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organic) media
Advances in Colloid and Interface Science, 42 (1992) 279-302 Elsevier Science Publishers B.V., Amsterdam
279
00133 A
DISPERSION
STABILITY
IN MIXED Brian
School
of Chemistry,
Paper
dedicated
Leverhulme
University
to Prof.
Chair
SOLVENT
of Physical
MEDIA
Vincent
of Bristol,
R .H.
(AQUEOUS/ORGANIC)
Bristol
Ottewill
F. R .S.,
Chemistry
at the
BS8
lTS,
U.K.
on his retirement University
from
the
of Bristol.
CONTENTS 1.
Introduction
280
2.
Experimental
280
3.
4.
5.
6.
280
2.1
Materials
2.2
Coagulation
2.3
Electrophoretic
281
Kinetics
281
Mobilities
282
Theoretical 3.1
Coagulation
3.2
Critical
3.3
Zeta
Rate
Constants
Coagulation
Potentials
from
Optical
Concentrations
from
Electrophoretic
from
Density Rate
282
Data
Constant
Data
287
Mobilities
287
Results 4.1
Rapid
4.2
Critical
4.3
Mobilities
Coagulation
Rate
Coagulation and
Zeta
287
Constants
289
Concentrations
291
Potentials
294
Discussion 5.1
Rapid
5.2
Critical
Coagulation
Rate
Coagulation
294
Constants
Concentrations
and
Zeta
295
Potentials
300
Conclusions
ABSTRACT The potentials
285
dependence
of critical
on composition
and
urea/water
are
also
mixtures
coagulation
for
polystyrene
are
compared.
concentrations latex
particles
Similar
data
and
zeta
in n-alkanollwater
from
other
authors
reviewed.
OOOl-8686/92/$15.00 0 1992 -
Elsevier Science Publishers B.V. All rights reserved.
280 INTRODUCTION
1.
Recently
Okubo
crystalline
arrays
water/organic and
of
concentration.
2.5
% methanol,
that
these
it
mixtures, the
in
electrical
turn
to
in
with
at
the
in
for
the
electrostatic
indicated,
although
10,
5 and
Okubo
suggested between
Debye
screening
the
alkanollwater
of
repulsion no
ethanol increasing
repulsion
the
each
of
(de-ionised)
with
around
electrostatic
changes
(Cl
methanol,
respectively.
Hence,
that
concentration
modulus
a maximum
occurred
in
elastic
dispersed
that,
through
maxima
related
the
particles
propan-l-01,
layers.
suggested
on
showed
G went
changes
double
is
alkanol
of
These
reflect
which
the
value
He
ethanol,
results
particles, of
latex
mixtures.
the
alkanol
a paper
polystyrene
solvent
propan-l-01,
mol
[l J published
the
length
is a maximum
fundamental
reason
at is
given. These Ron found
that
phoretic of
results
Ottewillls both
mol
indicated In
more
seems
of
This
discussed
2. 2.1
work,
more
(critical
latex of
went
three
out
in
[21.
Basically,
from
microelectro-
coagulation
particles the
I carried
work
determined
stability
Ottewill
has
dispersions, in
therefore,
recent and
observed
we
concentration
through
a maximum
n-alkanol/water
at
mixtures
as
aspect to
in
see
the
of if
the
particularly
of
this
his
there
various
considered
properties latex
commorative
work
with
could
be
properties
particles.
issue,
the
older
the
to
It bring
work
a common of
of
on
explanation
latices
as
and
stability
for
a function
concentration. paper
experiments
water
the
work
Ph.D.
Okubo.
dispersions,
alkanol
and
my
(< 1, as
polystyrene
appropriate,
maxima
of
% concentrations by
this
experimental
part
potential-
structured
very
together
the
zeta
of
recent
concentrated,
dilute
the
cc)
similar
those
some as
measurements,
electrolyte
very
recalled
laboratory,
therefore
referred above,
mixtures.
describes
to. data
A
In
are
also
survey
of
the
addition
electrophoretic to
reported other
work
the for
three
alkanol/water
mixtures,
butan-l-al/water
in
the
field
and
is also
urea/
given.
EXPERIMENTAL Materials Water,
described
methanol, in
a previous
ethanol, paper
propan-1-01 131.
Urea
and
butan-l-01
was
Hopkins
were and
purified
Williams
as
287 “AnalaR”
grade.
Barium
recrystallised
from
Two
polystyrene [4,51.
were
carboxylic
acid
groups.
(A,
mean
and
wetting
same
latex
few
stability by
Coaqulation The
rate
change
Most
in
mean
of
coagulation
optical
Unicam
SP600
spectrophotometer
density
10’
cms3).
latex
housing.
chart of
The
pH to
and
above
curves
in be
these
2.3
Electrophoretic
of ing
the
in
the
with
the
the addition.
a
prepared
by
give
determining
perchlorate
h. of
the
to
particle
adjusted
546.1
nm,
automatic
instrument
the
solution. using
a
recording was
of
thermostatted
to
8.1
(V)
V
is
required
in
optical
all
cases. placed
of
to
an
concentra-
fixed
cell
(adjusted
means
alkanol
concentration
+ 0.1
by
added
the
number
(6
3 cm3 in
the
the
same
added-mixer
x
of
the
cell alkanol
device
161,
housing. from
the
recorded of
as
optical The
derived.
described
spectrophotometer a function
density
(D)
calculation
of
in
the
was
of
time
of
the
By
(t).
to
rate
Section
a pen
calibration
dispersion,
coagulation
Theoretical
fed
D(t) constants
below.
Mobilities mobilities
horizontal lines
microscope.
across
studied barium
to of
adjusted
the
apparatus,
vertical
modified housing
was
terms
curves
the
ISI.
nm)
a wavelength.
solution
cell
Electrophoretic
viewed
in In
51
was
perchlorate
output
from
electrophoresis
used [3]. latex
adding
length
and
scale
could
was
pH)
the
voltage
V
on
a 10 mm path
barium
recorder,
the
at
were
keeping
added
concentration
The
that
surface
made
a similar
radius
latices
time
cell
dispersions
The
mounted
with
carried
were
as
I,
use.
polymerisation
particles
previously
made
out
The
weight),
were
nm)
materia before
C.
latex
(by
carried
[6].
? 0.5’
The
110
the
with
optical
tion
emulsion
the
measurements
particle
of
density
were
25.0
anhydrous
dessicator
Kinetics
Measurements
at
the
reported
were
an
cases
radius
studies
(B,
a vacuum by
both
of
particle
Shaw
in
prepared In
B . D. H.
was
dried
used.
measurements
previously 2.2
and
latices,
technique
adsorption
perchlorate
water
terminals
on
Field
were
plane,
were
a graticule strengths
of
determined
incorporating
two
blacked
using
a Mattson timed
with
mounted of
up
to
platinum
in 0.75
V coil
a purpose cell
[71.
built The
micro-
particles,
a stop-watch
between
the
of
mm
eyepiece -1 could
electrodes.
the
be The
two view-
applied positions
282 of
the
staitonary
equation
),
(7
curved
wall (23
Latex able
? 2’
of
system,
particle
(ca.
ten
by
Rate
The
of
calculating
experimental
optical
may
the
larger be
in
Rayleigh than
used.
expression
for of
a)
the
the
Analysis The
D(t) the
in
based
dispersion, concentration R A
N N,
1’
prepared
at
the
a suit-
is
this
on
not
case,
mobilities
Data rate
derive
is with
k,
depends
light
very nmj
particles
scattering
a simple
Rayleigh
for
1 = 545 For
used. of
constant,
Only
nm for
[lOI to
to
below.
plots,
be
theory
mean
must
analytical
theory.
A
here.
theory:
predicts
singlet
of
d < 90
possible it
Conversion
(tj
scattering
Average the
involved.
(i.e.
taken
as
Density
(D)/time
as
3%.
coagulation
is given
Rayleiqh
is given
Optical
Mie
than
was
system,
Section
particles
light
approaches
theory
containing
at
room
(8.2 2 0.2) and -3 dm j were adjusted
less
field.
X/2n
general it
two
Rayleigh
Mattson
at
directions,
each
absolute
the
d< of
field
for
from
of
191
more
both being
density
range
Unfortunately,
comparison
pH mol
Theoretical
the
(d)
theory
this,
the
Constants
diameter
particles,
the
refraction
made
were
The
1o-2
in
applied
in
Coaqulation
small
to
calculated
the
THEORETICAL
the
-3) .
deviation
is discussed
on
cm
( 10m5
were
3.1
on
from
for
were
mixtures
10’
standard
3.
critically
way [81
measurements
measurements,
divided
method
usual
a run.
the
velocity
based
correction
Henry
n-alkanol/water
mobilities
potentials
the
All
the
1.
C
to
average
each
in
concentration
prior
electrophoretic
calculated
cell.
in
perchlorate
An
the
concentration
immediately
zeta
of
dispersions
particle
barium
were
incorporating
inner
temperature
for
levels
that
particles
the of
optical volume
density, V,,
at
D,
of
a
(stable)
a number
by,
V:
D=
(1) 2.303
where
R is
the
path
length
of
the
optical
cell
containg
the
dispersion,
and
283 A
is
an
optical
constant,
given
by
1 2
24n3n4 A=-_.--??
n2 0
x4
where
n2
+ 2n2 0
[ n2
n and
-
n o are
the
(2)
refractive
indices
of
the
particle
and
medium,
respectively. For
a coaqulatinq
derived of
an
dispersion, for
D(t)
doublets,
and
higher
singlets,
m
For
and
Kruyt
a dispersion
aggregates,
[ll]
and
containing
by
analogy
Oster
with
eqn.
(11,
11 A
(3)
I I
c i=l
the
I121
a mixture
N.V.
2.303
assumption
that
aggregates
scatter
as
their
equivalent
spheres,
Vi i2N
D=
Smoluchowski
[131
(4)
i
c i=l
2.303
N.
.
2
D=‘1
Making
Troelstra
expression
has
derived
the
following
expression
for
Nl(t),
IkNot)‘-’
‘=
(5) (1
NO
+ kNot$+’
co Ni --
and c i=l where
N
No
is
1
_
(6) 1 + kNot
0
the
initial
number
concentration
of
(singlet)
particles
i.e.
at
t = 0. One
may
also
Thus,
Ni -=
X-.-=1_ N
N
0
eqn.
a parameter,
c
N -CN1 P=
define
(4)
for
0
D may
p
(the
extent
of
coagulation),
kNot (7) 1 + kNot be
transformed
[16.
171
either
to
D(t)
or
D(p).
(8)
284
or, D
-o= +%
(9)
D
From
eqn.
(8)
dD -=
2 RA
N2V2k o 0
dT
(10)
2.303
from
which
practice
D
does
higher
the
limit b)
if
[6]
usually
k
using
Rayleigh
Analysis
and
linearly
(10).
V.
do
are
with
behave
not the
themselves
known.
t, as
so.
initial
However,
particles
For
as
predicted
Rayleigh this
this
by
procedure
as
cannot
than
eqn.
(8) the
Ottewill
(dD/dtlo,
larger
in
scatterers,
reason
gradient,
are
However,
the
t
+ o,
be
in
used,
upper
size
scattering.
based
on
and
Shaw
Ottewill
may taking
eqn.
No
particles
present
singlet
if
vary
singlet
suggested
initial for
calculated,
the
aggregates Sirs
evaluating if
be
not
even
because,
and
k may
obtained
in
following
expression
the
&
case
theory: 151
of
showed
larger
for
how
The
particles.
