From Master–Slave to Peer-to-Peer Coupling in ... - ACS Publications

Subscriber access provided by HACETTEPE UNIVERSITESI KUTUPHANESI

Article

From Master-Slave to Peer-to-Peer Coupling in Chemical Reaction Networks Gábor Holló, Brigitta Dúzs, Istvan Szalai, and Istvan Lagzi J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b00179 • Publication Date (Web): 11 Apr 2017 Downloaded from http://pubs.acs.org on April 13, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry A is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

From Master-Slave to Peer-to-Peer Coupling in Chemical Reaction Networks Gábor Holló1, Brigitta Dúzs2, István Szalai2, István Lagzi1* 1

Department of Physics, Budapest University of Technology and Economics, H-1111 Budapest, Budafoki út 8, Hungary

2

Department of Analytical Chemistry, Eötvös Loránd University, H-1117 Budapest, Pázmány Péter 1/A, Hungary

AUTHOR EMAIL ADDRESS: [email protected]

RECEIVED DATE (to be automatically inserted after your manuscript is accepted if required according to the journal that you are submitting your paper to)

TITLE RUNNING HEAD

CORRESPONDING AUTHOR FOOTNOTE *Correspondence to: István Lagzi. Department of Physics, Budapest University of Technology and Economics, H-1111 Budapest, Budafoki út 8, Hungary. E-mail: [email protected], Tel.:+361-463-1341, Fax:+ 361-463-4180.

ACS Paragon Plus Environment

1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 24

Abstract Design strategy through linking a driving pH oscillator (master system) to a pH sensitive complexation, precipitation or protonation equilibrium (slave slave) has been widely used to create and control concentration oscillations of chemical entities (e.g., monovalent cations, DNA, nanoparticles) not participating in the pH oscillatory system. No systematic investigation has been carried out on how the components of these equilibria affect the characteristics of the driving pH oscillators, and this feedback effect has been often neglected in previous studies. Here we show that pH sensitive species (hydrogen carbonate, EDTA) through a pH dependent equilibrium could significantly affect the characteristics (time period and amplitude) of the driving pH oscillators. By varying the concentration of those species we are able to control the strength of the chemical feedback from slave system to master system thus introducing a transition from master-slave coupling to peer-to-peer coupling in linked chemical systems. To illustrate this transition and coupling strategies we investigate two coupled chemical systems, namely the bromate-sulfite pH oscillator and carbonate - carbon dioxide equilibrium and the hydrogen-peroxidethiosulfate-copper(II) and EDTA complexation equilibrium. As a sign of the peer-to-peer coupling the characteristics of the driving oscillatory systems can be tuned by controlling the feedback strength and the oscillations can be canceled above a critical value of this parameter.

INTRODUCTION The ability to control and drive reversible chemical systems with autonomous stimuli, in particular with pH oscillator, is of fundamental importance.1 These investigations contribute to the development of stimuli responsive materials,2 drug delivery applications3,4 and novel self-organization/self-assembly techniques.5,6 In the past few years a new concept has been introduced to drive and control chemical equilibria (e.g., complexation, precipitation) by autonomous way using core oscillators.1,7-13 The idea of this approach is that a pH oscillator provides concentration oscillations in a species participating in the ACS Paragon Plus Environment

2

Page 3 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


equilibrium complexation or precipitation of a target species that would otherwise be non-oscillatory. Examples incorporate periodic oscillations of non-redox chemical species such as calcium, aluminum, fluoride ions.1,9,10 Based on these studies a specific guideline has been formulated to design and couple chemical reaction networks, namely: “For successful coupling, several conditions must be fulfilled: a moderate equilibrium constant, a large change in pH, no interference between the components of the oscillator and those of the equilibrium.”9 This scientific approach discussed above represents a classical master-slave framework providing a way how to regulate and control the periodicity of a chemical subsystem. The main characteristic of this master-slave coupling is that the master system (pH oscillator) drives the phenomenon and the slave system (equilibrium reaction) does not interfere and change the main characteristics of the master system. Followed this basic idea several new slave systems have been introduced and coupled to pH oscillators.14-19 One example is a system in which a chemical oscillator operating at molecular scales was coupled to a system of nanoscopic components (pH responsive nanoparticles).14,16,17 The periodic pH change was translated into protonation and deprotonation process of pH responsive ligands (carboxylate terminated ligand) stabilizing metal nanoparticles and alter the subtle balance between the repulsive electrostatic and attractive van der Waals interparticle forces. In a continuously stirred-tank reactor (CSTR), these changes give rise to rhythmic aggregation and dispersion of the nanoparticles which is manifested by pronounced color changes of the nanoparticle solution.14 By similar fashion vesicle-micelle transformation15 and the volume of a pH responsive hydrogel20,21 were regulated by a pH oscillator in autonomous way in an open system. The feedback of the slave system on the core oscillator has been rarely mentioned, the buffering

