Mechanism and Kinetic Model for Autocatalysis in LiquidâLiquid

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Mechanism and Kinetic Model for Autocatalysis in Liquid–Liquid System: Oxidation of Dibutyl Sulfide with Aqueous Hydrogen Peroxide Ming Chen, Yang Jin, Jun Li, Yuqiang Zhang, and Xing Li Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b01416 • Publication Date (Web): 12 Jun 2017 Downloaded from http://pubs.acs.org on June 16, 2017

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Industrial & Engineering Chemistry Research

Mechanism and Kinetic Model for Autocatalysis in Liquid–Liquid System: Oxidation of Dibutyl Sulfide with Aqueous Hydrogen Peroxide Ming Chen, Yang Jin, Jun Li*, Yuqiang Zhang, Xing Li Department of Chemical Engineering, Sichuan University, Chengdu, Sichuan, 610065, P. R. China ABSTRACT: The oxidation of dibutyl sulfide with aqueous hydrogen peroxide as a liquid-liquid reaction was investigated. The autocatalysis, solubility of H2O2 in organic phase, effects of temperature, stirring speed, initial organic DBSO concentration and initial aqueous H2O2 concentration were studied. Solvent effect of dibutyl sulfoxide was proposed for liquid–liquid autocatalysis. The intrinsic reaction was considered as the determining step and all the other steps were considered as equilibrium processes. Considering interfacial reaction and dynamic equilibrium of hydrogen peroxide between the two phases, the reaction was divided into exterior and interior stages. Exterior and interior mechanisms were proposed for the corresponding stages and kinetic models were established. The parameters of kinetic model were estimated with the experimental data and the activation energies of exterior and interior reaction were 30.62 and 73.50 kJ/mol. The validity of the kinetic models with estimated parameters was studied and good agreements were observed between the experimental results and the model results. KEYWORDS: dibutyl sulfoxide; hydrogen peroxide; liquid–liquid autocatalysis; mechanism; kinetic model

1. INTRODUCTION Oxidations of the sulfides are the direct method to synthesize sulfoxides which play important 1

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roles in pharmaceutical, biologically active compounds, organic synthesis, and solvent extraction etc. Numerous researches about the oxidation of sulfides have been studied over the years

1-8

9-11

.

Aqueous H2O2 is considered as the excellent oxidant for the oxidation of sulfides, because it is cheap, efficient, high chemoselective and environmentally friendly

12-14

. Oxidation of sulfides with aqueous

H2O2 is heterogeneous liquid-liquid reaction because of the immiscibility of organic sulfides and aqueous H2O2. In order to enhance the mass transfer between the two phases, organic solvents are always used

15,16

. The organic solvents used in the process are usually toxic and environmentally

hazardous which limit its scale-up. Besides, the recovery of organic solvents will raise the cost of production. For the green and sustainable development of production, the green oxidation of sulfides with aqueous H2O2 was investigated. Most of the process was conducted in heterogeneous liquid-liquid system with no extra solvents added

13,17-20

, which avoided the toxic contamination and

simplified the process. In the research of green oxidation of sulfides with aqueous H2O2, an attractive autocatalytic phenomenon was found by Shi et al 21. Typical autocatalytic “S type” curve was shown in the plot of conversion versus reaction time and the self-generated product sulfoxides were proved to be the autocatalyst. However, the further study of this autocatalytic phenomenon in liquid-liquid system was not reported. The mechanism and kinetic model were not proposed, either. Mechanism and kinetic model were essential for the design, scale-up and optimization of reactor. Considering the great significance of the reaction system, the studies of mechanism and kinetic model were requisite. Autocatalytic phenomenon in liquid-liquid system has been studied. Three typical mechanisms were reported: (1) Surfactant effect mechanism or so-called “micellar autocatalysis”: the product was 2


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amphiphilic compound acted as surfactant which could largely increase the interfacial area. Bachmann et al

