Journal of Colloid and Interface Science 318 (2008) 477–486
www.elsevier.com/locate/jcis
Electrophoretic mobility does not always reﬂect the charge on an oil droplet
V. Knecht a,∗
, H.J. Risselada b
, A.E. Mark c
, S.J. Marrink b
a Max Planck Institute of Colloids and Interfaces, Science Park Golm, 14424 Potsdam, Germany
b Groningen Biomolecular Sciences and Biotechnology Institute, and Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4,
9747 AG Groningen, The Netherlands
c School of Molecular and Microbial Sciences, University of Queensland, St Lucia, Brisbane, QLD 4072, Australia
Received 7 September 2007; accepted 23 October 2007
Available online 3 December 2007
Abstract
Electrophoresis is widely used to determine the electrostatic potential of colloidal particles. Oil droplets in pure water show negative or positive
electrophoretic mobilities depending on the pH. This is commonly attributed to the adsorption of hydroxyl or hydronium ions, resulting in a
negative or positive surface charge, respectively. This explanation, however, is not in agreement with the difference in isoelectric point and point
of zero charge observed in experiment. Here we present molecular dynamics simulations of oil droplets in water in the presence of an external
electric ﬁeld but in the absence of any ions. The simulations reproduce the negative sign and the order of magnitude of the oil droplet mobilities
at the point of zero charge in experiment. The electrostatic potential in the oil with respect to the water phase, induced by anisotropic dipole
orientation in the interface, is positive. Our results suggest that electrophoretic mobility does not always reﬂect the net charge or electrostatic
potential of a suspended liquid droplet and, thus, the interpretation of electrophoresis in terms of purely continuum effects may need to be
reevaluated.
© 2007 Elsevier Inc. All rights reserved.
Keywords: Electrophoresis; Electrokinetic phenomena; Zeta potential; Water structure; Molecular dynamics; Computer simulation
1. Introduction
Electrophoresis is the migration of an ion in a homogeneous
electric ﬁeld, the migration rate being proportional to the ﬁeld
applied [1]. The electrophoretic mobility of an ion (i.e., its migration
rate divided by the intensity of the electric ﬁeld in the
surrounding medium) is proportional to the charge of the ion.
Remarkably, neutral particles also show electrophoretic activity.
Oil droplets [2–4] in the absence of surfactants at neutral or
high pH show negative electrophoretic mobilities. Their electrophoretic
mobilities correlate with pH and change sign at low
pH [5,6]. This behavior is often explained in terms of the charging
of oil droplets due to adsorption of hydroxyl (OH−) or
hydronium ions (H3O+) to the hydrophobic surface, leading to
an excess of hydroxyl ions at neutral or high pH [7,8] or of
hydronium ions at low pH. This view is supported by the obser*
Corresponding author.
E-mail address: vknecht@mpikg.mpg.de (V. Knecht).
vation that dispersion of oil droplets in water results in a change
in the pH of the bulk water. A drop in pH is observed at high
or neutral pH, and a rise in pH is observed at low pH [5,9]. Recent
molecular dynamics simulations have also suggested that
hydroxyl [10] or hydronium ion adsorption to a hydrophobic
surface [11] can be induced by anisotropic water dipole orientation
close to the surface. Remarkably, the isoelectric point
(the pH value at which the electrophoretic mobility vanishes)
and the point of zero charge (the pH value at which the dispersion
of particles in water does not change the pH of the bulk
water) do not coincide. For oil droplets, the isoelectric point
is at about pH 3, whereas the point of zero charge is at about
pH 6 [5]. At pH 6 where the surface charge suggested from the
dispersion-induced pH shift is zero, oil droplets exhibit negative
electrophoretic mobilities [5]. Alternative explanations for
negative electrophoretic mobilities of oil droplets are that ionic
impurities at the interface, or water ordering itself, could give
rise to a negative electrostatic potential in the oil phase, driving
the electrophoresis of oil droplets [5,8].
0021-9797/$ – see front matter © 2007 Elsevier Inc. All rights reserved.
doi:10.1016/j.jcis.2007.10.035
478 V. Knecht et al. / Journal of Colloid and Interface Science 318 (2008) 477–486
Fig. 1. The systems simulated were comprised of heptane (S, M, L, P, cyan or dark gray) or a hydrophobic wall (W, cyan or dark gray) and water (red or white). The
heptane phase was either in the form of a droplet with radius 1.5 nm (S), 4.7 nm (M), or 8.2 nm (L), or a slab (P). S, M, and L show a section through the middle of
the droplets. The direction of the external electric ﬁeld (green or gray arrows) and the direction of the migration of the oil phase (white arrows) are indicated. (For
interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article.)
Here we present results of molecular dynamics simulations
of oil (heptane) droplets that show negative electrophoretic mobilities
in the absence of hydroxyl or other ions. The results
suggest that electrophoretic mobility does not solely reﬂect the
net charge or electrostatic potential on a suspended particle. As
such, the work challenges the current theory of electrophoresis,
which is based primarily on simple continuum models, and
suggests that dipolar ordering at hydrophobic interfaces might
also play a role.
