Automatic simulation of electrochemical transients by the adaptive Huber method for Volterra integral equations involving Kernel terms exp[?α(t ? τ)]erex{[β(t ? τ)]1/2} and exp[?α(t ? τ)]daw {[β(t ? τ)]1/2}

Development of fully automatic methods for the simulation of transient experiments in electroanalytical chemistry is a desirable element of the contemporary trends of laboratory automation in electrochemistry. In accord with this idea, the adaptive Huber method, elaborated by the present author, is intended to solve automatically integral equations of Volterra type, encountered in the theory of controlled-potential transients. The coefficients of the method have been recently obtained for integral transformation kernels involving terms K(t, τ) = exp[−α(t − τ)]erex{[β(t − τ)]^1/2} and K(t, τ) = exp[−α(t − τ)]daw{[β(t − τ)]^1/2} with α ≥ 0 and β ≥ 0, which are known to occur in the above integral equations. In this work the validity of the resulting method, for electrochemical simulations, is examined using representative examples of electroanalytical models involving integral equations with various special cases of such kernel terms. The performance of the method is found similar to that previously reported for integral equations involving exclusively kernels K(t, τ) = 1, K(t, τ) = (t − τ)^−1/2, and K(t, τ) = exp[−λ (t − τ)](t − τ)^−1/2 with λ > 0.     

Sequestering Ability of Dicarboxylic Ligands Towards Dioxouranium(VI) in NaCl and KNO<Subscript>3</Subscript> Aqueous Solutions at <Emphasis Type="Italic">T</Emphasis>=298.15 K

The formation constants of dioxouranium(VI)-2,2′-oxydiacetic acid (diglycolic acid, ODA) and 3,6,9-trioxaundecanedioic acid (diethylenetrioxydiacetic acid, TODA) complexes were determined in NaCl (0.1≤I≤1.0 mol⋅L⁻¹) and KNO₃ (I=0.1 mol⋅L⁻¹) aqueous solutions at T=298.15 K by ISE-[H⁺] glass electrode potentiometry and visible spectrophotometry. Quite different speciation models were obtained for the systems investigated, namely: ML⁰, MLOH⁻, ML₂²⁻, M₂L₂(OH)⁻, and M₂L₂(OH)₂²⁻, for the dioxouranium(VI)–ODA system, and ML⁰, MLH⁺, and MLOH⁻ for the dioxouranium(VI)–TODA system (M=UO₂²⁺ and L = ODA or TODA), respectively. The dependence on ionic strength of the protonation constants of ODA and TODA and of both metal-ligand complexes was investigated using the SIT (Specific Ion Interaction Theory) approach. Formation constants at infinite dilution are [for the generic equilibrium pUO₂²⁺+q(L²⁻)+rH⁺ ⇌(UO₂²⁺) _p (L) _q H _r ^(2p−2q+r);β _pqr ]: log ₁₀ β ₁₁₀=6.146, log ₁₀ β ₁₁₋₁=0.196, log ₁₀ β ₁₂₀=8.360, log ₁₀ β ₂₂₋₁=8.966, log ₁₀ β ₂₂₋₂=3.529, for the dioxouranium(VI)–ODA system and log β ₁₁₀=3.636, log ₁₀ β ₁₁₁=6.650, log ₁₀ β ₁₁₋₁=−1.242 for dioxouranium(VI)–TODA system. The influence of etheric oxygen(s) on the interaction towards the metal ion was discussed, and this effect was quantified by means of a sigmoid Boltzman type equation that allows definition of a quantitative parameter (pL ₅₀) that expresses the sequestering capacity of ODA and TODA towards UO₂²⁺; a comparison with other dicarboxylates was made. A visible absorption spectrum for each complex reaching a significant percentage of formation in solution (KNO₃ medium) has been calculated to better characterize the compounds found by pH-metric refinement.     