22

proposed a representative mechanism called “micellar autocatalysis” in the research of the

alkaline hydrolysis of ethyl caprylate yielded sodium caprylate. In this reaction, surfactant-like sodium caprylate aggregated into micelles which could largely increase the surface area to accelerate the reaction rate. Based on the “micellar autocatalysis”, analogous inverse micelles, vesicles mechanism and corresponding kinetic model were reported

23-27

. (2) Solvent effect mechanism: the product acted

as solvent which could dissolve reactant in another phase 28,29. For the Biphasic Alkaline Hydrolysis of Aromatic Esters, Chen et al 30 demonstrated that the hydrotropic salts yielded by the hydrolysis itself could accelerate the apparent reaction rate by enhancing the solubility of the hydrophobic ester in water. In the phase transfer catalyst involved liquid-liquid system, Glatzer et al

31

proposed that the

autocatalytic product increased the solubility of the PT catalyst in the organic phase (where the reaction occurred) with consequent enhancement of the reaction rate. (3) Phase-transfer effect mechanism: the product was ionic compound acted as phase transfer catalyst which could improve the mass transfer between the two phases. Zhao et al

32,33

found that the autocatalytic product acted as

active phase transfer catalyst to accelerate the reaction rate on Horner-Wadsworth-Emmons reaction. In this paper, the oxidation of dibutyl sulfide (DBS) to dibutyl sulfoxide (DBSO) was selected as the model system. DBSO was valuable organic solvent widely applied in extraction of zirconium, palladium, platinum and gold

34,36

. The aim of the research was to explore the autocatalytic

phenomenon in the liquid-liquid system and establish reasonable mechanisms and kinetic models. The effects of temperature, stirring speed, equilibrium of aqueous H2O2 in two phases, initial aqueous H2O2 concentration and initial organic DBSO concentration were investigated. A mechanism 3



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considering the interfacial reaction and the dynamic equilibrium of H2O2 between the two phases was firstly proposed. The estimation of kinetic parameters and the validity of the kinetic model were studied. The mechanism and kinetic model could provide an inspiration for the oxidation reaction in liquid-liquid systems involved aqueous H2O2 as oxidant.

2. EXPERIMENTAL SECTION 2.1. Apparatus and Reagents. A gas chromatograph equipped with flame ionization detector (GC-FID, GC-122, Shanghai Precision & Scientific Instrument Co., Ltd) was used for the analysis of organic compositions. The chromatographic column was SE-54 with 5% diphenylpolysiloxane and 95% dimethylpolysiloxane as stationary phase. Parameters of the column were 30m of the length, 0.32mm of the internal diameter and 0.25um of the stationary phase thickness. Software N-2000 data stations used for collecting and analysis was developed by Zhejiang University. A thermostat within ±0.1K (DF-101S Henan Yuhua Instrument Co., Ltd) was used to maintain constant temperature. Aqueous H2O2 (purity, ≥30%) was supplied by Chengdu Kelong Chemical Reagents Company. Organic DBS (purity, ≥99%) was supplied by Chengdu Huana Chemical Reagents Company and the purity of DBS was determined by GC-FID. KMnO4 (purity, ≥99%) was supplied by Chengdu Chemical Reagents Company. 2.2. Equilibrium Studies. Aqueous H2O2 with known concentration and pure DBS or DBSO were added to a conical flask. The temperature was maintained by water bath thermostat with ±0.1K accuracy. The two phases were vigorously stirred for 10 min. Then, the mixtures were transferred to a separating funnel and settled till the two phases were totally separated. The concentration of H2O2 in 4


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aqueous phase was titrated by aqueous KMnO4 with known concentration

37

. The concentration of

H2O2 in organic phase was calculated by material balance. The calculated equation was as follow:

[H2O2 ]org =

Vaq0 ×[H2O2 ]0aq − Vaq ×[H2O2 ]aq Vorg

2.3. Kinetic Experiments. The oxidation of DBS with H2O2 was carried out in a 25ml round-bottom flask equipped with a reflux condenser. An elliptical magnetic stirrer (diameter: 10mm) covered with Polytetrafluoroethylene was placed in the central of the bottom. The reaction temperature was controlled and maintained in an oil bath thermostat (±0.1K). The reaction was carried out under the temperature of 323K, 333K, 343K, 353K and 363K, respectively. The reactor was subjected to a thermal pre-treatment at experimental temperature for 10 min. Organic DBS with DBSO and aqueous H2O2 were separately maintained at experimental temperature. The initial molar ratio of DBS: H2O2=10 mmol: 10 mmol. The initial organic DBSO concentrations were 0 mol/L, 0.24 mol/L, 0.46 mol/L, 0.67 mol/L, 0.87 mol/L and 1.04 mol/L, respectively. The initial aqueous H2O2 concentrations were 3.01 mol/L, 6.29 mol/L, 9.80 mol/L, 13.56 mol/L and 17.57 mol/L, respectively. Then, the reactants were added to the preheated reactor. The reaction time was counted as the magnetic stirrer started to mix the two phases. The reaction was carried out under the stirring speed of 300 r/min, 450 r/min, 600 r/min, 700 r/min, 750 r/min and 900 r/min, respectively. Samples were withdrawn from the organic layer and aqueous layer respectively at regular intervals after stopping the stirring and allowing the two phases to separate. Samples from the organic layer were analyzed by GC-FID

38

. Samples from the aqueous phase were titrated by aqueous KMnO4 with known

concentration 37. 5



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3. RESULTS AND DISCUSSION O

C4H9

O

+H2O2

S

O

+H2O2 S

C4 H9 C4 H9

S C4H9

C4H9

C4H9

Scheme 1. Oxidation steps of DBS with H2O2 3.1. Autocatalysis. The oxidation of DBS with aqueous H2O2 was a consecutive reaction as depicted in scheme 1. DBS was oxidized to DBSO as the desirable product. The further oxidation of DBSO yielded dibutyl sulfone (DBSO2) as the by-product. Mass percentages of three compositions in organic phase varied with reaction time were shown in Figure 1. The slope of the plot of organic DBS concentration versus reaction time could represent the reaction rate 21. Generally, reaction rate decreased with the reduction of reactant’s concentration, which meant the reaction rate was maximum at initiate then gradually reduced. While in our experiments, the reaction barely happened at initiate: only 1% DBS was converted within the first 10 min. Then, the reaction rate accelerated fiercely and almost 70% DBS was converted. The reaction rate accelerated in the middle stage which suggested the reaction was a typical autocatalytic reaction 39 and the product DBSO or DBSO2 could accelerate the reaction rate. In the accelerating stage, only few DBSO2 was produced and the percentage of DBSO2 in organic phase was less than 1%. So, it could be confirmed that the product DBSO accelerated the reaction rate, rather than DBSO2. Besides, the by-product DBSO2 was under low concentration in the whole process thus the further oxidation of DBSO was neglected. In this paper, we focused on the autocatalytic effect of DBSO.

6


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Figure 1. Mass percentages of organic compositions in the reaction process. Conditions: 323K, 700r/min, 10 mmol H2O2, 10 mmol DBS, 9.80 mol/L aqueous H2O2 concentration. 3.2. Solvent Effect of DBSO. Based on the three typical mechanisms in liquid-liquid system mentioned in the introduction 22-33, we believed that the solvent effect could be the most reasonable mechanism 28,29 for the autocatalytic phenomenon since the strong polarity of DBSO 39. The solubility experiments of aqueous H2O2 in pure DBS and DBSO were investigated and the results were shown in Figure 2. The concentration of H2O2 in DBS ranged from 0.11 to 0.25 mol/L with the aqueous H2O2 concentration increased from 3.14 to 17.27 mol/L. The concentration of H2O2 in DBSO increased from 1.31 to 5.96 mol/L with the aqueous H2O2 concentration increased from 1.52 to 11.25 mol/L. The concentration of H2O2 in DBSO was almost 10 to 20 times higher than the concentration of H2O2 7