D for
absolute
a mixture
of
rate Mie
constants
theory
aggregate
could
leads
to
be
the
sizes,
m Ni “a:
Kt
I
i
111)
i=l where
ai
is
the
radius
approximation*) Values iently
for
Kt
i,
tabulated
Again,
by
an
N
i
I on
an is
i-mer the
the
m
(again
total Mie
making
scattering
theory,
Heller
Pangonis,
and
the
equivalent
coefficient
have
and
Jacobson
may
be
been
of
sphere an
computed
[151,
as
i-mer. and
a function
convenof
Cm = n/no).
expressron
for
D(p)
derived
making
use
of
(5-71, i-l
N. 1
K,
based
(CY = 2 nnoailX)
eqns.
of
and
=
ll
(>
_ pji+l
P
Hence, *This
(12)
1-p
0
substituting is
suggested
not for
a very doublets
in
eqn.
good
(ll),
approximation, (i=21
1141.
but
corrections
have
only
been
Y
285
i+l
(’ - P)
~
D
i=l
-=
p
i-l
(1-p)
a?
, Kt I i (13)
2 al Kt, 1
Do Plots 546
of
nm),
(eqn. for
D/Do
based
131, the
are
range
converged
versus
on
the
p,
compared of
in
p values
rapidly
for
latex
Rayleigh
at
A
theory
fig.
1.
studied
In (p
(a,
=
leqn. the
110
9) latter
1,
< 0.15
nm.
and
m = 1.20, Mie
theory
it
was
found
case
the
h =
the
summation
in
that
eqn.
(12
1
i = 4.
I
Fig. 1. Theoretical D/D versus p plots: cornparis& of Rayleigh and Mie theories. a=110 nm, h=546 nm and m=l.20.
I I
Fig. indeed fit
1 indicates
and
then
knowing
3.2
the
value
(cc), (rapid
system.
Coaqulation
with
tions
the
Rayleigh
procedure, data
relationship
dispersions
increases
critical
better
of
to
based
the
(eqn.
analysis on
the
theoretical
7)
in Mie
this
analysis,
D(p)/Do
between
p and
case
is is to
equation
t,
to
(131,
evaluate
k,
0’
Critical For
use
D(t)/D(o)
use N
that A
incorrect.
experimental
Rayleigh
increasing
beyond
Concentration charged
it
constant,
concentration
behaviour
is
well
Rate the
Constant
for
(c)
independent ko); that
understood
of
cc
is
particular in
Da>
coagulation
concentration
becomes
rate
from
particles,
electrolyte
which
coagulation
coagulation This
of
terms
rate
up
to
electrolyte
referred
constant
some
(k)
critical concentra-
to
as
the
dispersion/electrolyte of
the
variation
of
the
particle
pair-potential, Vincent
following
V(h)
et
E
8
the
static
repulsion,
first
for
attraction,
term
between
permittivity
of
dielectric length;
the
y
layer;
is
y = tanh [ A
is
ze $ d 4kT
the
= (As
K(h
concentration.
expression
2n)
1-
r.h.s.
of
for
c
based
C
on
the
at
I:
of
the
is that the
E
the
free
Waals
is
space,
the
D the
screening
thickness
potential
der
4 nsoD)
I=
of
electro-
- van
Debye-Htickel
A is the Stern
for
London
h.
permittivity -1 is the
valency;
terms
for
separation
medium);
counter-ion
(14)
(14)
that
is the
(F~
Aa 12h
eqn.
term
particles
the
in
-
second
medium
defined
electrolyte an
[171,
the
the
of
z is the
-
two
constant
with
V(h)
of
and
1,
derived
a(kT)‘y2. exp (ze)2
where
A
[16],
expression
=
and
Vl h
al.
of
the
Stern
(ti,),
1
(15)
effective
Hamaker
constant
of
the
system,
given
by,
_ A$’
(16)
P Ap If
is
the
the
Hamaker
latter
constant
is composed
of of
the
particle
a mixture
(1
and + 21,
Am
is that
then
for
Vincent
the 1181
medium. has
shown
that,
(17)
where and the
A, M2
and
the
mixture
A2
at
Applying to
eqn.
2 =
(14)
are
the
molecular mole the
fraction
to
the
of x,
following
leads
klAz3c:
Hamaker
masses
p2’
constants, the (=
o(1 and components;
pure
the
densities,
p is the
density
= 0 and
dV/dh
M, of
l-x2).
conditions following
[171
for
implicit
cc:
equation
V for
= 0,
cc,
exp(-2k2zbc:)
(18)
yC
where 20’
k C)
1
= 1 92 .
and
k2
x
10’g(~3T5)-i
= 1.605
(ET)-~
(= (=
5.104
1.048
x x
10”
lo-2
for for
aqueous aqueous
solutions solutions
at at
287
20’
Cl,
in
S.I.
electrolyte Note assumed
that
that
this
is too
3.3
Zeta
Debye
-
and
from
(5)
((~d)c,
in
that
on
of
$d
at
Overbeek
medium
solvents.
factors
the
critical
1171.
have
permittivity Eqn.
are
for
(18)
the
illustrates
important.
Mobilities
particles,
( IJ).
(small
value
and
the
mixed
Electrophoretic
mobility
limit
Reerink
other
spherical
to
the
15).
was
the
derived
following by
equation
Henry
1191,
relating
in
the
< values),
f(Ka)
q is the
(19)
viscosity
neglects
of
the
double-layer
sophisticated
medium;
1211.
Loeb
and
which
and
However,
electrolyte
f( Ka)
relaxation
treatments
Wiersema,
White
simple,
Hijckel
= = 1.5n
by
concentration
non-conducting
potential
to
eqn.
authors, following 3 s E dependence
Potentials
For
relates
(c.f.
cc
coagulation
zeta
yc
many
a simple
critical
u
units.
concentration
include
Overbeek
these
concentrations
is given.
surface these
[20],
effects
and
become
(Ka > s
1001,
The
derivation,
conductance
effects.
effects
have
and
been
given
by
O’Brien
subsequently
insignificant in
however, More
at
e.g. and
sufficiently
particular
in
the
high
region
of
cC.
4.
RESULTS
4.1
Rapid For
k.
(c
2.12 1.7 k. the
Coaqulation latex
> cc) x
2 0.1
x
stated
R
based
error of
k.
Constants the
for
the Mie
mixtures.
of
the
rapid
coagulation
the
presence
of Ba(C104)
on
the
Rayleigh
analysis
on
latter over
the
value
in
based this
limits,
using
urea/water
where
latex
using
Values
= 4nR
water,
10-18m3s-1
determined
and
in the
10-18m3s-1
determined
k.
A
for
Rate
the
Mie
approach the
latex
in
analysis
range the (p
According
was
(eqn.
lOJ,
analysis.
Moreover,
was
to
found
rate found
be
constant to
but the
constant,
be
value
of
within
0 < p < 0.2. presence
= 0.1) to
for
of
Ba(C104),
the
Smoluckowski
various
were
also
alkanol/water
1131,
D, is the
be
to
(19) collision
radius
of
two
interacting
particles
and
D1
is the
288
Me01
n-PrOt
EtOH
I 20
20
40
Fig.
mol
%
40
2
k-17 values for IaYex A as a function of alkanol or urea concentration.
UREA I
I
5
10
mol%
289 diffusion
coefficient
the
Stokes
D,
kT = 8nrlah
where
-
Einstein
a singlet
particle.
This
latter
quantity
is given
by
equation,
(20)
a
is
h Hence,
the
hydrodynamic
combining
2R = -
ken
of
radius
eqns.
(19)
of
and
the
particles.
(20),
kT (21)
3ah Plots
of
In
all
In
the
ko;l
ken
cases
n-alkanol
4.2
versus
cases
of
the
or
urea
through
the
with
Coaqulation
concentration
a minimum
n-alkanols,
concentrations
Critical
log
n-alkanol
passes
with
position
increasing
are with
of
the
chain
shown
in
additive
fig.
2*.
concentration.
minimum
moves
to
lower
length.
Concentrations
Fig.
v
3
Log W versus log c for latex A in aqueous Ba(CI0412 solutions
0.
0
Rayleigh
0 p=
theory
.05
C xp=O.lO -1.3
-L.”
at
order
a given
W = k/k versus
shown three
* are
Thus,
0’
(at
Details given
overcome
electrolyte
log
are
to
c.
for
in
fig.
the 3,
p values).
of in
the ref.
problems
of
concentration,
for
c > cc, in
water
based
on
the
It
can
viscosity
data
[21
for
and
be
discussinq
one
W = 1;
latex
used
may
for and
define
the
as
analysis, in
for
urea/water
the
the
rate
region
Plots the
and
the
cscc
is
ratio. of
added
n-alkanol/water
mixtures
constants,
stability
> 1.
Ba(CI?4)2
that
here
absolute
c < c,,W
Rayleigh
seen
the
theory
gp=O.18
log c In
Mie
ref.
Mie
log
W
electrolyte analysis
(W ~11,
there
mixtures 1221.
-2
-3
-4 deOH
EtOH 20
40
60 0
n-PrOH 20
40
60 0
20
40
60 mol 9,
-l.E UC 0, 2
-2.0
l-BuOH 0
UREP
I
1
0.5
1.0
0
I
I
5
10
mol % Fig.
4.
Log c versus la%ex A 0.
n-alkanol
mol
or x,
urea concentration. latex B
%
291 is
little
dependence
discrepancy mental
at
times
given
by
become
the
the
= 1 /kN
0
from
data
is
may
not
perfectly
in
the
but to tf,
instrumental is
fig.
3,
as
the
for
ZNi
of
Thus,
is
quite the
two
although
absolute
determining
some
“drifts”) cc
intersection used.
is
experi-
= No/Z,.
(e.g.
determine
determining
for
there larger
when
to
method
used
satisfactory
that the
errors
possible
analysis
be
used, attributed
“half-life”,
it
shown of
analysis it
be
systematic
Nevertheless
the
analysis
may
coagulation
any
independent
Rayleigh
constants,
of
This
(the
. ’
acc:mulative.
shown,
method
c values.
involved
tl
accurately lines
on
low
rate
critical
coagulation
3 were
obtained
concentrations. Similar the
various
centration, the In
log
with
Rayleigh the
case
In
the
through
log
c plots
of
was
differ
in
of
a maximum
of
this
in
magnitude
maximum
moves
shown
the
added cc
data
a function
electrrolyte.
values are
are
shown
mixtures,
increasing to
as
In shown
for
these
in fig.
both
for
con-
of
cases, 4.
latices
A
size).
n-alkanol/water
for
in fig.
systems,
the
mixtures,
with
(except
as and
used,
particle
the
that
urea/water
a g ain
ethanol/water
case
to
and
Ba(Cl04)2
analysis
B (which
and
W -
n-alkanollwater
lower
n-alkanol n-alkanol
I,
butan-l-01
the
value
concentrations, with
of
and
increasing
cc
The
concentration.
passes position
is greater
n-alkanol
chain
urea
concentration.
length. The
opposite
Here
cc
4.3
Mobilities
TABLE
passes
and
is
seen
for
cc
a minimum
Zeta
as
with
a function
increasing
of urea
concentration.
Potentials
1
Mobility
and
Zeta
C
lmol
trend through
Potentials
u x dm
-3
for
lo8
/m2V-‘5-l
Aqueous
r
Latex,
(Henry) mV
A
<
I Wiersema mV
lo-2
0.73
9.8
9.8
lO-3
1.28
18.4
18.8
lo-4
1.68
25.9
28.5
10-5
1.48
45.0
c = concentration
of
Ba(C10412
1
292
3-
MeOH
I
0
I
40
20
-
EtOH
1
I
I
I
60
0
20
40
-
n-PrOH
I
I
I
I
60
0
20
40
I
60 wt%
0
n- BuOH
Y
10
l 10 x 10 UREA
I
I 15
Fig.
