Mechanistic insight into phase transfer agent assisted ultrasonic desulfurization

Abstract

This paper attempts to gain physical insight into the phase transfer agent (PTA) assisted ultrasonic oxidative desulfurization process. Essentially, the synergistic links between mechanisms of PTA and ultrasound/cavitation have been identified by coupling experimental results with simulations of cavitation bubble dynamics and Arrhenius & thermodynamic analysis of reaction kinetics. It is revealed that ultrasonic oxidative desulfurization has a radical-based mechanism with a low activation energy. However, due to the high instability of radicals, the frequency factor is small leading to low dibenzothiophene (DBT) oxidation. PTA-assisted oxidative desulfurization has an ionic mechanism with a much higher activation energy. The synergistic effect of fine emulsification generated by micro-convection due to ultrasound and cavitation, and PTA-assisted interphase transport of oxidant results in almost complete oxidation of DBT. It is thus established that synergy between the mechanisms of ultrasound/cavitation and PTA is predominantly of a physical nature. Moreover, the effect of PTA is more marked for an ultrasonic system than a mechanically agitated system.

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1. Introduction

Stringent restrictions on the sulfur content of fuel to curb pollution due to vehicular emissions have triggered significant research on new technologies for achieving deep desulfurization of fuels for transportation.¹ The conventional technology of hydro-desulfurization (HDS), in which sulfur in the fuel is removed as H₂S, is not suitable for achieving the required very low levels of sulfur. The principal cause contributing to this is low reactivity (and hence negligible removal) of substituted benzothiophene and dibenzothiophene.²

New technology for oxidative desulfurization has shown significant promise for achieving deep desulfurization. This technology is based on the conversion of non-polar aromatic hydrocarbons containing sulfur to the corresponding sulfones, which can subsequently be extracted from fuel. Oxidants used in this technique are organic or inorganic peroxyacids, which are immiscible with the fuel. Thus, the oxidative desulfurization reaction system is essentially a liquid–liquid heterogeneous system, which is limited by mass transfer. The kinetics as well as the yield of such a system depends on the interfacial area between the two phases. Ultrasound irradiation (or sonication) is a well-known technique for enhancing the interphase mass transfer in diverse physical and chemical processes through the generation of strong micro-convection.^3–6 Transient cavitation also generates highly reactive radicals through the thermal dissociation of solvent vapor entrapped in the cavitation bubble at the moment of collapse. Another means of enhancing the interfacial mass transfer in a liquid–liquid heterogeneous system is the use of a phase transfer catalyst or phase transfer agent (PTA).⁷ A PTA enhances interphase mass transfer through the formation of a complex with the nucleophilic reagent in the aqueous phase (or the oxidant in the context of the present study), and the transport of the complex to the organic phase. Simultaneous application of ultrasound and PTA for oxidation desulfurization has been attempted by several authors.^8–10 Hagenson et al.¹¹ and Hagenson and Doraiswamy¹² have analyzed the effect of ultrasound, a phase transfer agent and a microphase in the enhancement of the synthesis of benzyl sulfide from benzyl chloride and sodium sulfide. Ultrasound was revealed to enhance intrinsic mass transfer as well as the effective diffusivity of the organic reactant through the product layer. Ultrasound was revealed to boost the effects of the microphase and PTA on the enhancement of the reaction kinetics. This was attributed to enhancement of the interphase mass transfer due to strong micro-convection generated by ultrasound.

Most of the research in ultrasound-assisted oxidative desulfurization has focused on results rather than rationale. The physical mechanism of this process has remained largely unexplored. In a previous paper, we attempted to identify the physical mechanism of ultrasound assisted oxidative desulfurization by distinguishing between the individual effects of ultrasound and cavitation on the reaction system. We demonstrated that the generation of reducing species such as H₂, CO and CH₄ during transient cavitation in the organic phase hinders oxidation of sulfur compounds due to the competitive consumption of oxidant species.^13,14 In another paper, we explored the effect of PTA on oxidative desulfurization using different peracid oxidant systems (performic acid and peracetic acid). In this study we show that the interfacial transport of oxidant in the form of an oxidant–PTA complex reduces the undesirable consumption of oxidant by reducing species, as observed in our earlier study.¹⁵ Although the paper demonstrated the beneficial effect of PTA on the ultrasonic oxidative desulfurization system, the underlying physical mechanism was not established. In the present study, we have attempted to identify the physical mechanism of the PTA-assisted ultrasonic oxidative desulfurization process. Our approach is based on the determination of the kinetic (Arrhenius) and thermodynamic parameters of oxidative desulfurization in different experimental categories, and its concurrent analysis with the simulation of cavitation bubble dynamics. For the kinetic analysis of PTA-assisted oxidative desulfurization, we have used the model reported by Zhao et al.¹⁶ The principal objectives of this study are two-fold: (1) assessment of the relative contributions of ultrasound and PTA to the enhancement of oxidative desulfurization, and (2) determination of the relative influence of interfacial mass transfer and intrinsic reaction kinetics in the process.

2. Materials and methods

2.1 Chemicals

The following chemicals were used in the experiments: dibenzothiophene (98% from Sigma Aldrich), toluene (synthesis grade from Merck), 30% v/v H₂O₂ (AR grade from Merck), formic acid (∼86%, AR grade from Lobachem), tetrabutyl ammonium bromide (TBAB) (from Sigma Aldrich), and acetonitrile (HPLC grade from Merck). All of the chemicals were used as received without any pretreatment.