Solvation Structure and Complexation of the Manganese(II) Ion in N,N-Dimethylpropionamide and N,N,N′,N′-Tetramethylurea Studied by Means of Titration Calorimetry and Raman Spectroscopy

Aprotic N,N-dimethylpropionamide (DMPA) and N,N,N′,N′-tetramethylurea (TMU) are both strong donor solvents and coordinate to metal ions through the carbonyl oxygen atom. These solvents show a different conformational aspect in the bulk phase, i.e., DMPA exists as either a planar cis or a nonplanar staggered conformer, while TMU exists in a single planar cis conformer. It has been established that the manganese(II) ion is solvated by five molecules in both solvents. Interestingly, although the planar cis conformer of DMPA is more favorable than the nonplanar staggered one in the bulk phase, the reverse is the case in the coordination sphere of the metal ion, i.e., a conformational change occurs upon solvation. To reveal the thermodynamic aspect of this conformational change, the complexation of Mn(II) with bromide ions in DMPA and TMU has been studied by titration calorimetry at 298 K. It was found that the Mn(II) ion forms mono-, di- and tri-bromo complexes in both solvents, and their formation constants, enthalpies and entropies were obtained. The Δ H∘₁ value for MnBr⁺ strongly depends on the solvent, i.e., it is positive (19.4 kJ-mol⁻¹) in DMPA and negative (−8.7 kJ-mol⁻¹) in TMU, whereas the Δ H^∘₂ and Δ H∘₃ values for the stepwise formation of MnBr₂ and MnBr₃⁻ are both small and negative. The enthalpy of transfer Δ_tH^∘ from DMPA to TMU, which is evaluated on the basis of the extrathermodynamic TATB assumption, is 25.5 kJ-mol⁻¹ for Mn²⁺ and −3.6 kJ-mol⁻¹ for MnBr⁺. These values indicate that the difference between the formation enthalpy of MnBr⁺ in the two solvents, Δ H^∘₁ (DMPA) – Δ H∘₁ (TMU), is mainly ascribed to the value of Δ_tH^∘(Mn²⁺). It is found that the metal ion is also five-coordinated in the monobromo complex, MnBr(DMPA)₄⁺ . The enthalpy for the conformational change of DMPA from its planar cis to the nonplanar staggered form is evaluated to be −11 and −5.5 kJ-mol⁻¹ for Mn(DMPA)₅^{2 +} and MnBr(DMPA)₄⁺, respectively. Note that these values are significantly smaller than the corresponding value (5.0 kJ-mol⁻¹) in the bulk phase. We thus conclude that, although steric hindrance among solvent molecules is reduced by replacing one DMPA of Mn(DMPA)₅^{2 +} with the relatively small bromide ion, DMPA molecules are still sterically hindered in the MnBr(DMPA)₄⁺ complex.     

Effect of Ionic Strength and Temperature on the Protonation of Oxidized Glutathione

The protonation constants for oxidized glutathione, H _i−1L^(4−i+1)−, K _i ^H=[H _i L⁽⁴⁻ⁱ⁾⁻]/[H _i−1L^(4−i+1)−][H⁺] i=1,2,…,6 have been measured at 5, 25 and 45 °C as a function of the ionic strength (0.1 to 5.4 mol⋅[kg(H₂O)]⁻¹) in NaCl solutions. The effect of ionic strength on the measured protonation constants has been used to determine the thermodynamic values (K _i ^H0) and the enthalpy (ΔH _i ) for the dissociation reaction using the SIT model and Pitzer equations. The SIT (ε) and Pitzer parameters (β ⁽⁰⁾, β ⁽¹⁾ and C) for the dissociation products (L⁴⁻, HL³⁻, H₂L²⁻, H₃L⁻, H₄L, H₅L⁺, H₆L²⁺) have been determined as a function of temperature. These results can be used to examine the effect of ionic strength and temperature on glutathione in aqueous solutions with NaCl as the major component (body fluids, seawater and brines).     

Phenomenological theory of the kinetics of ultrasonic emulsification

Summary A working model is given for the rate of ultrasonic emulsification, considering the dispersion at the interface (areaA) and the coagulations in the volumeV of the emulsion. A bimolecular coagulation leads to the equationc=c _∞tanhbt;c _∞=(Aα/Vβ)^1/2;b=(Aαβ/V)^1/2 while a monomolecular coagulation givesc=c _∞{1−exp (−at)};c _∞=Aα/Vβ;a=β. The experiments on the dependence of c_∞,a andb uponA andV favour the bimolecular coagulation. The results are satisfactorily explained on general theoretical grounds.

