Journal of Environmental Chemical Engineering 2 (2014) 780–787

Cyclic reaction network modeling for the kinetics of photoelectrocatalyticdegradation

Rahul Shukla, Giridhar Madras *

Department of Chemical Engineering Indian Institute of Science, Bangalore, India

A R T I C L E I N F O

Article history:

Received 19 December 2013

Accepted 30 January 2014

Keywords:

External bias

Photoelectrocatalysis

Network model

Synergy

Degradation

A B S T R A C T

Among various advanced oxidation processes (AOPs) employed for the destruction of pollutants,

photocatalysis has witnessed a tremendous development over the past two decades. Studies have

reported the recombination of valence band holes and conduction band electron as a barrier in achieving

higher degradation rate. To avoid recombination, an external bias can be applied to keep the charge

carriers i.e. holes and electron separated. The present work investigates the synergistic effect of

photocatalysis and electrocatalysis. A reaction network model is also developed for obtaining better

insights of underlying complex processes. To validate the model, experiments were carried out for the

anionic dyes with combustion synthesized TiO2 as catalyst. The model has shown good agreement with

the experimental findings. Loop coefficients were calculated in each case to have an estimate of hydroxyl

radicals formed. Synergy, which is defined on the basis of first order rate constants, was observed in all

cases of photoelectrocatalysis and increased with applied bias.

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Introduction

Synthetic dyes are widely used in many industries such astextile, leather, and paper production. The annual dye productionexceeds 7 � 105 tons [1–3]. In order to protect the environmentfrom serious threats of organic pollutants such as dyes, agrowastes, volatile organic compounds, detergents and surfactants,photocatalysis has been used over the past two decades [4]. Theadvantage of photocatalysis is the destruction of pollutant ratherthan its transfer to another media [5–11]. Essentially being anoxidation process, it exhibits the use of hydroxyl radicals (OH�)which has higher oxidation potential (2.8 V) as compared to atomicoxygen (2.42 V), ozone (2.07 V), hydrogen peroxide (1.78 V),permanganate (1.67 V) [1,12,13]. Moreover, these oxidizingagencies destruct partially and can cause secondary pollution [3].

The mechanism of photocatalysis illustrates that recombina-tion of valence band hole and conduction band electron not onlyreduces the formation of hydroxyl radical but the heat generatedalso leads to desorption at the occupied sites [10,14–17]. Therecombination can take place at surface or in volume [18]. To

* Corresponding author. Tel.: +91 80 22932321; fax: +91 80 23601310.

E-mail addresses: giridhar@chemeng.iisc.ernet.in, giridharmadras@gmail.com

(G. Madras).

2213-3437/$ – see front matter � 2014 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.jece.2014.01.024

improve the removal rate of organics from wastewater, thecoupling of photocatalysis with other AOPs such as sonocatalysis,ozonation, electrocatalysis, Fenton and membrane processes hasbeen extensively studied [19–24]. Electrocatalysis coupled withphotocatalysis ensures the separation of photogenerated chargecarriers by the application of external bias [25,26]. In order tominimize the recombination rate (and hence increase the lifetime),photoelectrocatalysis (PEC) is a convincing strategy. The externalbias navigates the conduction band electron either to a non-photoactive electrode (counter electrode such as Pt) through a wireor from a surface site to a point, where an electron acceptor can bereduced [27,28]. The idea of increased recombination lifetimewhen the charge carriers are separated efficiently has beenproposed [29].

In a recent study, the mechanism of photocatalysis andphotoelectrocatalysis is elucidated with a special emphasis onthe effect of cocatalyst [30]. Shang et al. have examined electric-agitation-enhanced photodegradation of rhodamine blue usingplanar ITO/TiO2/ITO device at 1.5 V bias [25]. The increased rateconstant for phenol degradation with potential has also beenreported [31]. The problem of low efficiency involved in designingreactor for wastewater remediation and the use of tungstenelectrode has been suggested [32]. The coupling of photoelec-trocatalysis with cationic exchange membrane processes hasshown enhanced reduction of Cr (VI) and improved oxidation of

R. Shukla, G. Madras / Journal of Environmental Chemical Engineering 2 (2014) 780–787 781

EDTA [33]. A slurry reactor has also been used to carry out the PECin which the catalyst is taken in the suspension form [34,35].

