M Trassinelli

L Bernard Carlsson

S Cervera

M Eddrief

V H Etgens

V Gafton

E Lacaze

E Lamour

A Lévy

S Macé

C Prigent

J.-P Rozet

S Steydli

M Marangolo

D Vernhet

Low energy Ne ion beam induced-modifications of magnetic properties in MnAs thin films

Investigations of the complex behavior of the magnetization of manganese arsenide thin films due to defects induced by irradiation of slow heavy ions are presented. In addition to the thermal hysteresis suppression already highlighted in M. Trassinelli et al., Appl. Phys. Lett. 104, 081906 (2014), we report here on new local magnetic features recorded by a magnetic force microscope at different temperatures close to the characteristic sample phase transition. Complementary measurements of the global magnetization measurements in different conditions (applied magnetic field and temperatures) enable to complete the film characterization. The obtained results suggest that the ion bombardment produces regions where the local mechanical constraints are significantly different from the average, promoting the local presence of magneto-structural phases far from the equilibrium. These regions could be responsible for the thermal hysteresis suppression previously reported, irradiation-induced defects acting as seeds in the phase transition.

I. INTRODUCTION

Manganese arsenide (MnAs) is one of the most promising materials for the magnetic refrigeration [1][2][3]. It is in fact characterized by a giant magnetocaloric effect close to room temperature that makes it a very attractive material for common refrigeration applications. The giant magnetocaloric effect of MnAs is related to the large entropy change during the first-order magneto-structural transition close to room temperature (T C = 313 K) between a ferromagnetic α-phase with hexagonal structure (NiAs-type) and the paramagnetic β-phase with orthorhombic structure (MnP-type).

The possibility of epitaxial growth on standard semiconductors such as GaAs make MnAs thin films interesting also for spintronic research [4] and magneto-elastic applications [5,6]. The epitaxial strain disturbs the phase transition and leads to the αβ phase coexistence over a large range of temperatures (280-320 K). The refrigeration power associated to the giant magnetocaloric properties does not change but is spread out on the coexistence temperature interval [7]. In this range, an alternating structure of ridges (α phase) and grooves (β phase) organized in stripe-shaped domains parallel to MnAs[0001] is created to minimize the elastic energy due to the epitaxy. The periodicity λ of the ridge-groove structure is constant with the temperature and is related to the thickness t of the sample by the relation λ ≈ 4.8 t [8][9][10].

The richness of the MnAs thin films properties results in a complex dependency of the magneto-structural properties on the external temperature, applied magnetic field * martino.trassinelli@insp.jussieu.fr and constraints. In the past years, many studies have been dedicated to the characterization of epitaxial MnAs films [4,[8][9][10][11][12][13][14][15][16][17]. In particular, magnetic force microscopy (MFM) appeared to be a very useful tool to study the local magnetic properties as a function of different parameters such as: growing conditions [18,19], film thickness [20][21][22], temperature [23][24][25][26], applied magnetic field [27,28] and more recently, applied magnetic field and temperature at the same time [29]. In addition to the above investigations based on the out-of-plane magnetic leak field detection, measurement of the in-plane magnetic component imaging has been obtained on cleavage edges [30].

Recently it has been demonstrated that slow ions bombardment can interestingly change the thin film properties [31,32]. New irradiation-induced defects facilitate the nucleation of one phase with respect to the other one in the first-order magneto-structural MnAs transition, with a consequent stable suppression of the thermal hysteresis without any significant perturbation of the other properties. Transition temperature, saturation magnetization and structural properties are unchanged and, more importantly, the giant magnetocaloric properties of the film is maintained. When present, the thermal hysteresis induces energy losses in the thermal cycles that use giant magnetocaloric material for refrigeration. Its suppression opens new perspectives for the magnetic refrigeration applications based on MnAs-type material.

The origin of the hysteresis removal being not clear, we present here additional investigations on magnetic properties of the irradiated films under different temperatures and applied field conditions, in particular with the study of the local out-of-plane magnetic field via MFM imaging. These studies provide new findings that allow to elucidate many aspects of the ion bombardment effects and also reveal new phenomena.

II. FILM PRODUCTION AND IRRADIATION

All MnAs films considered here have a thickness of 150 nm, are monocrystalline and are issued from the same growth obtained by molecular beam epitaxy (MBE) on GaAs(001) substrate. The deposited MnAs is oriented with the α-MnAs[0001] and β-MnAs[001] axis parallel to GaAs [ 110]. Details on the growth process can be found in Ref. 10.

The samples are irradiated with a Ne 9+ ion beam at the SIMPA facility [33] (French acronym for highly charged ion source of Paris). The ion kinetic energy is set at 90 keV (4.5 keV/u) with an incidence angle of 60 • with respect to the normal of the sample surface. These settings were chosen for having the average penetration depth of ions corresponds to the half-thickness of the MnAs film [START_REF] Ziegler | Stopping and Range of Ions in Matter[END_REF], without any penetration into the substrate. In these conditions, the maximization of the effect arising from the ion irradiation is expected [START_REF] Zhang | [END_REF]. For the ion energy range considered here, the ion-induced defects are principally produced by the nuclear stopping power with a series of binary collisions between the projectile and the target atoms [START_REF] Ziegler | The stopping and range of ions in matter[END_REF][START_REF] Averback | [END_REF]. Target recoil atoms can also produce secondary collisions with the creation of collision cascades that involve many target atoms. For one incident atom, about 500 target atom displacements are expected in our conditions.

In the present paper, we focus our investigation on one particular sample that received a fluence Φ = 1.5 × 10 13 ions cm -2 and mainly reflect the effects of the ion bombardment in MnAs thin films. This sample is systematically compared to a non-irradiated one called reference or pristine sample. More details about the irradiation process can be found in Ref. 31 and 38.

III. RESULTS AND DISCUSSION

A. Measurements of the pristine sample

The magnetization dependency of the pristine sample with the temperature is mainly driven by the ratio between the α and β phases. For weak applied fields, the reciprocal alignment of the different magnetic domains in the ferromagnetic α phase regions, separated by the paramagnetic β phase, plays also an important role. This effect can be observed in the relative magnetization recorded at different increasing and decreasing values of the temperature shown in Fig. 1. The sample magnetization has been recorded by a Quantum Design MPMS-XL SQUID magnetometer with a sweep rate of ±2 K/min with 1 T magnetic field applied along the MnAs easy axis [11 20]. As visible in Fig. 1, the thermal hysteresis is smaller for intense fields than for weak fields, with ∆T ref ≈ 6.2 -6.5 K for H = 500 and 5000 Oe and ∆T ref ≈ 11.4 K for H = 50 Oe. This is probably due to the more difficult propagation of the domain walls of ferromagnetic regions separated by paramagnetic regions FIG. 1. Relative magnetization as a function of temperature and external magnetic field for the reference (solid lines) and for the irradiated samples (dashed lines) in proximity of the critical temperature. External applied fields are 50 Oe (top), 500 Oe (middle) and 5000 Oe (bottom). Data obtained by a temperature increase (from colder temperatures) and decrease (from hotter temperatures) are presented in blue and red, respectively. [39].

This interplay between magnetic domains in spatially separated α regions is also responsible of the high coercivity field for the temperatures where the two phases are coexisting (300-320 K). This is well visible from the sample magnetization measurements along the MnAs easy axis as function of the magnetic field (between ±1 T) obtained in a VSM magnetometer (Quantum Design PPMS 9T) at different temperatures. Note that before each magnetic cycle measurement, the history of the sample is erased by magnetic depolarization at T = 350 K to avoid the production of experimental artifacts like the so-called colossal magnetocaloric effect [40,41]. As we can observe in the Fig. 2, the domain direction flip takes place at H ∼ 50 Oe for low temperatures, but increases up to H ∼ 200 Oe during the phase coexistence. This singular behavior is characteristic of MnAs thin films and it has already observed previously [32,42,43] and successfully modeled [44] in the past.

The features of the MFM images obtained at different temperatures and no external field (Fig. 3, top) reflect the FIG. 2. Magnetic hysteresis cycles between H = -1000 and 1000 Oe for the reference (solid lines) and for the irradiated samples (dashed lines) at different temperatures.

complicate interplay between magnetic domains. The direct observation of the α-and β-phase regions layout is obtained with a MFM (Bruker Multimode AFM microscope equipped with a magnetic tip coated with Co/Cr, model MESP, with a lift height of 20 nm) equipped with a Peltier regulator to adjust the temperature. The measurement is performed under normal atmospheric pressure and it was limited to temperatures higher than the dew point (T ∼ 280 K) to avoid water condensation on the sample. The different images are acquired starting at decreasing and subsequently increasing sample temperatures, from the initial value of T = 329 K. During the temperature change, spatial drifts of the sample did not allow for the measurement of very high quality images. In particular it did not allow for a perfect correspondence between the different spatial regions in of a given area.

Because of the absence of applied external field, MFM images correspond to the visualization of the out-of-plane magnetic field component from α-phase regions separated by β-phase regions. Different temperatures correspond to different typical sizes of the α-phase regions that favor different domain types that are presented in Fig. 4 (see also [19,23,26,27,29]). When the ferromagnetic regions are sufficiently extended, the magnetic domains are normally aligned along the easy magnetization axis MnAs [11 20] with the formation of type-I magnetic domains, with meander-like contrast. We can also have entire portions of α-phase regions in a single domain state (type-III domains) aligned to other ferromagnetic regions orientation across different β-phase regions, forming what we call macro-domains. For very small α-phase regions, domains, with magnetic moment perpendicular to the surface, are present.

As visible in Fig. 3, when coexistence of α and β phases exists, those regions are elongated in fact along the MnAs[0001] direction, which is perpendicular to the easy magnetization axis (MnAs [11 20]). Point-like features, well visible at high temperatures, are due to growth process defects and they have a correspondence in the topography images. Similarly, the diagonal line in the lower row of the reference sample images is due to a topological defect.

Because of the reduced extension of α-phase regions, type-II domains are dominant at high temperatures. When more extended regions of α-phase are present (T = 283 -297 K), type-I domains start to appear and form macro-domains. As shown in Fig. 3, large domains are recognizable as elongated zones aligned width the easy magnetization axis MnAs [11 20] exhibiting blackwhite stripes alternation typical of MnAs MFM images during the phase coexistence [4]. To facilitate the readability of the MFM images, we indicate in the image relative to the reference sample at T = 289 K in Fig. 3 the extension of the macro-domains of opposite magnetization by means of over-imposed blue and red areas. The limits between different macro-domains are easily recognizable by the flip of the MFM phase contrast of the stripes. At lower temperatures (T = 283 K), β-phase regions disappear completely on large portions of the films leaving MFM image regions without any contrast.