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in DBS. Aqueous H2O2 barely dissolved in DBS while DBSO had large solubility for H2O2. At the initial stage, the organic H2O2 concentration was relatively low since aqueous H2O2 barely dissolved in DBS, thus the reaction rate was slow at initiate. With the proceeding of the reaction, the generated DBSO had large solubility for H2O2 which increased the organic H2O2 concentration. So the reaction rate accelerated in the middle stage. Based on the results, the autocatalytic phenomenon was caused by the solvent effect of DBSO could be confirmed.

Figure 2. Comparison of solubility of aqueous H2O2 in pure DBS and DBSO under 293K. For discerning the solvent effect further, the effect of initial organic DBSO concentration on reaction rate was investigated and the results were shown in Figure 3. Without DBSO added in initial organic phase, the initial reaction rate was really slow and it took almost 40min to accelerate the 8


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reaction rate. The organic H2O2 concentration was relatively low at initiate since aqueous H2O2 barely dissolved in DBS, thus the reaction rate was slow at initiate. When the initial organic DBSO concentration was 0.67 mol/L, the reaction rate was relatively faster at initiate compared with no extra DBSO added in initiate. That was because DBSO could dissolve H2O2 in organic phase which increased the organic H2O2 concentration. When the initial organic DBSO concentration increased to 1.04 mol/L, the reaction rate was fastest at initiate then gradually reduced without accelerating stage. The solvent effect of DBSO could not counteract the decreasing concentration of reactants when the initial organic DBSO concentration reached a certain concentration. Thus, the reaction rate would reach to maximum at initiate and the autocatalytic phenomenon was disappeared. The solvent effect of DBSO could perfectly explain the phenomena of the experimental results.

9



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Figure 3. Effect of initial organic DBSO concentration on reaction rate. Conditions: 323K, 700r/min, 10 mmol H2O2, 10 mmol DBS, 9.8mol/L aqueous H2O2 concentration. 3.3. Effect of Stirring Speed. Considering the mass transfer in the liquid-liquid system, the effect of stirring speed ranged from 300 to 900 r/min was investigated. The plots of organic DBS concentration versus reaction time at different stirring speed were shown in Figure 4. The absolute value of the slope within 1 min was increased from 0.0054 to 0.0606 with the stirring speed increased from 300 to 900 r/min. It was clearly observed that higher stirring speed could increase the reaction rate at initial stage. When the reaction accessed to the accelerating stage, the slopes at different stirring speed were nearly the same versus the corresponding organic DBSO concentration. An interesting phenomenon was found: the stirring speed only affected the initial reaction rate. Generally, the reaction rate of liquid-liquid system was determined by either mass transfer process or intrinsic reaction process. Higher stirring speed could intensify the mass transfer. Thus, higher stirring speed increased the initial reaction rate meant the mass transfer process was the determining step. While in the accelerating stage, higher stirring speed could not increase the reaction rate meant the intrinsic reaction was the determining step which was contradictory to the former conclusion. Based on the results, we thought that higher stirring speed increased the initial reaction rate was not caused by the intensification of mass transfer. Due to the immiscibility of DBS and H2O2, the reaction of initial stage could be considered as an interfacial reaction to explain the strange phenomenon. Higher stirring speed could break the liquid into smaller drops which generated more interfacial area. More interfacial area could undoubtedly increase the reaction rate in an interfacial reaction. Thus, intrinsic reaction was the determining step could be agreed during the whole stage of reaction. Based on the assumption, we 10


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could divide the reaction into two stages: exterior stage for the reaction occurred at the interfacial surface at initiate and interior stage for the reaction occurred in the bulk of organic phase when certain DBSO was generated.

