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Synthesis, Structure and Solvatochromism Studies on Copper(II)
Complexes Containing Ethylenediamine, Pyridine and Imidazol Ligands
Hamid Golchoubian,a* Omeleila Nazaria and Benson Kariukib
aDepartment of Chemistry, University of Mazandaran, Babolsar, Postal code 47416-95447, IranbSchool of Chemistry, Cardiff University, Main College, Park Place, Cardiff CF10 3AT, UK
Received June 2, 2010; Accepted December 14, 2010; Published Online January 4, 2011
Two copper(II) complexes type [Cu(en)X2](ClO4)2, where en = ethylenediamine and X = pyridine, 1
or imidazol, 2 have been synthesized and prepared on the bases of elemental analysis, spectroscopic andmolar conductance measurements. The X-ray crystal analysis of these complexes demonstrated that thecopper(II) ions are in square planar environments through coordination by two nitrogen atoms of theethylenediamine and two nitrogen atoms of two pyridine or imidazol molecules and the ClO4
- ions arebound weakly above and below of the molecular plane. The complexes show three ions behavior in all sol-vents. The complexes are soluble in various solvents and are solvatochromic. The solvatochromism of thecomplexes were investigated by UV-Vis spectroscopy with different solvent parameters such as DN, AN,� and � using multiple linear regression (MLR) method. The results suggested that the DN parameter ofthe solvent has the most contribution to the shift of the d-d absorption band of the complex 1 but in com-plex 2 the DN and � have almost similar importance in the observed variation in the shift of the �max valueswith solvent nature.
Keywords: Solvatochromism; Backward multiple linear regression; Crystal structure; Copper(II)
complex; Imidazol; Pyridine.
INTRODUCTION
The investigation of solvatochromic behavior of metal
complexes has been of importance, because it provides a
quantitative approach to recognize the solvent behavior
and the role of the solvent in physico-chemical studies.1,2
The effect of the solvent on the spectral properties of mole-
cules, generally referred as solvatochromism, has been in-
vestigated for many years, generating a copious literature.3
Solvatochromism of metal complexes can be divided into
two types;4,5 the first type comprises the case where the
color changes are brought about by the direct attachment of
solvent molecules onto metal center, and the second type is
due to the attachment of solvent molecules onto ligands.
Among the former whose color changes are due to those of
d–d transitions, copper(II) complexes with a strong Jahn-
Teller effect can be anticipated to show simple and regular
changes in their electronic spectra according to the strength
of interactions with solvent molecules at the axial sites.6-8
There are many applications for this phenomenon such as
Lewis acid-base color indicator,9 imaging,10-13 photo-
switching,14-16 and sensor materials.17
It has been known that wave numbers corresponds to
absorption maxima of the compounds in solvents of used
correlate well with the solvent parameters. Various sol-
vent parameters such as Dimroth and Reichardt’s ET, Z
Kosowar, Kamlet and Taft’s �, �, �* and Gutman’s donor
and acceptor number, DN and AN have been introduced in
literature.18-20 Each of these parameters is related to differ-
ent type of interaction exist between compound and sol-
vent. The existent dependencies between the spectral shifts
and solvent parameters can be verified by computational
methods.
In this work, which is a continuation of our studies on
the solvatochromic behavior copper(II) complexes we in-
tend to study the electronic properties imposed by the
N–donor atoms of the monodentate ligands pyridine and
imidazol on the copper(II) ion of the complexes type
[Cu(en)X2](ClO4)2 (Fig. 1) where en = ethylenediamine
and X = pyridine or imidazol. Based on our knowledge
such investigation has not been carried yet.
60 Journal of the Chinese Chemical Society, 2011, 58, 60-68
* Corresponding author. E-mail: [email protected]
RESULTS AND DISCUSSION
The complexes were prepared readily in high yield
with mixing of Cu(ClO4)2·6H2O, ethylenediamine and pyr-
idine or imidazole with mole ratio of 1:1:2, respectively in
solvent of water and methanol. The analytical data indi-
cated the formation of the desired complexes.
