A Polarographic Study of Tl + , Pb 2 and Cd 2+ Complexes with Dicyclohexano-18-Crown-6 in Some Binary Mixed Solvents

The complexes of Tl⁺, Pb²⁺ and Cd²⁺ cations with the macrocyclic ligand, dicyclohexano-18-crown-6\linebreak(DC18C6) were studied in water/methanol (H₂₊O/MeOH), water/1-propanol (H₂₊O/1-PrOH), water/acetonitrile (H₂₊O/AN), water/dimethylformamide (H₂₊O/DMF), dimethylformamide/acetonitrile (DMF/AN), dimethylformamide/methanol (DMF/MeOH), dimethylformamide/1-propanol (DMF/1-PrOH) and dimethylformamide/nitromethane (DMF/NM) mixed solvents at 22 °C using differential pulse polarography (DPP), square wave polarography and conductometry. In general, the stability of the complexes was found to decrease with increasing concentration of water in aqueous/non-aqueous mixed solvents with an inverse relationship between the stability constants of the complexes and the concentration of DMF in non-aqueous mixed solvents. The results show that the change in stability of DC18C6.Tl⁺, vs the composition of solvent in DMF/AN and DMF/NM mixed solvents is apparently different from that in DMF/MeOH and DMF/1-PrOH mixed solvents. While the variation of stability constants of the DC18C6.Tl⁺ and DC18C6.Pb²⁺ complexes vs the composition of H₂₊O/AN mixed solvents is monotonic, an anomalous behavior was observed for variations of log K_f vs the composition of H₂₊O/1-PrOH and H₂₊O/MeOH mixed solvents. The selectivity order of the DC18C6 ligand for the cations was found to be Pb²⁺ > Tl⁺ > Cd²⁺.     

Competitive Potentiometric Study of the Thermodynamics of Complexation of Some Transition and Heavy Metal Ions with Dibenzopyridino-18-crown-6 in Methanol using Ag+ Ion as a Probe

The complexation of dibenzopyridino-18-crown-6 with some transition and heavy metal ions in methanol solution at various temperatures was studied by a competitive potentiometric method using a Ag⁺/Agelectrode system. The stoichiometry and stability of the resulting complexes were computed by the MINIQUAD program. The stability of the resulting complexes varied in the order Ag⁺ > Pb²⁺ > Tl⁺ > Cu²⁺ > Cd²⁺ > Zn²⁺. The enthalpy and entropy of the resulting 1:1 complexeswere evaluated from the temperature dependence of the stability constants.The complexes of all cations were enthalpy-stabilized but entropy-destabilized,except for Ag⁺ and Pb²⁺ ions,which were also entropy-stabilized.     

A Conductometric Study of Complexation Reactions Between Dibenzo-18-Crown-6 (DB18C6) with Cu2+, Zn2+, Tl+ and Cd2+ Metal Cations in Dimethylsulfoxide–Ethylacetate Binary Mixtures

The complex formation between Cu²⁺, Zn²⁺, Tl⁺ and Cd²⁺ metal cations with macrocyclic ligand, dibenzo- 18-crown-6 (DB18C6) was studied in dimethylsulfoxide (DMSO)–ethylacetate (EtOAc) binary systems at different temperatures using conductometric method. In all cases, DB18C6 forms 1:1 complexes with these metal cations. The stability constants of the complexes were obtained from fitting of molar conductivity curves using a computer program, Genplot. The non-linear behaviour which was observed for variations of log K _f of the complexes versus the composition of the mixed solvent was discussed in terms of changing the chemical and physical properties of the constituent solvents when they mix with one another and, therefore, changing the solvation capacities of the metal cations, crown ether molecules and even the resulting complexes with changing the mixed solvent composition. The results show that the selectivity order of DB18C6 for the metal cations in pure ethylacetate and pure dimethylsulfoxide is: Tl⁺ > Cu²⁺ > Zn²⁺ > Cd²⁺ but the selectivity order is changed with the composition of the mixed solvents. The values of enthalpy changes (ΔH°_C) for complexation reactions were obtained from the slope of the van’t Hoff plots and the changes in standard enthalpy (ΔS°_C) were calculated from the relationship: ΔG°_C,298.15=ΔH°_C − 298.15 ΔS°_C. The obtained results show that in most cases, the complexes are enthalpy stabilized, but entropy destabilized and the values of ΔH°_C and ΔS°_C depend strongly on the nature of the medium.     