Figure 4. Effect of stirring speed on the reaction rate. Conditions: 363K, 10 mmol H2O2, 10 mmol DBS, 9.8mol/L aqueous H2O2 concentration. 3.4. Effect of Temperature. Considering the importance of the temperature on the reaction rate, the effect of temperature was investigated. The plots of organic DBS concentration versus reaction time at different temperature ranged from 323K to 363K were shown in Figure 5. The absolute value of the slope within 1 min increased from 0.0081 to 0.0299 with the temperature increased from 323K to 363K. Generally, higher temperature had positive influence on the intrinsic reaction rate. The 11



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reaction rate increased with higher temperature since the exterior stage was the intrinsic reaction determined. As expected, high temperature was also positive for the reaction rate of interior stage. The results again demonstrated that the intrinsic reactions of both exterior and interior stage were the determining step. Meanwhile, temperature shown a sensitive effect for the reaction rate of both exterior and interior stages.

Figure 5. Effect of temperature on the reaction rate. Conditions: 700 r/min, 10 mmol H2O2, 10 mmol DBS, 9.8mol/L aqueous H2O2 concentration.

3.5. Effect of Initial Aqueous H2O2 Concentration. Aqueous H2O2 concentration was important for the economic production since the concentration of aqueous H2O2 corresponded to different price. Meanwhile, the initial aqueous H2O2 concentration was essential for the estimation of the kinetic 12


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parameters. The effect of initial aqueous H2O2 concentration on reaction rate was investigated at different concentrations ranged from 3.01 to 17.57 mol/L. The plots of organic DBS concentration versus reaction time at different initial aqueous H2O2 concentration were shown in Figure 6. When the initial aqueous H2O2 concentration was 3.01 mol/L, it took almost 200 min in exterior stage. At low aqueous H2O2 concentration, the reaction rate of exterior stage was extremely slow. As the aqueous H2O2 concentration increased, the reaction rate of exterior stage was promptly increased. But for the interior stage, the effect of initial aqueous H2O2 concentration was inconspicuous: reaction rate increased slightly with the increased initial aqueous H2O2 concentration. The results indicated that higher initial aqueous H2O2 concentration largely increased the reaction rate of exterior stage while slightly increased the reaction rate of interior stage. The kinetic models of exterior and interior stage might have different expressions.

13



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Figure 6. Effect of initial aqueous H2O2 concentration on reaction rate. Conditions: 343K, 700 r/min, 10 mmol H2O2, 10 mmol DBS.

4. MECHANISM AND KINETIC MODEL The mechanism for oxidation of DBS with aqueous H2O2 in liquid-liquid system based on solvent effect of DBSO was proposed. Exterior and interior mechanisms were assumed for the exterior and interior stages respectively. At the exterior stage, aqueous H2O2 was immiscible with organic DBS thus the reaction occurred at the interfacial surface. The reaction rate was relatively slow since the collisions of the reactants were inefficient at the interfacial surface. As the proceeding of the reaction, the generated DBSO could dissolve aqueous H2O2 in organic phase which turned exterior mechanism 14


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to interior mechanism. The reaction occurred in the bulk of organic phase at interior stage. For the interior mechanism, the reaction rate was relatively fast since the collisions of the reactants in homogeneous phase were efficient. 4.1. Exterior Mechanism. As shown in Figure S1 in the Supporting Information, three steps were included in the exterior mechanism: (1) Mass transfer of aqueous H2O2 from bulk phase to interfacial border. (2) Mass transfer of organic DBS from bulk phase to interfacial border. (3) Intrinsic reaction at interfacial surface. The three steps were expressed as follows:

[H 2 O 2 ]aq

[H 2 O 2 ]int aq

(1)

[DBS]org

[DBS]int org

(2)

int int int [H 2 O 2 ]int aq +[DBS]org → [DBSO]org +[H 2 O]aq

(3)

Based on the effect of initial aqueous H2O2 concentration on reaction rate of exterior stage, the intrinsic reaction rate was assumed as a 2th order kinetic model of [H2O2]int aq :

N DBS =k × [H 2 O 2 ]int aq

2

(4)