30wt0 6
A1i2
-5 -4 -3
mol
dm
mol
dm
mol
dm
mol
dm
,
1
4
6
I
a
J
wt%
-3 -3 -3
Bat CI04)
5
Mobility (u) versus n-alkanol or urea concentrations at pH 8.2 2 0.2, and the Ba( C104 I2 concentrations indicated.
I
-3
293
r;
MeOH
EtOH
I
80 ImV t
L 0
I
I
I
10
20
30 0
I
1
t
10
20
30 0
I
1
L
10
20
30 mol%
. n-BuOH
5
mol dm 80-
0
1o-4 10 -5
x
10
A
‘0
ImV
-3 -2
mol dm -3
mol dm
-3
-3 mol dm Ba(C104)2
UREA L
5
L
1
I
l”mol%
/ 20
Fig. Q
1
0
1
1
I
0.5
1.0
1.5 mol%
6
Zeta potential (~1 versus n-alkanol or urea concentrations at pH 8.2 2 0.2 and the Ba(C104)2 concentrations indicated.
In
Table
Wiersema
et
[I201
al
experimental (neglect
a comparison
1 above,
analyses
mobility of
for
values.
relaxation,
is made
of
calculating It
surface
would
using
zeta
seem
Henry
is
use
El91
(
potentials
that
conductance)
the
of
the
reasonable
from
Henry
for
and
analysis
c > 10T3
mol
dm-3. Mobility
values
at
mixtures, the
corresponding
are
shown
in
mixture
The
mixtures
with
the
zeta
concentrations
greater
refractive
index
of
It
would
in
‘L
7 mol
medium
zeta
With
approaches
with
that
at
these
of
the
for at
the
the
low
to
lower
urea/water
increasing at
and
analysis, results
moving
possible
% because
5.
potential
length.
were
fig.
Henry
maximum
a minimum
measurements
in
potential
the
the
chain
through
the
zeta
of
urea/water
shown
urea
urea
concentrations latex
the
particles,
difficult. that
the
coagulation
trends
in
the
concentration
zeta
data
potential
shown
data
mimic
those
earlier.
DI SCUSSION Rapid
Coaqulation
According with
to
additive
a slight n-alkanols
other
and at
n-alkanols R
twice
is the
the of
in
the
a h,
butan-l-01 water
also
for
0.5
mol
Constants ken
of
the
medium.
urea.
for
an was
increase observed
is approached.
2 would
The
the
particles,
Any
decrease
radius
of
ah
is is
the
with
on
by
Quantitatively,
this
latex
is
not
to s
particles
its
case,
of
the
with With
taken
invarient
suggest
[3]
the
an
the
increase the
known
account,
in
particular
saturation the
as
with
could
concentration; as
be
30%.
Qualitatively,
however,
the
each
normally be
would
particles.
is
invariable
15%.
should
R/ah,
is
for
seems
than
R/ah
this
effect
less
n-alkanol
to form multilayers
that
reduced
and
in
if
concentration
which
n-alkanols in
indicate
ken
diameter
bare
a constant
maximum
reduction
(contact)
of
be
increasing
% butan-1-01,
hydrodynamic adsorption
should
Fig. with
urea
collision
the
preferential part,
Rate (211,
occurring
and
radius
nature
eqn.
concentration.
minimum
butan-l-01:
in
the
seem
critical
5.1
in
than
the
position
n-alkanol
no
using
of
a maximum
the
passes
that
observations
the
5.
with
and are
calculated feature
is again
potential Note
n-alkanol/water concentrations,
main
increasing
concentration.
making
various
potentials,
6.
concentrations,
concentrations
in
the
!3a(C104)2 zeta
fig.
n-alkanol/water n-alkanol
for
different
effects
concentration seem
to
be
295 too
large
to
lt
is
be
(eqn.
191,
241.
This
(1.70
x
value
predicted
media
the
neglects
10e6
appears
is
m3
any
)
s-’ by
is
close
for
(19)
for
the
(5.45
changes
k.
in
equation
low
10e6
In in
[23,
value
compared
s-l).
is complex;
k
interaczons
experimental
latex,
m3
ah for
hydrodynamic
aqueous
x
to
of
the
for
to case
0
the of
particular,
k
mixed
interfacial
factor.
of
% composition
the
with
at
additives.
the
which
For
the
the
minimum
n-alkanols
maximum/minimum
in
the
in koq
at
other
least,
parameters
noteworthy.
5.2
Critical
Coaqulation
TABLE
2
Values
of
additive
minima
(t)
occur
Concentrations
concentration in
various
(mol
7.5
Ethanol
t
which
Potentials
various
2.5
t
Butan-l-01
0.5
t
Urea
9.0
t
the
array
maxima
(“1
and
corresponds
dmm3.
N/A
The
= not
latex
paper
characteristic
131,
lo-12*
4*
5*
4*
3-4*
2.5*
2.6*
0.5*
N/A
3.6t
N/A
OA- 1 .o*
max.
[31
3.6t
and
particles
the
10*
C
is the
elastic
The
range
111.
Ba(C104)2
modules of
concentration
of
zeta
range,
10
an
ordered
potential values -5 to 1o-2 mol
available
particles
of was
latex to
7.5*
12”
N/A
excess of
quoted
conclusion
no.
adsorption
crystalline
10-15x
N/A
4t
Propan-1-01
earlier
%I at
Zeta
r
Methanol
is
and
parameters.
Additive
r
for
mol
each
correspondence
from seemingly
important the
terms
Smoluchowski
the
correction an
in
the
contributions
eqn.
2 below,
shown
purely that
obtained
necessary
Table
note
accounts
becomes
In
for
to
effect
structure
the
accounted
important
in
carry which
these
latex
reached
that
surface we
discussed
particles the
carboxylic
in
n-alkanol
the
acid
groups.
adsorption
and
n-alkanol/water molecules
In wetting
mixtures, adsorb
an
initially
the through
296 interaction
(H-bonding)
carbonyts
of
the
Thereafter,
they
towards
the
n-alkanol (as
in
zeta-potential,
the
maxima
virtually
may
the
+
.;+.
CTo
density the
( Ba2+)
could
(for
and
of
well
counter-ions for
pointing At
particles.
could
the
ethanol
adsorption
low
n-alkanol
lead
near
to
the
observed
and
particles.
tails
adsorption
account
since
potentials
express
(ionised)
increase
propan-l-01,
excesses
of
in
table
2)
n-alkanol
are
’ IS
the is
these
in
to
ions For
(table
and
to
1.
for
‘d
double
its
reflects
(18)
layer
ui
to an
values no
acid
Qd
avail-
just known
to
,
<
at
the
the
latex
and
hence
an
where
5
alkanol
in
,
ui
be
displaced)
higher
specifically
as
mixtures
concentrations,
all
in
are
( Ba2+
decrease
decrease if
(zero,
is
for
in
in
continuing
could, data
n-alkanol/water
reduced
n-alkanol
charge
densities
Nevertheless,
&
decrease
the
ui
in be
is the
charge
yet,
acetic
increase
o:
level
mixtures,
system.
cc.
the
Primarily to
the
than
indicates
of
in
0:
the
is
after adsorbed
1.
therefore values
as
mixtures. groups
small
concentrations
Eqn.
layer.
eventual
minimum
surface;
ud are
but,
implies
at
The
the
diffuse
Hence,
’
at and
studies
expect
does
displaced
a given
experimental
electrical
concentration
<
n-alkanol/water
interest
the
acid
in
oi
n-alkanol 2
It is of
are the
lower
the
equation,
0:
n-alkanol/water
similarly
merely
reduced
in
titration
n-alkanol
increase.
concentrations, is
at
density
layer;
carboxylic
increase
4 than
rapidly
observed
in
the
might
An
increase
by
increasing
so one
particles.
Stern
co-ions
latices of
charge
the
obtained
with
[251,
balance following
the
(22)
in
and
be
reduced
charge by
(negative) 0)
counter-
for
the
particles
;+ud=O
ionisation
cc
zeta
polystyrene
the
latex
n-alkyl
isotherms),
adsorbed This
with
of the
their
preferential
excess
groups
surface
with
the
strong
adsorption
the
( u;
principle,
of
the
adsorb of
particularly
latex
+u
S
where
at
surface
groups.
in
One
$2+
to
hydroxyl on the
coincident.
around
more
terminal groups
appear
specifically
acid
the
able
the
of
carboxylic
the
would
concentrations,
revealed
their acid
hydrophobic
displacement
of
of
carboxylic
maxima the
parameters these
calculate
Values
do
of
are
A, using
be
the in
which
(Qdlc, A may
in
maxima
c
C
the
values
determine
($,), eqn.
computed
the
(eqn.151, (18). from
occur
<-values value and from eqns.
(16)
A.
297 and
(17).
choice and
taking
for
A is more
(151,
two
A =
and
diameter
values
nm
one
7 where
($,I,
A =
0.41
it
nm
mixtures,
were
A,
is
is
but
in
A2
from
calculating
the
literature
IJidlc,
radius
molecule).
plotted
the
A = 0 Iignoring to
water
quite
and
chosen:
(corresponding
solvating
fig.
Ap,
difficult,
values
0.41 of
for
using layer 2+ Da ion
one
results
as
function
of
bulk
remarkable
that,
for
all
are
four
-\ AzO.41
t
least
at
lower
n-alkanol/water
in < and
around
12.5
is
values here
displaced
7
.
If
the
A
table
is
high
the
21,
equal
A =
0.41
(including all to
the 0,
on
nm,
the
the
layer
H*O
o
MeOH/H,O
and
the
the of
regions
($d)c
other
actual
no
choice
of
reflects
largely,
if
for
the
such
divergence
presumably are
where
converge
hand,
increasing
concentrations, 71 adsorbed Ba” ions
Stern
in
values
n-alkanol
specifically
from
set
For
seen.
at
.
concentrations
occur;
l %
not
the
fact
totally,
A itself
is then
so clear. It
is of
the
< values
interest
at
coagulation 6)
compare value
lower
of This
concentration.
electrophoresis
? 0.5
to
corresponding
coagulation
(fig.
cc
mV.
convergence
-. ‘9
nm
n-alkanol
maxima
7.5
With
(J, 1 versus dre 3 egtric constant ID1 for:
15
with
the
in
constant.
Fig.
t
not
plus
at
20
(vd)c that
(18)
effects)
shown
dielectric
The
eqns.
Stern
of
The
[~61.
electrolyte
and mV,
the
latex
can
only
cannot
particles.
extrapolating i.e.
value i.e.
somewhat
of
the
be
:
versus than
value
be
to
the
the
5,
data
c plot IJJJ~)~.
(12.5
at by
value
under
the log
obtained of
determined
made
Taking
lower
(IJJd)c
the
concentrations
measurements of
the 5,.
at
the
extrapolating cc,
conditions for to
the
log This
mV),
critical
since of
rapid
aqueous
(cc), implies
latex
gives that
(cl,= in
this
case
the
Stern
the
plane
of
shear
is
et
[291
have
data,
for
Rubio-Hernandez from
electrophoretic
mol
mixture,
dm3
containing
KBr.
maxima
and
in
the
n-alkanol,
The
are
by
the
or
are
they
mixtures
Only
are that
for the
more
1
and
data.
for
also
al.
also
able
various
is aware
[161
adsorbed
than
hydrated
(Li ‘1
deduce
be
the
shapes
for
butan-1-01
is
displaced of
the on
in
weakest by
curves Ag I
in [28].