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Zusammenfassung Ein Arbeitsmodell für die Geschwindigkeit der Ultraschallemulgierung wird entwickelt, das Dispersion in der Grenzfl?che (Fl?cheA) und Koagulation im Volumen (V) der Emulsion annimmt. Eine bimolekulare Koagulation führt zu der Gleichung:c=c _∞ tanhbt;c _∞=(Aα/Vβ)^1/2;b=(Aαβ/V)^1/2, eine monomolekulare dagegen zu:c=c _∞{1−exp (at−)};c _∞=Aα/Vβ;α=β. Die Versuche über die Abh?ngigkeit vonc _∞,a undb vonA undV scheinen für bimolekulare Koagulation zu sprechen. Die Ergebnisse werden auf der Basis dieser einfachen theoretischen Grundlagen befriedigend erkl?rt.

     

Additivity Factors in the Binding of the Diethyltin(IV) Cation by Ligands Containing Amino and Carboxylic Groups at Different Ionic Strengths

Complex formation constants were determined potentiometrically (by a ISE-H⁺, glass electrode) in the systems, M²⁺ – L^z – H⁺ [M²⁺ = (C₂H₅)₂Sn²⁺, L^z = malonate, glycinate and ethylenediamine] at t = 25 ^∘C and 0.1 mol-L⁻¹≤ I/ ≤ 1 mol-L⁻¹ in NaCl_aq (0.1 mol-L⁻¹ ≤ I ≤ 0.75 mol-L⁻¹ for the ethylenediamine system). Thermodynamic values of formation constants, at infinite dilution, are [± 95% confidence interval, ^Tβ_pqr refer to the equilibrium, pM²⁺ + qL^z + rH⁺ = M_pL_qH_r^(2+z+r)]: for malonate, log₁₀ ^Tβ₁₁₀ = (5.47 ± 0.10); for glycinate, log₁₀ ^Tβ₁₁₀ = (9.54 ± 0.08), log₁₀ ^Tβ₁₁₁ = (12.97 ± 0.10); and for ethylenediamine, log₁₀ ^Tβ₁₁₀ = (10.47 ± 0.10), log₁₀ ^Tβ₁₂₀ = (16.17 ± 0.12) and log₁₀ ^Tβ₁₁₁ = (15.46 ± 0.10). The dependence on ionic strength of the formation constants was modeled by a simple Debye–Hückel type equation and by the SIT approach. By analyzing the stability of the species in the three different systems we found a simple additivity rule that can be expressed by the relationship: log₁₀ K = 6.46 n_N + 3.96 n_O − 0.60 (n_N²+ n_O²), with a mean deviation, ε(log₁₀ K) = 0.15 (K = equilibrium constant for the interaction of the organometal cation with the unprotonated or protonated ligand, n_N = number of amino groups and n_O = number of carboxylic groups of the ligand(s) involved in the formation reaction of complex species).     

Reentrant behavior of poly(vinyl alcohol)–borax semidilute aqueous solutions

 The reentrant behavior of Poly(vinyl alcohol) (PVA)–borax aqueous semidilute solutions with a PVA concentration of 20 g/l and borax concentrations varies from 0.0 to 0.20 M was investigated using dynamic light scattering (DLS) and dynamic viscoelastic measurements. Two (fast and slow modes) and three (fast, middle, and slow) relaxation modes of PVA semidilute aqueous solutions without and with the presence of borax, respectively, were observed from DLS measurements. The fast and middle relaxation modes were q ²-dependent (q is the scattering vector) characteristic of diffusive behavior; however, the slow modes were q ³-dependent, characteristic of intraparticle dynamics. The experimental results showed that the slow relaxation mode dominates the DLS relaxation. The DLS slow mode relaxation time, τ_s, and the viscoelastic modulus G′(ω) and G′′(ω) data had a similar trend and demonstrated reentrant behavior as the borax concentration was increased from 0.0 to 0.20 M, i.e. τ_s, G′(ω), and G′′(ω) fluctuated with increasing borax concentration. The excluded-volume effect of polymers, charge repulsion among borate ions bound on PVA molecules, and intermolecular cross-linking didiol–borate complexation caused an expansion of the polymer chain; however, the screening effect of free Na⁺ ions on the negative charge of the borate ions bound on PVA and intramolecular cross-linking didiol–borate complexation led to a shrinkage of the polymer chain. The reentrant behavior was the consequence of the balance between expansion and shrinkage of the PVA–borate complex. Received: 26 March 1999/Accepted in revised form: 3 September 1999     

