The photochemical model for surface waters The model describes the transformation kinetics of a substrate, a generic pollutant P, as a function of water chemistry and substrate reactivity via the main photochemical reaction pathways (direct photolysis and reaction with •OH, CO3−•, 1O2 and 3CDOM*). It also calculates the steady-state concentrations of photogenerated transients in a cylindrical volume of 1 cm2 surface area and depth
SUPPLEMENTARY ONLINE MATERIAL
d. The model may use actual data of water absorption spectrum or, in their absence (as in the present case), it can approximate the spectrum from the dissolved organic carbon (DOC) values. The different aspects of the model will now be described in greater detail.
Surface-water absorption spectrum
Modelling photochemical transformation of emerging organic pollutants in surface waters: Effect of water level fluctuations following outflow or evaporation
It is possible to find a reasonable correlation between the absorption spectrum of surface waters and their content of dissolved organic matter, expressed as DOC. The following equation holds for the water spectrum, referred to an optical path length of 1 cm:1
A1 (λ ) = (0.45 ± 0.04) ⋅ DOC ⋅ e − (0.015± 0.002)⋅λ a
a
a
ab
(1)
Marco Minella , Valter Maurino , Claudio Minero and Davide Vione *
As an obvious alternative, A1(λ) can be spectrophotometrically determined on a real water sample.
a
Reaction with •OH 1
Università degli Studi di Torino, Dipartimento di Chimica, Via P. Giuria 5, 10125 Torino, Italy. http://www.chimicadellambiente.unito.it b Università degli Studi di Torino, Centro Interdipartimentale NatRisk, Via Leonardo da Vinci 44, 10095 Grugliasco (TO), Italy. http://www.natrisk.org
In natural surface waters under sunlight illumination, the main •OH sources are (in order of average importance) Chromophoric Dissolved Organic Matter (CDOM), nitrite, and nitrate. All these species produce •OH upon absorption of sunlight. The calculation of the photon fluxes absorbed by CDOM, nitrate and nitrite requires to take into account the mutual competition for sunlight
*
Corresponding
author.
[email protected]
Tel.
+39-011-6705296;
Fax
+39-011-6707615;
E−mail:
irradiance, also considering that CDOM is the main absorber in the UV region where also nitrite and nitrate absorb radiation. At a given wavelength λ, the ratio of the photon flux densities absorbed by two different species is equal to the ratio of the respective absorbances. The same is also true for the ratio of the photon flux density absorbed by species to the total photon flux density absorbed by the solution, patot(λ).2 Accordingly, the following equations hold for the different •OH sources (note that A1(λ) is the specific absorbance of the surface water layer over a 1 cm optical path length, in units of cm−1; d is the water column depth in m; Atot(λ) the total absorbance of the water column, and p°(λ) the spectrum of sunlight): Atot (λ ) = 100 A1 (λ ) ⋅ d
(2)
1
D. Vione, R. Das, F. Rubertelli, V. Maurino, C. Minero, S. Barbati, S. Chiron, Modelling the occurrence and reactivity of hydroxyl radicals in surface waters: Implications for the fate of selected pesticides. Intern. J. Environ. Anal. Chem. 90 (2010) 258-273. 2 S. E. Braslavsky, Glossary of terms used in photochemistry, 3rd edition. Pure Appl. Chem. 79 (2007) 293-465.
