Nicolas Cimetiere

Florence Dossier-Berne

Joseph De
email: joseph.delaat@esip.univ-poitiers.fr

Monochloramination of Resorcinol: Mechanism and 1 Kinetic Modeling 2

Keywords: Monochloramine, Resorcinol, Rate constants, Chlorine. 24

The kinetics of monochloramination of resorcinol, 4-chlororesorcinol and 4,6-dichlororesorcinol have 10 been investigated over the pH range of 5 -12, at 23 ± 2 °C. Monochloramine solutions were prepared 11 with ammonia-to-chlorine ratios (N/Cl) ranging from 1.08 to 31 mol/mol. Under conditions that 12 minimize free chlorine reactions (N/Cl > 2 mol/mol), the apparent second-order rate constants of 13 monochloramination of resorcinol compounds show a maximum at pH values between 8.6 and 10.2. 14

The intrinsic second-order rate constants for the reaction of monochloramine with the acid-base forms of 15 the dihydroxybenzenes (Ar(OH) 2 , Ar(OH)O -and Ar(O -) 2 ) were calculated from the apparent second-16 order rate constants. The stoichiometric coefficients for the formation of 4-chlororesorcinol by 17 monochloramination of resorcinol and 4,6-dichlororesorcinol by monochloramination of 4-18 chlororesorcinol were found to be equal to 0.66 ± 0.05 and 0.25 ± 0.02 mol/mol, respectively at pH 8.6. 19

A kinetic model that incorporates reactions of free chlorine and monochloramine with the different acid-20 base forms of resorcinol compounds simulated well the initial rates of degradation of resorcinol 21 compounds and was useful in order to evaluate the contribution of free chlorine reactions to the overall 22 rates of degradation of resorcinol at low N/Cl ratios. 23

effective in preventing waterborne diseases caused by pathogenic microorganisms. However, reactions 27 of chlorine with natural organic matter (NOM) also lead to the formation of many disinfection by-28 products (DBPs) which can have adverse effects for human health. Since the pioneering works of Bellar 29 et al. [START_REF] Bellar | Occurence of organohalides in chlorinated drinking waters[END_REF] and Rook [START_REF] Rook | Formation of haloforms during chlorination of natural waters[END_REF], who demonstrated the formation of trihalomethanes (THMs), more than 600 30

DBPs have been identified in chlorinated drinking water [START_REF] Richardson | Disinfection by-products and other emerging contaminants in drinking water[END_REF]. Many utilities have adopted the use of 31 monochloramine as a secondary disinfectant in order to comply with the current or future regulations 32 concerning the concentrations of DBPs in drinking water [START_REF] Epa | Alternative Disinfectants and Oxidants Guidance Manual[END_REF]. 33 Monochloramine is produced by the reaction of hypochlorous acid with ammonia and is quantitatively 34 formed at ammonia-to-chlorine ratio (N/Cl) higher than 1 mol/mol at pH ≈ 8. In the practice of 35 monochloramination, monochloramine is prepared with a small excess of ammonia (N/Cl ≈ 1.1 -1.2 36 mol/mol) in order to minimize the formation of dichloramine and trichloramine and to prevent the 37 breakpoint reactions [START_REF] Jafvert | Reaction scheme for the chlorination of ammoniacal water[END_REF]. As compared to free chlorine, monochloramine is a weaker disinfectant and 38 produces less DBPs (6). Monochloramine is also used as a secondary disinfectant in order to obtain a 39 long lasting residual of disinfectant in the distribution systems because monochloramine is less reactive 40 with NOM than free chlorine. The decay of monochloramine in drinking water can be attributed to 41 autodecomposition reactions, direct reactions of monochloramine with NOM and indirect reactions with 42 NOM involving free chlorine formed from monochloramine hydrolysis (7). 43 The reactivity of monochloramine with simple organic compounds is not well-documented. Only a 44 few second-order rate constants for the reaction of monochloramine have been published (8-10). The 45 objective of this research was to determine the rate constant for the reaction of monochloramine with 46 resorcinol. It is well-known that chlorination of resorcinol leads to the formation of 0.9-0.95 mole of 47 chloroform per mole of resorcinol (11) and that polyhydroxybenzenic functional groups of NOM 48 contribute to the formation of THMs (12-14). The rate and the mechanism of chlorination of phenolic 49 compounds have been investigated by several researchers (15-16). In a detailed kinetic study of the 50 chlorination of dihydroxybenzenes (resorcinol, 4-chlororesorcinol and 4,6-dichlororesorcinol), Rebenne 51 acid-catalyzed reaction at pH < 4 and to a mechanism involving the reactions of hypochlorous acid 53 (HOCl) with the un-ionized and the ionized forms of resorcinol compounds. 54

The mechanism of monochloramination of resorcinol and of its chlorinated derivatives in water has 55 been thoroughly investigated by Heasley et al. ( 17), but the reaction rate constants are unknown. 56 Therefore, this work was undertaken to determine intrinsic second-order rate constants for the reaction 57 of monochloramine with the un-ionized and ionized forms of resorcinol, 4-chlororesorcinol and 4,6-58 dichlororesorcinol. The kinetic study of monochloramination of resorcinol and of its chlorinated 59 derivatives has been conducted within the pH range 5 to 12 and under conditions that minimize the 60 equilibrium concentration of free chlorine in solutions pf monochloramine. A kinetic model has also 61 been tested in order to simulate the formation and the decay of 4-chlororesorcinol and of 4,6-62 dichlororesorcinol and to evaluate the effect of the ammonia-to-chlorine ratio on the contribution of free 63 chlorine reactions to the degradation of resorcinol. 64

Experimental Section 65

Chemicals and Preparation of solutions. All solutions were prepared from reagent-grade chemicals 66 and purified water delivered by a Millipore system (Milli RX75/Synergy 185). Stock solutions of 67 resorcinol (R) (Sigma-Aldrich, ACS reagent, > 99 %), 4-chlororesorcinol (4-MCR) (Aldrich, 98 %), 4,6-68 dichlororesorcinol (4,6-DCR) (Aldrich, 97 %), ammonium chloride (Fisher Scientific, > 99%) and free 69 chlorine (NaOCl, 13 %, Acros Organics) were stored in the dark at 4 °C. 70 Solutions of monochloramine (0.1 to 4 mM) were prepared daily by slowly adding free chlorine into 71 an ammonium chloride solution in a well-stirred reactor and using a nitrogen-to-chlorine ratio ranging 72 adding 5 mL of a stock solution of monochloramine, under vigorous magnetic stirring, to 95 mL of a solution containing the dihydroxybenzene. At various time intervals, a 4 mL-sample of the solution was rapidly transferred into a 10 mL vial containing 1 ml of KI 1 M (Acros Organics, > 99 % for analysis) and 100 µL of acetic acid 1.7 M (Riedel-de Haën, 99 -100 %). After a reaction time of 2 or 3 minutes, the mixture was then transferred into a 1 cm-spectrophotometer quartz-cell and the concentration of triiodide ion was determined by measuring the absorbance at 351 nm (Shimadzu UVmini 1240 spectrophotometer). The concentration of monochloramine was calculated using a molar extinction coefficient of 2.69 x 10 4 M -1 cm -1 for I 3 -at 351 nm. This value which has been determined in the present work from calibration curves obtained from various standard solutions of chlorine and of monochloramine was consistent with values reported in literature (19-21).

It should be noted that the oxidation reaction of iodide ion by monochloramine is very fast, being complete within a few seconds. Furthermore, the UV absorbance measured at 351 nm was stable indicating that the liberated triiodide ion did not react with the organic solutes present in the solutions.

A few experiments were carried out at pH = 8.6 with a large excess of monochloramine

Results and Discussion

Determination of reaction rate constants. The reactions of monochloramine with organic solutes are assumed to follow second-order kinetics, first-order with respect to each reactant. In the case of a dihydroxybenzenic compound (Ar(OH) 2 ), the rate can be expressed as (eq 1):

-

dt ] ) OH ( Ar [ d tot 2 = - dt ] Cl NH [ d 2 = k app [NH 2 Cl] [Ar(OH) 2 ] tot (1)
where k app represents the apparent second-order rate constant and [Ar(OH) 2 ] tot , the sum of the concentrations of the three acid-base species of the dihydroxybenzene (Ar(OH) 2 , Ar(OH)O -, Ar(O -) 2 ).

