PAPER
www.rsc.org/softmatter | Soft Matter
Mechanism of attraction between like-charged particles in aqueous solution
Ekaterina Nagornyak, Hyok Yoo and Gerald H. Pollack
Received 13th March 2009, Accepted 2nd July 2009
First published as an Advance Article on the web 21st July 2009
DOI: 10.1039/b905080a
Although it has been long known that like-charged particles attract one another in aqueous media, the
mechanism underlying this counter-intuitive phenomenon has remained controversial. We tested the
hypothesis put forth long ago by Langmuir and again by Feynman and by Ise, that the attraction
between like-charged entities lies in an intermediate of unlike charges. Tests were facilitated by the
observation that the attractive forces could be confirmed between widely separated particles of
macroscopic size. Two approaches showed comparable results. In the first, pH-sensitive dyes showed
intermediate zones of opposite charge: an accumulation of protons was found between
negatively charged spheres, whereas between positively charged spheres the intermediate zone
contained OH groups. In the second and complementary approach, microelectrode measurements
showed that in between negatively charged spheres, the electrical potential was relatively positive,
whereas between positively charged spheres it was relatively negative. Hence, both approaches confirm
theoretical expectations. The large number of unlike charges lying in between the like-charged spheres
may come from the build-up of the recently reported ‘‘exclusion zone’’ surrounding each particle.
Introduction
Like-charged colloidal particles attract one another. In aqueous
suspension, particles draw together to form a colloidal crystal, in
which particle separation is on the order of particle diameter.1–6
Although counter-intuitive, attraction between like-charged
particles has been confirmed time and again over more than half
a century.7–12
Given the classical expectation that attraction should occur
only between particles that are oppositely charged, Langmuir
suggested early on that the required opposites might come from
counter-ions situated in between the like-charged particles; these
counter-ions would create the attractive force.13 Feynman likewise emphasized the role of intermediate counter-charges, coining the phrase, ‘‘like-likes-like through an intermediate of
unlikes’’.14 Taking up the Langmuir–Feynman ideas, Ise and
Sogami derived a formal theory based on those suggestions,
demonstrating excellent agreement between theoretical expectations and experimental observations.15
On the other hand, the presence of counter-ions between the
like-charged particles has never, to our knowledge, been experimentally validated. A reason may be the demands on spatial
resolution: micron-scale separations typical of colloidal systems
demand nanometre-scale spatial resolution, which is not readily
achievable for charge-distribution measurements. Furthermore,
the source of unlikes has never been entirely clear—possible
candidates including various ions that might be present, and/or
protons and hydroxyl groups coming from hydrolyzed water.
Two recent findings have opened the possibility of testing the
like-likes-like mechanism. The first is the identification of
a potential source or abundant free charge. Adjacent to hydrophilic surfaces, extensive zones of organized water have been
Department of Bioengineering, University of Washington, Box 355061,
Seattle, WA 98195, USA
3850 | Soft Matter, 2009, 5, 3850–3857
found, which retain charge.16,17 As this charge builds, charges of
the opposite polarity are released to the region beyond, into the
bulk solution.18 These released charges could constitute the
suspected unlikes. In other words, if each colloidal particle is
enveloped by a shell of more-ordered water, then many charge
carriers would be released into the solution beyond. Such
enveloping shells have been confirmed for larger spherical
particles,19,20 and presumably exist for smaller particles as well, at
least for those whose characteristic dimension greatly exceeds the
size of the water molecule.
The second relevant finding is that the attraction implied in
colloid-crystal formation can also be observed with much larger
particles. As shown here, sub-millimetre-sized particles of like
charge are attracted to one another over separations on the order
of hundreds of micrometres. Such large-scale separation made it
feasible to explore whether indeed the suspected unlike charges
are situated between the like-charged particles.