2.2 Experimental setup

Experiments were conducted in an ultrasound bath (Make: Jeio-Tech, model: UC02, capacity: 2 L, frequency: 35 kHz, and power: 70 W). The actual power dissipated in the bath was determined calorimetrically, and the acoustic pressure amplitude generated in the bath was calculated as 150 kPa.¹⁷ Oxidative desulfurization reactions were carried out in a 38 mL test tube, which was placed at the center of the bath. Due to spatial variations of the ultrasound intensity in the bath, the position of the test tube inside the bath was carefully kept constant in all of the experiments.¹⁸ For determination of the activation energy, experiments were carried out at four temperatures (viz. 303, 313, 323 and 333 K) using a temperature controlled water bath (Make: International Commercial Traders, model: B/CH). A similar procedure was followed for the mechanically stirred system, in which a hot metal plate stirrer was used. A schematic of the experimental setup used in the experiments is given in the ESI (Fig. S1a and b†).

2.3 Experimental protocols

Toluene (20 mL) with an initial DBT concentration of 100 ppm was used as a model fuel. The oxidant system employed for oxidative desulfurization was H₂O₂ promoted by formic acid, which formed performic acid (PFA), HCOOOH, in situ in the reaction system. The experiments were planned in three categories, which are depicted in Table 1. The exact composition of the reaction mixture in each experimental protocol is given in Table S1 in the ESI.† The composition of reaction mixture was decided on the basis of preliminary experiments, which have been described in the ESI† provided with the manuscript (Fig. S2 and S3†). TBAB was used as a phase transfer agent (PTA). The amount of PTA added to the reaction mixture was varied in the range of 0.25–0.1 g. In some experiments, the static pressure on the reaction solution was raised to 1.6 bar using a nitrogen cylinder with a two-stage regulator. During the reaction, aliquots of the reaction mixture (0.5 mL) were withdrawn every 15 min and were analyzed for the residual DBT concentration. All experiments were done in triplicate to assess the reproducibility of the results.

Table 1 Summary of the four experimental categories of DBT oxidation

Experimental category	Solvent: toluene
	η^b%	k^a (min^−1)	R^2
a Pseudo-1^st order kinetic constant, k, obtained at a reaction temperature of 313 K for ultrasound assisted desulfurization experiments, and 333 K for experiments using mechanical stirring. Abbreviations: MS – mechanical stirring, US – ultrasound-assisted treatment (or under sonication), and ESP – elevated static pressure.b Percentage of DBT oxidation (η) calculated using: [(initial DBT concn − final DBT concn)/initial DBT concn] × 100.
(A.1) MS + PFA	28.30 ± 1.12	4.13 × 10^−3	0.97
(A.2) US + PFA	31.22 ± 0.98	4.43 × 10^−3	0.95
(B.1) MS + PFA + TBAB	63.50 ± 0.92	1.22 × 10^−2	0.96
(B.2) US + PFA + TBAB	96.65 ± 1.06	4.26 × 10^−2	0.97
(C.1) US + PFA + TBAB + ESP (1.8 bar)	77.63 ± 1.39	1.52 × 10^−2	0.85

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2.4 Analysis

The residual concentration of DBT in aliquots of the reaction mixture was analyzed using Shimadzu High Performance Liquid Chromatography equipment (HPLC, model: SPD-20A) with a reverse phase C-18 column (5 μm, 4.6 mm × 250 mm) and a UV detector at 287 nm. The mobile phase was a mixture of acetonitrile and water (80 : 20 v/v). The formation of sulfone in the oxidative desulfurization was confirmed using FTIR analysis after the completion of the reaction. To identify the intermediates during DBT oxidation, GC-MS analysis of the same reaction sample was performed using a Varian 240-GC equipped with a VF-5ms column (30 m × 0.25 m ID, DF = 0.25). The temperature program was as follows: injection temperature = 250 °C, column temperature = 100 °C at zero time and was increased to 300 °C at a ramping rate of 7 °C min⁻¹.

2.5 Characterization of oxidized product

HPLC chromatographs. Representative HPLC chromatographs of the aliquots of the reaction mixture are shown in Fig. 1. Peaks corresponding to DBT and DBT sulfone were obtained at retention times of 9.1 and 3.9 min, respectively.

Fig. 1 HPLC chromatograph of the reaction mixture before and after treatment for the oxidant system: performic acid + TBAB as a phase transfer agent.

FTIR analysis. Fig. 2 compares the IR spectra of the reaction mixture before and after the DBT oxidation reaction. Fig. 2 shows two different characteristic peaks of the sulfone compound at 1370 cm⁻¹ and 1035 cm⁻¹, while a characteristic peak at 917 cm⁻¹ represents the sulfoxide compound confirming the oxidation of DBT during the treatment.

Fig. 2 Comparison of the FTIR spectra before and after the oxidation reaction (protocol: experimental category B, i.e. ultrasound treatment with the oxidant performic acid in the presence of TBAB as a phase transfer agent).

GC-MS analysis. The high resolution GC-MS total ion chromatograms of the reaction mixture (initial and after completion of the reaction) are shown in Fig. 3A and B, respectively. The molecular mass of DBT was determined to be 184.3, which is close to the calculated value of 184.26. The oxidized products were found to have masses of 199.6 and 216.03 giving a mass difference of 16 and 32 units with respect to DBT, respectively. These additional units correspond to the mass of 1 and 2 oxygen atoms. The peaks obtained at 20.08, 22.1 and 25.3 min correspond to DBT, DBT sulfoxide and DBT sulfone, respectively. The major ions obtained at different m/z (% intensity, proposed derivation from the molecular ion, M) values are 200 (10, [M]⁺), 184 (100, [M − O]⁺), 171 (12.5, [M − CHO]⁺), 139 (20, [M − COH − S]⁺), 216 (100, [M]⁺), 187 (37.5, [M − COH]⁺), 168 (23, [M − O − S]⁺), 160 (10, [M − CO − CO]⁺), and 150 (7.5, [M − OH − OH − S]⁺). The mass spectra of DBT, DBT sulfone and DBT sulfoxide are shown in Fig. 4A–C.

