The anodic reactivity of 4,4′-dimethoxychalcone: a synthetic and mechanistic investigation

Article abstract of DOI:10.1007/s11164-016-2607-7

The anodic oxidation of the 4,4′-dimethoxychalcone (DMC) was investigated by different electrochemical methods at a platinum working electrode and in acetonitrile as a solvent. The DMC exhibited a single irreversible anodic peak around 1.6?V versus Ag/AgC

Full text of DOI:10.1007/s11164-016-2607-7

Res Chem Intermed
DOI 10.1007/s11164-016-2607-7
The anodic reactivity of 4,40-dimethoxychalcone:
a synthetic and mechanistic investigation
Imen Aribi1 Sahbi Ayachi2 Kamel Alimi2
•
•
•
Sadok Roudesli1 Ayoub Haj Said1
•
Received: 21 April 2016 / Accepted: 6 June 2016
Ó Springer Science+Business Media Dordrecht 2016
Abstract The anodic oxidation of the 4,40-dimethoxychalcone (DMC) was inves-
tigated by different electrochemical methods at a platinum working electrode and in
acetonitrile as a solvent. The DMC exhibited a single irreversible anodic peak
around 1.6 V versus Ag/AgCl. On the time scale of cyclic voltammetry experi-
ments, the highly reactive radical cation issued from the first electron transfer
underwent a second order rate-limiting reaction. The potential imposed electrolyses
of DMC led to the formation of a semi-conducting oligomer with 40 % yield. Using
different physico-chemicals methods, the structural study confirmed the formation
of an o-phenylenevinylene oligomer. The values of the corresponding optical and
electrochemical band gaps were calculated to be 3.15 and 2.86 eV, respectively.
Finally, a mechanism for the DMC electro-oligomerization was proposed on the
basis of the obtained results.
Keywords Anodic oxidation Á Chalcone Á Radical cation Á Conjugated oligomers Á
Photoluminescence
Introduction
In previous studies, we were interested in the anodic oxidation of substituted
methoxy-substituted arenes at a platinum electrode in acetonitrile [1, 2]. We
demonstrated that the coupling of the radical cations issued from the first electron
transfer was the governing reaction near the electrode. Particularly, under anhydrous
&
Ayoub Haj Said
ayoub.hajsaid@fsm.rnu.tn
1
2
´
Laboratoire Interfaces et Materiaux Avances, Faculte des Sciences de Monastir, Universite de
Monastir, 5000 Monastir, Tunisia
´
´
´
´
Unite de Recherche (UR 11ES55), Materiaux Nouveaux et Dispositifs Electroniques
Organiques, Faculte des Sciences de Monastir, Universite de Monastir, 5000 Monastir, Tunisia
´
´
´
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I. Aribi et al.
conditions, successive coupling reactions, according to an (EC)n mechanism, led to
conjugated oligomers from the polyphenylene family [3–8]. The methoxy group
plays a crucial role in decreasing the oxidation potential and in the distonic
character displayed by the generated radical cations. In the present work, we are
interested in the anodic oxidation of a substituted chalcone, containing the
methoxyphenyl moiety. In fact, chalcones belong to a class of a,b-unsaturated
ketones possessing highly conjugated alkenyl and carbonyl groups between two
phenyl rings. They are important and interesting natural compounds that can be
easily prepared in the laboratory. Recently, chalcone derivatives have been used in
the field of material science for non-linear optics, electrochemical and optical
chemosensing [9–16].
Although their electrochemical reduction has been well studied [17–20], few
researches have been devoted to the anodic oxidation of chalcones [21–24].
Flavones and flavanonols have been described as the resulting compounds of the
anodic oxidations of 20-hydroxychalcones [21–23]. On the other hand, the oxidation
of chalcones by different chemical agents leads to their cleavage [25–28] and to the
olefinic double bond hydroxylation [29].
In this work, 4,40-dimethoxychalcone (DMC) was studied. The investigation of
the electrochemical behavior of this product was carried out on an analytical and a
synthetic scale with cyclic voltammetry and potential imposed electrolysis,
respectively. The chemical structure of the electrolysis products was characterized
by different physico-chemical methods.
