Pattern formation in the NaOH + CuCl2 reaction

Article abstract of DOI:10.1021/jp992456c

A simple chemical process with inorganic reactants (NaOH and CuCl₂) is presented that leads to the formation of a great variety of spatial patterns previously observed only in much more complex systems. In particular, depending on the experimental conditions, Liesegang patterns and interacting chemical fronts may emerge. The latter can develop to form spirals and cardioids. At higher concentrations, unusual disordered patterns can build up, despite the striking simplicity of the experimental system. This type of pattern formation represents a new class of nonlinear chemical phenomena.

Full text of DOI:10.1021/jp992456c

4
266
J. Phys. Chem. B 2000, 104, 4266-4272
Pattern Formation in the NaOH + CuCl2 Reaction
P e´ ter Hantz*
Department of Theoretical Physics, E o¨ tV o¨ s UniVersity, H-1117 Budapest, P a´ zm a´ ny s e´ t a´ ny 1/A, Hungary,
Department of Biochemistry, E o¨ tV o¨ s UniVersity, H-1088 Budapest, Puskin utca 3, Hungary, and Department of
Plant Taxonomy and Ecology, E o¨ tV o¨ s UniVersity, H-1083 Budapest, LudoVika t e´ r 2, Hungary
ReceiVed: July 19, 1999; In Final Form: January 7, 2000
2
A simple chemical process with inorganic reactants (NaOH and CuCl ) is presented that leads to the formation
of a great variety of spatial patterns previously observed only in much more complex systems. In particular,
depending on the experimental conditions, Liesegang patterns and interacting chemical fronts may emerge.
The latter can develop to form spirals and cardioids. At higher concentrations, unusual disordered patterns
can build up, despite the striking simplicity of the experimental system. This type of pattern formation represents
a new class of nonlinear chemical phenomena.
Introduction
Pattern formations that are governed by reaction-diffusion
carried out at room temperature. Photos of the gel sheets were
taken by optical microscope, whereas those of the gel columns
were taken with a scanner.
1
-5
processes are common in chemical and biological systems.
Some examples include the Liesegang banding,6-9 cardioid and
rotating spiral-shaped chemical waves in the Belousov-Zhabo-
Patterns in Gel Sheets. First, the results are presented of
the investigations when the reaction was taking place in a gel
sheet, in which the concentrations of NaOH and CuCl2 were a0
) 8.0 M and b0 ) 0.732 M, respectively.
1
0-12
tinsky reactions,
retina.
and electrochemical waves in the chicken
1
3,14
Furthermore, several sea shell patterns appear to be
the result of pair production and mutual annihilation of traveling
biochemical waves.15 The simple chemical system presented in
this paper can lead to the formation of the most important
patterns that have been observed in the above systems.
The simplest structures appear through the following sequence
of events (Figure 1): The outer electrolyte, NaOH, diffuses into
the gel containing the CuCl2 inner electrolyte and a one-
dimensional diffusion front is formed. Behind this front, a gel
region is formed in which both of the reactants are present. This
gel portion, where precipitation and pattern formation can occur,
is referred to as the excitable region. Inside this excitable region
there is a zone known as the reaction front, at which a primary
precipitate is forming. This precipitate, assumed to be mainly
Cu(OH)2, has blue color in reflected light and green color in
transmitted light. The size of the primary precipitate seems to
be between 0.01 and 0.4 µm because it looks homogeneous by
investigations done with optical microscopy, but it is im-
mobilized in the gel having a pore size of the order of 10 nm.
Experimental Section
Two series of experiments have been performed, for which
the patterns were formed, either in gel sheets or in gel columns.
The inner electrolyte CuCl2 was distributed in a poly(vinyl
alcohol) (PVA) gel, and the outer electrolyte NaOH was poured
onto the top of the vertically placed gel and allowed to diffuse
into it. The gel was made as follows: An 8.6 w/w % PVA
solution was prepared by adding PVA powder (PVA 82 1038,
Merck, AR) to high-purity water (supplied by a Labconco filter
series) under continuous stirring at 70-80 °C. Complete
solubilization was achieved by stirring the solution for 4 h at
this temperature, and then it was allowed to cool to room
temperature. The inner electrolytes of the required concentrations
were obtained by adding different amounts of CuCl2 (Reanal,
AR) solutions to a series of PVA solutions, each of 100 mL
volume. The acidity and cross linking of the gels were set by
adding 1 mL of 1 M glutaraldehyde (Merck, AR) and 2 mL of
Later, the formation of the precipitate is halted at some points
in the reaction front (Figure 1A). During the motion of the
reaction front through the gel, these points expand into empty
(precipitate-free) regions. Thus, the reaction front is split up
into segments called reaction zones, each of them being limited
by regressing edges. The empty regions are limited from above
by two oblique, passive borders formed in the wake of the
regressing edges (Figure 1B).
1
8.5 w/w % HCl (Reanal, AR) to the above mixtures. Finally,
The angle of the passive borders, which limit the empty
regions from the area where the precipitate has already formed,
are determined by two perpendicular velocities: the speed of
the diffusion front and that of the reaction zone’s regressing
edges. Between minutes 60 and 180 of the experiment, the order
of magnitudes of both speeds were 0.1 mm/min. When the two
regressing edges of such a reaction zone meet, a small cusp
forms and the precipitation stops (Figures 1C and 2D). Note
that at ∼2 mm behind the region where the precipitate has
already formed, the gel starts to shrink and no longer adheres
to the glass plates. This effect, called syneresis, does not play
an essential role in the pattern formation. Similar experiments
high-purity water was used to top off each solution to 200 mL.
To prepare the experiments in gel sheets, the solutions were
poured between pairs of glass plates to a height of 50 mm. The
8
3 × 102 mm glass plates were placed parallel to each other at
a distance of 1.6 mm. For the experiments in gel columns, the
solutions were poured into glass test tubes of 14 mm i.d. to a
height of 100-120 mm.
Once the gelation took place (approximately 10 h), 3 and 6
mL of NaOH (Reanal, AR) outer electrolyte solutions of several
concentrations were poured on the top of the vertically placed
gel sheets and gel columns, respectively. The experiments were
1
0.1021/jp992456c CCC: $19.00 © 2000 American Chemical Society
Published on Web 04/08/2000

