Spectrophotometric and Spectroscopic Studies of Charge Transfer Complexes of m-Nitroaniline as an Electron Donor with Picric Acid as an Electron Acceptor in Different Polar Solvents
Department of Chemistry, Faculty of Science, Aligarh Muslim University, Aligarh -202002, India
*Corresponding Author E-mail: afaqahmad212@gmail.com
ABSTRACT
Charge transfer complexes of picric acid, with m-nitroaniline, were investigated by spectrophotometric method in three different organic solvents viz – acetone, ethanol, and methanol. The data are discussed in terms of association constant, (KCT) and molar extinction coefficient (εCT), standard free energy (∆G0), oscillator strength (ƒ), and transition dipole moment (μEN) were calculated. The spectrum obtained form the complex of picric acid and m-nitroaniline shows absorption bands at 450 nm for methanol, 445nm for ethanol and 440nm for acetone. The results reveal that the interaction between the donor and acceptor is due to π-π* transitions. The stiochiometry of the complexes was found to be in the ratio of 1:1 by straight line method. The influences of used solvents such as acetone, ethanol, and methanol, on spectroscopic parameters were investigated. The ionization potential (ID) of the donor was also determined.
KEYWORDS: Charge transfer complex ; m-Nitroaniline (MNA); Picric acid (PiOH); Visible region; formation constant; FTIR spectroscopy
INTRODUCTION:
Charge transfer complexation is important phenomenon in biochemical and bioelectrochemical energy transfer process1. Charge transfer phenomenon was introduced first by Mulliken. The term charge transfer gives a certain type of complex resulting from interactions of donor and acceptor with the formation of weak bands2,3 and discussed widely by Foster4. Molecular interactions between electron donors and acceptors are generally associated with the formation of intensely colored charge transfer complexes (CTCS) in which absorb radiation in the visible region5. Molecular complexation and structural recognition are important processes in biological systems, for example, drug action, enzyme catalysis and ion transfers through lipophilic membranes all involve complexation6. Charge transfer complexes are currently of great importance since these materials can be utilized as organic semiconductors7, photo catalysts8 and dendrimers9. They are also important in studying redox processes10, second order non- liner optical activity11 and micro emulsion12.
In the present studies the CT complex formed between picric -acid (acceptor) and m-nitroaniline (donor). Picric acid forms molecular complexes with aromatic hydrocarbons such as anthracene13, some aniline derivatives14 and also with aromatic amines15-17.
Mulliken suggested that the formation of molecular complexes from two aromatic molecules can arise from the transfer of an electron from a π – molecular orbital of a Lewis base to vacant π- molecular orbital of a Lewis acid, with resonance between this dative structure and the no-band structure stabilizing the complex18. He also noted the possibility of complex formation through the donation of an electron from a non- bonding molecular orbital in a Lewis base to a vacant π- orbital of an acceptor (n-π)19 with resonance stabilization of the combination. As part of such studies picric acid are able to from CT complex with m- nitroaniline in different polar solvents.
In this paper we investigated the interaction of PiOH(picric acid) with MNA(m-nitroaniline) in solvents of different polarity at room temperature by visible spectra data of CT complex (π-π) of m-nitroaniline with π acceptor, picric acid in said solvents viz- acetone, ethanol, and methanol and also studied the effect of solvents on the formation of CT complex. We have determined the formation constant and λCT for the CT complex of picric acid with m-nitroaniline in different polar solvents.
EXPERIMENTAL:
Materials:
m-nitroaniline (CDH), picric acid (Aldrich) were obtained commercially and used without further purification. Ethanol (Merck analytical grade), acetone (Merck), methanol (Merck) were redistilled prior to their uses.
Preparation of standard solutions
Solutions of donor of different concentrations, .01M, .015M, .02M, .03M. .05M, 0.1M, 0.2M, 0.3M, and 0.5M were prepared in different volumetric flask by dissolving m-nitroaniline accurately weighed in different solvents such as acetone, ethanol and methanol.
A standard solution of acceptor, picric acid (0.01M) concentration was prepared by dissolving accurate weight of acceptor in above solvents in different volumetric flask.
The electronic absorption spectra of the donor m-nitroaniline, acceptor picric acid and the resulting complex in acetone, ethanol and methanol were recorded in the visible range 400nm-600nm using a spectrophotometer ELICO SL 177 scanning mini spectrophotometer with a 1cm quartz cell path length are shown in Fig.(1,2 and 3).