effect

of

ethylenediaminetetraacetic

acid

(EDTA)

on

the

characteristics

the

bromate−sulfite−ferrocyanide and Ca2+ coupled oscillating system was first indicated in the work of Kurin-Csörgei and her cooworkers.7 The authors found that at high EDTA concentration pH oscillations can be damped or even eliminated.7 Nabika and his coworkers reported that mercaptododecanoic acid terminated gold nanoparticles can dramatically change the amplitude and time period of the driving ACS Paragon Plus Environment

3


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 24

oscillator (bromate-sulphite pH oscillator).16 In this study the authors account that this effect is due to catalytic activity of gold nanoparticles. In another report by Dolnik and his colleagues showed that a chemical buffer can control the frequency and amplitude of the oscillations in the ferrocyanide-iodatesulfite reaction.22 Inspired by recent studies on the coupling chemical subsystems (chemical equilibria) to core oscillators, we point out an important but often neglected aspect of this kind of coupling presenting two chemical examples. We hypothesized that a pH sensitive species through a pH dependent equilibrium could reversibly affect the characteristics (time period and amplitude) of the master system, and thereby induce chemical feedback from slave system to master system.

EXPERIMENTAL Sulphite-bromate pH oscillator coupled to carbonate – carbon dioxide equilibrium Our work was mainly based on a bromate-sulphite pH oscillator,23-26 and we used the following reagentgrade chemicals for the experiments, NaBrO3 (Sigma-Aldrich), Na2SO3 (Sigma-Aldrich), H2SO4 (Sigma-Aldrich), MnSO4 (Sigma-Aldrich) and NaHCO3 (Sigma-Aldrich). In a typical arrangement (Figure 1), pH oscillations were sustained in a continuously stirred tank reactor (CSTR) with a volume of 7.6 mL at 45.0 ± 0.2 °C. The aqueous solutions of NaBrO3, Na2SO3, H2SO4, MnSO4 and NaHCO3 were always prepared immediately before experiments to avoid any decay of chemicals and areal oxidation of sulphite. The CSTR was continuously fed by three channels with constant flows (0.265 mL/min in each channel using Ismatec peristaltic pump) of three stock solutions using a peristaltic pump: (i) a solution of acid and bromate ([H+]0 = 8.5 mM and [BrO3−]0 = 290 mM), (ii) a solution of sulphite and manganese ([SO32−]0 = 160 mM and [Mn2+]0 = 4 mM) and (iii) a solution of hydrogen carbonate. The components of the first two stock solutions constitute the sulphite-bromate pH oscillator, and these inflow concentrations were fixed throughout all experiments. The inflow concentration of the hydrogen carbonate was also fixed in experiments, but it was varied in the range of 0 ≤ [HCO3−]0 ≤ 3 ACS Paragon Plus Environment

4

Page 5 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


mM in each experiment. The pH was monitored by a computer-interfaced pH microelectrode (Mettler Toledo). We followed the reaction, the coupling strength and feedback by quantifying the evolution of carbon dioxide by measuring the carbon dioxide production, which was measured by flame ionization detector (FID). Figure 1 depicts the experimental setup used in our study. We used a silicone tube and gas stream (hydrogen and nitrogen) into it to remove partially the produced carbon dioxide from the CSTR as the silicon membrane is fully penetrable for carbon dioxide. Then carbon dioxide transported to methanizer (Ni catalyst) by the gas stream and the catalyst converts carbon dioxide using hydrogen into methane. Produced methane can be then directly detected and measured by FID.27-29

Figure 1 The scheme of the experimental setup. Catalyst: Ni catalyst; FID: flame ionization detector; MM: multimeter; PC: computer. Membrane is made of silicon, which is fully penetrable for the produced carbon dioxide. The hydrogen-peroxide-thiosulfate-copper(II) oscillator coupled to Cu(II) - EDTA complexation equilibrium The second system was the hydrogen-peroxide-thiosulfate-copper(II) oscillatory system coupled to copper(II) - EDTA complexation equilibrium.30 The CSTR experiments were carried out in a glass


5


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 24

reactor (with volume of 38 mL) which was continuously refreshed by constant flows of solutions of the initial reagents distributed in four separated reservoirs:

(i) solution of hydrogen-peroxide (Fluka,

[H2O2]0= 0.1 M), (ii) solution of sodium thiosulfate (VWR, [S2O32−]0 = 0.01 M), (iii) solution of sulfuric acid (Fluka, [H2SO4]0 = 0.001 M), (iv) solutions of copper(II)-sulfate (Reanal) and disodium ethylenediaminetetraacetate (Sigma), and these concentrations were varied in experiments. Equal flows were pumped by a peristaltic pump (Gilson Miniplus 2) from the reservoirs and premixed just before being injected into the CSTR. The residence time of the reactor was 5.25 min (corresponding to a total flow rate of 7.24 mL/min). Concentrations of copper(II) and EDTA were varied in the range of 0 ≤ [Cu2+]0 ≤ 0.05 mM and 0 ≤ [EDTA]0 ≤ 0.05 mM, respectively. The pH of the reacting mixture of the CSTR was monitored with a combined pH electrode, and the experiments were carried out at 25.0 ± 0.2 °C.

RESULTS AND DISCUSSION Figure 2 shows the scheme of coupling pH oscillator and carbonate – carbon dioxide equilibrium at the low inflow concentration of the hydrogen carbonate. The driving system is a pH oscillator, namely the bromate-sulfite oscillatory reaction. This system has been well studied and explored, and the pH oscillator can be operated in CSTR, in which the continuous flow of reactants and products is maintained.23,26,31,32 In this system, the pH oscillates autonomously between pH ~ 3 and pH ~ 7 and the period of the oscillation is ~ 20 min. It should be noted that these characteristics can be slightly varied by the concentrations of the reagents and flow rate.


6

Page 7 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 2 Scheme of the master-slave coupling in the bromate-sulfite pH oscillator and the carbonate – carbon dioxide equilibrium system.

The coupled system consists of the bromate-sulfite pH oscillator and the carbonate – carbon dioxide equilibrium in the CSTR. The coupling species is the H+ ion, because this chemical species is involved in both systems. The control species is the hydrogen carbonate, which concentration was varied to investigate the feedback of the slave (carbonate – carbon dioxide equilibrium) system to the driving system - pH oscillator. The target species is the species which behavior (usually oscillatory) is wanted to be quantify, here it is the carbon dioxide. When pH oscillates autonomously in the system the production of carbon dioxide changes according to carbonate – carbon dioxide equilibrium (Figure 3). At high pH (pH ~ 7) formation of carbonate and hydrogen carbonate dominates, however, at low pH (pH ~ 3) the equilibrium shifts towards carbon dioxide production, which can be detected by FID. The intensity of carbon dioxide production strictly follows the pH oscillation, and in the absence of any added hydrogen carbonate, the carbonate – carbon dioxide equilibrium existing due to areal carbon dioxide does not affect significantly the pH oscillator. This can be called a classical master-slave coupling, in which the main aim to avoid any feedback from the slave system to the master system. ACS Paragon Plus Environment

7


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 24

Figure 3 Coupled pH and carbon-dioxide concentration oscillation in the bromate-sulfite pH oscillator and carbonate – carbon dioxide equilibrium system in the CSTR in the absence of any hydrogen carbonate added.

no.

Reaction

R1 SO32− + H+ ⇌ HSO3− R2 HSO3− + H+ ⇌ H2SO3 R3 3HSO3− + BrO3− → 3SO42− + Br− + 3H+ R4 3H2SO3 + BrO3− → 3SO42− + Br−+ 6H+ R5 SO42− + H+ ⇌ HSO4− R6 3Mn2+ + BrO3− + 3H2O → 3MnO(OH)+ + Br− + 3H+ R7 MnO(OH)+ + 2HSO3− + 2H+→ Mn2+ + HS2O6− + 2H2O R8 CO32−+ H+ ⇌ HCO3− R9 HCO3− + H+ ⇌ H2CO3 R10 H2CO3 ⇌ CO2(aq) + H2O R11 CO2(aq) → CO2(gas)

Table 1 Chemical reactions for the bromate-sulphite pH oscillator (master system, R1-7) and carbonate – carbon dioxide equilibrium (slave system, R8-11).


8

Page 9 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The feedback of the slave system can be investigated by increasing the concentration of the control species (hydrogen carbonate) to the system and measuring the main characteristics of the pH oscillator (time period and amplitude). We carried out experiments by measuring at least three oscillation periods at the fixed inflow concentration of the hydrogen carbonate, and from these we determined the time period and amplitude of the oscillation for the corresponding hydrogen carbonate concentration by averaging the data. Figure 4 shows distinct data for the second oscillation period at various fixed inflow concentrations of the hydrogen carbonate (Figure 4a) and the corresponding oscillation in the carbon dioxide concentration (Figure 4b). It can be seen that increasing the control species concentration causes the decrease in both, time period and the amplitude of the oscillation. However, it is not surprising that the amplitude of carbon dioxide increases with increasing the inflow concentration of the hydrogen carbonate, which is the simple manifestation of mass conservation through chemical equations of R9-11 in Table 1.


