Thermal analysis of copolyphosphates

Summary DTA and TG were carried out on a number of sodium-containing copolyphosphates. The DTA curves were characteristic of long-chain polyphosphates and were similar in nature. All of them showed a sharp exothermic peak indicating crystallization temperature (T _c ) followed by a sharp endothermic peak giving the value of melting temperature (T _m ). TG curves showed weight loss occurring in two stages, the first one beginning at 50°C (loss of absorbed moisture) and the second one in the range 300-500°C (corresponding toT _c ). The values ofT _m andT _c appeared to decrease with increase in molecular weight. This could be due to the presence of crystallizable comonomer units in the copolyphosphate glasses.T _c andT _m also appeared to increase with increase in the atomic weight of the cation other than sodium.With 7 figures and 5 tablesTo whom correspondence should be addressed.     

Structure and physical properties of rare-earth zinc antimonides REZn1-xSb2 (RE=La, Ce, Pr, Nd, Sm, Gd, Tb)

The ternary rare-earth zinc antimonides REZn_1-xSb₂ (RE=La, Ce, Pr, Nd, Sm, Gd, Tb) were prepared by heating at 1050 °C followed by annealing at 600 °C. For all members, single-crystal X-ray diffraction studies indicated that the Zn deficiency is essentially fixed, corresponding to the formula REZn_0.6Sb₂, with no appreciable homogeneity range. These compounds adopt the HfCuSi₂-type structure (Pearson symbol tP8, space group P4/nmm, Z=2). Single-crystal electrical resistivity measurements confirmed the occurrence of an abrupt resistivity decrease near 4 K for RE=Ce, and a less pronounced one for RE=La, Pr, and Gd. Except for the ferromagnetic Ce (T_c=2.5 K) and antiferromagnetic Tb (T_N=10 K) members, all remaining compounds exhibit no long-range magnetic ordering down to 2 K, instead showing temperature-independent (RE=La), van Vleck (RE=Sm), or Curie-Weiss paramagnetism (RE=Pr, Nd, Gd).     

Potentiometric studies on the complexes of some trivalent rare earths with 5-chloropyridine-2,3-diol

The complexes of some rare earths [Ce(III), Pr(III), Nd(III), Sm(III), Tb(III), Dy(III), and Ho(III)] with 5-chloropyridine-2,3-diol (CPD) were studied potentiometrically in 50% dioxane-water at a ionic strength of 0.1M (NaClO₄) at 35±0.1 °C. The proton-ligand stability constant ofCPD and the stability constants of its complexes with the metals have been determined using theCalvin-Bjerrum technique as modified byIrving andRossotti. The order of the stability constants is found to be Ce < Pr < Nd < Sm < Tb < Dy < Ho.

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Potentiometrische Untersuchungen der Komplexe einiger trivalenter Seltenerdmetalle mit 5-Chlorpyridin-2,3-diol

Zusammenfassung Es wurden die Komplexe von Ce(III), Pr(III), Nd(III), Sm(III), Tb(III), Dy(III) und Ho(III) mit 5-Chlorpyridin-2,3-diol (CPD) in 50% Dioxan-Wasser bei einer Ionenstärke von 0,1M (NaClO₄) und einer Temperatur von 35±0,1 °C potentiometrisch untersucht. Die Proton-Ligand-Stabilitätskonstante vonCPD und die Stabilitätskonstanten der Metallkomplexe wurden nach der Methode vonCalvin-Bjerrum mit derIrving-Rossotti-Modifikation bestimmt. Die Reihenfolge der Stabilitätskonstanten ergab sich folgendermaßen: Ce < Pr < Nd < Sm < Tb < Dy < Ho.

     

Ternary metal borides [La,Ce,Pr,Nd,Sm] Os4B4 and [Y,La,Ce,Pr,Nd,Sm,Gd,Tb] Ir4B4 with NdCo4B4-type structure

New ternary metal borides with compositionR. E. T ₄B₄ (R. E.=rare earth metal,T=transition metal) have been synthesized within the systems [La,Ce,Pr,Nd,Sm]–Os–B and [Y, La, Ce, Pr, Nd, Sm, Gd, Tb]–Ir–B. All compounds were found to be crystallizing with NdCo₄B₄-type structure. Magnetic measurements (80–300 K,Curie-Weiss behaviour, _p ~ 16K and µ_eff=9.94µ_B for TbIr₄B₄) indicate Y andR. E. elements (except Ce) to be trivalent in these compounds. The crystal chemistry of the isotypic series [Y,R. E.] [Os,Ir]₄B₄ is discussed.