Fig. 3 Total ion chromatograms of the reaction mixture in experimental category B (protocol: ultrasound treatment with the oxidant performic acid in the presence of TBAB as a phase transfer agent). (A) Initial (before reaction) chromatogram; (B) final (after the oxidation reaction) chromatogram.

Fig. 4 Mass spectra of the reaction mixture after treatment in experimental category B (protocol: ultrasound treatment with the oxidant performic acid in the presence of TBAB as a phase transfer agent). (A) Mass spectrum of DBT; (B): mass spectrum of DBT sulfone; (C) mass spectrum of DBT sulfoxide.

3. Mathematical models

In the analysis of the physical mechanism of PTA-assisted ultrasonic oxidative desulfurization, we used two models, viz. a kinetic model for the PTA-assisted oxidative desulfurization system and a model for cavitation bubble dynamics, as described below:

3.1 Kinetic model for PTA-assisted oxidative desulfurization

In the classic review on the science and engineering of phase transfer catalysis, Naik and Doraiswamy¹⁹ described the general considerations in the modeling of PTA assisted reactions. PTA enhances slow (or kinetically controlled) reactions as well as fast reactions, which occur – either partially or completely – in a diffusion film at the interphase. Therefore, Naik and Doraiswamy¹⁹ have recommended that a model for a PTA-assisted reaction must consider all of the individual steps in the PTA cycle, i.e. the interphase mass transfer, ion exchange and the organic phase reactions. The active catalyst concentration (or the concentration of the PTA–anion complex) in the organic phase is an important parameter. However, the concentration of the PTA–anion complex in the organic phase remains constant in the presence of a large excess of a nucleophilic reagent (performic acid in the context of the present study). An enhanced mass transfer rate in the presence of ultrasound also contributes to achieving a constant concentration of the PTA–anion complex in the organic phase. The ion exchange rate has also been revealed to be much faster (∼10×) than the rate of reaction in the organic phase.²⁰ Under these circumstances, the organic reaction is the rate controlling step, and is usually modeled using pseudo-1^st order kinetics. Several studies on the modeling of phase transfer catalyzed liquid–liquid heterogeneous reactions have confirmed the suitability of pseudo-1^st order kinetics for the overall reaction.^21,22 Bhattacharya²³ has presented a general kinetic model for liquid–liquid phase transfer catalyzed reactions, in which he pointed out that the assumption of constant concentration of the PTA–anion complex is valid only when the rate of transfer of the nucleophile to the organic phase equals its consumption through the organic reaction.

As stated earlier, we have determined the kinetic constants of PTA-assisted oxidative desulfurization in different experimental protocols using the model proposed by Zhao et al.¹⁶ This model is based on the model reported by Maw-Ling and Chen²⁴ for the PTA-assisted synthesis of formaldehyde acetals from alcohols and dibromomethane in an alkaline solution of KOH and an organic solvent. This model was developed for a mechanically agitated system. We used this model for ultrasonic desulfurization in view of the predominant influence of micro-convection generated by ultrasound on the reaction system. Zhao et al.¹⁶ also proposed that complexation of the anion of the oxidant (HCOOO⁻) with the cation of the PTA reduces its polarity, which enables faster transport to the organic phase. Although this hypothesis is perceivable, it should be noted that the PTA–anion still has ionic character – as the net charge is not neutralized after complexation. For the convenience of the reader, we have reproduced this model below.

The oxidant in the present study, viz. performic acid, forms through the reaction between formic acid and H₂O₂ as follows:

HCOOH + H₂O₂ → HCOOOH + H₂O

Performic acid undergoes dissociation to yield the nucleophilic anionic oxidant species HCOOO⁻ as follows:

HCOOOH ⇄ HCOOO⁻ + H⁺

The nucleophile anion HCOOO⁻ forms a complex with the cation of PTA (quaternary ammonium salt), represented as Q⁺Br⁻, as follows:

HCOOO⁻ + Q⁺Br⁻ → [HCOOO⁻–Q⁻–Br] (1)

The desulfurization reaction occurs in the organic phase in two steps: (1) formation of a PTA–oxidant complex in the aqueous phase (represented by the subscript aq), and (2) transfer of the complex across the interphase to the organic phase (represented by the subscript org). This process is reversible and is characterized by two rate constants (k₁ and k₋₁, for the forward and backward reactions, respectively). Usually, the intrinsic reaction between PTA and the oxidant is very fast. Hence, the overall rate constants k₁ and k₋₁ are essentially functions of the interphase mass transfer rate (which can be called the rate limiting step). In a liquid–liquid heterogeneous system, the rate of mass transfer across the interphase is a function of the interfacial area. The second step (reaction (3)) is the irreversible oxidation of the sulfur compound in the organic phase and this is characterized by rate constant k₂.