2. Methods
2.1. Simulation setup
The systems considered in this work are shown in Fig. 1 and
speciﬁed in Table 1. Each system was composed of heptane or
two hydrophobic walls and water. The heptane phase was in
the form either of a droplet or of a slab in the xy plane. Heptane
droplets of radius 1.5 nm (system S), 4.7 nm (system M),
or 8.2 nm (system L), a slab (system P), or two hydrophobic
walls (system W) were simulated under periodic boundary conditions.
The droplet radius in system S was chosen to be somewhat
larger than the width of a water/oil interface suggested
from previous simulations [12]. The droplet size in system L
was chosen to maximize size while keeping the computations
feasible. The droplet radius in system M was chosen roughly
equal to the arithmetic mean of the droplet radii chosen in systems
S and L. In addition, a single heptane molecule in bulk water
was simulated at equilibrium to study the structure of water
in contact with heptane (system H). Here an octahedral box was
used. For systems S, M, and L, rectangular (system S) or cubic
(systems M and L) stacks of heptane molecules were placed
in a rectangular or cubic box, respectively, with a distance of
∼2.0 nm between the stack and the boundary of the box. The
Table 1
Systems simulated, oil droplets in water with radii 1.5 nm (S), 4.7 nm (M),
and 8.2 nm (L), respectively, a heptane slab of thickness 6 nm (P), and two
hydrophobic walls (W) in contact with water, or a single heptane molecule immersed
in water (H)
System NH NW R (nm) a × b × c (nm3)
S 64 3859 1.5 6.5 × 4.5 × 4.5
M 1792 34,327 4.7 11.6×11.6×11.6
L 10,547 143,948 8.2 19.6×19.6×19.6
P 420 3418 – 4.2 × 4.2 × 12.0
W – 3418 – 4.3 × 4.0 × 12.3
H 1 4147 – 56.3
Note. The systems were simulated at equilibrium and, except for system H,
exposed to external electric ﬁelds. Given are the number of heptane molecules,
NH, the number of water molecules, NW, the curvature radius, R, and the initial
size of the simulation box, a × b × c. The number of wall atoms in system W
was 720.
remaining space was ﬁlled with water molecules and the system
was energy-minimized and simulated for 1 ns. In each case
the heptane cluster adopted a spherical shape within ∼300 ps.
To generate system P, a periodic box of heptane molecules was
energy-minimized and equilibrated to give the appropriate heptane
density. The periodic box was extended in the z direction
and the space created was ﬁlled with water molecules to create
a two-dimensional slab of hexane in water. This system was
energy-minimized and equilibrated. Systems S, M, L, and P
were simulated at equilibrium and exposed to an external electric
ﬁeld. The electric ﬁelds were in the range 0.1–0.5 V/nm
and applied in the positive x direction (systems S or P) or in
the (1,1,1) direction (systems M and L) as depicted in Fig. 1
(green or gray arrows, color online).
To check for possible effects of the ﬁeld direction, an additional
simulation of system P was performed in which an electric
ﬁeld of 0.1 V/nm was applied in the positive y direction.
V. Knecht et al. / Journal of Colloid and Interface Science 318 (2008) 477–486 479
Note that the electric ﬁeld in the system is dependent not only
on the external ﬁeld but also on the boundary conditions used to
calculate electrostatic interactions [13]. The electric ﬁeld in the
water bulk (corresponding to the applied electric ﬁeld in experiments,
the effective ﬁeld) was determined as described below.
The box geometry and the direction of the electric ﬁelds were
chosen to maximize the distance between the oil droplets and
their periodic images in the direction of the ﬁeld, allowing for
the fact that an application of an electric ﬁeld can induce the
elongation of a oil droplet in the direction of the ﬁeld. Such
electrodeformation has been observed for lipid vesicles [14]
and arises from Maxwell stress in the (high/low dielectric) water/alkane
interface [15]. The systems were simulated for 40 ns
(systems S, P, and W), 6.5 ns (systems M), or 1 ns (system L),
at each ﬁeld intensity. System H was simulated for 4 ns at equilibrium.
To obtain sufﬁcient statistics for a spatially resolved
ﬂow proﬁle, the simulation of system P at an electric ﬁeld of
0.3 V/nm was extended to 150 ns.
To determine the electrophoretic force between the heptane
and the water phase, system P was also simulated at equilibrium
and various ﬁeld intensities subjecting the distance between the
centers of mass of the heptane and the water phase in ﬁeld direction,
x, to a harmonic potential V (x) = (k/2)x2 (umbrella
potential) with a force constant k = 10 J/molnm2. Similar simulations
were performed for a system in which the heptane slab
was replaced by two hydrophobic walls consisting of 360 atoms
ﬁxed on a triangular lattice with a lattice constant of 0.23 nm
(Fig. 1 (W), system W). The distance between the walls was
chosen such that the dimension of the hydrophobic phase normal
to the ﬁeld direction was similar to the thickness of the
heptane slab in system P. The electrophoretic force F was determined
from the time average of x, denoted as x , according
to
(1)F = −k x .
