Complexation Constants Research Articles

Исследование комплексообразующих свойств монопроизводных янтарной кислоты с ионами меди (II) и никеля (II).

Mono-derivatives of alkenyl succinic acid are considered in this paper, also their complexes with copper and nickel ions, which structure was studied by IR spectrometry method. Protonization constants and stability constants of complexes of mono-derivatives of succinic acid with copper and nickel ions are calculated by pH-metric titration method. It has been established, that mono-derivatives of succinic acid formed more stable complexes with the copper ion.

Synthesis, Characterization, and Biological Evaluation of Osmium(IV) Pyrazole Carbothioamide Complexes

Osmium(IV) pyrazole carbothioamide complexes with different substituted pyrazole carbothioamide heterocyclic ligands have been synthesized and characterized. The ligands have been characterized using 1H-NMR, 13C-APT, LC-MS, elemental analysis, and IR spectroscopy. Whereas, osmium(IV) compounds have been characterized using ESI-MS, ICP-OES, IR spectroscopy, magnetic, and conductance measurements. The compounds have been evaluated for various biological activities. The binding constant of ligands and complexes have been found in the range of 1.2–3.6 × 104 and 1.2–6.8 × 104 M−1, respectively. The docking energy values of complexes have been found in the range of −286.28 to −326.49 kJ/mol. The K sv and K f values of Os(IV) compounds evaluated using fluorescence quenching activity have been found in the range of 4.7–9.2 × 103 and 1.3–7.6 × 103 M−1, respectively. The minimum inhibitory concentration of osmium(IV) compounds and ligands have been found in the range of 50–75 µM and 120–135 µM, respectively. The LC50 values evaluated using brine shrimp lethality assay of osmium(IV) compounds and ligands have been found in a range of 7.52–16.12 µg/mL and 15.80–20.03 µg/mL, respectively.

Phase constants in the Fock–Goncharov quantum cluster varieties

A cluster variety of Fock and Goncharov is a scheme constructed by gluing split algebraic tori, called seed tori, via birational gluing maps called mutations. In quantum theory, the ring of functions on seed tori are deformed to non-commutative rings, represented as operators on Hilbert spaces. Mutations are quantized to unitary maps between the Hilbert spaces intertwining the representations. These unitary intertwiners are described using the quantum dilogarithm function $$\Phi ^\hbar $$ . Algebraic relations among classical mutations are satisfied by the intertwiners up to complex constants. The present paper shows that these constants are 1. So the mapping class group representations resulting from the Chekhov–Fock–Goncharov quantum Teichmüller theory are genuine, not projective. During the course, the hexagon and the octagon operator identities for $$\Phi ^\hbar $$ are derived.

A comprehensive study of the sorption mechanism and thermodynamics of f-element sorption onto K-feldspar

The mobility of heavy metal contaminants and radionuclides in the environment is directly controlled by their interactions with charged mineral surfaces, hence an assessment of their potential toxicity, e.g. in the context of radioactive waste disposal sites, requires understanding of sorption processes on the molecular level. Here, we investigate the sorption of a variety of rare earth elements (REE) and trivalent actinides (Am, Cm) on K-feldspar using batch sorption, time-resolved laser-induced fluorescence spectroscopy (TRLFS), and a surface complexation model. Initially, a reliable pKa for K-feldspar’s surface deprotonation reaction was determined as 2.5 ± 0.02 by column titration experiments, in excellent agreement with a measured pHIEP of 2.8. Batch sorption experiments over a broad range of experimental conditions in terms of mineral grain size, pH, [M3+], ionic radius, solid/liquid ratio, ionic strength, and equilibration procedures were carried out to quantify macroscopic retention. The trivalent d-block element Y, early, mid, and late lanthanides (La, Eu, Nd, Lu), as well as two minor actinides (Am, Cm) were used for batch sorption experiments and showed similar pH dependent uptake behavior, underlining their chemical analogy. In parallel, spectroscopic investigations provided insight into surface speciation. Cm TRLFS spectra indicate the formation of three inner-sphere sorption complexes with increasing hydrolysis. Additionally, a ternary K-feldspar/Cm/silicate complex was found for pH > 10, and batch and spectroscopic data at low pH (<4) point to small amounts of outer sphere sorption complexes. Based on TRLFS data, batch sorption, and titration data, a generic geochemical sorption model was developed, that describes sorption edges for all investigated M3+/K-feldspar systems satisfactorily. The derived stability constants for the binary sorption complexes (logK1-4 = −3.6, −7.7, −11.5, and −17.4, respectively) could successfully be used to reproduce literature data. The stability constants obtained for the surface complexes were included into the database for the Smart Kd-concept, which will further improve the safety assessment of potential repositories for radioactive waste.