Results
Attraction experiments
Preliminary experiments had shown hints of attraction between
like-charged beads. When two similarly charged beads were
dropped into chamber-1 filled with deionized water, spontaneous
interaction could be seen from time to time, even when bead
surfaces were separated by as much as several hundred micrometres. The attractive interaction was relatively weak, typically
100 mm displacement in 30 minutes. Such spontaneous attractions were noted in five out of 20 experiments. In 13 others the
beads did not move at all, while in two experiments they moved
apart. The phenomenon was present also when the chamber
contained several beads of the same polarity instead of two: when
the intervening distance between any two was several hundred
micrometres or less, the beads showed a tendency to move
This journal is ª The Royal Society of Chemistry 2009
spontaneously toward one another. This was observed three out
of 17 times, while in the rest of the observations the beads did not
move at all. These preliminary observations provided a reason to
believe that attractive forces might be present.
Hence, more systematic experiments were carried out to
explore the possibility of attraction. In these experiments the
strategy was to free the beads from any adhesion to the chamber
floor, by gently tapping from below. A representative result is
shown in Fig. 1. The graph shows the surface-to-surface distance
between the two beads during the course of a series of taps.
Above the graph are representative images of bead pairs from
which measurements were made. Overall, the beads moved
toward one another, although some net repulsive events were
recorded as well. In this particular experiment, from an initial
surface-to-surface separation of approximately 230 mm, the
beads wound up touching one another.
A series of experiments were carried out similar to those
depicted in Fig. 1. Initial distances between bead surfaces ranged
from 70 mm to 400 mm; the variation in initial separation distance
was a mere consequence of inability to place beads exactly at the
same position every time. Observations were made until the
moment when either of the following events occurred: the beads
touched, or the beads had separated by more than 1200 mm.
A summary of 21 experiments similar to the one depicted in
Fig 1 is shown in Fig 2. Initial separation (t ¼ 0) was normalized
to a value of 1.0 in each experiment, and all subsequent spacings
were normalized relative to that. To reduce clutter, spacings were
averaged among five successive taps and placed in bins, average
values for which correspond to time intervals of 10 s (t ¼ 0–10 s,
10–20 s, etc.). For the time interval t ¼ 0–10 s, the graph contains
data from all 21 experimental runs, while successive bins have
fewer and fewer experimental values because one of the two
termination criteria had been satisfied. The final bin contained
data from only eight experiments.
In 18 of the 21 experiments, the beads wound up touching,
while in the remaining three experiments, the beads apparently
separated enough that the attractive force never took control.
Because those large separation values were averaged into the
Fig. 2 Average distance change between two negatively charged bead
surfaces. Number of observations in successive bins: 21, 18, 15, 12, 12, 11, 8.
data set of Fig. 2, the graph shows less dramatic attraction than
was actually observed in the vast majority of bead pairs.
The experiments above confirm that attractive forces exist
between large, negatively charged beads separated by up to
several hundred micrometres. Thus, attraction apparently occurs
on a macroscopic scale in much the same way as it occurs on
a microscopic scale.
pH-dye experiments
The next series of experiments was designed to test whether
indeed counter-ions postulated to be responsible for the attraction exist in abundance in the span between the like-charged
beads.
To test for positive counter-ions between negatively charged
beads, pH-sensitive dyes were used. A representative result is
shown in Fig. 3. Panel a shows a low pH region (red; pH 3–4)
surrounding each bead, which could be seen after the dye had
been present for 10–20 seconds. The lighter color between the
bead surface and the red region corresponds to the exclusion
zone, where the dye molecules are excluded; its slightly red
appearance is likely the result of color contributions from above
and below the focal plane. The low pH region beyond the
exclusion zone grew with time (panel b). After approximately five
minutes the low pH clouds merged, creating a low-pH linkage
between beads (panel c). Subsequent to that time the low pH
region continued to spread, with clouds growing toward the
periphery (panel d). This phenomenon was observed consistently
in 27 experiments. The only notable variation was in the speed of
growth of the low pH regions, presumably as a result of
uncontrolled factors. Nevertheless, the low-pH zone between
beads was seen in every experiment, implying a consistently high
concentration of protons lying between the negatively charged
beads.