Stability constants of complexes formed by new Schiff-base lariat ethers derived from 4,13-diaza-18-crown-6 with Ag+, Pb2+, Cu2+ cations determined by competitive potentiometry

The stability of complexes formed by a series of Schiff-base lariat ethers, derived from 4,13-diaza-18-crown-6, 1 with Ag⁺, Pb²⁺, Cu²⁺ cations, has been comparatively determined, in methanol: dichloromethane solution. We present here the synthesis and an interesting competitive potentiometry method useful for the stability constant determination for a new family of Schiff-base bibracchial lariat ethers. The stability constants and the selectivity in competitive complexation of Ag⁺, Pb²⁺ and Cu²⁺ cations by macrocyclic receptors 1–7 (L), can be accurately evaluated and species distribution diagrams can be calculated for individual system. In all cases further functionalization of bibracchial lariat ethers 2–7 is accompanied by an increasing of the selectivity, relative to the complexes of the initial 4,13-diaza-18-crown-6 macrocycle 1.     

Study of Complex Formation Between 18-Crown-6 and Pb2+, Tl+ and Cd2+ Cations in Binary Aqueous/Non-aqueous Solvents Using Polarographic Techniques (DPP and SWP)

The complexation of Pb²⁺, Tl⁺ and Cd²⁺ cationsby 18-crown-6 was studied in water/propanol (H₂O/PrOH),water/acetonitrile (H₂O/AN) and water/dimethylformamide(H₂O/DMF) binary systems at 20 °C using squarewave polarography (SWP) and differential pulse polarography (DPP).It was confirmed that the stoichiometry of each of the complexes formed between 18C6 and the respective cations is 1 : 1. The formation constants of the complexes were found to increase with increasing concentration of the non-aqueous solvent. In all cases, a stability order of Pb²⁺ > Tl⁺ > Cd²⁺ was observed. In general,the stabilities of individual complexes were found to decrease as the binary solvent mixture varied from H₂O/AN to H₂O/PrOH to H₂O/DMF.     

Study of complexation of phenylaza-15-crwon-5, 4-nitrobenzo- 15-crown-5, and benzo-15-crown-5 with Ag+, Tl+ and Pb2+ ions in methanol by competitive potentiometry

The complexation reaction of phenylaza-15-crwon-5, 4- nitrobenzo- 15-crown-5, and benzo-15-crown-5 with Ag⁺, Tl⁺ and Pb²⁺ ions in methanol solution have been studied by a competitive potentiometric method. The Ag⁺/Ag electrode used both as an indicator and reference electrode in a concentration cell. The emf of cell monitored as the crown ethers concentration varies through the titration. The stoichiometry and stability constants of resulting complexes have been evaluated by MINIQUAD. The stoichiometry for all resulting complexes was 1:1. The stability of these metal ions with derivatives of 15-crown-5 are in order phenylaza-15-crown-5 > Benzo-15-crown-5 > 4-nitrobenzo-15-crown-5, and for the each used crown ethers are as Pb²⁺ > Ag⁺ > Tl⁺. The effect of the substituted group on the stability of resulting complexes was considered. The obtained results are novel and interesting.     

Study of Complex Formation Between Dicyclohexano-18-Crown-6 (DCH18C6) with Mg 2+, Ca2+, Sr 2+, and Ba2+ Cations in Methanol–Water Binary Mixtures Using Conductometric Method

The complexation reactions between Mg²⁺,Ca²⁺,Sr²⁺ and Ba²⁺ metal cations with macrocyclic ligand, dicyclohexano-18-crown-6 (DCH18C6) were studied in methanol (MeOH)–water (H₂O) binary mixtures at different temperatures using conductometric method . In all cases, DCH18C6 forms 1:1 complexes with these metal cations. The values of stability constants of complexes which were obtained from conductometric data show that the stability of complexes is affected by the nature and composition of the mixed solvents. While the variation of stability constants of DCH18C6-Sr ²⁺ and DCH18C6-Ba²⁺versus the composition of MeOH–H₂O mixed solvents is monotonic, an anomalous behavior was observed for variations of stability constants of DCH18C6-Mg²⁺ and DCH18C6-Ca²⁺ versus the composition of the mixed solvents. The values of thermodynamic parameters (ΔH_c°, ΔS_c°) for complexation reactions were obtained from temperature dependence of formation constants of complexes using the van’t Hoff plots. The results show that in most cases, the complexation reactions are enthalpy stabilized but entropy destabilized and the values of thermodynamic parameters are influenced by the nature and composition of the mixed solvents. The obtained results show that the order of selectivity of DCH18C6 ligand for metal cations in different concentrations of methanol in MeOH–H₂O binary system is: Ba²⁺>Sr²⁺>Ca²⁺> Mg²⁺.     