Deploying hydrogen bond donor/acceptor on arylethynyl scaffold II: Urea based tripodal ionophores for polymeric membrane nitrate selective electrodes

Along the line for developing ionophores by deploying hydrogen bond donor/acceptor on arylethynyl acaffold, two tripodal urea receptors were used as ionophores for the first time to fabricate polymeric membrane nitrate-selective electrodes. Replacing the hydrogens with fluorine atoms in the arylethynyl core facilitates the selectivity for nitrate over halides, originating from the additional anion–π interactions electron between nitrate and deficient fluorinated core. By optimizing membrane composition such as plasticizers and lipophilic additives, the proposed ISEs showed Nernstian response to nitrate with superior selectivity to both lipophilic ions and halides. Although the formation constants of anions-ionophore complex in membrane phase did not correlate well with the selectivity pattern of the ISEs, these data were consistent with that in solvent such as binary DMSO/CHCl3. The proposed ISEs could work in wide pH range solutions with short response time, good reversibility and reproducibility, which led to the success of determination of nitrate in real mineral water, tap water, as well as river water samples.

Germanium fractions in typical paddy soil and its interaction with humic substances.

Ge and Si differ strongly in their biogeochemical behavior due to the differences in binding capacity to organic matter. The mechanisms of soil organic matter affecting the mobility and bioavailability of Ge in soil-plant system remain unclear. This work aimed to investigate the soil Ge fractions and Ge binding to humic substances in paddy soil. Paddy soil samples taken from Changxing County, Zhejiang Province, China, were investigated by the sequential extraction method. Humic acid (HA) and fulvic acid (FA) isolated from paddy soils were characterized by Fourier transform infrared spectrometry (FT-IR) and 3-dimensional excitation-emission matrix (3D-EEM). The effect of humic substances on the binding of Ge was studied by fluorescence-quenching titration. Results showed that residual Ge was the dominant fraction in soil (up to 85%). The mobile Ge, organic matter bound Ge and easily reduceable compounds bound Ge accounted for approximately 10% of soil TGe and may represented critical labile pools of soil Ge. Organic matter bound Ge significantly correlated (r = 0.56, p < 0.01) with rice Ge concentrations. The fluorescence of HA and FA was markedly quenched by the addition of Ge. The conditional stability constant of HA-Ge complexes was larger than that of FA-Ge complexes, and the complexation capacity of HA-Ge complexes was lower than that of FA-Ge complexes. Humic substances played a dual role in affecting the behavior of dissolved Ge in paddy soil. HA formed stable complexes with Ge and tended to sequester Ge, while FA formed soluble and unstable complexes with Ge and tended to act as a Ge carrier in soil-plant system.

A Population Pharmacokinetic Model for Concizumab Based on Phase 1 and Phase 2 Trial Data

