Pattern formation during polymerization of acrylamide in the presence of sulfide ions

Article abstract of DOI:10.1021/jp982968b

When polyacrylamide gel is prepared from a mixture of acrylamide, N,Na?2-methylene-bisacrylamide and triethanolamine with a peroxodisulfate initiator in the presence of sulfide, spatial pattern formation occurs in the gel if water is spread on top of the gel after it solidifies. These patterns, typically arrays of spots or stripes, persist for many hours. Analysis of the effects of temperature, composition, stirring, and other factors suggests that the pattern formation occurs during polymerization due to convection driven by the highly exothermic polymerization reaction. The role of sulfide ion, which is essential for the pattern formation, appears to be to terminate the polymer chain elongation while maintaining the overall exothermic chain reaction. ? 1999 American Chemical Society.

Full text of DOI:10.1021/jp982968b

36
J. Phys. Chem. B 1999, 103, 36-40
Pattern Formation during Polymerization of Acrylamide in the Presence of Sulfide Ions
,†
†
,‡
‡
Mikl o´ s Orb a´ n,* Krisztina Kurin-Cs o1 rgei, Anatol M. Zhabotinsky,* and Irving R. Epstein
Department of Inorganic and Analytical Chemistry, L. E o¨ tV o¨ s UniVersity, H-1518 Budapest 112, P.O. Box 32,
Hungary, and Department of Chemistry, Brandeis UniVersity, Waltham, Massachusetts 02254-9110
ReceiVed: July 10, 1998; In Final Form: October 14, 1998
When polyacrylamide gel is prepared from a mixture of acrylamide, N,N′-methylene-bisacrylamide and
triethanolamine with a peroxodisulfate initiator in the presence of sulfide, spatial pattern formation occurs in
the gel if water is spread on top of the gel after it solidifies. These patterns, typically arrays of spots or
stripes, persist for many hours. Analysis of the effects of temperature, composition, stirring, and other factors
suggests that the pattern formation occurs during polymerization due to convection driven by the highly
exothermic polymerization reaction. The role of sulfide ion, which is essential for the pattern formation,
appears to be to terminate the polymer chain elongation while maintaining the overall exothermic chain reaction.
Introduction
Procedure. The gel components, AA, Bis, and TEA, were
2
-
mixed with S , and then (NH4)2S2O8 was added to initiate the
gelation process. The final volume, composed of the stock
1
Since the publication of Turing’s classic paper nearly a half
century ago, the reaction-diffusion patterns known as Turing
structures (TS) have attracted considerable attention from
chemists and biologists.2 Turing structures were observed
experimentally for the first time in a chemical system, the CIMA
3
solutions and water, was 12.6 cm , which formed a solution
layer about 2 mm in depth in a 9 cm i.d. Petri dish. In most
experiments, the concentration of the gel components was [AA]
3
-3
)
1.035 M (5.50 cm of stock solution), [Bis] ) 4.85 × 10
-
-
(
ClO2 / I /malonic acid) reaction, in a continuously fed gel
3
3
M (0.47 cm ), (TEA) ) 0.055 M (0.47 cm ). The polymerization
3,4
reactor. Prior to this discovery, there had been reports of
spatial patterns analogous to TS that appeared in potentially
oscillating liquid-phase chemical and biochemical reactions.
2-
2-
time varied significantly with [S ] and [S2O8 ]. For example,
2
-
-2
3
-2
3
at [S ] ) 1.5 × 10 M (1.20 cm ), 3 × 10 M (2.40 cm ),
-
2
3
2-
and 5 × 10 M (3.94 cm ) and [S2O8 ] ) 0.113 M (1.80
5
These patterns, however, proved to be of convective origin.
The convective patterns that arise via Rayleigh or Marangoni
instabilities strongly resemble Turing structures. Therefore,
prevention of convection is a necessary condition for observation
of true TS, and gels have been employed in majority of the
experiments on TS.
Recently, Turing-like structures have been observed in
polyacrylamide gels formed in the presense of the components
of the methylene blue oscillating reaction (MBO), methylene
3
3
cm ) or 0.226 M (3.60 cm ), gelation takes about 10 min, 20
min, and 3-4 h or 5, 10, and 40-50 min, respectively. After
6
the mixture became solid, the gel layer was covered with water
3
(
6 cm , at the ambient temperature of 21 or 25 °C). Observations
were made visually from above using illumination (light box)
from below. Images were recorded with a video camera, and
the data were processed with an OPTIMAS image-analysis
system (Bioscan).