Electrical potential
Fig. 1 Surface-to-surface distance between two beads following a series
of taps, imparted every 2–3 seconds.
This journal is ª The Royal Society of Chemistry 2009
While the high concentration of protons between beads is
consistent with the proposed hypothesis, it does not necessarily
Soft Matter, 2009, 5, 3850–3857 | 3851
Fig. 3 Growth and propagation of low pH zone formed around negatively charged beads. pH scale shown in left panel.
prove that this region is more positive than areas immediately
adjacent to the bead surface: some negative-charge carrier might
neutralize the protons. To evaluate the charge distribution
between beads, electrical potential was measured.
Fig. 4A shows an example of the measured electrical potential
as a function of position between two beads. The traces represent
the time course of voltage scans made from left to right. At the
left-bead surface, the potential ranged between 90 mV and
110 mV. It grew more positive with increasing distance from
the bead, reaching the highest values when the tip of the electrode
was roughly midway between the beads. With time, the midway
potential became more negative (c.f. 10 and 30 minutes), and
during scans made early on (t # 10 min) some measurements
showed slightly positive midpoint values.
The potential profile of Fig. 4A is slightly asymmetrical and we
wondered whether the asymmetry might be a result of the
microelectrode tip passing through the water and disturbing the
system. To examine the source of spatial asymmetry the electrode
was moved in the opposite direction, and the results are shown in
Fig. 4B. A similarly asymmetrical pattern can be seen, practically
the mirror image of panel A. Hence, the slight asymmetry most
likely arises from the measurement method itself.
More detailed analysis of the midway-potential time course is
shown in Fig. 5. The microelectrode was positioned midway
between the beads, and measurements were made every ten
minutes following initial bead placement in the chamber. Data
from twelve pairs of beads are summarized. The results show that
the midway potential was most positive during the first few
minutes after insertion, and became progressively less positive
with time. This result is in accord with the results of the pH-dye
experiments, which show the red color between beads most
Fig. 5 Time dependence of electrical potential midway between beads.
Standard deviations are shown as vertical lines. n ¼ 3 experiments.
intense early after bead immersion, then diffusing in all directions
with time. Presumably, the protons lodged between (and around)
the beads progressively diffuse throughout the rest of the solution, diminishing the potential gradients.
In the voltage-measurement experiments, the distance between
bead surfaces varied appreciably, from 350 mm to 1200 mm. To
determine how the potential profile varied with separation
between beads, observations were categorized into three groups
depending on bead separation: close (333 24 mm); medium
(610 19 mm); and far apart (1104 14 mm). Potential
measurements were made between 40 and 50 minutes following
bead immersion. To reduce clutter, collected voltage values were
averaged among ten successive measurements of the same
potential profile. Each group—close, medium, and far—contains
three experiments.
The results are shown in Fig. 6. They show that the potential
profile differs somewhat, depending on bead separation. When
beads were in relatively close proximity, the profile was shifted to
more positive values than when the beads were farther apart. One
possible interpretation is that when beads were closer together
the released protons were relatively more confined, giving the
higher potential.
Multiple-bead experiments
Fig. 4 Representative voltage scans between two negatively charged
beads. (A) The microelectrode moves from the surface of left bead to the
surface of right bead. Different traces correspond to different times after
bead immersion in water. (B) Similar to (A), but the microelectrode
moves from right to left.
3852 | Soft Matter, 2009, 5, 3850–3857
To check the influence of the presence of multiple beads on beadpair interaction, experiments were carried out with eight to 20
beads in the chamber. First, proton distribution was measured
using the pH-dye indicator. For these experiments, chamber-2
was used. The results of eight experiments were similar to those
This journal is ª The Royal Society of Chemistry 2009
Fig. 6 Voltage-profile dependence on bead separation. Each curve
represents average of three experiments.
obtained with only two beads. At low pH (pH z 3) clouds
formed around each bead. The clouds grew toward one another,
merging midway, and then spread peripherally. The only notable
difference from the two-bead results was that propagation was
faster: it took approximately half the time to turn the chamber
water, initially with pH z 6, into lower pH of 3. Presumably,
the rapidity is a result of both the larger number of beads and the
smaller water volume in the chamber.