Introduction Concizumab is a high-affinity anti-tissue factor pathway inhibitor (TFPI) monoclonal antibody in clinical investigation for the subcutaneous (SC) treatment of patients with hemophilia. The data generated from phase 1 and 2 concizumab trials have been used to develop a population pharmacokinetic (PK) model with the aim of supporting dose selection for phase 3 trials. WMethods The objective of this study was to develop a model to describe the PK of concizumab across administration routes in various groups of patients with hemophilia to generate a generally applicable population PK model of concizumab. The model was developed based on available PK data from four phase 1 trials (for both intravenous [IV] and SC concizumab administration) and two phase 2 trials (for SC concizumab administration). Trial populations in the phase 1 trials included both healthy subjects and patients with hemophilia, whilst the phase 2 trials enrolled patients with hemophilia A or B with inhibitors and patients with hemophilia A without inhibitors. A structural population PK model was first developed based on phase 1 data and the final population PK model was then estimated using data from both phase 1 and phase 2 trials. Simulations were performed for phase 3 concizumab exposure using a full parametric simulation (n=10,000), including both inter-individual and intra-individual variability for the selected population. Randomly sampled body weights from a normal distribution with mean and variance corresponding to body weight distribution from phase 2 trials were used to simulate patient profiles. WResults The population PK dataset used for the model comprised 1,504 observations from 119 subjects (89 patients and 30 healthy individuals), with a mean age of 35 years (range: 18-65 years) and mean body weight of 74.4 kg (range: 47.1-130 kg). The PK model parameters were first estimated based on phase 1 data alone, and after fixing the majority in order to ensure robustness of the model only a few parameters were re-estimated based on phase 1 and 2 data combined. The PK model (Figure 1) was evaluated by standard goodness-of-fit plots and qualification assessments. Using visual predictive checks, it was shown that the model was able to reproduce the median and the 5th and 95th percentiles of the observed concizumab concentrations from phase 1 and 2 trials, and so it was deemed suitable for simulation purposes. The PK model suggested a target-mediated drug disposition following concizumab binding to TFPI at the endothelium, and subsequent elimination of the complex to account for the non-linear elimination. WConclusions The developed model accurately described the PK of concizumab delivered at a wide dose range by either SC or IV administration to both healthy subjects and patients with hemophilia A or B with and without inhibitors. The model was used for simulations to select the dosing regimen for subsequent phase 3 studies. Figure 1. Concizumab pharmacokinetic model. Structure of the final concizumab PK model for SC and IV dosing with target-mediated drug disposition via the endothelial TFPI. CL, clearance; doseiv, intravenous dose; dosesc, subcutaneous dose; IV, intravenous; ka, absorption rate constant; kcom, elimination rate constant of the concizumab-TFPI complex; kon and koff, rate constants for binding of concizumab to the endothelial TFPI; ktr, rate constant from the transit compartment; Q, inter-compartmental clearance; Rtot, amount of endothelial TFPI available for concizumab binding; SC, subcutaneous; TFPI, tissue factor pathway inhibitor; V, volume. Figure Disclosures Høyer Rose: Novo Nordisk A/S: Current Employment, Divested equity in a private or publicly-traded company in the past 24 months. Hollensen:Novo Nordisk: Current Employment, Current equity holder in private company, Current equity holder in publicly-traded company. Agersø:Novo Nordisk A/S: Current Employment. Viig Overgaard:Novo Nordisk A/S: Current Employment, Current equity holder in publicly-traded company.

DFO@EVOH and 3,4-HP@EVOH: Towards New Polymeric Sorbents for Iron(III)

The paper presents the synthesis and preliminary characterization of two novel solid-phase sorbents for iron(III), resulting from the functionalization of ethylene-vinyl alcohol copolymer (EVOH) with deferoxamine, DFO (DFO@EVOH), and a novel tripodal 3-hydroxy-4-pyridinone, named 3,4-HP (3,4-HP@EVOH). DFO and 3,4-HP have been covalently bonded to EVOH, using carbonyldiimidazole as a coupling agent. Before their use as Fe(III) sorbents, they were warm-pressed to obtain a thin film. Polymers have been characterized by conventional physico-chemical techniques; furthermore, the sorption properties towards Fe(III) were investigated. The physico-chemical characterization of the new solid-state devices demonstrates the effective linkage of the two receptors on the polymeric support. Despite a relatively low sorption capacity for both materials, the stoichiometry and the complexation constants of Fe(III)/DFO@EVOH and Fe(III)/3,4-HP@EVOH are in pretty good agreement with those obtained for the same ligands in aqueous solutions.