The systems described above were studied using molecular
dynamics simulation techniques, which are based on iteratively
solving Newton’s equations of motion to propagate the system
in time and semiempirical force ﬁelds to describe interatomic
interactions, treating atoms as classical point masses [16].
The water was described using rigid water molecules with
ﬁxed charge distribution, employing the three-site simple point
charge (SPC) model [17]. To test the effect of the water model,
system P was also simulated at equilibrium and in an external
ﬁeld of 0.1 V/nm using the three-site SPC/E [18] and the
four-site TIP4P [19] models. Heptane was described using the
GROMOS-87 force ﬁeld [20], in which the (nonpolar) hydrogen
atoms of the heptane molecules are described using united
atoms, whereas bond angles and torsions are described using
standard potentials. For the wall atoms, Lennard–Jones parameters
of the methylene groups of the GROMOS-87 force ﬁeld
were used. Each wall atom and united atom of a heptane molecule
carried a partial charge of zero. Polarizability was not taken
into account. In this model, an external electric ﬁeld only interacts
with the water molecules.
Full electrostatic interactions were considered using the particle
mesh Ewald (PME) technique [21] using tinfoil boundary
conditions. To test the effect of the boundary conditions, system
M was also simulated for 4 ns using PME using vacuum
boundary conditions. All simulations were performed using
GROMACS [22]. The lengths of covalent bonds in heptane
molecules were constrained to ideal values using the LINCS
method [23]. The bond lengths and bond angle in water were
constrained using SETTLE [24]. In addition, the total mass of
the molecule was redistributed in order to increase the mass of
the hydrogen atoms, allowing the use of a 4-fs time step [25].
Heptane and water were separately coupled to an external temperature
bath of 300 K using a Berendsen thermostat [26] with
a coupling constant of 0.1 ps. The pressure was kept constant at
1 bar by coupling all directions simultaneously (systems S, M,
and L), only the xy direction (interface plane, system P), or only
the z direction (normal to interface plane, in the simulations using
the umbrella potential for systems W and P), respectively,
to a pressure bath using a Berendsen barostat [26] with a coupling
constant of τ = 1.0 ps. The coupling constants used for
the thermo- or barostat were chosen to be weak enough to minimize
the disturbance of the system and strong enough to keep
the average temperature or pressure close to the desired value,
based on empirical data [26]. In simulations at constant pressure,
the box volume is not constant, but ﬂuctuates over time.
The relative ﬂuctuations of the box volume were 0.2% and 0.1%
for system S and M, respectively. Fluctuations in box size are
realistic due to the ﬁnite (microscopic) size of the system. Relative
ﬂuctuations in volume vanish in the thermodynamic limit
of an inﬁnitely large (macroscopic) system. Atom coordinates
and velocities of the systems were saved every 20 ps for analy-
sis.
2.2. Analysis details
Analysis was performed omitting the initial 100 ps (system
S), 300 ps (system M), 100 ps (system L), or 1500 ps
(systems P and W), respectively, for equilibration. The electrophoretic
mobilities were determined from the migration rate
of the center of mass of the oil phase in the direction of the
ﬁeld. For the heptane droplets the absolute rate, and for the heptane
slab the rate of migration relative to the center of mass of
the water phase, were determined. For system P at an electric
ﬁeld of 0.3 V/nm, a spatially resolved ﬂow pattern was determined
from the ﬁnal 110 ns of a 150-ns simulation. Here,
the average velocity of atoms in ﬁeld direction as a function of
the distance s normal to the interface, was determined using a
0.6-nm bin width. Error bars for migration rates, ﬂow proﬁle,
or electrophoretic forces (Eq. (1)) give the standard error from
block averages obtained by dividing the trajectory into four segments.
Electrophoretic mobilities were obtained from linear ﬁts
to the observed migration rates of the droplets as a function of
the effective electric ﬁeld. The effective electric ﬁeld was taken
as equal to the electric ﬁeld in the water bulk. This assumption
was made because in electrophoresis experiments, the oil fraction
is very low (e.g., below 0.05 vol% in studies by Marinova
et al. [8]). Hence, in experiment, the average electric ﬁeld in the
water/oil emulsion is approximately equal to the electric ﬁeld
in the water phase. According to continuum electrostatics, the
480 V. Knecht et al. / Journal of Colloid and Interface Science 318 (2008) 477–486
local electric ﬁeld E in the water bulk is related to the polarization
PE in the water bulk via PE = 0( − 1)E, where is the
dielectric permittivity of water. For the molecular model used
here, the polarization is given by PE = nμ, where μ is the average
dipole moment of a water molecule in ﬁeld direction, and
n is the number density of water molecules. Using these equations,
the effective electric ﬁeld was determined from [13]
(2)E =
nμ
( − 1) 0
,
where n is the number density of the water molecules in the
bulk, n = 31 nm−3. The value used for the dielectric permittivity
of SPC bulk water was = 61 [27].