Mg2+
is
of
counter
more
quite
a wide
the
case the
ions
(Br-1,
n-alkanol/water
back
literature
many
data
the
for
presence
through
in
years.
negative of
and
that,
at
the
known
a variety titration
a maximum
with
studied.
They
adsorption, as
fig.
values,
a function
8.
strongly
Nevertheless,
the
ions
with
in
conditions,
shown
competing 8 reflect
in
that
specific
coagulation
adsorbed.
fig.
counter
electrolytes
relative
are
here scattered,
concentration.
potentiometric
the
counter-ions,
butan-1-01
in
passed all
i.e.
results
water,
monovalent the
,
under The
that,
for
oo
more
occurs
coagulation
values
%
here.
corresponding
cc
are
but
dating
mixtures,
the
3 mol reported
systems is
to
critical
the
o:/
there
referred
concentration,
counter-ions,
the
be
in
molecules.
latex
mixtures,
compared
that
groups,
one
mixtures,
n-alkanol
adsorption
but
butan-1-al/water
found
8 shows
of
will
with
5 data
n-alkanol
of
(positive)
values
molecules,
with
in
particles
specifically-adsorbed
specific
studies
other
% and
the
the
charge
n-alkanol/water
in
to
no
to
increasing
of
the latex,
12 mol
particles, with
particles
methanol/water)
close
competing
papers
not
potentials,
investigated:
and
negative
propan-1-01
other
concentration.
Fig.
to
is by
only
butan-l-01
butan-l-01
seem
or
there
in
sols
They
the
than
concentration
were
around
sulphate
2: 1 electrolytes,
increasing were
latex
maxima
with
recent at
iodide
the (but
observed
author
sols
Vincent
1:
surface
zeta
latex
groups,
remarkably
displaced the
the
other
silver
the
determined
particle
With
i.e.
ethanol
either not
These
[2]
from
electrolyte
latex
displacement
latex,
also
sulphate
positive
adsorbing
latex,
of
were
obvious
is that
negative
positive
a
the
no
implication
lK+), of
out
polystyrene
propan-1-al/water
< values
With
2). there
types
groups.
respectively,
(table
further
a background
surface
isobutyramidine
ethanol/water
and
at
Two
(negative)
surface
al.
mobility
n-alkanol/water 10-3
slightly
plane.
specifically of all
these, the
interface. “S-shaped”
the
most
counter-ions Indeed isotherm
of
299
0
0.5 cB/mol
Relative specific Fig. 8. as Ag I/soln. interface, pI=6.5 [161 These who
results
obtained
the
presence
found
to
cc
values KN03
decrease
de in
Rooy
is
ethanol
for
the
AgI
et
al.
[321
needs
i.e.
c c and implication
< go
of
Ghosh
addition
of
various
stability
of
aqueous
here:
increased
stability.
urea.
ferric
ethanol
led
However,
not
of
for
the
with
this
for
decreased from
in
titration
this
work
reported
4 and
older
61,
the
here
where
concentration. ions
efect
ethanol
and
oxide
sols,
is enhanced,
of
in
on
the to
urea to
by the
urea,
trends
whilst
experiments
the
mixtures,
experiments
the
opposite
stability,
sols)
La(N03)3. through
n-alkanol/water
manganese seemingly
other or
detail.
increasing urea 2+ counter Ba
including
molecule.
passes
of
molecules,
and for
(and
5 data
some
in
were
butan-l-01,
cc
studied
]
concentration.
Mg(N03)
in
and
the
regard,
and
C
AgI
(figs.
They
report
values
although
cc
[29-31
counter-ions
LiN03,
mixtures
Wit
a “displacer”
explored
with
c
is
La(N0313,
relevant.
to
than
values
adsorption
oxide
actually
is
with
observed
In
are
it
not
a minimum
organic
They
observed
that
de
the
mixtures,
the
bound
concentration,
account
specific
1331
least
urea/water
through
additions
Ba(N03)2.
to
is that
and
of
to in
cases
water
cc
was
and
ethan-1.2-diol
presence
ethanol
Lyklema
with
i.e.
at
region
is opposite
The
small
increasing
particles
with
strongly
the
that,
both
increasing
obtained
in
indication
one
behaviour
Prasad
have
by
ethan-1,2-diollwater
In
particles,
concentration
latex
in
miscible less
mixtures,
Finally,
work
sols
with
more
for various counter-ions at BuOH concentration (c,).
later
AgI
much
the
with
low
of
Ba(N03)2.
on
some
a maximum
by
much
ethanol/water
There
for or
compete
sites
with
continually
is
therefore
surface
contrast
of
Ethan-1,2-diol will
adsorption a function
1
-3
dm
the
presence
those
led
determine
to the
300
adsorption
of
ethanol
but
careful
in
2+
to
and
potentiometric
to less
positive
ally
The is that
potentials
with
6.
with
just
are
also
found
Agl
sols
example,
presence has
since
changes
in
observed
to
of
be
they
( eqn.
os+
with
increasing
opposite in
the
increasing
opposite
why
urea
a known at
ethanol
urea
trends
221, and
in
of
mixtures
zero
charge
moved
concentration,
concentrations.
of
the
n-alkanol/water point
n-alkanol
effects
may
water
3 sites
hydration
adsorption
the one
n-alkanols
but
Again
and
urea
on
to
this specific-
ions.
is
water
their
not
trends
of For
with
reflect
reason
it
in
Although
measurements,
and
[301
behaviour
potentials
could
adsorbed
decreased
urea.
adsorption
opposite
mixtures.
positive
behaviour
this
of
+ o:)
Lyklema
titration
urea/water
more
ion
(oz
that
that
presence
significance.
Bijsterbosch
in
in
fact
some
found
the
such
changes
the
is of
they
in
interpreting
neverthess,
and
ions,
increased
correspond
urea,
Ba
per
molecule.
in
urea/water
shells
energies
promote
to
specific
structure
charged
adsorption
“breaker”; It
may
be
mixtures
sites
on
it
of
can
that
counter-ions
itself
ions
H-bond
(partly)
resulting
in
loose
stronger
surfaces.
CONCLUSIONS It
has
been
demonstrated
organic/aqueous
media,
on
constant
the
but
Hamaker
so do
organic
more
counter-ions probing
the
Finally,
to
regarding
the
particles,
with
the
for
other
presence added Specific
to
maximum
in
increasing
properties added
electrolytes adsorption
of
the
with
opening
the
elastic
maximum
effects
can
layer,
with
such
a role,
between
or
Such
parameters
play
adsorption
comments modulus
of
latex, 2
but
are,
of is
1.
the
dehydration be
of
studied
by
techniques
as
albeit
in
that
colloidal
course,
still to
Introduction,
colloidal
so closely
The
likely
the
[ll:
corresponds
(table
counter-ions
in
concentration
dilute
there
such
medium,
counter-ions,
double
electrolyte
of
in
in
titration.
the
the
the
competitive
adsorption.
n-alkanol
this
as
stability
changes of
adsorbed
in
dispersion
macroscopic
such
potentiometric
return
position
of
their
studying
permittivity
specifically
distribution or
in
do
the
effects,
and
ion
only
and
increasing
electrophoresis
that
not
subtle
molecules
that
crystals it
is with
that
case
in
crystal
in
latex
found
the
contains
counter-ions
increase
of
remarkable
extent
no
present. the
more
302 25. 26. 27.
28. 29. 30. 31. 32. 33.
H.O. Spirey and Th.Shedlovsky. J.Phys.Chem., 71 (1967) 2171. J. N. Israelachvili, Intermolecular and Surface Forces, Academic Press (1985). F. J. Rubio-Hernandez, F.J. de las Nieves. B. H. Bijsterbosch and R. Hidalgo-Alvarez. Proc. Int. Conf. Polymer Latex III (London, 1989) 15/i. B.H. Bijsterbosch and J. Lyklema, J.Colloid Sci.. 20 (1965) 665. J. Lyklema and J.N. de Wit, J.‘Electroanal.Chem.. 65 (1985) 443. J. Lyklema, Pure and Appl. Chem., 48 11976) 449. J. Lyklema and J.N. de Wit, Colloid and Polymer Sci.. 256 (1978) 1110. N. de Rooy, P.L. de Bruyn and J.Th.G. Overbeck, J.Colloid Interface Sci., 75 (1980) 542. C. Prasad and S. Chosh, Kolloid Z., 175 (19611 134,: 176 (1961) 29: 177
(1961)
155.
301 concentrated
the
electrolyte
latex
modulus,
which
is again
displacement
n-alkanol
molecules.
1c.f.
counter-ion
condensation
possible
explanation
for
dispersion So one
solutions). reflects
a maximum of
in
specifically
the
repulsion
adsorbed
the
between
in
the
counter-ions
poly-
maximum
by
in
the
particles, competing
ACKNOWLEDGEMENTS
I his early
should
guidance in
my
intervening
like
whilst career,
to
express
carrying but
also
my
thanks
out
this
for
his
to
particular help
on
Ron
Ottewill,
piece many
of
not
only
research
occasions
over
for
work the
years.
REFERENCES 1. 2. 3. 4. 5. 6. 7. a. 9. 10. 11. 12. 13. 14. 15.
16. 17. 18. 19. 20. 21. 22. 23. 24.
T. Okubo, J.Chem.Soc. Faraday Trans., 86 (1991) 151. B. Vincent, Ph.D. thesis, Bristol University, 1968. R.H. Ottewill and B. Vincent, J.Chem.Soc.‘Faraday Trans. I, 68 (1972) 1533. J.H. Hearn, R.H. Ottewill and J.N. Shaw, Brit.Polymer Sci., 2 (1970) 116. R.H. Ottewill and J.N. Shaw, Disc. Faraday Sot., 42 (1966) 154. R. H. Ottewill and J.A. Sirs, Bull. Photoelectric Spectrometry Group 10 (1957) 262. S. Mattson, J.Phys.Chem., 37 (1933) 223. D.C. Henry, J.Chem.Soc., (1938) 997. Lord Rayleigh, Phil.Mag., 42 (1871) 107, 274, 447. C. Mie, Ann.Physik, 25 (1908) 377. S.A. Troelstra and H.R. Kruyt, Kolloid Beih., 45 (1943) 225. G. Oster, J.Colloid Sci., 15 (1960) 512. M. von Smoluchowski, Z.Physik.Chem., 92 (1917) 129. A. Lips, C. Smart and E. Willis, Trans. Faraday Sot., 67 (1971) 2979. W.J. Pangonis, W. Heller and A. Jacobson, Tables of Light Scattering Functions for Spherical Particles, Wayne State University Press (Detroit) 1957. B. Vincent, B.H. Bijsterbosch and J. Lyklema, J .Colloid Interface 37 (1971) 171. Sci., H. Reerink and J.Th.G. Overbeek, Disc. Faraday Sot., 18 (1954) B. Vincent, J.Colloid Interface Sci., 42 (1973) 370. D.C. Henry, Proc. Royal Sot.. Al33 (1931) 106. P.H. Wiersema, A.L. Loeb and J.Th.C. Overbeek, J.Colloid Sci., 22 (1966) 78. R.W. O’Brien and L.R. White, J.Chem.Soc. Faraday Trans. (1978) 1607. A. Campbell and E. Kartzman, Cam.J.Res., 28 (1950) 161. L.A. Spielman, J.Colloid Interface Sci., 33 (1970) 562. E.P. Honig, G.J. Roebersen and P.H. Wiersema, J.Colloid Sci . , 36 (1971) 97.