Under conditions that minimize the contribution of free chlorine reactions to the oxidation of organic solutes (N/Cl > 2 mol/mol, see section B in Supporting Information), the rates of disappearance of resorcinol, 4-chlororesorcinol and 4,6-dichlororesorcinol in the presence of a large excess of monochloramine ([NH 2 Cl] 0 / [Ar(OH) 2 ] tot,0 > 20 mol/mol) were first-order with respect to the organic compound :

- dt ] ) OH ( Ar [ d tot 2 = k obs [(Ar(OH) 2 )] tot with k obs = k app [NH 2 Cl] 0 (2)
The linear plots which could be drawn between the pseudo first-order rate constant (k obs ) and the initial concentration of monochloramine confirm that the rate of oxidation of the dihydroxybenzenic compound was also first-order with respect to the concentration of monochloramine (Figures S3-S8 in Supporting Information).

As illustrated by the data presented in figure S9, the consumption rates of monochloramine in the presence of a large excess of dihydroxybenzene ([Ar(OH) 2 ] tot,0 / [NH 2 Cl] 0 = 50 mol/mol) were firstorder with respect to monochloramine concentration (eq 3) :

- 7

dt ] Cl NH [ d 2 = k' obs [NH 2 Cl] with k' obs = k app [(Ar(OH) 2 )] tot,0 (3)
The pseudo first-order rate constants (k' obs ) were also found to be proportional to the initial concentration of the organic solute, thus confirming that the rates of monochloramination of the three dihydroxybenzenes follow a second-order kinetic law (eq 1).

All experimental conditions (pH, initial concentrations of reactants), apparent first-order kinetic constants (k obs and k' obs ) and apparent second-order rate constants (k app ) have been reported in tables S1 and S2 in Supporting Information. It should be noted that the apparent second-order rate constants calculated from k obs values were consistent with those calculated from k' obs .

pH Dependency of k app and Mechanism. A simple kinetic model which incorporates the acid-base dissociation reactions of dihydroxybenzenes and the reactions of monochloramine with the three forms of dihydroxybenzenes is proposed as follows:

Ar(OH) 2 Ar(OH)(O -) + H + (K Ar 1 a ) (4)
Ar(OH)(O -) Ar(O -) 2 + H + (K Ar 2 a ) (5)
Ar(OH) 2 + NH 2 Cl →  1 k Products (6) Ar(OH)(O -) + NH 2 Cl  →  2 k Products (7) Ar(O -) 2 + NH 2 Cl →  3 k Products (8)
By assuming that the reaction rate of monochoramine with each acid-base form of dihydroxybenzene is second-order, the apparent second-order rate constant k app can be expressed as follows:

+ 2 1 K K + ] [H + ] [H K K K k ] [H K k k k + + = + Ar 1 a 2 app ] H [ (9)
Additional information on this kinetic expression can be found in Section E of the Supporting Information.

The individual rate constants (k 1 , k 2 and k 3 ) for the reactions of monochloramine with dihydroxybenzenes were determined by a non-linear least-squares regression analysis of the experimental pH profiles of k app by using SigmaPlot 2000 software. The values of the acid dissociation constants used in the present work and the fitted values of all the individual rate constants are reported in Table 1.

As shown by the solid lines in Figures 123, the pH dependency of the apparent second-order rate constant of monochloramination of resorcinol, 4-chlororesorcinol and 4,6-dichlororesorcinol could be fitted reasonably well. For resorcinol and 4-MCR, the good fit was obtained with the pK Ar The individual reaction rate constants listed in Table 1 show that the Ar(OH)O -form of each dihydroxybenzene is more reactive toward monochloramine than the Ar(OH) 2 and the Ar(O -) 2 forms.

For the Ar(OH)O -form, the rate constant increases with increasing substitution of chlorine on the aromatic ring: k 2 ≈ 9.3 x 10 2 , 1.72 x 10 3 and 4.3 x 10 3 M -1 h -1 for resorcinol, 4-chlororesorcinol and 4,6dichlororesorcinol, respectively.

Table 1 also reports the individual rate constants for the reaction of hypochlorous acid with dihydroxybenzenes determined by Rebenne et al. (15). A comparison of the individual reaction rate

constants shows that resorcinol, monochloro and dichlororesorcinol are much more reactive with hypochlorous acid than with monochloramine. The k HOCl /k NH 2 Cl ratios are > 6 x 10 2 , ≈ (0.3-5.3) x 10 6 and ≈ (0.8 -2.4) x 10 9 for the intrinsic rate constants k 1 , k 2 and k 3 respectively -Table 1). Apparent second-order rate constants for the chlorination and for the monochloramination of resorcinol, 4chlororesorcinol and 4,6-dichlororesorcinol were also calculated from eq 9 and plotted in Figure 4. The data shows that the apparent rate constant of chlorination is 3-4 orders of magnitude greater than the apparent rate of monochloramination at any pH between 5 and 13, confirming that chlorine is much more reactive than monochloramine with the resorcinol derivatives. Computer simulations show that the best fits of the concentration-time profiles at pH 8.6 were obtained for S 1 = 0.66 ± 0.05 and S 2 = 0.25 ± 0.02 (Figures S13 andS14). It should be noted that these stoichiometric coefficients at pH = 8.6 represent apparent values because the stoichiometric coefficients for the reactions of monochloramine with the three acid-base forms of a dihydroxybenzene might be different, and therefore, the stoichiometric constants might be pH dependent.

The stoichiometric coefficient for the formation of 4-chlororesorcinol from resorcinol obtained at pH 8.6 (S 1 = 0.66 ± 0.05) suggests that 2-chlororesorcinol is formed with a yield of 0.34 mole per mole of 12 reasonably well the disappearance rates of resorcinol obtained at various N/Cl values at pH 8.6, thus validating the rate constants for the reactions of free chlorine and monochloramine with resorcinol listed in table 1. Contribution of free chlorine reactions to the overall degradation of resorcinol could also be estimated by kinetic modelling. Under the conditions used for the data presented in Figure 5, and for a N/Cl ratio of 1.08, 52 % of the overall rate of degradation of resorcinol can be attributed to free chlorine oxidation reactions. This contribution falls to 12 % when the N/Cl increases from 1.08 to 1.12. This result shows that the oxidation rates of resorcinol by monochloramine is highly sensitive to the N/Cl ratio when this ratio is close to unity.

Free chlorine concentration in monochloramine solutions is also pH-dependent (section I in supporting information). For a given N/Cl ratio, the concentration of free chlorine in organic-free water is at a minimum at pH = (pKa HOCl + pKa ammonia /2) ≈ 8.4 (Figure S17). The contributions of free chlorine oxidation reactions to the degradation of resorcinol, 4-chlororesorcinol and 4,6-dichloresorcinol were also calculated with our kinetic model for all the experiments conducted in the pH range 5. 5 -12 (examples are given in Figures S18 andS19). Computer calculations demonstrate that the contribution of free chlorine reactions could be neglected for all the experimental conditions used for the determination of the intrinsic rate constants for the reaction of monochloramine with the dihydroxybenzenic compounds (5 < pH < 12; N/Cl > 2 or 5).

Implications on water treatment

The results obtained in the present work show that monochloramine is much less reactive than chlorine toward dihydroxybenzenes. This study also confirms the reaction model proposed by the research group of Valentine for the monochloramination of Natural Organic Matter (NOM) (7, 23). These authors have demonstrated that the monochloramine hydrolysis reaction plays a key role in governing the overall rate of decomposition of monochloramine in water in the presence of NOM. It has also been demonstrated that free chlorine in equilibrium with monochloramine contributes to the oxidation of As(III) during monochloramination of water containing As(III) (24).

13

During monochloramination of drinking water, the indirect reactions involving free chlorine can also participate to DBP formation. Although the contribution of free chlorine to DBP formation should be of little importance under conditions typical for drinking water treatment, further investigation is needed to differentiate the role of monochloramine and of free chlorine on the formation of trihalomethanes and of other DBPs.

Supporting Information Available

Tables and figures addressing to stability and purity of monochloramine solutions prepared in this work, the determination of experimental conditions for minimizing the contribution of free chlorine reactions to the overall rates of decomposition of resorcinol compounds, experimental data obtained for the oxidation rate of resorcinol compounds in the presence of a large excess of monochloramine and for the effect of pH on the rate of monochloramination of resorcinol compounds in the presence of a large excess of organic solute, the effect of temperature on the rate of monochloramination of resorcinol, the determination of an acid dissociation constant of

from 1 .

