Determination of physical ( k q ) and chemical ( k r ) rate constants for singlet oxygen quenching using the thermolysis of a naphthalenic endoperoxide in H 2 O and D 2 O

A chemical source of singlet oxygen ( 1 O 2 : O 2 ( 1 ∆ g )), based on thermolysis of the water-soluble naphthalenic endoperoxide NDPO 2 is used to determine both the overall ( k r + k q ) and the chemical ( k r ) quenching rate constants of water-soluble substrates. Unlike current photochemical techniques, this chemical method is particularly suitable for sensitive and/or colored substrates, which can react directly with photosensitizers in their excited states or absorb incident light. This simple method has been applied to assess the reactivity of five organic compounds towards 1 O 2 . The first one (carminic acid) is a foodstuff coloring agent (C.I. Natural Red 4). The four other ones (methyl gallate, caffeic acid, trimethylhydroquinone, trolox) are well-known phenolic antioxidants. All of them exhibit high overall rate constants (10 7 M -1 s -1 < ( k r + k q ) < 10 9 M -1 s -1 ) and varying range of chemical quenching (0.1 < k r /( k r + k q ) ≤ 1). The limits of the method are also discussed in detail.


Introduction
][8][9][10] In all these processes, the scavenging of 1 O 2 by compounds involves two pathways : physical quenching which occurs through an energy transfer with the rate constant k q and the chemical quenching which results in the formation of oxidation products with the rate constant k r . 114][25][26][27][28][29][30] Reported values for the chemical rate constants k r are scarcer 12 since usual methods require the precise measurement of the amount of oxidation products formed when the starting material is submitted to a given amount of 1 O 2 .
However, for many applications it is essential to know separately the contributions of k r and k q .For instance, when the protective effect of additives against the photodegradation of polymers or fragrances is wanted, k q must be maximized whereas, ideally, k r must be negligible.On the contrary, in organic synthesis, singlet oxygenation of substrates will be feasible at a preparative level only if they significantly react with 1 O 2 and, in such cases, physical quenching is undesired since it leads to a waste of available 1 O 2 .
Several methods have been described in the literature to determine k r .Most of them are based on the determination of the consumption rate of the substrate in the presence of calibrated sources of 1 O 2 .Smooth chemical generators of 1 O 2 such as naphthalenic endoperoxides are particularly suitable for this purpose since upon warming they release a precise amount of 1 O 2 free of any other reactive species.For instance, endoperoxide of 1,4-dimethylnaphthalene can be used in organic solvents 23 whereas endoperoxides of sodium 3-(methyl-1-naphthyl)propioniate (MNPO 2 ) [24][25][26] and of disodium 3,3'-(1,4-naphthylidene)dipropionate (NDPO 2 ) [27][28][29][30] are suitable for aqueous solutions.
0][31][32][33] The method, which is essentially based on the huge difference between the lifetime of 1 O 2 in ordinary and deuterated water (3.1 µs vs 68 µs), 11,12 is exemplified with carminic acid 1, a well-known foodstuff coloring agent (C.I.Natural red 4).This highly colored compound cannot be studied via photochemical methods because it absorbs light on a wide range of the UV-visible spectrum (400-600 nm) and, accordingly, it perturbs strongly the photosensitized generation of 1 O 2 .Four phenolic antioxidants (methyl gallate 2, caffeic acid 3, trimethylhydroquinone 4, trolox 5) have also been studied because they are prone to suffer side reactions, such as electron transfer, when they are submitted to photochemical sources of 1

Kinetics of generation and quenching of singlet oxygen in water
The chemical generation of 1 O 2 and its different pathways of decay are presented through eqs.
(1) to (4) where k d is the pseudo-first-order constant of 1 O 2 decay in the solvent, k q and k r are the bimolecular rate constants for the physical and the chemical quenching respectively of Once generated in a reaction medium (eq. 1) in the presence of a substrate S, 1 O 2 mainly decays according to physical (eqs. 2 and 3) and chemical (eq.4) quenching.Under pseudo- = ) and after integration between zero time and time t, we obtain the following expression (5) for the cumulative amount of generated 1 The ratio k r /(k r + k q ) expresses the contribution of the chemical quenching in the overall quenching.k d , the rate constant of 1  ) and the first term of eq (5) gets much smaller than the second one.Under these conditions, k r /(k r + k q ) can be calculated according to eq (6).
If, however, the same substrate of low initial concentration [S] 0 reacts with 1 O 2 in H 2 O the second term of eq (5) gets much smaller than the first one because quenching of 1 O 2 occurs mainly through process (2) ([S] 0 (k r + k q ) << k d