Interface II
74
Interface
279
00133 A
DISPERSION
STABILITY
IN MIXED Brian
School
of Chemistry,
Paper
dedicated
Leverhulme
University
to Prof.
Chair
SOLVENT
of Physical
MEDIA
Vincent
of Bristol,
R .H.
(AQUEOUS/ORGANIC)
Bristol
Ottewill
F. R .S.,
Chemistry
at the
BS8
lTS,
U.K.
on his retirement University
from
the
of Bristol.
CONTENTS 1.
Introduction
280
2.
Experimental
280
3.
4.
5.
6.
280
2.1
Materials
2.2
Coagulation
2.3
Electrophoretic
281
Kinetics
281
Mobilities
282
Theoretical 3.1
Coagulation
3.2
Critical
3.3
Zeta
Rate
Constants
Coagulation
Potentials
from
Optical
Concentrations
from
Electrophoretic
from
Density Rate
282
Data
Constant
Data
287
Mobilities
287
Results 4.1
Rapid
4.2
Critical
4.3
Mobilities
Coagulation
Rate
Coagulation and
Zeta
287
Constants
289
Concentrations
291
Potentials
294
Discussion 5.1
Rapid
5.2
Critical
Coagulation
Rate
Coagulation
294
Constants
Concentrations
and
Zeta
295
Potentials
300
Conclusions
ABSTRACT The potentials
285
dependence
of critical
on composition
and
urea/water
are
also
mixtures
coagulation
for
polystyrene
are
compared.
concentrations latex
particles
Similar
data
and
zeta
in n-alkanollwater
from
other
authors
reviewed.
OOOl-8686/92/$15.00 0 1992 -
Elsevier Science Publishers B.V. All rights reserved.
280 INTRODUCTION
1.
Recently
Okubo
crystalline
arrays
water/organic and
of
concentration.
2.5
% methanol,
that
these
it
mixtures, the
in
electrical
turn
to
in
with
at
the
in
for
the
electrostatic
indicated,
although
10,
5 and
Okubo
suggested between
Debye
screening
the
alkanollwater
of
repulsion no
ethanol increasing
repulsion
the
each
of
(de-ionised)
with
around
electrostatic
changes
(Cl
methanol,
respectively.
Hence,
that
concentration
modulus
a maximum
occurred
in
elastic
dispersed
that,
through
maxima
related
the
particles
propan-l-01,
layers.
suggested
on
showed
G went
changes
double
is
alkanol
of
These
reflect
which
the
value
He
ethanol,
results
particles, of
latex
mixtures.
the
alkanol
a paper
polystyrene
solvent
propan-l-01,
mol
[l J published
the
length
is a maximum
fundamental
reason
at is
given. These Ron found
that
phoretic of
results
Ottewillls both
mol
indicated In
more
seems
of
This
discussed
2. 2.1
work,
more
(critical
latex of
went
three
out
in
[21.
Basically,
from
microelectro-
coagulation
particles the
I carried
work
determined
stability
Ottewill
has
dispersions, in
therefore,
recent and
observed
we
concentration
through
a maximum
n-alkanol/water
at
mixtures
as
aspect to
in
see
the
of if
the
particularly
of
this
his
there
various
considered
properties latex
commorative
work
with
could
be
properties
particles.
issue,
the
older
the
to
It bring
work
a common of
of
on
explanation
latices
as
and
stability
for
a function
concentration. paper
experiments
water
the
work
Ph.D.
Okubo.
dispersions,
alkanol
and
my
(< 1, as
polystyrene
appropriate,
maxima
of
% concentrations by
this
experimental
part
potential-
structured
very
together
the
zeta
of
recent
concentrated,
dilute
the
cc)
similar
those
some as
measurements,
electrolyte
very
recalled
laboratory,
therefore
referred above,
mixtures.
describes
to. data
A
In
are
also
survey
of
the
addition
electrophoretic to
reported other
work
the for
three
alkanol/water
mixtures,
butan-l-al/water
in
the
field
and
is also
urea/
given.
EXPERIMENTAL Materials Water,
described
methanol, in
a previous
ethanol, paper
propan-1-01 131.
Urea
and
butan-l-01
was
Hopkins
were and
purified
Williams
as
287 “AnalaR”
grade.
Barium
recrystallised
from
Two
polystyrene [4,51.
were
carboxylic
acid
groups.
(A,
mean
and
wetting
same
latex
few
stability by
Coaqulation The
rate
change
Most
in
mean
of
coagulation
optical
Unicam
SP600
spectrophotometer
density
10’
cms3).
latex
housing.
chart of
The
pH to
and
above
curves
in be
these
2.3
Electrophoretic
of ing
the
in
the
with
the
the addition.
a
prepared
by
give
determining
perchlorate
h. of
the
to
particle
adjusted
546.1
nm,
automatic
instrument
the
solution. using
a
recording was
of
thermostatted
to
8.1
(V)
V
is
required
in
optical
all
cases. placed
of
to
an
concentra-
fixed
cell
(adjusted
means
alkanol
concentration
+ 0.1
by
added
the
number
(6
3 cm3 in
the
the
same
added-mixer
x
of
the
cell alkanol
device
161,
housing. from
the
recorded of
as
optical The
derived.
described
spectrophotometer a function
density
(D)
calculation
of
in
the
was
of
time
of
the
By
(t).
to
rate
Section
a pen
calibration
dispersion,
coagulation
Theoretical
fed
D(t) constants
below.
Mobilities mobilities
horizontal lines
microscope.
across
studied barium
to of
adjusted
the
apparatus,
vertical
modified housing
was
terms
curves
the
ISI.
nm)
a wavelength.
solution
cell
Electrophoretic
viewed
in In
51
was
perchlorate
output
from
electrophoresis
used [3]. latex
adding
length
and
scale
could
was
pH)
the
voltage
V
on
a 10 mm path
barium
recorder,
the
at
were
keeping
added
concentration
The
that
surface
made
a similar
radius
latices
time
cell
dispersions
The
mounted
with
carried
were
as
I,
use.
polymerisation
particles
previously
made
out
The
weight),
were
nm)
materia before
C.
latex
(by
carried
[6].
? 0.5’
The
110
the
with
optical
tion
emulsion
the
measurements
particle
of
density
were
25.0
anhydrous
dessicator
Kinetics
Measurements
at
the
reported
were
an
cases
radius
studies
(B,
a vacuum by
both
of
particle
Shaw
in
prepared In
B . D. H.
was
dried
used.
measurements
previously 2.2
and
latices,
technique
adsorption
perchlorate
water
terminals
on
Field
were
plane,
were
a graticule strengths
of
determined
incorporating
two
blacked
using
a Mattson timed
with
mounted of
up
to
platinum
in 0.75
V coil
a purpose cell
[71.
built The
micro-
particles,
a stop-watch
between
the
of
mm
eyepiece -1 could
electrodes.
the
be The
two view-
applied positions
282 of
the
staitonary
equation
),
(7
curved
wall (23
Latex able
? 2’
of
system,
particle
(ca.
ten
by
Rate
The
of
calculating
experimental
optical
may
the
larger be
in
Rayleigh than
used.
expression
for of
a)
the
the
Analysis The
D(t) the
in
based
dispersion, concentration R A
N N,
1’
prepared
at
the
a suit-
is
this
on
not
case,
mobilities
Data rate
derive
is with
k,
depends
light
very nmj
particles
scattering
a simple
Rayleigh
for
1 = 545 For
used. of
constant,
Only
nm for
[lOI to
to
below.
plots,
be
theory
mean
must
analytical
theory.
A
here.
theory:
predicts
singlet
of
d < 90
possible it
Conversion
(tj
scattering
Average the
involved.
(i.e.
taken
as
Density
(D)/time
as
3%.
coagulation
is given
Rayleiqh
is given
Optical
Mie
than
was
system,
Section
particles
light
approaches
theory
containing
at
room
(8.2 2 0.2) and -3 dm j were adjusted
less
field.
X/2n
general it
two
Rayleigh
Mattson
at
directions,
each
absolute
the
d< of
field
for
from
of
191
more
both being
density
range
Unfortunately,
comparison
pH mol
Theoretical
the
(d)
theory
this,
the
Constants
diameter
particles,
the
refraction
made
were
The
1o-2
in
applied
in
Coaqulation
small
to
calculated
the
THEORETICAL
the
-3) .
deviation
is discussed
on
cm
( 10m5
were
3.1
on
from
for
were
mixtures
10’
standard
3.
critically
way [81
measurements
measurements,
divided
method
usual
a run.
the
velocity
based
correction
Henry
n-alkanol/water
mobilities
potentials
the
All
the
1.
C
to
average
each
in
concentration
prior
electrophoretic
calculated
cell.
in
perchlorate
An
the
concentration
immediately
zeta
of
dispersions
particle
barium
were
incorporating
inner
temperature
for
levels
that
particles
the of
optical volume
density, V,,
at
D,
of
a
(stable)
a number
by,
V:
D=
(1) 2.303
where
R is
the
path
length
of
the
optical
cell
containg
the
dispersion,
and
283 A
is
an
optical
constant,
given
by
1 2
24n3n4 A=-_.--??
n2 0
x4
where
n2
+ 2n2 0
[ n2
n and
-
n o are
the
(2)
refractive
indices
of
the
particle
and
medium,
respectively. For
a coaqulatinq
derived of
an
dispersion, for
D(t)
doublets,
and
higher
singlets,
m
For
and
Kruyt
a dispersion
aggregates,
[ll]
and
containing
by
analogy
Oster
with
eqn.
(11,
11 A
(3)
I I
c i=l
the
I121
a mixture
N.V.
2.303
assumption
that
aggregates
scatter
as
their
equivalent
spheres,
Vi i2N
D=
Smoluchowski
[131
(4)
i
c i=l
2.303
N.
.
2
D=‘1
Making
Troelstra
expression
has
derived
the
following
expression
for
Nl(t),
IkNot)‘-’
‘=
(5) (1
NO
+ kNot$+’
co Ni --
and c i=l where
N
No
is
1
_
(6) 1 + kNot
0
the
initial
number
concentration
of
(singlet)
particles
i.e.
at
t = 0. One
may
also
Thus,
Ni -=
X-.-=1_ N
N
0
eqn.
a parameter,
c
N -CN1 P=
define
(4)
for
0
D may
p
(the
extent
of
coagulation),
kNot (7) 1 + kNot be
transformed
[16.
171
either
to
D(t)
or
D(p).
(8)
284
or, D
-o= +%
(9)
D
From
eqn.
(8)
dD -=
2 RA
N2V2k o 0
dT
(10)
2.303
from
which
practice
D
does
higher
the
limit b)
if
[6]
usually
k
using
Rayleigh
Analysis
and
linearly
(10).
V.
do
are
with
behave
not the
themselves
known.
t, as
so.
initial
However,
particles
For
as
predicted
Rayleigh this
this
by
procedure
as
cannot
than
eqn.
(8) the
Ottewill
(dD/dtlo,
larger
in
scatterers,
reason
gradient,
are
However,
the
t
+ o,
be
in
used,
upper
size
scattering.
based
on
and
Shaw
Ottewill
may taking
eqn.
No
particles
present
singlet
if
vary
singlet
suggested
initial for
calculated,
the
aggregates Sirs
evaluating if
be
not
even
because,
and
k may
obtained
in
following
expression
the
&
case
theory: 151
of
showed
larger
for
how
The
particles.
