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Experimental studies of the chemical automat in the Mn2+KBrO3H2SO4KBr system
\‘O!Ume 66. number 3
EXPERIMENTAL
CIIE~IIC~L
PHYSICS LETTERS
STUDIES OF THE CHEMICAL
IN THE MI’+-KBr03-H2S0,-KBr
15
October
1979
AUTOMAT
SYSTEM
Jerzy MASEtKO
Kecched 2:! September 1976: in fiml form 1 September 1979
An exPaimenta1 stud> of a system with three steady states is reported_ The system can be switched over to mother stationary state b> ch.mgin~ the KBr concentation at the inlet of the reactor. This sxitching occ~rson a hysteresis cune.
1. Introduction The problem of the number and nature of the stationary states is J basic question of open-system kinetics in chemical reactions_ Chemical reaction systems with three stationary states are known as triggers or chemical automata. The first theoretical papers dealing with mode1 systems of these reactions were devoted to their significance in control processes in biochemical reaction networks [ I,?]_ Later a number of mathematical models of these systems appeared and were collected by RBssler [3] _The basic problem involves investigation of the switching process from one stationary process to another- This process is related to the problem of solution bifurcation for equations describing the stationary state of the system_ Bifurcation is connected with a qualitative change of the system’s phsse portrait_ As a rule a chemical reaction system has one stdtionary state which is a stable node. At the bifurcation point two stationary states are formed in the system - another stable node and a saddIe point. During a change of one system parameter, e.g. the parent substance concentration, the saddIe point may be shifted in the concentration space from one stable node to another. At another bifurcation point the stable node and saddle combine and both stationary states disappear_ Then the system jumps suddenly to another stationary state. There are only a few experimental papers dealing
with reaction systems of three station3ry states. In acid 1976 [4] the Ce4+- H2S04-KBr03-ma10nic systetn was found to exhibit three stationary states and hysteresis reIated to transitions from one stationary state to another- In ref_ [S] hysteresis was found to occur in the N,O,-NO, system and in ref. [6] in the CO-CO?-O?-nickel catalyst system. GeiseIer and F;?llner [7] experimentalIy found the occurrence of three stationary states in the Ce4+KBrO,-H,SO,-KBr system, but they did not find hysteresis in this system- In their paper a mathernatical model of the reactions under investigation was provide?. Mathematical modek of the Belousov-Zhabotinski oscillation reaction_ where three stationary states were found to occur, were provided :n refs. [8,9] _
2. Experimental Studies were carried out in a 70 cm3 flow-through reactor_ The solution was stirred by a magnetic stirrer. The reactor was supplied by means of pumps through separate inlets with two solutions: solution A: htiS0, (4 X 10B3 M), H,SO, (3 M), KBr (2 X IO-6 to 2 X lo-’ hl); soiution B: contained KBrO, at concentration 5 X 10d3, 1-25X IO-’ or 5 X 10m2_ MnS04 and H2SO4 concentrations were constant in all series of measurements. 549
I5 Octobrr The
uhiLf;ftion--r~~ttstiio:l
v3riatious
wr’rc nw3surai
pI3iinum clectrodc erence_ The results
poteutial 3s 3 I_unction
(MnS*~Mnz+) tS_ time ~iih
3
using 3 c3Iomsl electrode 3s 3 refwerr‘ rcwrded on 3 (‘rtrl Zeiss-Jcna
recorder_
The supply flow rate of tich solutitm v.t;tsO-1 15 cm3 s-t _ I-ix selected K;BrO, cwicentraiions the measurements were carried out by chzu~~ing stepa IX the KBr amcentwtion at the re.tctor inlet [t-or exnttpk. SLY fig. I. Ci!rvC 3). ,\t the begimkg_ sohltion A \\ithout ;Idmi\ture of KBr (point I) ~3s fed into the rextor. The cuncentrrttion of Br- ions in solution B \\3s ~ttes~~r~cl by mans of a selective bromide ciectrode and mtounted to I.0 X IO-’ &I_Xftcr 3 certrtin period of time the system rexshed a steady st;lte and the poteniiat bec3me constantXfter 3n interv31 of 30 ttiin in whi&i tIie potenti rv3s inrxhnt. tlte sohiiion A wrs repkud by 3nother in which the concentration of Brions ws equai to 2-0 X 10e6 bl (point 2). Since both solutions A and B xere supplied at the s;ime tluw rate. the Br- concentration at the inlet to the reactor was equal to 1.0 X 10B6 M. After the nesr period of 30 min in which the po:entiaI MS rephced
