PowerPoint Presentation 1 Dr Ngo Thanh An Email ngothanhan@gmail com COLLOID CHEMISTRY Chapter 3 – Effect of curvature 1 Effect of radius on equilibrium Assume a droplet in vapor, using Young Laplace[.]
Trang 1Dr Ngo Thanh An Email: ngothanhan@gmail.com
COLLOID CHEMISTRY Chapter 3 – Effect of curvature
Trang 81 Effect of radius on equilibrium
Assume a droplet in vapor, using Young-Laplace equation:
In general,
P Pl Pv
VdP SdT
l l
l
v v
v
At equilibrium, we have conditions: dG(L)= dG(V)
l l
l v
l l
v v
l v
dP V
dT S
dP V
dP V
dT S
S
Assuming Pv = const,
Trang 91 Effect of radius on equilibrium
V
dT
S
P d P P dP d
T T l
l v T
T l
v l
v l
o o
dT V
S dT
V
S d
P P
P
0
l v
l
S
V
T o
dT
0
Gibbs – Thomson coefficient
Trang 101 Effect of radius on equilibrium
T
For a sphere
r
Change to equilibrium as a function of radius expressed as an undercooling Thus during nucleation, the phase diagram is altered The actual equilibrium point is lower than that shown on the phase diagram due to curvature There is always undercooling during homogeneous nucleation!!!
Trang 11v V
G
3
4
4
G: overall excess free energy between a small solid particle of solute and the solute in the solution
GS: excess free energy between the surface of the particle and the bulk of the particle
GV: volume excess free energy: the excess free energy between a very large particle (r = ) and the solute in the solution
Gv: free energy change of the transformation per unit volume
GS: a positive quantity: (enlargement of area need supplying work, that means, work is negative dG = - dA > 0)
GV: a negative quantity: (increase of volume generate work, that means, work is positive dG = - dA < 0)
: interfacial tension between the developing crystalline surface and the supersaturated in which it is located
2 Nucleation
Trang 120 4
v
G r
r dr
G
v
c
G
r
2
4 3
2
3
c v
G
2 Nucleation
Trang 13p p
vapour
p v
RT P
d v
RT dP
v
G
o
'
ln ln
'
Mw
volume
2
3 2
] ln [
3
16
S RT
v
Gc
S RT
M
p
p RT
v G
r
w
o v
c
ln 2
ln
2
2
'
2 Nucleation
Trang 143 Droplet in gas
Convention
Symbol “: is use to denote the phase on the concave side of a
meniscus
Symbol ‘: is use to denote the phase on the convex side of a
meniscus
Thus, for a droplet in a gas, symbol “ is for the liquid and ‘ for the gas
For a droplet in gas, the centre is inside the liquid phase this is the convex meniscus?
-Concave meniscus (r < 0): the centre is outside of the liquid phase?????
Convex meniscus (r > 0): the centre is inside of the liquid phase????
r
2
= P' P"
=
Pressure
Trang 153 Droplet in gas
r
d r
d dP
dP P
Phase condition:
'
" d G G
d
surface flat
a
an droplet th a
for higher is
pressure vapor
m equilibriu and
'
"
2 '
ln
o
o
P P
RTr
V P
P
Pressure
Trang 163 Droplet in gas
Kelvin Equation
ln P'
Po 2 V"
RTr
All droplets are of uniform radius, r*, pressure is P' ,
Is this system stable?
Implication of Kelvin Equation:
1 In a mist containing various droplet
sizes, large droplets will grow at the expense of small and average
droplet size will increase with time
Ostwald Ripening.
2 A droplet in equilibrium with its
vapor is unstable.
Pressure
Trang 173 Droplet in gas
Temperature
"
"
"
' '
'
"
'
dP V
dT S
dP V
dT
S
dG
dG
S' S" dT V " dP " 0
r
d dP
dP
dP " ' " 2
0
2
"
1 1
0 1
T
T
r r
r
vap
r H
V T
T
vap
o
"
2
S"
S' where
Assume P’ = const
T < To
Trang 184 Bubble in liquid
Pressure
o
o
P P
RTr
V P
P
gas the
is as
P
d V
RT dP
V
V dP
V
V
V r
d
"
' 2
"
ln
"
"
ln '
"
'
'
"
'
'
"
2
Trang 194 Bubble in liquid
Temperature
0 '
2 ln
0
2 2
'
2
"
;
2 '
"
;
"
"
, 0
"
"
1 1
0 1 2
1 1
0 1 2
r r
r
T T
T T
r r
r
T T
T T
P r
d R
dT T
H
r
d r P
R dT
T H
r
d dP
r
P
P P
RT V
dP V
dT T
H
o
o
Trang 20exist to
bubbles for
'
'
2 ln 0
o
o
T T
P
P r
H
R TT
T T
4 Bubble in liquid
Temperature