IR spectra
The IR spectrum of complex 1 showed bands at 3270-
3325 cm-1 attributed to the symmetric stretch of C-H aro-
matic of pyridine moieties which is shifted to upper fre-
quency in compare with free pyridine molecule. Ring
stretching bands appear between 1450-1608 cm-1 and out
of plane bending of C-H of pyridine ring appeared at 705-
764 cm-1.21
CH2 rocking and Cu-N stretching vibration mode of
ethylenediamine were appeared about 850-950 cm-1 and
500-610 cm-1, respectively for both complexes.21 The IR
spectrum of complex 2 shows NH stretching at 3366 cm-1
and a band at 3056 cm-1 attributed to the symmetric stretch
of C-H in imidazole groups. The infrared spectra of two
complexes show two intense bands at around 1110 and 620
cm-1 which are attributed to presence of the ClO-4. These
bands are declared to the anti-symmetric stretching and
anti-symmetric bending vibration mode, respectively.22
The former is split with a poorly defined maximum show-
ing the deformation from Td symmetry. It is well known
that the degree of splitting of this band serves as a measure
of the degree of the coordination of perchlorate ions to the
copper(II) ion.23,24
Conductometric data
The molar conductivity values of the mixed-chelate
complex in solvents of nitromethane (NM), dimethyleform-
amide (DMF), methanol (MeOH) and acetonitrile (AN)
were studied. The data are listed in Table 1. The results re-
veal that the complexes are 1:2 electrolytes in all sol-
vents.25,26 Although the complexes are in molecular form in
solid state as X-ray crystal structures indicated they are
electrolytes in solution. That means ClO4- ions are bound
weakly above and below of the chelate planes and can be
driven out by solvent molecules which leading to their
solvatochromism.
Single crystal X-ray analyses
The view of ORTEP diagrams of the copper com-
plexes 1 and 2 are presented in Fig. 2 and 3, respectively.
The selected bond distances and bond angles for the com-
plexes are listed in Table 2. The bond distances Cu(1)-N(1)
in complex 1 and Cu(1)-N(2) in complex 2 are 2.591 Å and
1.991 Å, respectively. This difference is quiet normal be-
Synthesis and Solvatochromism Studies on Cu(II) Complexes J. Chin. Chem. Soc., Vol. 58, No. 1, 2011 61
Fig. 1. The copper(II) complexes of [Cu(en)Py2](ClO4)2,1 and [Cu(en)(Imzl)2](ClO4)2, 2.
Table 1. The molar conductance (�m) of the complexes (�-1 cm2
mol-1, at 25 �C) in some solvents
CompoundSolvent
1 2
Standard values for1:2 electrolytesa
Nitomethane (NM) 144 178 150-180Acetonitrile (AN) 234 268 220-300MeOH 204 220 160-220DMF 146 130 130-170a the standard values taken from ref. 26.
Fig. 2. ORTEP diagram of complex 1 with atom labelsand numbering scheme with fifty percent prob-ability.
cause pyridine and imidazole have different basicity power.
The basicity of free imidazole (Kb = 1.2 × 10-7) is about
hundred times stronger than pyridine (Kb = 2.3 × 10-9).27,28
The five-membered chelate ring in both complexes are
puckered; the torsion angles of N(3)-C(4)-C(4i)-N(3) and
N(2)-C(6)-C(6i)-N(2i) in complex 1 and 2 are 52.14� (18),
51.41� (18), respectively. The copper(II) ion resides in the
plane between the coordinating atoms N(1), N(2), N(1i)
and N(2i) in both complexes. The angle between this plan
and the pyridine plane is 54.21(2)� in complex 1. The angle
between the N4Cu plane and the imidazole plane in com-
plex 2 is 62.28(2)�. The mean Cu-N(amine) distance
(2.016(3) Å and 2.011(3) Å) and the bite angles N(2)-
Cu(1)-N(2i) of 84.34 (12)o and N(3)-Cu(1)-N(3i) of 84.05
(18) for complexes 1 and 2, respectively are close to the
corresponding average values of the copper(II) complexes
with ethylenediamine reported before.29,30 The angles be-
tween two pyridine rings in complex 1 and the rings of two
imidazol in complex 2 are 60.83(2)�, 68.87(2)°, respec-
tively. Two perchlorate ions lie above and below of the cop-
per ion in both complexes; the bond lengths of Cu-OClO3
are 2.591 Å and 2.632 Å in complex 1 and 2, respectively
and hence the ClO4- ions coordinated weakly to the cop-
per(II) ions and can be driven out by the solvent molecules
in solution which leads to their solvatochromism.