The present work examines the degradation of different classesof anionic dyes like Orange G (mono azo), Indigo carmine (indigo),Alizarine cyanine green (anthraquinonic), Amido Black (AB) andMethyl Blue (triaryl methane) using combustion synthesized TiO2

as catalyst in slurry reactor. We have investigated the synergisticeffect of photocatalysis and electrocatalysis. A network model isalso proposed, which reflects the general kinetics of degradationprocess. Thus, an integral form of rate expression obtained wasused to interpret the concentration variation during electrocata-lysis (EC), photocatalysis (PC) and photoelectrocatalysis (PEC)process for each dye.

Experimental

Materials

Analytical grade titanium tetra isopropoxide (TTIP – Alfa Aesar),glycine (H2N-CH2-COOH – S.D. Fine Chemicals), nitric acid (HNO3 –Merck India) were used for catalyst synthesis as received. The dyes,alizarine cyanine green (ACG), methyl blue (MB), were obtainedfrom Merck, India and orange G (OG), amido black (AB) from S.D.Fine Chemicals, India and indigo carmine from Rolex labs, India. Allchemicals were used without any further purification. Doubledistilled Millipore filtered water (0.22 mm) was used for allpurposes.

Preparation of catalyst

Nano size anatase TiO2 was synthesized by solution combustionmethod [36–38]. In the typical synthesis process, 20 mL of TTIPwas mixed with 80 ml cold distilled water under vigorous stirring.White precipitate of titanium hydroxide was separated and then

Fig. 1. Schematic of experimental set

mixed with 1:2 nitric acid (by volume) till it gets completelydissolved. Resulting transparent solution is titanyl nitrate withsmall quantity of unreacted reactants.

Based on the concentration of titanyl nitrate in the solution, thestoichiometric amount (to maintain oxidizer to fuel ratio 1) ofglycine (fuel) required for 100 mL of aqueous solution of titanylnitrate (oxidizer) was 0.7346 g. The reaction is as follows

9TiOðNO3Þ2ðaqÞ þ 10C2H5O2NðaqÞ �!350 �C

9TiO2ðgÞ þ 14N2ðgÞ

þ 20CO2ðgÞ þ 25H2OðgÞ (1)

The stoichiometric amount of oxidizer and fuel was kept at350 8C in a preheated furnace for 10 min. The combustion wassmoldering type. The product was ground to obtain a fine powderof anatase TiO2 (CS TiO2).

Degradation experiment

The schematic diagram of set up as shown in Fig. 1, consists ofan UV radiation lamp (125 W, Philips, India) surrounded by quartztube (3.8 cm i.d. � 4.5 cm o.d. � 21 cm height). Another quartzbeaker (4.5 cm i.d. and 7.5 cm height) contains the dye solutionand kept in front of UV lamp. The electrocatalysis, photocatalysisand photoelectrocatalysis were carried out separately with thehelp of switches K1 and K2.

Each dye was dissolved in water and degraded at its natural pH soas to avoid the effect of externally added anions or cations. The initialdye concentration was 50 mg L�1 and catalyst concentration was1 g L�1 in all the experiments. The dye solution was kept in dark for30 min in the presence of catalyst to attain adsorption–desorptionequilibrium. All degradation experiments were carried out for amaximum of 2 h. In order to avoid heating, water was circulatedthrough the lamp jacket. The solution was continuously stirred at600–700 rpm to maintain the homogeneity throughout the solution.

up for degradation experiment.

R. Shukla, G. Madras / Journal of Environmental Chemical Engineering 2 (2014) 780–787782

The incident photon rate and intensity of UV lamp source wasdetermined by photolyzing 6 mM solution of potassium ferrioxalate.The calibration based on FeSO4 solution was used to analyze theformation of Fe2+ ion. The absorbance was monitored at 510 nm bycomplexing the solution with 1:10-phenanthroline monohydrate.The photon rate and UV lamp intensity was 2.11 � 10�7 EinsteinL�1 s�1 and 1.44 W m�2 respectively as calculated by potassiumferrioxalate actinometry [39].