Materials and methods
Chemicals
Acetonitrile CH3CN (PANREAC) was distilled on calcium hydride CaH2 under
Argon. Chloroform was obtained from PROLABO and diethyl ether from
PANREAC. Tetrabutylammonium tetrafluoroborate (TBAF) used in the voltam-
metric study was prepared and purified in the same way as in Ref [1]. The tetraethyl
ammonium tetrafluoroborate (TEAF) used in the preparative electrolysis was
procured from ALDRICH.
The p-methoxyacetophenone, the p-anisaldehyde and the ferrocenecarboxalde-
hyde used in this work were provided by ‘ACROS ORGANICS’. All other used
reagents were commercially available and were used as received.
Synthesis of chalcones
The substituted chalcone DMC 1 (see Scheme 1) was prepared according to a
standard procedure of the base-catalyzed Claisen–Schmidt condensation by the
addition of a small amount of aqueous sodium hydroxide to an ethanolic equimolar
solution of a p-anisaldehyde and a p-methoxyacetophenone. Stirring was continued
for 2 h, after which the chalcone crystallized. The mixture was chilled in ice for
10–15 min, filtered on a Buchner funnel, and the precipitate was successively
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The anodic reactivity of 4,40-dimethoxychalcone: a…
Scheme 1 The chemical structures of 4,4’-dimethoxychalcone (DMC) 1 and ferrocenylchalcone
(Fc-chal) 2
washed with water until the washings were neutral, and then it was washed with ice-
cold ethanol. After drying, the product was recrystallized from 95 % ethanol to
afford the chalcone. A yellowish powder was obtained in 80 % yield. The
completion of the reaction was monitored by thin layer chromatography.
1H NMR (d/ppm): 8.02 (d, 2H, J = 8.7 Hz)–7.77 (d, 1H, J = 15.6 Hz)–7.69 (d,
2H, J = 8.7 Hz)–7.42 (d, 1H, J = 15.6 Hz)–6.97 (d, 2H, J = 9 Hz)–6.93 (d, 2H,
J = 8.7 Hz)–3.88 (s, 3H)–3.85 (s, 3H). 13C NMR (d/ppm): 55.46–55.54–113.
83–114.83–119.59–127.85–130.15–130.75–131.40–143.86–161.55–163.31–188.82.
M.p = 88 °C.
The ferrocenylchalcone Fc-chal 2 (see Scheme 1), chosen as a reference in cyclic
voltammetry, was prepared directly from ferrocenecarboxaldehyde and acetophe-
none according to the previously described procedure [30]. A red powder was
obtained in 62 % yield.
1H NMR (d/ppm): 4.19 (s, 5H), 4.49 (s, 2H), 4.60 (s, 2H), 7.13 (d, 1H,
J = 15.3 Hz), 7.47–7.59 (m, 3H), 7.75 (d, 1H, J = 15.3 Hz), 7.98 (d, 2H,
J = 7.2 Hz). 13C NMR (d/ppm): 69.06–69.84–71.41–119.24–128.38–128.56–
132.39–146.86–188.60. M.p = 124 °C.
The electrochemical properties of the Fc-chal were measured at a platinum
working electrode in acetonitrile 10-1 M TBAF solution. The cyclic voltammetry
analyses showed a reversible one-electron oxidation at Epa = 0.596 V versus Ag/
AgCl when v = 0.1 Vs-1 (Fig. 1). The peak potential separation (DEp) was close to
0.06 V and the anodic to cathodic current ratio was equal to unity, irrespective of
changing sweep rate.
Electrochemistry
The voltammetric study was performed with a Voltalab10 apparatus from
Radiometer driven by the Volta Master software. All cyclic voltammetric
measurements were conducted at room temperature in 25 mL of CH3CN solution
containing TBAF (0.1 M) as a supporting electrolyte. A three-electrode cell was
used for electrochemical oxidation under nitrogen gas. The working electrode was a
2 mm diameter platinum disk (Tacussel type EDI). The reference electrode was an
Ag/AgCl/3 M KCl electrode. The counter electrode was a Pt wire. The measure-
ments were carried out with six different potential scan rates in the region of
20–500 m Vs-1. The ohmic drop compensation was activated during the
experiments.
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I. Aribi et al.
Fig. 1 Cyclic voltammogram for oxidation of Fc-chal, 10-3 M in CH3CN, 10-1 M TBAF, recorded at a
platinum disk electrode (2 mm diameter). Potential scan rate: 100 m Vs-1, Counter electrode: Pt wire
The preparative electrolyses were carried out with 10-1 M 4,40-dimethoxychal-
cone solution in a two-compartment cell, under nitrogen, at a controlled potential.