For systems S and P at equilibrium, the density, ordering,
and electrostatic properties of water were determined as functions
of the coordinate s normal to the interface. Here the origin
was set to the point at which the water density equaled half
the bulk water density. Radial proﬁles for the oil droplets and
proﬁles along the interface normal (z direction) for the planar
interface or the wall were determined by dividing the distance
scale into bins with a width of 0.01 nm. The proﬁles were
smoothed using a Gaussian ﬁlter with a s = 0.2 nm bin width.
To analyze the water ordering, the average dipole moment μ(s)
of water molecules along the local interface normal was determined
as a function of distance. The number densities n of
atoms of water and heptane molecules (normalized to one) and
the charge density q(s) were evaluated in a similar manner. In
particular, the charge density q(s) was obtained from
(3)q(s) =
i;|si−s|< s/2
qi/dV (s) .
Here, si denotes the position of atom i normal to the interface,
qi is the partial charge of atom i, dV (s) denotes the volume
element associated with the interval [s − s/2,s + s/2], and
... indicates time averaging. Note that the charge density was
not determined from the divergence of the polarization, which
would only be correct if water molecules were ideal dipoles.
Rather, the full charge distribution was taken into account so
that higher moments (quadrupole, etc.) were also considered.
The electric ﬁeld E0(s) along the local interface normal was
determined from
(4)E0(s) =
1
0s2
s
0
q(s )ds
for the oil droplets. This equation is the solution of the ﬁrst
Maxwell equation for radial symmetry, (1/r2)∂(r2E0(r))/∂r =
(1/ 0)ρ(r). This equation gives the electric ﬁeld distribution in
a sphere concentric with the oil droplet and enclosed by the
simulation box, assuming approximate spherical symmetry in
this spherical region. For the planar interface the ﬁeld was determined
from
(5)E0(s) =
1
0
s
s0
q(s )ds .
Here, s0 denotes the position of the center of the oil slab.
Note that the dielectric permittivity = 1 was used in Eqs. (4)
and (5). This is correct for a molecular model of a dielectric
where all charges are taken into account explicitly, in contrast
to continuum electrostatics where a dielectric is modeled implicitly
using a dielectric permittivity > 1. The electrostatic
potential φ(s) with respect to bulk water was determined from
(6)φ(s) =
smax
s
E0(s )ds .
Here smax resides in the bulk water. Analysis of the average
water dipole moment μ was restricted to regions with a water
density larger than a fraction of 0.01 of the bulk density in order
to ensure sufﬁcient statistics.
Similar, for system H at equilibrium, the density, ordering,
and electrostatic properties of water were determined as a function
of the distance from the center of mass of a methyl(ene)
group, s, averaged over all methyl(ene) groups. Here, the initial
100 ps were omitted for equilibration. The number density
of water molecules was determined choosing a bin width of
0.03 nm. To analyze the water ordering, the average dipole moment
μ(s) of water molecules along the distance vector was
determined as a function of s denoting the distance between the
centers of mass of the methyl(ene) group and the water oxygen.
The charge density q(s) was evaluated using Eq. (3). For the
determination of μ(s) and q(s), a bin width of 0.002 nm was
chosen, and respective proﬁles were smoothed using a Gaussian
ﬁlter with a s = 0.12 nm bin width. The electric ﬁeld E0(s)
along the distance vector was determined from Eq. (4).
3. Results
3.1. Oil droplets exhibit negative electrophoretic mobilities
The systems considered in this work were composed of
heptane (Fig. 1, S, M, L, and P) or two hydrophobic walls
(Fig. 1, W) and water. The heptane phase was in the form either
of a droplet suspended in water (Fig. 1, S, M, L) or of a slab in
contact with water (Fig. 1, P). In the simulations we observed
that the oil droplets, when placed in a homogeneous electrostatic
ﬁeld (Fig. 1, S, M, L; green or gray arrows, color online)
started to migrate in the negative ﬁeld direction (Fig. 1, S, M,
L; white arrows).
Fig. 2a shows the rate of migration of the oil phase for the
different systems simulated as a function of the intensity of
the electric ﬁeld in the bulk water. The migration rates of oil
droplets with radii 1.5 and 4.7 nm show a linear dependence on
the ﬁeld strength in accord with experiment [28]. Note that due
to diffusion the migration rates at E = 0 appear nonzero. However,
estimating the uncertainty in the migration rates due to
diffusion as described in Section 2, we ﬁnd that, within the statistical
uncertainty, the migration rates do tend to zero at E = 0.
Oil droplets that were studied in experiment [4,8] are about
two orders of magnitude larger than the oil droplets simulated
in this study. Locally, the surface of the oil droplets studied
experimentally is almost ﬂat (compared with the molecular dimensions
of the interface). To model this case, a heptane slab
V. Knecht et al. / Journal of Colloid and Interface Science 318 (2008) 477–486 481
Fig. 2. (a) Migration rates v of heptane in water as a function of the effective
electric ﬁeld (see Fig. 1). For each system the data set and a linear ﬁt are shown.