The fluorine doped tin oxide (FTO) glass plate (working electrode– WE), platinum sheet (auxiliary or counter electrode – CE) andcalomel electrode (reference electrode – RE) were immersed in dyesolution and connected to Potentiostat (Techno Science, Bangalore).The potentiostat measures the voltage difference across workingelectrode and reference electrode and compares it with the presetvoltage. Based on the deviation from the set point, it forces thecurrent from counter electrode to the working electrode so as tooffset the difference between preset and existing voltage.

The samples were collected in vials at regular intervals of15 min for slow degrading dyes and at interval of 5 min for fastdegrading dyes. The aliquots were centrifuged to remove thecatalyst particles and the absorbance was measured using UV–visspectrophotometer at the characteristic wavelength (l) of the dye– orange G (l = 478 nm), indigo carmine (l = 610 nm), alizarinecyanine green (l = 640 nm), amido black (l = 618 nm) and methylblue (l = 600 nm). The absorbance was converted to concentrationusing a calibration curve. All experiments were repeated threetimes and the error in concentration was less than �1 mg L�1.

Network modeling

The overall photoelectrocatalytic degradation mechanism canbe explained by a network model, which includes contributionsfrom photocatalytic (PC) and electrolytic oxidation (EC). Thismodel is based on the investigation of sonophotocatalyticdegradation of dyes, where authors have coupled photocatalyticand sonocatalytic pathways to form a network to describe thedegradation kinetics [40]. A similar approach was used to describethe kinetics of photocatalytic degradation of methylene blue byWu and Chern [41]. However, such approaches have not beendeveloped for photoelectrocatalysis.

Adsorption–desorption

The first step is the adsorption of dye over the catalyst surfaceand the attainment of adsorption–desorption equilibrium.

TiO2 þ D @l01

l10

TiO2 � Dads (2)

Photocatalytic pathway (PC)

Charge – carrier generation

An electron hole pair is generated when UV radiation havingenergy equal to or greater than the band gap of a catalyst strikes it.This is because of the transfer of an electron from the valence bandto conduction band. These charge carriers i.e. e� and h+ canrecombine, if they do not transfer their charge to other species. Thisrecombination eventually turns up into decreased efficiency ofphotocatalytic process.

TiO2 � Dads þ IUV @l12

l21

TiO2ðe�cb; hþvbÞ � Dads (3)

Hydroxyl-radical generation

The following two pathways can produce hydroxyl radical.

Hole pathway

This pathway involves the oxidation of surface adsorbed watermolecules [reaction (4)] or hydroxyl ions [reaction (5)] by holesand thereby generates the hydroxyl radical.

TiO2ðhþvbÞ � Dads þ H2O�!l023

TiO2ðOH�Þads � Dads þ Hþ (4)

TiO2ðhþvbÞ � Dads þ OH��!l0023

TiO2ðOH�Þads � Dads (5)

Electron pathway

The electrons, promoted to conduction band when combinewith the oxygen, reduce later to form superoxide radical whichundergoes a series of reaction to form hydroxyl radicals.

TiO2ðe�cbÞ � Dads þ O2�!l00023

TiO2ðO2��Þ � Dads (6)

TiO2ðO2��Þads � Dads þ Hþ! TiO2ðHOO�Þads � Dads (7)

TiO2ðHOO�Þads � Dads þ Hþ! TiO2ðH2O2Þads � Dads (8)

TiO2ðH2O2Þads � Dads þ e�! TiO2ðOH�Þads � Dads þ OH� (9)

Fujishima et al. have described the necessity of balance in thesetwo pathways taking place in valence and conduction band as thephotocatalyst should not undergo any change [42].