9


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 24

Figure 4 pH (a) and carbon dioxide oscillations (b) at various inflow concentrations of the hydrogen carbonate: (i) 0 mM, (ii) 0.34 mM, (iii) 0.67 mM, (iv) 1.00 mM, (v) 1.33 mM, (vi) 1.67 mM and (vii) 2.00 mM. The inflow concentration of the hydrogen carbonate was fixed in each experiment. At 2.34 mM and at higher inflow concentrations of the hydrogen carbonate no oscillations were observed. Graphs show the second period of the oscillations.

From the investigation of the characteristics of the oscillations at various inflow concentration of ACS Paragon Plus Environment

10

Page 11 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the hydrogen carbonate, we can conclude that the time which the system spends at low pH (pH < 5.25) decreases with increasing the inflow concentration of the hydrogen carbonate compared to the time at high pH (pH ≥ 5.25). This behavior is due to an extra H+ binding capacity of the carbonate-carbon dioxide equilibrium. In the pH oscillatory system, Mn2+ ions overall consume H+ ions (see R6 and R7 in Table 1) thus increasing the pH in each period of oscillation. However, in the extended system (including carbonate-carbon dioxide equilibrium) there are another chemical species (carbonate and hydrogen carbonate) that can react with H+, and the consumption rate of H+ ions is increased, therefore, the system spends less time at low pH state. To support our experimental observation and findings we developed a chemical model based on the bromate-sulfite pH oscillator (master system) and carbonate-carbon dioxide equilibrium (slave system), for the details see Supporting Information (SI). Figure 5 presents the detailed results of the effect of the inflow concentration of the hydrogen carbonate on the characteristics of the master, pH oscillatory, system, namely the effect on time period and the amplitude of the pH oscillator, the amplitude of the carbon dioxide oscillation and the ratio of the time spent in low and high pH. The graphs contain also the results of the numerical simulations of the systems, and the data from the simulations have good agreement with the experimentally observed data. In one case, the simulations show a slight underestimation (~ pH = 0.5, which is ~ 10% relative error) in the amplitude of the pH oscillation compared to the experimental data (Figure 5b). However, other characteristics have been captured very accurately by the model (Figure S1). There is an interesting behavior of the coupling observed both in experiments and in numerical simulations, namely, there are no oscillations, when the inflow concentration of the hydrogen carbonate reaches a threshold value. These threshold concentrations are 2.00 mM and 1.45 mM in experiments and in simulations, respectively. Additionally, we found that the system shows critical behavior when the inflow concentration of control species is above this threshold concentration. We could see this behavior in our numerical simulations as well (Figures S2-S4). The characteristics of the system (time period, ACS Paragon Plus Environment

11


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 24

amplitude, etc.) changes continuously to a critical point, where a drastic and unexpected change happens in the behavior of the system, namely, oscillatory behavior suddenly vanishes. In experiments, we changed the inflow concertation of the hydrogen carbonate by 0.33 mM, we could observe sustained oscillations up to 2.00 mM with a continuous decrease with the time period and the amplitude of the oscillations, however, no oscillations were detected at the inflow concentration of 2.34 mM and higher. This critical behavior can be more vividly seen in numerical simulations, in which the step in concentration was finer compared to the step used in experiments with the value of 2.8×10−3 mM (Figures S2-S4). This critical behavior of the coupled system was also captured with our model showing that a simple H+ binding chemical species can dramatically change the oscillatory behavior of the driving, pH oscillatory system.

Figure 5 Effect of the inflow concentration of the hydrogen carbonate on the characteristics of the master system (bromate-sulfite pH oscillator): (a) time period, (b) amplitude of the pH oscillator, (c) amplitude of the carbon dioxide oscillation and (d) the ratio of the time spent in low and high pH. Blue ACS Paragon Plus Environment

12

Page 13 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


squares and red dots represent data obtained from experiments and numerical simulations, respectively.

Increasing the control species (hydrogen carbonate) concentration, the system would gradually transform from a master-slave coupling (in which the feedback from salve system to the driving system can be neglected due to low control species concentration and will not affect significantly the main characteristics of the master system) to peer-to-peer coupling, in which the feedback from slave system induces considerable effect on the characteristics of the driving system (Figure 6). In this way we introduce a new methodology for investigating complex chemical systems, in which the strength of master-slave coupling can be controlled and fine-tuned. We observed that at higher inflow concentration of the hydrogen carbonate (higher than 2.0 mM), the driving, master (pH oscillator), system can be even simple suppressed due to high proton binding capacity of carbonate-carbon dioxide equilibrium system.

