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8/11/2019 DIELECTROFORESIS 1915
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The Motion and Precipitation of Suspensoids in Divergent Electric Fields
Herbert A. Pohl
Citation: Journal of Applied Physics 22, 869 (1951); doi: 10.1063/1.1700065
View online: http://dx.doi.org/10.1063/1.1700065
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http://scitation.aip.org/search?value1=Herbert+A.+Pohl&option1=authorhttp://scitation.aip.org/content/aip/journal/jap?ver=pdfcovhttp://dx.doi.org/10.1063/1.1700065http://scitation.aip.org/content/aip/journal/jap/22/7?ver=pdfcovhttp://scitation.aip.org/content/aip?ver=pdfcovhttp://scitation.aip.org/content/aip/journal/jap/96/12/10.1063/1.1810201?ver=pdfcovhttp://scitation.aip.org/content/aapt/journal/ajp/72/1/10.1119/1.1624120?ver=pdfcovhttp://scitation.aip.org/content/aip/journal/jmp/14/10/10.1063/1.1666184?ver=pdfcovhttp://scitation.aip.org/content/aip/journal/jap/34/12/10.1063/1.1729282?ver=pdfcovhttp://scitation.aip.org/content/aapt/journal/ajp/28/6/10.1119/1.1935881?ver=pdfcovhttp://scitation.aip.org/content/aapt/journal/ajp/28/6/10.1119/1.1935881?ver=pdfcovhttp://scitation.aip.org/content/aip/journal/jap/34/12/10.1063/1.1729282?ver=pdfcovhttp://scitation.aip.org/content/aip/journal/jmp/14/10/10.1063/1.1666184?ver=pdfcovhttp://scitation.aip.org/content/aapt/journal/ajp/72/1/10.1119/1.1624120?ver=pdfcovhttp://scitation.aip.org/content/aip/journal/jap/96/12/10.1063/1.1810201?ver=pdfcovhttp://scitation.aip.org/content/aip?ver=pdfcovhttp://scitation.aip.org/content/aip/journal/jap/22/7?ver=pdfcovhttp://dx.doi.org/10.1063/1.1700065http://scitation.aip.org/content/aip/journal/jap?ver=pdfcovhttp://scitation.aip.org/search?value1=Herbert+A.+Pohl&option1=authorhttp://oasc12039.247realmedia.com/RealMedia/ads/click_lx.ads/www.aip.org/pt/adcenter/pdfcover_test/L-37/126952390/x01/AIP-PT/Hiden_JAPArticleDL_091714/1640x440px-BANNER-AD-GENERAL-25058.jpg/47344656396c504a5a37344142416b75?xhttp://scitation.aip.org/content/aip/journal/jap?ver=pdfcov8/11/2019 DIELECTROFORESIS 1915
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J O U R N A L
O F
A P P L I E D
P H Y S I C S
V O L U M E 2 2
N U M B E R 7
J U L Y 1915
The Motion and Precipitation of Suspensoids in ivergent Electric Fields
HERBERT A. POHL
*
Naval Research Laboratory, Anacosta, D.
C.
(Received November is, 1950
The motion of suspensoid particles relative to
that
of the solvent resulting from polarization forces pro
duced
by an
inhomogeneous electric field is defined as dielectrophoresis.
t
is analogous to
the
related
phenomenon of electrophoresis, in which motion of suspensoid particles is produced by the action of an
electrostatic field on the charged particles.
From a consideration of theoretical calculations and from experimental observations it is concluded that
the phenomena of dielectrophoresis and dielectro-precipitation can be observed under rather ideal
conditions, though it is ordinarily often difficult to do so because of the presence of the more easily produced
electrophoresis or ion-type migration of charged particles.
The usefulness of die1ectrophoresis (and/or electrophoresis) for removing suspended solid particles from
polymer solutions during analysis is described.
T
HE application of highly inhomogeneous, strong,
electric fields to suspensions of solids or of
liquids in fluids has been found helpful in coagulating
and precipitating finely dispersed material for analysis.
The
phenomenon seen in the relative motion
of
sus-.
pensoid and medium resulting from polarization forces
produced by
an
inhomogeneous electric field is defined
as dielectrophoresis; and when this leads to co
agulation, the process may be called dielectro
precipitation.