Electrochemical pathway (EC)

The first step is the generation of adsorbed hydroxyl radicalsby the electrochemical oxidation in water discharge regime[reaction (10)]. Hydroxyl radicals produced by this reaction candecompose to give proton and an electron along with oxygenevolution [reaction (11)]. On the other hand at cathode, waterreduction yields hydroxyl ion along with hydrogen evolution[reaction (12)].

At anode

H2O þ EP�!k1 ðOH�ÞðEPÞ þ Hþ þ e� (10)

Where, EP represents the electrochemical potential.

ðOH�ÞðEPÞ�!k2O2 þ Hþ þ e� (11)

At cathode

H2O þ e��!k31=2H2 þ OH� (12)

Formation of adsorbed hydroxyl radicals

The hydroxyl radical produced during the electrochemicaloxidation [reaction (10)] combines with the dye adsorbed TiO2 bythe following reaction,

TiO2 � Dads þ ðOH�ÞðEPÞ�!l13TiO2ðOH�Þads � Dads (13)

Degradation of dye by hydroxyl radical

In the final step surface adsorbed hydroxyl radicals react eitherwith surface adsorbed dye or dye in bulk to produce carbon dioxideand water.

TiO2ðOH�Þads � Dads þ TiO2

� Dads=D�!l30IntermediateðPÞ ! CO2 þ H2O (14)

Fig. 3. Reduction of multipath cyclic network to a single network (a) Introduction of

loop coefficient in photocatalysis and (b) Coupling of EC and PC pathways.

ental Chemical Engineering 2 (2014) 780–787 783

The rate equation for hydroxyl radicals generated in theelectrochemical pathway [reactions (10) and (11)] is given as

dðOH�ÞðEPÞ

dt¼ k1ðEPÞ � k2ðOH�ÞðEPÞ (15)

Because of the very short life time of hydroxyl radicals, pseudosteady state approximation (PSSA) can be applied to estimateequilibrium concentration of generated hydroxyl radicals throughthe electrochemical pathway.

ðOH�ÞðEPÞh i

¼ KðEPÞ (16)

where, K ¼ k1=k2

Thus, the production of hydroxyl radical from the electrochem-ical pathway solely depends on the applied electric potential (EP).

Derivation of network model

To deal with this large set of chemical reactions, a cyclicnetwork was developed which preserves whole information. Fig. 2shows a multipath cyclic network which begins from X0. The Xi

represents the different species playing role in chemical reactions.Each arrow represents a reaction over which pseudo first order rateconstants (li j) are written; subscript ‘i’ stands for main reactantand ‘j’ stands for main product. Pseudo rate constants are theproduct of rate constant and co-reactant concentration. The co-reactant and co-product are written over the branches coming inand going out respectively. Primed superscripts accounts fordifferent mechanisms which yield same product from samereactant.

The generation of hydroxyl radical by hole and electronpathways can be combined to a single step by introducing a loopcoefficient L23 (Fig. 3(a)). The adsorbed hydroxyl radical generatedby PC and EC pathways are coupled and reduced into a single stepin Fig. 3(b).

A network containing ‘m’ number of paths can be reduced intosingle step by using loop coefficients defined as [43],

Li j ¼Xm

k¼1

LðkÞi j ; L ji ¼Xmk¼1

LðkÞji (17)

R. Shukla, G. Madras / Journal of Environm

Fig. 2. Cyclic reaction network – inner cycle (solid curves) represents photocatalytic

(PC) pathway and the outer cycle (dashed curve) represents electrochemical (EC)

pathway. The inner cycle (dashed) encloses hole mediated oxidation and electron

mediated reduction steps and also shows the merging of electron and hole

pathways.

where L is the segment coefficient, and expressed as

L jk ¼

Yk�1

i¼ j

li;iþ1

D jk; Lk j ¼

Yk�1

i¼ j

liþ1;i

D jk(18)

where l is the pseudo first order rate coefficient (product of theactual rate coefficient and the co-reactant concentration) and Djk isdefined as,

D jk ¼Xk

i¼ jþ1

Yi�1

m¼ jþ1

lm;m�1

Yk�1

m¼i

lm;mþ1

0@

1A (19)

The pseudo first order rate coefficients for each step are asfollows,

l01 ¼ k01 CD½ �; l10 ¼ k10 (20)

l12 ¼ k12IUV ; l21 ¼ k21 (21)

l023 ¼ k023; l0023 ¼ k0023; l00023 ¼ k00023 (22)

l13 ¼ k13ððOH�ÞðEPÞÞ ¼ k13KðEPÞ (23)

l30 ¼ k30 (24)

where CD denotes dye concentration.