The elastic modulus of the gel was measured with a
homemade modulus balance instrument (manufactured by the
Department of Colloid Chemistry, L. E o¨ tv o¨ s University10 ). The
method is based on measuring the penetration of a hard ball
into the gel layer when known forces are imposed on the ball.11
2-
2-
7-9
blue (Mblue), sulfide (S ), sulfite (SO3 ), and oxygen.
Here, we show that patterns similar but not identical to TS arise
during the polymerization of acrylamide in the presence of
sulfide alone.
Experimental Section
Results
Chemicals. All reagents were of the highest grade com-
mercially available. These were: acrylamide (AA), Sigma,
electrophoresis reagent, g99%; N,N′-methylene-bisacrylamide
Pattern Formation in the AA/Bis/TEA/S2O8 -/S2- System.
2
2
-
The gel was prepared in the presence of S , and pure water
was spread on the surface of the gel. Structures appeared in the
gel 20-60 min after the water was added. The patterns were
clearly visible in the milky opaque gel, especially if the Petri
dish was placed on a light box. The first spots or stripes usually
appeared at the wall of the Petri dish and then spread to occupy
the entire gel surface. The structures were composed of white
circles (1-2 mm i.d.), deformed spots, or stripes, depending
on the composition of the system. The patterns persisted for
many hours. During this time, the gel swelled significantly,
eventually taking up the entire amount of water from the surface.
As a result of the swelling, the structure evolved in time; the
circular spots gradually took on an elipsoidal shape and then
transformed into stripes, or, if stripes appeared initially, their
(
Bis), Sigma, electrophoresis reagent, g98%; triethanolamine
2
-
(TEA), Fisher, 99%; ammonium peroxodisulfate (S2O8 ),
2
-
Sigma, electrophoresis reagent, g98%; sodium sulfide (S ),
Merck, 35% Na2S.
For preparation of stock solutions, the chemicals were
dissolved in deionized water. All stock solutions but (NH4)2S2O8
and Na2S could be stored for extended periods of time without
decomposition. The following stock solutions were made: [AA]
)
2.37 M, [Bis] ) 0.13 M, [TEA] ) 1.62 M, [(NH4)2S2O8] )
0
.79 M, and [Na2S] ) 0.16 M.
†
‡
L. E o¨ tv o¨ s University.
Brandeis University.
1
0.1021/jp982968b CCC: $18.00 © 1999 American Chemical Society
Published on Web 12/15/1998

Pattern Formation during Polymerization of Acrylamide
J. Phys. Chem. B, Vol. 103, No. 1, 1999 37
2
-/S2- gel system.
Figure 1. Spotted pattern in the AA/Bis/TEA/S
2
O
8
-
3
Composition of gel mixture: [AA] ) 1.035 M; [Bis] ) 4.85 × 10
2
-
2-
-2
M; [TEA] ) 0.055 M; [S
2
O
8
] ) 0.112 M; [S ] ) 3 × 10 M.
Initial temperature: T
0
) 40 °C. Covering solution: water. The domain
size is 27 mm × 25 mm. Average diameter of spots is about 1.5-2
mm.
3
Figure 3. Temperature vs time in mixtures (total volume ) 12.6 cm )
at standard composition with mechanical stirring (600 rpm). Initial
temperature T
0
) 21 °C. Gel point is defined as the time at which the
stirring bar stops rotating in the mixture. Curves are as follows: (a)
AA/Bis/TEA/S
2-
2- 2-
2- 2-
8
O
2 8
; (b) AA/Bis/TEA/S
2
O
8
/S ; (c) S
2
O
/S ; (d)
composition as in system b, but with [AA] ) half of standard value.
the gel, we selected the following concentrations as standard:
-
3
[
1
AA] ) 1.035 M, [Bis] ) 4.85 × 10 M, [TEA] ) 5.5 ×
-
2
2-
-2
2-
0
M, [S ] ) 3 × 10 M, and [S2O8 ] ) 0.112 M. At this
composition, the time required for solidification of the mixture
is about 5-6 min. We allowed the system to stand for about
1
0 min after the initiation of polymerization before covering
the gel layer with water. When the gel components were mixed
at room temperature (about 21 °C), a spot-type structure (see
Figure 1) started to develop about 1 h after water was added to
the gel. We describe below the effects of such factors as
temperature, oxygen, thickness and surface area of the layer,
light, stirring, and composition on the pattern formation using
a gel of standard composition as a reference.