Electrical potential experiments were also carried out in the
multiple-bead configuration. Approximately 20 negatively
charged beads were dropped into chamber-3. Measurements
were made between beads of a pair that were midway along the
line of multiple beads. Voltage profiles were, again, similar to
those obtained in the case of only two beads, with a voltage swing
of approximately 100 mV.
Positively charged beads
To determine whether the attractive behavior might be polarity
sensitive, a limited number of experiments were performed with
beads that were positively charged. In the chamber-tapping
experiment, the positively charged beads seemed to exhibit even
stronger attraction than the negatively charged beads (c.f.,
Fig. 1). In nine out of ten experiments they wound up touching
one another, and they reached the touch point with typically only
50 taps, compared to 100 taps in the case of the negatively
charged beads. One possible reason for the difference is their
relatively small mass (33% lighter than the negatively charged
beads), which allows them to translate more readily. Another
contributing factor might be weaker adherence to the chamber
floor.
Tapping was sometimes unnecessary for generating the
attraction. In three of four experiments with these positively
charged beads, the beads moved together immediately after they
were added to the bath, and it was difficult to separate them
either by tapping the chamber or by jarring one of the beads with
a pipette. With fairly brutal force they could be separated, only to
move back together within a few seconds.
When the pH indicator solution was added, a high-pH region
(purple) was formed around each bead (pH 9–10). The high pH
clouds were initially (10–20 s) relatively small and better defined
than the corresponding low pH clouds seen with the negatively
This journal is ª The Royal Society of Chemistry 2009
Fig. 7 Growth and propagation of high-pH zone formed around positively charged beads. pH scale shown in left panel.
charged beads. Within one minute a clear high-pH bridge formed
between the two positively charged beads—much the same as
with the other polarity (compare Fig. 3 and Fig. 7). One notable
difference, however, is that the link tended to diffuse in the
direction normal to the axis connecting the bead centers. After
about 5 to 10 minutes, the high pH region formed a boomeranglike figure (Fig. 7). In such instances the attractive bead movements were seen to be directed along the color lines rather than
directly toward the companion bead.
Perhaps, the most notable observation is the complementary
nature of the results: with the positively charged beads the pH
change was the opposite of that seen with the negatively charged
beads. Proton-rich bridges formed between negatively charged
beads, while hydroxyl-rich bridges formed between positively
charged beads. In both instances, therefore, the linkage between
‘‘likes’’ is indeed formed by ‘‘unlikes.’’
The electrical potential profile was measured as well. The
potential was 90 mV positive at the bead surface, and near zero
(10 mV to +10 mV) in the mid region. These measurements
may not be quantitatively accurate because of the abovementioned dye-distribution asymmetry. Nevertheless, the shape
did correspond roughly to that measured with the negatively
charged beads, except that it was inverted.
In summary, the results obtained with positively charged
beads are qualitatively similar to those obtained with negatively
charged beads. In both instances the beads attracted one another.
And, both pH and voltage measurements indicated that the
attraction results from oppositely charged species lying in
between the beads.
Uncharged beads
As a final control, a series of experiments were carried out with
bead pairs that had lost their charge in order to determine
whether inter-bead attraction was absent. In these experiments
positively charged beads were used, and the beads examined were
those that had lost their color and hence their ion-exchange
capacity. Such beads no longer showed exclusion zones (solutefree zones), and hence should not have contained the large charge
that lies within those zones. Ten trials were carried out. The
standard tapping strategy was used to free the beads from any
Soft Matter, 2009, 5, 3850–3857 | 3853
adhesion to the floor of the chamber. For each bead pair, 30 to
100 taps were made. Overall, the exhausted beads did not move
toward one another, although some net attractive events were
recorded and in one case the two beads finally touched one
another (possibly because of some residual charge; electrical
potential measurements showed that charge on the exhausted
beads had diminished appreciably, but not necessarily to zero).