Conductance Studies on Complex Formation Between Aza-18-Crown-6 with Ag+, Hg2+ and Pb2+ Cations in DMSO–H2O Binary Solutions

The complexation reactions between Ag⁺, Hg²⁺ and Pb²⁺ metal cations with aza-18-crown-6 (A18C6) were studied in dimethylsulfoxide (DMSO)–water (H₂O) binary mixtures at different temperatures using the conductometric method. The conductance data show that the stoichiometry of the complexes in most cases is 1:1(ML), but in some cases 1:2 (ML₂) complexes are formed in solutions. A non-linear behaviour was observed for the variation of log K _f of the complexes vs. the composition of the binary mixed solvents. Selectivity of A18C6 for Ag⁺, Hg²⁺ and Pb²⁺ cations is sensitive to the solvent composition and in some cases and in certain compositions of the mixed solvent systems, the selectivity order is changed. The values of thermodynamic parameters (ΔH _c^o, ΔS _c^o) for formation of A18C6–Ag⁺, A18C6–Hg²⁺ and A18C6–Pb²⁺ complexes in DMSO–H₂O binary systems were obtained from temperature dependence of stability constants and the results show that the thermodynamics of complexation reactions is affected by the nature and composition of the mixed solvents.     

Complex Formation of 1,10-Dibenzyl-1,10-diaza-18-crown-6 with Ni2+, Cu2+, Ag+ and Cd2+ Metal Cations in Acetonitrile–dimethylformamide Binary Solutions

Conductance measurements are reported for nickel(II), cupper(II), silver(I) and cadmium(II), salts in acetonitrile (AN)–dimethylformamide (DMF) binary solvents containing macrocyclic ligand, 1,10-dibenzyl-1,10-diaza-18-crown-6 (DBDA18C6) at different temperatures. The changes in molar conductance caused by addition of DBDA18C6 to solutions were analyzed by non-linear least squares to give stability constants of 1:1 metal cation–DBDA18C6 complexes. The results show that the stabilities of the complexes are sensitive to solvent composition and in some cases the sequence of stabilities is changed with changing the composition of the mixed solvents. The values of thermodynamic quantities (ΔH°c and ΔS°c) for formation of DBDA18C6-Ni²⁺, DBDA18C6-Cu²⁺, DBDA18C6-Ag⁺ and DBDA18C6-Cd²⁺ complexes were obtained from temperature dependence of the stability constants and the results show that the values of ΔH°c and ΔS°c for these complexes are sensitive to the nature and composition of AN–DMF binary solutions, but they do not vary monotonically with the solvent composition.     

Effect of Solvent on Competitive Bulk Membrane Transport of Transition and Post Transition Metal Cations Using Decyl-18-crown-6

A series of competitive metal ion transport experiments have been performed. Each involved transport from an aqueous source phase across an organic membrane phase into an aqueous receiving phase. The source phase contained equimolar concentrations of cobalt(II), nickel(II), cupper(II), zinc(II), cadmium(II), silver(I) and lead(II) metal cations. The membrane phase incorporated ionophore, decyl-18-crown-6. The membrane solvents include: chloroform, dichloromethane, 1,2-dichloroethane, nitrobenzene and chloroform–nitrobenzene binary solvents. A good transport efficiency and selectivity of Pb²⁺ transport from aqueous solutions are observed in this investigation. The selectivity order for competitive bulk liquid membrane transport of the studied transition and post transition metal cations through chloroform is: Pb²⁺>Co²⁺>Ni²⁺>Ag⁺>Cd²⁺, but in the case of dichloromethane, 1,2-dichloroethane and nitrobenzene as liquid membranes, the selectivity sequences were found to be: Pb²⁺>Co²⁺>Cd²⁺>Cu²⁺>Ag⁺>Ni²⁺>Zn²⁺, Pb²⁺>Co²⁺>Ag⁺>Ni²⁺>Zn²⁺ and Pb²⁺>Co²⁺>Ni²⁺>Zn²⁺>Cd²⁺>Ag⁺, respectively. The transport rate of the metal cations in chloroform–nitrobenzene binary solvents is sensitive to the solvent composition. The transport processes were studied in absence and presence of the stearic acid and the results show that the sequence of selectivities and ion transport rates change in the presence of stearic acid.     