H2O
).Then, the rate constant for chemical quenching, k r , can be assessed by eq (7).
Thus, by taking advantage of the strong H-D isotopic effect on k d and by using properly defined substrate concentrations, it is possible to determine k r and k r /k r + k q and hence k r + k q by the same experimental procedure.Of course, the accuracy is based on the validity of the assumption that the value of k r is the same in H 2 O and D 2 O.In fact, weak isotopic exchange with the solvent has been shown to slightly affect the rate constant (the rate constant is 1.4 to 1.5 times smaller in CD 3 OD than in CH 3 OH) of the chemical reaction towards singlet oxygen through deuteration of the labile hydrogen of phenols. 22

Chemical generation of 1 O 2 by thermolysis of NDPO 2
The water-soluble naphthalenic endoperoxide NDPO 2 34 , prepared from the commercially available NDP (Synchem OHG), was used as a source of 1 O 2 .It is able to generate a welldefined amount of 1 O 2 , free from any other reactive species in a wide range of pH (5-11).Thermolysis of NDPO 2 at 37 °C gives back the parent compound NDP and oxygen, 50% of which is in the singlet state (eq. COONa The thermolysis proceeds according to a first order kinetics with a half-time of decomposition of 23 min at 37 °C.Therefore, it may be calculated that 150 min are sufficient to release more than 99% of the trapped 1 O 2 .The amount of 1 O 2 released can thus be assessed by UV-spectrophotometry by monitoring the increase of NDP at 290 nm (Figure 1).Due to the low rate constant between 1 O 2 and NDP (k r + k q = 2.8 x 10 6 M -1 s -1 ) 35 , it is possible to find concentrations of NDPO 2 for which reversed reaction (8) can be negligible and for which Eq. ( 5) is validated.

Limits of the method
Two kinetic requirements must be fulfilled for the determination of (k r + k q ) and k r by this method.The first one depends on the relative concentrations of NDPO 2 , and S. The concentration of S must be sufficient to avoid a significant quenching of 1 O 2 by NDP formed during thermolysis (eq.8).This condition is expressed by relation (9) where the superscripts S and NDP refer to the quenching rate constants of S and NDP, respectively.
[S] 0 (k r + k q ) S >> [NDP] (k r + k q ) NDP (9) As [NDP] is always lower than [NDPO 2 ] 0 , the inequality (9) leads to a first condition with regard to the maximum amount of NDPO 2 that may be used.
The second kinetic requirement concerns the ratio of substrate consumed according to eq. 4. It must be higher than 5% ([S]<0.95[S]0 ) for an accurate determination by UV-visible spectrometry or by HPLC.Since half of the oxygen released during thermolysis is in the singlet state ([ 1 O 2 ] cum = 0.5[NDPO 2 ] 0 ), the minimum concentration of endoperoxide [NDPO 2 ] 0 min may be inferred from eq. ( 6) as Equations ( 10) and ( 11) lead to the double inequality (12) which simplifies to (13) by dropping the terms [NDPO 2 ] 0 and [S] 0 .
The inequality (13) will be satisfied if (k r + k q ) S /(k r + k q ) NDP is at least 10 times higher than 0.1(k r + k q ) S /k r S .Therefore we obtain (14).
S r S q r ) ( which implies that the chemical rate constant of S should be higher or equal to the overall rate constant of NDP: k r S ≥ (k r + k q ) NDP (15) Despite its simplicity, this condition is of little practical use since the absolute value of k r S is not known and because it is impossible to predict it from the chemical formula of S.However, this inequality can be graphically expressed in Figure 2. Substituting (k r + k q ) S by 10 log(k r + k q ) S in eq. ( 14) and (k r + k q ) NDP by its known value 2.8 x 10 6 M -1 s -1 35 one obtains: S / (k r +k q ) S versus log(k r +k q ) S showing the areas where the method is applicable (III), risky (II) or useless (I) and positions of the substrates 1-5.
Figure 2 plots k r S /(k r + k q ) S vs. log(k r + k q ) S .The overall area of Fig. 2 is divided in three parts by two curves calculated as k r S /(k r + k q ) S = 2.8 x 10 6 x 10 -log(k r + k q ) S (a) and k r S /(k r + k q ) S = 2.8 x 10 5 x 10 -log(k r + k q ) S (b).Part I corresponds to substrates for which the inequality ( 16) is not fulfilled.In this area, the method is not applicable since the substrates are not reactive enough towards 1 O 2. Part III is the location of substrates for which inequality ( 16) is fulfilled.This is the area, where highly reactive substrates may be studied according to the method presented here.In the intermediate area II, the technique is still usable but quenching by NDP is no more negligible and the values of k r S and of k q S are less reliable.
Finally, the inequalities ( 10) and ( 11) also lead to constraints on the minimum ([NDPO 2 ] 0 min ) and maximum ([NDPO 2 ] 0 max ) concentrations of NDPO 2 required, respectively.In order to make the choice of appropriate experimental conditions easier, the recommended concentrations of substrate and of endoperoxide have been reported in table 1 as a function of the substrate reactivity.