For statistical analysis, initial separation in each experiment was
normalized to a value of 1.0, and relative separation was then
measured following the 30th tap. Among the ten experiments the
mean value was 1.22 0.61. Hence, the exhausted beads showed
no attraction.
Discussion
Many experiments have demonstrated that like-charged particles
in aqueous solution attract one another.1,21–26 The attraction is
counter-intuitive, for we are schooled to think that like charges
must repel, and not attract. It is perhaps for this reason that some
have questioned whether the seemingly attractive movements
might actually not require attractive forces,27,28 although these
challenges have been vigorously rebutted.4,11
The results obtained here confirm that like-charged particles in
suspension attract one another, and provide evidence for the
mechanism. Attractive forces are observed over unexpectedly long
distances, and the results show that it is indeed the unlike charges
lying in between that are responsible for these attractive forces.
Forces between beads
We found that like-charged beads in solution are drawn toward
one another at separations up to several hundred micrometres.
Attraction was found between positively charged beads and also
between negatively charged beads, the former being slightly
stronger than the latter. Attractive forces are anticipated to fade
at distances beyond several Debye lengths, which are typically
less than 0.1 mm. However, the attractions observed here
evidently took place over much larger spans.
One potential artifact might arise from the method used. In
order to free the beads from adhesion to the floor of the chamber
and allow them to move as they may, the chamber was gently
tapped from beneath. This approach was fairly crude; nevertheless, with some practice the tapping procedure could be
carried out with a reasonable degree of consistency. However,
a possibility is that the tapping induced some kind of vibrationinduced convection that drew the beads toward one another, and
that the drawing together was not the result of a genuine
attractive force but this kind of convection.
Several arguments militate against such an explanation. First,
the bead pairs were situated at different positions within the
chamber from one experiment to the next; hence flow toward
some particular point in the chamber should not necessarily have
brought the beads together as consistently as they did. Second,
attractions were often seen in the absence of tapping; they
sometimes occurred spontaneously. When such beads were
forcibly pulled apart (with difficulty), they would spontaneously
return toward one another. For these reasons we believe that
attractive force between beads is not the result of a convective
artifact.
3854 | Soft Matter, 2009, 5, 3850–3857
A further reason to think the attractive forces are genuine is
that the attractive potential has been identified. Two methods
show that in between the like-charged beads are charge carriers
of opposite polarity.
The first method, the pH-dye indicator experiments, shows
that between negatively charged beads there is a region of low
pH. Protons emanating from the region around each bead
eventually build a bridge between the negatively charged beads,
thereby attracting the beads toward one another. The opposite
pH change occurs between positively charged beads. Hence,
a high concentration of unlike charge accumulates between the
like-charged beads, creating the attractive potential that can
draw the beads together. In the case of the positively charged
beads, the bridge often bends for some reason that is not yet
clear; yet the beads move together by following along the color
lines, reinforcing the view that it is indeed the opposite charges of
the bridge that attract the beads.
The second confirmatory method was that of the potential
distribution. Consistently, those results showed that for the
negatively charged beads, regions midway had potentials on the
order of 100 mV more positive than the zones immediately
surrounding the beads. The negatively charged beads are inevitably drawn toward the more positive region and hence toward
one another. For the positively charged beads the potential
distribution was opposite—more negative in between. Thus, the
electrical potential results are consistent with the results of the dye
experiments: both show that the like-charged entities are attracted
toward one another because of the unlike charges lying in between.
A slight difference of behavior between bead types was that the
positively charged beads tended to attract one another more
strongly than the negatively charged beads. One reason might be
the magnitude of the pH difference. The initial pH of the
chamber solution was commonly 6; it was slightly acidic, with
an abundance of protons. The negatively charged beads added
additional protons to this positive charge. Hence, the difference
between the final inter-bead pH and the bulk solution pH may
not have been as large as with the positively charged beads, which
released negatively charged OH groups. This explanation is
evidently conjectural, and requires additional study.
Source of unlikes
A question that arises is the source of the unlike charges lying
between the likes.
