Photoinduced Oscillations and Pulse Waves in the Hydrogen Peroxide

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Photo-Induced Oscillations and Pulse Waves in the Hydrogen Peroxide-Sulfite-Ferrocyanide Reaction Yang Liu, Ling Yuan, Changwei Pan, Jianmin Gao, Wenxiu Zhou, and Qingyu Gao J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b10025 • Publication Date (Web): 09 Jan 2018 Downloaded from http://pubs.acs.org on January 11, 2018

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The Journal of Physical Chemistry

Photo-Induced Oscillations and Pulse Waves in the Hydrogen Peroxide–Sulfite–Ferrocyanide Reaction Yang Liu,† Ling Yuan,*,† Changwei Pan,† Jianmin Gao,‡ Wenxiu Zhou,† Qingyu Gao*,†,‡ †

College of Chemical Engineering, China University of Mining and Technology,

Xuzhou 221116, China ‡

Department of Chemistry, Boston College, 2609 Beacon Street, Chestnut Hill, MA

02467-3860 Corresponding E-mail: [email protected], [email protected]

ABSTRACT The

hydrogen

peroxide-sulfite-ferrocyanide

reaction

shows

excellent

photosensitivity under pulse light illumination, which can be used to efficiently control the spatiotemporal dynamics of the nonlinear chemical system. Here, we numerically simulated the photo-induced pH oscillations by integrating two models which describe the oscillatory and photosensitive behaviors, respectively. A dynamic transition from the low-pH steady state to oscillations can be obtained using light illumination. In accordance with the simulation results, oscillatory dynamics was experimentally obtained under the light illumination through excitation of low-pH steady state. In the reactiondiffusion medium, corresponding multiple pulse waves were observed under suitable conditions of acid and illumination conditions. Hence light illumination can be efficiently employed to tune pattern formation in pH dynamic systems. Especially, the observation indicates that the local oscillations and pulse waves were promoted by the diffusion in the gel reactor when comparing with dynamics in homogenous system.

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INTRODUCTION Emergence of lifelike functionalities, such as oscillations,1 self-assembly2 and pattern formation,3 can be promoted with the aid of the photosensitivity of chemical systems. The effect of light illumination has been intensively studied in BZ (BelousovZhabotinsky),4 chlorite-iodide-malonic acid (CIMA) and chlorine dioxide-iodide-malonic acid (CDIMA)5-6 reactions. Although the photosensitive reactant is requisite in the system compared to the other external control,7-10 the facility on tuning illumination strength11 and wavelength12 makes light control an excellent and widely used method. Photoinduced oscillations13-14, chaos15 and chimera states16 have been observed in homogenous systems.17-18 In reaction-diffusion systems, similarly, the light illumination has been used to produce novel spatiotemporal patterns.19-20 As a periodic driving platform for active material systems, the ruthenium-catalyzed BZ reaction can be used to drive the directional motion of a photosensitive gel.21 Among the family of pH oscillators, several reactions are sensitive to the light, e.g., the

bromate-sulfite-ferrocyanide

(HPSF),

23

(BSF),22

hydrogen 24

hydrogen peroxide-ferrocyanide (HPF),

peroxide-sulfite-ferrocyanide

and hydrogen peroxide-sulfite-

ferrocyanide-carbonate (HPSFC) reactions.25 The photosensitive properties of these systems are derived from the Fe(CN)63- producing the negative feedback of proton, the protonation of cyanide, in oscillatory process.26 Fe(CN)64- oxidation and photosensitive reaction are shown in R1-R4. BrO3- + 6Fe(CN)64- + 6H+ → Br- + 6Fe(CN)63- + 3H2O

(R1)

IO3- + 6Fe(CN)64- + 6H+ → I- + 6Fe(CN)63- + 3H2O

(R2)

H2O2 + 2Fe(CN)64- + 2H+ → 2Fe(CN)63- + 2H2O

(R3)

hv → Fe(CN)5(H2O)2- + CNFe(CN)63- + H2O 

(R4)