The Hydrolysis of AuCl<Stack><Subscript>4</Subscript><Superscript>−</Superscript></Stack> and the Stability of Aquachlorohydroxocomplexes of Gold(III) in Aqueous Solution

The equilibria AuCl₄⁻+jOH⁻+kH₂O⇌AuCl_4−j−k (OH) _j (H₂O) _k ^k−1+(j+k)Cl⁻, β _jk (0≤j,k≤4) have been studied spectrophotometrically at 20 °C in aqueous solution. For I=2 mol⋅dm⁻³(HClO₄) the conventional constants, β _i ^*, of the equilibria, Au^*+iCl⁻ ⇌AuCl _i ^*, are equal to log ₁₀ β ₁^*=(6.98±0.08); log ₁₀ β ₂^*=(13.42±0.05); log ₁₀ β ₃^*=(19.19±0.09); and log ₁₀ β ₄^*=(24.49±0.07), where [AuCl _i ^*]=∑[AuCl _i (OH) _j (H₂O)_4−i−j ] at i=const. The hydrolysis and other transformations of AuCl₄⁻ in aqueous solution are discussed. On the basis of new and known data, a full set of equilibrium constants, β _jk , or their estimates has been obtained.     

Electron-pair radial density functions

We introduce and discuss a generalized electron-pair radial density function G(q; a) that represents the probability density for the electron-pair radius |r ₁+ar ₂| to be q, where a is a real-valued parameter. The density function G(q; a) is a projection of the two-electron radial density D ₂(r ₁, r ₂) along lines r ₁ + ar ₂ ± q = 0 in the r ₁ r ₂ plane onto a point in the qa plane, and connects three densities S(s), D(r), and T(t), defined independently in the literature, as a smooth function of a: For an N-electron (N ≥ 2) system, S(s) = G(s; + 1), D(r) = 2G(r; 0)/(N − 1), and T(t) = G(|t|;−1)/2, where S(s) and T(t) are the electron-pair radial sum and difference densities, respectively, and D(r) is the single-electron radial density. Simple illustrations are given for the helium atom in the ground 1s² and the first excited 1s2s ³S states.     

Solvent Effect on Deprotonation Equilibria of Acids of Various Charge Types in Non-aqueous Isodielectric Mixtures of Protic Ethylene Glycol and Dipolar Aprotic N,N-Dimethylformamide at 298.15 K

Deprotonation constants of phthalic (H₂A) and biphthalic (HA⁻) acids and of mono-protonated (BH⁺) and di-protonated (BH₂²⁺) piperazine acids have been determined at 25 °C by measuring the Emf of galvanic cells comprising H⁺-sensitive glass GE(H⁺) and Ag,AgCl electrodes in non-aqueous isodielectric mixtures of protic ethylene glycol (EG) and dipolar aprotic N,N-dimethylformamide (DMF). Solvent effects on deprotonation of the acids: ∂(ΔG _diss^o)=2.303RT[p(_s K _a)−p(_R K _a)], have been dissected into transfer Gibbs energies, ΔG _t^o _, of the species involved by evaluating ΔG _t^o of the uncharged phthalic acid and base piperazine (B) from the measured solubilities of the acid and base, respectively, and using ΔG _t^o of H⁺ based on the TATB reference electrolyte assumptions, as evaluated earlier. The contributions of the different species involved in the protolytic equilibria i.e., H⁺,H₂A,HA⁻,BH₂²⁺ and BH⁺ and their respective conjugate bases HA⁻,A²⁻,BH⁺ and B have been discussed in terms of their solvation behavior as guided by the ‘acid-base’, dispersion, structural and electronic characteristics of the acid-base species and of the co-solvent molecules and binary mixtures, ignoring the Born-type electrostatic interactions on the ionic species as the solvent system is quasi isodielectric.     