The rate of oxidation of DBT in the organic phase (or the formation of the product DBT sulfone [C₁₂H₈SO]_org) can be written as:

In order to determine the rate of reaction in the organic phase, we need to know the concentration of the PTA–anion complex in the organic phase. The formation of the PTA–oxidant complex (Q⁺HCOOO⁻)_org can be described by the following rate expression as per eqn (2) and (3) given above:

At steady-state, the net concentration of the PTA–oxidant complex in the organic phase stays constant and this produces the condition:

Other factors that also contribute to a constant concentration of the PTA–oxidant complex in the organic phase are fast ion exchange and mass transfer across the interphase, and a large excess of the oxidant and PTA, when compared to the concentration of the sulfur compound in the organic phase.¹⁹ It therefore follows that:

k₁[Q⁺Br⁻]_org[HCOOO⁻]_aq = k₋₁[Q⁺HCOOO⁻]_org[Br⁻]_aq + k₂[Q⁺HCOOO⁻]_org[C₁₂H₈S]_org (7)

The PTA exists in the organic phase of the reaction system in the pure form Q⁺Br⁻ as well as in the form of the complex. Hence, the total concentration of the PTA cation [Q⁺]_org, which forms a complex with the nucleophilic oxidant is written as:

[Q⁺]_org = [Q⁺Br⁻]_aq + [Q⁺HCOOO⁻]_org (8)

Substituting for [Q⁺Br⁻]_aq as [Q⁺]_org − [Q⁺HCOOO⁻]_org in eqn (7), we get:

Then, substituting eqn (9) into eqn (4), the rate of the reaction of DBT oxidation in the organic phase is:

Due to convection present in the system (either in the form of mechanical agitation or ultrasound irradiation), the rate of interphase mass transfer of (HCOOO⁻)_aq can be assumed to be very fast. This results in the rapid accumulation of (HCOOO⁻)_aq and (Q⁺)_org in the organic phase. This favors the forward reaction of eqn (2). Moreover, the intrinsic kinetics of the DBT oxidation reaction in the organic phase is also likely to be much slower than the dissociation of performic acid. Under these conditions, the following inequality holds true:

k₁[HCOOO⁻]_aq ≫ k₋₁[Br⁻]_aq + k₂[C₁₂H₈S]_org (11)

From this, the rate expression for product formation can be transformed into:

The stoichiometry of the reaction between DBT (reactant) and DBT–sulfone (product) is essentially one. Hence, one can easily substitute the rate of formation of product in terms of the rate of disappearance of reactant (DBT):

Therefore, eqn (12) becomes:

Since the PTA concentration is usually in large excess, and the mass transfer rate across the interphase is also fast, the total concentration of the quaternary cation (in free and complex form) in the organic phase remains constant. Hence, we can club together the rate constant k₂ and the concentration of PTC, [Q⁺]_org, to give a new constant, k₃.

Integrating the above equation between the limits, at t = 0, [C₁₂H₈S]_org = [C₁₂H₈S]_org,0, and at t = t, [C₁₂H₈S]_org = [C₁₂H₈S]_org,t, we get:

where k is the overall or gross pseudo-1^st order rate constant for the oxidative desulfurization process. Thus, the analysis by Zhao et al.¹⁶ essentially proves that with an excess of oxidant as well as employing PTA during oxidative desulfurization (as is the case in the present study), the overall oxidative desulfurization reaction follows pseudo-1^st order kinetics.

3.2 Simulations of cavitation bubble dynamics

In the present case, the reaction system is a two-phase mixture, viz. an organic phase (toluene) and an aqueous phase (performic acid). The passage of ultrasound through the reaction mixture induces micro-streaming (i.e. oscillatory motion of fluid elements) in both phases, but due to a larger volume fraction in the reaction mixture, the micro-streaming in toluene contributes mostly to emulsification of the organic and aqueous phases. The micro-streaming velocity is calculated from: u = P_A/ρ_Lc. The acoustic pressure amplitude (P_A) in the medium was determined as 150 kPa using calorimetric measurements. For toluene, ρ_L (density) = 867 kg m⁻³ and c (sonic velocity) = 1275 m s⁻¹, and thus, u = 0.137 m s⁻¹.

The magnitudes of the physical and chemical effects of cavitation bubbles have been determined using the diffusion limited ordinary differential equation model proposed by Toegel et al.²⁵ It should be noted that cavitation phenomena occur in both the organic medium (toluene) and the aqueous medium (performic acid). However, since the DBT oxidation reaction occurs in the organic phase, we have considered the cavitation bubble dynamics phenomena in toluene only in our model. Cavitation phenomenon occurring in an aqueous medium mainly contributes to emulsification of the two phases, due to the convection induced by the radial motion of transient cavitation bubbles. The diffusion limited model reported by Toegel et al.²⁵ is based on the comprehensive partial differential equation model reported by Storey and Szeri²⁶ who showed that solvent vapor transport and entrapment in the cavitation bubble, leading to the formation of radicals, is essentially a diffusion limited process. This model has been extensively described in previous papers.^27–29 For the convenience of readers, the essential equations and thermodynamic data of this model have been provided in the ESI (Tables S2 and S3†). The model is essentially a set of 4 ordinary differential equations: (1) the Keller–Miksis³⁰ equation for the radial motion of the bubble, (2) an equation for the diffusive flux of water vapor and heat conduction through the bubble wall, and (3) the overall energy balance. The thermal conductivity of the bubble contents and the diffusion coefficient of the water vapor inside the bubble are determined using Chapman–Enskog theory using the Lennard–Jones 12-6 potential. An air bubble has been considered for the simulations. The condition for bubble collapse was taken as the first compression after an initial expansion. Various parameters which were used in the simulation of the bubble dynamics equation and their numerical values were as follows: ultrasound frequency (f) = 35 kHz; ultrasound (or acoustic) pressure amplitude (P_A) = 150 kPa; equilibrium bubble radius (R_o) = 5 μm; the vapor pressure of toluene was calculated using an Antoine type correlation at the temperature of the reaction (298 K). Various physical properties of toluene are as follows: density (ρ_L) = 867 kg m⁻³, kinematic viscosity (ν) = 6.8 × 10⁻⁷ Pa s⁻¹, surface tension (σ) = 0.0285 N m⁻¹, sonic speed (c) = 1275 m s⁻¹, and static pressure (P_o) = 101.3 kPa (for experiments at atmospheric static pressure) or 162 kPa (for experiments with elevated static pressure).