When the temperature increases, regularly spaced stripes reappear at T = 297 -305 K (Figs. 3 and5). At T ∼ 313 K, type-I and II domains reappear, and only type-II domains are present at higher temperatures.

B. Effect of the ion irradiation

Irradiation of the thin film with slow ions produce new defects in the MnAs crystal. As reported in Refs. 31, 32, these new defects act as nucleation seeds of one phase with respect to the other during the magneto-structural transition leading to the elimination of the thermal hysteresis.

Investigations with X-ray diffraction for possible structural changes show that the α and β phases structure of irradiated samples, up to a fluence of 10 15 ions cm -2 , are unchanged as presented in Refs. 31, 32. The film remains monocrystalline and only a small increase of the average lattice spacing is noticed (less than 0.3% for a fluence of 1.6 × 10 15 ions cm -2 ).

In addition to the thermal hysteresis suppression previously reported, irradiation-induced modifications are additionally characterized by magnetometry measurements for different applied magnetic field values (M (H)) and temperatures (M (T )), and by MFM imaging. These measurements provide new insights on the nature of the bombardment damages. As we can see in the magnetization measurements as a function of the temperature in Fig. 1, for H = 500, 5000 Oe, the major difference between the pristine and irradiated samples is the suppression of the thermal hysteresis without variation of the critical temperature T c of the transition. This is not true when a magnetic field of 50 Oe is applied. There, the thermal hysteresis is still present and is ∆T irr ≈ 4.8 K (Fig. 1). Nevertheless, we note that the difference between ∆T ref -∆T irr has a constant value of about 6.2-6.6 K for any applied field. This suggests that for H = 50 Oe, the non-zero value of ∆T irr is not due to additional pinning caused by irradiation-induced defects but most likely to an intrinsic property of MnAs/GaAs film.

More information can be extracted from the magnetization measurements as a function of the applied magnetic field at different temperatures (Fig. 2). No major differences in the shape of M (H) between reference and irradiated samples are visible except at the temperatures T = 300 and 305 K where the inflection point position or the slope changes. In these cases, referring to Fig. 1, one can deduce that the α/β phase ratio plays a role due to the thermal hysteresis.

As previously reported [31,32], the ion irradiation does not affect the coercivity field values. Changes of the saturation magnetization are however visible. At T = 285 K the absolute value of the magnetization of the irradiated sample is slightly lower than in the reference one. This is also visible in the M (T ) measurement in Fig. 1. But no noticeable difference of the magnetic saturation is visible at lower temperature (T = 100 K). A possible explanation of this behavior is the presence of residual β-phase regions when only the α phase should be present. This hypothesis is confirmed by the MFM images that are discussed in the next paragraph. Finally it is worth mentioning that thin film magnetization reduction under action of ion irradiation is also commonly observed in samples that exhibit a second-order magnetic transition because of irradiation-induced crystal structure rearrangement and change of the dipole-dipole interaction [45][46][47][48][49][50][51][52]. However, compared to the results presented here, these past studies involved much higher ion fluences (> 10 15 ions cm -2 ) that, differently than in our case, can substantially change the sample structure and composition.

Additional insights can be extracted from the magnetic force microscope images and topography of the sample. The topography imaging does not show any differences between the pristine and irradiated sample. This is not surprising because the relative low-value of the potential energy carried by the ions does not allow the formation of new surface defects [53]. On the other hand, compared to the reference sample, the MFM images (Fig. 3) of the irradiated sample present several differences:

1. there is a qualitatively different dependency on the temperature, 2. they are characterized by an irregular pattern of the αβ phase region disposition, 3. at low temperature, persisting β-phase regions are observed.

Point 1 is due to the reduction or suppression of the thermal hysteresis that anticipates the appearance of one phase with respect to the other one in the irradiated sample compared to the pristine one. As discussed above, this reduction is caused by the easier nucleation of the phases due the irradiation-induced defects. These defects disturb also the regular αβ phase disposal, point 2, as clearly visible in Fig. 5. This phenomenon is similar to the effect of defects produced during the film growth that are observed to induce Y-shape stripe bifurcation in well defined positions (corresponding to the defect positions) [10,12].

Point 3 is particularly interesting. At low temperature, we can see in Fig. 3 that the macro-domains are disturbed by linear regions where the β phase is persisting. These regions are recognizable by a local contrast of the MFM phase that develop along lines and by a depression of a few nm in the topography lines (not shown) due to the smaller cell volume of the β phase [4,10]. These regions are particularly visible in the image relative to T = 297 K approaching from higher temperatures in Fig. 3. For lower T values, only one vertical β-phase region is persisting, down to the lowest reached temperature of 283 K. This effect is even more evident when the sample is cooled from about 350 K with an external field of about 5000 Oe before imaging it with the MFM. As we can see in Fig. 6, where a 5 × 5 µm 2 of the irradiated sample at the temperature of 298 K prepared in this way is shown, a β-phase diagonal region is visible in the MFM image together with a depression (of about 5 nm) in the topography image. When increasing temperature, this β-phase region is less and less contrasted with respect to the surrounding area in both MFM and topography images due to the global transition to the β phase.

The presence of the β phase at this low temperature may be due to local constraints induced by the ion irradiation. Past experimental and theoretical studies on ionmatter interaction show that, at this ion energy regime, collision cascades can lead to the formations of spatially localized regions rich in interstitial atoms or vacancies [START_REF] Averback | [END_REF][54][55][56]. Interstitial-rich regions could cause an increase of the local high internal pressure favoring the presence of the β phase that is characterized by a volume 2% larger than the α phase. In connection to the persistence of small β-phase regions, the sample magnetization is expected to be reduced with respect to the reference sample, which is the case as visible in the magnetometry measurements in Fig. 1. At very low temperature (T = 100 K) not monitored with the MFM, irradiated samples have practically the same saturation magnetization than pristine samples [31] suggesting that these "frozen" β-phase regions are thus suppressed.

Similarly, the presence of surviving α-phase regions at high temperatures seems plausible, but is difficult to observe due to the complex magnetic images caused by the transition between type-I and type-II magnetic domains. In correlation with vacancies-rich regions, a local low internal pressure is expected that can favor the presence of α phase regions. The high magnetization of irradiated samples at T = 330 K in the M (H) curve (Fig. 2) could be an indication of the persistence of α-phase regions at high temperatures. This persistence could be the reason for the presence of large macro-domains with the same orientation contrary to what happen in the pristine sample (Fig. 3, T = 283 -297). Remaining α-phase regions with a defined magnetic orientation could in fact seed the nucleation of domains with a specific direction (before the series of observation on the MFM the samples are initially cooled in presence of a persisting magnetic field of about 5000 Oe).

Recent studies on nanoindentation in NiMnGa Heusler alloy films [57] show that local constrains can favor the nucleation of one phase into the other phase in the characteristic first-order phase transition. Similarly, here local regions of α and β phase, which are persisting at a temperature respectively higher and lower than the transition temperature, could be at the origin of the thermal hysteresis suppression making easier the transition of one phase into the other phase.

IV. CONCLUSIONS

We report new investigations on the effect of ion bombardment on manganese arsenide thin films. These studies confirm that the thermal hysteresis is suppressed when an intense magnetic fields is applied due to local irradiation-induced defects. This is not the case for weak external field. At 50 Oe the surviving thermal hysteresis seems related to the intrinsic properties of MnAs/GaAs films and in particular to the high coercivity field value during the αβ phase coexistence. The local effects of the new defects are well visible on the MFM images where the self-organization of MnAs αβ phases is disturbed and where β-phase regions persist in specific spots at temperatures well below the phase transition temperature. This is in agreement with the observed magnetization of the irradiated sample which is lower than the pristine magnetization for T T c while at lower temperature, i.e. T = 100 K, the magnetization is the same for the two samples. Similarly, there are indications that small α-phase regions could resist to temperatures higher than the phase transition temperature. Nevertheless the nature of the irradiation-induced defects is still not completely revealed and it will require future investigation with different projectile masses and collision conditions.

FIG. 3 .

 3 FIG. 3. MFM images of the reference and irradiated samples at different temperatures. The colored arrow indicates the temperature progression between the images. Point-like defects visible at high temperatures are due to growth process defects and they have a correspondence in the topography images. Similarly, the diagonal line in the lower row of the reference sample images is due to a topological defect. In contrast, the diagonal and vertical lines in the irradiated sample images have no correspondence in the topography images and are purely due to magnetic features. In the image relative to T = 289 K (increasing temp.), we indicate the macro-domains of opposite magnetization by means of over-imposed blue and red areas. Squares indicate the zoom regions of Figs. 4 (in red) and 5 (in black).

FIG. 4 .

 4 FIG. 4. Different types of magnetic orientation of the α-phase regions in a reference sample MFM image at T = 305 K. The image correspond to the zoom of the red square in Fig. 3.

FIG. 5 .

 5 FIG.5. Zoom of the topography images at T = 305 K of the pristine (left) and irradiated (right) samples. These images correspond to the zoom of the black squares in Fig.3.

FIG. 6 .

 6 FIG.6. MFM (upper row) and AFM (bottom row) images at different increasing temperatures of the irradiated sample after a cooling in presence of a persisting magnetic field (H ∼ 5000 Oe).

ACKNOWLEDGMENTS This work was partially supported by French state funds managed by the ANR within the Investissements d'Avenir program under reference ANR-11-IDEX-0004-02, and more specifically within the framework of the Cluster of Excellence MATISSE led by Sorbonne Universités. V. Gafton acknowledges support from the strategic grant POSDRU/159/1.5/S/137750, Project, "Doctoral and Post-doctoral programs support for increased competitiveness in Exact Sciences research" co financed by the European Social Found within the Sectoral Operational Program Human Resources Development 2007-2013


Jamel Chikhi
email: jamel.chikhi@univ-evry.fr

D Épartement

Recurrence relations for a family of generalized Cauchy numbers

Keywords: 2010 Mathematics Subject Classification : 11B83, 11B73, generalized Cauchy numbers, shifted poly-Cauchy numbers, Stirling numbers, Bernoulli numbers, recurrences. 1

We obtain two sorts of recurrence relations for a class of generalized Cauchy numbers c (s) n,α . The first recurrences are especially adapted to the so-called shifted poly-Cauchy numbers. The second relations are generalization, for the numbers c (s) n,α , of the recurrences obtained by Agoh and Dilcher for the Bernoulli numbers of the second kind b n = c (1) n,1 /n!.