Study of Complex Formation between 5,7‐Diiodo‐8‐hydroxyquinoline and Zn2+, Cd2+, Pb2+ and Tl+ Cations in Binary Non‐Aqueous Solvents Using Square Wave Polarography Technique (SWP)

The complexation reaction between Zn²⁺, Pb²⁺, Cd²⁺ and Tl⁺ cations by 5,7‐diiodo‐8‐hydroxyquinoline (IQN) was studied in the Dimethylformamide /Acetonitril (DMF‐AN) binary system using square wave polarography technique. The stoichiometry and stability of the complexes were determined by monitoring the shifts in half‐wave or peak potential of the polarographic waves of metal ions against the ligand concentration. The stoichiometry of the complexes was found to be 1:1. The results obtained show that there is an inverse relationship between the formation constant of the complexes and the donor number of solvent base on the Guttmann donocity scale. In all cases the formation constants increased with increasing amounts of AN in these binary systems. The selectivity order for IQN complexes with the cations is Zn²⁺ > Pb²⁺ > Cd²⁺ > Tl⁺.     

Study of Bulk Membrane Transport of Some Heavy Metal Cations Using Three Macrocyclic Ligands Containing Oxygen and Nitrogen Heteroatoms

The transport experiments of Co²⁺, Ni²⁺, Cu²⁺, Zn²⁺, Cd²⁺, Ag⁺ and Pb²⁺ metal cations were carried out by dibenzo-18-crown-6 (DB18C6), dibenzyl-diaza-18-crown-6 (Dibenzyl-diaza-18C6) and di-tert-butyl-dibenzo-18-crown-6 (Di-tert-butyl-DB18C6) using chloroform (CHCl₃), 1,2-dichloroethane (1,2-DCE) and nitrobenzene (NB) organic solvents as liquid membranes. The source phase contained equimolar concentration of these metal cations and the source and receiving phases being buffered at pH=5 and pH=3, respectively. The obtained results show that the selectivity and the efficiency of transport for these heavy metal cations change with the nature of the ligand and also the organic solvents, which were used as liquid membranes in these experiments. A good selectivity was observed for silver (I) ion by dibenzyl-diaza-18C6 in all membrane systems. Dibenzo-18C6 and di-tert-butyl-DB18C6 showed the highest transport efficiency for cobalt (II) ion. The effect of stearic acid on transport efficiency was also investigated and the results show that the efficiency of transport of the heavy metal cations increases in the presence of this organic acid.     

过渡金属与新型硝基酚臂式氮杂18-冠-6配位性能的研究

合成并表征了1,10-二氧-4,7,13,16-四氮杂18-冠-6 (1)母体及其四取代硝基酚臂式衍生物 (2)。在H₂O-DMSO(V/V=1/4)混合溶剂中用UV-Vis光谱法对冠醚2与H⁺、Mn²⁺、Co²⁺、Ni²⁺、Cu²⁺、Zn²⁺、Cd²⁺和Hg^{2+相似文献}   

Study of Complex Formation between N-Phenylaza-15-Crown-5 with Mg2+, Ca2+, Ag+ and Cd2+ Metal Cations in Some Binary Mixed Aqueous and Non-aqueous Solvents using the Conductometric Method

