Journal of Engineering Science and Technology Review 1 (2008) 100-150
Journal of Engineering Science and Technology Review 1 (2008) 100-150
Journal of Engineering Science and Technology Review 1 (2008) 100-150
JJ
estr
estr
estr
Journal of Engineering Science and Technology Review 1 (2008) 1-3
Journal of Engineering Science and Technology Review 1 (2008) 1-3
Journal of Engineering
Science
and Technology Review 1 (2008) 1-3
Lecture
Note
Lecture Note
Lecture Note
What is a surface excess?
What is a surface excess?
What
is a surface excess?
A.
Ch. Mitropoulos*
JOURNAL OF
JOURNAL
OF Science and
Engineering
Engineering
Science
JOURNAL
OF and
Technology
Review
Technology
ReviewScience and
Engineering
Technology
Review
www.jestr.org
www.jestr.org
www.jestr.org
A. Ch. Mitropoulos*
A. Ch.
Mitropoulos*
Department of Petroleum Technology, Cavala
Institute
of Technology, St. Lucas 65 404 Cavala.
Department of Petroleum Technology, Kavala Institute of Technology, St. Lucas 65 404 Kavala.
19Technology,
October 2007;
Accepted
14 January
2008 St. Lucas 65 404 Kavala.
Department ofReceived
Petroleum
Kavala
Institute
of Technology,
Received 19 October 2007; Accepted 14 January 2008
_______________________________________________________________________________________________
_______________________________________________________________________________________________
Received 19 October 2007; Accepted 14 January 2008
_______________________________________________________________________________________________
Abstract
Abstract
Abstract
J. Willard
Gibbs in his pioneering work on the influence of surfaces discontinuity upon the equilibrium of heterogeneJ.ous
Willard
Gibbs
in his pioneering
work on the
of surfaces
discontinuity
upon the
equilibrium
heterogenemasses
suggested
for the measurement
of influence
the quantities
of a system
a geometrical
surface
dividingofthe
interfacial
ous
masses
suggested
for
the
measurement
of
the
quantities
of
a
system
a
geometrical
surface
dividing
the
interfacial
J.
Willard
Gibbs
in
his
pioneering
work
on
the
influence
of
surfaces
discontinuity
upon
the
equilibrium
of
heterogenelayer. Surface excess is the difference between the amount of a component actually present in the system,
and
that
layer.
Surface
excess
is
the
difference
between
the
amount
of
a
component
actually
present
in
the
system,
and
that
ous
masses
suggested
for
the
measurement
of
the
quantities
of
a
system
a
geometrical
surface
dividing
the
interfacial
which would be present in a reference system if the bulk concentration in the adjoining phases were maintained up
to
which
wouldSurface
be
present
in
a is
reference
system between
if position
the bulk
concentration
the adjoining
phases
were maintained
up to
layer.
excess
the determined
difference
thedividing
amountsurface.
of a incomponent
actually
present
in the system,
and that
the arbitrary
chosen
but
precisely
in
the arbitrary
butpresent
precisely
position
dividing
surface.
which chosen
would be
in determined
a reference in
system
if the
bulk concentration
in the adjoining phases were maintained up to
the
arbitrary
chosen
but
precisely
determined
in
position
dividing
surface.
Keywords: surface excess, Gibbs adsorption.
Keywords:
surface excess, Gibbs adsorption.
_______________________________________________________________________________________________
_______________________________________________________________________________________________
Keywords: surface excess, Gibbs adsorption.
_______________________________________________________________________________________________
volumes Vα α+Vβ β=V each one assumed to contain CαiαVα α=nαiα and
Adsorption of a component at the phase boundary of a system
β +V =V each αone assumed
to contain
Ci V =ni inand
volumes
Adsorption
of
a
component
at
the
phase
boundary
of
a
system
moles αwithβ Cαi and Cβiβ the bulk
concentrations
the α
CβiβVβ β=nβiV
results to a different concentration in the interfacial layer than
α α
V
=n
moles
with
C
and
C
the
bulk
concentrations
C
results
to
a
different
concentration
in
the
interfacial
layer
than
+V
=V
each
one
assumed
to
contain
Cin
=ni and
volumes
V
Adsorption
of
a
component
at
the
phase
boundary
of
a
system
i
i
i
i
i Vthe
real system
[5],
respectively.