Fig. 4. Degradation of orange G under EC, PC and PEC at (a) 1.5 V, (b) 2 V and (c)

2.5 V. The inset shows first order fit.

R. Shukla, G. Madras / Journal of Environmental Chemical Engineering 2 (2014) 780–787784

Introduction of loop coefficient in PC pathway

In PC pathway, the OH radicals generated by the holes (throughhydroxyl ions and water molecules) and electrons can be reducedto a single step by using loop coefficient L23 (Fig. 3(a)). The loopcoefficient is calculated by Eq. (17)

L23 ¼ l0

23 þ l00

23 þ l000

23 (25)

Reduction of PC and EC pathway into a single step

The formation of intermediate X3 (surface hydroxyl species) bythe PC and EC pathways from the X1 (dye adsorbed TiO2) is reducedinto single step by loop coefficient L13 (Fig. 3b).

L13 ¼ LPC13 þ LEC

13 (26)

where

LPC13 ¼ Segment coefficient of PC pathway ¼ l12L23

l21 þ L23(27.1)

LEC13 ¼ Segment coefficient of EC pathway ¼ l13 (27.2)

are obtained with the help of Eq. (18). Combining equations(21–27),

L13 ¼ kPCIUV þ kECðEPÞ (28)

Where,

kPC ¼k12ðl023 þ l0023 þ l00023Þ

k21 þ ðl023 þ l0023 þ l00023Þ; kEC ¼ k13K (29)

For a single cycle network, the rate expression is given by

r ¼

Yn

i¼0

li;iþ1 �Yn

i¼0

liþ1;i

!

Xn

i¼0

Dii

½XT � ; ðIndex n þ 1 ¼ 0Þ (30)

where, [XT] is the catalyst concentration and Dii is obtained from asquare matrix of order ‘n’. The square matrix is constructed bybreaking the cyclic network into a linear one or else by the use ofEq. (19).

The final rate expression is given according to Eq. (30)

r ¼ l01L13l30

D00 þ D11 þ D33½TiO2� (31)

D00 ¼ L13l30 þ l10l30 (32.1)

D11 ¼ l01l30 (32.2)

D33 ¼ l01L13 (32.3)

Combining Eqs. (21–25, 31) and (32)

� dCD

dt

� �¼ k01L13k30½TiO2�CD

ðL13 þ k10Þk30 þ ðL13 þ k30Þk01CD(33)

Integrating the above equation with initial condition, CD = CD0 att = 0, (CD0 is the initial dye concentration) gives the finalexpression,

AðCD0 � CDÞ þ lnCD0

CD

� �¼ Bt (34)

Where,

A ¼ k01ðL13 þ k30Þk30ðL13 þ k10Þ

(35.1)

B ¼ k01L13k30½TiO2�k30ðL13 þ k10Þ

(35.2)

k01 = adsorption rate constant, k10 = desorption rate constant,L13 = Loop coefficient to account for generation of hydroxyl radicalsvia EC and PC pathways, k30 = rate of reaction of hydroxyl radicalswith dye molecules.

The constants A and B given in Eq. (35) can be reduced to,

A ¼ ðL13=k30 þ 1ÞðL13=k01 þ 1=KÞ (36.1)

R. Shukla, G. Madras / Journal of Environmental Chemical Engineering 2 (2014) 780–787 785

B ¼ L13½TiO2�ðL13=k01 þ 1=KÞ (36.2)

where

K ¼ Equilibrium rate constant ¼ k01=k10 (37)

The adsorption rate constant (k01) can be calculated from Bassuming that 1=K < < L13=k01 and L13 is calculated from A byassuming that L13 < < k30.

k01 ¼ B=½TiO2� (38)

L13 ¼ k01=A (39)

From Eqs. (37) and (38) we get

L13 ¼B

A½TiO2�(40)

Results and discussion

The electrocatalysis (EC), photocatalysis (PC) and photoelec-trocatalysis (PEC) of dyes OG, IC, ACG, AB, MB were carried out inthe presence of combustion synthesized TiO2 (CS TiO2). In dark, nosignificant adsorption of dye over catalyst was observed. Theabsorbance, as measured by UV–vis spectrophotometer after30 min adsorption in dark was considered to be initial absorbancefor 50 ppm of dye.

