Kinetic and thermodynamic study of the photochemical degradation of patulin

Accepted Manuscript Kinetic and thermodynamic study of the photochemical degradation of patulin

Raquel Ibarz, Alfonso Garvín, Albert Ibarz PII: DOI: Reference:

S0963-9969(17)30229-6 doi: 10.1016/j.foodres.2017.05.025 FRIN 6716

To appear in:

Food Research International

Received date: Revised date: Accepted date:

13 March 2017 24 May 2017 27 May 2017

Please cite this article as: Raquel Ibarz, Alfonso Garvín, Albert Ibarz , Kinetic and thermodynamic study of the photochemical degradation of patulin, Food Research International (2017), doi: 10.1016/j.foodres.2017.05.025

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ACCEPTED MANUSCRIPT

Kinetic and thermodynamic study of the photochemical degradation of patulin Raquel Ibarz, Alfonso Garvín*, Albert Ibarz

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Food Engineering Unit, Food Technology Department, University of Lleida

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Av. Rovira Roure, 191, 25198, Lleida, Catalonia (Spain)

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*Corresponding author

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E-mail: [email protected]

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ABSTRACT

In a previous work, the UV photodegradation of patulin was concluded to follow a firstorder kinetic and to be faster at acidic pH. In this case, the UV photodegradation of

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aqueous patulin solutions was studied at acidic pH values (3-6) similar to the values of

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apple juices where patulin has been found, obtaingint that the first-order kinetic constant increased when the acidity of the reaction media was also increased (pH decreased). From the parameters obtained by fitting the experimental data to both the Arrhenius and

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Van’t Hoff equations, the existence of kinetic and thermodynamic compensations was studied. Apparent kinetic and thermodynamic compensations were concluded, the

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isokinetic and isoequilibrium temperatures being -13.4 and -15.4ºC, respectively. As the harmonic mean temperature was 34.3ºC, applying the statistical criterion, it was concluded that both compensations were real, the reaction mechanism control changing from enthalpic for temperatures lower than the isokinetic-isoequilibrium temperatures (13.4/-15.4ºC) to entropic for higher temperatures. It could also be concluded that the reaction rate depends on the pH value for the acidic range studied.

Keywords:

Photodegradation,

patulin,

kinetic

compensation, UV radiation.

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compensation,

thermodynamic

ACCEPTED MANUSCRIPT 1.- INTRODUCTION

Patulin (PAT) is a mycotoxin produced by fungi that has been found in apple juices and nectars (Marín et al., 2011). As PAT was shown to be mutagenic and to cause neurotoxin, immunotoxic, genotoxic and gastrointestinal effects in rodents (Hopkins, 1993), the maximum tolerance limit in juices was established

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at 10-50 g/L (European Commission, 2003; FDA-U.S. Food and Drug Administration, 2004; WHO, 1995). PAT has to be minimized by removing and

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trimming decayed and damaged fruit but fungal growth can occur internally

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(Bosco and Mollea, 2012) and the contamination can also appear or be increased during storage. So, as PAT is resistant to the usual thermal treatments (Acar et

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al., 1998; Wheeler et al., 1987), alternative methods to treat apple-based products are required once the juice has been contaminated.

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The main alternative methods studied are filtration (Huebner et al., 2000), adsorption (Kadakal and Nas, 2002), ozone (McKenzie et al., 2005), pressure (Bruna et al., 1999), ionizing irradiation (Zegota et al., 1988), pulsed light

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(Funes et al., 2013) and addition of chemical additives such as sulphur

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compounds (Burroughs, 1977), ascorbic acid (Brackett and Marth, 1979), thiamine hydrochloride, pyridoxine hydrochloride and calcium pantothenate (Yazici and Velioglu, 2002), sodium benzoate (Roland et al, 1984), potassium

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sorbate and sodium propionate (Lennox and McElroy, 1984). Most of these alternative methods provoke great changes to the final juice or are unable to

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eliminate the total PAT content. UV irradiation of PAT was previously studied (Assatarakul et al., 2012; Tikekar et al., 2014; Zhu et al., 2013 and 2014) but exclusively at the germicidal wavelength of 254 nm or within the UVC range. The effect of the UV irradiation on fruit juices was studied for apple (Falguera et al., 2011), grape must (Falguera et al., 2013) and pear (Falguera et al., 2014) and in all cases the application of UV irradiation almost totally inactivated Polyphenol oxidase (PPO), Peroxidase (POD) and Pectinmethylesterase (PME) 2

ACCEPTED MANUSCRIPT enzymes, as it was desired in order to avoid changes. However, no variations were observed in pH, soluble solid content, formol index, total phenolics and sugars. The colour changed slightly due to the probably impairment of some pigments present in the juice. The only undesirable change was the loos of vitamin C content, showing decreases from 4 to 70% after two-hour irradiation. In the previous study of Ibarz et al.(2014), PAT was concluded to absorb