ii
ANO 3− (λ ) = 100 ε NO 3− (λ ) ⋅ d ⋅ [ NO3− ]
(3)
Various studies have yielded useful correlation between the formation rate of •OH by the
ANO 2− (λ ) = 100 ε NO 2− (λ ) ⋅ d ⋅ [ NO ]
(4)
photoactive species and the respective absorbed photon fluxes of sunlight. In particular, it has been
ACDOM (λ ) = Atot (λ ) − ANO 3− (λ ) − ANO 2− (λ ) ≈ Atot (λ )
(5)
found that:1,4
− 2
p (λ ) = p°(λ ) ⋅ (1 − 10 tot a
p
CDOM a
− Atot ( λ )
)
R•CDOM = (3.0 ± 0.4) ⋅10 −5 ⋅ PaCDOM OH
(6)
(λ ) = p (λ ) ⋅ ACDOM (λ ) ⋅ [ Atot (λ )] ≈ p (λ ) −1
tot a
tot a
(7)
p aNO 2− (λ ) = p atot (λ ) ⋅ ANO 2− (λ ) ⋅ [ Atot (λ )]−1
(8)
p aNO 3− (λ ) = p atot (λ ) ⋅ ANO 3− (λ ) ⋅ [ Atot (λ )]−1
(9)
An important issue is that p°(λ) is usually reported in units of Einstein cm
−2
s
−1
NO 2− •OH
R
= ∫Φ λ
NO2− • OH
(λ ) p
NO 2− a
3− −2 ⋅ R•NO OH = ( 4.3 ± 0.2) ⋅ 10
nm
−1
(see for
instance Figure SOM1), thus the absorbed photon flux densities are expressed in the same units. To express the formation rates of •OH in M s−1, the absorbed photon fluxes Pai should be expressed in
(13)
( λ ) dλ
(14)
[ IC ] + 0.0075 ⋅ PaNO 3− 2.25 [ IC ] + 0.0075
(15)
where [IC] = [H2CO3] + [HCO3−] + [CO32−] is the total amount of inorganic carbon. The − 2 (λ ) are reported in Table 1. wavelength-dependent data of Φ NO • OH
Einstein L−1 s−1. Integration of pai(λ) over wavelength would give units of Einstein cm−2 s−1 that Table 1. Values of the quantum yield of •OH photoproduction by nitrite, for different wavelengths of environmental
represent the moles of photons absorbed per unit surface area and unit time.
significance.
λ, nm
−
2 Φ NO (λ ) • OH
λ, nm
−
2 Φ NO (λ ) • OH
λ, nm 350
−
2 Φ NO (λ ) • OH
292.5
0.0680
315.0
0.061
0.025
295.0
0.0680
317.5
0.058
360
0.025
297.5
0.0680
320.0
0.054
370
0.025
300.0
0.0678
322.5
0.051
380
0.025
302.5
0.0674
325.0
0.047
390
0.025
305.0
0.0668
327.5
0.043
400
0.025
307.5
0.066
330.0
0.038
410
0.025
310.0
0.065
333.3
0.031
420
0.025
312.5
0.063
340.0
0.026
430
0.025
Figure SOM1. Sunlight spectral photon flux density at the water surface per unit area. The corresponding UV irradiance is 22 W m−2.3
At the present state of knowledge it is reasonable to hypothesise that CDOM, nitrite and nitrate generate •OH independently, with no mutual interactions. Therefore, the total formation rate of •OH 2
Assuming a cylindrical volume of unit surface area (1 cm ) and depth d (expressed in m), the −1
absorbed photon fluxes in Einstein L s
−1
units would be expressed as follows (note that 1 L = 10
(R•OHtot) is the sum of the contributions of the three species:
3
cm3 and 1 m = 102 cm):
2− NO 3− R•totOH = R•CDOM + R•NO OH OH + R•OH
PaCDOM = 10 d −1
∫λ p
PaNO 2− = 10 d −1
∫λ p
PaNO 3− = 10 d −1
∫λ p
CDOM a
( λ ) dλ
NO 2− a
( λ ) dλ
(11)
NO 3− a
( λ ) dλ
(12)
−
Accordingly, having as input data d, A1(λ), [NO3 ], [NO2 ] and p°(λ) (the latter referred to a 22 W
(10)
m−2 sunlight UV irradiance, see Figure SOM1), it is possible to model the expected R•OHtot of the sample. The photogenerated •OH radicals could react either with the pollutant P or with the natural scavengers present in surface water (mainly organic matter, bicarbonate, carbonate and nitrite). The natural scavengers have a •OH scavenging rate constant:
4 3
(16) −
R. Frank, W. Klöpffer, Spectral solar photo irradiance in Central Europe and the adjacent north Sea, Chemosphere 17 (1988) 985-994.
iii
D. Vione, S. Khanra, S. Cucu Man, P. R. Maddigapu, R. Das, C. Arsene, R. I. Olariu, V. Maurino, C. Minero, Inhibition vs. enhancement of the nitrate-induced phototransformation of organic substrates by the •OH scavengers bicarbonate and carbonate. Wat. Res. 43 (2009) 4718-4728.