WZISconstant_ solution
A
by another in which tite KBr conccntration w3s 20 x io- 5 Al_ This procedure w;i~ repezrted untiI point I3 ~3s re3ched. Ax that point iite KBr concentrxion in soiution A ~3s equ3f to 2-0 X IO-? M_ Subsequently. the concyntmtion of soIutions A 3t the inlet to the reactor was changed in the reverse order so that the Br- ion concentntion decreased stepwise (points 13.12, ____3.2.1 in th3t sequence)_ The s;lme period of 30 mirt of constant potenti3I ~3s kept_ During the cbxmges of Br- concentmtion 3t the inlet to tile reztor. stepwise chzmges of the potenti were detected_ During the period of time in which the Brconcentntion MS incre;lsed. 3 viofent decrease in potential was observed when the I_6 X 10s3 bl solution of KBr (point 9) 1~3~ rephced by the 2.4 X IO-3 V soIution of KBr (point IO)_ Similarly, 3 vioIent incre3se of potential xrs observed during the period of time in which the Br- concentration at the inIet to the reactor was decreased. viz- when the 8.0 X 10e5 M sohrtion (point 5) was repked by the solution in which the concentration of Br- ions equzded 4.0 X 10e5 M (point 4)_ A simiktr sequence of experiments was carried auf for different KBrO, concentrations in soiution B_ 550
t 979
The purpose of the present stcdy ~2s to estriblish x\hether hysteresis is present in the system under in\estig3tion. In the course of rhe study the concentmtions were chdnged in 3 IogrtriIhnii~ s&e so th& the s~perinieni31 results presented in fig. I 3re giben in the xune wry_ In this work no rittempt ~3s made to determine precisely the position of the point at which the stepwise chtlnge of potenthl occurs. since such determin_ttion would require the estimation of esperimental error_ T!w esperimentsl results 3re not suitable for the ctilctdation of r3te const3nts or for the determin.ttion of rruction mechanisms. The 3im of the study reported here ws merely to obt.tin information of a qu3Iit3ii\e type.
3_ Rest&s
and discussion
For specific KBr03. l\lnSOA 3nd I I,SO, concentrawzs increased steptions, tlte Br - ion concentrrition wise 3t the resctor inlet. For 3 certtlin Br- ion toncentration range the potentisi in solution ~‘3s constant and corresponded to the oxidized form of the nunganese ions (fig_ I)_ The system v+x~ in the stdtionxy st3te which wrs assumed to be st3bIe (node I). If the Br- ion concentration exceeded 3 specific a sudden
KAI~
potential
drop occurred
in the system_
I
_i?mv
lo t
601 -7
v b
-6
-5
-4
-3
-2
-1
tog [ES?]
Fii. 1. Redos potenti in the system depending on the Brion mncentr3iion 3t the reactor inlet. Curve 3 - KBr03 concentration at the rextor i&et equal to 1.25 X IO-’ hl- Curve b - KBrOl concenimtion equz1 to 5 x ?Om3 hf_
CHIXICAL
Vohnnc 66. number 3 At :bis point.
known
JS the bifurcation
point.
PHYSICS LETTERS
the sad-
and both stmonxy states disappear. The system is switched over to stable node 2. A slow irtcrexx of the Br- ion concentration did not result in any poten& changes. If then the Br - ion concentration at the reactor inlet w;ts decreased. the potential remained constant up to the second bifurcation point. At this point stAbIe node 3 is combined with the saddle and both dis3ppear. The system switches over to stable node 1 and the potential in the system incretses suddenly_ The transitions took place at different Br- ion concentrstion. so that the system moled on a hysteresis curve. For KBrO; concentrations exceeding 1 X IO-’ hi the Iqsteresis curve is rect.uxguIar (fig. I, curve 3). As the #Br03 concentrstion decreases near the potentiometric titration point of AIn2* by KBrO; the shape of the hysteresis curve varies (Ilg_ 1, curve b). Fig 1 presents the curves which are patterns of the system switch-over points from one stationary state to mother_ As the KBrO% concentration decre,tses, dle point
and the stable
rhe switchover
points
nodr
1 are combined
are shifted
towards
lower
Br-
txch other at the potentiometric titration point. In the region between the two curves the system h3s 3 st3tionsry st3tes - two srabIe nodes and one saddle. To the Ieit from this region the system exhibits stationary-state 1 which corresponds to the predominance of bin3+ ions. whiie to the right there is stationary-state 2 corresponding to the predominance of Xln2+ ions. In the region between these curves the system nary ion concentrations.