A novel dibenzimidazole-based fluorescent probe with high sensitivity and selectivity for copper ions

A novel fluorescence probe TPA-BMZ for Cu2+, based on intramolecular charge transfer, was designed and synthesized. Probe was composed of triphenylamine as the fluorophore and benzimidazole derivative as the receptor. AFM measurement exhibits that TPA-BMZ possess an amorphous state without any crystallization, which benefits to its long-term stability due to application. Meanwhile, its optical character was studied and the results shown that TPA-BMZ could be used to recognize cupric ions in consequence of intramolecular charge transfer (ICT) and it even could be used to detect the presence of cupric ions in seawater. The Job’s plot curve demonstrated the molar ratio of probe to copper is 1:1. Moreover, from the fluorescence titration spectrum of copper ions to probe, the limit of detection of probe is obtained (0.094 μM) and the complex constant is 6.57 × 10−8 M−1 which shows a high sensibility towards copper ions. In addition, probe was also used to detect copper ions in tap water, river water and seawater which demonstrated a potential application in seawater. More importantly, the response time of the probe to copper ions is within 1 s.

Correlation complexation constants of Ce4+ and F−

Measured CeFn (n=1, 2, 3) complexation constant and solubility product constant of CeF4 and Na2CeF6 by ICP-AES and UV spectrophotometer, when Ce4+ and F− complexation reaction in water medium and nitric acid medium respectively, and the effects of Re3+and nitric acid concentration on Ce4+ and F− complexation reaction were studied. The experimental results show that the first-order complexation constant of Ce4+ and F− is CeF3 +=6.94*106, the second-order complexation constant is CeF2 2+=4.541*1011, and the third-order complexation constant is CeF3 +=6.232*1014. Compared with the complexation reaction of Ce4+ and F− in water medium and nitric acid medium, the complexation reaction of Ce4+ and F− in nitric acid medium is better. Re3+ appears, which affects the complexation reaction between Ce4+ and F−. When in nitric acid medium, the higher the concentration of nitric acid, the more unfavorable the complexation of Ce4+ and F−. The study of the relevant physical constants of Ce4+ and F− in this paper can be helpful for the separation of Ce4+ and F−, enrich the physical and chemical information of rare earth elements, and provide the basic theoretical basis for the rare earth fluoride that is difficult to be separated and recovered from the tailings, so as to reduce the harm to the soil environment.

Polymeric Membrane Fluoride-Selective Electrodes Using Lewis Acidic Organo-Antimony(V) Compounds as Ionophores.

Four Lewis acidic organo-antimony(V) compounds with strong binding affinity to fluoride were used for the first time as ionophores to fabricate polymeric membrane fluoride-selective electrodes. Improved detection limits and significant anti-Hofmeister selectivity could be achieved by optimizing ionophores, lipophilic additives, and plasticizers. Membrane electrodes fabricated with tetrakis-(pentafluorophenyl)stibonium (ionophore 2) performed best in detection limit, sensitivity, and selectivity. Optimal performance was obtained by fluoride with a slope of -59.5 mV/decade in the linear range of 1 × 10-5 to 4 × 10-2 M and a detection limit of 5 × 10-6 M. Studies on the influence of sample solution pH demonstrate that the best pH for fluoride determination is pH 3.0. All of the electrodes studied respond rapidly (in 1 min) in different concentrations of fluoride solutions. The anion-ionophore complex constants in the membrane phase determined using the segmented sandwich membrane method correlate well with the solution-phase binding data and determined selectivity sequence of the ion-selective electrodes. The possibility of real life application of the optimized electrodes was assessed by determination of fluoride concentrations in tap water.

Interactions of galeterone and its 3-keto-Δ4 metabolite (D4G) with one of the key enzymes of corticosteroid biosynthesis - steroid 21-monooxygenase (CYP21A2).