It is found that the hydrogen bonding affects the mo-
lecular packing. In complex 1 each molecule links with two
other molecules via intermolecular hydrogen bonds to form
one-dimensional polymer along crystallographic c axis as
illustrated in Fig 4. However, in complex 2 an additional
hydrogen bond also exist between O(4) of the perchlorate
ion and H(3A) of the ethylenediamine of neighboring mol-
ecules. These hydrogen bondings make a two-dimensional
sheet structure along crystallographic c axis as shown in
Fig. 5.
Solvatochromism
The UV-Vis spectra of the complexes show a broad
band at visible region due to d-d transition of copper(II)
ion. This transition is characteristic of copper(II) in the
square planar environment associated to the 2B1g�2A1g
transition.31,32 The position of the �max of the complexes
along with their molar absorptivity and respective solvent
parameter values are collected in Table 3. The Vis spectra
of the complexes in selected solvents are illustrated in Fig.
6 and 7, respectively.
The multiple linear regression used to deduce the
solvatochromic behavior of the complexes. In this regard,
hydrogen bonding ability �, electron pair donating ability
�, Gutmann’s DN, Mayer and Gutmann’s AN were used ac-
cording to Eq. (1). The frequencies of d-d absorption tran-
sition band (�max) of each complexes in various solvents
(Table 3) with their own solvent parameters were offered in
62 J. Chin. Chem. Soc., Vol. 58, No. 1, 2011 Golchoubian et al.
Fig. 3. ORTEP diagram of complex 2 with atom labelsand numbering scheme with fifty percent prob-ability.
Table 2. Selected bond lengths (Å) and angles (�) for compound 1 and 2
Compound 1 Compound 2
N(1)—Cu(1) 2.019(2) N(2)—Cu(1) 1.991(3)N(2)—Cu(1) 2.016(2) Cu(1)—O(2) 2.632(3)Cu(1)—O(1) 2.591(2) N(3)—Cu(1) 2.011(3)N(1)—Cu(1)—N(1i) 90.12(12) N(2)—Cu(1)—N(3) 176.95(13)N(2)—Cu(1)—N(2i) 84.34(12) N(2)—Cu(1)—N(2i) 89.32(18)N(2)—Cu(1)—N(1) 174.79(9) N(3)—Cu(1)—N(3i) 84.05(18)N(2i)—Cu(1)—N(1) 92.93(9) N(2)—Cu(1)—N(3i) 93.34(13)N(1i)-Cu(1)-N(2i) 174.80(9) O(2)—Cu(1)—O(2i) 177.44(13)O(2)—Cu(1)—O(2i) 178.97(18) N(3)-C(4)-C(4i)-N(3i) 51.41�(18)N(2)-C(6)-C(6i)-N(2i) 52.14�(18)
Eq. (1) pointed out in experimental section one by one to
the statistical computer program. Specifically, in first step
all variables are reviewed and evaluated to determine
which one will contribute most to Eq. (1). Then the weaken
variable is excluded in the model and process starts again.
The quality of the obtained equations and the percentage
contribution of the calculated solvatochromic parameters
are presented in Table 4. The regression coefficients re-
ported in the table suggest that the DN parameter of the sol-
vent has the dominate contribution (52.3%) in the shift of
d-d absorption band of the complex 1. However, in com-
plex 2 the DN and � are almost similar importance to ex-
plain the observed variation in the shift of the �max values
with solvent nature with relative contribution of 47.5 and
41.4%, respectively using normalized DNN. The negative
sign of the coefficient of the DN in complexes indicates a
red shift as the donor number of solvent increases. The pos-
itive sign of the � signifies opposite function of the basicity
power in the solvatochromism of complex 2.
The position of the band maxima in complexes shifted
Synthesis and Solvatochromism Studies on Cu(II) Complexes J. Chin. Chem. Soc., Vol. 58, No. 1, 2011 63
Fig. 4. Packing diagram of the complex 1 containing hydrogen bonding along crystallographic c axis.
Fig. 5. Packing diagram of the complex 2 containing hydrogen bonding along crystallographic c axis.
to the higher wave number as the donor number of the sol-
vents increases. This red shift is due to the strong repulsion
of the electrons in dz2 orbital by ion pair electrons of the
solvent molecules that are axially coordinated to the copper
center.33 The observed solvatochromism is a reverse pro-
cess so that the removal of the solvent under high vacuum
regenerate the original complexes.