Choice of the substrate and determination of rate constants, k r and k q
To exemplify our method, the anthraquinonic dye, carminic acid 1, was chosen as a substrate.3] Moreover, it exhibits a characteristic absorption at 530 nm which disappears by reaction with 1 O 2 allowing its monitoring by vis absorption spectrometry (Figure 3) since neither NDP nor NDPO 2 absorb light above 350 nm (Figure 1).Aqueous (H 2 O or D 2 O) phosphate buffered (pH 6.8) solutions of NDPO 2 and carminic acid were maintained at 37 °C for 3 hours.The reaction of carminic acid with the chemically generated 1 O 2 was monitored at 537 nm (Figure 3).
ARKAT USA, Inc.By applying relations ( 6) or (7) to the experimental results reported in Table 2, the values of the chemical (k r ) and of the overall (k r + k q ) rate constants were assessed to 1.5 x 10 8 M -1 s -1 and 4.5 x 10 8 M -1 s -1 respectively.Thus, carminic acid is highly reactive towards 1 O 2 but only 33% of the interacting 1 O 2 induces the irreversible oxidation of the substrate.
In order to confirm the value found for (k r + k q ) we resorted to flash photolysis which allows a direct measurement of this overall rate constant.A rough estimation of (k r + k q ) = 2.1 x 10 8 M -1 s -1 was obtained in D 2 O at pH = 7.5 using tetrasodium tetrakis(sulfonatophenyl) porphyrin as a sensitizer of 1 O 2 . 44This rate constant could not be determined very accurately by this photopphysical method because the screening effect of carminic acid on the absorbance of the photosensitizer restricted the practical range of substrate concentration.Keeping in mind this problem, we may consider that the values obtained by both methods are in reasonably good agreement.
In order to show the value of the method, the reactivity of a series of well-known phenolic antioxidants 2-5 towards 1 O 2 was determined.Due to the lack of screening effect for substrates 2-5, k r + k q were determined by flash photolysis.Results are reported in Table 3 and in Figure 2. Taking into account the experimental errors, rate constants can be evaluated with 20 % precision.In the case of substrate complete unknown S, we suggest to work first in D 2 O with a relatively high concentration of S (10 mM) and with three concentrations of NDPO 2 (1, 10 and 100 mM) to see if the reactivity of the substrate is high enough for our method.A first estimation of k r S / (k r + k q ) S should be obtained.In a second step, lower concentration of S (1 mM) can be tested with NDPO 2 concentrations (1, 10 and 100 mM), if necessary a supplementary dilution of S and NDPO 2 can be used to obtained k r S and thus (k r + k q ) S .

Conclusions
The method described in this paper for the determination of k r and (k r + k q ) of water-soluble substrates is easy to implement.It is well adapted for all substrates for which (k r + k q ) is higher than 10 7 M -1 s -1 .The UV/visible spectroscopy method is particularly convenient to monitor the concentration of substrates absorbing above 350 nm, but for colorless molecules any other chromatographic or spectroscopic method can also be applied.The singlet oxygen source, NDPO 2 , could be obtained either by chemical or photochemical methods, from the commercially available NDP.In opaque media, this method could also be applied in contrast with methods based on photochemical generation of 1 O 2 .
The same principle can be applied to many other solvents provided that the difference of 1 O 2 lifetime between the perdeuterated and the perhydrogenated forms of the solvent is large enough (CH 3 OH, CH 3 CN, CH 3 COCH 3 , CHCl 3 ).In this case a lipophilic naphthalenic compound such as 1,4-dimethylnaphthalene is used instead of NDP.