Dielectrophoresis does not require ionized particles
but rather depends on asymmetrical induction and
attraction of displacement charges within the particles,
and further that the resultant motions be different for
solvent and
solute. Migration in either alternating or
direct current fields is observed
to
take place. Figure 1
diagrammatically shows the effect of an inhomogeneous
field on a discrete particle lying in the field. The un
equal field force acting on all permanent or induced
dipoles causes them to be constrained to move towards
the region of highest field density.
When the polarizability of the suspensoid is greater
than
the solvent, the asymmetric field forces accelerate
the suspensoid particles more than the solvent, giving
rise to an increased concentration of the suspensoid
near the center of high field strength. The suspensoid
particles are then more prone to collision and coagula
tion. Agglomerations of suspensions may therefore fre
quently be accomplished with this technique using
simple apparatus.
The following equations are included to show the
relative importance of the factors involved. The force
on a small particle in a non-uniform field is expressed
to a good first approximation by
j=PiJE/iJr
(1)
=E E iJE/iJr (2)
=
k-1) EiJE/47riJr= k-1)
iJ(Jtl)/87riJr, (3)
*
Based on research
at
the Naval Research Laboratory, Ana
costa, D. C. Present address:
Du Pont
Experimental Station,
Wilmington, Delaware.
where j=force per unit volume,
P=polarization=EE,
E = field strength, E= proportionality factor of polariza
bility, and k=dielectric constant = 1+ 47rE
The excess force on the suspensoid of dielectric
constant, kl' over that on the solvent
of
dielectric
constant, k2 is
t:.j= EI - E2)iJ(Jtl)/iJr
=
k
l
-
k
)iJ(Jtl)/47riJr. (4)
This relation says that the motion of the suspensoid
under the influence of the inhomogeneous field will be
proportional to the absolute value of the electric field
strength applied, to its divergence,
and
to the differ
ences in dielectric constant of suspensoid and solvent.
The motion will be in the direction of the greatest field
strength and independent of field direction.
The force of the field on the particle will cause mo
tion opposed
by
viscous drag; hence, the force on the
particle is given by
F=
(volume of particle) : j = 4 7 r a 3 ~ j / 3 =
67ra?]v
(5)
using Stoke's equation and assuming spherical par
ticles, giving
v=
2
a
2
~ j / 9 ? ] =
a
2
(k
l
-
k
2
EiJE/187r?]iJr,
(6)
where F=force on the particle, a=radius of particle
in cm, ?]=viscosity of medium in poises, v=velocity
in cm/sec.
In the interesting case of the divergent field formed
in the liquid between two infinitely long concentric
cylinders, we have
E=iJV iJr= 2q/kr,
V
1
- V
2
= (2q/k)
In h/rl),
V
1
- V = (2q/k)ln(r/rt),
iJ(Jtl)/iJr=4q2/rk2,
7)
8)
(9)
10)
where V = potential in statvolts at
r
cm from the center,
V
1
- V
2
=potential in statvolts applied across the elec
trodes,
q=charge
per cm on
the
inner conductor,
k=dielectric constant of the mixture.
869
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8/11/2019 DIELECTROFORESIS 1915
3/4
870
HERBERT
A.
POHL
v
FIG.
1.
Diagram
of
forces operating on dipoles and suspended
particles in an inhomogeneous electric field.
Dielectrophoresis.
Combining Eqs. 8) and 9) and substituting in
Eq. (6), we get
v=a
2
(k
1
2
) V
1
-
V
2
)2j1811 ?)r
In(r2/rl)'
11)
In
a system, e.g., where
11
=
10
mils=
1.27X lQ-2
em,
2=5
em,
and
V l- V
2
=1()o1
volts=33.3 statvolts, and '1=1Q-2 poise (tolu
ene, etc.), we have
12)
E.g.,
i a= 101 =
10-
8
em,
r=
1 em, k
1
k
2
i= 108
as for a graphite
or Ni sol
in
toluene, then
we
have
V= 55 10-
3
)2108= 0.055 em/sec,
which is a reasonably determinable velocity in the laboratory.
However, for a very
fine
suspension of particles
of
not too
different dielectric constant we might observe, e.g., where
a=
11'
= 10-
4
em,
r=
1 em,
k
l
- k
2
i=
10; as for a polymer suspended in
toluene:
v=55(1Q-4)210=5.5X10-
6
em/sec, which is in the order
of
magnitude of diffusional velocities.
The
migration in this case
would be quite difficult to observe.
A calculation due to
J.