We have investigated interactions of galeterone and its pharmacologically active metabolite - 3-keto-Δ4-galeterone (D4G) - with one of the key enzymes of corticosteroid biosynthesis - steroid 21-monooxygenase (CYP21A2). It was shown by absorption spectroscopy that both compounds induce type I spectral changes of CYP21A2. Spectral dissociation constants (KS ) of complexes of CYP21A2 with galeterone or D4G were calculated as 3.1±0.7μm and 4.6±0.4μm, respectively. It was predicted by molecular docking that both ligands similarly bind to the active site of CYP21A2. We have revealed using reconstituted monooxygenase system that galeterone is a competitive inhibitor of CYP21A2 with the inhibition constant (Ki ) value of 12±3μm, while D4G at the concentrations of 10 and 25μm does not inhibit the enzyme. Summarizing, based on the in vitro analyses we detected inhibition of CYP21A2 by galeterone and lack of the influence of D4G on this enzyme.

Supramolecular Assemblies Constructed from Cucurbit[8]uril and N‐Alkyl Carboxymethylbenzotriazole through Host‐Guest Interactions

AbstractDifferent supramolecular self‐assembly between 1‐dodecyl‐3‐carboxymethylbenzotriazole (Lc12), 1‐octyl‐3‐carboxymethylbenzotriazole (Lc8) and 1‐butyl‐3‐carboxymethylbenzotriazole (Lc4) in the solid state and in aqueous solution has been investigated. For Lc12@CB[8] system, 1 : 1 host‐guest complexes were formed in aqueous solution and 2 : 2 host‐guest complexes were formed in the solid state, and the dodecyl chains adopted contorted conformations when bound to CB[8] molecules. For Lc8@CB[8] system, 1 : 1 host‐guest complexes were formed both in aqueous solution and in solid state, and the alkyl chain and benzotriazole moiety of guest Lc8 were both squeezed into the cavity of the CB[8]. The Lc4@CB[8] system was similar to Lc8@CB[8], 1 : 1 host‐guest complexes were formed in aqueous solution, the alkyl chain and benzotriazole moiety of guest Lc4 were encapsulated into the cavity of the CB[8]. Isothermal titrations in water afforded high apparent association constants for complexes Lc12@CB[8], Lc8@CB[8]and Lc4@CB[8].

Aquation and Anation Kinetics of Rhenium(I) Dicarbonyl Complexes: Relation to Cell Toxicity and Bioavailability.

The aquation reactions of four rhenium(I) dicarbonyl complexes, [Re(CO)2(NN)(PR3)(Cl)], where NN = 1,10-phenanthroline (Phen) and 2,9-dimethyl-1,10-phenanthroline (DMPhen) and PR3 = 1,3,5-triaza-7-phosphaadamantane (PTA) and 1,4-diacetyl-1,3,7-triaza-5-phosphabicylco[3.3.1]nonane (DAPTA). Additionally, the anation reactions of the corresponding aqua complexes with Cl- were investigated. Single crystals of [Re(CO)2(DMPhen)(PTA)(Cl)]·DMF and [Re(CO)2(DMPhen)(DAPTA)(Cl)] were obtained, and their structures were determined using X-ray diffraction. The Re-Cl interatomic distances are 2.4991(13) and 2.4922(6) Å, respectively, indicating a mild trans influence effect of the phosphine ligands. The rate constants, kaq, for the aquation reactions of these complexes spanned a range of (3.7 ± 0.3) × 10-4 to (15.7 ± 0.3) × 10-4 s-1 with the two Phen complexes having rate constants that are 2.5 times greater than those of the DMPhen complexes at 298 K. Similarly, the second-order anation rate constants (kCl) of the resulting aqua complexes, [Re(CO)2(NN)(PR3)(H2O)]+, with Cl- ions at 298 K varied between (2.99 ± 0.05) × 10-3 and (6.79 ± 0.09) × 10-3 M-1 s-1. Likewise, these rate constants for the Phen complexes were almost 2 times faster than those of the DMPhen complexes. The pKa values of the four aqua complexes were determined to be greater than 9.0 for all of the complexes with [Re(CO)2(Phen)(PTA)(H2O)]+ having the highest pKa value of 9.28 ± 0.03. From the pKa values and the ratios of the aquation and anation rate contants, which give thermodynamic Cl- binding constants, the speciation of the rhenium(I) complexes in blood plasma, the cytoplasm, and the cell nucleus were estimated. The data suggest that the aqua complexes would be the dominant species in all three environments. This result may have important implications on the potential biological activity of these complexes.