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Ternäre Metallboride. [La,Ce,Pr,Nd,Sm] Os₄B₄ und [Y,La,Ce,Pr,Nd,Sm,Gd,Tb] Ir₄B₄ mit NdCo₄B₄-Struktur

Zusammenfassung Es wurden neue Metallboride der ZusammensetzungR. E. T ₄B₄ (R. E.=Seltenerdmetall,T=Übergangsmetall) innerhalb der Systeme [La,Ce, Pr,Nd,Sm]–Os–B und [Y,La,Ce,Pr,Nd,Sm,Gd,Tb]–Ir–B hergestellt. Alle Verbindungen kristallisieren entsprechend dem NdCo₄B₄-Typ. Magnetische Messungen (80–300K,Curie-Weiss-Verhalten, _p ~ 16K und µ_eff=9.94µ_B für TbIr₄B₄) zeigen an daß Y und dieR. E.-Elemente (ausgenommen Ce) in diesen Verbindungen trivalent sind. Die Kristallchemie der isotypen [Y,R. E.][Os,Ir]₄B₄-Verbindungen wird diskutiert.

     

Double sulfates of some rare earths with tetramethylammonium

Double sulfates of rare earths and tetramethylammonium with empirical formula (CH₃)₄NLn(SO₄)₂ · 3H₂O (Ln=Ce, Pr, Nd, Eu, Gd, Tb and Dy) were synthesized and studied by the methods of TG, DTG and DTA in the temperature range from 20 to 500°C, and by X-ray powder diffraction and chemical analysis. Two isostructural groups were obtained: one from Ce to Eu and another from Gd to Dy. It was found that rare earth sulfates are obtained as final products at 500°C. For comparison, TG, DTG and DTA curves of the thermal decomposition of tetramethylammonium sulfate are given.

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Zusammenfassung Doppelsulfate von Seltenerden und Tetramethylammonium der empirischen Formel (CH₃)₄NLn(SO₄)₂ · 3H₂O mit Ln=Ce, Pr, Nd, Eu, Gd, Tb und Dy wurden synthetisiert und im Temperaturbereich 20–500°C mittels TG, DTG und DTA, weiterhin mittels Röntgenpulverdiffraktion und chemischer Analyse untersucht. Es wurden zwei isostrukturelle Gruppen erhalten, die eine von Ce bis Eu, die andere von Gd bis Dy. Man fand, daß man bei 500°C als Endprodukt die Seltenerdensulfate erhält. Zum Vergleich wurden die TG-, DTG- und DTA-Kurven der thermischen Zersetzung von Tetramethylammoniumsulfat gegeben.

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Financial support by the Research Council of Slovenia is gratefully acknowledged.     

Hydrazinium Oxalatometallates of Rare Earths(III)

Oxalates of La(III), Ce(III), Pr(III), Nd(III) and Sm(III) with the hydrazinium cation with the general formulae (N₂H₅)₄Ln₂(C₂O₄)₅7H₂O (Ln=La³⁺, Ce³⁺, Pr³⁺) and N₂H₅Ln(C₂O₄)₂·3.5H₂O (Ln=Nd³⁺, Sm³⁺) were synthesized. The thermal decompositions of these compounds take place in three stages: thermal dehydration at 65–100°C, exothermic decomposition of the N₂H₄ at 230–260°C, and oxidation of the oxalate ion.This revised version was published online in November 2005 with corrections to the Cover Date.     

Thermal studies on solid 1,4-bis(3-carboxy-3-oxo-prop-1-enyl) benzene of lighter trivalent lanthanides

Solid-state compounds of general formula Ln₂L₃·nH₂O, where L represents 1,4-bis(3-carboxy-3-oxo-prop-1-enyl)benzene and Ln = La, Ce, Pr, Nd, Sm, were synthesized. Complexometric titrations with EDTA, thermogravimetry (TG), differential thermal analysis (DTA), differential scanning calorimetry (DSC), X-ray powder diffractometry, elemental analysis and infrared spectroscopy have been employed to characterize and to study the thermal behavior of these compounds in dynamic air atmosphere. The results led to information about the composition, dehydration, crystallinity, and thermal decomposition of the synthesized compounds.     