Effect of applied potential

Fig. 4 shows that the degradation caused by EC and PECincreases, as the applied bias increases. It can be seen that theoverall degradation follows the order: EC (1.5 V) < EC (2 V) < EC(2.5 V) PC < PEC (1.5 V) < PEC (2 V) < PEC (2.5 V). This findingcan be attributed to the fact that increased potential offers moredriving force for the electron in valence band to migrate intoconduction band. This results in generation of higher number ofcharge carriers, which are the precursors of degradation. Moreover,the inset of Fig. 4(C) shows that the initial rate of degradation byelectrocatalysis is more than photocatalysis. The degradationcaused by PEC was higher than PC at all voltages. This is consistentwith the fact that external bias reduces the recombination ofphotogenerated excitons [44]. Synergy as defined by Eq. (41) is

Table 1First order rate constants, model fitted parameters, loop coefficients and synergy for d

Dye Mechanism Voltage (V) Rate constant � 102 (min�1) A

OG PC 0.24 10

EC 1.5 0.11 2

PEC 0.43 8

EC 2 0.20 8

PEC 0.77 0

EC 2.5 0.32 18

PEC 1.01 0

IC PC 7.71 0

EC 2.5 0.99 0

PEC 11.4 0

ACG PC 1.74 0

EC 2.5 0.43 0

PEC 3.19 0

AB PC 1.53 6

EC 2.5 0.41 68

PEC 2.54 1

MB PC 2.18 0

EC 2.5 0.31 1

PEC 3.78 0

observed at all voltages.

Synergy ¼ kPEC � ðkPC þ kECÞkPEC

� 100 (41)

where k is the rate constant based on the initial rates. We havechosen first order rate constant to define synergy as it is arepresentative parameter. Table 1 shows the value of the rateconstant for different dyes under various conditions. It alsoindicates that the synergy increases with voltage. A significantincrease in synergy from 19% to 43% was observed as the potentialincreased from 1.5 V to 2 V, while only a slight increase from 43% to45% as the potential was increased from 2 V to 2.5 V. This suggeststhat most of the recombination is overcome by 2 V bias. A similarfinding was reported for the degradation of rhodamine B (a cationicdye), wherein synergy increases up to a certain bias and thendecreases [25]. An increase in current density after certain valuedoes not enhance COD removal percentage [45]. In general, theoptimal voltage varies with the dye under consideration [44]. Asthe highest synergy is observed at 2.5 V, the other dyes were testedonly at this external bias.

Kinetics of photoelectrocatalytic degradation

Fig. 5 shows the concentration profile of various dyes. Amongthese dyes the degradation follows the order: AB < MB < ACG < ICfor PEC. So, indigo carmine is found to be fastest degrading dyeunder EC, PC and PEC [46]. It shows that the functional group ofdyes has significant impact on the degradation rate.

Effect of dye functional group on degradation rates

To correlate the degradation rates with dye structure, assess-ment of reactivity of azo, amino, nitro and sulfo groups attached toaromatic ring, their mutual interplay and their interaction withhydroxyl radical is required.

The cleavage of carbon sulfur bond depends on the bondstrength with which –SO3

� group is attached to carbon. Thereactivity for the formation of sulfate ions follows the order: –SO3

�

attached to benzene ring >–SO3� attached to naphthalene ring

[13]. Therefore, ACG undergoes higher degradation rate whencompared with AB.

The initial rate as well as total degradation of OG (mono azo)was found to be less than AB (di azo) in all three cases as evident byrate constant enlisted in Table 1 and concentration profiles

ifferent dyes.