Sot11 curves approach
Fig. 1. Positions of the cnnes corresponding to the chnngeover of the system from one stationary system to anotherPP is the potentiometric titration Point of %ln’+ by KBr03.
15 October
1979
occur in one of the stationary states_ The type of state is determined by the route covered by the system_ If the system srrived in this region through an increase of Br- ion concentration_ tt will be in stationary-state I_ On-the other hand, if this region is reached from Iarge Br-
ion concentrations.
it will be in stationary-
state2.
Fig. 3 shows schem3ticrlIIy the shape of the potcn-_ tial surface which depends on the Br- and Br03 ton concentrations at the reactor mIet_ A typical property of that surfxe is the existence of 3 bent fo!d_ In the system under investigation the properties of the system are chringed stepwise_ Mathematical principles of the theory of a system \\ith stepwise-varying properties were developed by the French m3thematician Thorn_ This theory is generaily known as catastrophe theory [IO] _ Fig. 3 suggests that there is a cusp-type catastrophe in the system_ Our studies confirm that catastrophe theory may be helpful in analysis and ciassification of the phenomen3 occurring in open chemical reaction systems. During switch-over from one st3tionary state to enother the coIour of the solution is changed due to the .\lnzT * Mn2+ transitionThe mangrtnese ions in the +z oxidation state in the Belousov-Zhabotinski oscillstion reaction catalyze the osidation of organic acids. For instance_ they convert mslic acid into osnlrtcetic acid. The process described In the present paper is related to the catalyst being switched on and off_ Studies of such reactions
Fig. 3. Potential in the system dependins on the BrOz and Br- concentrations at the reactor iniet.
551
Volume 66. numbe: 3
cxEYIC.\L
1’111SICS Lk-l-fLRS
may esplain control processes in biocImnic4 systems -and IUZIYbe a basis for de\elcrpnler;t of similar processes in cheniit~l tcchuoIogy_ The system inwstigted here is the second chemical rextion system taking pke in the sohltion where hysteresis was found to occur ;IS a result of transitions from one stationxy state to mother. This system. ;1s we11 3s systems witi: COrnpIiGlt~J oscilhttons [ 1 11. indimte tIut open chenkti reaction systems exhibit a number of new phcnonwn~. It should be expected that detailed
studies of
of interesting
these processes v.iII rev&
cIiscowries_
;L nunlber
15 October 1979
References II I J. JIonod and I_ J&ob_ Cold_ Spring Ii;lrb S) mp. Qunt. Bd_ 26 (1961) :89. I21 AN_ Turing. PkTmns. Roy. SOC_ B 237 (1952) 37. I31 OX. RBssler. 2. Nxurforsch. 17b (1971) 333. 1-l: P. de Keeper. A. Rossi and A_ Pxault. C!ompt_ Rend. And. Sci. (Paris) 263C ( 1976) 37 I_ ISI CL Creel md J- Ross. J. Chem. Phys. 65 (!976) 3779. I61 V. Hhvxek, J. Votruba and IL Ilofxnnn, Chem. Ens_ Sri_ 31 (1976) X7-10_ (?I \V_Oeiseicr and If-II_ Fiillner. Biophyr Chem_ 6 (1977) 107. ISI J_J_Tqson. J_ Chem_ Ph>s_ 67 (1977) 4197.
191 IL BmEIi md R-11. No) L’S,J. Phya Chem. 81 (1977) 1988_ [ lOI R. Thorn. StabiIity, structureand morphogenesis (Brmjamin. New York, 1977). I 11 I O.E. Riizskz. 2. Nrtturforsch. 321(1977) 199.