INTRODUCTION

The Bernoulli numbers of the second kind b n can be defined by the generating function

t log(1 + t) = ∞ ∑ n=0 b n t n , (|t| < 1) .
These numbers satisfy b 0 = 1 and the recurrence formulae (see [START_REF] Comtet | Advanced combinatorics[END_REF]),

n ∑ j=0 (-1) j (n -j + 1) b j = 0 (n ≥ 1) . (1.1)
In [START_REF] Agoh | Recurrence relations for Nörlund numbers and Bernoulli numbers of the second kind[END_REF], Agoh and Dilcher obtained among others, this first generalization (theorem 4.1),

n-k ∑ j=0 s(n -j, k) (n -j)! b j = s(n -1, k -1) (n -1)!k (n ≥ k ≥ 1) . (1.2)
We recall that the Stirling numbers of the first kind s(n, k) can be defined by

log k (1 + t) = k! ∞ ∑ n=k s(n, k) t n n! , (|t| < 1) .
Their theorem 4.2 is a more general result. For m ≥ 0, k ≥ 1 and

n ≥ k + m, n-k-m ∑ j=0 m + j m s(n -j, k, m)b m+1+ j + (-1) m s(n + m + 1, k, m) (1.3) = 1 n!m!(k + m) m ∑ j=0 (-1) m-j s(m, m -j)s(n, k -1 + j) k + m -1 k + j -1 -1
, where the numbers s(n, k, m) are given by

(1 + t) m log k+m (1 + t) = (k + m)! ∞ ∑ n=0
s(n, k, m)t n , (|t| < 1) . (1.4) Remark 1.1. For m = 0, The relations (1.3) reduce to the relations (1.2). For k = 1, the relations (1.2) reduce to the relations (1.1).

The aim of this note is to obtain some recurrence relations for the two parameters family of generalized Cauchy numbers defined by

F s,α (t) := ∞ ∑ n=0 log n (1 + t) n!(n + α) s = ∞ ∑ n=0 c (s) n,α t n n! , (|t| < 1) ,
where s and α are real parameters with, for simplicity, s ≥ 0 and α > 0. For s and α integers, they are called shifted poly-Cauchy numbers in [START_REF] Komatsu | A generalization of poly-Cauchy numbers and their proprieties[END_REF] .

Remark 1.2. For s = 0, F 0,α (t) = 1 + t, then c (0) 0,α = 1 = c (0)
1,α and c We introduce some other numbers to be used in the sequel.

(0) n,α = 0 for n ≥ 2. For s = α = 1, F 1,1 (t) = t/ log(1 + t),
(1) For a two indeterminate polynomial P(X,Y ) and a parameter β , we define the numbers s(n, β , P) by

log(1 + t) t β P(1 + t, log(1 + t)) = ∞ ∑ n=0 s(n, β , P))t n , (|t| < 1) . (1.5)
A few formulas may be noted. If m is a nonnegative integer, P = Y m m! and β = 0, then s(n, 0, P) = s(n, m)/n! . Also, If m and k are nonnegative integers, P = X m Y k+m (k+m)! and β = r is nonnegative integer, then

s(n, r, P) = r! k + m + r r s(n + r, k, m + r) .
(2) The weighted Stirling numbers of the second kind. For a nonnegative integer n and a parameter β , we define, see [START_REF] Carlitz | Weighted Stirling numbers of the first and second kind-I, II[END_REF],

(x + β ) n = n ∑ k=0 R(n, k, β )(x) k , (1.6)
where (x) k is the falling factorial defined by (x) 0 = 1 and, for k ≥ 1, (x) k = x(x -1)..(xk + 1). For β = 0, the coefficients in (1.6) are known to be the Stirling numbers of the second kind S(n, k), so R(n, k, 0) = S(n, k). Moreover we have (see [START_REF] Carlitz | Weighted Stirling numbers of the first and second kind-I, II[END_REF]) R(n, 0, β ) = β n , R(n, k, 1) = S(n + 1, k + 1) and the general expression R(n, k, β ) = ∑ n-k j=0 n j β j S(nj, k) .

THE FIRST RECURRENCE RELATIONS

Here is the first main theorem.

Theorem 2.1. For any positive integers n and N, we have

n ∑ k=1 α N (-1) n-k k! + min(k,N) ∑ j=1 s(n + j -k, 0, P N, j ) (k -j)! c (s+N) k,α (2.1)
+ n+N ∑ k=n+1 min(k,N) ∑ j=k-n s(n + j -k, 0, P N, j ) (k -j)! c (s+N) k,α = n ∑ k=1 (-1) n-k c (s) k,α k! .
where P N, j is the polynomial P N, j (X,Y ) = X j-1 ∑ N k= j R(N, k, α)S(k, j)Y k .

For s = 0, c

1,α = 1 and c (0) n,α = 0 for n ≥ 2 then we obtain, in particular for the shifted poly-Cauchy numbers, Corollary 2.2. For any positive integers n and N, we have

n ∑ k=1 α N (-1) n-k k! + min(k,N) ∑ j=1 s(n + j -k, 0, P N, j ) (k -j)! c (s+N) k,α (2.2)
+ n+N ∑ k=n+1 min(k,N) ∑ j=k-n s(n + j -k, 0, P N, j ) (k -j)! c (s+N) k,α = (-1) n-1 .
By more specialization, we obtain Corollary 2.3. If in addition of s = 0, α = N = 1, then we recover the recurrence relations (1.1) .

2.1. Proof of the corollary (2.3). For N = α = 1, the relations (2.2) write for positive integer n,

(-1) n-1 = n ∑ k=1 (-1) n-k k! + min(k,1) ∑ j=1 s(n + j -k, 0, P 1, j ) (k -j)! k!b k + n+1 ∑ k=n+1 min(k,1) ∑ j=1 s(n + j -k, 0, P 1, j ) (k -j)! k!b k = n ∑ k=1 (-1) n-k k! + s(n + 1 -k, 0, P 1,1 ) (k -1)! k!b k + s(0, 0, P 1,1 ) n! (n + 1)!b n+1 .
We have

P 1,1 = R(1, 1, 1)S(1, 1)Y = Y then s(0, 0, P 1,1 ) = 0 and s(l, 0, P 1,1 ) = (-1) l-1 /l for l ≥ 1. Hence (-1) n-1 = n ∑ k=1 (-1) n-k k! + (-1) n-k (k -1)!(n + 1 -k) k!b k = n ∑ k=1 (-1) n-k 1 + k n + 1 -k b k = (n + 1) n ∑ k=1 (-1) n-k n + 1 -k b k , but b 0 = 1, then (-1) n n + 1 b 0 + n ∑ k=1 (-1) n-k n + 1 -k b k = 0 = (-1) n n ∑ k=0 (-1) k n + 1 -k b k ,
and we arrive to desired recurrence (1.1).

Proof of theorem (2.1). Let us consider the function

E s,α (x) = ∑ ∞ n=0 x n
n!(n+α) s so that E s,α (log(1 + t)) = F s,α (t), the generating function of our generalized Cauchy numbers. Then, Lemma 2.1. For any positive integer N, any real number x , we have

E s,α (x) = ∞ ∑ k=0 R(N, k, α)x k d k dx k E s+N,α (x) . (2.3) Indeed, we write E s,α (x) = ∞ ∑ n=0 x n n!(n + α) s = ∞ ∑ n=0 (n + α) N x n n!(n + α) s+N , then by (1.6), E s,α (x) = ∞ ∑ n=0 N ∑ k=0 R(N, k, α)(n) k x n n!(n + α) s+N = N ∑ k=0 R(N, k, α)x k ∞ ∑ n=0 (n) k x n-k n!(n + α) s+N = N ∑ k=0 R(N, k, α)x k d k dx k E s+N,α (x) .
To translate this result to F s,α (t), we shall use the following lemma.

Lemma 2.2. If F(x) and F(log(1 + t)) admit m derivatives, then it holds

d m dt m F(log(1 + t)) = 1 (1 + t) m m ∑ j=0 s(m, j)F ( j) (log(1 + t)) (2.4) and F (m) (log(1 + t)) = m ∑ j=0 S(m, j)(1 + t) j d j dt j F(log(1 + t)) . (2.5)
Indeed, the first part is classical and given in [START_REF] Comtet | Advanced combinatorics[END_REF] with t in place of 1 + t. It is also used in [START_REF] Agoh | Recurrence relations for Nörlund numbers and Bernoulli numbers of the second kind[END_REF], lemma 4.1, with the function F(x) = 1/x. The proof is by recurrence and uses the fundamental relations on the Stirling numbers of the first kind, see [START_REF] Comtet | Advanced combinatorics[END_REF] :

s(n, k) = s(n -1, k -1) -(n -1)s(n -1, k) , n ≥ k ≥ 1 ; s(n, 0) = s(0, k) = 0, except s(0, 0) = 1 .
While the second part is the usual inversion formula based on the orthogonality of the Stirling numbers of the two kinds, see [START_REF] Comtet | Advanced combinatorics[END_REF]. By combining the lemma (2.3) and the lemma (2.4), we obtain for |t| < 1,

F s,α (t) = N ∑ k=0 R(N, k, α) log k (1 + t)E (k) s+N,α (log(1 + t)) = N ∑ k=0 R(N, k, α) log k (1 + t) k ∑ j=0 S(k, j)(1 + t) j d j dt j E s+N,α (log(1 + t)) = N ∑ k=0 k ∑ j=0 R(N, k, α)S(k, j)(1 + t) j log k (1 + t)F ( j) s+N,α (t) = R(N, 0, α)S(0, 0)F s+N,α (t) + N ∑ k=1 k ∑ j=1 R(N, k, α)S(k, j)(1 + t) j log k (1 + t)F ( j) s+N,α (t) = α N F s+N,α (t) + (1 + t) N ∑ j=1 (1 + t) j-1 N ∑ k= j R(N, k, α)S(k, j) log k (1 + t) F ( j) s+N,α (t) , then F s,α (t) 1 + t = α N F s+N,α (t) 1 + t + N ∑ j=1 P N, j (1 + t, log(1 + t)F ( j) s+N,α (t) . (2.6)
To conclude, we consider the corresponding expansions. On one hand, we have

F s,α (t) 1 + t = ∞ ∑ n=0   n ∑ k=0 (-1) n-k c (s) k,α k!   t n , F s+N,α (t) 1 + t = ∞ ∑ n=0   n ∑ k=0 (-1) n-k c (s+N) k,α k!   t n . (2.7)
On an other hand, we have

P N, j (1 + t, log(1 + t)F ( j) s+N,α (t) = ∞ ∑ n=0 s(n, 0, P N, j )t n ∞ ∑ n=0 c (s+N) n+ j,α t n n! = ∞ ∑ n=0   n ∑ k=0 s(n -k, 0, P N, j ) c (s+N) k+ j,α k!   t n = ∞ ∑ n=0   n+ j ∑ k= j s(n + j -k, 0, P N, j ) c (s+N) k,α (k -j)!   t n .
Hence, we obtain

N ∑ j=1 P N, j (1 + t, log(1 + t)F ( j) s+N,α (t) (2.8) = ∞ ∑ n=0 n+N ∑ k=1 min(k,N) ∑ j=max(1,k-n) s(n + j -k, 0, P N, j ) (k -j)! c (s+N) k,α t n .
The identities (2.6), (2.7) and (2.8) lead to the equality

∞ ∑ n=0   n ∑ k=0 (-1) n-k c (s) k,α k!   t n = α N ∞ ∑ n=0   n ∑ k=0 (-1) n-k c (s+N) k,α k!   t n + ∞ ∑ n=0 n+N ∑ k=1 min(k,N) ∑ j=max(1,k-n) s(n + j -k, 0, P N, j ) (k -j)! c (s+N) k,α t n .
Equating the coefficients of t n in the expansions above, achieves the proof of the theorem (2.1).