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radiation between 200 and 350 nm and its degradation was confirmed by UVVis irradiation (255-755 nm). The concentration of patulin to be irradiated was

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chosen to be 500 g/L, a value clearly higher than the legal limit of between 10

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and 50 g/kg, in order to know if a contaminated juice could be driven below the limit established by the rules. The reaction was concluded to follow first-order

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kinetics and showed a faster reaction rate for acidic pH (pH = 4) than for neutral value (pH = 7). The first-order kinetic constants also showed that the higher the

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temperature, the higher the value, although the values were not fitted to the Arrhenius equation. This study also calculated the absorbed radiation by PAT and also showed its degradation in apple juice, obtaining a lower rate than in the

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case of aqueous solutions, probably due to the fact that some juice components

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absorb radiaton causing a photoprotection effect.In this same previous study of Ibarz et al. (2014), a three-stage reaction mechanism was proposed (through an excited PAT molecule that could decline to its previous state or change to the

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photoproduct) and the absorbed radiation was concluded to depend linearly on the patulin concentration for levels below 500 g/L, as expected when the

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concentration of the absorbant is low enough (Garvin et al., 2015). Both considerations were used to conclude a first-order kinetic model (Equation 1) that matched the experimental data giving very good fits and obtaining the corresponding kinetic constants at pH 4 and 7. C P  C P0 exp  kt

(1)

CP being the concentration of PAT, C P0 the initial concentration of PAT, t the irradiation time and k the kinetic constant.

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ACCEPTED MANUSCRIPT Kinetic and thermodynamic compensations have been reported in many chemical, physical, biological and food processes (Liu et al., 2001). Kinetic compensation only takes place when the logarithm of the frequency factor (lnk0) depends linearly on the activation energy (Ea) (Garvín et al., 2017) (Equation 2), both parameters being the fittings of the linearized Arrhenius equation (Equation 3) for different values of an environmental variable (pH in this case).

Ea 1 R T

(2) (3)

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ln k  ln k 0 

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ln k 0  a  bEa

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The isokinetic temperature (Tisokin) is a mathematical consequence exclusively for this situation and is the temperature at which the kinetic constant is

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approximately the same for each pH value. Comparing Equations 2 and 3, the Tisokin can be obtained from the fitted parameters of Equation 2: 1 bR

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Tisokin 

(4)

and the kinetic constant at the Tisokin can be obtained as: (5)

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ln k Tisokin   a

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The thermodynamic compensation can similarly be found for equilibrium situations, from the Van’t Hoff equation (Equation 6) when the enthalpy variation (H) happens to depend linearly on the entropy variation (S)

ln K eq 

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(Equation 7) (Garvín et al., 2017). S H 1  R R T

(6)

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H  A  BS

(7)

From the equilibrium constant (Keq), the Gibbs free energy (G) can also be obtained: G   RT ln K eq

(8)

For these equilibrium situations, the isoequilibrium temperature (Tisoeq) is also a mathematical consequence and corresponds to the temperature at which the equilibrium constant is approximately the same for each pH value. Comparing

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ACCEPTED MANUSCRIPT equations 6 and 7, the Tisoeq can be obtained from the fitted parameters of Equation 6: Tisoeq  B

(9)

and the equilibrium constant and the Gibbs free energy both at the Tisoeq can be obtained as: A RTisoeq

(10)

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ln K eq Tisoeq    GTisoeq   A

(11)

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For chemical reactions, the transition state theory can be applied and thus the

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kinetic constant of the global reaction (k) can be related to the equilibrium constant between the reagent and the transition state (Keq) (Eyring, 1935). k BT K eq h

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k

(12)

kB being the Boltzmann’s constant (1.381·10-23 J·K-1) and h the Plank constant

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(6.626·10-34 J·s). For these cases, the thermodynamic parameters (enthalpy, entropy and Gibbs free energy) refer to this specific equilibrium stage between

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the reagents and the transition state (activation complex) and are called activation

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enthalpy (H≠), activation entropy (S≠) and activation Gibbs free energy (G≠). Thus, only when the transition state theory can be applied, if one kind of compensation happens to take place, it can be concluded (Garvín et al., 2017)

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that the other also has to occur and both the isokinetic and the isoequilibrium temperatures have to be approximately the same (e.g., Aguilar et al., 2016; Ibarz

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et al., 2016).

Krug et al. (1976a) demonstrated that the propagation of experimental errors tends to distribute the estimates of the kinetic compensation (lnk0 and Ea, both obtained from ordinary linear regression of the Arrhenius equation) following a linear relation that is called statistical compensation. Comparing the slope of the statistical compensation, it was concluded that if the experimental harmonic mean temperature (Thm) was outside the confidence interval for the isokinetic temperature, a real compensation could be concluded and the effect of the 5

ACCEPTED MANUSCRIPT environmental variable (pH) would be confirmed. However, if Thm fell within the confidence interval for the isokinetic temperature, it would have to be concluded that the linear relationship between lnk0 and Ea was the consequence of the propagation of experimental errors, the apparent observed compensation being actually statistical compensation. n

(13)

n

1  i 1 Ti

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Thm 

the same occurs for thermodynamic compensation.