 1 08 to 31 mol/mol. The pH of the sodium hypochlorite and ammonium chloride solutions were 73 preadjusted to 8.3 ± 0.1. As carbonate and phosphate ions are known to catalyse the decomposition of 74 monochloramine in water (18), all kinetic experiments were carried out without pH buffer, pH being 75 possibly regulated during the reaction by addition of hydrochloric acid or sodium hydroxide. All 76 monochloramine before the experiments. 78 79 Free chlorine and total chlorine concentrations in the stock solutions of sodium hypochlorite and 80 monochloramine were determined iodometrically with sodium thiosulfate 0.01 M (Prolabo, > 99.9 %). 81 Monochloramine concentrations were determined spectrophotometrically using a molar extinction 82 coefficient of 446 M -1 cm -1 for NH 2 Cl at 244 nm 83 Iodometric titrations and spectrophotometric analyses of freshly prepared solutions of NH 2 Cl showed 84 that free chlorine introduced in the solution of ammonium chloride was quantitatively converted into 85 NH 2 Cl at pH ≈ 8.3. In addition, the concentration of NH 2 Cl in organic-free solutions ([NH 2 Cl] 0 = 1-4 86 mM at pH = 8.6 or ([NH 2 Cl] 0 = 0.1 mM at 5 < pH < 12) remained essentially constant during the total 87 reaction times in any of our kinetic experiments. This is in good agreement with the concentration-time 88 profiles of NH 2 Cl predicted by the kinetic model of Jafvert and Valentine (1992). As shown the 89 experimental data and the model predictions in Section A of the Supporting Information, the 90 disproportionation reaction of NH 2 Cl and the decay of NH 2 Cl under experimental conditions can be 91 neglected. 92 Experimental Procedures. All experiments were conducted in batch reactors (125 -1250 mL Pyrex 93 bottles with PTFE screw caps) and under constant stirring using a magnetic bar. All experiments, 94 excepted for activation energy determination, were performed at room temperature (23 ± 2°C). 95 To determine reaction rates, experiments were performed in the presence of a large excess of 96 dihydroxybenzene ([Ar(OH) 2 ] 0 /([NH 2 Cl] 0 = 50 mol/mol) or monochloramine ([NH 2 Cl] 0 /[Ar(OH) 2 ] 0 > 97 20 mol/mol) in order to obtain pseudo-first decays of monochloramine or dihydroxybenzene, 98 respectively. In the presence of a large excess of dihydroxybenzene ([Ar(OH) 2 ] 0 /[NH 2 Cl] 0 = 50 99 mol/mol), the concentration of monochloramine ([NH 2 Cl] 0 = 100 µM) was monitored at different 100 reaction times by reaction with iodide and subsequent spectroscopic quantification at 351 nm of the 101 liberated triiodide ion. Kinetic experiments of the consumption of monochloramine were initiated by 102

([NH 2

 2 Cl] 0 /[Ar(OH) 2 ] 0 = 20 -100 mol/mol) and the reaction was followed by measuring the decay of the concentrations of the dihydroxybenzene (R, 4-MCR or 4,6-DCR) by HPLC. The reaction was started by introducing under vigorous magnetic stirring 5 mL of a solution of the dihydroxybenzene (10 mM) to 1000 mL of NH 2 Cl solution (1 -4 mM) at pH 8.6. At various reaction times, 4-mL samples were taken from the reactor, spiked with 10 µL of a sodium sulfite solution (1 M) in order to neutralize monochloramine. Then, concentrations of dihydroxybenzenes were determined by HPLC. Analyses were performed with a Waters system (W600 controller; W717plus Autosampler) equipped with a C18 Uptisphere 5 HDO column and a photodiode array detector (Waters W996) for the UV-VIS spectra acquisition. The organic compounds were eluted with a methanol/water mobile phase at a flow rate of 1.0 mL min -1 . rate constants, kinetic data were treated with a non-linear regression program (Sigma plot 2000). Model simulations were undertaken using the kinetic modeling software package Copasi Version 4.4. (22).

1 a + pK Ar 2 a )/ 2 ,

 122 Figures 1-3 show the experimental pH profiles of k app for the monochloramination of resorcinol, 4-chlororesorcinol and 4,6-dichlororesorcinol, respectively. pH values lower than 5 have not been investigated in the present work because of the acid-catalyzed disproportionation reaction of monochloramine into dichloramine and ammonia. As for chlorine (15), the pH dependency of the k app values of monochloramination of resorcinol compounds exhibits a maximum in weak-alkaline media : pH ≈ 10.2 ± 0.2 for resorcinol, pH ≈ 9.4 ± 0.2 for 4-chloro-resorcinol and pH ≈ 8.6 ± 0.2 for 4,6-dichlororesorcinol. Unlike the data obtained by Rebenne et al. (15), the acid-catalyzed oxidation of the resorcinol compounds is not observed with monochloramine. Under the experimental conditions used in the present work (5 < pH < 12), spectrophotometric analyses which have been conducted with aqueous solutions of monochloramine indicate that NH 2 Cl is the unique form of monochloramine. Therefore, the shape of the pH-rate profiles obtained in the present study can be attributed to the fact that the monoionized form (Ar(OH)O -) of a dihydroxybenzenic compound is more reactive with monochloramine than the unionized (Ar(OH) 2 ) and the diionized (Ar(O -) 2 ) forms. Hence, the highest value of the apparent second-order rate constant for the reaction of monochloramine with dihydroxybenzenes is obtained at pH equal to pH = (pK Ar In addition, it should be pointed out that trace amounts of dichloramine present in monochloramine solutions at pH 5 ([NH 2 Cl] 0 = 100 µM; FigureS3in Supporting Information) may also oxidize organic second-order rate constants for the reaction of NHCl 2 with resorcinol compounds are unknown. Nonetheless, the contribution of NHCl 2 to the degradation of resorcinol compounds under our conditions should be negligible because the concentrations of dichloramine are very low.

  Rebenne et al. (1996). In the case of 4,6-dichlororesorcinol, a poor fit for the monochloramination rate -pH dependency was obtained with the pK Ar 2 a value of 10.35 used by Rebenne et al. (15), (Figure S16 in Supporting Information). Given the large difference between the experimental and the calculated pH profiles of k app , an acid-base titration has been performed to determine the pK Ar 2 a value of 4,6-dichlororesorcinol. The acid-base titration (Figure S15) and the non-linear least-squares regression analysis of the reaction rate pH dependency (Figure S16), indicates that the best fit is obtained with a pK Ar 2 a value of 9.78 ± 0.05 for 4,6-dichlororesorcinol.

  FigureS12shows that the plot of ln(k app ) versus 1/T gave a straight line, in agreement with the

  , this distribution of by-products indicates that the three ortho positions to the hydroxyl groups on the aromatic ring of resorcinol have the same reactivity toward monochloramine at pH 8.6. As far as 4-chlororesorcinol is concerned, our study shows that monochloramination of 4-chlororesorcinol leads to 4,6-dichlororesorcinol with a molar yield of 0.25 at pH 8.6 (S 2 = 0.25 ± 0.02). In the absence of steric hindrance and of selective attack, the theoretical distribution should be approximately 50% of 4,6dichlororesorcinol and 50% of 2,6-dichlororesorcinol. The data obtained in our work indicates that the 2-position is about three times more reactive than the 4-position toward monochloramine.Effect of the N/Cl ratio on the rate of oxidation of resorcinol.The experimental data obtained in the present work suggest that free chlorine formed from monochloramine hydrolysis contributes to the oxidation of resorcinol when monochloramine was prepared by using low nitrogen-to-chlorine ratios (N/Cl < 1.5 mol/mol, Section B in Supporting Information). The concentration of free chlorine in solutions of monochloramine depends on various parameters such as the concentration of monochloramine, the N/Cl ratio and pH (Section I in Supporting Information).Since the individual rate constants for the reaction of resorcinol with monochloramine (this study) and with free chorine (15) are known, a kinetic model has been used to evaluate the contribution of free chlorine reactions to the rate of disappearance of resorcinol during monochloramination. The kinetic model incorporates acid dissociation reactions for ammonia, hypochlorous acid, resorcinol, 4chlororesorcinol and 4,6-dichlororesorcinol, formation and hydrolysis reactions of monochloramine and the reactions of hypochlorous acid and monochloramine with all the acid-base forms of resorcinol, 4chlororesorcinol and 4,6-dichlororesorcinol. The reaction model and the rate constants have been reported in tableS3in Supporting Information. It should be emphasized that our kinetic model cannot be used to predict the rate of consumption of monochloramine because reactions of monochloramine and chlorine with most of the oxidation intermediates of resorcinol are unknown. However, our model can be used to simulate the disappearance rate of resorcinol in the presence of a large excess of monochloramine ([NH 2 Cl] 0 /[Resorcinol] 0 > 20 mol/mol) because the concentrations of monochloramine is quite constant during the early stage of the reaction. Figure5shows that our kinetic model simulates

Figure 1 .Figure 2 .Figure 3 .