A plot of the �max values calculated using Eq. (1) ver-
sus the �max values observed for complexes 1 and 2 in dif-
ferent solvents is presented in Fig. 8 and 9.
CONCLUSION
The prepared two complexes are soluble in organic
solvents and show solvatochromism properties. Their
solvatochromism were examined with different solvent pa-
rameters models using backward MLR computational
method. The obtained results suggested that the complex 1
correlate well with DN whereas complex 2 shows good
correlation with DN and � (electron pair donating scale) of
the solvents. The d-d visible absorption band exhibits a red
shift with the increase of the donor number (DN) (in com-
plex 1) and DN plus electron pair donating ability of the
64 J. Chin. Chem. Soc., Vol. 58, No. 1, 2011 Golchoubian et al.
Table 3. The solvent parameter values and the maximal absorption frequencies, �max/103cm-1
(�/M-1 cm-1) of complex 1 and 2 in various solvents
Solvent DN AN � � Complex 1 Complex 2
Nitromethane 2.7 20.5 0.06 0.22 17.63 (81) 17.75 (73)Acetonitrile 14.1 18.9 0.31 0.19 17.38 (55) 17.53 (66)Acetone 17.0 12.5 0.48 0.08 17.08 (49) 16.38 (79)THF 20.0 8.0 0.55 0.0 16.00 (38) 17.33 (66)MeOH 23.3 41.3 0.62 0.9 15.87 (465) 16.85 (64)DMF 26.6 16.0 0.69 0.0 15.26 (49) 16.67 (70)DMSO 29.8 19.3 0.76 0.0 14.74 (55) 16.25 (42)H2O 18.0 54.8 0.47 1.17 15.60 (39) 16.65 (48)
Fig. 6. Absorption spectra of complex 1 in selectedsolvents.
Fig. 7. Absorption spectra of complex 2 in selectedsolvents.
Table 4. The correlation of the electronic spectral with the solvent parameters calculated by MLR technique
Complexnumber
Equation F S.E. R n
1 �max = 18.988 – 0.213 DN + 4.041 � – 0.050 AN + 1.174 �
DN = 52.25%, AN = 13.16%, � = 29.59%, � = 5.00%
5.747 0.545 0.941 8
2 �max = 17.359 – 0.550 DN + 18.689 � + 0.058 AN – 2.447 �
DN = 47.49%, AN = 6.10%, � = 5.10%, � = 41.39%9.359 0.228 0.962 8
solvents (in complex 2). This behavior was explained on
the bases of the weakly coordination of the perchlorate an-
ions in axial position of the copper(II) complexes in which
are replaced by solvent molecules with different donor
power or electron pair donating ability.
EXPERIMENTAL SECTION
All chemicals and solvents were obtained from
Merck and Fluka and used without further purification.
Caution: perchlorate salts are potentially explosive and
should be handled with appropriate care.
Conductance measurements were made at 25 oC with
a Jenway 400 conductance meter on 1.00 10-3 M samples
in selected solvents. Infrared spectra (potassium bromide
disk) were recorded using a Bruker FT-IR instrument. The
electronic absorption spectra were measured using a Braic
2100 model UV-Vis spectrophotometer. The elemental
analyses were performed on a LECO 600 CHN elemental
analyzer. Absolute metal percentages were determined by a
Varian-spectra A-30/40 atomic absorption-flame spec-
trometer.
Synthesis of complex 1
[Cu(en)Py2](ClO4)2, was prepared by adding pyridine
(8 mmol) in 10 mL MeOH to an aqueous solution of
Cu(ClO4)2·6H2O (4 mmol in 5 mL distillated water) and
stirring for about 1 h at room temperature. To the resultant
blue solution, ethylenediamine (4 mmole) was then added
and the reaction mixture was stirred at room temperature.
Blue-violet crystals obtained were filtered, washed with
cold water and dried in a dessicator. The yield was 85%.
Single crystals suitable for X-ray diffraction studies were
obtained by recrystallization of the complex in methanol.