The potentiostat (PRT 100-1X) and the current integrator (IG5-LN) were both
procured from Tacussel. The electrolysis cell was separated with a number 4 glass
frit. The working electrode was a 4 cm2 platinum grid. A Pt wire placed in a
separate compartment constituted the counter electrode. The working electrode
potential was adjusted versus an Ag/AgCl/3 M KCl reference electrode.
The electrolysis solutions were evaporated under vacuum until elimination of the
major part of acetonitrile, and the electrolysis products were extracted with
chloroform. The organic solution was dried with anhydrous MgSO4, concentrated
and then precipitated in diethyl ether.
Material characterization
An infrared (IR) analysis was performed with a Shimadzu 8400–Fourier Transform
spectrophotometer. The spectra were obtained with KBr pressed pellets
(4000–500 cm-1).
1
13C and H nuclear magnetic resonance (NMR) studies of the monomer and
oligomer were carried out with a Bruker 300 MHz in deuterated chloroform CDCl3.
UV–Vis spectrophotometric measurements were performed with a Shimadzu
spectrophotometer. The photoluminescence spectrum was collected from the front-
face geometry of the samples with a Jobin–Yvon Fluorolog spectrometer using
Xenon lamp (500 W) as an excitation source (k = 330 nm).
A l styragel 500 A–15 lm column was used in gel permeation chromatography
(with a length of 300 mm and a diameter of 7.8 mm). The temperature was 30 °C.
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The anodic reactivity of 4,40-dimethoxychalcone: a…
The solvent was tetrahydrofuran with a flow rate of 0.85 mL min-1. Polystyrene
was used as a standard.
The thermogravimetric analysis was carried out in a Perkin-Elmer TGS-1 thermal
balance with a Perkin-Elmer UV-1 temperature program control. The samples were
placed in a platinum sample holder and the thermal degradation measurements were
carried out between 0 and 500 °C at a speed rate of 10 °C min-1 under nitrogen.
Results
Voltammetric study
The voltammetric study of DMC was carried out in CH3CN (0.1 M TBAF) on a
platinum disk for different product concentrations and at different scan rates ranging
from 20 to 500 m Vs-1. A reproducible voltammetric pattern was obtained with a
single irreversible anodic peak. At 100 m Vs-1 and for a substrate concentration
C = 10-3 M, the corresponding oxidation peak potential was 1.586 V versus Ag/
AgCl, as shown in Fig. 2.
In order to obtain a better understanding of the electrochemical process, the
variation of the peak potential of DMC with the scan rate or substrate concentration
was studied. The peak potential variation is a linear function of both the logarithms
of the potential scan rate v and the DMC concentration (Ci). The slopes are close to
20 mV and -20 mV per decade of v and (Ci/v), respectively (Figs. 3, 4). These
results indicate that the first electron transfer is fast, and is followed by a rate-
determining second-order homogeneous reaction.
On the other hand, an approximate determination of the number of exchanged
electrons (ne) was achieved using the equations given in the literature [31]. This was
obtained from the comparison of the peak current of DMC to the one of the
Fig. 2 Cyclic voltammogram
for oxidation of DMC, 10-3
in CH3CN, 10-1 M TBAF,
recorded at a platinum disk
electrode (2 mm diameter).
M
Potential scan rate: 100 m Vs-1
counter electrode: Pt wire
,
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I. Aribi et al.
Fig. 3 Variation of the peak potential as a function of the logarithm of the scan rate for DMC in CH3CN,
10-1
M
TBAF, recorded at
a platinum disk electrode a b
C = 5 9 10-4 M; C = 10-3 M;
c C = 2 9 10-3 M; d C = 5 9 10-3
M
Fig. 4 Variation of the peak potential as a function of the log (C/v) (C concentration in M, v potential
scan rate in Vs-1) for DMC in CH3CN, 10-1 M TBAF, recorded at a platinum disk electrode
monoelectronic ferrocene/ferrocenium redox system of the Fc-chal recorded in the
same conditions (Figs. 1, 2). In fact, the peak currents for DMC and Fc-chal are
described by Eq. (1) and (2), respectively.