One putative source is the beads themselves. Counter-ions
diffusing from the bead may spread broadly within the fluid,
accounting for the observed pH changes. Although this is
anticipated, the rather extreme pH changes observed raise some
question whether the counter-ion source can account for what is
observed. The pH changes amounted to three pH units in the
acidic direction, and up to four units for the positively charged
beads. A pH change of three units implies a change of 1000 times
and one wonders whether any such massive change can be
accounted for by counter-ions alone.
Another potential source of unlikes is the ordered water
zone that grows around each bead. Such ordered zones are
surprisingly extensive. They vary from tens of micrometrers up to
hundreds of micrometres next to some polymeric surfaces such as
Nafion and next to gel beads.16,17,29,30 A critical feature of these
This journal is ª The Royal Society of Chemistry 2009
zones is that they are charged: negative next to negatively
charged surfaces, and positive next to positively charged
surfaces.31 Water, on the other hand, is neutral. In order for these
zones to transition from neutral to charged, they must release
carriers of opposite charge to the bulk, and such release has been
confirmed.32 Because such ordered zones are fairly massive, with
volume on the order of bead volume, large numbers of charges
must be released and it seems likely that this may account for
a major fraction of the unlikes.
Application to smaller scale particles
Another question that arises is whether the explanation of the
attractions found here also applies to smaller scale particles, or
even those on molecular scale. The reason for employing the
larger scale particles here is that various probes could be easily
applied. It was possible to measure the distribution of charge
carriers using pH-sensitive dyes; and, it was possible to
manoeuvre a microelectrode between beads to measure the
potential distribution. With smaller particles this would not have
been so easily feasible.
On the other hand, the question whether the results apply on
the smaller scale is not directly addressed. Attractive movements
are evidently seen at these smaller-scale levels.4,12,20,33 And, there
are arguments that indicate the likely presence of ordered water
at these small scales: For example, ordered water zones are
readily seen in one-micron thick slices of Nafion sandwiched
between glass plates.34 Ordered water is also broadly confirmed
within the living cell, the water molecules lying adjacent to
nanometre-scale structures.35 If such zones are found adjacent to
hydrophilic surfaces in general, then it seems reasonable that
scale is relatively unimportant so long as it is appreciably larger
than the size of the water molecule. Hence, we think it is likely
that the mechanisms uncovered here also apply on smaller scales,
possibly down to molecular scales.
One notable difference between the present observations and
those at the scale of microspheres is the ultimate particle separation relative to particle diameter. In the case of the microspheres, the attraction does not typically yield an end point of
microsphere contact: microspheres move attractively to a separation on the order of particle diameter, at which point the
attractive force is balanced by the repulsive force between likecharged particles. It is by such a mechanism that the colloid
crystal is formed. In the case of the larger spheres studied here,
the ultimate point, by contrast, is actual contact between spheres,
although a very thin film of water cannot be ruled out.
Several explanations seem possible. One reason could be the
higher surface-charge density of ion exchange beads compared to
that of microspheres. Higher surface charge might yield more
counter-ions and therefore higher attractive force. Another
possibility stems from the fact that the large spheres touch only at
one point, leaving ample intervening space for unlikes to reside.
Hence, the attractive force would derive from the unlikes residing
in those substantial gaps.
Applications of the like-likes-like mechanism
The observations made here would seem to have potentially
broad implications. The immediate implication is that similarly
This journal is ª The Royal Society of Chemistry 2009
charged particles in aqueous solution attract one another even at
distances very much greater than the Debye length. Attraction
occurs even at macroscopic separations. Hence, even in dilute
suspensions, where particles are greatly separated from one
another, attractive forces may be present. Further, one needs to
take into account the likely pH gradients that may be present
throughout the solution domain. At present, these are not
considered.
Similar attractions may occur even between particles outside
of aqueous solution. Consider, for example, water aerosols. One
long-standing question is why evaporating water often clusters
into discrete puffy clouds, instead of remaining uniformly
dispersed over space. If aerosol droplets consist of the kind of
organized water seen in other contexts, then an ample source of
unlikes is present, which can bring the particles together to
coalesce. Thus, the like-likes-like phenomenon may be significant
in cloud formation.