Experimental Section
General Procedures.Carminic acid, methyl gallate, caffeic acid, trimethylhydroquinone, trolox and tetrasodium tetrakis(sulfonatophenyl) porphyrin (Aldrich) were used without further purification.NDP can be purchased from Synchem OHG or synthetized from 1,4dimethylnaphthalene. 36 UV-VIS absorption spectra were recorded on a Varian CARY 50 spectrophotometer.HPLC was performed using a Waters 600 controller pumps, a Water 490E detector and a Nova-Pak C18 4µm 4.6x250 mm cartridge at a flow rate of 0.7 mL/min with a mixture wateracetonitrile or water-methanol. 1H NMR spectra were recorded at 200 MHz on a Bruker AC-200.
Endoperoxide of disodium 3,3'-(naphthalene-1,4-diyl)dipropionate (NDPO 2 ) was prepared as described. 363,3'-(Naphthalene-1,4-diyl)dipropionic acid (2 g, 7.3 mmol, 0.37 M) was dissolved in 20 mL of an aqueous solution of sodium hydroxide (0.59 g, 14.7 mmol), sodium hydrogen carbonate (0.2 g, 2.4 mmol), sodium carbonate (0.5 g, 4.7 mmol) and sodium molybdate dihydrate (2.5 g, 10.3 mmol, 0.51 M).The solution was immersed in a thermostated bath maintained at 20°C.Six fractions of 2 mL (20 mmol) of hydrogen peroxide were added within 90 min.The mixture was cooled to 0°C with an ice bath and was acidified under stirring at pH = 2.5 with cold phosphoric acid (2 M) (25 mL, 50 mmol).The white precipitate was collected on a sintered glass funnel and washed three times with iced water.The moist acid was dissolved in 300 mL of cold THF (0 °C) and dried with 15 g of MgSO 4 .After filtration, 7 mL (14 mmol) of 2 M sodium methylate in methanol were added, and the precipitate was collected by centrifugation, washed with cold ether, and dried 30 min in vacuum (0.1 Torr, 0 °C), yielding endoperoxide (2.34 g, 92%) as a white powder.Determination of the 1 O 2 chemical rate constant (k r ) for carminic acid.250 µL of a solution of carminic acid (7.7 mM) in D 2 O was added to 50 or 100 µL of NDPO 2 (0.088 M) in D 2 O.The final volume was adjusted to 2.75 mL by means of phosphate buffer (10 -2 M) in D 2 O (pD = 6.8).The solution was maintained at 37 °C for 3 hours and the absorbance was measured at 527 nm after dilution (1/10).k r can be calculated from eq. (7).Determination of the 1 O 2 overall rate constant (k r + k q ) for carminic acid.25 µL of a solution of carminic acid (7.7 mM) in D 2 O was added to 50 or 100 µL of NDPO 2 (0.088 M) in D 2 O.The final volume was adjusted to 2.75 mL by means of phosphate buffer (10 -2 M) in D 2 O (pD = 6.8).The solution was maintained at 37°C for 3 hours and the absorbance was measured at 527 nm.k r + k q can be calculated from eq. ( 6) using k r from eq. ( 7). 1 O 2 overall rate constants (k r + k q ) for compounds 2-5 were measured by flash photolysis by using a system already described in detail. 44,45 O 2 decay caused by the solvent is about 20 times larger in H 2 O (k d H 2 O = 3.2 x 10 5 s -1 ) than in D 2 O (k d D 2 O = 1.5 x 10 4 s -1 ) 11,12 .This strong H-D isotopic effect enables the separated determination of k r and k q .When a very reactive substrate of high initial concentration [S] 0 reacts with 1 O 2 in D 2 O the process (2) becomes negligible ([S] 0 (k x + k r ) >> k d D 2 O

Figure 2 .
Figure 2. Plots of k rS / (k r +k q ) S versus log(k r +k q ) S showing the areas where the method is

Table 1 .
Lower and upper limits of initial concentrations of substrate [S] 0 and endoperoxide [NDPO 2 ] 0 recommended for substrates of variable reactivity

Table 3 .
Overall chemical rate constants (k r + k q ) and (k r / k r + k q ) determined for substituted phenols Determined by the method described in this paper.b Determined by flash photolysis.
a c Analytical method used to measure [S].