Then, the process can suppress the autocatalytic formation of H+ between the oxidants and sulfur-containing compounds, typically bisulfite in the above systems. Nevertheless, the subsystem of the HPSF, i.e. HPF oscillatory reaction, was thought to be destabilized by the autocatalysis of the hydroxyl radical.27-28 The mechanisms for HPSF and HPF are different due to the presence of sulfite, which dominates the proton positive feedback of the former system. Studies on the response of HPSF to pulse light showed that ferricyanide, not ferrocyanide, acts as the primary photoabsorber.23 Thus, HPSF is a good

2


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candidate for pH oscillations under light perturbation because of its simple feedback loops and ability to tune feedback strength via light illumination easily. With the discovery of pH oscillations in homogeneous media, self-organizing pH patterns have been obtained using a systematic design method.29 Traveling wave and stable patterns have been observed supporting by the HPSF reaction.30-31 Phase waves was also obtained by coupling a temperature gradient to the H2O2-Na2S2O3-H2SO4CuSO4 reaction in a reaction-diffusion medium.32 Various dynamics behaviors are well understood in pH oscillators.33-34 However, few studies have been performed on the light effect on spatiotemporal patterns based on pH oscillatory systems. Using light stimulation, we investigated the response of the HPSF reaction spatiotemporal dynamics in both homogeneous and reaction-diffusion medium. Owing to the excellent photosensitivity of the HPSF reaction, photo-illumination experiment is expected to provide additional information on the photo-response of the system.

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EXPERIMENTAL SECTION Material Analytical grade reagents, H2O2 (30.0% w/v solution, Sinopharm Chemical Reagent, China), H2SO4 (98.0% w/v solution, Sinopharm Chemical Reagent, China), K4Fe(CN)6 (99.0%, Sigma-Aldrich, USA), and Na2SO3 (98.0%, Sigma-Aldrich, USA), were used without further purification. All solutions were prepared daily with deionized water (18.2 MΩ cm-1, Millipore system, Australia) and bubbled with N2 to prevent absorption of O2 and CO2. The concentration of H2O2 and H2SO4 were determined using standard titrations with potassium permanganate and potassium hydrogen phthalate, respectively. The reactant solutions were maintained in three separate reservoirs and transferred to the reactor by dual piston pumps (Model 1500, SSI, precision 0.001 mL min-1). The H2O2 and K4Fe(CN)6 were separately stored and the Na2SO3 and H2SO4 were premixed in the same reservoir. The bromocresol purple (90%, Sigma-Aldrich, USA) pH indicator, which switches from purple (above pH 6.8) to yellow (below pH 5.2), was added (0.13 g L-1, 0.08 mM in reactor) to the reservoir with Na2SO3 and H2SO4. The perturbation light was generated using an LED light source with a wavelength of 399 ± 5 nm, which is the main absorption band of ferricyanide.22 The light source was equipped with a digital controller to tune the light intensity, and the intensity was monitored by a handheld photometer (Model 1L1400A, International Light, USA). CSTR Experiment A continuously stirred tank reactor (CSTR) with an inner volume of 15.0 mL was thermostated at 25.0 °C by circulating water. The reactor was equipped with a combined pH electrode (5001-60, Cole Parmer, USA) and quartz windows for the light irradiation. The pH-time data were collected by an ecorder (ED201, eDAQ, Australia) and recorded on a computer. A magnetic stirrer was used to ensure uniform mixing at 800 rpm. The optical pathlength of the reactor was 2 cm. The residence time, τ, of the reactants in the reactor was 308 s, i.e., the flow rate was k0 = 3.25×10-3 s-1. OSFR Experiment The reaction-diffusion dynamics were studied in a one-side-fed gel reactor (OSFR) which has been described elsewhere.34 The light can act on the gel medium through the optical glass window. A CCD camera (TCC-3.3ICE, Tucsen, China) was used to record

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the evolution of the reaction-diffusion patterns. Snapshots were taken in an ambient illumination of 0.2 mW cm-2 with no illumination projected on the reactor. The flow rate was maintained at 3.25×10-3 s-1. Numerical Simulation For the simulation of homogeneous kinetics, stiff algorithm (Rosenbrock) was used to calculate the differential equations with the Berkeley Madonna software package.35 The tolerance was set at 10-10 and the same results were obtained with Gear algorithm.36 For the simulation of reaction-diffusion spatiotemporal dynamics, one-dimensional RD model was constructed along the longitudinal section of the gel.37 An implicit backward diﬀerentiation formula (BDF2) and three-point-diﬀerence approximations were used for calculating one-dimension waves and local dynamics. Detail description is shown in the Supporting Information (The simulation procedure for RD equations and Figure S4).