THE SECOND RECURRENCE RELATIONS

3.1. Preliminaries. The starting point is the following lemma.

Lemma 3.1. For any real number t, with 0 < |t| < 1, we have

F s+1,α (t) = 1 log α (1 + t) t 0 log α-1 (1 + u) F s,α (u) 1 + u du . (3.1)
Proof. We just compute, for |t| < 1, the derivative

d dt (log α (1 + t)F s+1,α (t)) = d dt ∞ ∑ n=0 log n+α (1 + t) n!(n + α) s+1 = 1 1 + t ∞ ∑ n=0 log n+α-1 (1 + t) n!(n + α) s = log α-1 (1 + t) F s,α (t) 1 + t ,
and observe that the function log α (1 + t)F s+1,α (t) vanishes for t = 0.

We define the function

G s,α (t) := 1 t α t 0 log α-1 (1 + u) F s,α (u) 1 + u du , (3.2)
and look for its expansion in powers of t .

Proposition 3.1. For any |t| < 1 , we have G s,α (t) = ∑ ∞ n=0 g (s)
n,α t n with g (s)

n,α = 1 α(n + α) n ∑ k=0 (n -k + α)s(n -k, α, 1) c (s) k,α k! . (3.3) Indeed, we first expand, for |u| < 1, log α-1 (1 + u) 1 + u = 1 α (log α (1 + u)) = 1 α ∞ ∑ n=0 s(n, α, 1)u n-α = 1 α ∞ ∑ n=0 (n -α)s(n, α, 1)u n-α-1 .
Next we put it in (3.2),

G s,α (t) = 1 αt α t 0 ∞ ∑ n=0 (n + α)s(n, α, 1)u n+α-1 F s,α (u) du = 1 αt α t 0 ∞ ∑ n=0 (n + α)s(n, α, 1)u n+α-1 ∞ ∑ n=0 c (s) n,α u n n! du = 1 αt α t 0 u α-1 ∞ ∑ n=0 n ∑ k=0 (n -k + α)s(n -k, α, 1) c k,α (s) k! u n du .
After integration, it holds

G s,α (t) = 1 α ∞ ∑ n=0   n ∑ k=0 (n -k + α)s(n -k, α, 1) c (s) k,α k!   t n n + α ,
and the expression of g

(s)
n,α appears clearly.

3.2. The second theorem. We are now able to state our second main result.

Theorem 3.1. Let N > m ≥ 0 be given integers. Then for any integer n ≥ N, we have

n-N ∑ j=0 s(n -j, α -1, Q m,N ) ( j -α) m j! c (s+1) j,α (3.4)
= m ∑ j=0 j ∑ l=0 m j (-α) l s( j, l) n-j-1 ∑ r=0 (r) m-j g (s) r,α s(n -j -1 -r, 0, Q m-j,N-l-1 ) ,
where the polynomials

Q N,m are Q N,m (X,Y ) = X m Y N .
Proof. We shall apply the operator (1 + t) m log N+α-1 (1 + t)d m /dt m on both sides of the equality

F s+1,α (t) t α = G s,α (t) log α (1+t)
obtained from (3.1). For the left side, we have for the derivatives

d m dt m F s+1,α (t) t α = d m dt m ∞ ∑ n=0 c (s+1) n,α t n-α n! = ∞ ∑ n=0 (n -α) m c (s+1) n,α t n-α-m n! , then (1 + t) m log N+α-1 (1 + t) d m dt m F s+1,α (t) t α = (1 + t) m log N+α-1 (1 + t) ∞ ∑ n=0 (n -α) m c (s+1) n,α t n-α-m n! = t -m-1 log(1 + t) t α-1 (1 + t) m log N (1 + t) ∞ ∑ n=0 (n -α) m c (s+1) n,α t n n! ,
and by (1.5), we expand

log(1 + t) t α-1 (1 + t) m log N (1 + t) ∞ ∑ n=0 (n -α) m c (s+1) n,α t n n! = t -m-1 ∞ ∑ n=0 s(n, α -1, Q m,N )t n ∞ ∑ n=0 (n -α) m c (s+1) n,α t n n! = t -m-1 ∞ ∑ n=0 n ∑ j=0 s(n -j, α -1, Q m,N ) ( j -α) m j! c (s+1) j,α t n .
Thus we have obtained that,

(1 + t) m log N+α-1 (1 + t) log N+α-1 (1 + t) d m dt m F s+1,α (t) t α (3.5) = t -m-1 ∞ ∑ n=0 n ∑ j=0 s(n -j, α -1, Q m,N ) ( j -α) m j! c (s+1) j,α t n .
For the second side, the derivatives are

d m dt m G s,α (t) log α (1 + t) = m ∑ j=0 m j G (m-j) s,α (t)
d j dt j log -α (1 + t) ,
and by lemma (2.4), we have

d j dt j log -α (1 + t) = 1 (1 + t) j j ∑ l=0 (-α) l s( j, l) log α+l (1 + t) , then we obtain d m dt m G s,α (t) log α (1 + t) = m ∑ j=0 j ∑ l=0 m j G (m-j) s,α (t) (-α) l s( j, l) (1 + t) j log α+l (1 + t) , then (1 + t) m log N+α-1 (1 + t) m ∑ j=0 j ∑ l=0 m j G (m-j) s,α (t) (-α) l s( j, l) (1 + t) j log α+l (1 + t) (3.6) = m ∑ j=0 j ∑ l=0 m j (-α) l s( j, l)G (m-j)
s,α (t)(1 + t) m-j log N-l-1 (1 + t).

According to (3.2) and (1.5), we have

G (m-j) s,α (t)(1 + t) m-j log N-l-1 (1 + t) = t j-m ∞ ∑ n=0 (n) m-j g (s) n,α t n ∞ ∑ n=0 s(n, 0, Q m-j,N-l-1 )t n = t j-m ∞ ∑ n=0 n ∑ r=0 (r) m-j g (s) r,α s(n -r, 0, Q m-j,N-l-1 ) t n = t -m-1 ∞ ∑ n=0 n ∑ r=0 (r) m-j g (s)
r,α s(nr, 0, Q m-j,N-l-1 ) t n+ j+1 .

By changing n + j + 1 to n in the summation, we obtain

G (m-j) s,α (t)(1 + t) m-j log N-l-1 (1 + t) = t -m-1 ∞ ∑ n= j+1 n-j-1 ∑ r=0 (r) m-j g (s) r,α s(n -j -1 -r, 0, Q m-j,N-l-1 ) t n ,
witch leads to the expression of the right hand of the equality (3.6),

m ∑ j=0 j ∑ l=0 m j (-α) l s( j, l)G (m-j) s,α (t)(1 + t) m-j log N-l-1 (1 + t) = t -m-1 m ∑ j=0 j ∑ l=0 m j (-α) l s( j, l) ∞ ∑ n= j+1 n-j-1 ∑ r=0 (r) m-j g (s) r,α s(n -j -1 -r, 0, Q m-j,N-l-1 ) t n = t -m-1 ∞ ∑ n=1 min(m,n-1) ∑ j=0 j ∑ l=0 m j (-α) l s( j, l) n-j-1 ∑ r=0 (r) m-j g (s) r,α s(n -j -1 -r, 0, Q m-j,N-l-1 ) t n .
We obtain here that

(1 + t) m log N+α-1 (1 + t) log N+α-1 (1 + t) d m dt m G s,α (t) log α (1 + t) (3.7) = t -m-1 ∞ ∑ n=1 min(m,n-1) ∑ j=0 j ∑ l=0 m j (-α) l s( j, l) n-j-1 ∑ r=0 (r) m-j g (s) r,α s(n -j -1 -r, 0, Q m-j,N-l-1 ) t n .
Finally, (3.5) and (3.7) together give

∞ ∑ n=0 n ∑ j=0 s(n -j, α -1, Q m,N ) ( j -α) m j! c (s+1) j,α t n = ∞ ∑ n=1 min(m,n-1) ∑ j=0 j ∑ l=0 m j (-α) l s( j, l) n-j-1 ∑ r=0 (r) m-j g (s) r,α s(n -j -1 -r, 0, Q m-j,N-l-1 ) t n .
To conclude, we equate the coefficients of t n , for n ≥ N, in the summations after observing that for nj > N, s(nj, α -1, Q m,N ) = 0 and min(m, n -1) = m for n > m .

3.3. The special case s = 0 and α = 1. We show here that we recover the recurrences of Agoh and Dilcher for the Bernoulli numbers of the second kind. Let n be an integer ≥ N and denote by L the left hand of the recurrence (3.4), with s = 0, α = 1, and R its right one.

L = n-N ∑ j=0 s(n -j, 0, Q m,N )( j -1) m b j and R = m ∑ j=0 j ∑ l=0 m j (-1) l s( j, l) n-j-1 ∑ r=0 (r) m-j g (0)
r,1 s(nj -1r, 0, Q m-j,N-l-1 ) .

As ( j -1) m = ( j -1)( j -2)..( jm) vanishes for j = 1, 2, .., m and equals (-1) m m! for j = 0, we have

L = (-1) m m!s(n, 0, Q m,N ) + n-N ∑ j=m+1 s(n -j, 0, Q m,N )( j -1) m b j = (-1) m m!N! s(n, N -m, m) + N! n-N ∑ j=m+1 s(n -j, N -m, m)( j -

  and the numbers c (1) n,1 are the ordinary Cauchy numbers c n = b n /n!.