At the smaller end of the size scale is the issue of molecular selfassembly. Newly minted molecules assemble into mesostructures
such as filaments and organelles, but the mechanism of assembly
has remained a mystery. In such situations the like-likes-like
mechanism may act at the sub-molecular level, creating distributions of unlikes that serve to bring like molecules together by
the simple physical mechanism described herein.
It appears, then, that the mechanism implied by Langmuir and
advocated by Feynman and Ise is not only adequate, but may
have broad application.
Methods
General
Deionized water (type I HPLC grade (18.2 MU cm)) collected
from a Barnstead D3750 Nanopure Diamond purification
system was used for all experiments. In order to minimize
contamination, experimental chamber materials were thoroughly
washed with water from the above-mentioned source.
The experiments involved two types of ion-exchange beads
(Bio-Rex MSZ 501(D) resin): anionic and cationic. Prior to use,
the beads were washed with spectroscopic grade methanol and
then with deionized water. The negatively charged beads, which
were used for all experiments unless otherwise specified, were
600–650 mm in diameter. They contained an irreversibly bound
yellow dye. The positively charged beads, which had an irreversibly bound blue dye, were 400–500 mm in diameter. Both
types of bead turned clear after long-term use, indicating
exhaustion of their ion-exchange capacity. To standardize
experiments, only the beads with highest ion-exchange capacity,
as shown by their color, were used.
Attractive force between beads
To observe bead displacements due to their attraction,
a chamber, (chamber-1) was placed on the sample stage of
a bright-field-inverted optical microscope (Zeiss Axiovert-35)
with a 5 objective lens and a color CCD a camera attached
(Color Digital Camera, model CFW-1310C, Scion Corporation).
Chamber-1 was used to monitor bead displacement and later
to visualize pH distribution around two beads of the same
polarity. It was constructed from a rectangular plastic plate,
Soft Matter, 2009, 5, 3850–3857 | 3855
1 mm thick, 6 cm long, and 3 cm wide. A 10 mm diameter hole
was drilled through the center of the plate. The bottom of the
hole was then sealed with a microscope coverslip (150 mm thick)
using UV-glue. This arrangement provided a 1 mm high cylindrical chamber, 10 mm in diameter. The coverslip facilitated
microscopic observation from below.
For bead-displacement measurements, chamber-1 was first
filled with deionized water. No dye was added. Then, two
negatively charged beads were placed into the chamber. After
five minutes, when the beads had settled for some time, the
chamber was lightly tapped from beneath, which slightly lifted
the beads from the chamber floor. This tapping procedure was
repeated every 2–3 seconds. Each time, the separation distance
was measured just after the beads had re-settled. Following this
procedure we could construct a graph of bead separation vs.
time.
Visualization of pH distribution with pH-sensitive dye
To detect local proton-concentration differences in the vicinity of
bead surfaces, we used a universal pH indicator (Catalog #:
SLU1051, Sciencelab.com, Inc., TX). The indicator changes
color in response to pH change, and solution pH can then be
determined from the color chart, acquired from acid–base titrations. The manufacturer’s instructions—1 ml indicator to 10 ml
water—were followed when diluting the concentrated pH-dye
solution for experimental use. Deionized water showed a yellow
color upon addition of the pH-dye solution, indicating pH of 6.
Chamber-2, created in order to observe pH distribution
around a network of more than two beads, was constructed from
a rectangular plastic plate the same as for chamber-1. Instead of
a circular hole, a 2 cm long 1 mm wide groove of height 1 mm
was cut from the plate to provide a long, thin box-like chamber.
The bottom of this groove was sealed with a coverslip (150 mm
thick) to facilitate optical microscopy. The groove configuration
permitted a linear alignment of beads. To prevent shadow artifacts on the collected images, the top edges of the groove were
smoothed.