Interface microstructure and diffusion kinetics in diffusion bonded Mg/Al joint

The interface microstructure, formation of diffusion bonded joint and regulation of atom diffusion were studied by means of scanning electron microscope (SEM), energy dispersion spectroscopy (EDS) and electron probe microanalyser (EPMA). The experimental results indicated that an obvious interfacial transition zone was formed between Mg and Al, and there are three intermetallic layers Mg₁₇Al₁₂, MgAl and Mg₂Al₃ in this zone. Diffusion activation energy of Mg and Al in the above layers was lower than that in the Mg and Al base metals. The thickness (x) of each layer can be expressed as x ² = 4.14exp(−28780/RT)(t−t ₀), x ² = 31.4exp(−25550/RT)(t−t ₀) and x ² = 0.6exp(−22600/RT)(t−t ₀) corresponding to Mg₁₇Al₁₂, MgAl and Mg₂Al₃ with heating temperature (T) and holding time (t).     

Approximate solution of the autocatalytic hydrolysis of cellulose

Depolymerization of cellulose in homogeneous acidic medium is analyzed on the basis of autocatalytic model of hydrolysis with a positive feedback of acid production from the degraded biopolymer. The normalized number of scissions per cellulose chain, S(t)/n° = 1 − C(t)/C₀, follows a sigmoid behavior with reaction time t, and the cellulose concentration C(t) decreases exponentially with a linear and cubic time dependence, C(t) = C₀exp[−at − bt ³], where a and b are model parameters easier determined from data analysis.     

Potentiometric and Multinuclear Magnetic Resonance Study of the Solution Equilibria Between Aluminium(III) Ion and L-Aspartic Acid

Summary. Solution equilibria between aluminium(III) ion and L-aspartic acid were studied by potentiometric, ²⁷Al, ¹³C, and ¹H NMR measurements. Glass electrode equilibrium potentiometric studies were performed on solutions with ligand to metal concentration ratios 1:1, 3:1, and 5:1 with the total metal concentration ranging from 0.5 to 5.0 mmol/dm³ in 0.1 mol/dm³ LiCl ionic medium, at 298 K. The pH of the solutions was varied from ca. 2.0 to 5.0. The non-linear least squares treatment of the data performed with the aid of the Hyperquad program, indicated the formation of the following complexes with the respective stability constants log β_p,q,r given in parenthesis (p, q, r are stoichiometric indices for metal, ligand, and proton, respectively): Al(HAsp)²⁺ (log β_1,1,1 = 11.90 ± 0.02); Al(Asp)⁺ (log β_1,1,0 = 7.90 ± 0.03); Al(OH)Asp⁰ (log β_1,1,−1 = 3.32 ± 0.04); Al(OH)₂Asp⁻ (log β_1,1−2 = −1.74 ± 0.08), and Al₂(OH) Asp³⁺ (log β_2,1,−1 = 6.30 ± 0.04). ²⁷Al NMR spectra of Al³⁺ + aspartic acid solutions (pH 3.85) indicate that sharp symmetric resonance at δ∼10 ppm can be assigned to (1, 1, 0) complex. This resonance increases in intensity and slightly broadens upon further increasing the pH. In Al(Asp)⁺ complex the aspartate is bound tridentately to aluminum. The ¹H and ¹³C NMR spectra of aluminium + aspartic acid solutions at pH 2.5 and 3.0 indicate that β-methylene group undergoes the most pronounced changes upon coordination of aluminum as well as α-carboxylate group in ¹³C NMR spectrum. Thus, in Al(HAsp)²⁺ which is the main complex in this pH interval the aspartic acid acts as a bidentate ligand with –COO⁻ and –NH₂ donors closing a five-membered ring.     

Potentiometric and Multinuclear Magnetic Resonance Study of the Solution Equilibria Between Aluminium(III) Ion and L-Aspartic Acid