3.3 Estimation of the physical and chemical effects of cavitation

The chemical effect of cavitation bubble dynamics (or the sonochemical effect) is the generation of small chemical species (including some radical species) from the thermal dissociation of gas and solvent vapor molecules entrapped in the bubble at the moment of transient collapse – when the temperature and pressure conditions in the bubble reach an extreme. The numerical solution of the diffusion-limited cavitation bubble dynamics model gives the number of solvent (toluene) vapor molecules present in the bubble at the point of minimum radius during radial motion along with the temperature and peak pressure reached in the bubble. Due to the extreme temperature and pressure in the bubble, and also the very high concentrations of chemical species due to the extremely small volume of the bubble, the rates of different chemical reactions occurring in the bubble are extremely fast, and thermal equilibrium is likely to prevail all through the radial motion of the bubble.³¹ In view of the hypothesis reported by Brenner et al.,³¹ the equilibrium mole fractions of various species in the bubble (at the conditions of temperature and pressure at the first compression of the bubble) resulting from the thermal dissociation of air (oxygen and nitrogen) and toluene molecules have been calculated using a Gibbs free-energy minimization technique.³²

The principal physical effect of cavitation is the generation of strong micro-convection in the bulk medium through two phenomena, viz. micro-turbulence, and shock or acoustic waves. The magnitudes of these two parameters can be calculated using the bubble dynamics model as follows:^33–35

where r is the distance from the bubble center. A representative value of r is taken as 1 mm.

3.4 Arrhenius (kinetic) and thermodynamic analysis

Arrhenius analysis was carried out using pseudo-1^st order kinetic constants (at various temperatures) obtained from the model reported by Zhao et al.¹⁶ in the different experimental categories. The activation energy (E_a) and frequency factor (A) of desulfurization in the different experimental categories were estimated using plots of ln k vs. 1/T. The basic thermodynamic properties of the reaction system could be determined using the Eyring equation as follows:

ΔH = E_a − RT (20)

ΔG = ΔH − TΔS (21)

where k_b and h are the Boltzmann and Planck’s constant, respectively. The results of the Arrhenius analysis can be used to determine the thermodynamic parameters ΔH, ΔS and ΔG.

4. Results and discussion

4.1 Trends in DBT oxidation

The time profiles of DBT oxidation in the different experimental categories are depicted in Fig. 5A and B. The results of DBT oxidation in the different experimental categories are summarized in Table 1. As stated earlier, the DBT oxidation was carried out at 4 temperatures. However, the temperature at which the highest DBT oxidation occurred (with the highest kinetic constant) was different for the mechanically stirred and ultrasound-assisted systems. For the mechanically stirred system, the highest DBT oxidation was obtained at 333 K, while for the ultrasound-assisted systems, the temperature for the highest DBT oxidation was 313 K. The results depicted in Table 1 and Fig. 5A and B correspond to these temperatures. The trends in DBT oxidation in the different experimental categories reveal the following distinct features:

(1) Comparing the extent of DBT oxidation for categories A.2 and B.2, a 3.1× (or 3.1-fold) rise in oxidation is seen when PTA is used in the presence of ultrasound. On the other hand, comparing the results for categories A.1 and B.1, a relatively lower rise of 2.25× (or 2.25-fold) in oxidation is seen for PTA when applied in the mechanically stirred systems. Thus, the enhancement in DBT oxidation in the presence of PTA is more pronounced for the ultrasonic systems than the mechanically stirred systems. This result is in complete concurrence with the conclusion reported by Hagenson et al.¹¹ that the enhancement effect of PTA on reaction kinetics acquires higher significance in the presence of ultrasound.

(2) Comparison of the results of categories B.1 and B.2 reveals that the effect of PTA is more pronounced for the ultrasound-assisted system than the mechanically agitated one. This is yet more proof of the synergism between the mechanism of ultrasound and PTA – which is corroborated by the conclusions reported by Hagenson et al.¹¹

(3) Reduction in DBT oxidation at elevated static pressure, which is evident from the comparison of the results of categories B.2 and C.1, is attributed to suppression of the transient cavitation phenomenon at elevated static pressure, as subsequently explained in greater detail.

Fig. 5 Time profiles of DBT oxidation in the different experimental categories. (A) Categories A.1 (MS + PFA) and A.2 (US + PFA). (B) Categories B.1 (MS + PFA + TBAB), B.2 (US + PFA + TBAB) and C.1 (US + PFA + TBAB at elevated static pressure). Temperature of reaction: mechanically stirred (MS) systems = 333 K, and ultrasound-assisted (US) systems = 313 K.

