Gibbs Adsorption Isotherm - PowerPoint PPT Presentation

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Gibb's Adsorption Isotherm. x0. ?A. P. Area left of x0: represents underestimated value of Pi ... A Property, P, of system vary across the interface (of ... – PowerPoint PPT presentation

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1
2
SURFACE EXCESS
A
A
?A
Interface
S
?B
B
B
x0
x
PB
PA
P
P
Pi
PA
PB
x0
x0
x
x
A Property, P, of system vary across the
interface (of thickness S) from that of phase A
and B If Pi is the value of the Property P at
the ideal border of the interface, then
• Area left of x0 represents underestimated value
of Pi
• Area right of x0 represents overestimated value
of Pi

3
SURFACE EXCESS (Cont.)
• X0 - may be selected such that two shaded areas
are equal
• -may divide the profiles of other
properties differently
• Property which is least convenient to handle
mathematically can be eliminated by selecting its
surface excess to be zero.
• Note - dividing surface only a Reference Level
rather than a physical boundary.
• - Surface excess can be positive or
negative.

4
• Amount of surfactant adsorbed per unit area can
be calculated from surface or interfacial tension
measurements
• Where, d? change in surface tension
• ?i surface excess concentration of
i
• dmi change in chemical potential of
i
• At equilibrium
• where ai activity of i in bulk phase
• mole fraction x activity
coefficient

5
• Therefore
• For dilute solutions containing one
non-dissociating surfactant
• Where C molar concentration of surfactant in
bulk
• At constant temperature
• Surface excess given by slope of plot of g versus
log C
• Knowing ?, area per molecule at the interface can
be calculated.

6
AREA PER MOLECULE AT THE INTERFACE
• Important in assessing
• Degree of packing
• a area per molecule (in Å2) at interface, given
by
• ? Surface excess in moles/m2

1 x 1020 N ?
a
7