Synthesis, structure, and characterization of hybrid materials: [Ce(H2O)]2[O2C(CH2)2CO2]3 and [Sm(H2O)]2[O2C(CH2)2CO2]3·H2O

The rare-earth dicarboxylate hybrid materials [Ce(H₂O)]₂[O₂C(CH₂)₂CO₂]₃ ([Ce(Suc)]) and [Sm(H₂O)]₂[O₂C(CH₂)₂CO₂]₃·H₂O ([Sm(Suc)]) have been hydrothermally synthesized (200°C, 3 days) under autogenus pressure. [Ce(Suc)] is triclinic, a=7.961 (3) Å, b=8.176 (5) Å, c=14.32 (2) Å, α=97.07° (7), β=96.75° (8), γ=103.73° (6), and z=2. The crystal structure of this compound has been determined using 3120 unique single crystal data. The final refinements let the agreement factors R₁ and wR₂(F²) converge to 0.0138 and 0.0363, respectively. [Ce(Suc)] is built up from infinite chains of edge-sharing nine-fold coordinated cerium atoms running along [100]. These chains are interconnected by the carbon atoms of the succinate anions, leading to a three-dimensional hybrid framework. The cell constants of [Sm(Suc)], isotypic with monoclinic C2/c [Pr(H₂O)]₂[O₂C(CH₂)₂CO₂]₃·H₂O ([Pr(Suc)]), were refined starting from X-ray powder data: a=20.275 (3) Å, b=7.919 (6) Å, c=14.130 (3) Å, and β=121.45° (1). Despite its lower symmetry, [Ce(Suc)] presents an important structural filiation with [Sm(Suc)]     

Die Anwendung der thermischen Zersetzung von Verbindungen der Seltenerdelemente in O2-Atmosphäre bei der Trennung

Zusammenfassung Da die Nitrate, Carbonate, Oxalate, Citrate, Succinate, Malonate und Komplexonate des Ce, Pr und Tb sich in O₂-Atmosphäre bei wesentlich niedrigeren Temperaturen (320–360° C) als die entsprechenden Verbindungen der übrigenSE (500 bis 550° C) zersetzen, kann die selektive thermische Zersetzung, kombiniert mit der selektiven Extraktion der Reaktionsprodukte mit komplexbildenden Lösungen und der Fällung durch Dekomplexierung, als Grundlage für neue Trennungsmethoden verwendet werden. Trennungsschemata zur Analyse und Bearbeitung der Ceriterden sowie zur Anreicherung des U, Th, Sc, Y und anderer radioaktiver Substanzen unter Berücksichtigung der oxydierenden und katalytischen Einwirkung des Cers bei der thermischen Zersetzung einiger Verbindungen derSE werden vorgeschlagen.

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The nitrates, carbonates, oxalates, citrates, succinates, malonates and complexonates of Ce, Pr and Tb decompose in an oxygen-atmosphere at much lower temperatures (320 to 360° C) than the corresponding compounds of the remaining rare earths (500–550° C). A new separation method, based on a selective thermal decomposition, combined with a selective extraction of the reaction products with complex forming solutions was worked out. This method is proposed for the analysis and investigation of the cerite earths, and for the enrichment of U, Th, Sc, Y and other radioactive substances.

     