D for
absolute
a mixture
of
rate Mie
constants
theory
aggregate
could
leads
to
be
the
sizes,
m Ni “a:
Kt
I
i
111)
i=l where
ai
is
the
radius
approximation*) Values iently
for
Kt
i,
tabulated
Again,
by
an
N
i
I on
an is
i-mer the
the
m
(again
total Mie
making
scattering
theory,
Heller
Pangonis,
and
the
equivalent
coefficient
have
and
Jacobson
may
be
been
of
sphere an
computed
[151,
as
i-mer. and
a function
convenof
Cm = n/no).
expressron
for
D(p)
derived
making
use
of
(5-71, i-l
N. 1
K,
based
(CY = 2 nnoailX)
eqns.
of
and
=
ll
(>
_ pji+l
P
Hence, *This
(12)
1-p
0
substituting is
suggested
not for
a very doublets
in
eqn.
good
(ll),
approximation, (i=21
1141.
but
corrections
have
only
been
Y
285
i+l
(’ - P)
~
D
i=l
-=
p
i-l
(1-p)
a?
, Kt I i (13)
2 al Kt, 1
Do Plots 546
of
nm),
(eqn. for
D/Do
based
131, the
are
range
converged
versus
on
the
p,
compared of
in
p values
rapidly
for
latex
Rayleigh
at
A
theory
fig.
1.
studied
In (p
(a,
=
leqn. the
110
9) latter
1,
< 0.15
nm.
and
m = 1.20, Mie
theory
it
was
found
case
the
h =
the
summation
in
that
eqn.
(12
1
i = 4.
I
Fig. 1. Theoretical D/D versus p plots: cornparis& of Rayleigh and Mie theories. a=110 nm, h=546 nm and m=l.20.
I I
Fig. indeed fit
1 indicates
and
then
knowing
3.2
the
value
(cc), (rapid
system.
Coaqulation
with
tions
the
Rayleigh
procedure, data
relationship
dispersions
increases
critical
better
of
to
based
the
(eqn.
analysis on
the
theoretical
7)
in Mie
this
analysis,
D(p)/Do
between
p and
case
is is to
equation
t,
to
(131,
evaluate
k,
0’
Critical For
use
D(t)/D(o)
use N
that A
incorrect.
experimental
Rayleigh
increasing
beyond
Concentration charged
it
constant,
concentration
behaviour
is
well
Rate the
Constant
for
(c)
independent ko); that
understood
of
cc
is
particular in
Da>
coagulation
concentration
becomes
rate
from
particles,
electrolyte
which
coagulation
coagulation This
of
terms
rate
up
to
electrolyte
referred
constant
some
(k)
critical concentra-
to
as
the
dispersion/electrolyte of
the
variation
of
the
particle
pair-potential, Vincent
following
V(h)
et
E
8
the
static
repulsion,
first
for
attraction,
term
between
permittivity
of
dielectric length;
the
y
layer;
is
y = tanh [ A
is
ze $ d 4kT
the
= (As
K(h
concentration.
expression
2n)
1-
r.h.s.
of
for
c
based
C
on
the
at
I:
of
the
is that the
E
the
free
Waals
is
space,
the
D the
screening
thickness
potential
der
4 nsoD)
I=
of
electro-
- van
Debye-Htickel
A is the Stern
for
London
h.
permittivity -1 is the
valency;
terms
for
separation
medium);
counter-ion
(14)
(14)
that
is the
(F~
Aa 12h
eqn.
term
particles
the
in
-
second
medium
defined
electrolyte an
[171,
the
the
of
z is the
-
two
constant
with
V(h)
of
and
1,
derived
a(kT)‘y2. exp (ze)2
where
A
[16],
expression
=
and
Vl h
al.
of
the
Stern
(ti,),
1
(15)
effective
Hamaker
constant
of
the
system,
given
by,
_ A$’
(16)
P Ap If
is
the
the
Hamaker
latter
constant
is composed
of of
the
particle
a mixture
(1
and + 21,
Am
is that
then
for
Vincent
the 1181
medium. has
shown
that,
(17)
where and the
A, M2
and
the
mixture
A2
at
Applying to
eqn.
2 =
(14)
are
the
molecular mole the
fraction
to
the
of x,
following
leads
klAz3c:
Hamaker
masses
p2’
constants, the (=
o(1 and components;
pure
the
densities,
p is the
density
= 0 and
dV/dh
M, of
l-x2).
conditions following
[171
for
implicit
cc:
equation
V for
= 0,
cc,
exp(-2k2zbc:)
(18)
yC
where 20’
k C)
1
= 1 92 .
and
k2
x
10’g(~3T5)-i
= 1.605
(ET)-~
(= (=
5.104
1.048
x x
10”
lo-2
for for
aqueous aqueous
solutions solutions
at at
287
20’
Cl,
in
S.I.
electrolyte Note assumed
that
that
this
is too
3.3
Zeta
Debye
-
and
from
(5)
((~d)c,
in
that
on
of
$d
at
Overbeek
medium
solvents.
factors
the
critical
1171.
have
permittivity Eqn.
are
for
(18)
the
illustrates
important.
Mobilities
particles,
( IJ).
(small
value
and
the
mixed
Electrophoretic
mobility
limit
Reerink
other
spherical
to
the
15).
was
the
derived
following by
equation
Henry
1191,
relating
in
the
< values),
f(Ka)
q is the
(19)
viscosity
neglects
of
the
double-layer
sophisticated
medium;
1211.
Loeb
and
which
and
However,
electrolyte
f( Ka)
relaxation
treatments
Wiersema,
White
simple,
Hijckel
= = 1.5n
by
concentration
non-conducting
potential
to
eqn.
authors, following 3 s E dependence
Potentials
For
relates
(c.f.
cc
coagulation
zeta
yc
many
a simple
critical
u
units.
concentration
include
Overbeek
these
concentrations
is given.
surface these
[20],
effects
and
become
(Ka > s
1001,
The
derivation,
conductance
effects.
effects
have
and
been
given
by
O’Brien
subsequently
insignificant in
however, More
at
e.g. and
sufficiently
particular
in
the
high
region
of
cC.
4.
RESULTS
4.1
Rapid For
k.
(c
2.12 1.7 k. the
Coaqulation latex
> cc) x
2 0.1
x
stated
R
based
error of
k.
Constants the
for
the Mie
mixtures.
of
the
rapid
coagulation
the
presence
of Ba(C104)
on
the
Rayleigh
analysis
on
latter over
the
value
in
based this
limits,
using
urea/water
where
latex
using
Values
= 4nR
water,
10-18m3s-1
determined
and
in the
10-18m3s-1
determined
k.
A
for
Rate
the
Mie
approach the
latex
in
analysis
range the (p
According
was
(eqn.
lOJ,
analysis.
Moreover,
was
to
found
rate found
be
constant to
but the
constant,
be
value
of
within
0 < p < 0.2. presence
= 0.1) to
for
of
Ba(C104),
the
Smoluckowski
various
were
also
alkanol/water
1131,
D, is the
be
to
(19) collision
radius
of
two
interacting
particles
and
D1
is the
288
Me01
n-PrOt
EtOH
I 20
20
40
Fig.
mol
%
40
2
k-17 values for IaYex A as a function of alkanol or urea concentration.
UREA I
I
5
10
mol%
289 diffusion
coefficient
the
Stokes
D,
kT = 8nrlah
where
-
Einstein
a singlet
particle.
This
latter
quantity
is given
by
equation,
(20)
a
is
h Hence,
the
hydrodynamic
combining
2R = -
ken
of
radius
eqns.
(19)
of
and
the
particles.
(20),
kT (21)
3ah Plots
of
In
all
In
the
ko;l
ken
cases
n-alkanol
4.2
versus
cases
of
the
or
urea
through
the
with
Coaqulation
concentration
a minimum
n-alkanols,
concentrations
Critical
log
n-alkanol
passes
with
position
increasing
are with
of
the
chain
shown
in
additive
fig.
2*.
concentration.
minimum
moves
to
lower
length.
Concentrations
Fig.
v
3
Log W versus log c for latex A in aqueous Ba(CI0412 solutions
0.
0
Rayleigh
0 p=
theory
.05
C xp=O.lO -1.3
-L.”
at
order
a given
W = k/k versus
shown three
* are
Thus,
0’
(at
Details given
overcome
electrolyte
log
are
to
c.
for
in
fig.
the 3,
p values).
of in
the ref.
problems
of
concentration,
for
c > cc, in
water
based
on
the
It
can
viscosity
data
[21
for
and
be
discussinq
one
W = 1;
latex
used
may
for and
define
the
as
analysis, in
for
urea/water
the
the
rate
region
Plots the
and
the
cscc
is
ratio. of
added
n-alkanol/water
mixtures
constants,
stability
> 1.
Ba(CI?4)2
that
here
absolute
c < c,,W
Rayleigh
seen
the
theory
gp=O.18
log c In
Mie
ref.
Mie
log
W
electrolyte analysis
(W ~11,
there
mixtures 1221.
-2
-3
-4 deOH
EtOH 20
40
60 0
n-PrOH 20
40
60 0
20
40
60 mol 9,
-l.E UC 0, 2
-2.0
l-BuOH 0
UREP
I
1
0.5
1.0
0
I
I
5
10
mol % Fig.
4.
Log c versus la%ex A 0.
n-alkanol
mol
or x,
urea concentration. latex B
%
291 is
little
dependence
discrepancy mental
at
times
given
by
become
the
the
= 1 /kN
0
from
data
is
may
not
perfectly
in
the
but to tf,
instrumental is
fig.
3,
as
the
for
ZNi
of
Thus,
is
quite the
two
although
absolute
determining
some
“drifts”) cc
intersection used.
is
experi-
= No/Z,.
(e.g.
determine
determining
for
there larger
when
to
method
used
satisfactory
that the
errors
possible
analysis
be
used, attributed
“half-life”,
it
shown of
analysis it
be
systematic
Nevertheless
the
analysis
may
coagulation
any
independent
Rayleigh
constants,
of
This
(the
. ’
acc:mulative.
shown,
method
c values.
involved
tl
accurately lines
on
low
rate
critical
coagulation
3 were
obtained
concentrations. Similar the
various
centration, the In
log
with
Rayleigh the
case
In
the
through
log
c plots
of
was
differ
in
of
a maximum
of
this
in
magnitude
maximum
moves
shown
the
added cc
data
a function
electrrolyte.
values are
are
shown
mixtures,
increasing to
as
In shown
for
these
in fig.
both
for
con-
of
cases, 4.
latices
A
size).
n-alkanol/water
for
in fig.
systems,
the
mixtures,
with
(except
as and
used,
particle
the
that
urea/water
a g ain
ethanol/water
case
to
and
Ba(Cl04)2
analysis
B (which
and
W -
n-alkanollwater
lower
n-alkanol n-alkanol
I,
butan-l-01
the
value
concentrations, with
of
and
increasing
cc
The
concentration.
passes position
is greater
n-alkanol
chain
urea
concentration.
length. The
opposite
Here
cc
4.3
Mobilities
TABLE
passes
and
is
seen
for
cc
a minimum
Zeta
as
with
a function
increasing
of urea
concentration.
Potentials
1
Mobility
and
Zeta
C
lmol
trend through
Potentials
u x dm
-3
for
lo8
/m2V-‘5-l
Aqueous
r
Latex,
(Henry) mV
A
<
I Wiersema mV
lo-2
0.73
9.8
9.8
lO-3
1.28
18.4
18.8
lo-4
1.68
25.9
28.5
10-5
1.48
45.0
c = concentration
of
Ba(C10412
1
292
3-
MeOH
I
0
I
40
20
-
EtOH
1
I
I
I
60
0
20
40
-
n-PrOH
I
I
I
I
60
0
20
40
I
60 wt%
0
n- BuOH
Y
10
l 10 x 10 UREA
I
I 15
Fig.