Figure 6 Scheme of the peer-to-peer coupling in the bromate-sulfite pH oscillator and the carbonate – carbon dioxide equilibrium system.

To illustrate our concept we show another example for master-slave to peer-to-peer coupling and for regulating the transition between master-slave to peer-to-peer coupling. Hou and coworkers reported ACS Paragon Plus Environment

13


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 24

complexation amplified pH oscillations in the hydrogen-peroxide-thiosulfate-copper(II) (HPTCu) system, when EDTA was added to the system.33 The authors pointed out that the coupling between the periodic protonation of EDTA and the complexation of copper(II)-ions by EDTA results in the observed amplification phenomenon. The appearance of pH oscillations in the HPTCu systems can be accounted by the model reported in Ref. [34], which includes different autocatalytic loops (Table 2). One is the hydroxide ion autocatalytic reaction of thiosulfate with hydrogen peroxide catalyzed by copper(II) ions in R1. The other autocatalytic loops are formed in the production and oxidation of the tetrathionate by reactions R3 and R4 and in the oxidation of sulfite in reactions R5 and R6. We carried out experiments to clarify how the behavior of the master systems, that is the HPTCu pH oscillator, is affected by the slave system that is the protonation/deprotonation of EDTA (see R10). In our terminology, here the coupling species is H+ ion, and the control species is the EDTA. The feedback of the slave system is provided by the complex formation between copper(II)-ions and EDTA described by reaction (R11).

no.

Reaction 2−

R1 H2O2 + S2O3 → HOS2O3− + OH− R2 H2O2 + HOS2O3− → 2 HSO3− + H+ R3 S2O32− + HOS2O3- → S4O62- + OHR4 S4O62− + H2O2 → 2 HOS2O3− R5 H2O2 + HSO3− → SO42− + H2O + H+ R6 H2O2 + SO32− → SO42− + H2O R7 H2O2 ⇌ HO2− + H+ R8 H2O ⇌ OH− + H+ R9 HSO3− ⇌ SO32− + H+


14

Page 15 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


R10 H3Y− ⇌ H2Y2− + H+ R11 H2Y2− + Cu2+ ⇌ CuY2− + 2H+ Table 2 Chemical reactions for the hydrogen-peroxide-thiosulfate-copper(II) (master system, R1-9) and EDTA complexation equilibria (slave system, R10-11).

Figure 7 The effect of EDTA on the pH oscillations in the hydrogen-peroxide-thiosulfate-copper(II) system with [Cu2+]0 = 3.0×10−5 M, black solid line [EDTA]0 = 0 M; red solid line [EDTA]0 = 1.5×10−5 M; blue solid line [EDTA]0 = 2.0×10−5 M.

In accordance with the report of Hou and coworkers,33 we observed significant increase in the amplitude of the pH oscillation in presence of EDTA (Figure 7). However, above a critical input flow concentration EDTA cancels the oscillations. At the conditions applied in the experiments, this critical EDTA concentration was ~ 2×10−5 M. Coupled protonation equilibria can quench the oscillations in pH oscillators, but it typically happens at a much higher concentration of the added weak base.35 Since, the feedback of EDTA on the master HPTCu system appears through the complexation equilibrium (R11), we also studied the effect of copper(II)-ions on the oscillatory dynamics. At the applied conditions we did not observe oscillation in the absence of Cu(II). In the range of 9.5×10−6 M ≤ [Cu2+]0 ≤ 4.0×10−5 M the amplitude and the time period of oscillations decreases as the concentration of Cu(II) increases. The oscillations stops above [Cu2+]0 = 4.5×10−5 M trough a subcritical bifurcation. Typical oscillatory curves ACS Paragon Plus Environment

15


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 24

are shown in Figure 8. We found a great correspondence between the effect of Cu(II) and EDTA. If the amplitude of oscillations are plotted as a function of [Cu2+]0 in the absence of EDTA and as a function of the concentration of excess copper ion, that is [Cu2+]’= [Cu2+]0 – [EDTA]0, in the presence of EDTA, they fit to the same curve (Figure 9). It demonstrates as EDTA binds the copper(II)-ions, the amount of the free catalyst decreases and it creates a feedback on the dynamics of core oscillatory the system.

Figure 8 The effect of copper ion on the pH oscillations in the hydrogen-peroxide-thiosulfate-copper(II) system in the absence of EDTA, black solid line [Cu2+]0 = 1.0×10−5 M M; red solid line [Cu2+]0 = 1.3×10−5 M; blue solid line [Cu2+]0 = 2.0×10−5 M; green solid line [Cu2+]0 = 3.0×10−5 M.