Non-monotonic dependence of reaction rate on rate constants: Role of time-averaging

• Non-monotonic dependence of rate on rate constant(s) is explicitly shown in a few solvable cases. • Intuitively expected behaviors are found only after a long-time averaging. • The topic possesses a very general appeal in enriching chemical wisdom. • Deterministic enzyme kinetics case is noted to be plagued with similar problems. • A simpler solvable model is used to rationalize numerical findings of the enzymatic problems. The rate of a reaction may not always show a monotonic dependence on some specific rate constant. In the context of stochastic single-substrate enzyme kinetics, such a behavior has recently [PNAS 111 (2014) 4391] been demonstrated; specifically, rate is noted to increase with increasing dissociation rate constant of the enzyme-substrate complex, contrary to standard expectation. In this work, we identify this counter-intuitive trait in several solvable and deterministic situations too. However, these anomalies are also analytically shown to disappear after a time-averaging. Numerical results of the deterministic enzyme kinetics scheme reveal similar features. The age-old intuitive chemistry thus retains its significance as an average.

Polymeric Membrane Electrodes Using Calix[4]pyrrole Bis/Tetra-Phosphonate Cavitands as Ionophores for Potentiometric Acetylcholine Sensing with High Selectivity.

A handful of bis/tetra-phosphonate calix[4]pyrroles with recognition sites embedding in hydrophobic cavitands were evaluated for the first time as ionophores for polymeric membrane Ach+-selective electrodes. Highly selective potentiometric Ach+ could be achieved over its analogues, especially for Ch+, which differs only by an acetate tail from Ach+. The superior performance of the proposed ISEs might be ascribed to a dual-site binding mode, in which the trimethylammonium head and acetate tail were accommodated by the phosphonate group-bridged aryl walls and the bowl-shaped aromatic cavity, through cation-π/charge-dipole interaction and the convergent four N-H···O hydrogen bonds, respectively. To gain more insight into the performance of the proposed ISEs, the cation-ionophore complex constants in the membrane phase were determined, and the binding affinity trend correlates well with the selectivity pattern. These results suggest that conformational preorganization of the ionophores and complementary weak interactions do change the selectivity of the ionophores. Studies on the influence of the sample solution pH demonstrated that the developed ISEs can be employed in a wide pH range of 4.0-9.6 with a fast response (<60 s), good reversibility, and long lifetime. Optimizing the membrane components, such as ionophores, lipophilic additives, and plasticizers, yielded ISEs, showing Nernstian responses to Ach+ with improved linear ranges and detection limits (a slope of -59.5 mV/dec in the linear range of 1 × 10-6-1 × 10-2 M with a detection limit of 3 × 10-7 M), which led to the success of the determination of Ach+ in spiked urine and milk samples.

Exothermic adsorption of chromate by goethite

Goethite is a common Fe oxyhydroxide coating soil particle surfaces, which has a high Cr(VI) adsorption capacity under acidic pH conditions. Batch equilibrium adsorption experiments with chromate concentrations of 0.1, 0.2, and 0.3 mM were performed using solutions with ionic strengths of 0.1, 0.05, and 0.01 M and pH values of 3–11 and at four temperatures between 10 and 75 °C. The results of these experiments show that the amount of chromate adsorbed decreases as the pH increases towards the zero-point-of-surface-charge of goethite (pHPZC 9.1), which is typical for anions. The chromate adsorption efficiency also depends on the ionic strength of the solution. The amount of chromate adsorbed decreases as the ionic strength increases, indicating that outer-sphere surface complexation affects the adsorption process. The data were interpreted using the charge distribution multisite surface complexation (CD-MUSIC) model framework. Variations in the complexation constants with temperature were fitted using the two-term van't Hoff equation to give partial molar enthalpy and entropy constants. The enthalpies were negative, indicating that chromate adsorption is exothermic, whereby outer-sphere binding was found to be less exothermic (ΔrGOS,298 −62.19 kJ mol−1) than inner-sphere binding (ΔrGIS,298 −112.25 kJ mol−1). The adsorption strength, therefore, decreases as the temperature increases because of the exothermic nature of surface complexation.