iv
Σi kSi [Si] = 5×104 DOC + 8.5×106 [HCO3−] + 3.9×108 [CO32−] + 1.0×1010 [NO2−] (units of s−1; DOC is expressed in mg C L−1, the other concentration values are in molarity). Accordingly, the reaction rate between P and •OH can be expressed as follows: k P ,•OH [ P]
•
RPOH = R •totOH
(17)
k P ,•OH [ P] + ∑i k Si [ S i ]
sample over a 1 cm optical path length, Atot(λ) the total absorbance of the water column, p°(λ) the spectrum of sunlight, referred to a UV irradiance of 22 W m−2 as per Figure 1, εP(λ) the molar absorption coefficient of P, in units of M−1 cm−1, and paP(λ) its absorbed spectral photon flux density; it is also paP(λ) « patot(λ) and AP(λ) « Atot(λ) in the very vast majority of the environmental cases):
where kP,•OH is the second-order reaction rate constant between P and •OH and [P] is a molar concentration. Note that, in the vast majority of environmental cases it would be kP,•OH [P] « Σi kSi [Si], thus the kP,•OH [P] term can be neglected at the denominator of equation (17). The pseudo-first
(20)
AP (λ ) = 100 ε P (λ ) ⋅ d ⋅ [ P] patot (λ ) = p°(λ ) ⋅ (1 − 10 − Atot ( λ ) )
(21) (22)
paP (λ ) = patot (λ ) ⋅ AP (λ ) ⋅ [ Atot (λ )]−1
order degradation rate constant of P is kP = R•OHP [P] −1, and the half-life time is tP = ln 2 kP−1. The
time tP is expressed in seconds of continuous irradiation under sunlight, at 22 W m−2 UV irradiance.
Atot (λ ) = 100 A1 (λ ) ⋅ d
(23) −1
P
To express the rate of P photolysis in M s , the absorbed photon flux Pa should be expressed in
It has been shown that the sunlight energy reaching the ground in a summer sunny day (SSD) such
Einstein L−1 s−1. Integration of paP(λ) over wavelength would give units of Einstein cm−2 s−1 that
−2
represent the moles of photons absorbed per unit surface area and unit time. Assuming a cylindrical
UV irradiance.5 Accordingly the half-life time of P, because of reaction with •OH, would be
volume of unit surface area (1 cm2) and depth d (expressed in m), the absorbed photon flux in
as 15 July at 45°N latitude corresponds to 10 h = 3.6⋅10 s of continuous irradiation at 22 W m 4
expressed as follows in SSD units:
τ PSSD = , OH •
ln 2 ∑ik Si [ S i ] 3.6 ⋅10 4 R•totOH k P ,•OH
= 1.9 ⋅10 −5
∑k
i Si
[ Si ]
PaP = 10 d −1 ∫ paP (λ ) dλ
(18)
R•totOH k P ,•OH
be: [ OH ] =
R •totOH
∑k i
Si
[ Si ]
(24)
λ
Note that 1.9⋅10−5 = ln 2 (3.6⋅104)−1. The steady-state [•OH] under 22 W m−2 UV irradiance would
•
Einstein L−1 s−1 units would be expressed as follows (note that 1 L = 103 cm3 and 1 m = 102 cm):
The rate of photolysis of P, expressed in M s−1, can be expressed as follows (note that 1 L = 103 cm3 and 1 m = 102 cm): RateP = 10 d −1 ∫ Φ P (λ ) paP (λ ) dλ
(25)
λ
(19)
where ΦP(λ) is the photolysis quantum yield of P in the relevant wavelength interval, and d is expressed in cm (also note that 1 L = 103 cm3). In most cases only the average value ΦP of the photolysis quantum yield is known, and it can be placed outside the integral. The pseudo-first order
Direct photolysis
degradation rate constant of P is kP = RateP [P] −1, which corresponds to a half-life time tP = ln 2
6,7
(kP)−1. The time tP is expressed in seconds of continuous irradiation under sunlight, at 22 W m−2 UV
The calculation of the photon flux absorbed by P requires taking into account the mutual