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Due to the similarity between the Arrhenius and Van’t Hoff equations, exactly

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In order to distinguish between real and statistical compensation, Krug et al. (1976b) proposed a method that makes estimates independent of one another,

temperature about its mean (1/Thm).

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consisting of centering the independent variable defined as inverse experimental

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Many authors have concluded that both kinds of compensation are unreal and arise from the uncertainties and errors in the measurements of the kinetic or

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equilibrium parameters along with the statistical problems associated with the linear regression of parameters previously also fitted by linear regression that are

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mutually interdependent (Petersen et al., 1961; Exner, 1964; Sharp, 2001; Starikov et al., 2007; Barrie et al., 2012a and 2012b; Starikov, 2013; Perez-

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Benito, 2013). They all seem to be right, but this argument is included in the criterion defined by Krug et al. (1976a) to distinguish real compensation from

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statistical one. Some other authors have stated that both kinetic and thermodynamic compensation are artefacts or a phantom phenomenona (e.g., McBane, 1998; Cornish-Bowden, 2002; Perez-Benito, 2013), but none of them have been able to demonstrate that it is always an artefact or a phantom phenomenon, nor found the reason why the linear relationship related to any kind of compensation is obtained when the statistical compensation (Krug et al., 1976a) is discarded.

Leffler (1955) stated that if the experimental arithmetic mean temperature is higher than the isokinetic one, the mechanism that controls the change is entropy 6

ACCEPTED MANUSCRIPT and in the contrary case the mechanism that controls the change is enthalpy and thus the temperature. As a consequence of the statistical compensation criterion published by Krug et al. (1976a), some authors compared the isokinetic temperature with the experimental harmonic mean temperature, although each experimental temperature has its own mechanism control, depending on whether

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it is higher or lower than the isokinetic one (Garvín et al., 2017).

The aim of this work was to go in depth into the previous study of the UV-Vis

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photodegradation of patulin (Ibarz et al., 2014)by adding the study of the effect

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of the pH acidic value and checking whether the reaction follows the kinetic and thermodynamic compensations. If real compensations were concluded, the

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reaction mechanism that controls the reaction (between enthalpic and entropic) could also be known. The pH range was set from 3 to 6, due to the fact that these

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acidic values were the ones expected for fruit juices where the patulin could be present.

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2.- MATERIAL AND METHODS

3, 4, 5

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Aqueous solutions of PAT were prepared at a concentration of 500 g/L at pH and 6. The pH of each solution was obtained by the buffer

phosphate/citric acid (McIlvaine, Germany).

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The irradiation of samples was performed in an installation consisting of a black chamber containing the reactor and the lamp (Ibarz et al., 2014). Eight

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hundred mL of the samples were placed in the 12.5×10.5×10 cm reactor made of methacrylate, so that the surface of the sample was 23.9 cm from the lamp and the solution height was 6.1 cm. The reactor was mixed using a magnetic stirrer. In order to maintain a constant temperature in the sample contained in the reactor, a refrigerant coil was used. This allowed the working temperatures (8, 25, 45, and 65 ° C) to be set with a variation of ± 1° C. The lamp used was a midpressure 460 W nominal power mercury Philips HPM 12 (Philips, The Netherlands) emitting on the 250-735 nm wavelength range. In order to maintain a constant lamp UV emission, it was turned on 10 minutes before placing the 7

ACCEPTED MANUSCRIPT samples to be radiated. Aqueous solutions of PAT were irradiated for 90 minutes, taken 2 mL-aliquots to analyze the PAT content. The PAT content in the different samples tested was determined using a 1260 Infinity HPLC chromatograph (Agilent Technologies, Germany) according to the method used in the previous study (Ibarz et al., 2014). The analytical column used was a ZORBAX Eclipse Plus C18 4.6x100 mm, 3.5 m (Agilent

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Technologies, Germany). The detector was a DAD (Agilent Technologies, Germany) at 276 nm. The solvents used were miliQ water and acetonitrile

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(Sigma, Germany), with a water/acetonitrile ratio 99/1 as the mobile phase. The

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column worked in the reverse phase and with a flow of 1 mL/min and 1 µL of aqueous solution of PAT was injected into it. This solution was filtered prior to

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injection with a 0.45 µm filter Chromafil GF/PET-45/25 (Macherey-Nagel, Germany).

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All the UV radiation treatments and the sample analysis were carried out in duplicate. The experimental results were fitted to different kinetic and mathematical models by linear regressions with a 95% significance level, using the Microsoft Office

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Excel (Microsoft, Co., USA, v. 2010) statistic data processing software.