RESULTS AND DISCUSSION I. Model The HPSF reaction system is a delicate pH oscillator, and the hydrogen ion oscillation is obtained through the positive feedback reaction between hydrogen peroxide and sulfite and the negative feedback from proton consumption by ferrocyanide.27 Additionally, light can affect both ferrocyanide and hydrogen peroxide, which further affects the oscillatory reaction dynamics.28 The reaction mechanism is shown in Table 1. We employed the reaction steps proposed by Rabai et al., M1 to M9, as the main body of the model, which can produce oscillations in the HPSF reaction in the dark.38 The illumination process, M10, was referenced by Vanag et al.,26 and Fe(CN)63- accounts for the reaction photosensitivity when a light with a specific wavelength is used. Additionally, due to the cyanide produced during the photolysis of ferrocyanide, the protonation of cyanide, M8, resulting in the additional proton negative feedback, was included in the model. The process can act as a proton trap, which significantly influences the dynamics of the model. Different initial reactant concentrations were used in the modeling, and the remarkable light illumination effect was obtained. The corresponding rate laws and rate constants are

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shown in Table 1 and 2, respectively. Table 1 Mechanism for the photosensitive HPSF reaction No.

Reaction

M1

H2O2 + HSO3- → SO42- + H2O + H+

M2

H2O2 + 2Fe(CN)64- + 2H+ → 2Fe(CN)63- + 2H2O

M3

SO32- + H+ ↔ HSO3-

M4

H2O2 + SO32- → SO42- + H2O

M5

H2O2 + 2Fe(CN)63- → 2Fe(CN)64- + O2 + 2H+

M6

Fe(CN)64- + H+ ↔ HFe(CN)63-

M7

H+ + OH- ↔ H2O

M8

H+ + CN- ↔ HCN

M9

2Fe(CN)63- + SO32- + H2O → 2Fe(CN)64- + SO42- + 2H+

hν M10 Fe(CN)63- + H2O → Fe(CN)5(H2O)2- + CN-

Table 2 Rate laws and constants for the photosensitive HPSF reaction Rate law

Rate constants (a)

R1 = k1[H2O2][HSO3-] + k1'[H+][H2O2][HSO3-]

k1 = 14.7 M, k1' = 1.48×107 M-1 s-1

R2 = k2[H2O2]

k2 = 2.1×10-4 s-1

R3 = k3[SO32-][H+], R3' = k3'[HSO3-],

K3 = 1×10-7 M

R4 = k4[H2O2][SO32-]

k4 = 0.2 M-1 s-1

R5 = k5[H2O2][Fe(CN)63-][OH-]

k5 = 1×105 M-2 s-1

R6 = k6[Fe(CN)64-][H+], R6' = k6'[HFe(CN)64-],

K6 = 1.8×10-4 M

R7 = k7[H+][OH-], R7' = k7'[H2O],

k7 = 1×1011 M-1 s-1 k7'[H2O] = 1×10-3 M s-1,

R8 = k8[H+][CN-], R8' = k8'[HCN],

K8 = 1×10-7 M

R9 = k9[Fe(CN)63-][SO32-]

k9 = 2.0 M-1 s-1

R10 = αk10[Fe(CN)63-]Q(t, τ)

k10 = 0 – 12 s-1

a

Corresponding parameters were taken from Rábai et al.38 except k1 and k10, which were estimated in this

work.