(b) Electrophoretic mobilities μE of heptane droplets in water determined from
the simulations, and of Nujol droplets in distilled water [29], as a function of
the droplet radius R.
in contact with water was simulated (Fig. 1, P). The application
of an electric ﬁeld parallel to the heptane–water interfaces
(Fig. 1, P; green or gray arrow, color online) induced a tangential
movement of the two phases relative to each other (Fig. 1, P;
white arrow, and Fig. 2a; squares). Again, the migration rates
scaled linearly with the ﬁeld intensity.
The simulations mimic conditions at the point of zero charge
of oil droplets, pH 6 [5]. The electrophoretic mobilities of
the heptane droplets in our simulations might be compared to
the electrophoretic mobilities of oil droplets at pH 7, as electrophoretic
mobilities of oil droplets at pH 6 and 7 are equal
(within the experimental accuracy) [8]. Fig. 2b shows electrophoretic
mobilities of heptane droplets determined from the
simulations and electrophoretic mobilities of oil droplets in distilled
water determined from experiment [29], as a function of
radius. For droplets with radii in the order of micrometers a
pronounced increase of electrophoretic mobilities with droplet
size is observed in experiment. For droplets in the simulations
with radii in the nanometer range, no clear size dependence
is observed. Given the uncertainty in the simulations, it is not
possible to conclude if for droplets with radii in the nanometer
range there is or is not a signiﬁcant size dependence. Most importantly,
the electrophoretic mobilities of the oil droplets in the
simulations are of the same order of magnitude as those found
in the experiment.
All simulation studies are model- and system-dependent.
Control simulations have therefore been performed to check
for possible effects due to the water model, the direction of
the electric ﬁeld, and the boundary conditions used to calculate
electrostatic interactions (see Section 2). No signiﬁcant effect
on mobilities of the heptane phase was found.
In the interpretation of electrophoresis experiments, the solvent
ﬂow around a migrating particle is assumed to be laminar
(i.e., not turbulent). Our systems are in the laminar regime, as
suggested from an estimation of the order of magnitude of the
Reynolds number, giving the ratio of inertial to viscous forces.
The Reynolds number Re of a ﬂow process is deﬁned as
(7)Re = ρvL/η.
Here ρ is the density of the ﬂowing liquid, v the characteristic
velocity of the ﬂow process, L the dimension of the object
through or around which the ﬂuid ﬂows, and η the viscosity of
the liquid. The ﬂow process is laminar if Re is smaller than a
critical value Recrit depending on the ﬂow process. The critical
Reynolds number for the electrophoresis of the oil droplets in
a periodic box in our simulations is expected to be in a range
given by the Reynolds numbers for a sphere dragged through a
liquid (Recrit ≈ 350 [30]) and a liquid ﬂowing through a tube
(Recrit = 2320 [31]). An upper bound Remax for the Reynolds
numbers of our simulations can be obtained from the density
of water, ρ = 1000 kg/m3, the maximal velocity observed in
the simulations of the droplets, v ≈ 1.5 m/s, the dimension of
the box normal to the ﬂow direction for the largest system (system
L), L ≈ 19.6 ×
√
3 nm, and the viscosity of heptane at 25◦,
η ≈ 0.4 mPas [32] (the viscosity of heptane, being smaller than
that of water [32], is used here to estimate an upper bound of
Re). These values yield Remax ≈ 0.1. Our systems should thus
be well into the laminar regime.
To induce signiﬁcant electrophoretic motion on the time
scale that could be simulated (tens of nanoseconds), high electric
ﬁelds in the range 0.1–0.3 V/nm were applied (the values
refer to the value of the electric ﬁeld in the water bulk).
These exceed those typically used in electrophoresis experiments
[8] by several orders of magnitude. However, in recent
microsecond electrophoresis studies of photoreaction intermediates,
electric ﬁelds exceeding 0.01 V/nm have been used [33],
and despite the relatively high ﬁeld intensities used in these
experiments, the migration rates were found to scale linearly
with the ﬁeld intensity. We note that the migration rates of the
oil droplets observed in the simulations show a linear dependence
on the ﬁeld intensity, indicating that nonlinear effects are
not signiﬁcant. Recent molecular dynamics simulations of the
electrophoresis of small single-stranded RNA oligomers [34] at
ﬁeld intensities similar to those used in the present study also
show migration rates scaling linearly with the ﬁeld intensity,
with electrophoretic mobilities agreeing well with experiment.
This suggests that the simulations performed at high electric
482 V. Knecht et al. / Journal of Colloid and Interface Science 318 (2008) 477–486
Fig. 3. Steady state properties for planar heptane/water interface parallel to an
effective electric ﬁeld of 0.26 V/nm. Shown are (a) the heptane and water density
n and (b) the average velocity v in the ﬁeld direction, as a function of the
distance s normal to the interface.
ﬁeld intensities can be directly related to the available experimental
data. Furthermore, it gives conﬁdence that the very good
agreement in terms of both the sign and the order of magnitude
of the electrophoretic mobilities of the oil droplets observed in
the simulations is due to an appropriate representation of the
underlying physical process and not artifactual.