3.- RESULTS AND DISCUSSION Photochemical degradation

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All experimental data of the evolution of the PAT concentration with irradiation time for the different pH and temperatures were fitted to a first-order

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kinetic equation (Equation 1), obtaining the kinetic constants of the global photodegradation. Table 1 shows the kinetic constants and correlation coefficient (R2) for each pH and temperature value. It can be seen that for each temperature value, the lower the pH value (higher acidity), the higher the value of the kinetic constant, matching the conclusion obtained in the previous work (Ibarz et al., 2014) that the acidity of the solution increased the photodegradation rate. The higher the temperature, the higher the effect of the pH value, i.e. at 8ºC, the kinetic constant varies from 3.25·10-2 min-1 at pH 3 to 2.60·10-2 min-1 at pH 6,

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ACCEPTED MANUSCRIPT while for 65ºC, the variation goes from 6.08·10-2 to 3.30·10-2 min-1 for the same pH values. Table 1 also shows how the kinetic constant increases for each pH value if the temperature also rises, as expected for most chemical reactions, according to the Arrhenius equation (Equation 3). The lower the pH value, the higher the effect of the temperature, i.e. for pH 3, the kinetic constant varies from 3.25·10-2 min-1 at

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8ºC to 6.08·10-2 min-1 at 65ºC (an increase of 87.08%), while for pH 6, the kinetic constant goes from 2.60·10-2 to 3.30·10-2 min-1 for the same temperatures

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(an increase of only 26.92%).

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Table 2 includes the fitting parameters of the Arrhenius equation (Equation 3) for each pH value, i.e. the activation energy (Ea) and the frequency factor (k0),

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along with the correlation coefficient (R2). It can be seen that the activation energy decreases when the pH increases. Considering the Arrhenius equation, the

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activation energy can be seen as sensitivity to temperature, so this tendency matches the one observed previously in Table 1. For a same increase in the value of temperatures, the increase in the kinetic constant, and thus in the

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photodegradation rate, will be higher the lower value of the pH.

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The first study (Ibarz et al., 2014) concluded that patulin was also degraded when present in apple juice and that the time needed to reach the germicide radiation dosage is lower than the time needed for the photo-degradation of the

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PAT. As it was stated above, some studies (Falguera et al., 2011; 2013 and 2014) showed that UV-Vis irradiation of fruit juices did not change the main

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physicochemical properties of the juice, except the desired inactivation of enzymes and the undesired degradation of vitamin C. So, this alternative method could be used for microorganism inactivation in fruit juices and in the cases that patulin is present in the apple juice it would be also degraded without changing significantly the physicochemical properties. The degradation of vitamin C could be corrected by adding it later.

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ACCEPTED MANUSCRIPT Kinetic compensation In order to study the kinetic compensation, the estimated values of lnk0 and Ea for each pH value (shown in Table 2) were fitted to Equation 2. Figure 1 shows that these data clearly followed a linear relationship, this being the condition for the existence of kinetic compensation, or at least to an apparent kinetic compensation. The equation fitted was the following:

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ln k 0   3.734  0.125  0.4633  0.0196Ea

(14)

As the correlation coefficient was good enough (R2 = 0.9998), comparing

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Equations 2, 4, 5 and 14, the Tiso and the kinetic constant at the Tiso could be

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calculated. Tisokin = (-13.4 ± 10.5) ºC

(16)

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k(Tisokin) = (2.39 ± 0.28)·10-2 min-1

(15)

According to the criterion of Leffler (1955), as the Tisokin was lower than the

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arithmetic mean temperature (35.75ºC), it could be concluded that the control was entropic. Since Krug et al. (1976a) published the criterion for distinguishing statistical compensation, some authors have used the harmonic mean temperature

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(Thm) defined by Equation 13. As the Thm is 34.1ºC, the conclusion about the

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control would be the same. However, Garvin et al. (forthcoming a) stated that every working temperature has its own control mechanism, thus, this mechanism seemed to be enthalpic for working temperatures lower than the Tisokin (-

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13.4±10.5ºC) and entropic for higher temperatures, including the whole experimental range of temperatues (8-65ºC).

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When the control is enthalpic (temperatures lower than -13.4ºC), any change in the environmental variable (pH in this case) causes changes in both the lnk0 and the activation energy (Ea). In this case, the new value that most affects the new kinetic constant is the new activation energy (Ea), what means that the reaction is more sensitive to the change in the temperature than the change in agitation. On the contrary, when the control is entropic (temperatures higher than -13.4ºC), any change in the environmental variable causes higher changes in the new lnk0 value and thus the reaction is less sensitive to changes in the temperature and more sensitive to such entropic changes as agitation. 10

ACCEPTED MANUSCRIPT The whole confidence interval for the Tisokin (from -23.9 to 2.9ºC) did not clearly contain the value of the Thm. Therefore, applying the criterion of the statistical compensation (Krug et al., 1976a), the kinetic compensation could be concluded to be real because the propagation of the experimental errors could not justify this level of compensation. Figure 2 shows the kinetic constants of the global photodegradation at each pH

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and temperature. This figure also includes the isokinetic point (-13.4ºC, 2.39·10-2 min-1). It can be seen that the kinetic constant tends toward the same isokinetic

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point for all the pH values, i.e. the kinetic constant seems to be the same value

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for all pH values as long as the temperature is the isokinetic point (-13.4ºC), as shown in many other cases (e.g., Flores-Andrade et al., 2009; Ibarz et al., 2016;

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Aguilar et al., 2016).