In the simulation, the light perturbation is controlled by its duration, τ, and intensity, I, as involved in R10. The duration τ is regulated by a built-in square pulse function, Q(t, τ), starting at time t. The intensity, I, is included in the photokinetic rate constant, k10, which is defined as k10 = k10'I.26 The α in R10 is the photokinetic factor defined as α = (1-exp(2.3A))/A.39 The A is the total absorbance, defined as A = (ϵFe(III)[Fe(CN)63-] + ϵBPB[BPB])l, where ϵFe(III) = 1000 M-1 cm-1 and ϵBPB = 40000 M-1 cm-1 are the molar extinction

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coefficients of ferricyanide and the protonated pH indicator, respectively, and l is the optical pathlength of the reactor. We applied the perturbation at the 1×104 s during the simulation because the state of the system is sufficiently stable at that point. II. Effect of the light intensity on the homogeneous dynamics of HPSF reaction At the beginning of the numerical simulation, k10 was varied while τ was fixed at 10 s to determine a suitable region for the perturbation. The results are shown in Figure 1. 8 7

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Figure 1. Calculated pH-time curve under different illumination intensities. Initial concentrations: [H2O2]0 = 25.0 mM, [SO32-]0 = 14.0 mM, [H2SO4]0 = 0.9 mM, and [Fe(CN)64-]0 = 6.0 mM. k0 = 3.25×10-3 s-1. The illumination started at 100 s as the blue arrows indicated. The illumination duration was 10 s. The k10 were 0 (a), 2 (b), 4 (c), 7 (d), 9 (e), and 12 (f), respectively.

When the reactant concentration and flow rate were controlled in the simulation, the system can be maintained in a low pH state. However, the oscillatory-peaks gradually developed as k10 increased from zero. At different illumination thresholds, the number of oscillatory-peaks increased as the k10 increased. The acceleration of the photosensitive reaction M10, due to the increase in the light intensity effectively strengthens the negative feedback of the reaction system via the following paths. The removal of ferricyanide in M10 can slow the formation of H+ in M5 and M9, where the part of H+ is produced due to the ferricyanide oxidation. Meanwhile, the cyanide formation in M10 can consume H+ through fast protonation and slow dissociation steps, producing proton negative feedback. Therefore, the system experienced a series of states varying from excitability to oscillations. Using the specific concentrations and flow rate from the simulation, the same transitions were experimentally observed by controlling the light intensity (Figure 2). Moreover, the oscillatory-peak number versus the light intensity was in good agreement with the numerical results. As the light intensity increased, the number of oscillatory-

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peaks increased. This implies that the amplitude and the number of the excited oscillations are determined by the intensity of the illumination light. The phase diagram of the experimental system was portrayed in the k0 - [H2SO4]0 plane (Figure S1, Supporting Information). The experimental conditions for the photoinduced excitable oscillations are located in the low pH state near the edge of the transition boundary, indicating that the light illumination can effectively cause the Hopf bifurcation of the system.26 The photo-induced excitation mainly functions through M10 and M8 in Table 1, which is in essentially the same way as the OH- induced “inhibitory excitability” in the BSF reaction.9-10 a

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0

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Figure 2. Time evolution of the pH curves in the H2O2-SO32--Fe(CN)64- reaction system at a low pH state disturbed by single light irradiation with different light intensity. The illumination started at about 600 s as the blue arrows indicated. The illumination duration was 10 s. The input concentrations were: [H2O2]0 = 25.0 mM, [SO32-]0 = 14.0 mM, [Fe(CN)64-]0 = 6.0 mM, and [H2SO4]0 = 0.9 mM. k0 = 3.25×10-3 s-1. The light intensities were I = 0 mW cm-2 (a), 3.42 mW cm-2 (b), 5.59 mW cm-2 (c), 13.25 mW cm-2 (d), 16.40 mW cm-2 (e), and 24.40 mW cm-2 (f).

III. Effect of the light duration on the homogeneous dynamics of the HPSF reaction If the reaction is continuously exposed to light illumination, sustained oscillations can be observed because the photo-induced sub-reaction creates other effective negative proton feedback paths (M8 and M10 in Table 1) in the system. The light duration can be used to induce bifurcation from the stable steady state to the oscillation state.23 Consequently, the duration of the light illumination plays a critical role in the perpetuation of the oscillation as shown above. To confirm the effect of the light duration on the low pH state, an additional study was performed changing τ during the pulse process. As shown in Figure 3, more oscillatory-peaks were obtained by gradually increasing the light duration.