Selected IR data (�/cm-1 using KBr): 3325 (s), 3270 (s),
2035 (w), 1608 (m), 1592 (s), 1490 (w), 1467 (w), 1450 (s),
1112 (s), 1080 (s), 764 (m), 705 (s), 623 (s), 523 (m). Anal.
calcd. for C12H18Cl2CuN4O8 (Mr = 480.75) C, 29.98; H,
3.77; N, 11.65; Cu, 13.22; found: C, 30.10; H, 3.51; N,
11.51; Cu, 13.27%.
Synthesis of complex 2
This compound was prepared with the same proce-
dure as complex 1 except that imidazol was used in place of
pyridine. The violet crystals were obtained with the yield of
85%. The recrystallization of the complex in MeOH pro-
vided suitable crystals for X-ray crystallography. Selected
IR data (�/cm-1 using KBr): 3366 (w), 3328 (w), 3057 (w),
2935 (w), 1660 (s), 1605 (m), 1573 (w), 1542 (s), 1470 (s),
1443 (m), 1340 (m), 1286 (m), 1264 (w), 1220 (s), 1091
(s), 946 (w), 930 (w), 864 (m), 756 (m), 623 (s), 551 (w).
Anal. calcd. for C8H14Cl2CuN6O8 (Mr = 456.69): C, 21.04;
H, 3.09; N, 18.40; Cu, 13.91; Found: C, 21.31; H, 2.95; N,
18.26; Cu, 13.99%.
X-ray crystallography
A suitable single crystal of complex 1 and 2 were
glued on the tip of glass fibers. The X-ray data were col-
lected by -scans on Nonius BV diffractometer with graph-
ite-monochromated Mo K� radiation (� = 0.71073 Å).
Data reduction, including the absorption correction, was
performed with the HKL DENZO and SCALEPACK soft-
ware package.34 Solution, refinement and analysis of the
structure were performed by using SHELXTL programs.35,36
The structure was solved by direct methods (SIR92)37 and
refined by the full-matrix least-squares method based on F2
against all reflections.38 Geometrical calculations were car-
ried out with PLATON39 and the figures were made by the
use of the ORTEP9940 and MERCURY41 programs. The
complete conditions of data collection and structure refine-
ments are given in Table 5. The H(C) atom positions were
Synthesis and Solvatochromism Studies on Cu(II) Complexes J. Chin. Chem. Soc., Vol. 58, No. 1, 2011 65
Fig. 8. Plot of the �max observed against �max calcu-lated from Eq. (1) for complex 1.
Fig. 9. Plot of the �max observed against �max calcu-lated from Eq. (1) for complex 2.
calculated. All hydrogen atoms were refined in isotropic
approximation in riding model with the Uiso(H) parame-
ters equal to 1.2 Ueq(Ci), for methyl groups equal to 1.5
Ueq(Cii), where U(Ci) and U(Cii) are respectively the
equivalent thermal parameters of the carbon atoms to
which corresponding H atoms are bonded. Refinement of
F2 was against all reflections. The weighted R-factor wR
and goodness of fit S are based on F2, conventional R-fac-
tors R are based on F, with F set to zero for negative F2. The
threshold expression of F2 > 2�(F2) is used only for calcu-
lating R-factors(gt) etc., and is not relevant to the choice of
reflections for refinement. R-factors based on F2 are statis-
tically about twice as large as those based on F, and R-fac-
tors based on all data will be even larger.
Method of calculation
All the absorption maxima reported were taken from
experimental curves of d-d transition of the complexes.
Multivariate statistical methods have been used in the clas-
sification and selection of solvents. Empirical parameters
of solvent polarity were used as basic data sets. These pa-
rameters can be obtained directly from literature.43-45 The
extraction of chemical information contained in such a data
set can be carried out by statistical method of Multiple Lin-
ear Regression analysis (MLR). In this method, a depend-
ent variable Y is described in terms of a series of explana-
tory variables X1…Xn, as given in Eq. (1):
Y = Y0 + a2.X2 +….+ anXn + a1.X1 (1)