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Thermodynamic compensation

If the global photodegradation process is considered to follow the transition state theory, where a transition state or complex can be supposed, the equilibrium

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constant of the activation stage can be calculated from the global kinetic

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constants by using Equation 12. Table 3 shows the equilibrium constant values (Keq) obtained at each pH and temperature value. Table 3 also shows the Gibbs free energy of activation (G≠) calculated from Equation 8, these equilibrium

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parameters corresponding to the equilibrium stage between the reagent and the transition state, as defined by the transition state theory. In any case, these

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equilibrium parameters cannot be related to the global reaction. From the equilibrium constant and the temperature values, the estimates of the activation enthalpy (H≠) and the activation entropy (S≠) were obtained at each pH value by fitting the Van’t Hoff equation (Equation 6). Table 4 shows these estimates and the correlation coefficients (R2). It can be seen that all the correlation coefficients were good enough, the minimum value being 0.8836. As thermodynamic compensation takes place when the activation enthalpy (H≠) depends linearly on the activation entropy (S≠), the values of Table 4 were fitted to Equation 7 by linear regression. Figure 3 shows the values and the 11

ACCEPTED MANUSCRIPT linear

regression

obtained,

showing

a

good

apparent

thermodynamic

compensation. The equation of the linear regression was: H   7.95  0.36·104  257.6  3.1S 

(17)

As the correlation coefficient (R2) was 0.9998, a very close linear relationship could be concluded.

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By comparing Equations 7, 9, 10 and 17, the isoequilibrium temperature (Tisoeq) and the equilibrium constant at this specific temperature were obtained: -17

(18) (19)

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Keq(Tisoeq) = (7.41±0.62)·10

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Tisoeq = (-15.4 ± 11.2) ºC

The G(Tisoeq) was obtained from Equation 11 and found to be (7.95 ±

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0.36)·104 J·mol-1. This value being positive means that the equilibrium stage between the reagent and the activation state is not spontaneous, but nothing can

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be stated about the spontaneity of the global photodegradation process. Figure 4 shows the dependence of the equilibrium constant (Keq) on the temperature at the different pH values studied. It can be seen that the equilibrium

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constant tends towards the isoequilibrium point (-15.4ºC, 7.51·10-17) for each pH

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value. Therefore, the equilibrium constant seems to be the same as (or at least very close to) this specific isoequilibrium temperature (-15.4ºC), regardless of the pH value. Similarly, the Gibbs free energy of activation (G≠) also tends towards

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the same isoequilibrium point (-15.4ºC, 7.95·104 J·mol-1) for all the different acidic pH values studied.

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As in the case of the isokinetic temperature, the criterion of Leffler (1955) states that when the Tisoeq is lower than the arithmetic mean temperature (35.75ºC), the control could be concluded as entropic. In this case, some authors also used the Thm to compare to the Tisoeq, the conclusion about the control being the same for this case. However, as every working temperature has its own control mechanism (Garvín et al., 2017), the control mechanism seems to be enthalpic for working temperatures lower than the Tisoeq (-15.4±11.2ºC) and entropic for higher temperatures. Obviously, the control mechanism that was inferred did not depend on the kind of compensation studied. 12

ACCEPTED MANUSCRIPT In a similar way to the kinetic compensation, when the control is enthalpic (temperatures lower than -15.4ºC), any change in the pH causes changes in both the activation enthalpy (H≠) and the activation entropy (S≠), but the new value that most affects the new equilibrium constant (or Gibbs energy of activation) is the new activation enthalpy (H≠). The activation enthalpy is related to the activation energy (Ea) through the following empirical equation (Daniels et al.,

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1975). Ea  H   RT

(20)

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Thus, with the activation energy being the sensitivity of the reaction rate on the

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temperature, it implies that the reaction is more sensitive to changes in the temperature. On the contrary, when the control is entropic (temperatures higher

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than -15.4ºC), any change in the pH causes higher changes in the new activation entropy (S≠) value and thus the reaction is less sensitive to changes in the

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temperature and more sensitive to such entropic changes as agitation. When the criterion of the statistical compensation (Krug et al., 1976a) is applied in a similar way as for the kinetic compensation, as the Thm does not

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belong to the confidence interval for the Tisoeq (from -26.6 to -4.2ºC), it can be

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concluded that the thermodynamic compensation is real and not due to the propagation of experimental errors. As expected, the isokinetic and the isoequilibrium temperatures were very

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similar (Garvín et al., 2017). Mathematically, they should be equal, but the experimental errors and the fact that both the Arrhenius and the Van’t Hoff

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equations are empirical and no scientific laws causes little differences between both values.