A. Wheeler of the time re
quired to sweep out a cell by dielectrophoresis is given
below:
dt=dr/ ar/at) =dr/v=const rdr,
13)
since
rlr.
Hence, the time in seconds is
t sec) 911 ?)r4[ln(r/rl)]2/2a
2
(k
1
2
)
(V1- V
2
. (15)
E.g., in the above apparatus [see Eq. (12)J,
we
have
t
,4/220a
2
kl- k
2
.
For the case
of
the graphite or
Ni
sol described,
t=
103108/220103=4.55 sec, which is a reasonably short experi
mental period.
For
the polymer suspension described
t= lQ410
4
/22010=4.55
I )o1 sec=
12.6 hr.
In the absence of disturbing influences such as con
vection, the weight, w, of material migrating to the
central electrode in time,
t,
will be
W=c vol. swept out)=ch(1I r,2)i
hence, we have,
W = hca[(V1 V
2)/ln(r2/rl)][211 (k1-
k
2
)/?)]lt
1
,
where c=conc of sol in grams/cm
3
, h=height of cylin
drical cell, and rt=radius swept clean in time t.
At this point it is well to sum up our expectations
about the occurrence of dielectrophoresis and compare
it with the related phenomenon
of
electrophoresis.
Dielectrophoresis, arising because
of
the tendency
of
matter to become polarized
and
move into regions
of highest field strength,
1.
Produces motion
of
the particles in which the direction of
motion is independent
of
the direction of the field; Le., either dc
or ac voltages can be employed.
2.
Should be observable most readily in relatively coarse sus
pensions (e.g., particle diameter
~ 2 1 )
3.
Requires highly divergent fields. No motion should be ob
served in the nondivergent field between centers of parallel plates.
4. Requires relatively high
field
strengths, e.g., 10,000 v across
a 5-cm cell.
5.
Would be most apparent in fluids of
low
viscosity (thin
liquids, gases).
6. Generally requires a large difference in dielectric constant
between solvent and
s o l u t ~ . g .
(k
l
- k
2
)
>
10-100.
7.
Will deposit weights
of
sol in direct proportion to the voltage
applied in equal times of deposition.
Electrophoresis, arising from the electrostatic attrac
tion
of
charged electrodes for charged particles,
1.
Produces motion of the particles in which the direction of the
motion is dependent on the direction
of
the field. Reversal of the
field reverses the direction
of
travel. Care must be taken in the
application of this rule for distinction between electro- and
dielectrophoresis as motion
of
charged particles towards a sharp
electrode can occur even in alternating fields of high strength
because of the occurrence of partial rectification effects making
the applied alternating voltage cause predominantly direct current.
For
example, a milky
20
percent suspension
of
Hycar rubber in
methyl ethyl ketone was readily precipitated to form a thick
adherent coat on parallel electrode plates 5 cm apart by dc
but
not
by
ac voltage
of 2000
to
6000
v. This shows the suspension
to consist mainly of charged particles capable of deposition fol
lowing electrophoresis. The suspension was also precipitated
at
the wire
of
the wire and sheet pair
by
either dc or 6O-cycle ac
voltage as above. The latter observation by itself might
at
first
sight be considered as caused by dielectro-precipitation; however,
the further consideration shows this cannot be the case as the
dielectric constant of the medium (18.4) exceeds
that
of the sus
pended particles
ca
15). This leaves deposition following electro
phoresis as the more probable explanation with the assumption
that partia l rectification of the ac occurred.
2. Is
observable with particles of any molecular size.
3. Operates in either divergent or uniform fields.
4. Requires relatively
low
voltages.
5. Requires relatively small charges per unit volume
of
the
particles.
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8/11/2019 DIELECTROFORESIS 1915
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S U S P E N S O I D S
IN D I V E R G E N T E L E C T R I C F I E L D S
871
With these guides for examination of particle motion
in electric fields, it is instructive to examine some of
the experimental facts available. Hatschek and Thorne
l
studied nickel sols in anhydrous toluene in which rubber
acted as a protective colloid.
As
electrodes, they used
small parallel plates having sharp edges. They observed
equal quantities of precipitate forming
at
each elec
trode, with considerable rubber present n the pre
cipitate. The
sol
precipitated in quantities proportional
to the first power
of the applied voltage during equal
times. This, they concluded, was a principal reason for
interpreting the results as electrophoretic and not di
electrophoretic, since they expected first-power de
pendence in the first and second-power dependence in
the second instance. The present theory indicates that
first power dependence on voltage for the weight de
posited would be expected for cells of cylindrical sym
metry, an approximation of the field at the sharp edge
of the parallel sheet electrodes.