The subscript aq and org were aqueous and organic phase, respectively. The superscript int was the interfacial border. NDBS was the reaction rate of DBS at interfacial surface and k was the rate constant. Since the mass transfer resistance could be neglected, so the concentration of interfacial surface was equal to bulk phase. We assumed that the organic phase dispersed in aqueous phase as drops. The interfacial area was the sum of the surface area of the drops. The global reaction rate in organic phase could be written as 23:

15



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n

d[DBS]org dt

∑A =-k ×

i

× [H 2O2 ]aq 2

i

Vorg

(5)

Where Ai was the surface area of the drops i. Vorg was the total volume of organic phase. We assumed that the effect of stirring speed on the total interfacial area with the following equation: n

∑A

i

i

Vorg

(6)

=c × eσ ×S

Where c was the geometrical structure factor of reactor, σ was the parameter of stirring speed and S was the stirring speed. k from equation (4) could be expressed as the Arrhenius equation: 0

k=k e

-

Ea ex RT

(7)

Taken the equation (6) and (7) into equation (5):

d[DBS]org dt

=-k 0 × c × e

-

Ea ex +σ ×S RT

[H 2O2 ]aq 2

(8)

Since the geometrical structure factor of the reactor was the same, the parameter c was considered as constant. Thus, we emerged the two parameters k0 and c into one parameter:

k 0ex =k 0 × c

(9)

Thus, equation (8) could be written as function of rate constant multiplied concentration of reactants:

d[DBS]org dt

=-k ex [H 2 O2 ]aq 2

(10)

Where kex was the analogical rate constant. Compared the equation (8) with equation (10), kex 16


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was expressed as analogical Arrhenius equation:

k ex =k 0ex × e

-

Ea ex +σ ×S RT

(11)

Where k0ex was the analogical pre-exponential factor and Eaex was the activation energy of exterior stage. 4.2. Interior Mechanism. The exterior mechanism turned to the interior mechanism when certain DBSO was produced. As shown in Figure S2 in the Supporting Information, reaction steps included: (1) Mass transfer of aqueous H2O2 from bulk phase to interfacial border. (2) Mass transfer of aqueous H2O2 from aqueous border to organic border. (3) Mass transfer of H2O2 from organic border to the bulk phase. (4) Intrinsic reaction in the bulk of the organic phase. The four steps could be expressed as:

[H 2 O 2 ]aq

[H 2 O 2 ]int aq

(12)

[H 2 O 2 ]int aq

[H 2 O 2 ]int org

(13)

[H 2 O 2 ]int org

[H 2 O 2 ]org

(14)

[H 2 O 2 ]org +[DBS]org → [DBSO]org +[H 2 O]org

(15)

Based on the effect of initial aqueous H2O2 concentration on reaction rate of interior stage, the intrinsic reaction was assumed as 3th order reaction:

d[DBS]org dt

=-k in × [DBS]org × [H2O2 ]org 2

(16)

The intrinsic reaction was the determining step, so the mass transfer resistance was negligible. Mass transfer of aqueous H2O2 from aqueous border to organic border was considered as equilibrium and the distribution coefficient of H2O2 between the two phases could be written as: 17



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D=

Page 18 of 38

[H 2 O 2 ]org

(17)

[H 2 O 2 ] aq

The overall distribution coefficient of H2O2 was contributed by the composition of organic mixtures. We assumed that the overall distribution coefficient could be described as linear combinations of pure DBS and DBSO in organic phase. Based on the assumption, the overall distribution coefficient of H2O2 could be written as:

D=

[DBS]org [DBS]org +[DBSO]org

× DDBS +

[DBSO]org [DBS]org +[DBSO]org

× DDBSO

(18)

Since aqueous H2O2 was barely dissolved in DBS, the contribution of DBS was negligible and the overall distribution coefficient of H2O2 was simplified as the following equation:

D=


× DDBSO

(19)

The distribution coefficient of H2O2 between aqueous phase and pure DBSO could be given by the following equation 41:

D DBSO =

γ aq γ org

× e

-

∆G # DBSO RT

(20)

γaq/γorg was assumed as a linear function of [H2O2]aq:

γ aq γ org

=φ[H 2O2 ]aq +θ

(21)

Taken the equation (17) (19) (20) (21) into equation (16), the reaction rate of interior mechanism represented as

d[DBS]org dt

=-k in [DBS]org [H 2 O 2 ]aq 2 {(φ[H 2 O 2 ]aq +θ) × e

-

∆G # DBSO RT

×


}

2

(22)

Where D, DDBS and DDBSO were the distribution coefficient of H2O2 between organic 18


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mixtures-H2O, DBS-H2O and DBSO-H2O, respectively. γaq and γorg were the activity coefficients of aqueous H2O2 and organic H2O2, respectively. △G#DBSO was the value of standard chemical potential change of H2O2 in DBSO and H2O. φ and θ were the linear regression factor for [H2O2]aq.

5. ESTIMATION OF PARAMETERS IN KINETIC MODEL AND VALIDITY STUDY 5.1. Exterior Mechanism. The parameters of exterior mechanism were estimated by the experimental data of stirring speed and temperature. The instantaneous reaction rate was calculated by the Difference quotient method. The instantaneous reaction rates of 1 min were selected for the estimation of exterior mechanism. The Arrhenius plots of lnkex against stirring speed and 1/T were obtained respectively. As shown in Figure 7 and Figure 8, the plots of lnkex versus stirring speed and 1/T both shown a great linear correlation. The linear regression equations were displayed in Figure 7 and Figure 8, respectively.

19



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Figure 7. Plot of lnkex versus stirring speed. Conditions: instantaneous reaction rate of 1 min, 363K, 10 mmol H2O2, 10 mmol DBS, 9.8mol/L aqueous H2O2 concentration.

20


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Figure 8. Arrhenius plot of lnkex versus 1/T. Conditions: instantaneous reaction rate of 1 min, 700 r/min, 10 mmol H2O2, 10 mmol DBS, 9.8mol/L aqueous H2O2 concentration. Taken the natural logarithm on the both sides of equation (11):

lnk ex =lnk 0ex -

Ea ex +σ × S RT

(23)

The parameter σ could be determined from the slope of the plot of lnkex versus stirring speed when the temperature was maintained as constant. The activation energy Eain and pre-exponential factor k0ex were obtained from the slope of the Arrhenius plot of lnkex versus 1/T and the intercept of the Arrhenius plot. The estimated parameters were listed in Table 1. Table 1. Estimation of parameters in exterior stage. Eaex (kJ/mol)

k0ex ((mol/L)-1min-1)

σ (min/r) 21



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30.62

0.4474

Page 22 of 38

0.0041

5.2. Equilibrium of H2O2 between Organic and Aqueous Phase. The equilibrium experiments were carried out at the temperature ranged from 278K to 298K since DBS and DBSO barely reacted with H2O2 at the scope of temperature. Meanwhile, the equilibrium time set as 10 min rather than hours since the mass transfer between the two phases was transient. The plots of equilibrated organic H2O2 concentration versus equilibrated aqueous H2O2 concentration at different temperature were shown in Figure S3 in the Supporting Information. The equilibrium data shown that the equilibrated organic H2O2 concentration increased with higher equilibrated aqueous H2O2 concentration. The increasing temperature could slightly raise the equilibrated organic H2O2 concentration. The distribution coefficients D versus the equilibrated aqueous H2O2 concentration were shown in Figure 9. The results shown that the distribution coefficients D were ranged from 0.46 to 0.89. The distribution coefficients D shown a linear correlation to the equilibrated aqueous H2O2 concentration. The regression equations with different temperature were obtained and displayed in the Figure 9.

22


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Figure 9. Effect of aqueous H2O2 concentration on the distribution coefficient with temperature ranged from 278K to 298K.