30wt0 6
A1i2
-5 -4 -3
mol
dm
mol
dm
mol
dm
mol
dm
,
1
4
6
I
a
J
wt%
-3 -3 -3
Bat CI04)
5
Mobility (u) versus n-alkanol or urea concentrations at pH 8.2 2 0.2, and the Ba( C104 I2 concentrations indicated.
I
-3
293
r;
MeOH
EtOH
I
80 ImV t
L 0
I
I
I
10
20
30 0
I
1
t
10
20
30 0
I
1
L
10
20
30 mol%
. n-BuOH
5
mol dm 80-
0
1o-4 10 -5
x
10
A
‘0
ImV
-3 -2
mol dm -3
mol dm
-3
-3 mol dm Ba(C104)2
UREA L
5
L
1
I
l”mol%
/ 20
Fig. Q
1
0
1
1
I
0.5
1.0
1.5 mol%
6
Zeta potential (~1 versus n-alkanol or urea concentrations at pH 8.2 2 0.2 and the Ba(C104)2 concentrations indicated.
In
Table
Wiersema
et
[I201
al
experimental (neglect
a comparison
1 above,
analyses
mobility of
for
values.
relaxation,
is made
of
calculating It
surface
would
using
zeta
seem
Henry
is
use
El91
(
potentials
that
conductance)
the
of
the
reasonable
from
Henry
for
and
analysis
c > 10T3
mol
dm-3. Mobility
values
at
mixtures, the
corresponding
are
shown
in
mixture
The
mixtures
with
the
zeta
concentrations
greater
refractive
index
of
It
would
in
‘L
7 mol
medium
zeta
With
approaches
with
that
at
these
of
the
for at
the
the
low
to
lower
urea/water
increasing at
and
analysis, results
moving
possible
% because
5.
potential
length.
were
fig.
Henry
maximum
a minimum
measurements
in
potential
the
the
chain
through
the
zeta
of
urea/water
shown
urea
urea
concentrations latex
the
particles,
difficult. that
the
coagulation
trends
in
the
concentration
zeta
data
potential
shown
data
mimic
those
earlier.
DI SCUSSION Rapid
Coaqulation
According with
to
additive
a slight n-alkanols
other
and at
n-alkanols R
twice
is the
the of
in
the
a h,
butan-l-01 water
also
for
0.5
mol
Constants ken
of
the
medium.
urea.
for
an was
increase observed
is approached.
2 would
The
the
particles,
Any
decrease
radius
of
ah
is is
the
with
on
by
Quantitatively,
this
latex
is
not
to s
particles
its
case,
of
the
with With
taken
invarient
suggest
[3]
the
an
the
increase the
known
account,
in
particular
saturation the
as
with
could
concentration; as
be
30%.
Qualitatively,
however,
the
each
normally be
would
particles.
is
invariable
15%.
should
R/ah,
is
for
seems
than
R/ah
this
effect
less
n-alkanol
to form multilayers
that
reduced
and
in
if
concentration
which
n-alkanols in
indicate
ken
diameter
bare
a constant
maximum
reduction
(contact)
of
be
increasing
% butan-1-01,
hydrodynamic adsorption
should
Fig. with
urea
collision
the
preferential part,
Rate (211,
occurring
and
radius
nature
eqn.
concentration.
minimum
butan-l-01:
in
the
seem
critical
5.1
in
than
the
position
n-alkanol
no
using
of
a maximum
the
passes
that
observations
the
5.
with
and are
calculated feature
is again
potential Note
n-alkanol/water concentrations,
main
increasing
concentration.
making
various
potentials,
6.
concentrations,
concentrations
in
the
!3a(C104)2 zeta
fig.
n-alkanol/water n-alkanol
for
different
effects
concentration seem
to
be
295 too
large
to
lt
is
be
(eqn.
191,
241.
This
(1.70
x
value
predicted
media
the
neglects
10e6
appears
is
m3
any
)
s-’ by
is
close
for
(19)
for
the
(5.45
changes
k.
in
equation
low
10e6
In in
[23,
value
compared
s-l).
is complex;
k
interaczons
experimental
latex,
m3
ah for
hydrodynamic
aqueous
x
to
of
the
for
to case
0
the of
particular,
k
mixed
interfacial
factor.
of
% composition
the
with
at
additives.
the
which
For
the
the
minimum
n-alkanols
maximum/minimum
in
the
in koq
at
other
least,
parameters
noteworthy.
5.2
Critical
Coaqulation
TABLE
2
Values
of
additive
minima
(t)
occur
Concentrations
concentration in
various
(mol
7.5
Ethanol
t
which
Potentials
various
2.5
t
Butan-l-01
0.5
t
Urea
9.0
t
the
array
maxima
(“1
and
corresponds
dmm3.
N/A
The
= not
latex
paper
characteristic
131,
lo-12*
4*
5*
4*
3-4*
2.5*
2.6*
0.5*
N/A
3.6t
N/A
OA- 1 .o*
max.
[31
3.6t
and
particles
the
10*
C
is the
elastic
The
range
111.
Ba(C104)2
modules of
concentration
of
zeta
range,
10
an
ordered
potential values -5 to 1o-2 mol
available
particles
of was
latex to
7.5*
12”
N/A
excess of
quoted
conclusion
no.
adsorption
crystalline
10-15x
N/A
4t
Propan-1-01
earlier
%I at
Zeta
r
Methanol
is
and
parameters.
Additive
r
for
mol
each
correspondence
from seemingly
important the
terms
Smoluchowski
the
correction an
in
the
contributions
eqn.
2 below,
shown
purely that
obtained
necessary
Table
note
accounts
becomes
In
for
to
effect
structure
the
accounted
important
in
carry which
these
latex
reached
that
surface we
discussed
particles the
carboxylic
in
n-alkanol
the
acid
groups.
adsorption
and
n-alkanol/water molecules
In wetting
mixtures, adsorb
an
initially
the through
296 interaction
(H-bonding)
carbonyts
of
the
Thereafter,
they
towards
the
n-alkanol (as
in
zeta-potential,
the
maxima
virtually
may
the
+
.;+.
CTo
density the
( Ba2+)
could
(for
and
of
well
counter-ions for
pointing At
particles.
could
the
ethanol
adsorption
low
n-alkanol
lead
near
to
the
observed
and
particles.
tails
adsorption
account
since
potentials
express
(ionised)
increase
propan-l-01,
excesses
of
in
table
2)
n-alkanol
are
’ IS
the is
these
in
to
ions For
(table
and
to
1.
for
‘d
double
its
reflects
(18)
layer
ui
to an
values no
acid
Qd
avail-
just known
to
,
<
at
the
the
latex
and
hence
an
where
5
alkanol
in
,
ui
be
displaced)
higher
specifically
as
mixtures
concentrations,
all
in
are
( Ba2+
decrease
decrease if
(zero,
is
for
in
in
continuing
could, data
n-alkanol/water
reduced
n-alkanol
charge
densities
Nevertheless,
&
decrease
the
ui
in be
is the
charge
yet,
acetic
increase
o:
level
mixtures,
system.
cc.
the
Primarily to
the
than
indicates
of
in
0:
the
is
after adsorbed
1.
therefore values
as
mixtures. groups
small
concentrations
Eqn.
layer.
eventual
minimum
surface;
ud are
but,
implies
at
The
the
diffuse
Hence,
’
at and
studies
expect
does
displaced
a given
experimental
electrical
concentration
<
n-alkanol/water
interest
the
acid
in
oi
n-alkanol 2
It is of
are the
lower
the
equation,
0:
n-alkanol/water
similarly
merely
reduced
in
titration
n-alkanol
increase.
concentrations, is
at
density
layer;
carboxylic
increase
4 than
rapidly
observed
in
the
might
An
increase
by
increasing
so one
particles.
Stern
co-ions
latices of
charge
the
obtained
with
[251,
balance following
the
(22)
in
and
be
reduced
charge by
(negative) 0)
counter-
for
the
particles
;+ud=O
ionisation
cc
zeta
polystyrene
the
latex
n-alkyl
isotherms),
adsorbed This
with
of the
their
preferential
excess
groups
surface
with
the
strong
adsorption
the
( u;
principle,
of
the
adsorb of
particularly
latex
+u
S
where
at
surface
groups.
in
One
$2+
to
hydroxyl on the
coincident.
around
more
terminal groups
appear
specifically
acid
the
able
the
of
carboxylic
the
would
concentrations,
revealed
their acid
hydrophobic
displacement
of
of
carboxylic
maxima the
parameters these
calculate
Values
do
of
are
A, using
be
the in
which
(Qdlc, A may
in
maxima
c
C
the
values
determine
($,), eqn.
computed
the
(eqn.151, (18). from
occur
<-values value and from eqns.
(16)
A.
297 and
(17).
choice and
taking
for
A is more
(151,
two
A =
and
diameter
values
nm
one
7 where
($,I,
A =
0.41
it
nm
mixtures,
were
A,
is
is
but
in
A2
from
calculating
the
literature
IJidlc,
radius
molecule).
plotted
the
A = 0 Iignoring to
water
quite
and
chosen:
(corresponding
solvating
fig.
Ap,
difficult,
values
0.41 of
for
using layer 2+ Da ion
one
results
as
function
of
bulk
remarkable
that,
for
all
are
four
-\ AzO.41
t
least
at
lower
n-alkanol/water
in < and
around
12.5
is
values here
displaced
7
.
If
the
A
table
is
high
the
21,
equal
A =
0.41
(including all to
the 0,
on
nm,
the
the
layer
H*O
o
MeOH/H,O
and
the
the of
regions
($d)c
other
actual
no
choice
of
reflects
largely,
if
for
the
such
divergence
presumably are
where
converge
hand,
increasing
concentrations, 71 adsorbed Ba” ions
Stern
in
values
n-alkanol
specifically
from
set
For
seen.
at
.
concentrations
occur;
l %
not
the
fact
totally,
A itself
is then
so clear. It
is of
the
< values
interest
at
coagulation 6)
compare value
lower
of This
concentration.
electrophoresis
? 0.5
to
corresponding
coagulation
(fig.
cc
mV.
convergence
-. ‘9
nm
n-alkanol
maxima
7.5
With
(J, 1 versus dre 3 egtric constant ID1 for:
15
with
the
in
constant.
Fig.
t
not
plus
at
20
(vd)c that
(18)
effects)
shown
dielectric
The
eqns.
Stern
of
The
[~61.
electrolyte
and mV,
the
latex
can
only
cannot
particles.
extrapolating i.e.
value i.e.
somewhat
of
the
be
:
versus than
value
be
to
the
the
5,
data
c plot IJJJ~)~.
(12.5
at by
value
under
the log
obtained of
determined
made
Taking
lower
(IJJd)c
the
concentrations
measurements of
the 5,.
at
the
extrapolating cc,
conditions for to
the
log This
mV),
critical
since of
rapid
aqueous
(cc), implies
latex
gives that
(cl,= in
this
case
the
Stern
the
plane
of
shear
is
et
[291
have
data,
for
Rubio-Hernandez from
electrophoretic
mol
mixture,
dm3
containing
KBr.
maxima
and
in
the
n-alkanol,
The
are
by
the
or
are
they
mixtures
Only
are that
for the
more
1
and
data.
for
also
al.
also
able
various
is aware
[161
adsorbed
than
hydrated
(Li ‘1
deduce
be
the
shapes
for
butan-1-01
is
displaced of
the on
in
weakest by
curves Ag I
in [28].