4.2 Arrhenius and thermodynamic analysis

The kinetic analysis of the DBT oxidation reactions at different temperatures (viz. 303, 313, 323, and 333 K) in the various experimental categories using the pseudo-1^st order model (eqn (16)) is presented in Fig. S4A.1–D.1 in the ESI.† The corresponding Arrhenius plots are shown in Fig. S4A.2–D.2 in the ESI.† The Arrhenius and thermodynamic parameters of the oxidative desulfurization in the different experimental categories are summarized in Table 2A and B, respectively. The characteristic variations in the Arrhenius parameters evident from results presented in Table 2A are as follows:

(1) Use of PTA in the mechanically stirred system reduces the activation energy of oxidative desulfurization, as can be observed from comparison of the activation energies in categories A.1 and B.1. This result is in concurrence with the observations of Zhao et al.¹⁶

(2) The ultrasound-assisted systems (categories A.2 and B.2) have significantly lower activation energies compared to the mechanically stirred systems (categories A.1 and B.1, respectively). Moreover, it is interesting to note that the use of PTA in the ultrasound assisted desulfurization systems leads to an increase in activation energy, as can be seen from the Arrhenius parameters for categories A.2 and B.2.

(3) The frequency factors for the ultrasound assisted systems (categories A.2 and B.2) are one to two orders of magnitude smaller than for the mechanically stirred system (categories A.1 and B.1). The use of PTA with ultrasound leads to a rise in the frequency factor, as is evident from comparison of the frequency factors for categories A.2 and B.2.

(4) Scatter of the data points in the Arrhenius plots and the low regression coefficients in Fig. S4B.2 and S4D.2† (corresponding to the systems with ultrasound) are attributed to the inverse effect of temperature on the intensity of transient cavitation. Both the physical and chemical effects of cavitation diminish with increasing temperature. The reason underlying this effect is large evaporation of solvent vapor (due to high vapor pressure) and subsequent entrapment in the bubble at elevated temperature. The entrapped vapor “cushions” the transient collapse of the cavitation bubble. This causes reduction in the intensity of the collapse (the peak temperature and pressure reached in the bubble) and also the physical/chemical effects associated with it. Consequently, the rates of the reactions that are accelerated by the physical/chemical effects of cavitation also reduce with temperature. This phenomenon violates the postulation of an increase in the rate of reaction with temperature in the Arrhenius theory. Therefore, the kinetic data of the ultrasound-assisted reactions (in the present context experimental categories A.2 and B.2) show scatter when fitted to the Arrhenius model leading to low regression coefficients as can be seen in Fig. S4B.2 and S.4D.2 in the ESI.† However, despite this limitation, the trends in the Arrhenius parameters obtained for the different experimental categories reveal a physically meaningful picture of the mechanism of PTA-assisted ultrasonic oxidative desulfurization.

Table 2 Arrhenius and thermodynamic analysis of PTA-assisted oxidative desulfurization^a

(A) Kinetic and Arrhenius analysis
Experimental category	Parameter	Temperature (K)				Ea (kJ mol^−1)	A (mol L^−1 min^−1)
		303	313	323	333
a Notation: k – pseudo-1^st order kinetic constant (min^−1), R^2 – regression coefficient, Ea – activation energy (kJ mol^−1), and A – frequency factor or pre-exponential factor (mol L^−1 min^−1).
MS + PFA	k (min^−1)	1.12 × 10^−3	2.63 × 10^−3	3.42 × 10^−3	4.20 × 10^−3	38.74	5805.14
	R^2	0.92	0.97	0.94	0.95
US + PFA	k (min^−1)	4.40 × 10^−3	6.10 × 10^−3	5.80 × 10^−3	5.59 × 10^−3	5.96	0.052
	R^2	0.95	0.94	0.96	0.96
MS + PFA + TBAB	k (min^−1)	6.70 × 10^−3	9.80 × 10^−3	1.22 × 10^−2	2.02 × 10^−2	29.52	805.93
	R^2	0.95	0.96	0.97	0.97
US + PFA + TBAB	k (min^−1)	1.80 × 10^−2	4.26 × 10^−2	3.67 × 10^−2	3.59 × 10^−2	16.43	15.96
	R^2	0.92	0.97	0.98	0.95

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(B) Thermodynamic analysis
Experimental category	Thermodynamic property
	ΔH (kJ mol^−1)				−ΔS (kJ mol^−1 K^−1)				ΔG (kJ mol^−1)
	Temperature
	303 K	313 K	323 K	333 K	303 K	313 K	323 K	333 K	303 K	313 K	323 K	333 K
(A.1) MS + PFA	36.22	36.13	36.05	35.97	0.22	0.21	0.22	0.22	101.96	102.92	105.57	108.34
(A.2) US + PFA	3.44	3.36	3.28	3.91	0.31	0.31	0.31	0.31	98.23	100.72	104.14	107.55
(B.1) MS + PFA + TBAB	27.00	26.91	26.83	26.75	0.23	0.23	0.23	0.23	97.12	99.47	102.15	104.00
(B.2) US + PFA + TBAB	13.91	13.82	13.74	13.67	0.27	0.26	0.27	0.27	94.68	95.65	99.23	102.40

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The trends in the thermodynamic parameters that can be identified from the results presented in Table 2B are as follows: (1) the use of PTA in mechanically stirred systems leads to a reduction in ΔH and ΔG and an increase in −ΔS. (2) The use of PTA in ultrasound assisted systems shows rather the opposite trend in that ΔH increases, while −ΔS and ΔG reduce in the presence of PTA. (3) Compared to mechanically stirred systems, the ΔH and ΔG values for ultrasound-assisted systems are significantly smaller, while −ΔS values are higher.