 123 Figure 1. Experimental (symbol) and modeled (solid line) pH profile of the second-order apparent rate 373

Figure 4 .Figure 5 .PageTable 1 .aPage

 451 Figure 4. Apparent second-order reaction rate constants for the chlorination (upper curves) and for 390

  4,6-dichlororesorcinol, the description of the kinetic model used in this work and computed data or model predictions obtained to determine stoichiometric coefficients, free chlorine concentration in NH 2 Cl solutions, the overall reaction rates and the contribution of free chlorine reactions to the degradation of resorcinol compounds. Heasley, V. L.; Alexander, M. B.; Deboard, R. H.; Hanley Jr, J. C.; McKee, T. C.; Wadley, B. D.; Shellhamer, D. F. Reactions of resorcinol and its chlorinated derivatives with monochloramine: Identification of intermediates and products. Environ. Toxicol. Chem. 1999, 18, 2406-2409. (18) Valentine, R. L.; Jafvert, C. T. General acid catalysis of monochloramine disproportionation.

	Page 15 of 22	Submitted to Environmental Science & Technology Submitted to Environmental Science & Technology	Page 14 of 22
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(16) Gallard, H.; Von Gunten, U. Chlorination of phenols: Kinetics and formation of chloroform. Environ. Sci. Technol. 2002, 36, 884-890. (22) Hoops, S.; Gauges, R.; Lee, C.; Pahle, J.; Simus, N.; Singhal, M.; Xu, L.; Mendes, P.; Kummer, U. COPASI -A COmplex PAthway SImulator. Bioinformatics 2006, 22, 3067-3074. (23) Duirk, S. E.; Valentine, R. L. Modeling dichloroacetic acid formation from the reaction of monochloramine with natural organic matter. Water Res. 2006, 40, 2667-2674. (24) Dodd, M.C.; Vu, N.D.; Amann, A.; Le, V.C.; Kissner, R.; Pham, H.V.; Cao, T.H.; Berg, M.; Von Gunten, U. Environ. Sci. Technol. 2006, 40, 3285-3292.

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Dr Daniel Jolley
email: daniel.jolley@nottingham.ac.uk

Anthony Lantian

WORKPLACE BULLYING AND CONSPIRACY BELIEFS 1 in press, Social

Keywords: workplace bullying, conspiracy beliefs, paranoia Bullying and Conspiracy Theories: Experiences of Workplace Bullying and the Tendency

Experiences of bullying in the workplace can increase anxiety, paranoia, and hypervigilance to threat in victims. Such factors are also associated with conspiracy beliefs. Two preregistered studies (cross-sectional and experimental) tested whether bullying experiences may be linked to the development of conspiracy beliefs. Study 1 (n = 273) demonstrated that experiences of workplace bullying were positively associated with conspiracy beliefs, an effect that could be explained by paranoia. In Study 2 (n = 206), participants who imagined being bullied (vs. supported) reported increased belief in conspiracy theories. Our research uncovers another antecedent of conspiracy beliefs: workplace bullying. Future research should endeavour to explore how best to support victims and avert the link between being bullied and conspiracy theorising emerging.

Worryingly, conspiracy beliefs are popular [START_REF] Oliver | Conspiracy theories and the paranoid style (s) of mass opinion[END_REF], often thought to be because they promise to meet psychological needs (Douglas, et al., 2017). Psychologists have identified a range of psychological correlates of conspiracy beliefs such as feelings of uncertainity [START_REF] Van Prooijen | Belief in conspiracy theories: The influence of uncertainty and perceived morality[END_REF] and anxiety [START_REF] Grzesiak-Feldman | The effect of high-anxiety situations on conspiracy thinking[END_REF].

Association also exists between paranoia and conspiracy beliefs (e.g., [START_REF] Grzesiak-Feldman | Paranoia and conspiracy thinking of Jews, Arabs, Germans, and Russians in a Polish sample[END_REF]. Whilst it could be argued paranoia and conspiracy beliefs are the same construct, [START_REF] Imhoff | How paranoid are conspiracy believers? Toward a more fine-grained understanding of the connect and disconnect between paranoia and belief in conspiracy theories[END_REF] provided evidence of their distinctions and divergent associations with other factors (i.e., conspiracy beliefs attribute evil to the powerful, whereas paranoia attributes evil to people in general). Further supporting this notion, [START_REF] Alsuhibani | Why conspiracy theorists are not always paranoid: Conspiracy theories and paranoia form separate factors with distinct psychological predictors[END_REF] also demonstrated that conspiracy beliefs, but not paranoia, predicted poorer analytical thinking. It is clear that some of these psychological correlates can be frustrated during times of societal crisis, such as rapid political change, a terrorist attack, or a virus outbreak [START_REF] Van Prooijen | Conspiracy theories as part of history: The role of societal crisis situations[END_REF]. Indeed, societal crises breed feelings of uncertainty, anxiety and threat (such as during the COVID-19 pandemic, [START_REF] Lalot | Aversion amplification in the emerging COVID-19 pandemic: The impact of political trust and subjective uncertainty on perceived threat[END_REF], where citizens try to make sense of a turbulent society [START_REF] Franks | Beyond "monologicality"? Exploring conspiracist worldviews[END_REF]. Such conditions make fertile ground for conspiracy beliefs to flourish.

Another contributor to the development of conspiracy beliefs is experiences of collective victimhood and discrimination. Early work by [START_REF] Abalakina-Paap | Beliefs in conspiracies[END_REF] showcased how African-American participants who reported they had been subject to police harassment were more likely to subscribe to HIV conspiracy theories that propose HIV is human-made. More recently, [START_REF] Jolley | Discrimination, HIV conspiracy theories and pre-exposure prophylaxis acceptability in gay men[END_REF] demonstrated in a sample of UK White gay males, experiences of discrimination (because of their sexual orientation) were associated with heightened HIV conspiracy beliefs. In turn, HIV conspiracy beliefs were then associated with less favourable attitudes towards Pre-Exposure Prophylaxis (PrEP), a bio-medical approach preventing the risk of HIV. [START_REF] Jolley | Discrimination, HIV conspiracy theories and pre-exposure prophylaxis acceptability in gay men[END_REF] propose that the roots of HIV conspiracy beliefs could be in adverse social experiences (i.e., victimisation), and its consequences may be the rejection of biomedical therapies.

In a similar vein, [START_REF] Pantazi | Historia est magistra vitae"? The impact of historical victimhood on current conspiracy beliefs[END_REF] found across a series of studies with Greek participants, historical collective victimhood fostered conspiracy theorising, but only for those who identified strongly with being Greek. [START_REF] Armaly | Why Me?' The role of perceived victimhood in American politics[END_REF] also provided evidence that victimhood is linked to increased conspiracy beliefs. However, the researchers demonstrated that believing one is a victim does not appear to depend on true oppression and instead cut across political and sociodemographic lines. For example, they found that a roughly equal fraction of White (53%) and non-White (57%) participants agreed that "the system is rigged to benefit a select few", which was associated with heightened conspiracy beliefs. In other words, people do not need to be victimised due to group status to feel like a victim; they can subjectively feel like their group is a victim even in the absence of true oppression. [START_REF] Pantazi | Historia est magistra vitae"? The impact of historical victimhood on current conspiracy beliefs[END_REF] proposed that conspiracy endorsement may take the form of protecting the ingroup from enemies, especially when the ingroup is (perceived to be) a victim. Taken together, it is plausible that hostile experiences (such as specific forms of victimisation and discrimination) in one's everyday life could be a precursor to conspiracy theorising.

Bullying and Belief in Conspiracy Theories

In the literature to date on the antecedents of conspiracy beliefs, discrimination and victimisation that is not based on collective identities have not yet received attention. An important specific form of discrimination and victimisation to consider is workplace bullying.

Bullying is interpersonal, where there is a power imbalance between the bully and the victim (e.g., co-worker is bullied by a superior or informal power imbalance between co-workers, [START_REF] Einarsen | Bullying and harassment at work and their relationships to work environment quality. An exploratory study[END_REF][START_REF] Shetgiri | Bullying and victimization among children[END_REF]. Importantly, bullying is a multi-causal phenomenon, since it can result from a range of factors [START_REF] Salin | Ways of explaining workplace bullying: a review of enabling, motivating and precipitating structures and processes in the work environment[END_REF]. Compared to collective victimhood, individuals could end up being bullied because of individual differences between workers (i.e., personality clashes that inspire interpersonal conflict), appearance (e.g., size or height), or even displayed aggression (e.g., Anti-Bullying Alliance, 2021;[START_REF] Salin | Ways of explaining workplace bullying: a review of enabling, motivating and precipitating structures and processes in the work environment[END_REF]. As the root cause of workplace bullying can be so diverse, researchers typically focus on the 'acts' to define bullying [START_REF] Hewett | Bullying at work: Cognitive appraisal of negative acts, coping, wellbeing, and performance[END_REF]. Specifically, the negative acts toward the bullied victim can be work-related (such as withholding work-related information) or personal (such as gossiping about them), but they must be experienced by the victim repeatedly over time (i.e., at least weekly for six months or more, [START_REF] Leymann | The content and development of mobbing at work[END_REF]. Bullying can include direct (e.g., name-calling) and indirect (e.g., gossiping) behaviours (see [START_REF] Shetgiri | Bullying and victimization among children[END_REF].