Synthesis of CT complex
Picric acid, (solid) was mixed with m- nitroaniline, (solid) in agate mortar in the stoichiometric ratio 1:1.The start of the reaction was indicated by a color change (dark yellow). The mixture was thoroughly mixed and kept in oven below their mp. For a week, occasionally mixed during this period .The reaction product was washed several times with benzene to remove untreated components. The color of the final product was dark yellow. The product was dried and kept in a desiccator.
Reaction product from solution
The saturated solution of picric acid and m-nitroaniline in acetone were mixed and crystallized from benzene. The solution was kept at room temperature for 16 days, giving yellow colored crystals.
Solid state reaction in capillary (reactants in contact)
A Pyrex glass capillary having inner diameter (0.186cm) and length about 5cm was used for this purpose one end of the capillary was sealed, half of the capillary was filled with m- nitroaniline of particle size below 100 mesh, for uniform packing, each capillary was tapped for 5 min. the surface was smoothened with the help of a thin glass rod. The remaining half of the capillary was filled with picric acid (particle size < 100 mesh) in such a way that the two components came in close contact. After filling the capillary, the other end was also sealed and kept in oven below their mp. At the junction of the two components, the reaction started with a color change (dark yellow), and grew in the side of picric acid.
FTIR spectra of picric acid , m-nitroaniline and the reaction product obtained from solid state reaction between acceptor and donor were recorded with the help of FTIR spectrometer INTERSPEC – 2020 (spectra lab U.K.) measured in KBr pellets.
Observation of CT bands
A 3ml volume of donor and 3ml volume of acceptor were scanned separately through a spectrophotometric titration20 at room temperature with their wavelength of maximum absorption, which were: 380nm for picric acid, 420nm for m-nitroaniline in acetone and for blank solvent(acetone) 340nm shown in Fig 4. For preparing the reaction mixture 10ml donor and 10ml acceptor mixed together in different solvents viz- acetone, ethanol and methanol. A dark yellow color charge transfer complex was formed in each solvent (The complex for each of the reaction mixture stood overnight at room temperature to form stable couple before analysis at the maximum absorbance 440nm for acetone, 445nm for ethanol and 450nm for methanol). The concentration of the donor in the reaction mixture was kept greater than acceptor, [D0]>> [Ao]21,22 and changed over a wide range of concentration from 0.01M to 0.5M while concentration of π- acceptor(picric acid) was kept fixed[21] at 0.01M in each solvents, these produced solutions with donor: acceptor molar ratios varying from 1:1 to 50:1, these concentrations ratios were used to straight line diagram for determination of the formation constants of CTC were shown in Table 3.
Fig 1 . Absorption spectra of picric acid (1 × 10-2M) in acetone with addition of m- nitroaniline concentrations ranging 0.01M to 0.5M are shown with increasing concentrations bottom to top.
To obtain the CT bands, the spectrum of solution of 0.01M PiOH, and 0.01 M MNA in different solvents were recorded with solvents used as a reference, it is observed that new absorption peak appear in the visible region. In some cases multiple peaks were obtained, the longest wavelength peak was considered as CT peak23.The change of the absorption intensity to higher for all complexes in this study when adding the donor was detected and invested are shown in Table 3. These measurements were based on the CT absorption bands exhibited by the spectra of the systems which were above mentioned and given in Fig. [1,2 and3]. In all the system studied, the absorption spectra are of similar nature except for the position of absorption maxima λCT of the complex. The CT absorption spectra were analysed by fitting to the Gaussian function y = y0 + [A/ w√ (π/2))] exp [−2 (x- xc)2/w2] where x and y denote wavelength and absorbance, respectively. The results of the Gaussian analysis for all systems under study are shown in Table [1]. The wavelengths at these new absorption maxima (λCT = xc) and the corresponding transition energies (hν) are summarized in Table 2
Determination of Ionization potentials of the donor
The ionization potentials of the donor (ID) in the charge transfer complexes are calculated using empirical equation derived by Aloisi and Piganatro24:
ID (eV) = 5.76 + 1.53 × 10-4 νCT -----Eq. (1)
Where, νCT is the wave number in cm-1 corresponding to the CT band formed between donor and acceptor(PiOH).