  1) m b j = (-1) m m!N! s(n, Nm, m) + m!N! n-N ∑ j=m+1 s(nj, Nm, m) j -1 m b j ,and by a little shiftL = (-1) m m!N! s(n, Nm, m) + m!N! n-N-m-1 ∑ j=0 s(njm -1, Nm, m) j + m m b j+m+1 . (3.8)For the right hand R, as G 0,1 (t) = 1

1 . 1 - 1 . 1 - 1 ,

 11111 l s( j, l)(0) m-j s(nj -1, 0, Q m-j,N-l-1 ) .But (0) m-j vanishes for m > j and equals 1 for m = j, thenR = m ∑ l=0 (-1) l l!s(m, l)s(nm -1, 0, Q 0,N-l-1 ) = m ∑ l=0 (-1) l l!s(m, l)(Nl -1)! s(nm -1, Nl -1, 0) . We use s(nm -1, Nl -1, 0) = s(nm -1, Nl -1) and introduce a binomial coefficient, l s(m, l)s(nm -1, Nl -1) N -1 N -1l -Now, put l = mj in the summation above and obtain R = (N -1)! (nm -1)! m ∑ j=0 (-1) m-j s(m, mj)s(nm -1, Nm + j -1) N -1 Nm + j -(3.9)Finally, we put N = m + k in both (3.8) and (3.9) with n + m + 1 instead of n and obtainL = (-1) m m!(m + k)! s(n + m + 1, k, m) + m!(m + k)m-j s(m, mj)s(n, k + j -1) m + k -1 k + j -and L m!(m+k)! = R m!(m+k)! is exactly the desired identity (1.3).


domain: chim sde

text:
Tao Zhang

Yin Chen

Yuru Wang

Julien Le Roux

Yang Yang

Jean-Philippe Croué
email: jp.croue@kaust.edu.sa

Efficient peroxydisulfate activation process not relying on sulfate radical generation for water pollutant degradation

Peroxydisulfate (PDS) is an appealing oxidant for contaminated groundwater and toxic industrial wastewaters. Activation of PDS is necessary for application because of its low reactivity. Present activation processes always sulfate radicals as actual oxidants which unselectively oxidize organics and halide anions reducing oxidation capacity of PDS and producing toxic halogenated products.

Here we report that copper oxide (CuO) can efficiently activate PDS under mild conditions without producing sulfate radicals. The PDS/CuO coupled process is most efficient at neutral pH for decomposing a model compound, 2,4-dichlorophenol (2,4-DCP). In a continuous-flow reaction with an empty-bed contact time of 0.55 min, over 90% 2,4-DCP (initially 20 µM) and 90% of adsorbable organic chlorine (AOCl) can be removed at the PDS/2,4-DCP molar ratio of 1 and 4, respectively.

Based on kinetic study and surface characterization, PDS is proposed to be first activated by CuO through outer-sphere interaction, the rate-limiting step, followed by a rapid reaction with 2,4-DCP present in the solution. In the presence of ubiquitous chloride ions in groundwaters/industrial wastewater, the PDS/CuO oxidation shows significant advantages over sulfate radical oxidation by achieving much higher 2,4-DCP degradation capacity and avoiding the formation of highly chlorinated degradation products. This work provides a new way of PDS activation for contaminant removal.

INTRODUCTION

Persulfates, including peroxymonosulfate (PMS) and peroxydisulfate (PDS), have received increasing interest in recent years in both research and application for the remediation of organic pollutants in groundwater and wastewaters. They are relatively stable, thus favoring storage and transportation. When activated by alkaline, UV, heat and transition metals, they can produce strong sulfate radicals. [START_REF] Anipsitakis | Radical generation by the interaction of transition metals with common oxidants[END_REF][START_REF] Johnson | Persulfate Persistence under Thermal Activation Conditions[END_REF][START_REF] Furman | Mechanism of Base Activation of Persulfate[END_REF][START_REF] Guan | Influence of pH on the Formation of Sulfate and Hydroxyl Radicals in the UV/Peroxymonosulfate System[END_REF][START_REF] Drzewicz | Impact of Peroxydisulfate in the Presence of Zero Valent Iron on the Oxidation of Cyclohexanoic Acid and Naphthenic Acids from Oil Sands Process-Affected Water[END_REF] PDS ($0.74 per kg) is much cheaper than PMS (sold as Oxone (KHSO5•1/2KHSO4•1/2K2SO4), $2.2 per kg) and even cheaper than H2O2 ($1.5 per kg), thus having a better application potential. [START_REF] Anipsitakis | Degradation of organic contaminants in water with sulfate radicals generated by the conjunction of peroxymonosulfate with cobalt[END_REF][START_REF] Lau | The aqueous degradation of butylated hydroxyanisole by UV/S2O82-: Study of reaction mechanisms via dimerization and mineralization[END_REF][START_REF] Saien | Homogeneous and heterogeneous AOPs for rapid degradation of Triton X-100 in aqueous media via UV light, nano titania hydrogen peroxide and potassium persulfate[END_REF] Activated PDS is applied for in situ chemical oxidation (ISCO) for contaminated groundwater. [START_REF] Tsitonaki | In situ chemical oxidation of contaminated soil and groundwater using persulfate: a review[END_REF] It could also be an alternative to Fenton or Fenton-like oxidation for the treatment of toxic wastewaters containing high concentrations of organic contaminants. [START_REF] Deng | Sulfate radical-advanced oxidation process (SR-AOP) for simultaneous removal of refractory organic contaminants and ammonia in landfill leachate[END_REF][START_REF] Li | Degradation of diphenylamine by persulfate: Performance optimization, kinetics and mechanism[END_REF] Since PDS itself has very low reactivity towards organic pollutants, activation processes are necessary for its application. [START_REF] Tsitonaki | In situ chemical oxidation of contaminated soil and groundwater using persulfate: a review[END_REF][START_REF] Lau | The aqueous degradation of butylated hydroxyanisole by UV/S2O82-: Study of reaction mechanisms via dimerization and mineralization[END_REF] Heating and alkaline addition are usually recommended as feasible PDS activation methods for ISCO. [START_REF] Furman | Mechanism of Base Activation of Persulfate[END_REF][START_REF] Waldemer | Oxidation of chlorinated ethenes by heat-activated persulfate: Kinetics and products[END_REF] UV irradiation leading to homolytic cleavage of PDS is a well-known wet oxidation technique applied in TOC analyzers. Electron donors such as low valent metals (Fe o , Fe 2+ and Ag + ) can also react with PDS to generate sulfate radicals. [START_REF] Anipsitakis | Radical generation by the interaction of transition metals with common oxidants[END_REF][START_REF] Liang | Mass Transfer and Chemical Oxidation of Naphthalene Particles with Zerovalent Iron Activated Persulfate[END_REF][START_REF] Zou | Rapid Acceleration of Ferrous Iron/Peroxymonosulfate Oxidation of Organic Pollutants by Promoting Fe(III)/Fe(II) Cycle with Hydroxylamine[END_REF] All these activation methods intensively consume energy or chemicals. It was recently reported that some organic compounds (e.g. quinones and phenoxides) could also react with PDS to generate sulfate radicals, [START_REF] Ahmad | Mechanism of Persulfate Activation by Phenols[END_REF][START_REF] Fang | Activation of Persulfate by Quinones: Free Radical Reactions and Implication for the Degradation of PCBs[END_REF] but these organics cannot be artificially introduced into contaminated waters for technical and environmental reasons (i.e., toxicity). Metal oxides or minerals (e.g., Fe2O3, α-FeOOH and MnO2) received particular attention to heterogeneously activate PDS, because they are not consumed during the activation and no additional energy is required. [START_REF] Ahmad | Persulfate activation by subsurface minerals[END_REF][START_REF] Teel | Persulfate activation by naturally occurring trace minerals[END_REF] However, the low efficiency of present heterogeneous activation processes in terms of long contact time (usually in days) and high PDS dose requested (over 100 times higher than the pollutant concentration) is still a major limitation for its industrial application. Development of efficient and cost-effective new activation processes is necessary for PDS application.

Nearly all present PDS activation processes generate sulfate radical as the main oxidant species.

Sulfate radical (E o = 2.5-3.1 V) is very reactive toward organic contaminants and competing organic/inorganic constituents in water, [START_REF] Tsitonaki | In situ chemical oxidation of contaminated soil and groundwater using persulfate: a review[END_REF][START_REF] Hori | Efficient decomposition of environmentally persistent perfluorocarboxylic acids by use of persulfate as a photochemical oxidant[END_REF][START_REF] Zhang | Production of Sulfate Radical from Peroxymonosulfate Induced by a Magnetically Separable CuFe2O4 Spinel in Water: Efficiency, Stability, and Mechanism[END_REF] exerting considerable negative side effects to the treatment of real water/wastewaters. For example, ubiquitous chloride ions in water/wastewater can be easily oxidized to chlorine radicals (Cl2˙-), which not only reduces pollutant degradation rate but also leads to the formation of highly chlorinated products. [START_REF] Anipsitakis | Cobalt-mediated activation of peroxymonosulfate and sulfate radical attack on phenolic compounds. Implications of chloride ions[END_REF] Bromide in water can also be oxidized to bromate by sulfate radicals. [START_REF] Fang | Bromate Formation from Bromide Oxidation by the UV/Persulfate Process[END_REF] Industrial application of such technology requires simultaneous minimization of hazardous product formation and maximization of PDS oxidation capacity. We anticipate that this objective could be approached through partial PDS activation without generating the unselective sulfate radicals. However, it is unknown yet whether PDS can be activated without generating sulfate radicals and how effective such activation can be.

In this work, CuO particles were tested in improving PDS oxidation of a model compound, 2,4-dichlorophenol (2,4-DCP), without generating sulfate radicals. The efficiency and durability of the PDS/CuO oxidation were evaluated with a continuous-flow reaction mode. The kinetics, mechanism, and selectivity of this oxidation process were further investigated. Its advantages over sulfate radical oxidation were also demonstrated in aspects of oxidation capacity and degradation products.

EXPERIMENTAL SECTION

Metal oxide preparation and characterization. Seven metal oxides (i.e., Fe2O3, MnO2, CuO, ZnO, TiO2, MoO3, and CeO2) were prepared with calcination of their derivatives (Fe(NO3)3•9H2O ( ≥ 98%), Mn(NO3)2•xH2O (98%), Cu-(NO3)2•3H2O (98%), Zn(NO3)2•6H2O (98%), Ti(OC3H7)4 (98%), (NH4)2MoO4 (>99%), and Ce(NO3)3•6H2O (99%)) (Sigma-Aldrich) under 450 o C for two hours. BET surface area and average pore size of these oxides were determined on a Micromeritics ASAP 2420 analyzer. Average particle size was measured on a Mastersizer 2000 laser particle size analyzer. pHpzc (pH at which the surface is zero-charged) was determined with acid-base titration. All the surface characterization results are listed in Table S1 of the Supporting Information (SI). The density of surface exposed Cu II on CuO prepared at 450 o C was determined with O2 adsorption on a Micromeritics ASAP 2020C. A density of 3.3 µmol g -1 was determined, approximating 7 Cu II sites per nm [START_REF] Johnson | Persulfate Persistence under Thermal Activation Conditions[END_REF] . Its crystalline was characterized with XRD (Bruker D8 A25).