To measure the experiences of being bullied in the workplace, two approaches are typically used [START_REF] Nielsen | Measuring exposure to workplace bullying[END_REF]. First is the self-labelling method, where participants simply report if they have been bullied within the last six months. The second approach lists a range of negative (bullying) behaviours, which participants respond to, indicating if they have experienced such acts in the workplace. Using such measures of bullying, researchers have demonstrated that bullying experiences can impact a victim's wellbeing and performance at work. For example, in a meta-analysis that included 90 studies, [START_REF] Bowling | Workplace harassment from the victim's perspective: A theoretical model and meta-analysis[END_REF] uncovered that workplace bullying was predictive of burnout, stress, decreased job satisfaction and increased turnover intentions.

Furthermore, bullying can contribute to a negative work climate (e.g., affect relationship with peers, reduce morale and oragnisational commitment, see Barlett & Bartlett, 2011). Such a negative work climate has been linked with conspiracy beliefs. Specifically, [START_REF] Douglas | Suspicion in the workplace: Organisational conspiracy theories and work-related outcomes[END_REF] found that a work place with negative features (e.g., little autonomy over their work, frequent conflict and gossip in the workplace, vs. a positive climate) increased belief in conspiracy theories. Whilst this study did not examine bullying, we argue that the acts included as part of their experimental manipulation could be stemmed from bullying. Thus, as bullying behaviours can contribute to a negative work environment (Barlett & Bartlett, 2011), this work provides initial support for the assertion that because bullied victims may seek explanations for their difficult circumstances, being bullied could inspire conspiracy theorising.

In supporting such a view, research has also found that victims report increased feelings of anxiety and paranoid thinking [START_REF] Hawker | Twenty years' research on peer victimisation and psychosocial maladjustment: A meta-analytic review of cross-sectional studies[END_REF][START_REF] Singham | Concurrent and longitudinal contribution of exposure to bullying in childhood to mental health:The role of vulnerability and resilience[END_REF], alongside being hypervigilant to threats in the environment [START_REF] Jack | Childhood bullying, paranoid thinking and the misappraisal of social threat: Trouble at school[END_REF]. Such variables also predict belief in conspiracy theories [START_REF] Douglas | Understanding conspiracy theories[END_REF]. Victims of bullying may find conspiracy theories appealing because bullying experienceswhich contribute to a negative work environmentfrustrate the exact psychological factors that are a route to developing conspiracy beliefs. A route that is appealing because conspiracy beliefs promise to satisfy psychological needs and restore a sense of control and meaning [START_REF] Douglas | Understanding conspiracy theories[END_REF]. Whilst such a route likely explains the link between collective victimisation and conspiracy theorising (e.g., sexual orientation, [START_REF] Jolley | Discrimination, HIV conspiracy theories and pre-exposure prophylaxis acceptability in gay men[END_REF], it is plausible that victimisation caused by more interpersonal factors (i.e., bullying) can also inspire conspiracy beliefs through the same mechanisms.

In a similar vein, bullying can also include being socially excluded, such as where an individual is excluded from a work environment [START_REF] Gamian-Wilk | Ostracism in the workplace[END_REF].

However, scholars have argued that exclusion and bullying are theoretically and empirically separate concepts (e.g., [START_REF] Ferris | The development and validation of the Workplace Ostracism Scale[END_REF]. Nonetheless, [START_REF] Poon | Beliefs in conspiracy theories following ostracism[END_REF] have recently demonstrated that socially excluded participants (ostracised) were more likely to endorse conspiracy theories. While ostracism and bullying are distinct concepts, because of the overlap between the two, this work provides further support for the idea that bullying experiences could be an antecedent to conspiracy theorising. In sum, it is plausible that experiences of workplace bullying may be linked to heightened belief in conspiracy theories.

An effect explained by increased feelings of anxiety and paranoia, alongside being hypervigilant to threats in the environment; all grounded in victims seeking to understand their circumstances.

The Present Research

In two studies, we investigated the relationship between the experience of bullying and belief in conspiracy theories. In Study 1, we examined this relationship in a crosssectional study, where we tested whether prior experiences of being bullied in the workplace predicted belief in conspiracy theories. We also examined whether paranoia, anxiety, and hypervigilance to threat mediated this relationship. We predicted that bullying experiences would be associated with increased paranoia, anxiety, and hypervigilance, which would then be associated with heightened belief in conspiracy theories. In Study 2, we experimentally manipulated exposure to a bullying work environment (vs. support) and measured belief in conspiracy theories. State paranoia was tested as a mediator. We predicted that exposure to a bullying work environment would increase feelings of (state) paranoia, which would be associated with increased belief in conspiracy theories. The materials of our two studies, the data and the corresponding statistical code, are made available on: https://osf.io/4t6bp/?view_only=1a5b47d4a50f4a319c3c7f9bec0efec8

Study 1

Method

Participants and Design

Following recommendations to receive stable correlations (n = 250; [START_REF] Schönbrodt | At what sample size do correlations stabilise[END_REF], 274 participants (69 male, 204 female, and 1 transgender; Mage = 34.90, SD = 10.15) were recruited via the online platform, Prolific in early January 2020. All participants were residents in the UK. Based on a pre-registered exclusion criterion (see https://aspredicted.org/CCP_GBD), 1 participant was excluded because they do not wish their data to be used in the analysis. Our remaining sample consisted of 273 participants (69 male, 203 female, and 1 transgender; Mage = 34.93, SD = 10.16). The predictor variables comprised of experiences of bullying at work, and the criterion variable was a measure of belief in conspiracy theories. Paranoia, anxiety, and hypervigilance were measured as mediators of this relationship.

Materials and Procedure

Participants indicated their informed consent before beginning the questionnaire.

Participants were then asked to complete two measures of bullying at work. First, participants completed the Short Negative Acts Questionnaire (SNAQ, [START_REF] Notelaers | Measuring bullying at work with the Short-Negative Acts Questionnaire: Identification of targets and criterion validity[END_REF], where there were nine statements (e.g., "Someone withholding information which affects your performance", α = .88). Participants were asked how often they have experience each behaviour at work on a five-point scale (1 = never, 2 = now and then, 3= monthly, 4 = weekly, 5 = daily). Second, participants were provided with a definition of bullying (e.g., "Bullying at work means harassing, offending, socially excluding someone or negatively affecting someone's work tasks…"), before being asked if they consider themselves to have been bullied over the past 6 months ("Do you consider yourself to have been bullied at your workplace over the past 6 months ", Trenberth, et al., 2013). Participants answered on a 5point scale (1 = no, 2 = yes, but only rarely, 3 = yes, now and then, 4 = yes, several times a week, 5 = yes, almost daily), which was turned into a dichotomous variable (-1 = no, 1 = yes).

Next, participants completed a measure of paranoia (Paranoid Ideation Scale, [START_REF] Fenigstein | Paranoia and self-consciousness[END_REF] made up of twenty items (e.g., "Someone has it in for me", α = .93) where participants signified their applicability to themselves on a five-point scale (1 = not at all applicable to me, 5 = extremely applicable to me). Anxiety was then measured using seven items (e.g., "I feel tense of 'wound up", Snaith, 2003, α = .88) on a 4-point scale (e.g., 0 = not at all, 1 = not often, 2 = usually, 3 = definitely), followed by hypervigilance with 5 items (e.g., "As soon as I wake up and for the rest of the day, I am watching for signs of trouble", Bernstein et al., 2015, α = .87) on a 5-point scale (1 = not at all like me to 5 = very much like me). These three measures were counterbalanced. A measure of conspiracy beliefs was then completed using 15 items (e.g., "A small, secret group of people is responsible for making all major world decisions, such as going to war" α = .93; [START_REF] Brotherton | Measuring belief in conspiracy theories: The generic conspiracist beliefs scale[END_REF] on a five-point scale (1 = definitely not true, 5 = definitely true). Participants then provided demographic details, before being debriefed, paid and thanked for their time.

Results and Discussion

Confirmatory Analyses

Bivariate correlations between all the variables measured in our study are presented in Table 1. As predicted, we found a positive and significant relationship between belief in conspiracy theories and bullying at work (measured with the SNAQ), r(271) = .28, p < .001, 95% CI [.16, .38].