1=2
DMC
1=2
IpDMC ¼ 0; 527 n3e=2F A ðF/RTÞ
D
CDMC v1=2
ð1Þ
ð2Þ
1=2
FcÀchal
IpFcÀchal ¼ 0; 446 n3=2 F A ðF/RTÞ
D
CFcÀchal v1=2
1=2
1
With, Ip, C and v correspond to peak current, substrate concentration and
potential scan rate, respectively. ne and n1 are the number of the exchanged
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The anodic reactivity of 4,40-dimethoxychalcone: a…
electrons for DMC and Fc-chal, respectively. Actually, n1 = 1 for the monoelec-
tronic Fc-chal electrochemical system. Taking no account of the difference between
the diffusion coefficients DDMC and DFc-chal, ne was then deduced by combining
Eqs. 1 and 2:
1=2
n3e=2 ¼ 0; 446=0; 527 ½ IpDMC=IpFcÀchalŠ ½CFcÀchal=CDMCŠ ½v=vŠ
ne value was calculated to be close to one electron.
Preparative scale electrolysis
In the light of the cyclic voltammetry results, DMC preparative electrolyses were
performed at a fixed potential located at 1.600 V versus Ag/AgCl reference
electrode in a divided cell. Homogenization of the electrolytic solution was assured
by a magnetic stirring under nitrogen. The oxidative electrolyses were stopped after
consumption of 2F/mole of the starting material. The brown dark solution obtained
at the end of the electrolysis was treated as described in the experimental
section. After precipitation in diethyl ether, a brown powder P1 was collected by
filtration and dried under vacuum. The rough yield calculated from the ratio of the
collected powder weight by that of the DMC starting material was around 40 %. P1
is soluble in common organic solvents such as chloroform, dichloromethane and
acetone.
Structure characterization of the electrolysis product P1
The collected powder P1 was characterized by different physico-chemical
techniques. Firstly, the 1H NMR spectrum of DMC (Fig. 5a) in deuterated
chloroform was recorded. This spectrum showed multiplet resonance signals at
chemical shift 6.90–8.05 ppm corresponding to the aromatic protons. Doublets of
the ethylenic protons appeared at 7.77 ppm (J = 15.6 Hz) and 7.42 ppm
(J = 15.6 Hz). The peaks at 3.85 and 3.88 ppm were assigned to the methoxy
protons.
The electrosynthesized powder spectrum (Fig. 5b) exhibited two broad resonance
peaks, at the same shift as the DMC’s spectrum, attributed to the methoxy and
aromatic protons. These large signals are characteristic of polymeric material. The
GPC analysis confirmed that P1 was a short-chain oligomer with Mw = 1040 and
Mn = 919 corresponding to an average degree of polymerization (DP) close to 4
and a dispersity of 1.1.
The 13C NMR spectra of DMC and the oligomer P1 are given in Figs. 6 and 7,
respectively. Carbons of DMC were assigned as depicted by Fig. 6. Both spectra
presented a great similarity. However, we note that the ethylenic carbons peaks (C6
at 119.59 ppm and C7 at 143.86 ppm) were sharply attenuated in the oligomer
spectrum.
Moreover, the broad signal in the aromatic region around 130–135 ppm, in the
oligomer spectrum, revealed that aromatic carbons were involved in the oligomer-
ization reaction. The 13C NMR spectrum recorded with DEPT using a 135° pulse
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I. Aribi et al.
angle (Fig. 7b) showed that signals corresponding to quaternary carbons were
merged with this broad signal at 130–135 ppm. Finally, we note the presence of new
weak and well-resolved signals appearing around 23, 42 and 170 ppm.
The IR spectra of DMC and the oligomer are given in Fig. 8. The position of
various vibration bands and their attribution are given in Table 1. It is worth noting
that the bands located at 990 and 525 cm-1, observed with DMC, completely
Fig. 5 1H NMR spectra of the DMC (a) and the collected powder (b) (asterisk denote the signals of
diethyl ether and CDCl3)
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The anodic reactivity of 4,40-dimethoxychalcone: a…
Fig. 6 13C NMR spectrum of DMC
Fig. 7 13C NMR spectrum of the oligomer P1
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I. Aribi et al.