Pattern Formation in the NaOH + CuCl2 Reaction
J. Phys. Chem. B, Vol. 104, No. 17, 2000 4267
can be performed in agarose gel and thin liquid layers,
respectively, in which syneresis does not occur but reaction
fronts with similar dynamical properties emerge.
Some time later, the precipitate also emerges in the empty
regions, beginning at the top of the regions (Figures 1C and
2
A). Soon, the reaction zone of the younger precipitate formed
in the empty region splits again. Thus, besides a new empty
region, two new reaction zones are formed that propagate in
the excitable region below the passive border of the preceding
precipitate (Figures 1D and 2A). The precipitate, which was
produced by these new reaction zones, is limited from above
by the passive borders of the preceding precipitate and from
below by the passive borders formed in the wake of the new
regressing edges (Figures 1D,E, and 2A-E). At a later stage,
the new reaction zones are no longer parallel with the diffusion
front (Figures 1D and 2C). When approaching reaction zones
meet, they annihilate each other, probably because of the
depletion of the reactants in their surroundings. A small cusp
forms at these annihilation points (Figure 2E).
In the next stage of the pattern formation, a ripening process
starts in the primary blue-green precipitate, which then decays
into a colloidal brown precipitate. According to the results of
X-ray-scattering experiments, the brown precipitate is composed
of CuO crystallites. The ripening process does not take place
in a band of approximately 100 µm thickness below the passive
border of the preceding upper precipitate. Thus, between the
regions filled with CuO, a thin band remains free of this
precipitate at any time (Figures 1E and 2F). These blind bands
are the dark oblique lines shown in Figure 2A,C-E.
Pair production and annihilation of traveling waves have been
observed on several sea shell patterns. This behavior has been
reproduced by mathematical models based on nonlinear reac-
1
5
tion-diffusion equations.
Patterns in Gel Columns. When the outer electrolyte
(NaOH) is poured onto the top of a gel column, the diffusion
front is expected to have the form of a disk, in contrast with
the previous case, in which it has the shape of a thin line. In
this case, the reaction zones involved in the pattern formation
can perform a more complicated motion in the excitable region,
leading to more complex patterns than in the previous case. A
series of patterns were observed that depend on the outer and
inner electrolyte concentrations,.
Liesegang Bands (a0 ) 0.5 M, b0 ) 0.0293 M). Quasi-
periodic precipitation in the wake of a moving reaction-
diffusion front is called the Liesegang phenomenon. So far, three
main classes of these patterns have been observed. The bandings
are considered to be normal when the distance between
consecutive bands increases with the band order, inverse when
it decreases, and irregular when no regularity can be observed
Figure 1. Main stages of pattern formation in gel sheets. (A) In some
points of the reaction front, the formation of the precipitate is halted.
The reaction front is split into reaction zones: (a) outer electrolyte;
(b) primary precipitate; (c) reaction front; (d) points at which the
formation of the precipitate is halted; (e) excitable region; and (f)
approximate position of the diffusion front. (B) The points at which
the formation of the precipitate is halted expand into empty regions:
7
-9
in the positions of the precipitate zones.
(a) reaction zones; (b) regressing edges; (c) empty (precipitate-free)
In our experiments a green-colored substance is formed
behind the diffusion front. This compound is optically more
dense in separate, but randomly spaced regions along the gel
column (Figure 3), and thus, it can be considered as an example
of irregular Liesegang banding. The substance formed in this
experiment does not seem to be a colloid because no particles
are visible, even at 20 Å resolution using electron microscopy.
In this case, syneresis of the gel has not been observed, and the
ripening process leading to the brown precipitate mentioned
above does not take place at all.
region; and (d) passive edge. (It should be noted that the topmost empty
regions usually form on bubbles located on the gel-outer electrolyte
border). (C) Some time later, precipitation begins again at the top of
the empty regions. The newly formed precipitate starts to fill the empty
region: (a) encounter of two regressing edges and the formation of a
small cusp and (b) new precipitate born in the empty region. (D) Pair
production of reaction zones takes place when the reaction zone of the
newly formed precipitate also splits: (a) new reaction zones formed
by pair production and (b) pair production of reaction zones. (E) The
process of the formation of the colloidal CuO precipitate (ripening):
(a) Colloidal CuO (brown) precipitate in an elder pattern; (b) blind
region that is never filled by the brown precipitate; (c) CuO formed in
the primary precipitate generated by the reaction zone (e); (d) passive
borders of the elder and younger precipitates; and (e) traveling reaction
zone. The arrows show the progressing directions of the reaction zone
and the invasion of the brown precipitate, respectively.
Multiarmed Spirals (a0 ) 7.5 M, b0 ) 0.644 M). At these
concentrations, usually a trivial pattern (homogeneous precipita-
tion) emerged only, if the outer electrolyte was simply layered
on the gel column and allowed to diffuse into it. To obtain