Solvation compensation Some authors (e.g., Gallicchio et al., 1998; Gilli et al., 1994; Leung et al., 2008) have stated that the thermodynamic compensation (and thus the kinetic compensation) observed for both complex processes and complex reagents can be due to the thermodynamic compensation due exclusively to the nonpolarwater solvation process. The prior desolvation process that takes always place 13

ACCEPTED MANUSCRIPT before any complex process causes rearrangement of the hydrogen bonds and this process has been shown to follow thermodynamic compensation (Garvín et al., 2017). Taking into account that the pH of the solution will probably affect the solvation stability and that the PAT molecule is relatively complex, with both nonpolar and polar zones, both the thermodynamic and kinetic compensation

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observed could be due to the desolvation process of the molecule prior to the

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subsequent photodegradation process.

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CONCLUSIONS

The UV irradiation degrades the PAT and the photodegradation follows a

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first-order kinetic order. The more acidic the solution, the faster the reaction rate. The dependence of the kinetic constant on the temperature allowed the

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Arrhenius parameters to be obtained for each acidic pH value, from which a linear relationship was observed and thus kinetic compensation was concluded, the isokinetic temperature being -13.4ºC. As the harmonic mean temperature was

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not included in the confidence interval of the isokinetic temperature, the kinetic

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compensation was concluded to be real and thus not masked by the statistical one. This isokinetic temperature also defines two control mechanism zones, so for temperatures lower than -13.4ºC the control was enthalpic and entropic for

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higher temperatures.

Considering that the whole process follows the transition state theory, the

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equilibrium constant of the stage between PAT and the transition state was calculated at each pH and temperature value. From these values, the thermodynamic compensation was also concluded, obtaining an isoequilibrium temperature of -15.4ºC. From this value, it was also concluded that the thermodynamic compensation was real and the control mechanism entropic for temperatures higher than -15.4ºC. As expected, the isokinetic and isoequilibrium temperatures were very similar.

14

ACCEPTED MANUSCRIPT As real compensations were concluded, the pH was assumed to affect the global reaction rate without changing the reaction mechanism for the range of pH values studied. Not only can UV-Vis treatment be used in any fruit juice treatment to inactivate microorganisms and the undesirable enzymes (PPO and POD) without changing significantly the physicochemical properties but also to degrade patulin

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in apple juices when it is present. The undesired degradation of vitamin C can be

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corrected by adding it later.

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ACCEPTED MANUSCRIPT REFERENCES

Acar, J., Gokmen, V., Taydas, E.E. (1998). The effects of processing technology on the patulin content of juice during commercial apple juice concentrate production. Zeitschrift fuer Lebensmittel-Untersuchung und-Forschung A/Food Research and Technology, 207(4), 328-331.

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Aguilar, K., Garvín, A., Azuara, E., Ibarz, A. (2016). Rate-controlling mechanisms in the photo-degradation of HMF. Food and Bioprocess

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Technology, 9, 1399-1407.

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Assatarakul, K., Churey, J.J., Manns, D.C., Worobo, R.W. (2012). Patulin reduction in apple juice from concentrate by UV radiation and comparison of

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kinetic degradation models between apple juice and apple cider. Journal of Food Protection, 75, 717-724.

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Barrie, P.J. (2012a). The mathematical origins of the kinetic compensation effect: 1. The effect of random experimental errors. Physical Chemistry Chemical Physics, 14, 318-326.

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Barrie, P.J. (2012b). The mathematical origins of the kinetic compensation

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effect: 2. The effect of systematic errors. Physical Chemistry Chemical Physics, 14, 327-336.

Bosco, F. and Mollea, C. (2012). Mycotoxins in food. In Benjamin Valdez (Ed.),

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Food Industrial Processes-Methods and Equipment. InTech978-953-307-905-9, http://dx.doi.org/10.5772/33061

(Available

from:

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http://www.intechopen.com/books/foood-industrial-processes-methods-andequipment/mycotonxins-in-food). Cornish-Bowden, A. (2002). Enthalpy-entropy compensation: a phantom phenomenon. Journal of Biosciences, 27, 121-126. Daniels, F., Alberty, R. A. (1975). Physical chemistry, 4th edn. John Wiley and Sons, 318-322. Exner, O. (1964). On the enthalpy-entropy relationship. Collection of Czechoslovak Chemical Communications, 26, 1094-1113. Eyring, H., Wynne-Jones, F.K. (1935). Journal of Chemical Physics, 3, 492. 16

ACCEPTED MANUSCRIPT European Commission. (2003). Commission Regulation (EC) No. 1425/2003 of 11 August 2003 amending Regulation (EC) No. 466/2001 as regards patulin. Official Journal of the European Union of 12 August 2003 L 230 (pp. 1–3). Falguera, V., Pagán, J., Ibarz, A. (2011). Effect of UV irradiation on enzymatic activities and physicochemical properties of apple juices from different varieties. LWT- Food Science and Technology, 44, 115-119.