3.2. Shear in the water/oil interface
Fig. 3 shows steady state properties for the planar heptane/water
interface parallel to an effective electric ﬁeld of
0.26 V/nm. The heptane and water density (Fig. 3a) and the average
velocity v in the ﬁeld direction (Fig. 3b), are plotted as a
function of the distance s normal to the interface. The data suggest
that v(s) exhibits (i) plateau regions in the bulk of heptane
and water, and (ii) a smooth transition at the interface. These
ﬁndings reveal that shear arises at the interface.
3.3. Electrostatic potential in oil phase is positive
To check if the negative electrophoretic mobilities of the
heptane droplets arise from a negative electrostatic potential
in the oil phase, the properties of water–heptane interfaces at
equilibrium were analyzed. Fig. 4 shows the ordering of water
and the electrostatic properties of a curved (radius 1.5 nm)
and a planar heptane–water interface. In Fig. 4, the heptane
and water densities (a), the average water dipole normal to the
interface (b), the charge density (c), and the electrostatic potential
(d) are shown as a function of the distance s normal to
the interface. The same qualitative picture is obtained for the
curved as for the planar interface. Fig. 4b shows the presence
of a negative dipole moment for water molecules on the oil
side of the interface (residing at negative s values). This indicates
that water molecules close to the oil phase point with
their hydrogen atoms toward the oil phase. Fig. 4c shows that
a pseudo electric double layer of positive and negative charge
emerges with the region of positive excess charge located close
Fig. 4. Equilibrium properties of a curved (curvature radius 1.5 nm) and a planar
water–heptane interface. Shown are (a) the heptane and water density n,
(b) the average water dipole moment along the local interface normal (μ),
(c) the charge density (q), and (d) the electrostatic potential (φ) as a function of
the distance s normal to the interface.
to the oil phase. The term pseudo electric double layer is used
to distinguish it from the term electric double layer commonly
used to denote interfacial charge separation due to inhomogeneous
distribution of free charges such as ions. In our system,
charge separation arises from bound charges due to anisotropic
dipole orientation. It is clear, however, that, independent of its
origin, interfacial charge separation, as evident from Fig. 4c,
will induce a difference in electrostatic potential between the
two phases in contact. Fig. 4d shows that the electrostatic potential
of the heptane with respect to the water phase is posi-
tive.
Previous studies of water/oil or water/vapor interfaces have
yielded conﬂicting results for the sign of the electrostatic potential
Φ in the hydrophobic phase relative to the water
phase. Theoretical estimates of Φ induced by anisotropic dipole
orientation were dependent on the water model as well as
the method used to calculate Φ. A mean-ﬁeld approach by
Stillinger and Weber [35] in which a water molecule in a water/vapor
interface was described as a point dipole and quadrupole
within a region of slowly varying dielectric permittivity
suggested Φ > 0. A similar model by Croxton in which a different
quadrupole moment for water was used yielded Φ < 0
[36]. In molecular dynamics studies of a water/vapor interface
by Matsumoto and Kataoka [37] and Barraclough et al. [38],
Φ was determined from the polarization density normal to
the interface, yielding Φ < 0. Wilson et al. showed that it
V. Knecht et al. / Journal of Colloid and Interface Science 318 (2008) 477–486 483
Fig. 5. Electrophoretic force between water and a heptane slab or a smooth
hydrophobic wall (see Fig. 1) as a function of the effective electric ﬁeld. For
each system the data set and a linear ﬁt are shown.
is essential to determine Φ by integrating the charge density
normal to an interface, thus considering the quadrupole
moment and the ﬁnite dimension of the water molecules, to obtain
the correct sign of Φ from a simulation [39]. Molecular
dynamics studies of a water/vapor interface yielded Φ < 0
for the TIP3P water model [40] and Φ > 0 for the TIP4P
[39] or the SPC/E water model [41]. A molecular dynamics
study of a water/decane interface yielded Φ ≈ +0.4 V
for the SPC water model [12]. Recent molecular dynamics
studies of a water/hexane interface using a polarizable water
model yielded Φ ≈ +0.1 V for a ﬁxed-charge hexane
force ﬁeld and Φ ≈ +0.4 V for a polarizable hexane force
ﬁeld [42].
Experimentally, Φ cannot be determined unambiguously.
This is because the measured potential difference includes the
difference in the chemical potential which is not easily estimated
[1]. Experimental estimates of Φ for an air/water interface
for example were mainly based on the changes in the
potential with electrolyte concentration and range from −0.5 to
+1 V (a survey is given in [43]).
3.4. Electrophoretic force requires interfacial roughness
Electrophoretic motion arises from a balance between a
driving force we shall denote here as the electrophoretic force
and a frictional force. The electrophoretic force between a heptane
and a water slab in contact was determined by restraining
the distance between the centers of mass of heptane and water
in the ﬁeld direction using a harmonic force. The force was
determined from the deﬂection using Eq. (1). Fig. 5 shows the
electrophoretic force as a function of the electric ﬁeld which
can be well ﬁt using a linear function. The slope of the linear
ﬁt is Q = −0.18(2)e, where e denotes the elementary charge.