4268 J. Phys. Chem. B, Vol. 104, No. 17, 2000
Hantz
Figure 2. Patterns in gel sheets (a
0
) 8.0 M, b ) 0.732 M). Parts A, C, D, and E were taken using reflected light, whereas B and F were taken
0
with transmitted light. (A) Precipitate begins to form at the top of an empty region. Note that the reaction zones on the two sides are no longer
parallel with the diffusion front (scale bar ) 0.25 cm). (B) Primary precipitate bands produced by propagating reaction zones: They are limited
from above by the passive border of an elder precipitate and from below by the passive border formed in the wake of the regressing edge of the
reaction zones. In this experiment, the gel sheet in which the pattern formation took place was 0.17 mm thick. (scale bar ) 0.5 mm). (C-E) Three
consecutive stages of the pattern development. Elapsed time from the beginning of the experiment is 97, 131, and 137 min, respectively (scale bar
)
0.25 cm). (C) The reaction zone in the middle is getting smaller. (D) The regressing edges of the reaction zone in the center of the picture met,
and therefore, the precipitation in this reaction zone stopped. Two small reaction zones can also be seen just before their annihilation. (E) The
pattern after the annihilation of the reaction zones. (F) The colloidal CuO precipitate-free, blind band between an older (right) and a younger (left)
precipitate (scale bar ) 50 µ).
nontrivial patterns, it was necessary to create special initial
conditions, i.e., to increase the excitability at the top of the gel
column. This was achieved by increasing the concentration of
the inner electrolyte in a narrow top region by pouring 2.96 M
CuCl2 solution on the gel for 10 min. It is important to note
that the increasing of the inner electrolyte’s concentration at
the top of the gel column is needed only to start the splitting of
the reaction front because this process requires a higher degree
of excitability than that for maintaining the reaction zones.
Having removed the CuCl2 solution, the outer electrolyte was
poured on the gel. The reaction front split while passing through
the gel region with increased inner electrolyte concentration,
and the resulting reaction zones survived as they moved into
the part of the gel column where the inner electrolyte concentra-
tion was homogeneous and isotropic.
After a short transient, the reaction zones took the form of
spiral arms, rotated around the axis of the gel column and moved
down the gel as the diffusion front advanced (Figure 4A). Note
that at first, the primary blue-green precipitate was formed in
the wake of the reaction zones. Then, in a few minutes, it started
to transform into the brown, colloidal CuO precipitate, except
for a thin, blind region below the passive borders of the regions
filled with precipitate by different reaction zones (Figure 4B,D).
In a central region, called the core, the reaction front did not
split (Figure 4A,B). The diameter of the core is approximately
4 mm. Note that the diameter of the core is larger for the