Fig. 8 FT–IR spectra of DMC (a) and the oligomer P1 (b)
Table 1 Positions and assignments of different bond vibrations of DMC and P1
Mode assignment
Wavenumber [cm-1
]
DMC
P1
C–H stretching
3052
3024
CH3–O– protons stretching
C=O stretching
2969–2857
1660
2960–2859
1680
C=C stretching
1602–1513
1418
1607–1516
1458
–C–H (CH3) deformation
C–O–C stretching
1020–1260
990
1030–1260
Absent
C=C–H ethylenic out of plane deformation
C=C–H aromatic out of plane deformation
C=C ethylenic out of plane deformation
820
839
525
Very weak
vanished in the oligomer spectrum. These bands are characteristic of the out of
plane deformation of H–C bond (HC=CH, E configuration) and the C=C bond of the
ethylenic group, respectively [32].
Optical study
The UV–visible absorption spectra of the DMC and the oligomer P1 in chloroform
are given in Fig. 9. The DMC spectrum showed two absorption maxima at 335 nm
(B I, p–p* transition) and 232 nm (B II, n–p*). The B I was attributed to the
substituted cinnamoyl chromophore (ArCH=CH–CO–) involving the whole conju-
gated system corresponding to the intramolecular charge transfer from the electron-
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The anodic reactivity of 4,40-dimethoxychalcone: a…
Fig. 9 UV–visible absorption spectra of DMC (a) and the oligomer P1 (b) in chloroform solution
donor methoxy substituent to the carbonyl group acting as an electron acceptor. B II
was assigned to the substituted benzoyl chromophore (ArCO–). The oligomer
spectrum exhibited two absorption bands with maxima located at 222 and 279 nm.
Moreover, the spectrum presents a shoulder at 335 nm.
A preliminary photoluminescence study revealed that when an oligomer powder
was excited with a 330 nm wavelength laser radiation, it showed a light emission with
kmax located around 390 nm (Fig. 10). The broad emission spectrum could be related
to the presence of oligomers with different conjugation lengths [33].
Thermal analysis
Thermogravimetric Analysis (TGA) and Differential Thermal Analysis (DTA) were
used to study the oligomer thermal degradation. The obtained results are shown in
Fig. 11. TGA measurements revealed that synthesized material had a satisfactory
thermal stability until 500 K. It should be noted that a small weight loss (around 5 %)
from *300 to *500 K was observed, most probably related to evaporation of the
residual solvents used during oligomer purification. Beyond this zone of thermal
stability, two fast degradations were found: the first occurred from *500 to 648 K
with a maximum weight loss of nearly 28 %, and the second fastest degradation
starting from 648 K.
Discussion
The obtained results supported the formation of a semiconducting conjugated
material as the main product of the chalcone oxidation. Indeed, the voltammetric
study indicated that the rate-limiting step is the coupling of two radical cations
issued from the first electron transfer. This assumption is in agreement with an
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I. Aribi et al.
Fig. 10 Photoluminescence spectrum of P1
Fig. 11 TGA and TDA thermograms of electro-synthesized oligomer P1
electronic stoichiometry close to one electron at the time scale of the voltammetric
experiments. It is accepted that the electropolymerization of aromatic and hetero-
aromatic rings occurs by a general (EC)n mechanism, where E and C represent the
electron transfer and chemical reaction steps, respectively. The NMR and the
Fourier transform infrared spectroscopy (FTIR) studies corroborated that the phenyl
ring (A) and the chalcone double bond were both involved in the coupling reaction.
Actually, the vanishing of the corresponding CH signals in the 13C NMR spectra
123

The anodic reactivity of 4,40-dimethoxychalcone: a…
and the characteristic bands in the infrared spectra confirmed this deduction. This
phenyl-vinyl cross-linking reaction of DMC molecules led to a phenylene vinylene
like oligomer. This non-symmetric linkage was induced by the distonic effect
displayed by the methoxy group as described in earlier works [1, 2]. In fact, the
structure of the radical cation of DMC can be described by two mesomeric forms
involving the donating effect of the methoxy group (I and II in Scheme 2). This
intuitive assumption has been corroborated by a recent theoretical calculation of the
charge and the spin density distributions for the DMC radical cation [34]. This latter
0
study, showed that the highest spin densities were located on carbons C5 and C6.
The non-symmetric coupling of two radical cations appears to give a better
0
compromise between steric and electronic effects. Consequently, the C5 -C6 cross-
linking led, after a proton loss, to the intermediate III as described by the
mechanism given in Scheme 2. This intermediate rearranges to give the dimers V.