4.3 Results of cavitation bubble dynamics simulations

A summary of the results of cavitation bubble dynamics simulations for a 5 micron air bubble in toluene are presented in Table 3. Representative graphical simulations of the radial motion of the cavitation bubble are shown in Fig. S5 and S6 in the ESI.† It can be seen that the temperature and pressure conditions in the cavitation bubble reach an extreme during transient collapse at static atmospheric pressure, which are sufficient to cause thermal dissociation of N₂, O₂ and toluene (C₆H₅–CH₃) molecules entrapped in the bubble into numerous chemical species – some of which are radical species. The predominant species generated during transient cavitation, which can contribute to DBT oxidation, is the O˙ radical. Shock waves with high pressure amplitude emitted by the cavitation bubble can create a very fine emulsion of the aqueous/organic phases with an enormous interfacial area, which can boost the reaction kinetics.

Table 3 Summary of the simulations of cavitation bubble dynamics^a

a Data reproduced from ref. 14.
Species	Toluene
	Air bubble	Air bubble
	Ro = 5 μm	Ro = 5 μm
	Po = 101.3 kPa	Po = 162 kPa
	Tmax = 4835 K	Tmax = 1076 K
	Pmax = 961 MPa	Pmax = 80.25 bar
	Vturb = 0.15 m s^−1	Vturb = 0.014 m s^−1
	PAW = 30.20 MPa	PAW = 0.69 bar
	xN2 = 0.79	xN2 = 0.79
	xO2 = 0.21	xO2 = 0.21
	xTOL = 2.77 × 10^−6	xTOL = 4.91 × 10^−7
Equilibrium mole fraction
N2	7.11 × 10^−1	7.90 × 10^−1
O2	1.25 × 10^−1	2.10 × 10^−1
O	2.05 × 10^−2	—
O3	3.80 × 10^−5	—
N	1.91 × 10^−4	—
N3	3.82 × 10^−6	—
NO	1.41 × 10^−1	7.60 × 10^−5
NO2	2.27 × 10^−3	2.18 × 10^−5
NO3	1.64 × 10^−6	—
N2O3	1.14 × 10^−6	—
N2O	7.41 × 10^−4	—
CO	1.23 × 10^−6	—
CO2	2.18 × 10^−6	—
OH	3.37 × 10^−6	—
H2O	—	—
HO2	—	—
H2O2	—	—
HNO2	—	—

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Raising of the static pressure in the reaction mixture results in a drastic reduction of the physical and chemical effects of transient cavitation. Not only do the temperature and pressure peaks generated at transient bubble collapse drop sharply, but the magnitudes of shock waves (or acoustic pressure waves) and micro-turbulence generated by the bubble also show marked reduction. Moreover, no formation of any radical species is seen from the thermal dissociation of the bubble contents at the moments of transient collapse at elevated static pressure.

4.4 Discussion

Concurrent analysis of the DBT oxidation in different experimental categories, simulations of cavitation bubble dynamics, and the trends in Arrhenius and thermodynamic parameters give an interesting mechanistic account of the PTA-assisted oxidative desulfurization as described below:

(1) Mechanical agitation of the reaction mixture at 300 rpm generates a limited interfacial area, which results in low (∼28.3%) DBT oxidation. The PTA cation forms a complex with the oxidant anion, which is transported across the interphase. After completion of the oxidation reaction in the organic phase, the PTA–cation returns to the aqueous phase. The chemical mechanism of PTA-assisted oxidative desulfurization with mechanical agitation is depicted in Scheme S1 in the ESI.† It could be perceived from Scheme S1† that the process has purely ionic character. The addition of PTA to this system enhances DBT oxidation by more than 2× as a result of faster and more effective transfer of oxidant across the interface. This is reflected in the reduction of the activation energy of the oxidative desulfurization, as pointed out by Zhao et al.¹⁶ For the same reason, the net enthalpy change (ΔH) for oxidative desulfurization also reduces with the use of PTA.

(2) Despite very low activation energy and intense emulsification, the extent of DBT oxidation in the ultrasound assisted system (category A.2) is almost same as that for the mechanically agitated system (category A.1). This result is attributed to a radical based mechanism of ultrasound-assisted oxidative desulfurization (as shown in Scheme S2 in the ESI†). The oxidative radicals (O˙) generated by transient bubble collapse are highly unstable and do not diffuse or penetrate much in the reaction medium from the point of bubble collapse. Hence, the probability of their interaction with DBT molecules is rather limited, which is reflected in the low value of the frequency factor (A) compared to the mechanically agitated system (category A.1), and low DBT oxidation. Nonetheless, since O˙ radicals are extremely energetic species (with an oxidation potential of 2.42 eV), the activation energy for the DBT oxidation induced by these species is quite small. For the same reasons, ΔH for category A.2 is much smaller than that for category A.1.