More
formally:
that in the adjoining bulk phases. The adsorbate density and
β β
β
α
β
real
system
[5],
respectively.
More
formally:
that
in
the
adjoining
bulk
phases.
The
adsorbate
density
and
V
=n
moles
with
C
and
C
the
bulk
concentrations
in the
C
results
to
a
different
concentration
in
the
interfacial
layer
than
i
i
i
i
composition profiles within that layer cannot be measured by
composition
within
thatamounts
layer
cannot
measured
by and
real system [5], respectively. More formally:
that
inprofiles
the adjoining
bulk
phases.
The be
adsorbate
density
today’s
technology;
the
actual
adsorbed
are not meantoday’s
technology;profiles
the
actual
amounts
adsorbed
are not
meanwithin
layerthis
cannot
be measured
ingfulcomposition
experimental
variables.
To that
resolve
problem
Gibbs by
ingful
experimental
variables.
To
resolve
this
problem
Gibbs
today’s
technology;
the
actual
amounts
adsorbed
are
not mean[1] suggested that: “…it will be convenient to be able to refer
[1]
that: surface,
“…it will
be convenient
to bethis
ablecoincident
to refer Gibbs
ingful experimental
variables.
To be
resolve
problem
to suggested
a geometrical
which
shall
sensibly
towith
a geometrical
which
shall
be sensibly
[1]
that: “…it
be convenient
tocoincident
be have
able toa refer
the suggested
physicalsurface,
surface
of will
discontinuity,
but shall
with
the
physical
surface
of
discontinuity,
but
shall
have
a
to
a
geometrical
surface,
which
shall
be
sensibly
coincident
precisely determined position. For this end, let us take some
precisely
determined
Forofthis
end, letofus
takeshall
somehave a
the
discontinuity,
but
point with
in or
veryphysical
nearposition.
to surface
the physical
surface
discontinuity,
point
in
or very
near to the position.
physical
surface
ofend,
discontinuity,
precisely
thisthrough
letthis
us point
take some
and imagine
a determined
geometrical
surface toFor
pass
and
imagine
a
geometrical
surface
to
pass
through
this
point
point
in
or
very
near
to
the
physical
surface
of
discontinuity,
and all other points which are similar situated with respect to
and
other
points
are matter.
similar
situated
withthrough
respectthis
to point
and
imagine
geometrical
surface
to pass
the all
condition
of theawhich
adjacent
Let
this
geometrical
surthe
condition
of
the
adjacent
matter.
Let
this
geometrical
surand
all
other
points
which
are
similar
situated
with
respect
to
face be called the dividing surface.”
face be
called
the
dividing
surface.”
the
condition
of
the
adjacent
matter.
Let
this
geometrical
surSurface excess [2] is the difference between the amount of
Surface
[2]
the difference
betweenand
the amount
of
face beexcess
called
theispresent
dividing
a component
actually
insurface.”
the system,
that which
awould
component
actually
present
in
the
system,
and
that
which
Surface
excess
[2]
is
the
difference
between
the
amount
be present in a reference system if the bulk concentra- of
would
be
present
in actually
a reference
system
bulk
concentraa
component
in ifthethesystem,
and
that which
tion in the
adjoining
phases present
were
maintained
up to
a chosen
tion
inwould
the adjoining
phases
were
upthe
to
a interface
chosen
be
present
in a reference
if
concentrageometrical
dividing
surface
[3]; maintained
i.e. system
as though
thebulk
geometrical
surfacephases
[3]; i.e.
as maintained
though the up
interface
individing
the
adjoining
were
to a chosen
had notion
effect.
Schematically:
had nogeometrical
effect. Schematically:
dividing surface [3]; i.e. as though the interface
had
no
effect.
]surface==[n[ni]]real−Schematically:
(1)
− [n i ]reference .
Figure 1. Concentration profiles of a binary system as a function of dis[n[ni i]surface
[ni ]reference .
(1)
Figure
1. Concentration
of aBold
binary
system
as ainfunction
of disi real
tance normal
to the phaseprofiles
boundary.
curved
lines,
both frames,
are
normal
theConcentration
phase boundary.
Boldand
curved
lines,
ininboth
are of dis[ni ]surface =σ[ni ]real − [ni ]reference .