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pH

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Figure 3. Calculated pH-time curves with different illumination duration. Initial concentration: [H2O2]0 = 25 mM, [SO32-]0 = 14 mM, [H2SO4]0 = 0. 9 mM, and [Fe(CN)64-]0 = 6 mM. k0 = 3.25×10-3 s-1. The k10 was maintained at 1 s-1.The illumination started at 100 s as the blue arrows indicated. The illumination durations τ were 25 s (a), 45 s (b), 50 s (c), 100 s (d), 220 s (e), and sustained (f).

The number of oscillatory-peaks obviously increased as the illumination duration increased until the continuous illumination generated sustained oscillations in the modeling. However, the duration required for an additional peak slowly increased for the first three pulses. Then, the duration was higher for additional peaks (Figure S2, Supporting Information). In the experimental study, the dependence of the pH oscillatory-peak number on the illuminating duration was obtained when the HPSF reaction was perturbed with a constant intensity illumination (Figure 4). Under an intensity of 0.28 mW cm-2, the excitation of a single pH peak requires 80 s (Figure 3b), but a multiple-peak excitation requires a longer illumination duration. In addition, the excited oscillatory-peak number increases as the irradiation time increases. This result was similar to the changing irradiation intensity under optimal conditions. However, the excited oscillatory-peak number could continuously increase if the irradiation time was long enough. When the light was steadily applied at an intensity of 0.28 mW cm-2, sustained oscillations were obtained under flow conditions.

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Figure 4. Time profile of the H2O2-SO32--Fe(CN)64- reaction system in a low pH state using a single light irradiation. Input concentrations: [H2O2]0 = 25.0 mM, [SO32-]0 = 14.0 mM, [Fe(CN)64-]0 = 6.0 mM, and [H2SO4]0 = 0.9 mM. k0 = 3.25×10-3 s-1. The light intensity was 0.28 mW cm-2. The illumination started at about 600 s as the blue arrows indicated. The illumination durations were 0 s (a), 80 s (b), 160 s (c), 200 s (d), 440 s (e), and sustained (f).

The experimental phase diagrams based on the response to UV light are presented in Figure 5 and Figure 6 for the light intensity and duration, respectively, against the acid concentration. When the light intensity is fixed, an increase in the acid concentration can suppress the oscillatory cycles after the light perturbation. This result proves that the hydrogen ions imported from the reservoir can inhibit the proton negative feedback (M8 and M10), which are triggered by light illumination. An increase in both the duration and intensity can cause oscillations in the excitable low pH state of the HPSF system. However, distinct differences exist in the perturbations due to the light intensity and light duration. Increasing the illumination duration can quantitively increase the photokinetic factors produced in the reactor, but it cannot qualitatively change the state of the system if the acid concentration is higher than a certain threshold. In contrast, the light intensity can overcome this restriction and effectively neutralize the excess hydrogen ions in the influx, especially in the high acid concentration region.

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1.0

0.9

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H SO ]

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Figure 5. Phase diagram for the photo-induced oscillatory-peaks in the light intensity-acid concentration plane. Initial concentrations: [H2O2]0 = 25 mM, [SO32-]0 = 14 mM, and [Fe(CN)64-]0 = 6 mM. k0 = 3.25×10-3 s-1. The illumination duration was 10 s. Symbols: ■, single excited peak; ●, dual excited peaks; ▲, triple excited peaks; ▼, multiple excited peaks (no less than four period). 1.2

1.0

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Figure 6. Phase diagram for the photo-induced oscillatory-peaks in the light duration-acid concentration plane. Initial concentrations: [H2O2]0 = 25 mM, [SO32-]0 = 14 mM, and [Fe(CN)64-]0 = 6 mM. k0 = 3.25×10-3 s-1. The illumination intensity was 0.28 mW cm-2. Symbols: ■, single excited peak; ●, dual excited peaks; ▲, triple excited peaks; ▼, multiple excited peaks (no less than four period).