irradiance. The sunlight energy reaching the ground in a summer sunny day (SSD) such as 15 July
competition for sunlight irradiance between P and the other lake water components (mostly
at 45°N latitude corresponds to 10 h = 3.6×104 s continuous irradiation at 22 W m−2 UV irradiance.5
Chromophoric Dissolved Organic Matter, CDOM, which is the main sunlight absorber in the
Accordingly, the half-life time expressed in SSD units would be given by:
τSSDP = (3.6×104)−1 ln 2 (kP)−1 = 1.9×10−5 [P] d 10−1 (ΦP PaP)−1 =
spectral region of interest, around 300-500 nm). Under the Lambert-Beer approximation, at a given wavelength λ, the ratio of the photon flux densities absorbed by two different species is equal to the ratio of the respective absorbances.2 Accordingly, the photon flux absorbed by P in a water column of depth d (expressed in m) can be obtained by the following equations (note that A1(λ) is the specific absorbance of the surface water 5
6
7
C. Minero, S. Chiron, G. Falletti, V. Maurino, E. Pelizzetti, R. Ajassa, M. E. Carlotti, D. Vione, Photochemical processes involving nitrite in surface water samples. Aquat. Sci. 69 (2007) 71-85. D. Vione, J. Feitosa-Felizzola, C. Minero, S. Chiron, Phototransformation of selected human-used macrolides in surface water: Kinetics, model predictions and degradation pathways. Wat. Res. 43 (2009) 1959-1967. D. Vione, M. Minella, C. Minero, V. Maurino, P. Picco, A. Marchetto, G. Tartari, Photodegradation of nitrite in lake waters: role of dissolved organic matter. Environ. Chem. 6 (2009) 407-415.
v
= 1.9×10−6 [P] d (ΦP
∫λ p
NCP a
= 1.9×10−6 [P] d (ΦP
∫λ p
tot a
(λ ) dλ )−1 =
(λ ) ⋅ AP (λ ) ⋅ [ Atot (λ )]−1 dλ )−1 =
1 . 9 × 10 − 6 d [ P ]
= ΦP
∫λ p °( λ ) (1 − 10
− 100 A1 ( λ ) d
)
ε P (λ ) dλ A1 ( λ )
(26)
Note that 1.9⋅10−6 = (ln 2) 0.1 (3.6⋅104)−1.
vi
Reaction with CO3−• 8
Note that 1.9⋅10−5 = ln 2 (3.6⋅104)−1. The steady-state [CO3−•] under 22 W m−2 UV irradiance would be:
The radical CO3−• can be produced upon oxidation of carbonate and bicarbonate by •OH, upon carbonate oxidation by 3CDOM*, and possibly also from irradiated Fe(III) oxide colloids and
[CO3− • ] =
carbonate. However, as far as the latter process is concerned, there is still insufficient knowledge
tot R CO −•
(35)
3
k 30 ⋅ DOC
about the Fe speciation in surface waters to enable a proper modelling. The main sink of the carbonate radical in surface waters is the reaction with DOM, which is considerably slower than that between DOM and •OH. •
OH + CO32− → OH− + CO3−• OH + HCO3− → H2O + CO3−• 3 CDOM* + CO32− → CDOM−• + CO3−• DOM + CO3−• → DOM+• + CO32− •
[k27 = 3.9×108 M−1 s−1] [k28 = 8.5×106 M−1 s−1] [k29 ≈ 1×105 M−1 s−1] [k30 ≈ 102 (mg C)−1 s−1]
The formation of singlet oxygen in surface waters arises from energy transfer between ground-state
(27) (28) (29) (30)
The formation rate of CO3−• in reactions (27, 28) is given by the formation rate of •OH times the fraction of •OH that reacts with carbonate and bicarbonate, as follows: R
•
OH CO3−•
=R
tot • OH
8.5 ⋅ 106 ⋅ [HCO3− ] + 3.9 ⋅ 108 ⋅ [CO32 − ] ⋅ 4 5 ⋅ 10 ⋅ D OC+ 1.0 ⋅ 1010 ⋅ [NO2− ] + 8.5 ⋅ 106 ⋅ [HCO3− ] + 3.9 ⋅ 108 ⋅ [CO32 − ]
Reaction with 1O2 9
