determine the surface charge of organisms like bacteria, viruses and blood cells, and, in biochemistry, to characterize or fractionate mixtures of macro-ions, such a proteins.
• Electroosmosis can be used to remove pollutants from contaminated soils.
• Streaming potentials should be prevented in the transport of apolar liquids, for example oil in pipelines.