2-/S2- gel system.
2 8
Figure 2. Striped pattern in the AA/Bis/TEA/S O
2
-
-2
All conditions and concentrations, except [S ] ) 5 × 10 M, as in
Figure 1.
width increased with time. The structures can be seen more
easily if methylene blue (Mblue) is present either in the gel or
in the solution above the gel layer because the blue color gives
better contrast. Other dyes such as chrysoidines, erioglaucine,
or ferroin have a similar effect, offering the possibility of orange,
green, or red patterns.
Effect of Temperature. The polymerization of acrylamide is
highly exothermic. The temperature was monitored as a function
of time using the standard concentrations in the following
2
-
2- 2-
systems: (a) AA/Bis/TEA/S O ; (b) AA/Bis/TEA/S O /S ;
2
8
2
8
2
-
2-
2- 2-
(c) S O /S ; (d) 0.5 × AA/Bis/TEA/S O /S . The reac-
2
8
2
8
2
-
The presence of sulfide in the initial mixture is essential for
the development of patterns in the gel. Without sulfide, no
structure developed under any conditions we tried. The question
remains whether sulfide can be replaced by other chemicals.
Figures 1 and 2 show spotted and striped patterns developed
at the same gel matrix composition but different concentrations
of sulfide. The surface of the structured gel is smooth initially
but then becomes very uneven with tiny hills and valleys
developing along the boundaries of the spots and stripes. In
contrast, a layer of pure polyacrylamide gel, which is completely
transparent, undergoes only a slight and uniform swelling, and
its surface remains smooth indefinitely. If we allow the
structured gel to dry out, which takes about a day, the thickness
of the layer shrinks to about a tenth of a millimeter without
cracking. This hard film retains the pattern, which can be
regarded as a “fossil print” of the structure that existed in the
swollen gel.
tions were started by adding the initiator S2O8 to a mixture
of the other components. The reactions were run in a covered
Dewar flask equipped with a magnetic stirrer to maintain quasi-
adiabatic conditions. The results are shown in Figure 3.
During polymerization of pure acrylamide (Figure 3, curve
a), the temperature in the solution increases linearly (∼10 °C/
min) until about 1 min, when the mixture becomes solid. This
transition is referred to as the gel point. The polymerization
continues after the gel point (the length of the polymer chains
and the degree of cross-linking increase further), and the
temperature approaches a final value of 39 °C about 4-5 min
after the initiation of polymerization. In system b, the temper-
ature first rises slowly, but after 90 s, it changes in a manner
similar to system a. The gel point in system b occurs at a much
longer time and at a somewhat higher temperature, with the
constant final temperature of 42 °C being reached in 7-8 min
2-
2-
(Figure 3, curve b). In the reaction between S O
2
8
and S ,
Factors Influencing Pattern Formation in the Polyacryl-
amide/Sulfide System. After preliminary experiments to assess
the effect of various parameters on the evolution of patterns in
the increase in temperature is less than 3 °C (Figure 3, curve
c). The sum of the final temperature increases in systems a and
c is equal to that measured in system b, which suggests that the

38
J. Phys. Chem. B, Vol. 103, No. 1, 1999
Orb a´ n et al.
overall heat production in system b is the sum of the heat of
TABLE 1: Elastic Modulus (in kPa) of Pure Polyacrylamide
2
-
Gel (G ), Prepared at T ) 21 °C and of Gel Prepared with
polymerization and the heat of reaction between S2O8 and
p
0
-
2
2
-
3 × 10 M Sulfide at T
0
) 21 °C (G21) and at T ) 40 °C
0
S , since the heat capacities of all the systems are very close
to each other. The heat production in system b was unchanged
when [Bis] was either increased or decreased by a factor of 2,
but halving the amount of AA present in the mixture reduced
the heat measured by 50% (Figure 3, curve d), and no gelation
occurred at this composition.