23



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Page 24 of 38

Figure 10. Effect of temperature on the distribution coefficient. 5.50mol/L equilibrated aqueous H2O2 concentration. Taken aqueous H2O2 concentration as 5.50mol/L into the regression equations from Figure 9, we could obtain the corresponding distribution coefficient DDBSO at different temperature. DDBSO could be expressed as the following equation: -∆G #DBSO

D DBSO =(φ[H 2 O 2 ]aq +θ) × e

RT

(24)

Taken the natural logarithm on the both sides of equation (23):

lnD DBSO =ln(φ[H 2 O 2 ]aq +θ)-

∆G #DBSO

(25)

RT

The plot of lnDDBSO versus 1/T shown a great linear correlation and the regression equation was 24


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displayed in Figure 10.The △G#DBSO was obtained from the slope of the plot of lnDDBSO versus 1/T at the condition of 5.5 mol/L aqueous H2O2 concentration. The parameters φ and θ could be estimated by the regression equations in Figure 9. The estimated parameters were listed in Table 2. Table 2. Estimation of parameters in interior mechanism. Eain (kJ/mol)

k ((mol/L) min )

△G#DBSO (kJ/mol)

73.50

1.15×1010

3.65

0 in

-2

-1

φ ((mol/L)-1)

θ

-0.15

4.07

5.3. Arrhenius Equation of Interior Mechanism. The rate constants of interior mechanism were estimated using the experimental data at different temperature ranged from 323K to 363K. Levenberg-marquardt algorithm was often used for the estimation of rate constant

42-44

. The optimum

values of rate constants were estimated by minimizing the following equation: n

n

∑ (rexpti -restii )2 =∑ (rexpti -k in esti [DBS]iorg [H 2O2 ]iaq 2 Di 2 )2 i

(26)

i

Where r was the instantaneous reaction rate, superscript i was the reaction time of i min, subscript expt and esti were the experimental and estimated data, respectively. Optimized rate constants were listed in Table 3. It was observed from Table 3 that the rate constants increased as expected with the increase of temperature. Table 3. Optimized rate constants with temperature ranged from 323K to 363K. Temperature (K)

323

333

343

353

363

0.016

0.034

0.064

0.154

0.334

Rate constants kin -2

-1

((mol/L) min ) kin could be expressed as Arrhenius equation, taken the natural logarithm on the both sides: 25



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lnk in =lnk in0 -

Ea in RT

Page 26 of 38

(27)

The plot of lnkin versus 1/T was shown in Figure 11, the regression equation shown a great linear correlation. The pre-exponential factor and activation energy could be determined from the intercept and slope of the Arrhenius plot, respectively. The estimated parameters of interior mechanism were listed in Table 2.

Figure 11. Arrhenius plot of rate constants. Conditions: 700 r/min, 10 mmol H2O2, 10 mmol DBS, 9.8mol/L aqueous H2O2 concentration. 5.4. Validity of the Kinetic Model with Estimated Parameters. At initial stage, the reaction proceeded with exterior mechanism and equation (10) was applied for the reaction rate. When certain DBSO was produced, exterior mechanism turned into interior mechanism thus equation (22) was 26


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applied for the reaction rate. As shown in Figure 4, Figure 5 and Figure 6, the transition points of exterior stage to interior stage were approximately at 5% mole fraction of DBSO was generated. We assumed that the reaction proceed with exterior mechanism when the mole fraction of DBSO in organic phase was below 5%. As the mole fraction of DBSO in organic phase increased over 5%, interior mechanism was applied for the reaction. The iterations of the differential equations were carried out using a fourth-order Runge-Kutta algorithm 45-48. The solution procedure was started with initial aqueous H2O2 concentration and initial organic concentration of DBS and DBSO. The calculated organic DBS concentrations at different conditions were compared with experimental results. Exterior mechanism:

d[DBS]org dt

=-k 0ex × e

-

Ea ex + σ ×S RT

[H 2 O 2 ]aq 2


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