IV. Effect of the light on the spatiotemporal dynamics of the HPSF RD system The spatiotemporal pattern of the HPSF reaction-diffusion system has been previously studied.30 In an OSFR, two qualitatively different spatial states can be observed with the aid of appropriate pH indicators. When the gel is in the F-state, i.e., the

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basic form of the indicator,29 the state of the gel is close to that of the CSTR contents, which is a low reaction extent state. In contrast, in the M-state, i.e., the acidic form of the indicator, a high reaction extent occurs in the OSFR.29 In the reaction-diffusion system, multiple experimental parameters can adjust the state of the system, such as the reactant concentrations, flow rates, temperature, light intensity and light duration, especially in a photosensitive system. To study the effect of light irradiation on the M-state of the gel, a systematic experiment was performed on the OSFR to determine the regions with different dynamics, and a phase diagram was obtained. When the time scale of diffusion is introduced to homogeneous dynamics, the resulting RD dynamics of the HPSF reaction is indeed different from that in the homogeneous medium. By fixing experimental control parameters ([H2O2]0 = 25.0 mM, [SO32-]0 = 14.0 mM, [Fe(CN)64-]0 = 6.0 mM, and k0 = 3.25×10-3 s-1), the system displayed pulse waves and high pH state in OSFR and CSTR, respectively, with the concentration of sulfuric acid in the range of 0.35 to 0.40 mM. Furthermore, the low pH state and homogeneous bistability were obtained in an OSFR and a CSTR, respectively, when the concentration of sulfuric acid was in the range of 0.40 to 0.60 mM (See the two dashed rectangles of Figure S1 and S3 in Supporting Information). On the same way, with other fixed parameters ([H2O2]0 = 25.0 mM, [SO32-]0 = 14.0 mM, [Fe(CN)64-]0 = 4.0 mM, and k0 = 3.25×10-3 s-1), spatial bistability was observed in an OSFR when the CSTR belonged to a low pH stationary state with concentration of sulfuric acid of 0.275 mM. In summary, the reaction system shows higher reaction extent in the OSFR than that in the neighboring CSTR. According to Figure S3 in the Supporting Information, along the ([Fe(CN)64-]0, [H2SO4]0) plane, the homogenous M-state was observed when the acid concentration was higher than 0.42 mM. Therefore, we fixed the acid concentration at 0.45 mM to obtain the homogeneous M-state of the gel initially. Under this condition, the homogeneous medium in the CSTR always showed a high pH state due to the high flow rate. Figure 7 shows the time evolution of the triggered pulse waves responding to the light illumination. Once illuminated in the initial, homogenous M-state (Figure 7a) for 20 s, the gel was quickly dominated by the F-state (Figure 7b). Then, after an induced period of approximate 20 min, a ring in the M-state emerged near the rim of the OSFR where an

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acid-producing (+) front accompanied the transition from the F to M-state (Figure 7c).40 The former (+) front traveled inward, and a new (+) front was generated at the edge of the F-state (Figure 7d-e). During this process, however, the rim of the OSFR was gradually occupied permanently by the M-state, which left less space for the F-state and the (+) front. Finally, the whole domain was restored to the homogeneous M-state (Figure 7f). Therefore, the low-pH steady state is an excitable stable focus of the system. The space-time plot (Figure 7 g) illustrates the excitability of the system and the following damping process. The changes in the gray scale at a local point in the OSFR demonstrated the good periodicity of the process, and 12 cycles were observed during the whole process.

Figure 7. Response of the pH pulses to UV light in the H2O2-SO32--Fe(CN)64- reaction-diffusion system. Initial concentrations: [H2O2]0 = 25 mM, [SO32-]0 = 14 mM, [H2SO4]0 = 0.45 mM, and [Fe(CN)64-]0 = 6 mM. k0 = 3.25×10-3 s-1. The illumination strength was 1.20 mW cm-2. The illumination duration was 20 s. Snapshots were taken at 0 min (a), 2 min (b), 13 min (c), 14 min (d), 17 min (e), and 90 min (f) after the perturbation. Space-time plot (g) was taken along a dot line across the OSFR indicated in (a). The oscillations of a local point, the red point in (a), is illustrated according to the gray scale change (h). The movie can be seen in the electronic supplementary material (Movie S1).