Additional batch experiments show that the kinetic effect of Cu(II) is much more significant above pH = 7 than in the first period of the reaction. As it can be seen in Figure S5, there is a clear breaking point in the pH vs. time curves at ~ pH = 7. In the presence of Cu(II) a pH jump appears after this point. The height of this jump is determined by the amount of the Cu(II) ions. This helps to understand why only the excess of copper ion concentration counts in the presence of EDTA. Above pH = 7 the complexation equilibrium (R11) is shifted to the right direction. Since, in our experiments the Cu(II) concentration is always higher than the applied EDTA concentration, above pH = 7, the effective amount of the catalyst can be approximated [Cu2+]’ = [Cu2+]0 – [EDTA]0. We can conclude that in this


16

Page 17 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


example the dynamics of the master system is strongly affected by the feedback of the slave system. The HPTCu pH oscillators can induce oscillations in the different forms of EDTA (H3Y−, H2Y2− and CuY2−), but the binding of the catalyst in an inert form (CuY2−) lowers the effective concentration of the catalyst in the alkaline phase of the reaction. This lowering of the Cu(II) concentrations results in the observed increase of the pH amplitudes and finally in the quenching of the oscillations.

Figure 9 The amplitude of oscillations in the hydrogen-peroxide-thiosulfate-copper(II) system as a function of [Cu2+]0 in the absence of EDTA (black squares) and as a function of [Cu2+]’=[Cu2+]0 – [EDTA]0 (red dots).

CONCLUSIONS In this study we showed a new approach and provided a new terminology to study and analyze the coupling strategy between driving (master) and slave systems. In the presented examples the driving system is a pH oscillator and the slave subsystem is a pH dependent equilibria. Design strategies in previous studies published in the literature have been focused on oscillatory dynamics of the target ACS Paragon Plus Environment

17


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 24

species participating only in the chemical equilibria (slave system) and on diminishing the feedback and the effect of the chemical equilibria (slave system) on the main driving system.1,7-11,13 The main characteristic of this, so-called master-slave, coupling is that the master system (pH oscillator) drives the phenomenon and the slave system (equilibrium reaction) should not interfere and change the main characteristics of the master system. We studied two coupled systems, which were the bromate-sulfite pH oscillator and carbonate - carbon dioxide equilibrium and the hydrogen-peroxide-thiosulfatecopper(II) pH oscillator and EDTA complexation equilibrium. From our investigations, we revealed that in one-volume homogeneous chemical reaction network pure master-slave coupling cannot be possible through a single coupling species, which is incorporated both in the kinetics of the master and slave subsystem. Especially, if the coupling species directly involved in the autocatalytic pathway of the oscillator (such as H+ in a pH oscillator), even a small perturbation of its concentration made by the slave system, might result in a significant feedback on the parameters of the oscillations. The coupling strength can be varied and controlled by addition of control species (in our studies hydrogen carbonate and EDTA), which react with H+ ions reversibly, thus affecting its effective concentration in the system. At low concentration of the control species the feedback from the slave system to the driving one can be seemingly negligible (but definitely accountable), however, the oscillatory behavior of the target species (participating only in the slave system) can be strong enough to be measured and detected. This has been considered as master-slave coupling, and usually this strategy has been followed, when coupled systems were designed in the past.1,7-10,14,15 Increasing the coupling species concentration the feedback from the slave system to master system is more pronounced resulting in significant changes in the characteristics of the master system. However, there is no clear border line between the master-slave and peer-to-peer coupling, because the transition is continuous between them. Therefore, the manner of the coupling is somewhat “user-defined” in a wide range of the parameters. In particular above a critical concentration of the coupling species (due to its H+ binding capacity) the oscillatory behavior of the system can vanish. We found in the experiments as well as in the numerical ACS Paragon Plus Environment

18

Page 19 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


model simulations that the system shows critical behavior when the inflow concentration of the control species reaches a threshold concentration. This threshold inflow concentration defines the point where the coupling is clearly peer-to-peer type, since a small variation of the concentration results in a bifurcation from the oscillatory state to a stationary one. Additionally, our system is the first one in which oscillations of a gas phase species has been successfully realized using coupling strategy between a pH oscillator and a pH dependent equilibrium. We highlight the importance of the controlling the feedback strength, using this approach we can fine-tune and change the characteristics of the driving system, which otherwise would be hard to be realized. For instance, the amplitude and the time period of pH oscillators can be modified by varying the concentration of the reagents, flow rate and other experimental parameters (temperature, etc.), however, the ratio of time that the system spends at low and high pH states cannot be achieved by this way (Figure 4a). To achieve it, such coupling strategy would be a perfect candidate for doing it, and in this way, new oscillatory systems can be designed that have different characteristics compared to the original oscillatory systems. This approach is not limited to pH oscillators, this control and coupling strategy could be also used in other chemical or biochemical network systems, where the driving oscillation manifests in other forms of oscillation (e.g., redox potential).