� 102 (L mg�1) B � 102 (min�1) L13� 102 (min�1) Synergy (%)

.0 1.80 0.018

.50 0.27 0.010 19

.20 2.37 0.028

.10 0.91 0.011 43

.57 0.88 0.154

.0 3.00 0.016 45

.39 1.03 0.264

.15 9.74 6.493 24

.10 0.72 0.720

.08 11.8 14.75

.80 2.96 0.370 32

.20 0.44 0.220

.80 4.07 0.508

.07 7.46 0.122 24

.8 10.6 0.015

.43 2.28 0.159

.47 2.37 0.504 34

.15 0.62 0.054

.40 3.64 0.910

Fig. 5. Concentration variation of (a) indigo carmine, (b) alizarine cyanine green, (c) amido black and (d) methyl blue under EC-2.5 V, PC and PEC. The inset shows first order fit.

The solid curves represent the network model fitting.

R. Shukla, G. Madras / Journal of Environmental Chemical Engineering 2 (2014) 780–787786

[Figs. 4(c) and 5(c)]. The cleavage in the vicinity of azo bond, wherenitrogen is present in +1 oxidation state leads to the formation ofN2, where nitrogen is present in zero oxidation state. In the case ofAB, this breakdown of molecule is facilitated by simultaneousoxidation of ammonium (N in -3 oxidation state) and nitro group(N in +3 oxidation state) to NO3

� (N in +5 oxidation state) [13]. Asimilar finding has been reported for photocatalytic degradation ofAB and OG [47].

The fastest degradation of indigo carmine is due to the fact thatintra-molecular hydrogen bonds (–O� � �H–) of indigo are replacedby intermolecular hydrogen bonds with water, which leads to theloss of molecular planarity followed by reduced barrier tomolecular breakdown [48].

Network model fitting

The data points were fitted in the integral form of model(Eq. (34)). The fitted curve is in agreement with the data (R2 > 0.98)for all the dyes. Model equation suggests that the parameter Aaccounts for the contributions due to the zero order rate. The closeinspection of Table 1 reveals that value of parameter A is large forthe EC and PC as compared to PEC for all the dyes.

The differential form of model equation in terms of parametersA and B is as follows:

� dCD

dt

� �¼ BCD

1 þ ACD

The large value of A indicates the reduction of degradationrates. Theoretically, application of bias reduces recombination andthat effect can be seen on parameter A mathematically. Biassuppresses the value of this parameter and thereby enhances therate. This suggests that application of bias reduces the zero ordercontributions. Parameter B is not seen to follow a particular trendsuggesting the kinetics is more sensitive to the values of A. The loop

coefficients (L13) are calculated using Eq. (40) and listed in Table 1,where the concentration of TiO2 was taken to be 1 g L�1. Thisparameter accounts for the formation of hydroxyl radical duringEC, PC and PEC. It can be seen that the loop coefficient increaseswith voltage in case of orange G degradation with EC as well as PEC.This finding validates Eq. (16), which states that the concentrationof hydroxyl ion is proportional to the applied potential in case ofelectrocatalysis. While for the case of photoelectrocatalysis, asexplained in mechanism [from Eqs. (4)–(13)], loop coefficientsshows that most of the charge carriers do participate in reactionleading to the formation of hydroxyl radicals. The rapid rate ofdegradation of dyes – IC, ACG, AB and MB is well captured by theloop coefficient values. This shows the versatility of the model overa range of dyes.

Conclusions

The current work shows the synergistic effect of photocatalyticand electrocatalytic degradation of anionic dyes. Synergism isfound to increase as the applied bias increases. The experimentaldata were used to validate the lumped parameter model, obtainedby reducing a cyclic reaction network. The model captures thedegradation of other dyes from different classes as well. Loopcoefficient which is closely related to the hydroxyl radicalformation, is higher in case of PEC as compared with PC or EC.This is in accordance with the fact that increased resistance torecombination of photoholes and photoelectrons can improve theefficiency of photocatalysis.

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