a
(G40) as a Function of the Applied Force (Weight)
weight (g)
G
p
G
21
G
40
1
2
3
4
5.76
5.55
5.75
6.25
1.77
1.79
2.05
2.25
0.61
0.68
0.76
0.91
From the data shown in Figure 3, we conclude that the high
exothermicity of polymerization is primarily associated with the
formation of polyacrylamide chains, and the contribution of
cross-linking processes to the total heat production is not
significant. The observations in system b also suggest that, in
experiments on pattern formation in polyacrylamide gel layers,
the time that polymerization is allowed to proceed before
spreading water on the top surface may be a factor that needs
to be controlled in order to obtain reproducible results.
a
Standard deviation in the value of G measured at a given weight
is about 5-8%.
Effect of Gel Preparation Technique. We have noted that if
the gel layer is prepared by spreading the appropriate mixture
of gel components in an open Petri dish, patterns form and are
observable after the gel is covered with water. We also carried
out the polymerization of the same mixture under closed
conditionssa 2 mm thick gel layer was made between two glass
plates. The gel in this case showed no sign of being structured
after one of the plates was removed and the free gel surface
was exposed to water. This gel swelled to the same extent as
the structured gel in the Petri dish, but the swelling was uniform.
Effect of Composition. We looked at the results of varying
The initial temperature in the mixture of gel components
(denoted T0) influences significantly both the time (denoted t)
required for the appearance of a pattern after layering water on
the gel and the evolution of the pattern. As T0 is increased from
2
1 to 50 °C, t decreases from 100 to 15 min. At T0 e 5 °C or
2-
T0 g 50 °C, no pattern formation was observed. We found that
T0 ) 40 °C gave the most clearly defined patterns. At T0 ) 40
the concentration of each component in the system. If [S2O8 ]
2-
and [S ] are kept at the standard levels, [AA], [Bis], and [TEA]
in the gel matrix must be maintained in a narrow range between
0.75 and 1.5 times the concentrations present in our standard
composition; otherwise, the result is not a solid gel but a jelly-
like layer or a liquid. In the jelly, wide convective stripes may
appear without speading water on the top (adding water usually
destroys the jelly layer). The ratio of [S ] to [S2O8 ] affects
the time of gelation as described above. When a gel forms, the
character of the pattern is determined by [S ]. For example,
using the standard composition for all other components but
°
C, t is about 15-20 min and the structure evolves rapidly,
occupying almost the entire surface area of the Petri dish.
We also tested whether structure formation occurs under
quasi-isothermal conditions by carrying out the gelation process
in a thermostated Petri dish. Although we were unable to
maintain perfectly isothermal conditions, because of the long
lasting highly exothermic nature of the reaction, we did observe
that when all processes took place at nearly constant temperature
pattern formation was suppressed.
2
-
2-
2
-
2
-
2-
-2
varying [S ], at [S ] ) 1 × 10 M the gel is almost
transparent, the structure is barely visible, whereas at [S ] )
System a is colorless in each phase of the process, while
systems b and c undergo similar changes in color and turbidity.
After the colorless components are mixed, systems b and c first
become yellow then give rise to a yellowish-white precipitate,
followed by formation of a white precipitate. The gel formed
in system b shows a milky opacity.
2-
-
2
2-
-2
3
× 10 M and [S ] ) 5 × 10 M, the gel is opaque in the
former case and well-developed spots and stripes (see Figures
1
and 2) appear in the gel layer in the latter case.
Elastic Moduli of Pure Polyacrylamide and the Sulfur-
Containing Gel. The elastic modulus (G) is an indicator of the
degree of polymerization and cross-linking in the gel. The higher
the value of G, which is inversely proportional to the swelling
capacity of the gel, the harder is the gel.
To obtain information about the physical properties of
different polyacrylamide gels, 2 mm thick layers of standard
Effect of Oxygen. The effect of oxygen was assessed by
comparing experiments run in air and in an argon atmosphere.
These experiments suggest that patterns develop much more
easily in the presence of oxygen than when the polymerization
is carried out in an argon atmosphere.
