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Surface and Interface Chemistry

Thermodynamics of Surfaces
(LG and LL Interfaces)
Valentim M. B. Nunes
Engineering Unit of IPT
2014
Adsorption in liquid surfaces
Certain materials, such as fatty acids or alcohols, are soluble in
water or in (e.g.) hydrocarbons. The nonpolar part is responsible
for the solubility in "oil" and the polar part (-OH or -COOH) by
solubility in water (Intermolecular forces).
C2H5COOH
C3H7COOH
C4H9COOH
Hydrophilic part
Hydrophobic part
Adsorption of molecules occurs (surfactants) in water-oil or
water-air interfaces.
ar
The solutes that decrease the surface tension of a solvent are
positively adsorbed in the interface, and the surface layers are
enriched of solute.
The solutes that increase surface tension tend to stay within the
solution (e.g. Ionic salts) and are adsorbed negatively in the
interface.
The adsorption on solutions does not conduct in general to more
than monolayers. The molecules that have a pronounced effect
on surface tension are designated surfactants or surfactants.
If the surface tension between two liquids is sufficiently reduced
by the addition of surfactants it may form micro emulsions.
GIBBS ADSORPTION ISOTHERM.
The thermodynamic treatment of
Gibbs allows the estimation of the
adsorption on a liquid surface from
the surface tension.
Since the interface is a material
system, with a given volume, they
thermodynamic properties can be
calculated.
Let us consider a binary mixture containing ni moles of each
component, and two homogeneous phases α and β, separated
by an arbitrarily located interface.



ni
i 
A

Surface excess concentration.
From the laws of Thermodynamics:
U   TS   pV   A   i ni
i
dU   TdS   S  dT  pdV   V  dp  dA  Ad   i dni   ni di
i
The combination of the 1st and 2nd laws gives:
dU   TdS   pdV   dA   i dni
i
S  dT  V  dp  Ad   ni di  0
i
i
At constant p and T, we have:
ni
d   di   i di
A
For a binary mixture (solvent + solute):
d  Ad A  B dB
Considering A = 0,
d  B dB
Introducing the chemical potential,
 B    RT ln aB
d B  RTd ln aB

B
We finally obtain:
And for dilute solutions:
1 
B  
RT  ln aB
cB 
B  
RT cB
Gibbs Isotherm
cB 
B  
RT cB
1
AB 
B ,máx  N A
Monolayers
Pockels and Rayleigh (1899): some poorly soluble substances
spread on the surface to form films with thickness of a molecule
 monolayers
This superficial film causes a lowering of the surface tension. It is
determined by measuring the force, f, exerted in a calculated
barrier to separate the region with film of the pure liquid.
gas
liquid + film
liquid
f      
0
Considering now,
    kc
0
kc   


RT
RT
0
Designating the difference of surface tensions 0 -  by superficial
pressure, , so that  = 0 - , we obtain:
ni


A RT
Rearranging:
A  ni RT
Dividing both members of equation by the Avogadro constant:
Am  k BT
The isothermal for the monolayer has the meaning of an
equation of state (note the similarity to the equation of State of a
perfect gas: pV = nRT)
The type of isotherms (,Am) depends on the compounds
structure.
Materials with large surface
activity tend to form micelles.
The concentration from which
the micelles are formed is called
critical micelle concentration
(c.m.c.)


~0
c
c.m.c.
concentration
Surfactants forming micelles exhibit a solubility increase above a
certain temperature – kraft point. This is due to the high
solubility of the micelles. At temperatures below kraft point, the
solubility of the surfactant is insufficient to form micelles.
Kraft points for sodium alkyl sulfates
Nº de átomos de carbono
10
12
14
16
18
Temperatura kraft / ºC
8
16
30
45
56
Spreading
The work or energy of adhesion between two immiscible liquids
is equal to the work necessary to separate a unit area of the
liquid/liquid interface. By the Dupré equation:
Wa         
For the cohesion work:
Wc  2 
Let us consider a drop of oil over water:
AW
OA
oil
air
water
OW
We define the initial spreading coefficient in the following way:
S   WA   OA   OW 
The spreading occurs if S  0. Replacing in the Dupré equation
we obtain:
S  WOW  Wóleo
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