The complexation reactions between Mg²⁺, Ca²⁺, Ag⁺ and Cd²⁺ metal cations with N-phenylaza-15-crown-5 (Ph-N15C5) were studied in acetonitrile (AN)–methanol (MeOH), methanol (MeOH)–water (H₂O) and propanol (PrOH)–water (H₂O) binary mixtures at different temperatures using the conductometric method. The conductance data show that the stochiometry of all of the complexes with Mg²⁺, Ca²⁺, Ag⁺ and Cd²⁺ cations is 1:1 (L:M). The stability of the complexes is sensitive to the solvent composition and a non-linear behaviour was observed for variation of log K _f of the complexes versus the composition of the binary mixed solvents. The selectivity order of Ph-N15C5 for the metal cations in neat MeOH is Ag⁺>Cd²⁺>Ca²⁺>Mg²⁺, but in the case of neat AN is Ca²⁺>Cd²⁺>Mg²⁺>Ag⁺. The values of thermodynamic parameters (ΔH _c ^o , ΔS _c ^o ) for formation of Ph-N15C5–Mg²⁺, Ph-N15C5–Ca²⁺, Ph-N15C5–Ag⁺ and Ph-N15C5–Cd²⁺ complexes were obtained from temperature dependence of stability constants and the results show that the thermodynamics of complexation reactions is affected by the nature and composition of the mixed solvents.     

A Thermodynamic Study Between 18-Crown-6 with Mg2+, Ca2+, Sr2+and Ba2+ Cations in Water–Methanol and Water–Ethanol Binary Mixtures Using The Conductometric Method

The complexation reactions between Mg²⁺, Ca²⁺, Sr²⁺ and Ba²⁺ cations with the macrocyclic ligand, 18-Crown-6 (l8C6) in water–methanol (MeOH) binary systems as well as the complexation reactions between Ca²⁺ and Sr²⁺ cations with 18C6 in water–ethanol (EtOH) binary mixtures have been studied at different temperatures using conductometric method. The conductance data show that the stoichiometry of all the complexes is 1:1. It was found that the stability of 18C6 complexes with Mg²⁺, Ca²⁺, Sr²⁺ and Ba²⁺ cations is sensitive to solvent composition and in all cases, a non-linear behaviour was observed for the variation of log K _f of the complexes versus the composition of the mixed solvents. In some cases, the stability order is changed with changing the composition of the mixed solvents. The selectivity order of 18C6 for the metal cations in pure methanol is: Ba²⁺ > Sr²⁺ > Ca²⁺ > Mg²⁺. The values of thermodynamic parameters (Δ H _c ° and Δ S _c °) for formation of 18C6–Mg²⁺, 18C6–Ca²⁺, 18C6–Sr²⁺ and 18C6–Ba²⁺complexes were obtained from temperature dependence of the stability constants. The obtained results show that the values of (Δ H _c ° and Δ S _c °) for formation of these complexes are quite sensitive to the nature and composition of the mixed solvent, but they do not vary monotonically with the solvent composition.This revised version was published online in July 2005 with a corrected issue number.     

Poly(vinyl chloride)-membrane ion-selective bulk optode based on 1,10-dibenzyl-1,10-diaza-18-crown-6 and 1-(2-pyridylazo)-2-naphthol for Cu and Pb ions

An ion-selective bulk optode (ISBO) for sensing Cu²⁺ and Pb²⁺ ions based on plasticized poly(vinyl chloride) containing 1,10-dibenzyl-1,10-diaza-18-crown-6 (DBzDA18C6) as ionophore and 1-(2-pyridylazo)-2-naphthol (PAN) as chromoionophore was prepared. The effects of DBzDA18C6/PAN and NaTPB/PAN mole ratios on the response behavior of the ISBO were investigated. The ISBO membrane shows enhanced selectivities for Cu²⁺ (at 530 nm) and Pb²⁺ (at 467 nm) over alkali, alkaline earth and other transition metal ions. The optical selectivity coefficients were measured using the separate solution method (SSM) in the two corresponding wavelengths at pH=5. The detection limit for Cu²⁺ and Pb²⁺ are 3.2×10⁻⁷ and 1.0×10⁻⁸ M, respectively.     