552
EXPERIMENTAL
CIIE~IIC~L
PHYSICS LETTERS
STUDIES OF THE CHEMICAL
IN THE MI’+-KBr03-H2S0,-KBr
15
October
1979
AUTOMAT
SYSTEM
Jerzy MASEtKO
Kecched 2:! September 1976: in fiml form 1 September 1979
An exPaimenta1 stud> of a system with three steady states is reported_ The system can be switched over to mother stationary state b> ch.mgin~ the KBr concentation at the inlet of the reactor. This sxitching occ~rson a hysteresis cune.
1. Introduction The problem of the number and nature of the stationary states is J basic question of open-system kinetics in chemical reactions_ Chemical reaction systems with three stationary states are known as triggers or chemical automata. The first theoretical papers dealing with mode1 systems of these reactions were devoted to their significance in control processes in biochemical reaction networks [ I,?]_ Later a number of mathematical models of these systems appeared and were collected by RBssler [3] _The basic problem involves investigation of the switching process from one stationary process to another- This process is related to the problem of solution bifurcation for equations describing the stationary state of the system_ Bifurcation is connected with a qualitative change of the system’s phsse portrait_ As a rule a chemical reaction system has one stdtionary state which is a stable node. At the bifurcation point two stationary states are formed in the system - another stable node and a saddIe point. During a change of one system parameter, e.g. the parent substance concentration, the saddIe point may be shifted in the concentration space from one stable node to another. At another bifurcation point the stable node and saddle combine and both stationary states disappear_ Then the system jumps suddenly to another stationary state. There are only a few experimental papers dealing
with reaction systems of three station3ry states. In acid 1976 [4] the Ce4+- H2S04-KBr03-ma10nic systetn was found to exhibit three stationary states and hysteresis reIated to transitions from one stationary state to another- In ref_ [S] hysteresis was found to occur in the N,O,-NO, system and in ref. [6] in the CO-CO?-O?-nickel catalyst system. GeiseIer and F;?llner [7] experimentalIy found the occurrence of three stationary states in the Ce4+KBrO,-H,SO,-KBr system, but they did not find hysteresis in this system- In their paper a mathernatical model of the reactions under investigation was provide?. Mathematical modek of the Belousov-Zhabotinski oscillation reaction_ where three stationary states were found to occur, were provided :n refs. [8,9] _
2. Experimental Studies were carried out in a 70 cm3 flow-through reactor_ The solution was stirred by a magnetic stirrer. The reactor was supplied by means of pumps through separate inlets with two solutions: solution A: htiS0, (4 X 10B3 M), H,SO, (3 M), KBr (2 X IO-6 to 2 X lo-’ hl); soiution B: contained KBrO, at concentration 5 X 10d3, 1-25X IO-’ or 5 X 10m2_ MnS04 and H2SO4 concentrations were constant in all series of measurements. 549
I5 Octobrr The
uhiLf;ftion--r~~ttstiio:l
v3riatious
wr’rc nw3surai
pI3iinum clectrodc erence_ The results
poteutial 3s 3 I_unction
(MnS*~Mnz+) tS_ time ~iih
3
using 3 c3Iomsl electrode 3s 3 refwerr‘ rcwrded on 3 (‘rtrl Zeiss-Jcna
recorder_
The supply flow rate of tich solutitm v.t;tsO-1 15 cm3 s-t _ I-ix selected K;BrO, cwicentraiions the measurements were carried out by chzu~~ing stepa IX the KBr amcentwtion at the re.tctor inlet [t-or exnttpk. SLY fig. I. Ci!rvC 3). ,\t the begimkg_ sohltion A \\ithout ;Idmi\ture of KBr (point I) ~3s fed into the rextor. The cuncentrrttion of Br- ions in solution B \\3s ~ttes~~r~cl by mans of a selective bromide ciectrode and mtounted to I.0 X IO-’ &I_Xftcr 3 certrtin period of time the system rexshed a steady st;lte and the poteniiat bec3me constantXfter 3n interv31 of 30 ttiin in whi&i tIie potenti rv3s inrxhnt. tlte sohiiion A wrs repkud by 3nother in which the concentration of Brions ws equai to 2-0 X 10e6 bl (point 2). Since both solutions A and B xere supplied at the s;ime tluw rate. the Br- concentration at the inlet to the reactor was equal to 1.0 X 10B6 M. After the nesr period of 30 min in which the po:entiaI MS rephced
WZISconstant_ solution
A