Fig 2. Absorption spectra of picric acid (1 × 10-2M) in ethanol with addition of m- nitroaniline concentrations ranging 0.01M to 0.5M are shown with increasing concentrations bottom to top.
Determination of oscillator strength, (ƒ), and transition dipole moment, (μEN)
From the CT absorption spectra, one can extract oscillator strength. The oscillator strength ƒ is estimated using the formula:
ƒ = 4.32 × 10-9 ∫ εCT dν ----Eq. (2)
Where ∫εCTdν is the area under the curve of the extinction coefficient of the absorption band in question vs. frequency.
To a first approximation:
ƒ = 4.32 × 10-9 εCT ∆ν1/2 ---- Eq. (3)
Where, εCT is the maximum extinction coefficient of the band and ∆ν1/2 is the half- width, i.e., the width of the band at half the maximum extinction. The observed oscillator strengths of the CT bands are summarized in Table2.
The extinction coefficient is related to the transition dipole by:
μEN = 0.0952 [εCT ∆ν1/2/∆ν]1/2 -----Eq. (4)
Where, ∆υ ≈ υ at εmax and μEN is defuned as –e ∫ ψex∑iriψg dτ. μEN for the complexes of PiOH with MNA are given in Table 2.
Determination of resonance energy (RN)
Briegleb and Czekalla 25 theoretically derived the relation:
εCT = 7.7 × 10-4 / [hνCT/ [RN] - 3.5 ] ---Eq. (5)
Where, εmax is the molar extinction coefficient of the complex at the maximum of the CT absorption, νCT is the frequency of the CT peak and RN is the resonance energy of the complex in the ground state, which, obviously is a contributing factor to the stability constant of the complex (a ground state property). The values of RN for the complexes under study have been given in Table 2.
Fig 3. Absorption spectra of picric acid (1 × 10-2M) in methanol with addition of m- nitroaniline concentrations ranging 0.01M to 0.5M are shown with increasing concentrations bottom to top.
Determination of Standard free energy changes, (∆Go), and transition energy (ECT), of the π-π* interaction between donor and acceptor:
The standard free energy changes of complexation (∆Go) were calculated from the association constants by the following equation derived by Martin, Swarbrick and Cammarata26:
∆Go = - 2.303 RT log KCT ---Eq. (6)
Where, ∆Go is the free energy change of the complexes (kJ mol-1), R is the gas constant (8.314 J mol-1 k), T is the temperature in Kelvin degrees (273 + 0C) and KCT is the association constant of the complexes (l mol-1) in different solvents at room temperature. The values thus calculated are represented in Table4.
The energy (ECT) of the π –π* interaction between donor (MNA), and acceptor, (PiOH), is calculated using the following equation derived by G. Briegleb and Z. Angew27:
The calculated values of ECT given in Table 5.
1243.667
ECT = ———— ---------Eq. (7)
λCT nm
Where, λCT is the wavelength of the CT band
Fig 4. Absorption spectra of (A) Blank solvent (acetone); (B) Picric acid .01 M; (C) m- nitroaniline.01 M; (D) CTC of MNA .01M and PiOH .01M in acetone
RESULT AND DISCUSSION:
Spectrophotometric study of formation constants of the charge transfer complexes of PiOH/MNA in different polar solvents:
Stoichiometries and the formation constants of the charge transfer complex of m-nitroaniline with picric acid have been determined in different polar solvents viz- acetone, ethanol and methanol at room temperature using Benesi–Hildebrand equation28, 29. The spectrophotometric data were employed to calculate the values of formation constants, KCT of the complex. The changes in the absorbance upon addition of MNA to a solution of PiOH of fixed concentration follow the Benesi- Hildebrand28, 29 equation in the form.
[A]o / [A] = (1 / KCTεCT) × 1 / [D] 0 + 1/εCT Eq. (8)
Where, [D]o and [A]o are the concentrations of the m-nitroaniline donor, and picric acid acceptor, respectively, A is the absorbance of the donor-acceptor mixture at λCT, against the solvents as reference, KCT is the formation constant and εCT is the molar extinction coefficient, is not quite that of complex Eq.(8)28,29 is valid under the condition [D]o >> [A]o21,22 for 1:1donor-acceptor complexes. The concentration of the donor (MNA) was changed over a wide range from 0.01M to 0.5M while concentration of π acceptor PiOH was kept fixed at 0.01M in each reaction mixture. These produced solution with donor: acceptor molar ratio varying from 1:1 to 50:1, experimental data are given in Table 3.