Thermal stabilization of TEMPO-oxidized cellulose

A partially C6-carboxylated cellulose with carboxylate content of 1.68 mmol/g was prepared by 2,2,6,6-tetramethylpiperidine-1-oxyl radical (TEMPO)-mediated oxidation of a softwood bleached kraft pulp. Thermogravimetric analyses of the TEMPO-oxidized cellulose (TOC) and its related materials were studied to improve thermal stability of the TOC. Thermal decomposition (T_d) points of the TOC with sodium carboxylate groups, alkali-treated TOC with free carboxyl groups of 0.23 mmol/g and the original cellulose were 222 °C, 264 °C and 275 °C, respectively. Thus, the anhydroglucuronic acid units formed by TEMPO-mediated oxidation of the native wood cellulose and present in the TOC cause the decrease in T_d point by decarbonation during heating process. When carboxyl groups in the TOC were methylated with trimethylsilyl diazomethane (TMSCHN₂), the T_d point increased from 222 °C to 249 °C, and the peak temperature in its derivative thermogravimetric (DTG) curve increased from 273 °C to 313 °C, which was almost equal to that of the original cellulose. Thus, the methyl esterification of carboxyl groups in the TOC is effective in improving thermal stability. When sodium ions present in the TOC as counter ions of carboxylate groups were exchanged to some other metal ions, thermal stability was improved to some extent. Especially, when CaCl₂, Ca(OAc)₂, Ca(NO₃)₂ and CaI₂ solutions were used in the ion-exchange treatments, the peak temperatures in the DTG curves increased to approximately 300 °C. MgCl₂, NiCl₂, SrCl₂ and Sr(OAc)₂ solutions were also effective to some extent in increasing the peak temperatures of DTG curves. Thus, thermal stability of the fibrous TOC can be improved to some extent by methyl esterification of the sodium carboxylate groups present in the original TOC with TMSCHN₂ or ion-exchange treatments with some metal salt solutions.     

Neue Pyridiniumchlorometallatverbindungen der Seltenerdelemente

Summary Reaction of the rare earth chlorides with pyridinium chloride in tetrahydrofuran (THF) under anhydrous conditions gave nearly insoluble precipitates of the composition (pyH)₃ RECl₆·THF (RE=La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Y, Er, Tm, Yb, and Lu). They were characterized by chemical analysis and IR spectroscopy; decompositionin vacuo was studied, yielding the hithero unknown complexes (pyH)₃ RECl₆ (RE=La, Ce, Pr, Sm, Tb, Ho, Y, Tm, and Lu).

     

Solid-state 2-methoxybenzoates of light trivalent lanthanides

Solid-state LnL₃ compounds, where L is 2-methoxybenzoate and Ln is light trivalent lanthanides, have been synthesized. Thermogravimetry (TG), differential scanning calorimetry (DSC), X-ray powder diffractometry, infrared spectroscopy and elementary analysis were used to characterize and to study the thermal behaviour of these compounds. The results led to information on the composition, dehydration, thermal stability and thermal decomposition of the isolated compounds. On heating these complexes decompose in three (Ce, Pr) or five (La, Nd, Sm) steps with the formation of the respective oxide: CeO₂, Pr₆O₁₁ and Ln₂O₃ (Ln=La, Nd, Sm) as final residues. The theoretical and experimental spectroscopic study suggests predominantly the ionic bond between the ligand and metallic center.     

Thermal decomposition of light lanthanide diglycolates

The conditions of thermal decomposition of La, Ce(III), Pr, Nd, Sm, Eu and Gd diglycolates have been studied. On heating, the diglycolates of Ce(III), Pr, Eu and Gd lose crystallization water and yield anhydrous salts, which are then transformed into oxides. The diglycolates of La, Nd and Sm are decomposed in three stages. First, the diglycolates undergo dehydration to form the anhydrous salts, which are next decomposed to Ln₂O₂CO₃. In the last step the thermal decomposition of Ln₂O₂CO₃ to Ln₂O₃ takes place, accompanied by an endothermic effect.     

Thermal behavior and other properties of Pr(III), Sm(III), Eu(III), Gd(III), Tb(III) complexes with 4,4′-bipyridine and trichloroacetates

A novel mixed-ligand complexes with empirical formulae: Ln(4-bpy)_1.5(CCl₃COO)₃·nH₂O (where Ln(III) = Pr, Sm, Eu, Gd, Tb; n = 1 for Pr, Sm, Eu and n = 3 for Gd, Tb; 4-bpy = 4,4′-bipyridine) were prepared and characterized by chemical, elemental analysis and IR spectroscopy. Conductivity studies (in methanol, dimethylformamide and dimethylsulfoxide) were also described. All complexes are crystalline. The way of metal–ligand coordination was discussed. The thermal properties of complexes in the solid state were studied under non-isothermal conditions in air atmosphere. During heating the complexes decompose via intermediate products to the oxides: Pr₆O₁₁, Ln₂O₃ (for Sm, Eu, Gd) and Tb₄O₇. TG-MS system was used to analyze principal volatile thermal decomposition and fragmentation products evolved during pyrolysis of Pr(III) and Sm(III) compounds in air.     