Then, we ran a multiple mediation model, with bullying at work (SNAQ) as the independent variable, hypervigilance, anxiety, and paranoia as the mediators, and conspiracy belief as the dependent variable (see Figure 1). We first tested the total effect of bullying in the workplace on belief in conspiracy theory. The more the participants reported having being bullied the more they believed in conspiracy theories, β = .28, B = 0.36, SE = .08, t( 271 The last regression model (testing the mediators to DV path) showed that the more people express paranoia, the more they believe in conspiracy theories, controlling for all the other predictors in the model, β = .32, B = 0.36, SE = .09, t(268) = 3.82, p < .001, η 2 p = .052.

The two other mediators were not significantly related to the DV (ps > .652) 1 . The residual direct effect of bullying became not significant, β = .07, B = 0.09, SE = .09, t(268) = 1.05, p = .295, η 2 p = .004. As for paranoia, the IV to mediator and mediator to DV paths are both significant, we can conclude that this indirect effect is significant [START_REF] Judd | Mediation and moderation[END_REF]. A percentile bootstrap procedure (5,000 bootstrap samples; using the package 'PROCESS ' [v. 4.1;Hayes, 2022] in R [v. 3.6.1]) also leads to the same conclusions with the confidence interval of the indirect effect of paranoia (ab = 0.24), that does not include zero, 95% CI [0.10; 0.39]. Therefore, paranoia was shown to be the only significant mediator (when controlling for hypervigilance and anxiety) explaining the effect between bullying experiences and belief in conspiracy theories.

1 When each mediator is entered independently in a simple mediation (i.e., not controlling for each other), anxiety (ab = 0.09, 95% CI [0.02; 0.18]) and hyperviligance (ab = 0.12, 95% CI [0.05; 0.19]) are significant mediators, in addition to paranoia (ab = 0.26, 95% CI [0.15; 0.39]). It is when controlling for each other (in a test of multiple mediation as reported in the main text) that paranoia is shown to be the star player in explaining the effect of bullying and conspiracy beliefs. See the General Discussion for a discussion on this point. *** p < .001.

Exploratory Analyses

As not all the paths of the hypothetical multiple mediation were conclusive, we have chosen not to pursue a serial mediation analyses (e.g., anxiety -> paranoia) any further as detailed in our pre-registration. Interestingly, as indicated in Table 1, the participants who reported experience of bullying experience at work in the previous 6 months believe more in conspiracy theories than those who reported an absence of bullying experience at work over this same period. In a similar vein, if we run the same multiple mediation model as the one reported in the Confirmation Analyses section by replacing the independent variable by this self-labelled bullied item (-1 = absence of bullying experience at work, 1 = bullying experience at work) we then find the same pattern of results as the one observed previously, with paranoia as the only significant mediator explaining the effect between bullying experiences and belief in conspiracy theories, ab = 0.13, 95% CI [0.06; 0.21].

The results from Study 1 demonstrated that experiences of bullying-measured by experiences of a range of negative (bullying) acts and self-labelled-were associated with heightened belief in conspiracy theories. Whilst bullying was associated with paranoia, anxiety, and hypervigilance to threat, we found that only paranoia was a significant mediator between bullying and conspiracy beliefs in a test of multiple mediation. Specifically, bullying experiences were associated with increased paranoia, which in turn, were associated with a higher endorsement of conspiracy beliefs. However, these findings are based on crosssectional data, where causation is not possible to be concluded. Study 2 sought to address this limitation and explore causation.

Study 2

Study 1 has provided evidence that an antecedent to conspiracy theorising could be bullying experiences, an effect that increased levels of paranoid thinking may explain. Study 2 seeks to develop this work by exploring causation. Specifically, using an experimental design, participants were asked to imagine a new work environment that included behaviours defined as bullying (such as being harassed, [START_REF] Notelaers | Measuring bullying at work with the Short-Negative Acts Questionnaire: Identification of targets and criterion validity[END_REF] or a supportive work environment that did not include the same negative acts. We predicted that exposure to a bullying environment (vs. support) would increase belief in conspiracy theories. Further, as we did not expect a short experimental prime to increase trait paranoia (which was our mediator in Study 1), we also included a measure of state paranoia. We expected that being exposed to a bullying prime (vs. support) would increase (state) paranoia, which in turn, would be associated with heightened belief in conspiracy theories.

Method

Participants and Design

We recruited 218 participants with complete data (63 male, 154 female, and 1 transgender; Mage = 39.77, SD = 11.46) via the online platform, Prolific in early-March 2020

(importantly before any COVID-19 restrictions). All participants were resident in the UK.

Following our pre-registered exclusion criterion (see https://aspredicted.org/5M4_X8M), a total of 12 participants were excluded (8 because they spent an unrealistic short time [less than 36 sec] on the Study, 2 because they did not want their data to be used, and 3 because their answer was considered in a non-consensual manner by two independent judges as "nonserious participants" regarding the content of the task of imagination; including 1 participant who failed two exclusion criteria). Our remaining sample consisted of 206 participants (58 male, 147 female, and 1 transgender; Mage = 40.12, SD = 11.38). Ninety-nine participants were in the bullying condition and 107 were in the support condition. This sample size was above the desired sample size (N = 200) that we had specified in our pre-registration. This latter was based on a statistical power calculation showing that this sample size allows us to have 80% power to detect a difference corresponding to a Cohen's ds ≥ 0.40 (with α = .05).

Materials and Procedure

Participants provided their informed consent, before being asked to imagine either being bullied (experimental condition) or supported (comparison condition) in a new workplace. In both conditions, participants were asked to imagine that they have in past 6months joined a new workplace. They were then asked to imagine the described scenario, followed by being asked to write down as many aspects of the scenario that they imagined as possible in their own words. The term 'bullying' was not used in either scenario. In the bullied condition, participants were asked to imagine that during the first 6 months in their new job, they have experienced a range of behaviours (taken from [START_REF] Notelaers | Measuring bullying at work with the Short-Negative Acts Questionnaire: Identification of targets and criterion validity[END_REF], see also Shetgiri, 2014), that are direct (e.g., shouting) and indirect (e.g., gossiping). We did not include a specific prompt to imagine being socially excluded (e.g., ignored and left out of social activities). The full bullying scenario is as follows:

"I would like you to take a minute to imagine that you have in In the non-bullying condition (supported), participants were asked to imagine that during the first 6 months in their new job, they have experienced behaviours a range of behaviours such as being supportive by colleagues. The full supported scenario is as follows:

"I would like you to take a minute to imagine that you have in the past 6-months joined a new workplace. During that time, your new colleagues have been welcoming

and supportive, which is having a positive impact on you settling into the new work environment."

Next, participants completed a measure of state paranoia [START_REF] Freeman | A measure of state persecutory ideation for experimental studies[END_REF] using 10 statements (e.g., "someone was hostile towards me", α = .99) on a 5-point scale (1 = strongly disagree, 5 = strongly agree), followed by belief in conspiracy theories (as in Study 1, α = .92). The participant then answered three manipulation check measures. First, participants were asked to complete the SNAQ [START_REF] Notelaers | Measuring bullying at work with the Short-Negative Acts Questionnaire: Identification of targets and criterion validity[END_REF] as in Study 1, adapted to the experimental scenario. Specifically, participants completed the following sentence:

"During the scenario that you imagined, someone was…" for each of the 9 items (e.g., "…withholding information which affected your performance.") on a five-point scale (1 = strongly disagree, 5 = strongly agree). Participants were then asked to complete two further items that explicitly measured bullying ("during the imagined scenario, I felt bullied") and ostracism ("during the imagined scenario, I felt socially excluded (ostracised)"), each on a five-point scale (1 = strongly disagree, 5 = strongly agree). Participants who were in the bullied condition were then asked to imagine a supportive new work environment to eliminate any discomfort. Finally, participants provided demographic details and were debriefed, paid, and thanked for their time.

Results and Discussion

Confirmatory Analyses

Bivariate correlations between all the variables measured in our study are presented in 11.76,95% CI [10.58,12.93]). Although social exclusion was not explicitly prompted in the manipulation text, because of the overlap between bullying and exclusion, participants did also report feeling ostracized (bullying: M = 4.54, SD = 0.65, n = 97; support: M = 1.05, SD = 2 For this statistical analysis, we detected 8 observations with large studentized deleted residual (i.e., > 4, see [START_REF] Mcclelland | Unruly, ill-mannered observations can ruin your analysis[END_REF]. Following our pre-registering document, we removed these participants from the sample for this analysis. Keeping these participants did not change the result. The following analyses also include some statistical outliers and their inclusion or not did not change the results either 0.21, n = 106], t(201) = 52.54, p < .001, Cohen's ds = 7.38, 95% CI [6.61,8.15]). Taken together, there is consistent evidence that the manipulation was successful in eliciting the perception of being bullied.