Experimental procedure. Batch reaction. Experiments were conducted in a brown glass bottle. Predetermined volumes of model compound and PDS (K2S2O8 from SigmaAldrich) stock solutions were injected into 100 mL Milli-Q water to get the desired initial concentrations. Tetraborate (10 mM) rather than phosphate was used as a buffer for most of the reactions, because phosphate is a strong coordinate for transition metals. The mixture was magnetically stirred at a rotary speed of 600 rpm and room temperature (20 o C). Specified doses of oxide particles were introduced into the prepared solution to start the reaction. Samples withdrawn at different time intervals were filtered through 0.45 μm glass fiber filters. To analyze the concentration of model compounds, sodium nitrite was immediately introduced into the filtrate to quench residual PDS. To analyze PDS residuals, EDTA stock solution (4 mM) prepared in a phosphate buffer (pH = 7.0, 500 mM) was introduced into the filtrate with a volume percentage of 2% to scavenge any PDS decomposition initiated by metal ions.

Continuous flow reaction.

An empty Waters HPLC column (4.6 × 75 mm) was filled up with 3.0 g of CuO particles (450 o C calcined). A prepump (LabAlliance) was used to pump the reaction solution through the column at a flow rate of 2 mL min -1 . The empty bed contact time was 0.55 min.

This column was rinsed with Milli-Q water at the same flow rate for 30 min before reaction.

Analysis. Phenol and chlorophenols were analyzed on a Waters HPLC equipped with an Atlantis column (4.6 × 250 mm, 5 µm) at a UV wavelength of 280 nm. The separation was performed using an isocratic mobile phase composed of ammonium formate (4 mM in Milli-Q water) and methanol at a volume ratio of 80/20 and a flow rate of 0.8 mL min -1 . PDS concentration was analyzed on the same HPLC equipment at a UV wavelength of 230 nm with a Waters SunFire column (3.0×150 mm, 5μm) and an isocratic mobile phase (methanol/0.3% H3PO4 at a volume ratio of 20/80 and a flow rate of 0.8 mL min -1 ).Trichloroethylene (TCE) was analyzed on GC-ECD (Agilent 7890A) with a DB-1701 column (30 m×0.25 mm×0.25μm) following EPA Method 551. Dissolved copper was determined on an ICP-MS (Agilent 7500) with a detection limit of 0.1 μg L -1 .

For the analysis of adsorbable organic chlorine (AOCl), 30 mL of sample was filtered through tandem activated carbon cartridges (Mitsubishi Chemical Analytech) specifically manufactured for adsorbable organic halogen analysis on a TOX sample preparatory unit. Then, the carbon was calcined at 950 °C on an Adsorbable Organic Halogen Analyzer (AOX-200, Mitsubishi Chemical Analytech). Chloride ions formed during the calcination was collected into 50 mL of Milli-Q water.

The chloride concentration was determined using a Dionex 1600 IC analyzer equipped with a conductivity detector and an AS-15 column which was eluted isocratically with a 30 mM KOH solution.

To identify degradation products of 2,4-DCP, both GC/MS and HPLC-UV were used. Before GC/MS analysis, 50 mL of sample was extracted with 1.5 mL of dichloromethane. The extracts were analyzed on a GC/MS (Agilent7890/5975C) equipped with a DB-1701 column (30 m×0.25 mm×0.25 μm) in EI mode using a full scan range of 40-400 m/z (splitless; injector temp.: 280 o C; oven temp.: 50 o C held for 5 min then ramped to 250 o C at 5 o C min -1 ; auxiliary temp.: 270 °C). The retention times of the compounds generated during the oxidation were compared with those of carboxylate standards on a Waters HPLC-UV (210 nm) equipped with an XBridge column (4 mm ×150 mm, 5μm). An isocratic mobile phase (methanol/0.3% phosphoric acid at the volume ratio of 20/80 and theflow rate of 0.8 mL min -1 ) was used for separation. The presence of these carboxylates was further confirmed with GC/MS after methylation. Conditions of the methylation and the GC/MS analysis were described in the Supporting Information.

Surface interactions between PDS and CuO particles were characterized with ATR-FTIR and confocal Raman, following similar procedures to our previous work (Text S1, SI). [START_REF] Zhang | Production of Sulfate Radical from Peroxymonosulfate Induced by a Magnetically Separable CuFe2O4 Spinel in Water: Efficiency, Stability, and Mechanism[END_REF]

RESULTS AND DISCUSSION

PDS activation with metal oxides for 2,4-DCP degradation. The efficiency of seven metal oxides (i.e., Fe2O3, MnO2, CuO, ZnO, TiO2, MoO3 and CeO2) to activate PDS for the degradation of 2,4-DCP was compared (Figure 1). indicating that the 2,4-DCP was degraded in PDS/CuO and PDS/ MoO3 but not adsorbed on oxide particles. The result clearly show that CuO is the most active among the metal oxides tested for PDS activation, although its surface area is one of the lowest (Table S1, SI). MoO3 is much less active than CuO. Fe2O3, MnO2, ZnO, TiO2, and CeO2 have very low capacity in PDS activation under our experimental conditions.

Cu 2+ was reported to donate one electron to PDS, thus inducing PDS decomposition into sulfate and sulfate radical. [START_REF] Liu | Oxidative degradation of propachlor by ferrous and copper ion activated persulfate[END_REF] However, this process is very slow, making effective degradation of water pollutants nearly impossible. For example, only 2% of PDS can be decomposed at a PDS/Cu 2+ molar ratio of 1:1 in 10 h. [START_REF] Kimura | Catalyzed reaction between oxalate ion and peroxodisulfate. I. Copper (II) as catalyst[END_REF] In this PDS/CuO oxidation, Cu 2+ leached from CuO after 1 h reaction was 0.68 mg L -1 (10. It can be assumed that S2O8 2-in this pH range can be adsorbed on the positively charged CuO surface. The pKa of 2,4-DCP is 7.89. [START_REF] Barták | Determination of phenols by solid-phase microextraction[END_REF] At pH higher than 7.89, over half of 2,4-DCP is deprotonated, which favors electrostatic interaction with the positively charged CuO surface. However, the 2,4-DCP degradation rate was reduced as the pH was further raised above 7.0. One possible reason could be that the interaction between deprotonated 2,4-DCP and negatively charged S2O8 2-species adsorbed on CuO (≡Cu II ⋯ -O3SOOSO3 -) is unfavorable. To support this hypothesis, degradation of 2,4,6-trichlorophenol (2,4,6-TCP) was also tested in the same pH range (Figure 2). The 2,4,6-TCP has a lower pKa (6.23) than 2,4-DCP. [START_REF] Barták | Determination of phenols by solid-phase microextraction[END_REF] If the anticipated reaction mechanism between the pollutant and the adsorbed S2O8 2-is true, the 2,4,6-TCP should be degraded most efficiently at a lower pH The influent with PDS/2,4-DCP molar ratio of 1 was applied during the first phase of the experiment (from 0 to 48 L of treated influent volume). A steady 2,4-DCP removal and AOCl removal (over 90% and 60%, respectively) were achieved for the first 30 L of influent followed by a gradual decrease of the removal to 35% and 30% respectively at the end of this phase. Then, the CuO column was rinsed with 50 mL of Milli-Q water at the same flow rate. The next phase of the experiment (from 49 to 58 L of treated influent volume in Figure 3) was started at the same PDS/2,4-DCP molar ratio of 1. Interestingly, both 2,4-DCP and AOCl removal were recovered after the Milli-Q water rinsing. This finding indicates that the decline of PDS/CuO oxidation efficiency at the end of the first phase (first 48 L) is possibly due to weak adsorption of solutes, such as 2,4-DCP degradation intermediates, on CuO particles. As the PDS/2,4-DCP molar ratio was raised to 2 (from 59 to 66 L of treated influent volume in Figure 3) and 4 (from 67 to 74 L of treated influent volume), the 2,4-DCP was completely removed, and the AOCl removal was increased from 80% to 90%.

When the PDS/2,4-DCP molar ratio was reduced to 0.5 (from 75 to 82 L of treated influent volume in Figure 3), the 2,4-DCP removal was about 55%, and the AOCl removal decreased to 15%. During thefinal phase of the experiment (from 83 to 90 L of treated influent volume in Figure 3), the pH of the influent with the PDS/2,4-DCP molar ratio of 1 was adjusted to 7.0. The 2,4-DCP was nearly completely removed, and the average AOCl removal was about 70%.

The concentration of leached copper in the effluent increased with PDS dosage. It was significantly reduced to less than 1.0 μM when the pH of the influent was raised to 7.0, which is consistent with the result shown in Figure 2. In addition, no decline of the PDS/CuO oxidation efficiency was observed after the first phase of the experiment. In the second to last phase of the experiment (PDS/2,4-DCP = 0.5), less degradation intermediates might have been produced from 2,4-DCP due to reduced PDS dosage, which could mitigate the adsorption of the degradation intermediates onto the CuO particles or lead to desorption of previously adsorbed ones. The neutral pH in the last phase of the experiment could have similar effects, as the adsorption of compounds having carboxyl/hydroxyl groups on metal oxides usually decreases with increasing pH. [START_REF] Gu | Adsorption and desorption of different organic matter fractions on iron oxide[END_REF] The results of the continuous-flow reaction indicate that 1) the CuO prepared has durable activity in PDS activation for 2,4-DCP degradation, on the understanding that periodical rinsing can be applied to eliminate adsorbed oxidation products from the CuO; 2) the PDS/CuO has a high oxidation efficiency, removing over 90% of 2,4-DCP at the PDS/CuO molar ratio of 1 and over 90% of AOCl at the PDS/CuO molar ratio of 4 in a short contact time of 0.55 min; and 3) copper leaching can be reduced to a low level if the PDS/CuO process is operated at neutral pH. In operations where rinsing with clean water is impractical such as in situ treatment of groundwater, intermittent operation without introduction of PDS might be a choice to recover the efficiency of the PDS/CuO, which can be tested in future studies.