molecular oxygen and the excited triplet states of CDOM (3CDOM*). Accordingly, irradiated CDOM is practically the only source of 1O2 in aquatic systems. In contrast, the main 1O2 sink is the energy loss to ground-state O2 by collision with water molecules, with a pseudo-first order rate constant k 1O = 2.5×105 s−1. Dissolved species, including dissolved organic matter that is certainly 2
able to react with 1O2, would play a minor role as sinks of 1O2 in aquatic systems. The main processes involving 1O2 and P in surface waters would be the following:
(31)
CDOM* + O2 → CDOM + 1O2 1 O2 + H2O → O2 + H2O + heat 1 O2 + P → Products 3
The formation of CO3−• in reaction (29) is given by:
R CDOM = 6.5 ⋅ 10 −3 ⋅ [CO 32 − ] ⋅ PaCDOM CO −•
(32)
3
The total formation rate of CO3
−•
is R
tot CO3− •
= R
•
OH CO3−•
In the Rhône delta waters it has been found that the formation rate of 1O2 by CDOM is R1CDOM = O 2
+ R
CDOM CO3−•
. The transformation rate of P by
CO3−• is given by the fraction of CO3−• that reacts with P, in competition with reaction (30) between CO3−• and DOM: 3
RPO2 = R1CDOM ⋅ O 1
(33)
3
k 30 ⋅ DOC + k P, CO −• ⋅ [P]
3
1.25⋅10−3 PaCDOM.10 Considering the competition between the deactivation of 1O2 by collision with the solvent (reaction 37) and reaction (38) with P, one gets the following expression for the degradation rate of P by 1O2 (note that k P ,1O ⋅ [ P] « k 1O ): 2
tot ⋅ [P] R CO −• ⋅ k P, CO −•
R P, CO −• =
(36) (37) (38)
2
3
2
k P ,1O ⋅ [ P]
(39)
2
k 1O
2
where k P,CO−• is the second-order reaction rate constant between P and CO3−•. In the very vast
In a pseudo-first order approximation, the rate constant for P transformation is kP = RPO2 [P] −1 and
majority of the environmental cases, it is k P,CO−• [P] « k30 DOC.
half-life time is tP = ln 2 kP−1. Considering the usual conversion (≈ 10 h) between a constant 22 W m−2 sunlight UV irradiance and a SSD unit, the following expression for τ PSSD is obtained ,1O
3
3
In a pseudo-first order approximation, the rate constant of P transformation is kP = R P,CO−• [P]
−1
3
−1
and the half-life time is tP = ln 2 kP . Considering the usual conversion (≈ 10 h) between a constant
1
2
= 1.25⋅10−3 PaCDOM and that PaCDOM = 10 3 d −1 (remembering that R1CDOM O 2
22 W m−2 sunlight UV irradiance and a SSD unit, the following expression for τNCP,CO3−•SSD is
τ
obtained:
k ⋅ DOC 30 R tot −• ⋅ k −• CO P ,CO3 3
τ PSSD = 1.9 ⋅10−5 ⋅ ,CO −• 3
SSD P ,1O2
4.81 3.85 ⋅ d = CDOM = R1O k P ,1O k ⋅ p CDOM (λ ) dλ 1 P, O ∫ a 2 2 2
CDOM ∫ pa (λ ) dλ ):
λ
(40)
λ
(34) 9
8
D. Vione, V. Maurino, C. Minero, M. E. Carlotti, S. Chiron, S. Barbati, Modelling the occurrence and reactivity of the carbonate radical in surface freshwater. C. R. Chimie 12 (2009) 865-871.
D. Vione, R. Das, F. Rubertelli, V. Maurino, C. Minero, Modeling of indirect phototransformation processes in surface waters. In: Ideas in Chemistry and molecular Sciences: Advances in Synthetic Chemistry, Pignataro, B., ed., Wiley-VCH, Weinheim, Germany, 2010, pp. 203-234. 10 F. Al-Housari, D. Vione, S. Chiron, S. Barbati, Reactive photoinduced species in estuarine waters. Characterization of hydroxyl radical, singlet oxygen and dissolved organic matter triplet state in natural oxidation processes. Photochem. Photobiol. Sci. 9 (2010) 78-86.