Thermal properties of globulin from buckwheat (<Emphasis Type="Italic">Fagopyrum esculentum</Emphasis> Moench)

The thermal properties of buckwheat (Fagopyrum esculentum Moench) proteins with different lipid contents (2.5, 6.5 and 17.8%) were studied by differential scanning calorimetry (DSC) under various medium conditions. From DSC curves, many DSC characteristics including denaturation temperature (T _d), enthalpy change (ΔH) and the width at half peak height (ΔT _1/2) of endothermic peaks were obtained and evaluated. The DSC curves of various buckwheat proteins (BWPs) in the 0.05 M phosphate buffer (pH 7.0) showed a major endotherm at about 102°C and a minor endotherm at about 80°C, attributed to thermal transitions of 13S and 8S globulins, respectively. T _d and ΔH of the globulins of BWPs were independent of their lipid contents, while the presence of high lipid content (17.8%) to some extent increased the ΔT _1/2. The progressive increase in T _d of 13S globulins with increase in NaCl concentration, suggests a more compact conformation with higher thermal stability. The influence of chaotropic salts on the DSC characteristics of 13S globulins was also independent of their lipid contents. Thermal analysis of the 13S globulins in the presence of protein perturbants (including urea, sodium dodecyl sulfate, ethylene glycol, dithiothreitol and N-ethylmaleimide) indicated that hydrophobic and hydrogen bondings are the major interactions for stabilizing protein conformation of buckwheat 13S globulins and the SS-SH interchange also attributes to the stabilization of the protein conformation.     

Thermogravimetrische Untersuchung von Seltenerdbromid—Tetrahydrofuran-Verbindungen

Zusammenfassung Die TetrahydrofuranverbindungenMBr₃·4THF (M=La, Ce, Pr),MBr₃·3,5THF (M=Nd bis Er einschließlich Y) undMBr₃·3THF (M=Tm, Yb, Lu) wurden thermogravimetrisch untersucht. Die Solvate von La, Ce und Pr ergaben hierbei VerbindungenMBr₃·THF, das von Sm eine der FormelMBr₃·0,5THF; NdBr₃·3,5THF zeigte ein Übergangsverhalten. Die übrigen Verbindungen gaben die Solvensmolekeln weitgehend in einem ab. Bei den Solvaten von Tm-, Yb- und Lu-Bromid erfolgte dieTHF-Abgabe gleichzeitig mit der Bildung von Oxidbromid, bei allen anderen trat solvatfreies Bromid als Stufe auf, welches besonders leicht bei Ce und bei den Yttererd-bromiden bei höherer Temperatur in Oxidbromid überging. EuBr₃ zerfield oberhalb 220° in EuBr₂ und Brom.

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The tetrahydrofuran compoundsMBr₃·4THF (M=La, Ce, Pr),MBr₃·3,5THF (M=Nd to Er including Y) andMBr₃·3THF (M=Tm, Yb, Lu) were subjected to thermogravimetric analysis. The solvates of La, Ce and Pr gave compoundsMBr₃·THF, the Sm-compound one of the formulaMBr₃·0,5THF; NdBr₃·3,5THF behaved in a transitory manner. The rest of the bromide compounds evolvedTHF more or less in one stage. The solvates of Tm-, Yb- and Lu-bromide yielded the solvens under simultaneous formation of oxide bormide, all the others showed a plateau of solvent-free bromide which at higher temperatures, especially with Ce and the higher lanthanides, was converted to oxide bromide. EuBr₃ decomposed above 220° into EuBr₂ and bromine.

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Herrn Prof. Dr. Dr. h. c.F. Wessely zum 70. Geburtstag gewidmet.     