Influence of radical scavengers and ionic strength. Sulfate radical is usually considered to be the actual oxidant species in activated PDS processes. At neutral and alkaline pHs, hydroxyl radical can also be generated due to the reaction of sulfate radical with OH -. The two radical species react very rapidly with ethanol (k·OH = (1.2-2.8) × 10 9 M -1 s -1 ; k·SO4-= (1.6-7.8) × 10 7 M -1 s -1 ). [START_REF] Anipsitakis | Degradation of organic contaminants in water with sulfate radicals generated by the conjunction of peroxymonosulfate with cobalt[END_REF] For example, 2,4-DCP degradation by sulfate radical generated in Co 2+ /PMS coupled process was nearly completely scavenged at the ethanol/PMS molar ratio of 1000. We noticed that ethanol at a dose up to 1000 times of PDS's molar concentration had no influence on 2,4-DCP degradation in the PDS/CuO coupled process (Figure 4), which indicates that PDS activation by CuO does not follow the sulfate radical generation mechanism. Chloride ions can be oxidized by sulfate radical to Cl· (k·SO4-= 2.0 × 10 8 M -1 s -1 ) which rapidly combines with another chloride in water forming Cl2· -(chlorine radical). [START_REF] Anipsitakis | Cobalt-mediated activation of peroxymonosulfate and sulfate radical attack on phenolic compounds. Implications of chloride ions[END_REF] The reducing potential of chlorine radical (E o Cl2·-/2Cl-= 2.09 V) is lower than sulfate radical (E o SO4·-/SO42-= 2.5-3.1 V). The influence of chloride ions on the pollutant degradation rate during sulfate radical oxidation is dependent on the target pollutant. [START_REF] Yang | Comparison of halide impacts on the efficiency of contaminant degradation by sulfate and hydroxyl radical-based advanced oxidation processes (AOPs)[END_REF] For example, iopromide degradation rate by sulfate radical was reduced by 50% in the presence of 2 mM chloride. [START_REF] Zhang | Production of Sulfate Radical from Peroxymonosulfate Induced by a Magnetically Separable CuFe2O4 Spinel in Water: Efficiency, Stability, and Mechanism[END_REF] In contrast, it was reported that the degradation rate of 2,4-DCP was improved by the presence of chloride during sulfate radical oxidation, [START_REF] Anipsitakis | Cobalt-mediated activation of peroxymonosulfate and sulfate radical attack on phenolic compounds. Implications of chloride ions[END_REF] probably because chlorine radical is more reactive with 2,4-DCP than its degradation intermediates as compared with the relatively nonselective sulfate radical. Figure 4 shows that the presence of 2 and 5 mM chloride slightly reduced the 2,4-DCP degradation rate (by about 9%), which could be caused by the negative effect of increased ionic strength as indicated in Figure S6 (SI). This result also suggests that sulfate radical is not the oxidant species responsible for 2,4-DCP degradation in the PDS/CuO coupled process.

Because the PDS/CuO is not a sulfate radical generation process, the 2,4-DCP degradation should be related to surface activation of PDS or 2,4-DCP or both of them. Under slightly acidic conditions, PDS, 2,4-DCP, and CuO are negatively, neutrally, and positively charged, respectively. The increase of the ionic strength will reduce the zeta potential of the CuO particles through compressing the thickness of the electric double layer. with a slope of 0.688 (Figure 5C). It is clear that the dosages of CuO and PDS have significant influence on the reaction. PDS activation by CuO is the reaction rate-limiting for the PDS/CuO oxidation of 2,4-DCP. Since the reaction involves three species, i.e., PDS, surface Cu II and 2,4-DCP, the overall reaction rate (ν) can be expressed in eq 1. k is the apparent reaction rate constant; n1, n2 and n3 are reaction orders in PDS, surface Cu II and DCP concentrations, respectively. According to the experimental result, 0.335, 0.688 and 0 can be assigned to n1, n2 and n3, respectively. Values of k (0.062 ± 0.003 min -1 )

were calculated with eq 2 and the data of Figure 5C. Then, the overall reaction rate under our experimental conditions can be expressed in eq 3 with a unit of µM min -1 . The overall reaction order (i.e., n1 + n2) is close to 1, meaning that the overall reaction rate is in first order.

(E1) [DCP] ] [Cu [PDS] dt d[DCP] dt d[PDS] n3 n2 surf II n1 k v      (E2) [PDS] ] [Cu [PDS] dt d[PDS] obs 0.688 surf II 0.335 k k    (E3) ] [Cu [PDS] 062 . 0 0.688 surf II 0.335  v
PDS activation mechanism. It was shown in our previous studies that ATR-FTIR and confocal Raman are useful protocols for in situ characterization of solute-solid surface interactions in water. [START_REF] Zhang | Production of Sulfate Radical from Peroxymonosulfate Induced by a Magnetically Separable CuFe2O4 Spinel in Water: Efficiency, Stability, and Mechanism[END_REF][START_REF] Zhang | Catalytic ozonation of oxalate with a cerium supported palladium oxide: an efficient degradation not relying on hydroxyl radical oxidation[END_REF] Characterization of PDS-CuO interaction using the two techniques showed that there were neither shift of the typical vibration bands of PDS nor new peak formation (Figure S7 and S8, SI), which means that 1) the interaction between PDS and CuO does not form a chemical bond which can change the vibration frequencies of the adsorbed PDS molecules, and 2) there are no decomposition intermediates (like peroxo species) of PDS on the CuO surface. The first conclusion can also explain the influence of ionic strength on the PDS/CuO (Figure S6, SI). If the PDS strongly interacted with CuO, the increase of ionic strength would have no influence on the PDS/CuO oxidation of 2,4-DCP, because the increase of ionic strength does not influence inner-sphere interactions (covalent bonding or a combination of covalent and ionic bonding) between the particle's surface and the solute. On the contrary, the increase of ionic strength significantly influences outer-sphere interactions (electrostatic bonding) in both equilibrium and kinetics. [START_REF] Stumm | Chemistry of the solid-water interface: Processes at the mineral-water and particle-water interface in natural systems[END_REF] As shown for the PMS activation in our previous work, the inner-sphere coordination between PMS and the surface Cu(II) sites of CuO caused significant dissolution of CuO even at neutral pHs. [START_REF] Zhang | Production of Sulfate Radical from Peroxymonosulfate Induced by a Magnetically Separable CuFe2O4 Spinel in Water: Efficiency, Stability, and Mechanism[END_REF] The low copper leaching in the PDS/CuO coupled process at neutral pH (Figure 2) can also be interpreted with the weak PDS-CuO interaction. The second conclusion is consistent with the fact that PDS was nearly not decomposed on the CuO surface in the absence of 2,4-DCP (Figure S3, SI).

Unlike CuO activated PMS and base activated PDS, [START_REF] Furman | Mechanism of Base Activation of Persulfate[END_REF][START_REF] Zhang | Production of Sulfate Radical from Peroxymonosulfate Induced by a Magnetically Separable CuFe2O4 Spinel in Water: Efficiency, Stability, and Mechanism[END_REF] no gas bubble was formed in the PDS/CuO system at a high PDS concentration (200 mM) (not shown), indicating again that the PDS activation mechanism is different from those processes. Furman et al. reported that superoxide (O2 •-) was produced in base activated PDS. [START_REF] Furman | Mechanism of Base Activation of Persulfate[END_REF] Superoxide can reduce highly oxidized compounds like hexachloroethane. However, superoxide cannot exist in the PDS/CuO system, because traces pf Cu(II) can rapidly dismutate superoxide into oxygen and hydrogen peroxide. [START_REF] Zafiriou | Chemistry of the superoxide radical (O2-) in seawater: Reactions with inorganic copper complexes[END_REF] Since no gas was formed from the PDS/CuO suspension, it can be confirmed that superoxide was not produced.

When activated by CuO, PDS is not"directly" dissociated, because significant decomposition of PDS only occurred when 2,4-DCP coexisted in the solution but not in the absence of 2,4-DCP (Figure S3, SI), indicating that an electron donor is needed for the decomposition of activated PDS.

It is reasonable to propose that the outer-sphere interaction between the positively charged CuO surface and the PDS anion induced some slight rearrangement of the PDS electrons. This interaction is not strong and thus does not form chemical bonds. However, it already makes the PDS much more reactive toward 2,4-DCP, thus leading to significant PDS decomposition in the presence of 2,4-DCP.

The outer-sphere interaction between PDS and CuO was indirectly proved in this work. In situ X-ray adsorption spectroscopy (XAS) usually can provide direct evidence for outer-sphere and inner-sphere interactions between metal oxides and oxyanions, [START_REF] Hayes | In situ X-ray absorption study of surface complexes: Selenium oxyanions on α-FeOOH[END_REF][START_REF] Farquhar | Mechanisms of arsenic uptake from aqueous solution by interaction with goethite, lepidocrocite, mackinawite, and pyrite: An X-ray absorption spectroscopy study[END_REF] which could be applied to verify this PDS-CuO interaction in future studies.

Comparison with sulfate radical oxidation. PMS/Co 2+ , a well-known sulfate radical generation process, was compared with the PDS/CuO coupled process for 2,4-DCP degradation at the same oxidant dosages. The redox couple of Co 2+ /Co 3+ was reported to be efficient in initiating PMS decomposition into sulfate radicals. [START_REF] Anipsitakis | Degradation of organic contaminants in water with sulfate radicals generated by the conjunction of peroxymonosulfate with cobalt[END_REF] Co 2+ (3 µM) in the PMS/Co 2+ process was dosed at a similar concentration to surface Cu II (3.3 µM at the CuO dosage of 1.0 g L -1 ) in the PDS/CuO process. 4 mM of chloride ions were also introduced into the reaction solution as it ubiquitously exists in water. In order to identify degradation products, a high 2,4-DCP concentration (500 µM) was applied. The reaction time was extended long enough to ensure complete consumption of the oxidants. Figure 6 shows that, at the oxidant/2,4-DCP molar ratio of 1, the PDS/CuO coupled process achieved 90% 2,4-DCP removal, while the PMS/Co 2+ process removed only 24% of 2,4-DCP. When the ratio was raised to 4, the 2,4-DCP was nearly completely removed by PDS/CuO oxidation compared with 55% removal by PMS/Co 2+ oxidation. The PDS/CuO process showed a much higher 2,4-DCP degradation capacity than the sulfate radical oxidation process even at 4 times lower oxidant dosage. Control experiments conducted with PDS alone and PMS alone removed less than 5% 2,4-DCP (data not shown). sulfate radical generated from two PDS for one electron abstraction from organics (eq 6)) which is presently one of the most important PDS activation methods for ISCO. At least half of the oxidation capacity was also wasted in the Fe 2+ activated PDS which is usually proposed for wastewater treatment (eq 7).