For experiments, two or more beads of the same polarity were
dropped into the appropriate chamber filled with a solution of
water and, when required, pH dye (50 ml for chamber-1 and
30 ml for chamber-2). Images were acquired using a stereo
microscope (Nikon, model 75860, Japan) and a color CCD
camera (model #: CFW-1310C, Scion Corporation). A white
LED-ring array was used as a light source. The acquired images
were then analyzed with ImageJ.
then direct-filled using a flexible long syringe needle. Tip resistance was measured to be 10 MU, indicating tip diameters on
the order of 1 mm.
A micro Ag/AgCl electrode (World Precision Instruments,
Driref-450) with tip diameter 450 mm was used as reference
electrode.
For the measurement of electrical potential distribution,
chamber-3 was used. This chamber was constructed from 1 mm
thick microscope slide pieces glued together such that the final
chamber was an open box, 2 cm high, 5 mm wide and 5 cm long
(see Fig. 8). To facilitate a linear arrangement of beads inside the
chamber, a custom-made alignment piece, consisting of two glass
slides, 4.5 cm 0.5 cm, glued together with a 300 mm gap, was
inserted into the chamber. The alignment of beads simplified the
potential-distribution measurement to a two-dimensional
problem.
Chamber-3 was first filled with deionized water. No dye was
added. Then, the microelectrode and reference electrode were
inserted into the chamber from the top. The reference electrode
was situated 20 mm away from the beads in the bulk region.
Two or more beads were immediately dropped onto the groove
(Fig 8). Surface-to-surface separation was on the order of bead
diameter, but never exceeding 1.5 mm. Microelectrode position
was monitored from the side of the chamber with a stereo
microscope (model #: Wild M7, Heerbrugg, Switzerland) coupled
to a CCD camera (Scion Corporation, Model CFW-1310C).
Potential distribution was measured while translating the
microelectrode from the surface of one bead to the surface of the
other. A step-motor (DC Motor Mike, Lot-Oriel, Germany)
imposed translation at constant velocity. Before making the
measurement, the system was calibrated by placing the reference
electrode close (<2 mm) to the probe electrode and verifying
a near-zero potential difference. Then, by using micromanipulators (Daedal, Inc., PA), the reference electrode was placed
several millimetres ([ distance between the beads) beyond the
network of two (or more) beads, while the tip of the probe
electrode was brought to the right surface of the left bead. The
microelectrode tip was then moved horizontally, toward the
surface of the neighboring bead, at a speed of 20 mm s1.
A custom-written LabView program was used to monitor and
record the electrical potentials. Measurements were taken at
100 Hz, giving voltage values every 0.2 mm.
Electrical potential distribution
Voltage measurements were made using tapered glass microelectrodes and a standard electrometer (Electro 705, World
Precision Instruments, Fl). Thin-walled, single-barrel capillary
tubes (o.d. ¼ 1.2 mm, World Precision Instruments, Model
TW150F-6) were used as blanks to fabricate the electrodes using
a standard electrode puller (Electrode Puller P-87, Sutter
Instruments, CA). The pulled electrodes were immersed with
their tips up in 3 M KCl solution. The solution climbed to the tips
by capillary action, and microscopic examination ensured that
the tip regions were bubble-free. The microelectrode shanks were
3856 | Soft Matter, 2009, 5, 3850–3857
Fig. 8 Experimental setup (chamber-3) used for electrical potential
measurements.
This journal is ª The Royal Society of Chemistry 2009
Conclusion
Despite its central role in self-assembly, the mechanism of
attraction between like-charged particles in aqueous solution has
remained controversial. It is demonstrated here that abundant
charge separation around each particle is the agent responsible
for the attraction. This conclusion fits with earlier hypotheses.
The mechanism should be valid not only on the colloidal scale
explored here, but also at smaller scales possibly down to the
nano and molecular levels, which would have important implications for self-assembly.
Acknowledgements
The authors thank Jeff Magula for fabrication of the experimental chambers and Ronnie Das for software development.
This study was supported by NIH Grants (AT-002362 and
AR-44813), and ONR Grant (N00014-05-1-0773).
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