(3) With the simultaneous use of PTA and ultrasound (as in categories B.2 and C.1), the chemical mechanism of the oxidative desulfurization has dual character, viz. ionic and radical. The cation of PTA forms a complex with the anion of the oxidant. This reduces the polarity of the oxidant anion, which assists its effective transfer across the interface to the non-polar organic phase. It should however be noted that complexation of the oxidant–anion with PTA–cation does neutralize the polarity of the latter, and hence, the overall mechanism of oxidative desulfurization still has ionic character. On a comparative basis, the process of complex formation between PTA–cation and oxidant–anion, the transfer of this complex across the interface and the reaction between the oxidant and DBT molecules, requires higher activation energy than the radical-induced DBT oxidation within the organic phase. However, as the amount of oxidant and PTA present in the system is in large excess compared to DBT (more specifically 1.24 mM of PTA, 25 mM of PFA oxidant, and 0.54 mM of DBT), the contribution of PTA-based oxidation to the overall DBT oxidation is much higher than radical-induced oxidation. Thus, the chemical mechanism of PTA-assisted ultrasonic oxidative desulfurization is predominantly ionic, which is manifested in terms of a higher activation energy compared to ultrasonic oxidative desulfurization. An explanation for the ∼4× higher ΔH value for category B.2 compared to category A.2 can also be given along similar lines. Due to the contribution of radical-induced reactions to the overall DBT oxidation in category B.2, the activation energy for this category is ∼2× less than that for category B.1, in which PTA is applied with mechanical stirring. The role of ultrasound and cavitation in experimental categories B.2 and C.1 is more or less of a physical nature, i.e. emulsification between the organic and aqueous phases.

(4) The reduction in the intensity of transient cavitation at elevated static pressure in category C.1, as indicated by the results of the simulation of cavitation bubble dynamics, is manifested in terms of less emulsification and interfacial area, compared to category B.2. The physical and chemical effects of transient cavitation are practically eliminated at elevated static pressure. This causes significant reduction in the intensity of micro-convection in the reaction system, which in turn, adversely affects emulsification and interfacial area. In this case, the ultrasonic system resembles a mechanically stirred system (as in category B.1). This essentially results in lower DBT oxidation in category C.1. However, the micro-streaming induced by ultrasound (which remains unaffected by the elevated static pressure) generates finer emulsion between the phases, compared to (macroscopic) mechanical stirring. The addition of PTA to the reaction system further boosts the extent of DBT oxidation. The beneficial effect of these two factors is manifested in significantly higher (>2×) DBT oxidation, compared to categories A.1 and A.2.

(5) The entropy change values (−ΔS) in the different experimental categories are again manifestations of the predominant chemical mechanism of oxidative desulfurization. The highest −ΔS values are seen for category A.2, in which the chemical mechanism for oxidative desulfurization is purely radical-based and reactions occur almost instantly. The −ΔS values for mechanically stirred systems increase with the addition of PTA, indicating faster reactions. The −ΔS values for category B.2 are intermediate between those of categories B.1 and A.2, indicating the dual (ionic and radical induced) nature of the chemical mechanism of the PTA-assisted oxidative desulfurization. The dual nature of the chemical mechanism in category B.2 also results in pseudo-1^st order kinetics constants of intermediate value between the constants for categories A.2 and B.1.

(6) Despite significantly dissimilar chemical mechanisms that lead to dissimilar values of ΔH and −ΔS, the Gibbs energy change (ΔG) is similar (±5%) for experimental categories B.1 and B.2, in which PTA was simultaneously applied with ultrasound. This essentially is an indication of the physical role played by ultrasound in PTA assisted oxidative desulfurization. Moreover, lower ΔG values for categories B.1 and B.2, compared to categories A.1 and A.2, respectively, point to a supportive effect of the PTA in the enhancement of the oxidative desulfurization through effective interphase transport of the oxidant anion.

5. Conclusion

Concurrent analysis of the extent of DBT oxidation and the Arrhenius and thermodynamic parameters for different experimental conditions, and the results of simulations of cavitation bubble dynamics presented in this study has revealed a cogent and coherent picture of the physical mechanism of the PTA-assisted ultrasonic oxidative desulfurization process. Essentially, this study has identified and established the links (or interactions) between the individual mechanisms of PTA and ultrasound/cavitation in the oxidative desulfurization process. Although ultrasonic oxidative desulfurization has the lowest activation energy and enthalpy change with the highest negative entropy change, the overall DBT oxidation achieved in this process is lower due to the low frequency factor, which is a consequence of high instability of the radicals generated by transient cavitation. Thus, the contribution of the chemical effect of transient cavitation to DBT oxidation is relatively small. The predominant mechanism of PTA-assisted oxidative desulfurization is ionic, which results in relatively higher activation energy and enthalpy change compared to ultrasonic oxidative desulfurization. The synergistic effect of fine emulsification generated due to the physical effect of micro-convection induced by transient cavitation and ultrasound, and PTA-assisted effective interphase transport of the oxidant leads to almost complete conversion of DBT to DBT sulfone. It is thus established that the prevalent role of ultrasound and cavitation in the PTA-assisted ultrasonic oxidative desulfurization process is physical in nature which helps in boosting the beneficial effect of PTA for the enhancement of DBT oxidation.

Acknowledgements

The authors would like to thank Mr Pritam Kumar Dikshit for his help in manuscript preparation.

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Footnote

† Electronic supplementary information (ESI) available: The following supplementary materials have been provided with this manuscript: (1) schematic diagram of the experimental setup, (2) preliminary experiments for determination of the composition of the reaction mixture, (3) model equations and thermodynamic data for cavitation bubble dynamics, (4) experimental categories with the exact composition of the reaction mixture, (5) kinetic analysis of oxidative desulfurization under ultrasound treatment and mechanical stirring using performic acid as oxidant coupled with TBAB as a phase transfer agent, (6) simulations of radial motion of a 5 micron air bubble in toluene at elevated static pressure, (7) simulations of radial motion of a 5 micron air bubble in toluene at atmospheric static pressure, (8) reaction mechanism for only ultrasound assisted oxidative desulfurization and PTA-assisted ultrasonic oxidative desulfurization. See DOI: 10.1039/c5ra12178g

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