This rearrangement, previously described for a similar case [1], is accomplished
with aromatization as driving force and occurs in a similar way to the acid catalysed
rearrangement of 4,40 disubstituted cyclohexadienones [35, 36]. However, it is very
difficult to describe rigorously the dimers structure because of the complexity of the
possible stereostructures related to the trans–cis configuration. This structural issue
is further complicated by the presence of possible rotamers (s-cis/s-trans) relative to
the conformation of the carbonyl groups.
The subsequent oxidation of the resulting dimers V, at the electrolysis time scale,
results in further coupling (chain growth) with other oxidized monomers, dimers, or
oligomers. The observed low degree of polymerization could be partially explained
by the presence of a side reaction limiting the chain growth. In Scheme 3, we
depicted a plausible mechanism for the corresponding process. Accordingly, the
oxidized C=C bond is subjected to the solvent attack to form an acetamide. This
Ritter-like reaction is well known when electrolyses are carried out in acetonitrile,
particularly for ketone anodic oxidation [37]. Simultaneously, a stabilized free
radical was formed on the oligomer. The latter, could undergo a hydrogen atom
abstraction from the solvent [37] to afford a keto-enol system. The new signals
appearing around 23, 42 and 170 ppm, in the oligomer 13C spectrum, supported the
introduction of the acetamide moiety in the oligomer structure. These signals could
be attributed to the aliphatic and to the carbonyl carbons of the acetamide.
Despite this limited chain growth, the semi-conducting character of the obtained
material was confirmed by the optical study. In fact, in the UV–visible absorption
spectrum, the band located at 335 nm is attributed to the ArC=C–CO–Ar conjugated
system absorption in a similar way to the starting chalcone. However, the band
located at 279 nm is assigned to the conjugated backbone. This low value resulted
most probably from the less extended conjugation due to the short chain length, the
lack of planarity and to the stereostructure irregularity. A very similar UV spectrum
was observed for oligo o-phenylene vinylene [38]. The optical band gap of the
oligomer was calculated from the onset of absorption and the energy band gap was
estimated to be 3.15 eV for the oligomer in solution. In addition, the electrochem-
ical study of oligomer was used to calculate the HOMO, LUMO and the
electrochemical band gap [39, 40]. The corresponding values were estimated to be
-5.82, -2.96 and 2.86 eV, respectively.
123

I. Aribi et al.
Scheme 2 The mechanism of dimer formation
In addition, the emission spectrum of the oligomer exhibited a large band with a
maximum at 390 nm. The band broadness revealed the presence of different
emissive centers. This result might be explained by the previously evoked structural
problem and the presence of oligomer inter-chain interactions.
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The anodic reactivity of 4,40-dimethoxychalcone: a…
Scheme 3 The mechanism of solvent attack side reaction
Finally, the thermal study revealed that the obtained oligomer underwent a two-
step degradation most probably corresponding to the decomposition of the pendant
chains and the conjugated backbone, successively. However, the oligomer presented
a satisfactory thermal stability for use in opto-electronic devices.
Conclusions
In this paper, the electrochemical behaviour of a substituted chalcone, the 4,40-
dimethoxychalcone (DMC), was investigated by cyclic voltammetry and potential
imposed electrolyses in acetonitrile at a platinum working electrode. This study
123

I. Aribi et al.
showed that, at the analytical scale, the coupling of the radical cations, issued from
the first electron transfer, was the governing reaction near the electrode. The
preparative scale electrolyses led to a di-substituted oligo-phenylene vinylene. The
obtained material was characterized by different physico-chemicals methods. The
primary optical study confirmed the semi-conducting character of the obtained
material with an optical and an electrochemical bandgap of 3.15 and 2.86 eV,
respectively. On the basis of the obtained results, a mechanism describing the
radical cation evolution toward oligomer formation was evoked. This work
described a new electrochemical reactivity of a methoxy-substituted chalcone
affording an original route for the preparation of an organic semi-conducting
material. In a future work, other substituted chalcones will be studied to test the
generalization of this synthetic method.
Acknowledgments This research was supported by the Ministry of Higher Education and Scientific
Research, Tunisia. Authors are grateful to Mr Adel Rdissi for English revision.
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