Pattern Formation in the NaOH + CuCl2 Reaction
J. Phys. Chem. B, Vol. 104, No. 17, 2000 4269
Figure 3. Irregular Liesegang pattern (a
scale bar ) 1 cm).
0
) 0.5 M, b ) 0.0293 M;
0
experiments in which the concentration of the inner electrolyte
is slightly lower than the above value. Similar types of
multiarmed spirals with well-defined cores have been observed
in the experiments on the Belousov-Zhabotinsky reac-
1
1,16,17
tions.
The oblique motion of the spiral arm shaped reaction zones
led to telescoped helicoid-like regions filled with colloidal CuO
separated by the thin, blind areas (Figure 4C,D). The handedness
of the helicoids present in a gel was determined by the random
split and annihilation of the reaction zones at the upper end of
the gel column. The pitch of the helicoids was constant during
this experiment; i.e., the ratio of the reaction zone’s horizontal
and vertical velocities was constant (Figure 4C,D). Note that
the latter is determined by the velocity of the diffusion front,
which decreases in time.
Cardioid-Like Patterns (a0 ) 8.0 M, b0 ) 0.732 M). At
these concentrations, the types of patterns formed were unpre-
dictable: in 70% of the experiments, rotating reaction zones
were formed similar to the spiral arms presented above, and in
Figure 4. Patterns formed in a gel column by reaction zones shaped
like spiral arms (a
0
) 7.5 M, b
0
) 0.644 M). (A) The structure of the
3
0% of the cases, cardioid-shaped patterns emerged. The
reaction zones: (a) growing direction of the reaction zones; (b) core;
development of the latter passed through various stages as the
diffusion front moved through the gel column (Figure 5A,B).
At a certain point in the central part of the reaction front, a
small, arch-shaped split occurred, in which precipitation did not
take place. The external border of the arch was a regressing
edge, leaving behind an empty area that subsequently filled with
precipitate. In the next stage of the development, the arch grew,
and its ends turned against each other. When they met, the
pattern took the form of a closed cardioid (Figure 5A). At that
moment, the reaction front was split into two parts. As the
diffusion front advanced, the outer reaction zone, which had a
cardioid-shaped regressing edge, was getting smaller, whereas
the inner one was filling the empty region let by the outer zone
(
(
c) advancing direction of the diffusion front; and (d) reaction zones
B). Cross section of the gel column after the reaction took place. The
black curves are the traces of the blind, empty areas. In the central
region (core), no front split took place (scale bar ) 0.25 cm). (C-D)
The gel column and its longitudinal section after the reaction took place.
The “plastic” form is caused by the syneresis of the gel (scale bar )
1
cm).
with precipitate. When the diameter of the cardioid reached ∼6
mm, a new split occurred in the inner reaction zone (Figure
5
B).
A few minutes after the reaction zones produced the blue-
green precipitate, the ripening process began to generate the

4270 J. Phys. Chem. B, Vol. 104, No. 17, 2000
Hantz
Figure 5. (A-B) Cardioid-like patterns in a gel column (a
0
) 8.0 M, b
0
) 0.732 M). Two cross sections of the gel column after the reaction took
place, representing consecutive stages of the pattern development. Enlargement of the elder and birth of the younger, blind band (dark curve) can
be observed (scale bar ) 0.25 cm). (C) Patterns in gel placed in a Petri dish of 8.7 cm inner diameter. Cardioid and spiral-shaped patterns can also
be observed. The dish was put on the scanner while the reactions were going on, and the picture was taken from below. The light curves are the
passive borders of the precipitates produced by the consecutive reaction zones.
brown precipitate. Only the thin, blind bands below the passive
borders of the regions precipitated by different reaction zones
remained empty of the brown precipitate. Note that spiral and
cardioid-shaped patterns are not the result of border effects
caused by the test tubes. Similar patterns also appeared in
experiments performed in gels having much larger diameters
(Figure 5C).
It is remarkable that the evolution of the cardioid-shaped