Solution equilibria between aluminium(III) ion and L-aspartic acid were studied by potentiometric, ²⁷Al, ¹³C, and ¹H NMR measurements. Glass electrode equilibrium potentiometric studies were performed on solutions with ligand to metal concentration ratios 1:1, 3:1, and 5:1 with the total metal concentration ranging from 0.5 to 5.0 mmol/dm³ in 0.1 mol/dm³ LiCl ionic medium, at 298 K. The pH of the solutions was varied from ca. 2.0 to 5.0. The non-linear least squares treatment of the data performed with the aid of the Hyperquad program, indicated the formation of the following complexes with the respective stability constants log β_p,q,r given in parenthesis (p, q, r are stoichiometric indices for metal, ligand, and proton, respectively): Al(HAsp)²⁺ (log β_1,1,1 = 11.90 ± 0.02); Al(Asp)⁺ (log β_1,1,0 = 7.90 ± 0.03); Al(OH)Asp⁰ (log β_1,1,−1 = 3.32 ± 0.04); Al(OH)₂Asp⁻ (log β_1,1−2 = −1.74 ± 0.08), and Al₂(OH) Asp³⁺ (log β_2,1,−1 = 6.30 ± 0.04). ²⁷Al NMR spectra of Al³⁺ + aspartic acid solutions (pH 3.85) indicate that sharp symmetric resonance at δ∼10 ppm can be assigned to (1, 1, 0) complex. This resonance increases in intensity and slightly broadens upon further increasing the pH. In Al(Asp)⁺ complex the aspartate is bound tridentately to aluminum. The ¹H and ¹³C NMR spectra of aluminium + aspartic acid solutions at pH 2.5 and 3.0 indicate that β-methylene group undergoes the most pronounced changes upon coordination of aluminum as well as α-carboxylate group in ¹³C NMR spectrum. Thus, in Al(HAsp)²⁺ which is the main complex in this pH interval the aspartic acid acts as a bidentate ligand with –COO⁻ and –NH₂ donors closing a five-membered ring.     

Mechanisms and parameters of transients and oscillations of delayed chlorophyll fluorescence in the thylakoid membrane of the intact maize leaf

Standard induction processes of delayed fluorescence (DF) of chlorophyll (induction signals) occur when an intact leaf segment of maize inbreds and hybrids is initially kept in the phosphoroscope darkroom for more than 15 min (τ > 15 min), and then the leaf is illuminated with the intermittent white light and measured. Resolved induction processes of DF chlorophyll into transients: A, B, C, D, and E occur when the intact leaf segment of maize inbreds and hybrids is kept in the phosphoroscope darkroom for a significantly shorter period (30 s ≤ τ ≤ 240 s), with the time rate τ of 30 s, prior to its illumination with the intermittent white light. Induction transients: A, B, C, D, and E are characterised with their temporal parameters: t _A, t _B, t _C, t _D, and t _E, dynamics of changes in transients intensities and mechanisms of their generation. The induction processes of chlorophyll DF of the intact leaf of maize inbreds and hybrids resolved into transients: A, B, C, D, and E are accompanied by the occurrence and different levels of activation energy (E _a, kJ mol⁻¹) that correspond to different critical temperatures. The generation mechanisms of induction transients: A, B, C, D, and E are classified into two groups. Transients A and B are of a physical character, while the transients: C, D, and E are of a chemical character. It is shown that the generation of the induction transients: B, C, D, and E simultaneously follows establishing of the oscillations of induction processes of the DF chlorophyll. Oscillating of induction processes of DF chlorophyll is explained by the ion (K⁺, Na⁺, H⁺, Cl⁻) transport mechanism across the thylakoid membrane of the intact leaf of maize inbreds and hybrids grown under conditions of air drought, increased temperatures and water deficiency in the medium. The article is published in the original.     

A criterion for the confluence of two seams of conical intersection in triatomic molecules

It is shown that the cross product t ^{I J} (R _x )≡g ^{I J} (R _x )×h ^{I J} (R _x ), where g _τ ^{I J} (R)=(c ^I (R _x )−c ^J (c ^I (R _x )+c ^J (R _x )), h _τ ^{I J} (R)=c ^I (R _x )^† c ^J (R _x ), τ is an internal nuclear coordinate, the c ^I (R) satisfy [H(R)−E _I (R)]c ^I (R)=0 and H(R) is the electronic Hamiltonian matrix, is a unique property of a conical intersection at R _x . t ^{I J} (R _x )=0 when R _x is located at the intersection of two (or more) seams of conical intersection. This criterion for an intersection of two seams of conical intersection has important implications for algorithms that seek to locate such points. Here it␣is␣used to analyze the trifurcation of a generic C_2v ^2S+1 A−^2S+1 B seam of conical intersection, analogous to those recently found in AlH₂ and CH₂. Received: 31 July 1997 / Accepted: 27 August 1997     

The forcing number of toroidal polyhexes

The forcing number, denoted by f(G), of a graph G with a perfect matching is the minimum number of independent edges that completely determine the perfect matching of G. In this paper, we consider the forcing number of a toroidal polyhex H(p,q,t) with a torsion t, a cubic graph embedded on torus with every face being a hexagon. We obtain that f(H(p,q,t)) ≥ min{p,q}, and equality holds for p ≤ q or p > q and t∈{ 0,p−q,p−q + 1,..., p−1}. In general, we show that f(H(p,q,t)) is equal to the side length of a maximum triangle on H(p,q,t). Based on this result, we design a linear algorithm to compute the forcing number of H(p,q,t).     