SUPPORTING INFORMATION Model description for the bromate-sulfite pH oscillator and carbonate - carbon dioxide equilibrium system, effect of the inflow concentration of the hydrogen carbonate on the characteristics of the master system (bromate-sulfite pH oscillator) in numerical simulations and the effect of the copper(II)-ion on the batch behavior of the hydrogen-peroxide-thiosulfate-copper(II) system in experiments.


19


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 24

ACKNOWLEDGMENT Authors acknowledge the financial support of the Hungarian Scientific Research Fund (OTKA K104666 and K119360). The authors declare no competing financial interest.

REFERENCES (1) Kurin-Csörgei, K.; Epstein, I. R.; Orbán, M. Systematic Design of Chemical Oscillators Using Complexation and Precipitation Equilibria. Nature 2005, 433, 139–142. (2) Dai, S.; Ravi, P.; Tam, K. C. pH-Responsive Polymers: Synthesis, Properties and Applications. Soft Matter 2008, 4, 435–449. (3) Gao, W.; Chan, J. M.; Farokhzad, O. C. pH-Responsive Nanoparticles for Drug Delivery. Mol. Pharm. 2010, 7, 1913–1920. (4) Gupta, P.; Vermani, K.; Garg, S. Hydrogels: From Controlled Release to pH-Responsive Drug Delivery. Drug Discov. Today 2002, 7, 569–579. (5) Fan, C.; Bian, T.; Shang, L.; Shi, R.; Wu, L.-Z.; Tung, C.-H.; Zhang, T. pH-Responsive Reversible Self-Assembly of Gold Nanoparticles into Nanovesicles. Nanoscale 2016, 8, 3923–3925. (6) Morrow, B. H.; Payne, G. F.; Shen, J. pH-Responsive Self-Assembly of Polysaccharide through a Rugged Energy Landscape. J. Am. Chem. Soc. 2015, 137, 13024–13030. (7) Kurin-Csörgei, K.; Epstein, I. R.; Orbán, M. Periodic Pulses of Calcium Ions in a Chemical System. J. Phys. Chem. A 2006, 110 (24), 7588–7592.


20

Page 21 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(8) Orbán, M.; Kurin-Csörgei, K.; Epstein, I. R. pH-Regulated Chemical Oscillators. Acc. Chem. Res. 2015, 48, 593–601. (9) Poros, E.; Kurin-Csörgei, K.; Szalai, I.; Horváth, V.; Orbán, M. Periodic Changes in the Distribution of Species Observed in the Ni2+-Histidine Equilibrium Coupled to the BrO3--SO32pH Oscillator. J. Phys. Chem. A 2014, 118, 6749–6756. (10) Horvath, V.; Kurin-Csörgei, K.; Epstein, I. R.; Orbán, M. Oscillatory Concentration Pulses of Some Divalent Metal Ions Induced by a Redox Oscillator. Phys. Chem. Chem. Phys. 2010, 12, 1248–1252. (11) Horváth, V.; Kurin-Csörgei, K.; Epstein, I. R.; Orbán, M. Oscillations in the Concentration of Fluoride Ions Induced by a pH Oscillator. J. Phys. Chem. A 2008, 112, 4271–4276. (12) Szalai, I.; Kurin-Csörgei, K.; Orbön, M. Modelling pH Oscillators in Open, Semi-Batch and Batch Reactors. React. Kinet. Mech. Catal. 2012, 106, 257–266. (13) Molnár, I.; Kurin-Csörgei, K.; Orbán, M.; Szalai, I. Generation of Spatiotemporal Calcium Patterns by Coupling a pH-Oscillator to a Complexation Equilibrium. Chem. Commun. 2014, 50, 4158– 4160. (14) Lagzi, I.; Kowalczyk, B.; Wang, D.; Grzybowski, B. A. Nanoparticle Oscillations and Fronts. Angew. Chem.-Int. Ed. 2010, 49, 8616–8619. (15) Lagzi, I.; Wang, D.; Kowalczyk, B.; Grzybowski, B. A. Vesicle-to-Micelle Oscillations and Spatial Patterns. Langmuir 2010, 26, 13770–13772. (16) Nabika, H.; Inumata, Y.; Oikawa, T.; Unoura, K. Effect of Gold Nanoparticle Dispersion Solution on the Oscillation Behavior of Nonlinear Chemical Reaction. Chem. Lett. 2012, 41, 1139–1141. (17) Nabika, H.; Oikawa, T.; Iwasaki, K.; Murakoshi, K.; Unoura, K. Dynamics of Gold Nanoparticle Assembly and Disassembly Induced by pH Oscillations. J. Phys. Chem. C 2012, 116, 6153–6158. (18) Liedl, T.; Olapinski, M.; Simmel, F. C. A Surface-Bound DNA Switch Driven by a Chemical Oscillator. Angew. Chem. Int. Ed. 2006, 45, 5007–5010. ACS Paragon Plus Environment