Pattern Formation in the NaOH + CuCl2 Reaction
J. Phys. Chem. B, Vol. 104, No. 17, 2000 4271
Figure 7. Concentration space of the reagents for the patterns formed
in gel columns: (a) irregular Liesegang banding; (b) homogeneous
brown precipitate; (c) distorted helicoidal patterns; (d) helicoidal
patterns; (e) cardioid patterns; (f) random helicoidal patterns; (g)
cabbage-like patterns; (h) homogeneous green or purple precipitate;
(i) the precipitation stops near the top of the gel column because of
the depletion of the outer electrolyte; and (j) other types of quasiperiodic
patterns.
chemical systems, but no other simple inorganic reaction is
known to produce such a wide variety of spatial formations.
Some of the main characteristics of the patterns formed in
the gel sheets can be explained by assuming that a diffusive
substance is formed along the reaction zones, and a critical
concentration of this intermediate (not yet determined) is needed
for the formation of the blue-green precipitate. If we suppose
that this substance is produced only by the reaction zones (and
not also by the passive borders), then its concentration decreases
around the regressing edges. Thus, the formation of the blue-
green primary precipitate is forced to regress in the direction
along the reaction zone. Note that the reaction takes place in
nonreexcitable media, but as the diffusion front advances, the
reaction zones penetrate in new, excitable gel regions. This
supposition also explains why the precipitation stops when two
regressing edges of a reaction zone meet: at the meeting point,
the concentration of the intermedier becomes so low that no
precipitation can occur. The annihilation of traveling reaction
zones moving toward each other can be explained by supposing
that the electrolytes are depleted from the surroundings of the
meeting point during the formation of the intermedier. Colloidal
Figure 6. Disordered patterns formed in a gel column. The electrolyte
concentrations were very high (a
0
) 15.0 M, b ) 0.879 M). Scale bar
0
)
1 cm. (A) The gel column after the reaction took place. (B)
Longitudinal section of the gel column. Frequent birth and annihilation
of reaction zones can be observed.
electrochemical waves detected in chicken retina goes through
approximately the same developmental stages as those men-
1
8,19
growth processes,
which take place in the wake of the
1
3,14
reaction zones, are relevant only in the second stage of the
pattern formation, i.e., the birth of the brown precipitate.
tioned above.
Irregular, “Cabbage-Like” Patterns (a0 ) 15 M, b0 )
.879 M). At these high concentrations, regular, ordered patterns
The chemical instability arising from differential transport
of heat and matter is known to produce temperature and
0
no longer formed. The traveling reaction zones were very close
to each other; they frequently met and annihilated. At the same
time, splitting of the reaction zones was very frequent. All these
phenomena resulted in the pattern shown in Figure 6A,B.
The conditions for obtaining the above-mentioned patterns
in gel columns are summarized in Figure 7. Note that the most
relevant patterns are located near the diagonal of the diagram.
For the experiments using gel sheets, this variety of patterns
did not appear.
2
0
concentration waves and may contribute to the pattern
formation. Although the thermochemistry of the processes is
not known, it is assumed that thermal effects do not contribute
significantly to the pattern formation. Precipitation after the first
experimental hour is very slow, and therefore, local temperature
changes in the reaction front are probably insignificant. Note
that the results are quite temperature-insensitive: the patterns
observed in gel columns at room temperature are also forming
at 10 and 55 °C, too.
The phenomena presented in this article are not specific to a
single chemical system. Slightly different patterns form when
other copper or silver salts (e.g., Cu(NO3)2 and AgNO3) are
used instead of CuCl2, or the reaction proceeds in PVA solution
without gelation, and even in thin electrolyte layers. Also, a
rich variety of patterns emerge when agarose gel is used instead
of PVA.
Discussion
No detailed theoretical explanation for these structures has
been found. Each of these patterns has been observed in various
reaction systems, but no other system is known that produces
all of these phenomena. Also, traveling waves and spiral patterns
have been produced by mechanistically very complicated

4272 J. Phys. Chem. B, Vol. 104, No. 17, 2000
Hantz
Acknowledgment. I am indebted to L. Szil a´ gyi, Z. R a´ cz,
(5) Scott, S. Oscillations, WaVes and Chaos in Chemical Kinetics;
Oxford University Press: Oxford, 1995.
T. Tur a´ nyi, Z. Noszticziusz, E. K _o r o¨ s, M. Orb a´ n, E. Szathm a´ ry,
and E. Keszei for useful discussions; D. Sherrington (University
of Oxford), M. Zr ´ı nyi (Budapest University of Technology), I.
Ol a´ h, M. Palkovits, and A. Magyar (Semmelweis University
Medical School, Budapest) for the opportunity to work at their
departments; Gy. Faigel, G. Zboray, G. Bortel, J. Kov a´ cs, and
A. Reichard for their help in some experiments. I acknowledge
the support of Gy. K e´ ri, L. Gr a´ f, K. T o´ th, A. M a´ ln a´ si, and I.
Jalsovszky. Also, I am thankful for the financial assistance of
the O¨ szt o¨ nd ´ı j Foundation, of the Orb a´ n Bal a´ zs Foundation, of
the Hungarian Ministry of Education, and of the Hungarian
Research Funds (Grant No. OTKA T029792). Additional
experimental details are available from the author on request
(
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(
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(
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(
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