vii
viii
Note that 3.85 = (ln 2) k1O2 (1.25⋅10−3 ⋅ 3.60⋅104 ⋅ 103)−1. The steady-state [1O2] under 22 W m−2 UV
[3CDOM *] =
irradiance would be:
[1O2 ] =
R1CDOM O
(47)
k 3 CDOM *
Correction for the solar zenith angle
(41)
2
k 1O
R 3 CDOM *
2
When considering the path length travelled by sunlight in lake water, one should take into account 3
Reaction with CDOM*
the solar zenith angle (z) and the refraction of sunlight at the air-water interface. Light reflection at
9
the interface also takes place, but it is of lesser importance and can be neglected.12 The geometry of The formation of excited triplet states of CDOM (3CDOM*) in surface waters is a direct consequence of radiation absorption by CDOM. In aerated solution, 3CDOM* could undergo thermal deactivation or reaction with O2, and a pseudo-first order quenching rate constant k 3CDOM * =
irradiation can be represented by the scheme below. Sunlight
5⋅105 s−1 has been observed.11 The quenching of 3CDOM* would be in competition with the reaction between 3CDOM* and P: CDOM + hν → 3CDOM* 3 CDOM* (O2)→ Deactivation and 1O2 production 3 CDOM* + P → Products
θ
1.28⋅10 Pa . Considering the competition between reaction (44) with P and other processes (reaction 43), the following expression for the degradation rate of P by 3CDOM* is obtained (note that k P ,3CDOM * ⋅ [ P] « k 3CDOM * , where k P ,3CDOM * is the second-order reaction rate constant between P CDOM 10
and 3CDOM*): R
3
CDOM * P
= R 3CDOM * ⋅
k P ,3CDOM * ⋅ [ P] k 3CDOM *
air water
(42) (43) (44)
In the Rhône delta waters it has been found that the formation rate of 3CDOM* is R3CDOM * = −3
z
The solar zenith angle z (horizontal system of coordinates) is a function of sun declination δ (geocentric equatorial system of coordinates) and of the hour angle τ. The sun hour angle is defined as the difference between sun’s right ascension (geocentric equatorial system of coordinates) and the right ascension of a star on the local meridian. At local noon (when sun is on the local meridian) it is τsun = 0. Furthermore, every 1 h difference from the local noon gives τ ∼ 15°. This means that after 3 h from local noon, the sun has τ ∼ 45°. Assume ϕ as the latitude of the place and (δ,τ) for the sun as above. The following equation holds for the solar zenith angle:13
(45)
cos z = cos δ cosτ cos ϕ + sin δ sin ϕ
In a pseudo-first order approximation, the rate constant for P transformation is kP = RPCDOM * [P] −1
(48)
3
and the half-life time is tP = ln 2 kP−1. Considering the usual conversion (≈ 10 h) between a constant 22 W m−2 sunlight UV irradiance and a SSD unit, one gets the following expression for τ PSSD ,3CDOM * (remembering that PaCDOM = 10 3 d −1
CDOM ∫ pa (λ ) dλ ):
3
7.52 ⋅ d k P ,3CDOM * ⋅ ∫ paCDOM (λ ) dλ
sunlight and the water column depth d: d = l cos θ = l 1 − (sin θ ) 2 .12 Therefore, for depth d and
solar zenith angle z the optical path length l of sunlight inside the water body would be expressed as
λ
τ PSSD = , CDOM *
Water has refraction index n ∼ 1.34 that undergoes relatively limited variation with wavelength. It is sin z = n sin θ , from which the following relationship can be obtained between the path length l of
follows:
(46)
l=
λ
Note that 7.52 = (ln 2) k 3CDOM * (1.28⋅10−3 ⋅ 3.60⋅104 ⋅ 103)−1. The steady-state [3CDOM*] under 22 −2
W m UV irradiance would be:
11
d 1 − (sin θ )
2
=
d
(49)
−1
1 − (n sin z ) 2
This means that water depth could be corrected by a factor ψ =
( 1 − (n
−1
sin z ) 2
)
−1
(ψ > 1) that
depends on latitude, hour and season.
S. Canonica, M. Freiburghaus, Electron-rich phenols for probing the photochemical reactivity of freshwaters. Environ. Sci. Technol. 35 (2001) 690-695.
ix
12 13
R.G. Zepp, D.M. Cline, Rates of direct photolysis in aquatic environment. Environ. Sci. Technol. 11 (1977) 359-366. O. Montenbruck, T. Pfleger, Astronomy on the Personal Computer, 2nd Edition. Springer, Berlin, 1994.
x