Preparation,infrared spectra and differential thermal analyses of rare-earth dithiodiacetates

Dithiodiacetates of the rare-earths of the general formulaMH(DTDA)₂·2H₂O, whereM=La, Ce, Pr, Nd, Sm, Ho, and Y, and H₂ DTDA=dithiodiacetic acid, have been prepared and characterised by analyses, i.r. and differential thermal analysis. The i.r. data show that the bonding of the carboxylate group to the metal ion is bidentate. The i.r. andDTA studies reveal the presence of one water molecule in the coordination sphere. A coordination number of nine is suggested for the rare-earth metal ion in these compounds.With 2 Figures     

Herstellung von Seltenerdcyaniden

Zusammenfassung Seltenerd-cyanoargentateM[Ag(CN)₂]₃ wurden hergestellt (M=La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er und Y), die aus wäßriger Lösung mit 3–4 Mol H₂O kristallisieren. Pr-cyanoargentat wurde entwässert und mit Li reduziert; hierbei konnte das in Tetrahydrofuran (THF) unlösliche Pr(CN)₃ im Gemisch mit anderen Stoffen erhalten werden. Da sich LiCN als inTHF löslich erwies, wurde die Herstellung aus AgCN und Li inTHF in Gegenwart von Naphthalin verbessert. LiCN wurde mit Seltenerdbromid-THF-Solvaten inTHF umgesetzt; hierbei fielen die bisher unbekannten einfachen Erdcyanide aus, die sehr zersetzlich sind und nach dem Trocknen die ZusammensetzungM(CN₃)· ·2THF besaßen (M=Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm Yb, Lu und Y). Die Umsetzung verläuft bei den Verbindungen der Ceriterden schwieriger als bei denen der Yttererden; die Cyanide von La und Ce wurden nur mit überschüssigemTHF erhalten.

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Rare-earth cyanoargentatesM[Ag(CN)₂]₃ were prepared (M=La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er and Y), crystallising from aqueous solution with 3–4 moles of water. Pr-cyanoargentate was dehydrated and reduced with Li yielding some Pr(CN)₃, insoluble in tetrahydrofurane (THF), in mixture with other substances. Because LiCN proved to be soluble inTHF, the preparation from AgCN and Li inTHF in the presence of naphthalene was refined. LiCN was reacted with rare-earth bromide-THF-solvates inTHF, whereupon precipitation occured of the hitherto unknown, very sensitive to moisture simple rareearth cyanides, which after drying had the compositionM(CN)₃· ·2THF (M=Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu and Y). The reaction is more difficult with the lighter lanthanon bromides than with the heavier ones; the cyanides of La and Ce were prepared only with excessTHF.

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Preparation and Thermal Decomposition of Solid-state Cinnamates of Lighter Trivalent Lanthanides

Some new compounds of cinnamic acid with lighter trivalent lanthanides were prepared in the solid state. The compounds have general formula ML₃ H₂ O, where L is cinnamate (C₆ H₅ –CH=CH–COO^– ) and M is La, Ce, Pr, Nd or Sm. Thermogravimetry, derivative thermogravimetry, differential scanning calorimetry, infrared absorption spectra and X-ray diffraction powder patterns were used to characterize and to study the thermal stability and thermal decomposition of these compounds. This revised version was published online in July 2006 with corrections to the Cover Date.     

Herstellung von Tetrahydrofuranverbindungen der Seltenerdchloride

Zusammenfassung Die wasserfreien Chloride der Seltenerdmetalle geben mit Tetrahydrofuran (THF) stabile, kristalline Verbindungen, von denen folgende hergestellt wurden: MeCl₃·1,4–1,5THF (Me=La, Ce), MeCl₃·2THF (Me=Pr, Nd, Sm, Gd), MeCl₃·3,3–3,6THF (Me=Dy, Ho, Er, Y) und YbCl₃·2,9THF. Die Löslichkeiten inTHF wurden bestimmt; sie liegen entsprechend den unterschiedlichen Bodenkörpertypen auf verschiedenen Kurvenzügen.

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The anhydrous chlorides of the rare earth elements form stable crystalline compounds with tetrahydrofurane (THF). The following compounds were prepared: MeCl₃·1,4–1,5THF (Me=La, Ce), MeCl₃·2THF (Me=Pr, Nd, Sm, Gd), MeCl₃·3,3–3,6THF (Me=Dy, Ho, Er, Y) and YbCl₃·2,9THF. Their solubilities inTHF were determined. Two different curves are obtained, corresponding to different compositions of the solid phases in equilibrium with the solutions.

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