Conductometric and 1H NMR studies of thermodynamics of complexation of Zn2+, Cd2+ and Pb2+ ions with tetrathia-12-crown-4 in dimethylsulfoxide-nitrobenzene mixtures

The complex formation between Zn²⁺, Cd²⁺ and Pb²⁺ ions with macrocyclic ligand, tetrathia12-crown-4 (12S4) was studied in dimethylsulfoxide (DMSO)–nitrobenzene binary mixtures at different temperatures using conductometric and ¹H NMR methods. In all cases, 12S4 found to form 1:1 complexes with these cations. The formation constants of the resulting 1:1 complexes in different solvent mixtures were determined by computer fitting of the resulting molar conductance- and chemical shift-mole ratio data. There is an inverse relationship between the complex stability and the amount of DMSO in the solvent mixtures. The stability of the resulting M²⁺-12S4 complexes found to decrease in the order Pb²⁺ > Cd²⁺ > Zn²⁺. The values of ?H°, ?S° and ?G° for complexation reactions were evaluated from the temperature dependence of formation constants via van’t Hoff method. The obtained results revealed that, in all cases, the complexes are enthalpy stabilized, but entropy destabilized and the values of ?H° and ?S° are strongly depend on the nature of medium. There is also a linear relationship between all ΔH° and TΔS° values indicating the existence of entropy–enthalpy compensation in complexation of the three cations and ligand in the solvent systems studied.     

Thermodynamic behavior of complexation of 18-crown-6 with Tl<Superscript>+</Superscript>, Pb<Superscript>2+</Superscript>, Hg<Superscript>2+</Superscript>, and Zn<Superscript>2+</Superscript> metal cations in methanol-water binary media

The equilibrium constants and thermodynamic parameters for complex formation of 18-Crown-6 (18C6) with Tl⁺, Pb²⁺, Hg²⁺, and Zn²⁺ metal cations have been determined by conductivity measurements in methanol (MeOH)-water (H₂O) binary solutions. 18-Crown-6 forms 1:1 complexes with Hg²⁺ and Zn²⁺ cations, but in the case of Tl⁺ and Pb²⁺ cations, in addition to 1:1 stoichiometry, 1:2 (ML₂) complexes are formed in some binary solvents. The thermodynamic parameters (ΔH _c⁰ and ΔS _c⁰), which were obtained from the temperature dependences of equilibrium constants, show that in most cases the complexes are enthalpy destabilized but entropy stabilized. Non-linear behavior is observed between the equilibrium constants (log K _f ) of complexes and the composition of the mixed solvent. The selectivity of the ligand for these metal cations is sensitive to the solvent composition, and, in some cases, the selectivity order is reversed in certain compositions of the mixed solvent. The results also show that the mechanism of complexation reactions and the stoichiometry of complexes of some metal cations change with the nature and even with the composition of the mixed solvent. The article was submitted by the authors in English.     

Crown-containing butadienyl dyes 8. Structures and complexation of chromogenic dithia-15(18)-crown-5(6) ethers

The structures of new butadienyl dyes of the benzothiazole series containing the dithia-15-crown-5 (2a) or dithia-18-crown-6 (2b) fragments were established by X-ray diffraction. Complexation of dyes 2a,b with Hg²⁺, Pb²⁺, Cd²⁺, Ag⁺, Zn²⁺, and alkaline-earth cations in aqueous-acetonitrile solutions was studied by spectrophotometry. At a high percentage of water in solutions (P _w ≈ 50%), these dyes have a very low ability to bind Pb²⁺ cations (logK < 2) and virtually do not bind Cd²⁺, Zn²⁺, and alkaline-earth cations. At the same time, these dyes form stable 1: 1 complexes with Hg²⁺ and Ag⁺ cations at all P _w. The stability constants of complexes with the Ag⁺ cation increase with increasing P _w because the free energy of hydration of this cation is much lower than the free energy of solvation in acetonitrile. In the P _w range from 0 to 75%, the stability constants of the complexes of dyes 2a,b with the Hg²⁺ cation are larger than those of the corresponding complexes with the Ag⁺ cation by more than four orders of magnitude. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 90–96, January, 2006.     

Synthesis, complex-formation, and extracting ability of new derivatives of dithia-13(16)-crown-4(5) ethers

Various methods of synthesizing functional derivatives of dithia-13(16)-crown-4(5) ethers are proposed. Complex-formation of the obtained compounds with Ag⁺ and Pb²⁺ ions has been studied using ¹H NMR. A radiometric method was used to investigate the extracting ability of substituted dithia-13(16)-crown-4(5) ethers in relation to Ag⁺ and Cd²⁺ ions from aqueous solution in the presence of anions of various degree of hardness, with determination of the metal content. __________ Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 233–243, February, 2006.