(1)tance
the concentration
profiles
of theprofiles
solute
solvent
the
real
system,
Figureto 1.
of
athe
binary
system
asframes,
a function
where [ni]surface=nσi is the surface excess amount [4] of compo- the
concentration
profiles
of
the
solute
and
the
solvent
in
the
real
system,
respectively,
and again
vertical
lines
are curved
the concentrations
the are
tance normal
to the
phase broken
boundary.
Bold
lines, in bothinframes,
=ni is the surface excess amount [4] of compowhere
[ni][n
surface
respectively,
and again
broken
lines
thethe
concentrations
the
nent (i);
i]real=ni is theσ total amount of that component in the
reference
(beingvertical
actually
thethe
extend
ofand
the
bulk
concentrations
upsystem,
the system
concentration
profiles
of
soluteare
solvent
in theinreal
a
β
=n
amount
that component
thecomponent
[ni]real[nand
=ni total
is =n
the
surfaceofexcess
amount [4]inof
where
i is
reference
systemsurface).
(being
the extend
of
the
i]surface
to the dividing
Chainvertical
dotted
lines
indicate
theconcentrations
boundaries
of up
the in the
real (i);
system;
[nthe
respectively,
and actually
again
broken
linesbulk
are
the
concentrations
i]reference
ai +nβi is the amount of the same
tointerfacial
the dividing
surface).
Chain
indicate
thethe
boundaries
the
]=n
+n
the amount
theequal
sametoin the
real
system;
and
]arealireference
theisystem
total
amount
of
thatofcomponent
nent (i);
[n
reference
i is
layer.
Bold horizontal
linelines
isthethe
dividing
surface
and ofdotted
i is =n
reference
system
(beingdotted
actually
extend
of
bulk concentrations
up
component
(i)
ini[n
having
volume
V
a
β
interfacial
layer.
Bold
horizontal
line
is
the
dividing
surface
and
dotted of the
component
(i)
in
a
reference
system
having
volume
V
equal
to
horizontal
line
is
another
choice
for
the
location
of
the
dividing
surface.
to
the
dividing
surface).
Chain
dotted
lines
indicate
the
boundaries
]
=n
+n
is
the
amount
of
the
same
real
system;
and
[n
i reference byi a hypothetical
i
the real system which is divided
surface into horizontal line is another choice for the location of the dividing surface.
surface
excess
is the
sumhorizontal
of the shaded
above and
underand
the dotted
interfacial
layer.
Bold
line isareas
the dividing
surface
the realcomponent
system which
bysystem
a hypothetical
surface V
into
(i) inisadivided
reference
having volume
equal The
toThesurface
excessline
is the
sum inofchoice
the case
shaded
areas
aboveof
and
under
the
dividing
surface.
Notice
that
the
ofthe
the
solvent
by
choosing
thesurface.
horizontal
is
another
for
location
the
dividing
the real system which is divided by a hypothetical surface into
______________
dividing surface. Notice that in the case of the solvent by choosing the
upper dividing
surface
(a suitable
one)of
thethe
resulted
is zero,
The surface
excess
is the sum
shadedsurface
areas excess
above and
under the
upper
dividing
surface
(a Notice
suitable
one)
excessbyis choosing
zero,
whereas
by choosing
the
lower one
surface
excess
not zero.
dividing
surface.
that
inthe
theresulted
case ofissurface
the
solvent
the
whereasupper
by choosing
lower (a
onesuitable
surfaceone)
excess
not zero.
dividingthesurface
theisresulted
surface excess is zero,
______________
* E-mail address: [email protected]
* E-mail
address:
ISSN:
1791-2377
© [email protected]
2008 Kavala Institute of Technology. All rights reserved.
______________
ISSN: 1791-2377
©
2008
[email protected]
Institute of Technology. All rights reserved.
* E-mail
address:
ISSN: 1791-2377 © 2008 Kavala Institute of Technology. All rights reserved.
whereas by choosing the lower one surface excess is not zero.
1
1
11
A. Ch. Mitropoulos/ Journal of Engineering Science and Technology Review 1 (2008) 1-3
A. Ch. Mitropoulos/ Journal of Engineering Science and Technology Review 1 (2008) 1-3
A. Ch. Mitropoulos/ Journal of Engineering Science and Technology Review 1 (2008) 1-3
niσσ = ni − C iaaV aa − C iββ V ββ .
ni = ni − C i V − C i V .