Next, we ran a mediation model, with bullying as the independent variable (support condition coded -1 vs. bullied condition coded 1), state paranoia as the mediator, and conspiracy belief as the dependent variable (see Figure 2). A first regression model tests our main hypothesis, that is, the (total) effect of bullying on belief in conspiracy belief. As predicted, belief in conspiracy theories was significantly higher in the bullying condition (M = 2.79, SD = 0.83, n = 99) than in the support condition (M = 2.55, SD = 0.69, n = 107), β =

.15, B = 0.12, SE = .05, t(204) = 2.19, p = .029, η 2 p = .023. A second regression model (testing the IV to mediator path) revealed that participants from the bullied condition (M = 4.31, SD = 0.48, n = 99) reported higher level of state paranoia than participants in the support condition (M = 1.07, SD = 0.22, n = 107), β = .98, B = 1.62, SE = .03, t(204) = 62.69, p < .001, η 2 p = .951. Finally, a third regression model (testing the mediator to DV path) examining the relationship between state paranoia and belief in conspiracy theories, controlling for the experimental condition, was not significant, β = .14, B = 0.07, SE = .14, t(203) = 0.46, p = .65, η 2 p = .001. The residual direct effect of bullying was not significant, β = .01, B = .009, SE = .24, t(203) = 0.04, p = .97, η 2 p < .001. As the mediator to DV path was not significant, mechanically, the indirect effect could not be significant [START_REF] Judd | Mediation and moderation[END_REF][START_REF] Yzerbyt | New recommendations for testing indirect effects in mediational models: The need to report and test component paths[END_REF]. Estimation of the indirect effect (point estimate: 0.108, 95% [-0.331; 0.560]) included zero and was obtained by using a Monte Carlo simulation (5,000 iterations, [START_REF] Yzerbyt | New recommendations for testing indirect effects in mediational models: The need to report and test component paths[END_REF]. The results of Study 2 provided experimental evidence that exposure to an imagined bullying environment in a new workplace (vs. a support condition) directly increased belief in conspiracy theories. However, whilst we found that exposure to a bullying prime increased feelings of (state) paranoia, this factor did not act as a mediator between the experimental condition and belief in conspiracy theories. This was unexpected and highlighted that primed state paranoia does not explain this effect. Nonetheless, our findings extend Study 1 by providing causal evidence of the link between bullying experiences and the development of conspiracy beliefs.

using JSmediation package [v. 0.1.1] in R [v. 3.6.1],

General Discussion

Across two studies, the current research has uncovered a link between experiences of workplace bullying and belief in conspiracy theories. In Study 1, prior experiences of workplace bullying were associated with heightened conspiracy beliefs, an effect that could be explained by paranoid thinking. Specifically, bullying was associated with paranoia, which in turn, was associated with heightened conspiracy beliefs. Anxiety and hypervigilance to threats did not act as mediators in a test of multiple mediation. Study 2 then demonstrated that participants who were asked to imagine being bullied in a new workplace (vs. supported) indicated an increased belief in conspiracy theories. Unexpectedly, (state) paranoia did not mediate this effect. Together, to our knowledge, the link between workplace bullying and belief in conspiracy theories has been revealed for the first time.

These findings extend previous work by showcasing the detrimental link between hostile work experiences (bullying) and the development of conspiracy beliefs. Previous work has examined the role of victimhood and discrimination, but was often restricted to group characteristics (e.g., [START_REF] Pantazi | Historia est magistra vitae"? The impact of historical victimhood on current conspiracy beliefs[END_REF]. Here, we offer a demonstration of how the experiences of bullying that are removed from collective identities can increase beliefs in conspiracy theories. Our findings include both a cross-sectional (Study 1) and an experimental (Study 2) design, allowing a robust investigation of our pre-registered predictions. Bullying has been shown to impact wellbeing and workplace behaviours, such as anxiety, burnout, and turnover intentions (e.g., [START_REF] Bowling | Workplace harassment from the victim's perspective: A theoretical model and meta-analysis[END_REF][START_REF] Hawker | Twenty years' research on peer victimisation and psychosocial maladjustment: A meta-analytic review of cross-sectional studies[END_REF]. Our work also showcases that bullying can also increase belief in conspiracy theories.

We know that conspiracy beliefs can have serious consequences for individuals and wider society (see [START_REF] Jolley | Shining a spotlight on the dangerous consequences of conspiracy theories[END_REF]). In the work place, for example, conspiracy theories can reduce job satisfaction and increase turnover intentions [START_REF] Douglas | Suspicion in the workplace: Organisational conspiracy theories and work-related outcomes[END_REF]. It is plausible that bullying inspired conspiracy theorising may further cement an employee's intention to leave the company. However, it is also worth noting that work based problems do not limit themselves to the workplace, but can spread to other domains (e.g., workplace bullying jeopardizing life satisfaction, [START_REF] Nauman | How workplace bullying jeopardizes employees' life satisfaction: The roles of job anxiety and insomnia[END_REF]. The emergence of conspiracy beliefs from bullying could have much wider consequences than first envisaged. A timely question for future research to tackle.

We also demonstrated the role that (trait) paranoid thinking could play in explaining the relationship between bullying and belief in conspiracy theories. In Study 1, bullying experiences were associated with higher levels of paranoia, which was associated with conspiracy beliefs. However, in Study 2, after participants imagined a bullying experience (vs. support), (state) paranoia was increased, but did not act as a mediator between the bullying manipulation and belief in conspiracy theories. This result may indicate that the effects may lie in more trait-based cognitions. Alternatively, whilst the manipulation was successful in increasing belief in conspiracy theories and state paranoia, more prolonged exposure to a bullying environment would need to be required to influence levels of trait paranoia. Future research could explore such a possibility.

We also found that anxiety and hypervigilance to threats in the environment did not explain the effects in Study 1. While each factor was correlated with both bullying experiences and belief in conspiracy theories (and were each a significant mediator when not controlling for each other, see Footnote 1), paranoia was the key mediator in a multiple mediation model. This might not be that surprising. Paranoia, anxiety, and hypervigilance to threat, whilst distinct concepts, are interconnected. For example, maltreatment (such as emotional abuse) is linked with paranoia, via feelings of anxiety [START_REF] Fisher | Anxiety and negative self-schemas mediate the association between childhood maltreatment and paranoia[END_REF].

Bullying, paranoia, and overestimation of threat (i.e., hypervigilance) have also been found to be associated (Jack & Egan, 2017). As paranoia is likely a product of anxiety exasperating hypervigilance, in a model that seeks to explain the unique links between bullying and conspiracy beliefs, paranoia rose as the star player. Therefore, our research provides the first test of exploring the mechanisms between bullying experiences and belief in conspiracy theories and sets up a new line of inquiry for future research.

Our work is not without limitations. Study 2 relied on a scenario where participants (who had never been bullied) imagined being bullied (vs. supported) in a new work environment. While imagination scenarios have been shown to be effective in several topic areas, including workplace social exclusion (e.g., [START_REF] Sjåstad | Social exclusion reduces happiness by creating expectations of future rejection[END_REF], the real experience is likely a very different experience than what a naïve participant imagined. We also experimentally manipulated a supportive condition (rather than a neutral) as a comparison, thus, overshadowing the conclusion slightly that the effect is purely down to bullying (vs. a neutral control). However, in Study 1, we find that the effects were replicated when comparing participants who had been bullied in the previous 6 months (vs. those who had not). Specifically, those who had been bullied (vs. not) reported higher levels of paranoia, which in turn, was associated with belief in conspiracy theories. This can provide some reassurance that the effects appear to replicate for participants who have been bullied

(subjective experience). However, with that specific point in mind, our bullying measures in Study 1 did rely upon self-reported bullying experiences. Participants may have over or underestimated their experiences. Further, our measures were based on the acts of bullying, thus we did not take into account any contextual factors that may have led to the bullying experience. There are diverse factors involved that can include personality clashes to displaced aggression (e.g., [START_REF] Salin | Ways of explaining workplace bullying: a review of enabling, motivating and precipitating structures and processes in the work environment[END_REF]. Future research could aim to utilise a more objective measure of bullying behaviour to explore whether our reported effects replicate, alongside exploring how different contextual factors (e.g., bullying due to appearance vs. interpersonal conflict) may strengthen or weaken the reported effects.