Mg2+
is
of
counter
more
quite
a wide
the
case the
ions
(Br-1,
n-alkanol/water
back
literature
many
data
the
for
presence
through
in
years.
negative of
and
that,
at
the
known
a variety titration
a maximum
with
studied.
They
adsorption, as
fig.
values,
a function
8.
strongly
Nevertheless,
the
ions
with
in
conditions,
shown
competing 8 reflect
in
that
specific
coagulation
adsorbed.
fig.
counter
electrolytes
relative
are
here scattered,
concentration.
potentiometric
the
counter-ions,
butan-1-01
in
passed all
i.e.
results
water,
monovalent the
,
under The
that,
for
oo
more
occurs
coagulation
values
%
here.
corresponding
cc
are
but
dating
mixtures,
the
3 mol reported
systems is
to
critical
the
o:/
there
referred
concentration,
counter-ions,
the
be
in
molecules.
latex
mixtures,
compared
that
groups,
one
mixtures,
n-alkanol
adsorption
but
butan-1-al/water
found
8 shows
of
will
with
5 data
n-alkanol
of
(positive)
values
molecules,
with
in
particles
specifically-adsorbed
specific
studies
other
% and
the
the
charge
n-alkanol/water
in
to
no
to
increasing
of
the latex,
12 mol
particles, with
particles
methanol/water)
close
competing
papers
not
potentials,
investigated:
and
negative
propan-1-01
other
concentration.
Fig.
to
is by
only
butan-l-01
butan-l-01
seem
or
there
in
sols
They
the
than
concentration
were
around
sulphate
2: 1 electrolytes,
increasing were
latex
maxima
with
recent at
iodide
the (but
observed
author
sols
Vincent
1:
surface
zeta
latex
groups,
remarkably
displaced the
the
other
silver
the
determined
particle
With
i.e.
ethanol
either not
These
[2]
from
electrolyte
latex
displacement
latex,
also
sulphate
positive
adsorbing
latex,
of
were
obvious
is that
negative
positive
a
the
no
implication
lK+), of
out
polystyrene
propan-1-al/water
< values
With
2). there
types
groups.
respectively,
(table
further
a background
surface
isobutyramidine
ethanol/water
and
at
Two
(negative)
surface
al.
mobility
n-alkanol/water 10-3
slightly
plane.
specifically of all
these, the
interface. “S-shaped”
the
most
counter-ions Indeed isotherm
of
299
0
0.5 cB/mol
Relative specific Fig. 8. as Ag I/soln. interface, pI=6.5 [161 These who
results
obtained
the
presence
found
to
cc
values KN03
decrease
de in
Rooy
is
ethanol
for
the
AgI
et
al.
[321
needs
i.e.
c c and implication
< go
of
Ghosh
addition
of
various
stability
of
aqueous
here:
increased
stability.
urea.
ferric
ethanol
led
However,
not
of
for
the
with
this
for
decreased from
in
titration
this
work
reported
4 and
older
61,
the
here
where
concentration. ions
efect
ethanol
and
oxide
sols,
is enhanced,
of
in
on
the to
urea to
by the
urea,
trends
whilst
experiments
the
mixtures,
experiments
the
opposite
stability,
sols)
La(N03)3. through
n-alkanol/water
manganese seemingly
other or
detail.
increasing urea 2+ counter Ba
including
molecule.
passes
of
molecules,
and for
(and
5 data
some
in
were
butan-l-01,
cc
studied
]
concentration.
Mg(N03)
in
and
the
regard,
and
C
AgI
(figs.
They
report
values
although
cc
[29-31
counter-ions
LiN03,
mixtures
Wit
a “displacer”
explored
with
c
is
La(N0313,
relevant.
to
than
values
adsorption
oxide
actually
is
with
observed
In
are
it
not
a minimum
organic
They
observed
that
de
the
mixtures,
the
bound
concentration,
account
specific
1331
least
urea/water
through
additions
Ba(N03)2.
to
is that
and
of
to in
cases
water
cc
was
and
ethan-1.2-diol
presence
ethanol
Lyklema
with
i.e.
at
region
is opposite
The
small
increasing
particles
with
strongly
the
that,
both
increasing
obtained
in
indication
one
behaviour
Prasad
have
by
ethan-1,2-diollwater
In
particles,
concentration
latex
in
miscible less
mixtures,
Finally,
work
sols
with
more
for various counter-ions at BuOH concentration (c,).
later
AgI
much
the
with
low
of
Ba(N03)2.
on
some
a maximum
by
much
ethanol/water
There
for or
compete
sites
with
continually
is
therefore
surface
contrast
of
Ethan-1,2-diol will
adsorption a function
1
-3
dm
the
presence
those
led
determine
to the
300
adsorption
of
ethanol
but
careful
in
2+
to
and
potentiometric
to less
positive
ally
The is that
potentials
with
6.
with
just
are
also
found
Agl
sols
example,
presence has
since
changes
in
observed
to
of
be
they
( eqn.
os+
with
increasing
opposite in
the
increasing
opposite
why
urea
a known at
ethanol
urea
trends
221, and
in
of
mixtures
zero
charge
moved
concentration,
concentrations.
of
the
n-alkanol/water point
n-alkanol
effects
may
water
3 sites
hydration
adsorption
the one
n-alkanols
but
Again
and
urea
on
to
this specific-
ions.
is
water
their
not
trends
of For
with
reflect
reason
it
in
Although
measurements,
and
[301
behaviour
potentials
could
adsorbed
decreased
urea.
adsorption
opposite
mixtures.
positive
behaviour
this
of
+ o:)
Lyklema
titration
urea/water
more
ion
(oz
that
that
presence
significance.
Bijsterbosch
in
in
fact
some
found
the
such
changes
the
is of
they
in
interpreting
neverthess,
and
ions,
increased
correspond
urea,
Ba
per
molecule.
in
urea/water
shells
energies
promote
to
specific
structure
charged
adsorption
“breaker”; It
may
be
mixtures
sites
on
it
of
can
that
counter-ions
itself
ions
H-bond
(partly)
resulting
in
loose
stronger
surfaces.
CONCLUSIONS It
has
been
demonstrated
organic/aqueous
media,
on
constant
the
but
Hamaker
so do
organic
more
counter-ions probing
the
Finally,
to
regarding
the
particles,
with
the
for
other
presence added Specific
to
maximum
in
increasing
properties added
electrolytes adsorption
of
the
with
opening
the
elastic
maximum
effects
can
layer,
with
such
a role,
between
or
Such
parameters
play
adsorption
comments modulus
of
latex, 2
but
are,
of is
1.
the
dehydration be
of
studied
by
techniques
as
albeit
in
that
colloidal
course,
still to
Introduction,
colloidal
so closely
The
likely
the
[ll:
corresponds
(table
counter-ions
in
concentration
dilute
there
such
medium,
counter-ions,
double
electrolyte
of
in
in
titration.
the
the
the
competitive
adsorption.
n-alkanol
this
as
stability
changes of
adsorbed
in
dispersion
macroscopic
such
potentiometric
return
position
of
their
studying
permittivity
specifically
distribution or
in
do
the
effects,
and
ion
only
and
increasing
electrophoresis
that
not
subtle
molecules
that
crystals it
is with
that
case
in
crystal
in
latex
found
the
contains
counter-ions
increase
of
remarkable
extent
no
present. the
more
302 25. 26. 27.
28. 29. 30. 31. 32. 33.
H.O. Spirey and Th.Shedlovsky. J.Phys.Chem., 71 (1967) 2171. J. N. Israelachvili, Intermolecular and Surface Forces, Academic Press (1985). F. J. Rubio-Hernandez, F.J. de las Nieves. B. H. Bijsterbosch and R. Hidalgo-Alvarez. Proc. Int. Conf. Polymer Latex III (London, 1989) 15/i. B.H. Bijsterbosch and J. Lyklema, J.Colloid Sci.. 20 (1965) 665. J. Lyklema and J.N. de Wit, J.‘Electroanal.Chem.. 65 (1985) 443. J. Lyklema, Pure and Appl. Chem., 48 11976) 449. J. Lyklema and J.N. de Wit, Colloid and Polymer Sci.. 256 (1978) 1110. N. de Rooy, P.L. de Bruyn and J.Th.G. Overbeck, J.Colloid Interface Sci., 75 (1980) 542. C. Prasad and S. Chosh, Kolloid Z., 175 (19611 134,: 176 (1961) 29: 177
(1961)
155.
301 concentrated
the
electrolyte
latex
modulus,
which
is again
displacement
n-alkanol
molecules.
1c.f.
counter-ion
condensation
possible
explanation
for
dispersion So one
solutions). reflects
a maximum of
in
specifically
the
repulsion
adsorbed
the
between
in
the
counter-ions
poly-
maximum
by
in
the
particles, competing
ACKNOWLEDGEMENTS
I his early
should
guidance in
my
intervening
like
whilst career,
to
express
carrying but
also
my
thanks
out
this
for
his
to
particular help
on
Ron
Ottewill,
piece many
of
not
only
research
occasions
over
for
work the
years.
REFERENCES 1. 2. 3. 4. 5. 6. 7. a. 9. 10. 11. 12. 13. 14. 15.
16. 17. 18. 19. 20. 21. 22. 23. 24.
T. Okubo, J.Chem.Soc. Faraday Trans., 86 (1991) 151. B. Vincent, Ph.D. thesis, Bristol University, 1968. R.H. Ottewill and B. Vincent, J.Chem.Soc.‘Faraday Trans. I, 68 (1972) 1533. J.H. Hearn, R.H. Ottewill and J.N. Shaw, Brit.Polymer Sci., 2 (1970) 116. R.H. Ottewill and J.N. Shaw, Disc. Faraday Sot., 42 (1966) 154. R. H. Ottewill and J.A. Sirs, Bull. Photoelectric Spectrometry Group 10 (1957) 262. S. Mattson, J.Phys.Chem., 37 (1933) 223. D.C. Henry, J.Chem.Soc., (1938) 997. Lord Rayleigh, Phil.Mag., 42 (1871) 107, 274, 447. C. Mie, Ann.Physik, 25 (1908) 377. S.A. Troelstra and H.R. Kruyt, Kolloid Beih., 45 (1943) 225. G. Oster, J.Colloid Sci., 15 (1960) 512. M. von Smoluchowski, Z.Physik.Chem., 92 (1917) 129. A. Lips, C. Smart and E. Willis, Trans. Faraday Sot., 67 (1971) 2979. W.J. Pangonis, W. Heller and A. Jacobson, Tables of Light Scattering Functions for Spherical Particles, Wayne State University Press (Detroit) 1957. B. Vincent, B.H. Bijsterbosch and J. Lyklema, J .Colloid Interface 37 (1971) 171. Sci., H. Reerink and J.Th.G. Overbeek, Disc. Faraday Sot., 18 (1954) B. Vincent, J.Colloid Interface Sci., 42 (1973) 370. D.C. Henry, Proc. Royal Sot.. Al33 (1931) 106. P.H. Wiersema, A.L. Loeb and J.Th.C. Overbeek, J.Colloid Sci., 22 (1966) 78. R.W. O’Brien and L.R. White, J.Chem.Soc. Faraday Trans. (1978) 1607. A. Campbell and E. Kartzman, Cam.J.Res., 28 (1950) 161. L.A. Spielman, J.Colloid Interface Sci., 33 (1970) 562. E.P. Honig, G.J. Roebersen and P.H. Wiersema, J.Colloid Sci . , 36 (1971) 97.
Interface II
74
Interface