Effect of Stirring. It is possible to stir either the mixture of
gel components prior to polymerization or the water layer above
the gel after solidification. When the gel components were
constantly stirred by tilting and rotating the Petri dish until the
gel point was reached, no structures were formed in the resulting
gel layer. When the water layer above a previously prepared
gel was stirred, the structures developed in the same fashion as
in the unstirred system.
composition were prepared at an initial temperature of T ) 21
0
°C in the absence of sulfide (G ) and at temperatures of T )
P
0
21 and 40 °C with sulfide ions (G21 and G ) added to the
40
mixture to be polymerized, and the elastic moduli of these layers
were measured. The results are summarized in Table 1.
Comparing the average values of the elastic moduli shown
in Table 1, we find G , the elastic modulus of the sulfide-free
p
gel, to be about 3 times larger than G . Increasing the
21
Effects of Other Factors. The gel layer was illuminated from
below the Petri dish because the pattern is more easily observed
in transmitted light than in reflected light. The intensity of
illumination did not appear to affect the pattern evolution.
temperature to 40 °C lowers G by about a factor of 2.7. These
results clearly demonstrate that the physical properties of the
gel depend very sensitively on the way it is prepared. The sulfur-
containing gel is much softer than the pure gel. A higher initial
temperature also results in a softer gel.
The thickness (0.5, 1.0, and 2.0 mm) and the surface area
2
(
(
23.8, 56.7, and 113 cm ) of the gel and the volume of water
Discussion
3
6, 12, and 20 cm ) above the gel did not have any noticeable
effect on the pattern formation. We prepared gels in both plastic
and glass Petri dishes. The only observable difference was that
in several cases the patterns found in the glass dishes were
sharper and more regular.
The pattern formation observed in sulfur-containing poly-
acrylamide gel layers results from a combination of chemical
and physical processes that occur during polymerization. The
predominant driving force of the pattern formation is the heat

Pattern Formation during Polymerization of Acrylamide
J. Phys. Chem. B, Vol. 103, No. 1, 1999 39
of polymerization. The high exothermicity, however, is only a
necessary but not a sufficient condition for appearance of the
structure. Additional chemical processes associated with the
sulfide in the mixture to be polymerized also contribute to
establishing conditions under which patterns can develop in the
two-dimensional gel system.
Chemistry behind the Pattern Formation. The polymeri-
zation of the monomer AA in the presence of Bis is initiated
by free monomer radicals, which are produced by the base TEA-
catalyzed formation of oxygen free radicals from peroxodisul-
fate. Molecular oxygen and other free radical scavengers are
known to inhibit or even prevent polymerization. Here, we
discuss the effect of sulfide ions on the polymerization and on
the properties of the gel.
Physics behind the Pattern Formation. The polymerization
of acrylamide is strongly exothermic. In the systems in which
pattern formation is observed, the temperature rises significantly
above the initial value (T0) during the transformation of
monomer AA to polyacrylamide. At T0 ) 5, 21, 40, and 50 °C,
the temperature rises to 25, 42, 55, and 63 °C, respectively.
The contributions of other processes, such as the oxidation of
2
-
2-
S
by S2O8 or cross-linking, to the total heat production are
not significant.
The large difference in temperature between the reaction
mixture and its environment results in Benard convection in
the layer during the time that the mixture exists in a liquid state.
The relatively small effect of the layer thickness during
polymerization suggests that the driving force for the convection
is surface tension rather than buoyancy, that is, that convection
is more likely of the Marangoni-B e´ nard than of the Rayleigh-
The added sulfide reacts in a relatively fast reaction with the
initiator peroxodisulfate. Under our experimental conditions,
S2O82 ] . [S ]. The overall reaction between these species
-
2-
B e´ nard type. Oxygen is consumed when it terminates the
12
[
is therefore
polymerization chain propagation. Consequently, the highest
oxygen concentration is found in the downward flow and the
lowest [O2] in the upward flow. As a result, a nonuniform
polymerization takes place in the solution layer, which retains
the pattern of convection and becomes “fossilized” when the
liquid turns to a solid gel. The pattern in the gel layer cannot
be seen with the naked eye. After water is spread on the top of
the gel, a rapid, nonuniform swelling occurs, which makes the
fossilized pattern visible.