Fig 5. Relation between [A] 0/A and 1/ [D] 0 of PiOH +MNA in acetone
The Benesi – Hildebrand28, 29 method is an approximation that has been used many times and gives decent results. But the extinction coefficient is really a different one between the complex and free species that absorbs at the same wavelength. The intensity in the visible region of the absorption bands, measured against the solvent as reference, increases with increased in the polarity and addition of MNA. The typical absorbance data for charge transfer complexes of MNA with PiOH in different polar solvents at room temperature are reported in Table 1 and 3. In all systems very good linear plots according to Eq. (7)28, 29 are obtained, shown in Fig 5, 6, 7. Formation constants for the complex in different polar solvents at room temperature determined from the BH plots are summarized in Table 3. The correlation coefficients of all such plots were above than 0.995. Plots of [A]0/[A] against 1/[D]o were found to be linear in all systems in Fig. 5,6and7 showing 1:1 charge transfer complex, i.e. the straight lines are obtained with the slopes 1/KCTεCT, these results prove the formation of the 1:1 CTC. From slope 1/KCTεCT and intercept, 1/εCT, KCT and εCT of the complex were calculated.
Table 1. Gaussion curve analysis for the CT in spectrum of PiOH with MNA different polar solvents
|
system |
Area of the curve (A) |
Width of the curve (W) |
Centre of the curve (xc) |
Y0 |
|
PiOH+MNA (Acetone) PiOH+MNA (Ethanol) PiOH+MNA (Methanol) |
141.92 ± 7.70
121.95 ± 7.50
162.63 ± 11.58 |
67.00± 3.57
64.44 ± 3.77
88.30 ± 5.53 |
425.58 ± 1.51
430.63 ± 1.49
434.44 ± 2.13 |
-0.00512±0.0281
-0.0052±0.03162
0.01969±0.03815 |
Table 2. CT absorption maxima (λCT), transition energies (hνCT), of the PiOH complexes, experimentally determined values of ionization potentials (ID), oscillator strength (ƒ), dipole moments (μEN), and resonance energies (RN) of complexes
|
system |
λCT (nm) |
hνCT (ev) |
ID(eV) |
ƒ × 105 |
μEN (Debye) |
[RN] |
|
PiOH+MNA (Acetone) PiOH+MNA (Ethanol) PiOH+MNA (Methanol) |
425.58
430.63
434.44 |
2.92
2.88
2.86 |
9.34
9.30
9.27 |
2.77
2.49
3.37 |
0.932
0.900
0.894 |
0.0072
0.0066
0.0065 |
Table. 3. Data for spectrophotometric determination of stoichometry, absorption maxima (λCT), and association constants (KCT), molar absorptivities (εCT), of CTC of PiOH and MNA in acetone, ethanol, and methanol at 298 K
|
system |
Temperature (K) |
Donor concentration in M |
[A]0 in M |
Absorbance at λCT (nm) |
λCT (nm) |
KCT (lmol-1) |
εCT (1mol-1 cm-1) |
|
PiOH/MNA (Acetone)
PiOH/MNA (Ethanol)
PiOH/MNA (Methanol) |
298
298
298
|
0.01 0.015 0.02 0.03 0.05 0.1 0.2 0.3 0.5
0.01 0.015 0.02 0.03 0.05 0.1 0.2 0.3 0.5
0.01 0.015 0.02 0.03 0.05 0.1 0.2 0.3 0.5 |
0.01
0.01
0.01 |
1.698 1.756 1.798 1.832 1.865 1.895 1.905 1.918 1.932
1.532 1.592 1.642 1.689 1.733 1.755 1.772 1.785 1.795
1.458 1.548 1.593 1.643 1.689 1.732 1.752 1.768 1.785 |
440
445
450 |
729
569
470 |
192
179
177 |
Table: 4 Association constant (KCT), correlation coefficients (r) and standard free energy changes (∆Go) of PiOH/MNA complexes obtained from Benesi-Hildebrand plots
|
System |
KCT (lmol-1) |
-∆Go(298K) (kJmol-1) |
R |
|
PiOH/MNA (Acetone) PiOH/MNA ( Ethanol ) PiOH/MNA (Methanol) |
729
569
470 |
16.318
15.691
15.234 |
0.995
0.996
0.997 |
Table 5. The CTC transition energies (ECT), CTC absorption maxima (λCT), and Ionization potential (ID) of donor of in different polar solvents
|
System |
ECT (eV) |
λCT(nm) |
ID(eV) |
|
PiOH/MNA ( Acetone) PiOH/MNA (Ethanol) PiOH/MNA (Methanol) |
2.82
2.79
2.76 |
440
445
450 |
9.23
9.19
9.15 |
Table6. Characteristic infrared frequencies *(cm-1) and tentative assignments for PiOH, MNA and their complex.