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Falguera, V., Garza, S., Pagán, J., Garvín, A., Ibarz, A. (2013). Effect of UV-Vis irradiation on enzymatic activities and physicochemical properties of four grape

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musts from different varieties. Food and Bioprocess Technology, 8, 2223-2229.

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Falguera, V., Garvín, A., Garza, S., Pagán, J., Ibarz, A. (2014). Effect of UV-Vis photochemical processing on pear juices from six different varieties. Food and

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Bioprocess Technology, 7, 84-92.

FDA-U.S. Food and Drug Administration. (2004). Apple juice, apple juice

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concentrates, and apple juice products-adulteration with patulin. Compliance policy guidance for FDA staff. Sec. 510.150. Available

at:

http://www.fda.gov/ora/compliance_ref/cpg/cpgfod/cpg510-

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150.htm.

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Flores-Andrade, E., Beristain, C.I., Vernon-Carter, E.J., Gutiérrez, G.F., Azuara, E. (2009). Enthalpy–entropy compensation and water transfer mechanism in osmotically dehydrated agar gel. Drying Technology, 27(9), 999–1009.

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Gallicchio, E., Kubo, M.M., Levy, R.M. (1998). Entropy-enthalpy compensation in solvation and ligand binding revisited. Journal of the American Chemical

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Society, 120, 4526-4527. Garvín, A., Ibarz, R., Ibarz, A. (2015). Modelling of UV absorption in a plane photoreactor for solutions with high-patulin concentration. Food Research International, 66, 158-166. Garvín, A., Ibarz, R., Ibarz, A. (2017). Kinetic and thermodynamic compensation. A current and practical review for foods. Food Research International. Doi: 10.2016/j.foodres.2017.03.004

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ACCEPTED MANUSCRIPT Gilli, P., Ferretti, V., Gilli, G., Borea, P.A. (1994). Enthalpy-entropy compensation in drug-receptor binding. Journal of Physical Chemistry, 98, 1515-1518. Hopkins, J. (1993). The toxicological hazards of patulin. Food and Chemical Toxicology, 31, 455-456. Ibarz, R., Garvín, A., Falguera, V., Pagán, J., Garza, S., Ibarz, A. (2014).

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Modelling of patulin photo-degradation by a UV multi-wavelength emitting lamp. Food Research International, 69, 266-273.

RI

Ibarz, R., Garvín, A., Rojas, S., Azuara, E., Ibarz, A. (2016). Rate-controlling

Technology, 73, 147-152. R.R.,

Hunter,

W.G.,

Grieger,

R.A.

(1976a).

Enthalpy-entropy

NU

Krug,

SC

mechanism in the photo-degradation of ochratoxin A. LWT-Food Science and

compensation. 1. Some fundamental statistical problems associated with the

80 (21), 2335-2341. Krug,

R.R.,

Hunter,

W.G.,

MA

analysis of Van’t Hoff and Arrhenius data. The Journal of Physical Chemistry,

Grieger,

R.A.

(1976b).

Enthalpy-entropy

D

compensation. 2. Separation of the chemical from the statistical effect. The

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Journal of Physical Chemistry, 80 (21), 2341-2351. Leffler, J.E. (1955). The enthalpy-entropy relationship and its implications for organic chemistry. Journal of Organic Chemistry, 20 (9), 1202–1231.

CE

Leung, D.H., Bergman, R.G., Raymond, K.N. (2008). Enthalpy-entropy compensation reveals solvent reorganization as a driving force for

AC

supramolecular encapsulation in water. Journal of the American Chemical Society, 130, 2798-2805. Liu, L., Guo, Q. (2001). Isokinetic relationship, isoequilibrium relationship, and enthalpy-entropy compensation. Chemical Reviews, 201, 673-695. Marín, S., Mateo, E.M., Sanchis, V., Valle-Algarra, F.M., Ramos, A.J., Jiménez, M. (2011). Patulin contamination in fruit derivatives, including baby food, from the Spanish market. Food Chemistry, 124(2), 563-568. McBane, G.C. (1998). Chemistry from telephone numbers: the false isokinetic relationship. Journal of Chemical Education, 75, 919-922. 18

ACCEPTED MANUSCRIPT Perez-Benito, J.F. (2013). Some tentative explanations for the enthalpy-entropy compensation effect in chemical kinetics: from experimental errors to the Hinshelwood-like model. Monatshefte für Chemie, 144, 49-58. Petersen, R.C., Markgraf, J.H., Ross, S.D. (1961). Solvent effects in decomposition

of

1,1’-diphenylazoethane

and

2,2’-azobis-(2-

methylpropionitrile). Journal of American Chemical Society, 83, 3819-3823.