by another in which tite KBr conccntration w3s 20 x io- 5 Al_ This procedure w;i~ repezrted untiI point I3 ~3s re3ched. Ax that point iite KBr concentrxion in soiution A ~3s equ3f to 2-0 X IO-? M_ Subsequently. the concyntmtion of soIutions A 3t the inlet to the reactor was changed in the reverse order so that the Br- ion concentntion decreased stepwise (points 13.12, ____3.2.1 in th3t sequence)_ The s;lme period of 30 mirt of constant potenti3I ~3s kept_ During the cbxmges of Br- concentmtion 3t the inlet to tile reztor. stepwise chzmges of the potenti were detected_ During the period of time in which the Brconcentntion MS incre;lsed. 3 viofent decrease in potential was observed when the I_6 X 10s3 bl solution of KBr (point 9) 1~3~ rephced by the 2.4 X IO-3 V soIution of KBr (point IO)_ Similarly, 3 vioIent incre3se of potential xrs observed during the period of time in which the Br- concentration at the inIet to the reactor was decreased. viz- when the 8.0 X 10e5 M sohrtion (point 5) was repked by the solution in which the concentration of Br- ions equzded 4.0 X 10e5 M (point 4)_ A simiktr sequence of experiments was carried auf for different KBrO, concentrations in soiution B_ 550
t 979
The purpose of the present stcdy ~2s to estriblish x\hether hysteresis is present in the system under in\estig3tion. In the course of rhe study the concentmtions were chdnged in 3 IogrtriIhnii~ s&e so th& the s~perinieni31 results presented in fig. I 3re giben in the xune wry_ In this work no rittempt ~3s made to determine precisely the position of the point at which the stepwise chtlnge of potenthl occurs. since such determin_ttion would require the estimation of esperimental error_ T!w esperimentsl results 3re not suitable for the ctilctdation of r3te const3nts or for the determin.ttion of rruction mechanisms. The 3im of the study reported here ws merely to obt.tin information of a qu3Iit3ii\e type.
3_ Rest&s
and discussion
For specific KBr03. l\lnSOA 3nd I I,SO, concentrawzs increased steptions, tlte Br - ion concentrrition wise 3t the resctor inlet. For 3 certtlin Br- ion toncentration range the potentisi in solution ~‘3s constant and corresponded to the oxidized form of the nunganese ions (fig_ I)_ The system v+x~ in the stdtionxy st3te which wrs assumed to be st3bIe (node I). If the Br- ion concentration exceeded 3 specific a sudden
KAI~
potential
drop occurred
in the system_
I
_i?mv
lo t
601 -7
v b
-6
-5
-4
-3
-2
-1
tog [ES?]
Fii. 1. Redos potenti in the system depending on the Brion mncentr3iion 3t the reactor inlet. Curve 3 - KBr03 concentration at the rextor i&et equal to 1.25 X IO-’ hl- Curve b - KBrOl concenimtion equz1 to 5 x ?Om3 hf_
CHIXICAL
Vohnnc 66. number 3 At :bis point.
known
JS the bifurcation
point.
PHYSICS LETTERS
the sad-
and both stmonxy states disappear. The system is switched over to stable node 2. A slow irtcrexx of the Br- ion concentration did not result in any poten& changes. If then the Br - ion concentration at the reactor inlet w;ts decreased. the potential remained constant up to the second bifurcation point. At this point stAbIe node 3 is combined with the saddle and both dis3ppear. The system switches over to stable node 1 and the potential in the system incretses suddenly_ The transitions took place at different Br- ion concentrstion. so that the system moled on a hysteresis curve. For KBrO; concentrations exceeding 1 X IO-’ hi the Iqsteresis curve is rect.uxguIar (fig. I, curve 3). As the #Br03 concentrstion decreases near the potentiometric titration point of AIn2* by KBrO; the shape of the hysteresis curve varies (Ilg_ 1, curve b). Fig 1 presents the curves which are patterns of the system switch-over points from one stationary state to mother_ As the KBrO% concentration decre,tses, dle point
and the stable
rhe switchover
points
nodr
1 are combined
are shifted
towards
lower
Br-
txch other at the potentiometric titration point. In the region between the two curves the system h3s 3 st3tionsry st3tes - two srabIe nodes and one saddle. To the Ieit from this region the system exhibits stationary-state 1 which corresponds to the predominance of bin3+ ions. whiie to the right there is stationary-state 2 corresponding to the predominance of Xln2+ ions. In the region between these curves the system nary ion concentrations.