A fundamental equation for surfaces of discontinuity befundamental
equation
surfaces ofisdiscontinuity
betweenA fluid
masses at
constantfortemperature
given by Gibbs
tween
temperature
is given by Gibbs
having,fluid
in themasses
case ofataconstant
binary system,
the form:
having, in the case of a binary system, the form:
(2)
(2)
If As is the area of the interface [6], the areal surface excess
of defined
the interface
If As is the area
as: [6], the areal surface excess
concentration
Γiσ is
concentration Γiσ is defined as:
niσσ
Γiσσ = ni .
Γi = As .
As
dσ = −Γ1σσ dμι − Γ2σσ dμ 2 .
dσ = −Γ1 dμι − Γ2 dμ 2 .
(3)
(3)
(6)
(6)
where σ is the surface tension, and μ1 and μ2 are the chemical
and μ2 are
chemical
where σ isofthethesurface
tension,
andBy
μ1deciding
potentials
adjacent
phases.
to the
choose
a diσ phases. By deciding to choose a dipotentials
of
the
adjacent
viding surface such as Γ1σ=0, eq.(6) takes the form:
viding surface such as Γ1 =0, eq.(6) takes the form:
In a binary system, where (1) is e.g. the solvent and (2) is
In a binary
where (1)
is e.g. the
solvent
and divid(2) is
the solute
and bysystem,
(΄) is denoted
a second
choice
for the
the surface
solute and
(΄) is can
denoted
a second
ing
(seebyFig.1),
be easily
shownchoice
that: for the dividing surface (see Fig.1), can be easily shown that:
dσ = −Γ211 dμ 2 .
dσ = −Γ2 dμ 2 .
(7)
(7)
According to this equation [9] for a system involving a solvent
According
to there
this equation
[9] for
a system
involving aofsolvent
and a solute,
is an excess
surface
concentration
solute
(4)
and
a solute,
there is anthe
excess
surface
concentration
of solute
if
the
solute
decreases
surface
tension
and
a
deficient
sur(4)
if
theconcentration
solute decreases
the surface
and a deficient
surface
of solute
if the tension
solute increases
the surface
face
concentration of solute if the solute increases the surface
tension.
tension.
Since the location of the dividing surface was arbitrary chosen,
Direct measurements of surface excess quantities were
Since
the location
of can
the dividing
chosen,
Direct
measurements
of surface
excess[10]
quantities
werea
the above
equation
only be surface
true if was
eacharbitrary
side separately
carried
out by
several investigators.
McBain
constructed
the
above
equation
berelative
true if adsorption
each side of
separately
carried
out by
several
investigators.
McBain
[10]
constructed
equals
a constant
[7];can
thatonly
is, the
compomicrotome
device
consisted
of
a
sharp
blade,
Salley
et
al.
[11]a
equals
a constant
[7]; that
the relative(1):
adsorption
of compo-a
microtome
device
consisted
of a sharp
blade, is
Salley
et al.
[11]a
nent (2)
with respect
to is,
component
Γ211. Obviously,
developed
a
tracer
method
where
the
solute
labeled
with
Obviously,
a
nent (2) with
respectoftoΓ12component
(1):
Γ2 . way
developed
a
tracer
method
where
the
solute
is
labeled
with
exists
too
[8].
One
to
detersymmetric
definition
radioisotope, and Smith [12] studied the ellipticity of lighta
toothe
[8].
One way
to detersymmetric
definition Γof21 Γis12 toexists
radioisotope,
[12]ofstudied
the ellipticity
of light
mine
experimentally
locate
dividing
surface
at
a
reflection fromand
theSmith
thickness
an adsorbed
film on mercury.
1
mine
experimentally
to locate
the dividing
surface atthea
reflection
from
the thickness
of an
adsorbed
on mercury.
reference
system contains
position
where Γ1σσ=0;Γ2i.e.is the
Application
of Gibbs
adsorption
isotherm
onfilm
electrolyte
solu=0; i.e. the(1)reference
system
the
position
whereofΓ1component
Application
of Gibbs
adsorption
isotherm on electrolyte solusame
amount
as the real
one. contains
In this case
tion
was
introduced
by
Wagner
[13].
same
(1) as the
one. where
In thistocase
tion was
introduced
Wagner [13].
is real
not clear
loeq.(4) amount
reduces of
to component
Γ211=Γ2σσ. If however
In this
note an by
elementary
review on the concept of sur1however is not clear where to lo=Γ
.