Hatschek and Thorne found several contradictory
phenomena in their interesting study. For one, alter
nating potential did not cause coagulation (migration
was
not
studied) as did static voltage in their large
apparatus,
an
observation which led them to interpret
the phenomenon in this instance to be electrophoresis.
On the other hand, in a smaller cell used
on
their
microscope stage they observed the particles in the
middle of the field between two narrow parallel plates
to be unaffected by the field. Further, particles away
from the exact middle, which were caused to migrate
under the influence
of
the field, did not reverse their
direction of travel on changing the field direction. The
last two observations cannot easily be explained as
electrophoresis but can easily be interpreted as typical
examples
of
dielectrophoresis.
t
would seem that both
electrophoresis and dielectrophoresis were being ob
served in their experiments despite their conclusion that
only electrophoresis was present.
Soyenoff2
noted the coalescence of coal dust in
toluene occurring at over 5000 volts/em to be equally
effective by dc or ac voltage. This he attributed to
dielectric pohtrization, remarking
that
any sus
pensoid body of higher conductivity or dielectric con
stant
than the medium
is
caused) to move toward the
region of highest field intensity.
Reising,S in a study of the migration of pigment
particles in paint vehicles observed in several cases
that roughly equal quantities
of
precipitate collected
on his relatively narrow electrodes. He used static
voltages. Whether or
not
this is an instance of dielectro
phoresis is not certain from the descriptions given.
1 E. Hatschek and P. C. L. Thorne, Kolloid-Z. 23, 1 (1923).
2
B
C. Soyenoff, J. Phys. Chern. 35, 2993 (1931).
S J. A. Reising, Ind. Eng. Chern. 29, 565 (1937).
Winslow' produced rotary migration and alignment
of elongated semiconducting particles suspended in
media
of
low dielectric constant (e.g., moist silica gel
particles suspended in kerosene), and also observed
migration of particles under the influence of field gradi
ents. The latter seems describable as dielectrophoresis.
Studies in our laboratory have been concerned prin
cipally with the use of dielectrophoretic technique to
aid in polymer analysis. t proved difficult, e.g., to
remove carbon-black filler from polyvinyl chloride
samples by other means such as filtration or centrifuga
tion;
but
removal was rapidly and simply accomplished
in a powerful, divergent electric field.
For
example, a
one-gram sample of the polymer sample was taken up
in 50 ml of di-isopropyl ketone with the aid
of
gentle
heating, then placed in the coagulation cell. The cell
consisted of a Petri dish of c lO-cm diameter containing
the electrodes. A lO-mil tungsten wire formed the
central electrode and dipped vertically into the liquid.
A band
of
tinfoil 8 rum high resting on the inner wall
of the cell formed the outer electrode. A high voltage,
either dc or ac
of
10,000 volts, was then applied.
The
liquid immediately underwent considerable action, small
ripples formed, and the carbon particles underwent
rapid migration toward the central wire to form a
coating. The solution
of
polymer became water clear in
a few minutes of what was very likely dielectro-pre
cipitation and was then removed for further analysis.
Similar results were obtained with polyvinyl chloride
polyvinyl acetate copolymers .When parallel plates,
with carefully rounded edges to avoid high field gradi
ents, were used instead of the wire and sheet combina
tion, no precipitation was observable with either dc or
ac. This adds confirmation to the conclusion
that
di
electrophoresis occurred under these conditions.
Similar results were obtained with suspensions of
coal dust or of charcoal dust in toluene.
t is concluded
that
the phenomenon
of
dielectro
phoresis can be observed, though it is often difficult
to do so because of the presence of the more easily
produced electrophoresis or ion-type migration of
charged particles. Calculations of the magnitudes of the
effects of various variables on
it
show
that
dielectro
phoresis, to be observed, requires rather ideal condi
tions. A number of experiments are cited as examples
of
these conclusions. The usefulness
of
dielectrophoresis
and/or electrophoresis) for polymer analysis
is
de
scribed.
The
author wishes to acknowledge the many helpful
suggestions
and
criticisms made by Drs. Maurice B.
Hall, Harold F. Ring, and John A. Wheeler.
4 W.
M. Winslow, J. App\. Phys. 20, 1137 (1949).
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