2-
2-
2-
S
+ S O8 f S + 2SO4
(1)
2
Polysulfides (Sx2-) are formed as intermediates in reaction 2,
2-
2-
S
+ (x - 1)S f Sx
(2)
Reactions 1 and 2 represent the underlying chemistry taking
place in system c of Figure 3. Curve c in Figure 3 suggests that
the overall process terminates within about 2 min. We also
The initial temperature of the mixture (T ) has a significant
0
influence on the time needed for the appearance and the
development of the structure after adding water. This finding
followed the oxidation of S2 by S2O8 both in aqueous
solution and in a gel mixture, using Pb2 ions to monitor the
sulfide concentration qualitatively in time. The product PbS is
black, while all other products of the reaction are white. We
-
2-
+
can be interpreted by analyzing how T affects the rate and the
0
degree of polymerization as well as the temperature gradient in
the system. At T e 5 °C, no pattern occurs. At this low
0
3
added Pb(NO3)2 to 1 cm aliquots of the reaction mixture at 30
temperature, relatively long polymer chains are formed owing
s intervals. An intense black color appeared only in the first 30
s, a less intense coloration was observed after 60 s, and the
sample mixture remained white after 120 s, which is somewhat
shorter than the time required for gelation using the standard
concentrations. The colors of the end product S and the
intermediate Sx2 are white and deep yellow, respectively. The
changes in color and turbidity during the polymerization of
acrylamide in the presence of initial sulfide are the same as in
reaction 1 both in character and in time scale. From the time of
reaction 1 and from the gel point in system b (Figure 3, curve
b), we conclude that reaction 1 is complete when the AA/Bis/
TEA/S2O82 /sulfur species mixture is still in the liquid phase.
to the low concentration of radicals. The viscosity of the mixture
increases rapidly, the time of gelation is short, and the gel
formed is hard. The heat generated drives the temperature of
the gel mixture toward the ambient value. All of these effects
work against formation and detection of the convective pattern.
0
-
At 5 °C < T < 50 °C, all physical properties of the system
change with temperature. With increasing T , the polymer chains
0
become shorter, the time of gelation is longer, the gel is softer,
its swelling capacity is higher, and the temperature difference
between the polymerizing system and its environment increases
with time. The optimal initial temperature, that is, the optimal
physical parameters for structure formation, come together at
T ≈ 40 °C. At T g 50 °C, no gel is formed and therefore no
-
Reaction 1 between S2 and S2O8 takes place according to
-
2-
0
0
a radical mechanism, producing radical intermediates both from
gel structures can occur.
2
-
•
•
2-
•-
•
S
(e.g., HS and HSS ) and S2O8 (e.g., SO4 , HO ). The
high concentration of radicals initiates the polymerization of
more AA molecules but also increases the probability of chain
termination owing to the reactions of polymer radicals with each
other and with the inorganic radicals. Therefore, in the presence
of sulfide, more but shorter polymer coils are formed in the gel
mixture in a given time interval compared to the sulfide-free
case.
The physical properties of the gel mixture before and after
gelation are largely determined by the average length of the
polymer chains in the system. A shorter average length is
associated with a longer time for the liquid to reach the gel
state. The sulfide ions present in the initial mixture and the
higher initial temperature lengthen the gelation time, resulting
in a gel that is much softer (cf. G21 with Gp and G21 with G40
in Table 1), has a higher penetrability for water, and shows a
significantly higher swelling capacity than sulfur-free polyacryl-
amide prepared under the same conditions.
Conclusion
In a thin gel layer prepared by polymerization of acrylamide,
Benard-type convective patterns can be observed after swelling
if sulfide ions are also present in the initial mixture of monomer
2-
AA/Bis/TEA and initiator S2O8 . The strong exothermicity of
the polymerization and the chemical processes associated with
the sulfide ions are both essential in bringing about the pattern
formation. The steep temperature gradient induces and maintains
convective heat and mass currents in the liquid layer until the
gel point is reached. The role of sulfide appears to be to ensure
optimal physical properties of the system (e.g., time of gelation,
viscosity, mechanical strength of the gel, elasticity, swelling,
...) for effective convection and stucture formation and detection
in the liquid and gel states.
Acknowledgment. This work was supported by the Chem-
istry Division of the National Science Foundation (NSF), by a

40
J. Phys. Chem. B, Vol. 103, No. 1, 1999
Orb a´ n et al.
U.S.-Hungarian cooperative grant from the NSF and the
Hungarian Academy of Sciences (HAS), by the HAS (OTKA
T 016680, F 017073, and BO/00096/98.), and by a grant from
MKM (FKFP 0188/1997).
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