|
H PiOH MNA Complex Assignments
|
|
3108s,br 3433sharp 3253ms ν(O-H) ,H bonded - 3322br - ν (N-H) - 3190sh 3090ms ν (C-H) 2875 w 2664sh 2857br νs(C-H) - - - 1630νs - - νas(C-H) 1606ms 1621 νs 1632ms νasNO2 1529 br 1585sh 1608sh ν(C=C) - 1519br 1536br δ def (N-H), + NH2 ring breathing bands - 1484sh 1425 νs C-H deformation 1437ms - - - 1342w 1344br ν(C-C), νsNO2 1341νs 1322sh - ν(C-N) 1275 νs 1261 νs 1278w ν(C-O) 1154ms 1048 νs 1148ms (C-H) in plane Bending 1083ms - 1171ms - - 1090ms 916ms 993ms 913ms δ rock , +NH2 830w 922 sharp 892sh 779sharp 866sharp 842ms CH2 rock skeletal vibrations - 811νs 807ms 735νs 781νs 734ms 664νs 731νs C-H out of plane Bending 703ms - 704ms
|
S, strong, w, weak ; m, medium , sh , shoulder , v , very ; vs, very strong , br, broad ; ν, stretching; νs, symmetrical stretching ; νas, asymmetrical stretching
Effect of solvents on the formation of CT- complexes:
The experimental results of the CT interaction between PiOH with MNA in different polar solvents shown in Table 3. The values of association constants (KCT) are: 729 mol-1 in acetone, 569 mol-1 in ethanol, and 470 mol-1 in methanol and the values of molar extinction coefficient, (εCT) are: 192 mol-1cm-1 in acetone, 179 mol-1cm-1 in ethanol, and 177 mol-1cm-1 in methanol and spectroscopic properties were markedly affected by the variation in solvent polarity in which measurements were carried out. In the present investigation the KCT values increases significantly from methanol to acetone with decreasing solvents polarity. Moreover, the increase in KCT values with decreasing
solvents polarity, may also be due to the fact that, CTC should be stabilized in less polar solvent30. Dissociation of the complexes into D+ ——A- radicals have been found to occur in the ground state31. It means that the CTC should be strong in less polar solvent than polar solvent. The red shift occurred in CTC complex caused by polarity change from using acetone to methanol.
Fig 6. Relation between [A] 0/A and 1/ [D] 0 of PiOH + MNA in ethanol
However the data given in Table3, shows that PiOH interacts more strongly with MNA in acetone among the other two solvents. The experimentally determined values of the oscillator strength,(ƒ) are: 2.77 × 10-5 in acetone, 2.49 × 10-5 in ethanol, and 3.37 × 10-5 in methanol, and the values of transition dipole moment,(μEN) are: 0.932(Debyes) in acetone, 0.900 (Debyes) in ethanol, and 0.894 (Debyes)in methanol and values of resonance energy (RN) are: 0.0072 in acetone, 0.0066 in ethanol, and 0.0065 methanol, are given in Table 2. The data indicate that complex should be stable in a less polar solvent (acetone) than the other two solvents (ethanol and methanol). The very low values of ƒ, indicate that CT complex studied here have almost neutral character in its ground state.
Fig 7. Relation between [A] 0/A and 1/ [D] 0 of PiOH+MNA in Methanol.