Future research should also explore bullying in other contexts, specifically bullying in school-aged children. Recently [START_REF] Jolley | Measuring adolescents' beliefs in conspiracy theories: Development and validation of the Adolescent Conspiracy Beliefs Questionnaire (ACBQ)[END_REF] have demonstrated that conspiracy theorising flourishes in adolescents, with age 14 being a peak age for conspiracy beliefs to develop. As in the workplace, bullying in school can negatively impact the victim (e.g., [START_REF] Berger | Update on bullying at school: Science forgotten?[END_REF], with the consequences remaining in adulthood (e.g., [START_REF] Bender | Bullying at school as a predictor of delinquency, violence and other anti-social behaviour in adulthood[END_REF]. As with adults in our work, it is plausible that bullying could also inspire the development of conspiracy theorising in young populations. Moreover, as we continue to uncover the connections between victimhood and conspiracy beliefs, a timely question for future research is to explore how victims can be supported to help buffer the development of conspiracy beliefs. Whilst conspiracy theories may act as a potential adaptive function, where victimhood helps protect the individual from harm [START_REF] Pantazi | Historia est magistra vitae"? The impact of historical victimhood on current conspiracy beliefs[END_REF], due to the severe consequences of conspiracy theories, conspiracy beliefs may harm the individual rather than protect. It might be that support that is already available to victims of bullying could help reduce the likelihood of conspiracy beliefs developing (e.g., see a systematic review by [START_REF] Vreeman | A systematic review of school-based interventions to prevent bullying[END_REF]. Exploring such a possibility would be an important future research endeavour.

Conclusion

Our timely research has uncovered a link between the experiences of workplace bullying and the endorsement of conspiracy beliefs. We also provide initial evidence that (trait) paranoia may explain this effect. Bullying experiences can significantly impact the victim in numerous ways (e.g., [START_REF] Bowling | Workplace harassment from the victim's perspective: A theoretical model and meta-analysis[END_REF], with the development of conspiracy beliefs being another detrimental consequence. As conspiracy beliefs can impact the smooth functioning of a society (see [START_REF] Jolley | Shining a spotlight on the dangerous consequences of conspiracy theories[END_REF], understanding how conspiracy beliefs form is timely. Our work encourages the development of tools to support victims to try and avert the link between being bullied and conspiracy theorising emerging.

  ) = 4.77, p < .001, η 2 p = .077. Then, a series of three regression models (testing the IV to mediators path) showed that bullying at work was positively related to hypervigilance, β = .42, B = 0.57, SE = .08, t(271) = 7.53, p < .001, η 2 p = .173, anxiety, β = .40, B = 2.79, SE = .39, t(271) = 7.15, p < .001, η 2 p = .159, and paranoia, β = .57, B = 0.66, SE = .06, t(271) = 11.43, p < .001, η 2 p = .325.

  Notes. N = 273. Values in square brackets indicate the 95% confidence interval for each correlation.a Values represent point-biserial correlations, an absence of bullying experience at work in the previous 6 months (value of 1 on the original scale) was coded -1, experience of bullying experience at work in the previous 6 months (values ranging from 2 to 5 on the original scale) was coded 1. b These values do not correspond to the mean but the sum. *** p < .001.

Figure 1 A

 1 Figure 1

Figure 2 A

 2 Figure 2

Table 1

 1 Bivariate Correlations (With 95% Confidence Intervals) Between all the Variables (Study 1)

	Variable	M	SD	1	2	3	4	5	6
	1. Bullying at work	1.70	0.64	-
	2. Self-labelled bullied item a	-0.67	0.74	.58 ***	-
				[.50, .66]
	3. Hypervigilance	1.89	0.88	.42 ***	.25 ***	-
				[.31, .51]	[.14, .36]
	4. Anxiety b	12.90	4.50	.40 ***	.28 ***	.67 ***	-
				[.29, .49]	[.17, .39]	[.60, .73]
	5. Paranoia	2.14	0.75	.57 ***	.34 ***	.66 ***	.60 ***	-
				[.48, .65]	[.23, .44]	[.59, .72]	[.52, .67]
	6. Belief in
	conspiracy	2.70	0.84	.28 ***	.23 ***	.29 ***	.26 ***	.40 ***	-
	theories
				[.16, .38]	[.11, .34]	[.18, .40]	[.15, .37]	[.29, .49]

Table 2

 2

. As a preliminary analysis, we first conducted independent t-tests on our manipulation checks. As expected, the mean level of bullying (SNAQ) is significantly higher in the bullying condition (M = 3.81, SD = 0.38, n = 96) than in the support condition (M = 1.05, SD = 0.15, n = 102), t(196) = 68.49, p < .001, Cohen's ds = 9.74, 95%

CI [8.73, 10.74]

2 .

We also found the same pattern with the 1-item bullying measure (bullying: M = 4.82, SD = 0.38, n = 96; support: M = 1.07, SD = 0.25, n = 107], t(201) = 83.63, p < .001, Cohen's ds =

Table 2

 2 Bivariate Correlations (With 95% Confidence Intervals) Between all the Variables (Study 2)

	Variable	M	SD	1	2	3	4	5	6
	1. Experimental condition a	-0.04	1.00	-
	2. State paranoia	2.63	1.67	.98 *** [.97, .98]	-
	3. Belief in conspiracy theories	2.66	0.77	.15 * [.02, .28]	.16 * [.02, .29]	-
	4. Bullying (SNAQ)	2.45	1.44	.92 *** [.90, .94]	.91 *** [.88, .93]	.18 * [.04, .31]	-
	5. Bullying (1-item)	2.84	1.89	.98 *** [.97, .98]	.98 *** [.97, .98]	.15 * [.02, .28]	.93 *** [.90, .94]	-
	6. Ostracised (1-item)	2.71	1.80	.95 *** [.94, .96]	.96 *** [.95, .97]	.13 [-.00, .27]	.91 *** [.88, .93]	.97 *** [.96, .98]	-
	Notes. N = 206. Values in square brackets indicate the 95% confidence interval for each correlation.
	a Values represent point-biserial correlations, support condition was coded -1, bullied condition was coded 1.

* p < .05, *** p < .001.

The materials of our two studies, the data and the corresponding statistical code, are made available on: https://osf.io/4t6bp/?view_only=1a5b47d4a50f4a319c3c7f9bec0efec8


Martina Bracco

Xavier Corominas-Teruel

Traian Popa

Antoni Valero- Cabré

Cécile Gallea

Impact of cerebellar beta entrainment using non-invasive brain stimulation: Insights from an ongoing rhythmic TMS-EEG study in healthy human participants

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Oscillations play a pivotal role in shaping cerebellar local activity and its communication with neocortical areas involved in learning motor skills. Previous studies have emphasized the presence and the potentially important role of beta (15-30 Hz) cerebellar oscillations in such processes. Yet, the distribution and causal nature of local and interregional synchronization patterns at such frequencies remain elusive. The present study aims to better understand the functional mechanisms by which the cerebellum synchronizes with widespread cortical regions. This will pave the way to identify and better modulate the specific electrophysiological properties of these networks.

To this end, we sought to entrain beta frequency cerebellar oscillations with transcranial magnetic stimulation (TMS) and to characterize the cerebello-cortical synchronization patterns in the sensory-motor networks. A cohort of 20 healthy adult participants received trial-by-trial blocks of 4-pulses bursts of either rhythmic (20 Hz, experimental condition) or arrhythmic (control condition) TMS delivered over the right cerebellum, while EEG was also recorded. The stimulation of a right occipital/parietal cortical site performed in separate blocks served to assess the specificity of cerebellar stimulation.

After cleaning and pre-processing, we computed and averaged the power and the inter-trial coherence of EEG signals elicited by TMS in frontal, central and parietal areas. Current interim analyses support the tolerability and feasibility of cerebellar TMS-EEG recordings, and our ability to assess signs of beta-induced entrainment while ruling out unspecific effects (artifacts triggered by the TMS clicking-sound, scalp-tapping, etc).

This is the first study overcoming the limitations of 'offline' repetitive TMS approaches assessing effective connectivity between cerebellar and cerebral systems using TMS-EEG approaches. The outcome of this study will characterize the neurophysiological properties of cerebello-cortical communication based on frequency-specific synchronization mechanisms, which would ultimately influence learning processes.

  Impact of cerebellar beta entrainment using non-invasive brain stimulation: Insights from an ongoing rhythmic TMS-EEG study in healthy human participants Martina Bracco, Xavier Corominas-Teruel, Traian Popa, Antoni Valero-Cabré, Cécile Gallea To cite this version: Martina Bracco, Xavier Corominas-Teruel, Traian Popa, Antoni Valero-Cabré, Cécile Gallea. Impact of cerebellar beta entrainment using non-invasive brain stimulation: Insights from an ongoing rhythmic TMS-EEG study in healthy human participants. 5th International Brain Stimulation Conference, Feb 2023, Lisbonne, Portugal. 10.1016/j.brs.2023.01.619. hal-04310561