PT

Sharp, K. (2001). Entropy-enthalpy compensation: fact or artifact?. Protein Science, 10, 661-667.

RI

Starikov, E.B., Norden, B. (2007). Enthalpy-entropy compensation: a phantom or

SC

something useful?. Journal of Physical Chemistry B, 111, 14431-14435. Starikov, E.B. (2013). Valid entropy-enthalpy compensation: fine mechanisms at

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microscopic level. Chemical Physics Letters, 564, 88-92. Tikekar, R.V., Anantheswaran, R.C., LaBorde, L.F. (2014). Patulin degradation

MA

in a model apple juice system and in apple juice during ultraviolet processing. Journal of Food Processing and Preservation, 38, 924-934. Wheeler, J.L., Harrison, M.A. and Koehler, P.E. (1987). Presence of patulin in

D

pasteurized apple cider. Journal of Food Science, 52, 479-480.

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WHO. (1995). World Health Organization, 44th Report of the joint FAO/WHO expert committee on food additives. In Technical report series (Vol. 859, p. 36). Zhu, Y., Koutchma, T., Warriner, K., Shao, S., Zhou, T. (2012). Kinetics of

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Patulin degradation in model solution, apple cider and apple juice by ultraviolet radiation. Food Science and Technology International, 19, 291-303.

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Zhu, Y., Koutchma, T., Warriner, K., Zhou, T. (2014). Reduction of Patulin in apple juice products by UV light of different wavelengths in the UVC range. Journal of Food Protection, 77, 963-971.

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ACCEPTED MANUSCRIPT 0.5 0

ln k0

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Ea (kJ/mol)

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Figure 1.- Linear relationship between lnk0 and Ea. Mathematical requirement for the isokinetic compensation.

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0.07 0.06

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pH=6

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Figure 2.- Kinetic constants for the global PAT photodegradation for all the pH and temperature values. The isokinetic point is also included.

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5000 4000 3000 2000 1000 0 -310

-305

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S# (J·mol-1·K-1)

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Figure 3.- Linear relationship between the activation enthalpy and entropy. Mathematical requirement for thermodynamic compensation.

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Figure 4.- Equilibrium constant of the equilibrium stage between PAT and the transition state at each pH and temperature value. The isoequilibrium point is also included.

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ACCEPTED MANUSCRIPT Table 1.- Fitting parameters of first-order kinetic photodegradation of patulin for an initial aqueous concentration of 500 g·L-1.

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0.9998 0.9999 0.9998 0.9999 0.9979 0.9962 0.9970 0.9903 0.9979 0.9996 0.9988 0.9993 0.9997 0.9956 0.9998 0.9992

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k·102 (min-1) 3.25 ± 0.08 4.20 ± 0.02 5.00 ± 0.07 6.08 ± 0.01 2.97 ± 0.09 3.93 ± 0.10 4.64 ± 0.09 5.18 ± 0.18 2.71 ± 0.12 3.49 ± 0.06 3.59 ± 0.09 3.88 ± 0.04 2.60 ± 0.05 2.91 ± 0.15 3.10 ± 0.03 3.30 ± 0.04

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T (ºC) 8 25 45 65 8 25 45 65 8 25 45 65 8 25 45 65

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ACCEPTED MANUSCRIPT Table 2.- Fitting parameters of the Arrhenius equation for all the acidic pH values studied. pH

Ea (kJ·mol-1) 8.69 7.59 4.57 3.22

0.9833 0.9643 0.8467 0.9782

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k0 (min-1) 1.339 0.798 0.203 0.105

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9.3 ± 0.4 11.3 ± 0.5 12.6 ± 0.6 14.4 ± 0.7 8.5 ± 0.4 10.5 ± 0.5 11.7 ± 0.5 12.3 ± 0.6 7.7 ± 0.3 9.37 ± 0.4 9.02 ± 0.5 9.18 ± 0.5 7.40 ± 0.4 7.81 ± 0.4 7.79 ± 0.5 7.81 ± 0.5

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G#·103 (J·mol-1) 86.2 91.0 96.8 102.5 86.5 91.1 97.0 103.0 86.7 91.4 97.7 103.8 86.8 91.9 98.1 104.2

Keq·1017

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Table 3.- Equilibrium parameters of the equilibrium stage between the patulin and the transition state for the global first-order kinetic photodegradation of patulin for an initial aqueous concentration of 500 g·L-1.

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H# (J·mol-1) 5928 5031 2017 658

R2 0.9848 0.9156 0.8836 0.8942

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S# (J·mol-1·K-1) -285.7 -289.4 -300.8 -306.3

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ACCEPTED MANUSCRIPT Highlights Patulin was photo-degradated at acidic pH values.

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Kinetic and thermodynamic compensation were concluded.

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Both the isokinetic and isoequilibrium temperatures were very similar.

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The reaction mechanism follows entropic control at room temperature

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