Critical Evaluation of Protonation Constants. Literature Analysis and Experimental Potentiometric and Calorimetric Data for the Thermodynamics of Phthalate Protonation in Different Ionic Media

The protonation constants of phthalate were determined in aqueous NaCl (0.1 ≤ I ≤ 5,mol⋅L⁻¹) and in aqueous Me₄NCl (0.1 mol⋅L⁻¹ ≤ I ≤ 3,mol⋅L⁻¹) at t = 25,^∘C. Experimental data were employed in conjunction with literature data from studies in different ionic media (Et₄NI: 0 ≤ I ≤ 1,mol⋅L⁻¹; NaClO₄: 0.05 mol⋅L⁻¹ ≤ I ≤ 2,mol⋅L⁻¹)to study the dependence on ionic strength using different models, such as the SIT and Pitzer equations, and an Extended Debye-Hückel type equation. Experimental calorimetric data in NaCl and protonation constants at different temperatures in Et₄NI (5 ≤ t ≤ 45^∘C) and in NaClO₄ (15 ≤ t ≤ 35 ^∘C) were also used to study their dependence on temperature. Recommended equilibrium data are reported together with a short discussion of a prospective protocol for drawing these data.     

Bioaccumulation and biosorption of stable strontium and <Superscript>90</Superscript>Sr by <Emphasis Type="Italic">Oscillatoria homogenea</Emphasis> cyanobacterium

The ability of living filamentous cells of the cyanobacterium Oscillatoria homogenea to separate stable strontium and ⁹⁰Sr from aqueous solution is demonstrated in this study. On a basis of filamentous cell biovolume, the removal were 43.78 nM·ml·(mm³)⁻¹ and 3129.48 mBq·ml·(mm³)⁻¹ after 240 hour incubation. The optimum pH for strontium uptake is 9±0.3. The increasing biovolume of the blue-green alga elevates sorption. In the liquid culture containing 21.2 mm³·ml⁻¹ filamentous cells and 1000 nM·ml⁻¹ initial strontium concentration, the maximum strontium removal was 455.34 nM·ml·(mm³)⁻¹. At 1200 Lux illumination, the maximum removal value was 58.62 nM·ml·(mm³)⁻¹, and at the initial strontium concentration of 6590 nM·ml⁻¹, 235.40 nM·ml·(mm³)⁻¹ removal was observed. The experimental data fitted to Langmuir isotherm and the model parameters and correlation coefficient (R ²) were q _max = 7.143 μg·(mm³)⁻¹, b = 0.003 and 0.99, respectively.     

Kinetic Analysis of Thermal Decomposition of Ca(OH)2 Formed During Hydration of Commercial Portland Cement by DSC

In this paper, evaluation of kinetic parameters (the activation energy – E,the pre-exponential factor – A and the reaction order – n) with simultaneous determination of the possible reaction mechanism of thermal decomposition of calcium hydroxide (portlandite), Ca(OH)₂ formed during hydration of commercial Portland-slag cement, by means of differential scanning calorimetry (DSC) in non-isothermal conditions with a single heating–rate plot has been studied and discussed. The kinetic parameters and a mechanism function were calculated by fitting the experimental data to the integral, differential and rate equation methods. To determine the most probable mechanism, 30 forms of the solid-state mechanism functions, f(α_c) have been tried. Having used the procedure developed and the appropriate program support, it has been established that the non-isothermal thermal decomposition of calcium hydroxide in the acceleratory period (0.004<α_c<0.554) can be described by the rate equation: d α_c/dT=A/βexp(−E/RT)f(α_c), which is based on the concept of the mechanism reaction:f(α_c)=2(α_c)^1/2. The mechanism functions as well as the values of the kinetic parameters are in good agreement with those given in literature. This revised version was published online in August 2006 with corrections to the Cover Date.