( Selectivity of the PDS/CuO oxidation. The PDS/CuO coupled process was also tested for the degradation of trichloroethylene (TCE), p-chlorobenzoic acid iopromide, phenol and three chlorophenols (Figure S11, SI). The p-CBA is a well-known probe compound for hydroxyl radicals. Iopromide is also a refractory compound which cannot be effectively degraded in advanced oxidation process like O3/H2O2, but can be degraded with sulfate radical oxidation. [START_REF] Zhang | Production of Sulfate Radical from Peroxymonosulfate Induced by a Magnetically Separable CuFe2O4 Spinel in Water: Efficiency, Stability, and Mechanism[END_REF][START_REF] Westerhoff | Fate of endocrine-disruptor, pharmaceutical, and personal care product chemicals during simulated drinking water treatment processes[END_REF] The two compounds were nearly not degraded in the PDS/CuO oxidation. In contrast, TCE, phenol and chlorophenols were effectively degraded. The result indicates that the surface activated PDS has a lower oxidation potential than hydroxyl radical and sulfate radical. It can be classified as a moderately strong oxidant with certain selectivity for organic pollutants. Since not only phenol and chlorophenols but also TCE were effectively degraded, the PDS/CuO oxidation is not selective only to phenolic compounds. The efficiency of this process on various organic pollutants should be tested in future studies to have a better knowledge on its selectivity and oxidation potential. For contaminated groundwater, the competition of low concentrations of dissolved organic matter could reduce the degradation efficiency for the target pollutants, which also should be evaluated for the design of the PDS/CuO oxidation process.

To sum up, results of this study showed that PDS activation without generation of sulfate radicals can be achieved with the PDS/CuO coupled process. Its cost in oxidant would be over 10 times lower than sulfate radical oxidation. Its efficacy for various other pollutants should be further tested to get more detailed knowledge on its selectivity. Since the PDS/CuO process demonstrated a good dechlorination capacity for 2,4-DCP, it would be interesting to study whether it is also good for other halogenated pollutants. Copper leaching could be a problem when the PDS/CuO is applied at acidic pH and high PDS dosage. It was reported that metal leaching can be significantly reduced with appropriate support materials or fabrication of ferrite spinel structures. [START_REF] Querol | Immobilization of heavy metals in polluted soils by the addition of zeolitic material synthesized from coal fly ash[END_REF][START_REF] Shih | Nickel stabilization efficiency of aluminate and ferrite spinels and their leaching behavior[END_REF] These protocols should be tested to anchor CuO for PDS activation in future studies. ASSOCIATED CONTENT Supporting Information. Procedures of ATR-FTIR and Raman characterization, one table and 11 figures. This material is available free of charge via the Internet at http://pubs.acs.org.

2 PDS/MoO 3 PDS/CeO 2 Figure 1 .

 2321 Figure 1. 2,4-DCP removal in PDS solution activated by metal oxides. Conditions: [PDS]o = 40 µM, [2,4-DCP]o = 5 µM, oxide dose = 200 mg L -1 , pH = 5.8, T = 20 o C, error bars representing the deviation of three replicates.

Figure 2 .

 2 Figure 2. Influences of pH on the degradation rates of 2,4-DCP and 2,4,6-TCP in PDS/CuO oxidation and copper leaching in 2,4-DCP degradation. Conditions: [PDS]o = 20 µM, [2,4-DCP]o/ [2,4,6-TCP]o = 5 µM, CuO dose = 200 mg L -1 , reaction time = 20 min, T = 20 o C, error bars representing the deviation of three replicates.

than 2 , 4 -

 24 DCP. As shown in Figure2, the optimum pH for the degradation of 2,4,6-TCP in the PDS/CuO oxidation system shifted to a lower value (ph 6.0) as compared to 2,4-DCP.The strong inverse H + -dependency of the degradation rate of 2,4-DCP in PDS/CuO could be related to the degradation pathway, because OH -is needed for the replacement of chlorine atoms from the 2,4-DCP molecule (shown later). Another reason could be similar to that suggested for the adverse impact of H + on PMS activation.[START_REF] Guan | Influence of pH on the Formation of Sulfate and Hydroxyl Radicals in the UV/Peroxymonosulfate System[END_REF] H + would probably form an H-bond with the negatively charged O in the S2O8 2-molecule and thus inhibit its interaction with positively charged Cu II of CuO.Efficiency and durability in continuous-flow reaction. Long-term performance is a critical factor to be considered for potential application of the PDS/CuO coupled process. A CuO particle packed column (1.1 mL) was used to test the efficiency and durability of the coupled process in a continuous-flow reaction. An experiment conducted in the absence of PDS (20μM of 2,4-DCP and pH 5.8) showed no adsorption of 2,4-DCP on CuO particles of the column. Figure3shows 2,4-DCP degradation, remaining AOCl and copper leaching over a 750 h continuous-flow reaction.

5 Figure 3 .

 53 Figure 3. Concentrations of 2,4-DCP, AOCl and leached Cu 2+ in the effluent of a continuous-flow reaction. Conditions: inflow concentration of 2,4-DCP = 20 µM, inflow PDS concentration depends on the PDS/2,4-DCP molar ratio as indicated inside the graph, pH = 5.8 (without buffer addition) if not indicated in the graph, flow rate = 2 mL min -1 , empty-bed contact time = 0.55 min, T = 20 o C.

Figure 4 .

 4 Figure 4. Influence of ethanol and chloride on 2,4-DCP degradation in the PDS/CuO oxidation. Conditions: [PDS]o = 20 µM, [2,4-DCP]o = 5 µM, CuO dose = 200 mg L -1 , initial pH was adjusted with diluted NaOH/HNO3 to 5.8, T = 20 o C.

  FigureS6(SI) shows that the 2,4-DCP degradation rate at high ionic strength (represented with NaClO4 concentration) was much lower than that at low ionic strength. The 2,4-DCP degradation rate logarithmically decreased as the NaClO4 concentration was increased from 10 to 100 mM. The result suggests that the reaction is dominated by the interaction of two oppositely charged species, i.e., S2O8 2-and positively charged CuO. Taking the significantly reduced reactivity of deprotonated 2,4-DCP (favoring interaction with positively charged CuO) during the PDS/CuO oxidation also into account (Figure2), the promoted 2,4-DCP oxidation cannot be ascribed to surface activation of 2,4-DCP or simultaneous activation of 2,4-DCP and PDS.Surface activation of PDS on CuO particles is most likely the only reason.Kinetics. The kinetic study was carried out at pH 5.8. In an excess of PDS(20-200 µM), the degradation rate of 2,4-DCP (with an initial concentration of 5 µM) below 60% removal was well fitted with a pseudo-first order reaction model at each given PDS concentration (Figure5A). Plotting ln(kobs) vs ln([PDS]o) yielded a linear curve with a slope approximating 0.335. The decomposition rate of PDS was independent of the 2,4-DCP concentration which was in excess (Figure5B). The ln(kobs) of PDS decomposition during 2,4-DCP degradation was linearly correlated to ln([Cu II ]surf) ([Cu II ]surf is the CuO dose (g L -1 ) multiplied by the density of surface Cu II of CuO i.e., 3.3 µmol g -1 )

Figure 5 .

 5 Figure 5. Influences of PDS dose on 2,4-DCP decomposition (A: [2,4-DCP]o = 5 µM, CuO dose = 400 mg L -1 ), 2,4-DCP dose on PDS decomposition (B: [PDS]o = 20 µM, CuO dose = 400 mg L -1 ), and CuO dose on PDS decomposition (C: [PDS]o = 20 µM, [2,4-DCP]o = 10 µM) during PDS/CuO oxidation. Conditions: pH = 5.8, T = 20 o C.

Figure 6 .

 6 Figure 6. Comparison of PDS/CuO with Co 2+ /PMS for 2,4-DCP degradation. Conditions: [2,4-DCP]o = 500 µM, CuO dose = 1 g L -1 , [Co 2+ ]o = 3 µM, [Cl -]o = 4 mM, initial pH was adjusted with diluted NaOH/HNO3 to 5.8, T = 20 o C, error bars representing the deviation of three replicates.

Figure S9 (

 S9 Figure S9 (SI) shows GC/MS chromatograms of 2,4-DCP after reaction in the two oxidation

ACKNOWLEDGEMENTS

The authors want to thank Dr. Haibo Zhu of KAUST Catalysis Center for BET analysis and Ms.

Tong Zhan of WDRC for ICP-MS analysis. We also want to thank the anonymous reviewers for their valuable revision suggestions which significantly improved this manuscript.

systems, it was noticed that despite the two monochlorinated products identified in PDS/CuO oxidation, the PMS/Co 2+ process (especially at the PMS/2,4-DCP molar ratio of 4) generated highly chlorinated products (i.e., 1,1,3,3-pentachloropropanone, 1,1,3,3-tetrachloropropanone, 2,2,4-trichloro-1,3-cyclopentenedione and 2,4,6-trichlorophenol), among which 2,4,6-trichlorophenol was observed in high peak intensity even at the PMS/2,4-DCP molar ratio of 1

(Figure S9A and S9B, SI). The production of all these additionally formed highly chlorinated products increased as the PMS/2,4-DCP molar ratio was raised from 1 to 4 (Figure S9B, SI). The formation of these highly chlorinated products can be ascribed to reactions of 2,4-DCP [START_REF] Li | One-electron redox potentials of phenols in aqueous solution[END_REF] as well as its degradation intermediates with chlorine radicals [START_REF] Anipsitakis | Cobalt-mediated activation of peroxymonosulfate and sulfate radical attack on phenolic compounds. Implications of chloride ions[END_REF] which were generated from the oxidation of chloride ions by sulfate radicals in the PMS/Co 2+ process. The result indicates that unlike sulfate radical the CuO surface activated PDS is not strong enough to oxidize chloride ions into reactive radical species. Therefore, the second advantage of PDS/CuO oxidation over sulfate radical oxidation is the absence of highly chlorinated product formation. The PDS/CuO could be more preferable than sulfate radical generating processes in reducing oxidant cost by achieving a high pollutant degradation rate while simultaneously avoiding the formation of more hazardous products.

The formation of 2-chlorobenzoquinone from 2,4-DCP needs two electron abstraction by the oxidant (eq 4). Its further transformation to maleic acid and oxalic acid requires abstraction of more electrons by the oxidant. Since over 90% 2,4-DCP was degraded at the PDS/2,4-DCP molar ratio of 1 and all three products were present (Figure S9 and S10, SI), it can be speculated that all of the oxidation capacity of PDS (i.e., two electron abstraction from organics by one PDS (eq 5)) was utilized in the PDS/CuO process. It is more efficient than the alkaline activated PDS process (one