Assuming Q to be proportional to the interfacial area, this corresponds
to a pseudo-charge density of σ = −0.011(1) e/nm2.
In contrast, for water in contact with a hydrophobic wall, no
signiﬁcant electrophoretic force is detected.
Fig. 6. Equilibrium properties of the interface between water and heptane or
a smooth hydrophobic wall. (a) Water (and heptane) density as a function of
the distance s normal to the interface. (b) Conﬁguration of a water/heptane
interface. (c) Conﬁguration of a water in contact with a smooth hydrophobic
wall. The representation is similar to that chosen in Fig. 1.
Fig. 6a shows a comparison between the equilibrium properties
of the interface between water and heptane or the hydrophobic
wall. Whereas the density of water in contact with heptane
shows a smooth transition normal to the interface, a sharp transition
and density oscillations are observed for water close to
the wall. A similar density proﬁle has been observed in a previous
study of water in contact with a hydrophobic wall [10].
Fig. 1b shows a conﬁguration of a water/heptane interface. It
is evident that some interfacial heptane molecules protrude into
the water phase such that the interface is rough on a molecular
scale. In contrast, the wall/water interface is smooth on
this scale. Comparison of Figs. 5 and 6 suggests that molecular
roughness is required for electrophoretic forces between
water and a hydrophobic phase.
484 V. Knecht et al. / Journal of Colloid and Interface Science 318 (2008) 477–486
4. Discussion
4.1. Simulations challenge current continuum picture
The simulation conditions for oil droplets in water chosen
here are comparable to experimental conditions at the point of
zero charge in the absence of electrolytes or ionic surfactants.
At the point of zero charge, the surface concentrations of hydronium
and hydroxyl ions in a water/oil interface are equal,
and, in the absence of electrolyte ions or ionic surfactants, the
surface charge of an oil droplet in water is zero.
The oil droplets in our simulations showed negative electrophoretic
mobilities, in agreement with the experimental observation
of negative electrophoretic mobilities for oil droplets
at the point of zero charge. Our ﬁndings suggest that negative
electrophoretic mobilities of oil droplets require neither the
presence of ions nor a negative electrostatic potential in the oil
phase. This in turn implies that the electrophoresis of a liquid
droplet does not solely reﬂect the charge or electrostatic
potential of the droplet, challenging the current theory of elec-
trophoresis.
Electrophoresis of a colloidal particle is generally attributed
to the presence of an electrical double layer in the interface creating
a difference in the electrostatic potential between the two
phases [28]. An electric ﬁeld parallel to the interface induces
shear stress and, hence, a ﬂow of the suspending ﬂuid relative
to the particle. The electrophoretic mobility of a particle is expected
to be proportional to the electrokinetic potential or zeta
potential (the electrostatic potential on the shear plane, measured
with respect to the bulk of the suspending medium). The
zeta potential, conversely, is proportional to the net charge of
the particle, denoting the sum of (i) the bare charge of the particle
arising from ions or ionic groups attached to the surface and
(ii) the charge of the part of the counterion cloud dragged along
with the particle during electrophoresis, reducing the effective
charge of the particle [44]. In our simulations of oil droplets in
water in the absence of any ions or ionic molecules, the bare as
well as the net charge of the oil droplets is zero. Furthermore,
in a continuum description of the systems we have simulated,
no charges would be present. In such a model, application of an
external electric ﬁeld would not result in any net nor even local
forces. Hence, the electrophoretic mobility of the oil droplets
would necessarily be zero.
In general, continuum theory predicts the electrophoretic
mobility, net charge, and zeta potential of a particle to be equal
in sign. The zeta potential inferred from electrophoresis experiments
is generally considered to be a measure of the difference
in the electrostatic potential in two phases in contact (contact
potential). As noted above for a water/oil or a water/vapor interface,
the contact potential itself cannot be determined unambiguously.
This is because the measured potential difference
includes the difference in the chemical potential, which is not
easily estimated [1]. The above interpretation of electrophoretic
mobility, however, is based on continuum theory. In particular,
it ignores the fact that due to nanoscale dimensions of an
interface, molecular details may play a signiﬁcant role in determining
electrophoretic mobility. Even though no molecules
in the system carry a net charge, the individual atoms in water
molecules carry partial charges. The interaction of these partial
charges with the external ﬁeld will lead to local forces.
Although the total charge of a water molecule is zero, a net
translational force on interfacial water molecules could result
from local gradients in water dipole energies. Our simulation
results showing electrophoretic activity of oil droplets in water
in the absence of any ions suggest this may be the case.
4.2. Dipolar ordering around a heptane molecule in water
The current continuum theory based interpretations of electrophoretic
mobility implicitly assumes that mobility arises
from the inhomogeneous distribution of free charges such as
ions. Dipolar ordering in the interface that appears to be the
primary origin of mobility in our system is not considered. Our
results suggest that shear forces arise in the interface and not
in the bulk, and molecular protrusions from the oil phase are
crucial for electrophoretic forces between the oil and the water
phase. To determine the structure of water in contact with
a heptane molecule, a single heptane molecule in bulk water
was simulated at equilibrium, and various properties of water
were determined as a function of the distance from the center
of mass of a methyl(ene) group. In Fig. 7, the water density (a),
the average dipole moment of water molecules along the distance
vector (b), the charge density (c), and the electric ﬁeld
along the distance vector (d), are shown as a function of distance.