It is assumed that all the explanatory variables are in-
dependent of each other and truly additive as well as rele-
vant to the problem under study.46,47 Y is the value of a sol-
vent dependent physicochemical property (�max in this
study) in a given solvent and Y0 is the statistical quantity
corresponding to the value of this property in the gas phase
or in an inert solvent. X1, X2, ···Xn represent independent
but complementary solvent parameters, which account for
the different solute/solvent interaction mechanisms. a1,
a2,···an are the regression coefficients describing the sensi-
tivity of property Y to the different solute/solvent interac-
66 J. Chin. Chem. Soc., Vol. 58, No. 1, 2011 Golchoubian et al.
Table 5. Crystal data and structure refinement parameters for compounds 1 and 2
Compound 1 2
Empirical formula C12H18Cl2CuN4O8 C8H14Cl2CuN6O8
Formula weight 480.74 456.70color Blue VioletTemperature/K 150 299Wavelength/nm 0.71073 0.71073Crystal system Monoclinic MonoclinicSpace group C 2/c C 2/cUnit cell dimension a = 7.6520(3)
b = 17.0720(4)c = 14.0750(7)� = 99.945(3)�
a = 7.5070(3)b = 15.9110(4)c = 14.5140(6)� = 98.964(2)�
Volume 1811.06(12) 1712.44(11)Z 4 4Calculated density 1.763 1.771F (000) 980 924Max. and min. transmission 0.969 and 0.742 0.849 and 0.745Limiting indices -9 h 9, -22 k 22,
-18 l 18-9 h 9, -20 k 20,-18 l 18
� (mm-1) 1.55 1.63Reflections collected/unique 2074/123 1933/114R indices (all data) R = 0.0382, wR2 = 0.0829 R = 0.0540, wR2 = 0.1467Completeness to � = 27 99.6% 99.1%Refinement method Full-matrix least-squares on F2 Full-matrix least-squares on F2
S 1.07 1.04
a R = �||Fo| � |Fc||/�|Fo|.b wR = [(� [Fo
2 � Fc2)2] / � [w(Fo
2)2]½.c S = �[w(Fo
2 � Fc2)2/(Nobs � Nparam)]½.
tion mechanisms. The postulate is that the solvent effect on
a solute property Y can be represented as a linear function
of some independent but complementary parameters de-
scribing the Lewis acidity and basicity of a given solvent.
The AN and �, values are chosen as a measure of Lewis
acidity. In addition, Gutmann’s donor number DN and �
were chosen as a measure of solvent basicity.45-51 In this ap-
proach, the backward procedure was used for selection of
the most relevant variables. A final set of selected equa-
tions was examined for stability and validity through a va-
riety of statistical methods. The choice of equation suitable
for further consideration was made by using four criteria,
namely, multiple correlation coefficients (R), standard er-
ror (S.E.), F-statistic and the number of variables (n) in the
model. The best multiple linear regression model is one
that has high R and F-values, low standard error, least num-
ber of variables and high prediction ability. In Parameter
selection, variables with small variance t (not significant at
the 5% level) were then removed. t value is the solvent-in-
dependent coefficients divided by SE. To determine the rel-
ative significance of solvent parameters, the regression co-
efficients are described in terms of percentage contribution
value. Eq. (2) could be statistically qualified into percent-
age contribution factor [P(Xi)]. To attain this, the regres-
sion coefficients, which emerge from multiple regression
equations are normalized to numerical range 0-1.52 Hence,
percentage contribution P(Xi) of a solvent parameter in
multiple regression is calculated53 as in the following equa-
tion:
P(Xi) =100
1
| |
| |
a
a
i
i
i
n
�
�(2)
Comparison of relative importance of solvent prop-
erty can easily be defined using P(Xi), which show a good
agreement between various system under study.
The effects of solvents on the absorption spectra of
two copper complexes were recorded in the range of 13000-
22000 cm-1 using UV-Vis spectroscopy. Thus two equa-
tions were obtained for each probe (the copper(II) com-
plexes 1 and 2) by using multiple linear regression (MLR)
method and SPSS software.54 The role of Solvatochromic
parameters, such as �, �, DN and AN in the above equa-
tions have been studied in the mechanism of the interac-
tions between probe and solvent.55-57
Supplementary data
CCDC 737100 and 737099 contain the supplemen-
tary crystallographic data for compounds 1 and 2 of this pa-
per, respectively. These data can be obtained free of charge
via www.ccdc.cam.ac.uk/conts/retrieving.html (or from
the Cambridge Crystallographic Data Centre, 12, Union
Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033).
ACKNOWLEDGEMENT
We are grateful for the financial support of the
Mazandaran University of the Islamic Republic of Iran.
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