Sot11 curves approach
Fig. 1. Positions of the cnnes corresponding to the chnngeover of the system from one stationary system to anotherPP is the potentiometric titration Point of %ln’+ by KBr03.
15 October
1979
occur in one of the stationary states_ The type of state is determined by the route covered by the system_ If the system srrived in this region through an increase of Br- ion concentration_ tt will be in stationary-state I_ On-the other hand, if this region is reached from Iarge Br-
ion concentrations.
it will be in stationary-
state2.
Fig. 3 shows schem3ticrlIIy the shape of the potcn-_ tial surface which depends on the Br- and Br03 ton concentrations at the reactor mIet_ A typical property of that surfxe is the existence of 3 bent fo!d_ In the system under investigation the properties of the system are chringed stepwise_ Mathematical principles of the theory of a system \\ith stepwise-varying properties were developed by the French m3thematician Thorn_ This theory is generaily known as catastrophe theory [IO] _ Fig. 3 suggests that there is a cusp-type catastrophe in the system_ Our studies confirm that catastrophe theory may be helpful in analysis and ciassification of the phenomen3 occurring in open chemical reaction systems. During switch-over from one st3tionary state to enother the coIour of the solution is changed due to the .\lnzT * Mn2+ transitionThe mangrtnese ions in the +z oxidation state in the Belousov-Zhabotinski oscillstion reaction catalyze the osidation of organic acids. For instance_ they convert mslic acid into osnlrtcetic acid. The process described In the present paper is related to the catalyst being switched on and off_ Studies of such reactions
Fig. 3. Potential in the system dependins on the BrOz and Br- concentrations at the reactor iniet.
551
Volume 66. numbe: 3
cxEYIC.\L
1’111SICS Lk-l-fLRS
may esplain control processes in biocImnic4 systems -and IUZIYbe a basis for de\elcrpnler;t of similar processes in cheniit~l tcchuoIogy_ The system inwstigted here is the second chemical rextion system taking pke in the sohltion where hysteresis was found to occur ;IS a result of transitions from one stationxy state to mother. This system. ;1s we11 3s systems witi: COrnpIiGlt~J oscilhttons [ 1 11. indimte tIut open chenkti reaction systems exhibit a number of new phcnonwn~. It should be expected that detailed
studies of
of interesting
these processes v.iII rev&
cIiscowries_
;L nunlber
15 October 1979
References II I J. JIonod and I_ J&ob_ Cold_ Spring Ii;lrb S) mp. Qunt. Bd_ 26 (1961) :89. I21 AN_ Turing. PkTmns. Roy. SOC_ B 237 (1952) 37. I31 OX. RBssler. 2. Nxurforsch. 17b (1971) 333. 1-l: P. de Keeper. A. Rossi and A_ Pxault. C!ompt_ Rend. And. Sci. (Paris) 263C ( 1976) 37 I_ ISI CL Creel md J- Ross. J. Chem. Phys. 65 (!976) 3779. I61 V. Hhvxek, J. Votruba and IL Ilofxnnn, Chem. Ens_ Sri_ 31 (1976) X7-10_ (?I \V_Oeiseicr and If-II_ Fiillner. Biophyr Chem_ 6 (1977) 107. ISI J_J_Tqson. J_ Chem_ Ph>s_ 67 (1977) 4197.
191 IL BmEIi md R-11. No) L’S,J. Phya Chem. 81 (1977) 1988_ [ lOI R. Thorn. StabiIity, structureand morphogenesis (Brmjamin. New York, 1977). I 11 I O.E. Riizskz. 2. Nrtturforsch. 321(1977) 199.
552