21


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 24

(19) Liedl, T.; Simmel, F. C. Switching the Conformation of a DNA Molecule with a Chemical Oscillator. Nano Lett. 2005, 5, 1894–1898. (20) Crook, C. J.; Smith, A.; Jones, R. a. L.; Ryan, A. J. Chemically Induced Oscillations in a pHResponsive Hydrogel. Phys. Chem. Chem. Phys. 2002, 4, 1367–1369. (21) Varga, I.; Szalai, I.; Meszaros, R.; Gilanyi, T. Pulsating pH-Responsive Nanogels. J. Phys. Chem. B 2006, 110, 20297–20301. (22) Dolnik, M.; Gardner, T. S.; Epstein, I. R.; Collins, J. J. Frequency Control of an Oscillatory Reaction by Reversible Binding of an Autocatalyst. Phys. Rev. Lett. 1999, 82, 1582–1585. (23) Alamgir, M.; Orbán, M.; Epstein, I. R. Systematic Design of Chemical Oscillators. Part 16. Inorganic Bromate Oscillators. Bromate-Manganous-Reductant. J. Phys. Chem. 1983, 87, 3725– 3728. (24) Rabai, G.; Hanazaki, I. pH Oscillations in the Bromate-Sulfite-Marble Semibatch and Flow Systems. J. Phys. Chem. 1996, 100, 10615–10619. (25) Hanazaki, I.; Rabai, G. Origin of Chemical Instability in the Bromate-Sulfite Flow System. J. Chem. Phys. 1996, 105, 9912–9920. (26) Szántó, T. G.; Rábai, G. pH Oscillations in the BrO3-−SO32-/HSO3- Reaction in a CSTR. J. Phys. Chem. A 2005, 109, 5398–5402. (27) Noszticzius, Z. Periodic Carbon Monoxide Evolution in an Oscillating Reaction. J. Phys. Chem. 1977, 81, 185–186. (28) Noszticzius, Z.; Bodiss, J. A Heterogeneous Chemical Oscillator. The Belousov-Zhabotinskii-Type Reaction of Oxalic Acid. J. Am. Chem. Soc. 1979, 101, 3177–3182. (29) Szabó, G.; Csavdári, A.; Onel, L.; Bourceanu, G.; Noszticzius, Z.; Wittmann, M. Periodic CO and CO2 Evolution in the Oscillatory Briggs-Rauscher Reaction. J. Phys. Chem. A 2007, 111, 610– 612.


22

Page 23 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(30) Orbán, M.; Epstein, I. R. Systematic Design of Chemical Oscillators. 39. Chemical Oscillators in Group VIA: The copper(II)-Catalyzed Reaction between Hydrogen Peroxide and Thiosulfate Ion. J. Am. Chem. Soc. 1987, 109, 101–106. (31) Edblom, E. C.; Luo, Y.; Orbán, M.; Kustin, K.; Epstein, I. R. Systematic Design of Chemical Oscillators. 45. Kinetics and Mechanism of the Oscillatory Bromate-Sulfite-Ferrocyanide Reaction. J. Phys. Chem. 1989, 93, 2722–2727. (32) Sato, N.; Hasegawa, H. H.; Kimura, R.; Mori, Y.; Okazaki, N. Analysis of the Bromate−Sulfite−Ferrocyanide pH Oscillator Using the Particle Filter: Toward the Automated Modeling of Complex Chemical Systems. J. Phys. Chem. A 2010, 114, 10090–10096. (33) Ji, L.; Wang, H.; Hou, X. Complexation Amplified pH Oscillation in Metal Involved Systems. J. Phys. Chem. A 2012, 116, 7462–7466. (34) Kurin-Csörgei, K.; Orbán, M.; Rábai, G.; Epstein, I. R. Model for the Oscillatory Reaction between Hydrogen Peroxide and Thiosulfate Catalysed by copper(II) Ions. J. Chem. Soc., Faraday Trans. 1996, 92, 2851–2855. (35) Misra, G. P.; Siegel, R. A. Ionizable Drugs and pH Oscillators: Buffering Effects. J. Pharm. Sci. 2002, 91, 2003–2015.


23


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 24

TOC Graphic


24

From Master–Slave to Peer-to-Peer Coupling in ... - ACS Publications

Recommend Documents