To investigate the photosensitivity properties of the pH pulses, different light illumination durations and light intensities were applied to the OSFR in a homogeneous low pH state. Figure 8 shows the gray scale changes of a local point under different illumination durations in the OSFR. Similar to the CSTR experiment, when the illumination duration was from 5 s to 40 s, the number of pH pulses obviously increased

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along with the relaxation time, i.e., the time from the perturbation to the restoration of the high pH state. The RD simulation based on the identical photo-induced reaction mechanism showed the similar tendency to experimental results (Figure S5 in Supporting Information). 130

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However, the illumination duration cannot convert the front to a pulse if the initial acid concentration is high, even if a continuous light is used. For example, when the sulfuric acid concentration was 0.48 mM, only a front was obtained in the system for all durations at an intensity of 1.20 mW cm-2. Nevertheless, the transition to a pulse can be obtained if the light intensity is higher. The responses to different light intensities and local oscillations in the HPSF reaction-diffusion medium are illustrated in Figure 9. The induction periods before the pulses are all approximately 8 min, which is almost the same as the period in the experiment with different durations. However, when the light intensity increased, the number of pH pulses during the damping increased, and the oscillatory period was shortened. When the light intensity was greater than 3.02 mW cm-2, the pulse was much denser. In that case, the intervals between the pulses were indiscernible, a long period front appeared, and the whole period was shortened. Using the same reactant parameters, the local dynamics were simulated under different light

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intensities in the RD system (Figure S6 in Supporting Information). The numerical results also showed an increase in the number of local oscillations, which was qualitatively 130

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An irradiation threshold exists to induce the oscillations. When the acid concentration is higher than 0.53 mM, only a transient front occurs responded to the light excitation, no matter what the applied light intensity is (Figure 10). On the other hand, when the acid concentration is lower than 0.35 mM, the system is in high pH state. (See Figure S1 in Supporting Information for [Fe(CN)64-]0 = 6 mM) The light perturbation would not excite the high pH state to initiate the proton autocatalysis since the light still induced pH increase from H+ consumption according to M10 and M8 in Table 1. This means that the OSFR state also depends on the acid concentration. The response of the system to the light excitation is limited by the concentration of autocatalyst.

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The effect of diffusion on the chemical dynamics showed that complex oscillations can be observed in the reaction-diffusion system,37 especially for a multiple feedback system.41 In the homogeneous system corresponding to patterns in Figure 7 to 10, the light illumination on HPSF reaction system caused tiny dynamic response at high-pH steady state. However, in the gel reactor, the dynamics of the gel depend not only on the chemical reactions but also on the diffusion coupling of the chemical species. Proton has higher diffusion rate resulting in low-pH excitable state (i.e. M-State, Figure S3 in SI) in gel. Furthermore, the number of pulses and local oscillations significantly increased where diffusion takes effect. The reason is that diffusion can repeatedly excite proton autocatalysis.

CONCLUSION In this paper, we established the low-pH steady state response dynamics of the H2O2-SO32--Fe(CN)64- reaction systems on temporary UV light perturbation in the CSTR and OSTR. Our experimental results demonstrated that UV light can be used as an external control parameter to investigate the photosensitivity in reaction-diffusion media of nonlinear pH systems. Additionally, the diffusion transport can promote local oscillations that produce multiple pulses in the reaction-diffusion system.

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AUTHOR INFORMATION Corresponding Author E-mail: [email protected] (L. Yuan), [email protected] (Q. Gao) ORCID Q. Gao: 0000-0002-5520-0240 Notes The authors declare no competing financial interest.

SUPPORTING INFORMATION The Supporting Information is available free of charge on the ACS Publications website. State diagram of HPSF reaction system in flow rate-[H2SO4]0 plane; Light duration against the number of peaks in the numerical simulation; State diagram of the HPSF reaction system in OSFR; The simulation procedure for RD equations; Schematic for the one-dimensional simulation; Simulated local dynamics in the HPSF RD system with different light intensities; Simulated local dynamics in the HPSF RD system with different illumination durations.

ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (Grant No. 21573282), the Fundamental Research Funds for the Central Universities (Grant No. 2015XKMS045), the Natural Science Foundation of Jiangsu Province (Grant No. BK20160240), Gao Q. acknowledges CUMT for the financial supporting to visit Boston College. The authors thank Dr. Lin Ren for the great help on the RD simulation and fruitful discussion on the MS.

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Photo-perturbation

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Photoinduced Oscillations and Pulse Waves in the Hydrogen Peroxide

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