Complex modes in an open lossless periodic waveguide.

Guided modes of an open periodic waveguide, with a periodicity in the main propagation direction, are Bloch modes confined around the waveguide core with no radiation loss in the transverse directions. Some guided modes can have a complex propagation constant, i.e., a complex Bloch wavenumber, even when the periodic waveguide is lossless (no absorption loss). These so-called complex modes are physical solutions that can be excited by incident waves whenever the waveguide has discontinuities or defects. We show that the complex modes in an open dielectric periodic waveguide form bands, and the endpoints of the bands can be classified to a small number of cases, including extrema on dispersion curves of the regular guided modes, bound states in the continuum, degenerate complex modes, and special diffraction solutions with blazing properties. Our study provides an improved theoretical understanding of periodic waveguides and a useful guidance to their practical applications.

Simulating uranium sorption onto inorganic particles: The effect of redox potential

An analytical expression is proposed to simulate the effects of pH and redox potential (E) on the sorption of uranium onto model inorganic particles in aquatic environments instead of following an experimental approach providing a list of empirical sorption data. The expression provides a distribution coefficient (Kd) as function of pH, E and ligand concentration (complex formation) applying a surface complexation model on one type of surface sites (>SuOH). The formulation makes use of the complexation and hydrolysis constants for all species in solution and those sorbed at the surface, using correlations between hydrolysis constants and surface complexation constants, for the specific sorption sites. The model was applied for the sorption of uranium onto aluminol, iron hydroxide and silanol sites, mimicking respectively ‘clean’ clay or ‘dirty’ clay and ‘clean’ sand or ‘dirty’ sand (‘dirty’ referring to iron hydroxide contaminated), in absence or presence of carbonates in solution. The calculated distribution coefficients are very sensitive with the presence or absence of carbonates. The Kd values obtained by applying the model are compared with values reported in the literature for the sorption of uranium onto specific adsorbents. It is known that in surface water, U(VI) and its hydroxides are the primary stable species usually observed. However, reduction to U(IV) is possible and may be simulated during sorption or when the redox potential (E) decreases. Similar simulations are also applicable to study the sorption of other redox sensitive elements.

On Computing the Number of Short Cycles in Bipartite Graphs Using the Spectrum of the Directed Edge Matrix

Counting short cycles in bipartite graphs is a fundamental problem of interest in many fields including the analysis and design of low-density parity-check (LDPC) codes. There are two computational approaches to count short cycles (with length smaller than $2g$ , where $g$ is the girth of the graph) in bipartite graphs. The first approach is applicable to a general (irregular) bipartite graph, and uses the spectrum $\{\eta _{i}\}$ of the directed edge matrix of the graph to compute the multiplicity $N_{k}$ of $k$ -cycles with $k through the simple equation $N_{k} = \sum _{i} \eta _{i}^{k}/(2k)$ . This approach has a computational complexity $\mathcal {O}(|E|^{3})$ , where $|E|$ is number of edges in the graph. The second approach is only applicable to bi-regular bipartite graphs, and uses the spectrum $\{\lambda _{i}\}$ of the adjacency matrix (graph spectrum) and the degree sequences of the graph to compute $N_{k}$ . The complexity of this approach is $\mathcal {O}(|V|^{3})$ , where $|V|$ is number of nodes in the graph. This complexity is less than that of the first approach, but the equations involved in the computations of the second approach are complex and tedious, particularly for $k \geq g+6$ . In fact, the computational complexity of the equations increases exponentially with $k$ . In this paper, we establish an analytical relationship between the two spectra $\{\eta _{i}\}$ and $\{\lambda _{i}\}$ for bi-regular bipartite graphs. Through this relationship, the former spectrum can be derived from the latter through simple equations with computational complexity constant in $k$ . This allows the computation of $N_{k}$ using $N_{k} = \sum _{i} \eta _{i}^{k}/(2k)$ but with a complexity of $\mathcal {O}(|V|^{3})$ rather than $\mathcal {O}(|E|^{3})$ .