Four distance regions, I–IV, can be distinguished, where
regions I–III contain the ﬁrst hydration shell, and region IV
shows bulk-like behavior. In region I, where the water density
is low, a narrow subregion exists in which the water dipole is
negative, i.e., pointing toward the methyl(ene) group. In contrast,
the water dipole is positive everywhere in regions II and
III containing the density maximum (region II) and a local density
minimum (region III). The water ordering results in a strong
positive charge in region I, a negative charge in region II, and
a weak positive charge in region III. The dipolar ordering and
charge distribution here are similar to the interfacial charge distribution
shown in Fig. 4, except for the region of weak positive
charge missing in the interfacial proﬁles. The inhomogeneous
charge distribution results in local electric ﬁelds. A strong positive
ﬁeld between regions I and II, a negative electric ﬁeld
between regions II and III, and a weak positive ﬁeld between
regions III and IV are observed. In regions I and II, ﬁeld intensities
exceeding 4 V/nm, an order of magnitude larger than the
intensities of the electric ﬁelds applied, are observed. Thus, interestingly,
the ﬁeld intensities applied were small compared to
the intensities of the local electric ﬁelds from dipolar ordering
at equilibrium.
4.3. Role of ions
The electrophoresis of oil droplets is pH-dependent. Clearly
ions do also play a role in this system. Hydroxyl or hydronium
ion adsorption onto a water–oil interface would be expected
to change the contact potential between oil and water
and hence the zeta potential of oil droplets in water. Hy-
V. Knecht et al. / Journal of Colloid and Interface Science 318 (2008) 477–486 485
Fig. 7. Dipolar ordering and electrostatics around methyl(ene) groups of a single
heptane molecule in water at equilibrium, as a function of distance s from
the center of mass of the methyl(ene) group. The number density of water molecules
(a), the average dipole moment μ of a water molecule along the distance
vector, in fractions of the total dipole moment μ0 of water molecule (b), the
charge density q (c), and the electric ﬁeld E0(s) along the distance vector are
shown. The inset in (b) shows the deﬁnition of μ. Here, a methyl(ene) group
and a water oxygen are depicted in light and dark gray, respectively.
droxyl or hydronium ion adsorption onto a water–oil interface
would also change the spontaneous ordering of interfacial water
dipoles. In the pH range between the isoelectric point, pH 3,
and the point of zero charge, pH 6, oil droplets show negative
electrophoretic mobilities despite an excess of hydronium
ions adsorbed to the water/oil interface. We propose that for
3 < pH < 6, the effect of the hydronium ions on the mobilities
is overcompensated for by mobility associated with the
water ordering and surface roughness. At the isoelectric point,
the effects from hydronium ions and dipolar ordering/surface
roughness-induced mobility compensate for each other. Here
the positive surface charge from excess hydronium ions is expected
to be equal in magnitude to the negative pseudo-charge
from dipolar ordering/surface roughness-induced mobility, σ =
−0.011(1) e/nm2, suggesting an excess of one hydronium ion
per 91(1) nm2 at the isoelectric point.
Electrophoretic mobilities of oil droplets in water suggest a
change of −80 mV in the respective zeta potentials for a change
in pH from 2 to 9 [8]. The respective change in the contact
potential between oil and water is likely of the same order of
magnitude as the change in the zeta potential. This change in
zeta potential is an order of magnitude smaller than the contact
potential between oil and water arising purely from water
ordering in the interface suggested by our simulations. Thus it
appears that the structure of the interfacial water would determine
the sign of the contact potential between oil and water in
the whole pH range typically studied in electrophoresis mea-
surements.
5. Conclusion
Electrophoresis experiments are extensively used to probe
charge separation in interfacial regions of colloid systems [1].
Knowledge of such charge distributions is of major interest
in colloid chemistry and electrochemistry. It is, for example,
essential in understanding electrode kinetics, electrocatalysis,
corrosion, adsorption, crystal growth, colloid stability, and ﬂow
behavior of colloidal suspensions [1]. We have shown that the
electrophoretic mobility of a liquid droplet does not necessarily
reﬂect the actual electrostatic potential or surface charge of the
droplet. If true, the electrostatic potential of suspended droplets
deduced from electrophoretic mobilities could thus be misleading,
and the interpretation of electrophoresis experiments in
terms of purely continuum effects and the neglect of the dipolar
ordering may need to be reevaluated.
Acknowledgments
The authors thank M. Deserno, J.B.F.N. Engberts, R. Zangi,
B.L. de Groot, H.J.C. Berendsen, M. Müller, and J. Menche
for useful discussions. This project was funded by the From
Molecule to Cell program of the Netherlands Organization for
Scientiﬁc Research (NWO), Grant 80547091.
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