If
eq.(4)
reduces
to
Γ
2
2
this was
note given.
an elementary
review out,
on the
concept
of even
surcate the dividing surface, Γ21 may still be calculated by rearface In
excess
It must pointed
however,
that
may
still
be
calculated
by
rearcate
the
dividing
surface,
Γ
2
face
excess
was
given.
It
must
pointed
out,
however,
that
even
ranging eq.(4) such as:
in the frame of formal surface thermodynamics the characterisranging eq.(4) such as:
in
frame ofinvolved
formal surface
thermodynamics
the characteristic the
quantities
need further
specification
in order to
β
a
tic
quantities
involved
need
further
specification
in order for
to
a
a
became
operational
and
again
need
different
specification
n 2 − C 2a V n1 − C1aV C 2a − C 2β
1
became
operational
and
again
need
different
specification
for
(5)
Γ21 = n 2 − C 2 V − n1 − C1 V × C 2a − C 2β .
each different type of interface (e.g. sold/gas [14], etc).
(5)
Γ2 =
−
× C1a − C1β .
As
As
each different type of interface (e.g. sold/gas [14], etc).
As
As
C1 − C1
Acknowledgments: The author would like to thank Archimedes
Acknowledgments:
The
author would
to thank
Archimedes
The quantities on the right hand side of eq.(5) are all directly
research Project and
INTERREG
III like
“Hybrid
Technology
for
The
quantities
on
the
right
hand
side
of
eq.(5)
are
all
directly
research
Project
and
INTERREG
III
“Hybrid
Technology
for
measurable, provided that As is known.
Separation” for funding this work
measurable, provided that As is known.
Separation” for funding this work
______________________________
______________________________
References and Notes
References and Notes
⎡ C 2a
⎡⎢ C a
Γ2 − Γ1 ⎢⎣ C12aa
⎢⎣ C1
Γ2σσ
− Γ1σσ
− C 2ββ
− C 2β
− C1β
− C1
⎤
⎡C a
⎤⎥ = Γ2′σσ − Γ1′σσ ⎡⎢ C 22a
⎥⎦ = Γ2′ − Γ1′ ⎢⎣ C1aa
⎥⎦
⎢⎣ C1
− C 2ββ
− C 2β
− C1β
− C1
⎤
⎤⎥ .
⎥⎦ .
⎥⎦
5.
5.
6.
6.
For liquid/vapour interfaces, at low vapor pressures, Ciβ, where β is
For
liquid/vapour
at low vapor pressures, Ciβ, where β is
the gaseous
phase, interfaces,
may be neglected.
the
gaseous
may be
neglected.
Interface
is phase,
the plane
ideally
marking the boundary between two
Interface
is the plane
ideally
between
phases. Interphase,
however,
is amarking
differentthe
termboundary
which refers
to thetwo
inphases.
however,
is a different term
refers
to the interfacialInterphase,
layer; being
the inhomogeneous
spacewhich
region
intermediate
terfacial
layer;
being
the ininhomogeneous
spaceproperties
region intermediate
between two
bulk
phases
contact, and where
are signifibetween
two bulk
phases
in contact,
andproperties
where properties
are phases.
significantly different
from,
but related
to, the
of the bulk
cantly different
from, but
to, the properties
When
the interfacial
layerrelated
is regarded
as a phaseofitthe
is bulk
calledphases.
interWhen
interfacial
is regarded as a phase it is called interphase; the
IUPAC:
58, 439layer
(1986).
1
58, 439 (1986).
7. phase;
Since ΓIUPAC:
form the location of the dividing surface it is
2 is independent
7. possible
Since Γ21tois dispense
independent
the location
of the dividing
it is
the form
geometric
interpretation
of excesssurface
quantities
possible
to dispense
the geometric
interpretation
of excess
quantities
and formulate
a suitable
algebraic method;
i.e. without
explicit
referand
a suitable
algebraic
i.e. and
without
explicit
referenceformulate
to a dividing
surface.
For bothmethod;
geometric
algebraic
methods
ence
to a dividing
surface.
For both geometric
algebraic
methods
see: Ref.2;
R.S.Hansen,
J.Phys.Chem.
66, 410 and
(1962);
F.C.Goodrich,
see:
Ref.2;
R.S.Hansen,
410 (1962);inF.C.Goodrich,
Trans.
Faraday
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