The parameters thus obtained are represented in Table 4, and these values show that complexation is thermodynamically favored. The free energy change of the complexation also reveals that the CTC formation between used donor (MNA) and acceptor (PiOH) is of exothermic in nature. The values of (∆G0) are: - 16.318(kJmol-1) in acetone, -15.691(kJmol-1) in ethanol and -15.234(kJmol-1) in methanol and are also shown in Table4. They are generally more negative as the association constants of the molecular complex increases. As the bond between the components becomes stronger and thus the components are subjected to more physical strain or loss of freedom, the values of ∆G0 become more negative.
The ionization potentials ID, (eV) of the donor can be calculated using the experimentally determined λCT of the CTC from Eq. (1), [24]. The calculated values of (ID) are: 9.23(eV) in acetone, 9.19 (eV) in ethanol and 9.15(eV) in methanol of PiOH/MNA system and they are shown in Table 5. The approximate consistency of ID values, indicates that the ionization potential show a negligibly small effect on KCT values.
Comparative study of FT- IR spectra of CT complex and reactants:
FT-IR spectra of the free acceptor and donor as well as the formed CT complex are given in Fig 8, 9, and 10, and their bands assignments reported in Table 6. However the appearance of a group of FT-IR spectral bands in the spectra of CT complex support the conclusion that a deformation of the electronic environment of m-nitroaniline has occurred by accepting a proton from PiOH. The shift of the FT-IR bands of the acceptor to lower wave numbers and those of the donor part to higher values reflects a donor to acceptor charge transfer of π-π* interaction, i.e. DHOMO → ALUMO transition32.
The FT-IR spectrum of the complex of PiOH and MNA in Fig 10. Shows the presence of characteristic absorption bands due to the varied forced constants in the donor and the acceptor species on account of the prevalent charge transfer mechanism. This makes the crystals of this type more ionic than other organic crystals. The asymmetric and symmetric stretching vibrations of the –NO2 group are observed at 1536.52 cm-1 and 1344.13 cm-1 respectively. Normally the asymmetric stretching vibration of the –NO2 group is sensitive to polar influences and the electronic states of the species. Therefore, it has been realized that the shift to lower frequency of νasym NO2 vibration (1536.52cm-1) in the spectrum of the complex compared with free picric acid (1606 cm-1) is due to the increased electron density on the picric acid moiety owing to the charge transfer interaction in the complex33. In the spectra of CT- complex of m-nitroaniline and picric acid, MNA almost completely consumed evidence of H- bonding and –OH intensity decreased and position of the peak also shifted.
CONCLUSION:
The UV –Vis spectrophotometric method for the study of CTC of picric acid with m-nitroaniline reveals that it forms 1:1 (A: D) complex in all three solvents, viz; acetone, ethanol and methanol. In all systems the stoichiometry is unaltered by changing the solvent. The association constants, KCT and molar extinction coefficients, εCT, of all systems were evaluated by the Benesi - Hildebrand method. The values of association constant of the CTC decrease with increasing solvent polarity, due to the destabilization of CTC in polar solvents and then the dissociation of the complex into D+ A-. The interaction between the donor and acceptor was found to be π-π* transitions by the formation of radical ion pairs. The spectroscopic and thermodynamic parameters of the complexes were found to be solvents dependent. The values of the oscillator strengths,(ƒ) transition dipole moments,(µEN) resonance energies,(RN) and standard free energies, (∆Go) have been estimated for the PiOH/MNA systems in different polar solvents. The results show that the investigated complex is stable, exothermic and spontaneous. From the trends in the CT absorption bands, the ionization potentials of the donor molecules have been estimated. The FT-IR spectrum shows that the complex was formed by transferring a proton from the acceptor (PiOH) to the donor (MNA).
ACKNOWLEDGEMENT:
The Authors thank Dr. Arunima Lal Chairperson of chemistry department of Aligarh Muslim University, India, for providing instruments time for the FT-IR Spectrometer, U.V. - Visible spectrophotometer. Financial assistance by the UGC, New Delhi extended through the scholarship, is also gratefully acknowledged. The authors also thank the referee for making valuable comments.
Fig 8. The FT-IR spectra of picric acid (acceptor)
Fig 9. The FT-IR spectra of m-nitroaniline (donor)
Fig 10. The FT-IR spectra of complex of picric acid and m-nitroaniline.
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Received on 22.07.2009 Modified on 15.09.2009
Accepted on 19.10.2009 © AJRC All right reserved
Asian J. Research Chem. 2(4):Oct.-Dec. 2009 page 476-484