On the Nitroxide Quasi‐Equilibrium in the Alkoxyamine‐Mediated Radical Polymerization of Styrene

Summary: The range of validity of two popular versions of the nitroxide quasi‐equilibrium (NQE) approximation used in the theory of kinetics of alkoxyamine mediated styrene polymerization, are systematically tested by simulation comparing the approximate and exact solutions of the equations describing the system. The validity of the different versions of the NQE approximation is analyzed in terms of the relative magnitude of (dN/dt)/(dP/dt). The approximation with a rigorous NQE, k_c[P][N] = k_d[P N], where P, N and P N are living, nitroxide radicals and dormant species respectively, with kinetic constants k_c and k_d, is found valid only for small values of the equilibrium constant K (10⁻¹¹–10⁻¹² mol · L⁻¹) and its validity is found to depend strongly of the value of K. On the other hand, the relaxed NQE approximation of Fischer and Fukuda, k_c[P][N] = k_d[P N]₀ was found to be remarkably good up to values of K around 10⁻⁸ mol · L⁻¹. This upper bound is numerically found to be 2–3 orders of magnitude smaller than the theoretical one given by Fischer. The relaxed NQE is a better one due to the fact that it never completely neglects dN/dt. It is found that the difference between these approximations lies essentially in the number of significant figures taken for the approximation; still this subtle difference results in dramatic changes in the predicted course of the reaction. Some results confirm previous findings, but a deeper understanding of the physico‐chemical phenomena and their mathematical representation and another viewpoint of the theory is offered. Additionally, experiments and simulations indicate that polymerization rate data alone are not reliable to estimate the value of K, as recently suggested.

Validity of the rigorous nitroxide quasi‐equilibrium assumption as a function of the nitroxide equilibrium constant.     

Diffusion of cesium and selenium in crushed mudrock

In this study, the diffusion behavior of cesium and selenium with 10⁻⁴M concentration in mudrock was studied by trough-diffusion tests and summarized in order to provide confidence on long-term performance assessment of nuclear waste repositories. The diffusion process of Cs and Se reached equilibrium after 60 and 500 days, respectively. Besides, it also displays that the distribution coefficients (K _d ) of Se in through-diffusion tests is higher than that of Cs in agreement with that obtained from the batch method. The K _d value (15.14±1.99 mL/g) of Cs by diffusion techniques is equivalent to that of batch method (15.10±0.40 mL/g) because sorption of Cs was assumed to fast sorption step. However, the K _d value of Se (137.58±12.20 mL/g) derived from the diffusion technique is higher than that from batch tests (76.72±2.96) and showed an obvious variation with K _d of Cs. The difference of K _d between diffusion and batch methods resulted from the fact that 14 days were not long enough to reach equilibrium or stable state in the batch method.     

Increase of the average reactivity of active species due to a shift to the more reactive species in ionic propagation accompanied by termination

The presented simulations demonstrate that in polymerizations proceeding on two kinds of species, differing in reactivity and being in equilibrium, the expected decrease of the rate of polymerization due to termination may happen to be compensated by the relative increase of concentration of the more reactive species. This takes place, for instance, in the polymerization proceeding simultaneously on ions and ion pairs if ions are more reactive. Because of termination the total concentration of ionic species during the course of polymerization decreases while the proportion of ions increases due to increasing dilution. The maximum compensation is observed when simultaneously k_(ions)/k_{(ion pairs)} → and K_d/[I]₀ → 0, where k are the propagation rate constants, K_d is the equilibrium constant of dissociation and [I]₀ is the starting concentration of initiator. Then, the degree of compensation (the ratio of the rate with compensation to the rate without termination) is becoming equal to ([P*]/[P*]₀)^1/2, where [P*] is the actual, total concentration of the growing species and [P*]₀ is the initial total concentration (before any termination has taken place).     

Solute partition study in aqueous sodium dodecyl sulfate micellar solutions for some organic reagents and metal chelates

The partition constants (K _d) have been estimated for nitrophenols, thiazolylazo dyestuffs and metal chelate compounds into the sodium dodecyl sulfate (SDS) micellar phase at an ionic strength of 0.10M [(H⁺, Na⁺)Cl^–] and at 20 °C. The equilibrium partition data obtained by batch-wise solution spectrophotometry (equilibrium shift method) agree well with those by the micellar electrokinetic capillary chromatography (MECC) with the SDS micellar pseudo-stationary phase. The MECC clearly discriminates a very small difference (0.03) in the logK _d values of some metal chelates. The plot of theK _d values with the van der Waals volume of the solute molecules obviously shows the leveling-off of theK _d values over solute size near 110 ml/mol, which seems to be consistent with the results obtained in the Triton X-100 micellar system. This phenomenon arises most probably from the rigidity of the micellar pseudo-phase (a micellar volume-constraint effect) in sharp contrast with true two-phase partitioning such as solvent extraction systems.     

Transient Incomplete Separation Facilitates Finding Accurate Equilibrium Dissociation Constant of Protein–Small Molecule Complex

Current practical methods for finding the equilibrium dissociation constant, K_d, of protein–small molecule complexes have inherent sources of inaccuracy. Introduced here is “accurate constant via transient incomplete separation” (ACTIS), which appears to be free of inherent sources of inaccuracy. Conceptually, a short plug of the pre‐equilibrated protein–small molecule mixture is pressure‐propagated in a capillary, causing fast transient incomplete separation of the complex from the unbound small molecule. A superposition of signals from these two components is measured near the capillary exit and used to calculate a fraction of unbound small molecule, which, in turn, is used to calculate K_d. Herein the validity of ACTIS is proven theoretically, its accuracy is verified by computer simulation, and its practical use is demonstrated. ACTIS has the potential to become a reference‐standard method for determining K_d values of protein–small molecule complexes.     

The kinetics of solid-phase microextraction measured for freshly added and aged hydrophobic compounds in two different soils

The proper choice of exposure times is critical if the freely dissolved concentration of chemicals in soil porewater is to be measured via the equilibrium solid-phase microextraction (SPME) as the times to equilibrium may vary depending on compound and soil properties. To reveal the effects of compound hydrophobicity, ageing and soil organic matter content on times to equilibrium, the SPME uptake was measured for five freshly added and aged hydrophobic organic compounds (phenanthrene, pyrene, lindane, p,p′-DDT and polychlorinated biphenyl (PCB) 153) in two contrasted soils (arable and forest soil). The tested compound-soil systems behaved kinetically different. Longer equilibrium times were observed with increasing hydrophobicity of compounds for aged compared to freshly added chemicals and for the forest soil in comparison to the arable soil. The calculated soil–porewater partition coefficients (i.e. sorption coefficients, K_d) of chemicals differed between soil types mainly due to various organic carbon (OC) contents as evidenced by the comparable K_oc values (i.e. K_d values normalised to soil OC content). Similar K_oc values were also found with the various extent of ageing, indicating that both the freshly added and aged compounds linearly partitioned between the soil organic matter and porewater. Our results suggest that, for a respective compound, variations in equilibrium times may be expected depending upon the residence time and the organic matter content in soil where the longest equilibrium times seems to appear for a combination of aged compounds and high organic soils. With regard to this outcome, the effect of the level of sample depletion due to the SPME extraction (LD_SPME) on equilibrium times was assessed. At LDs_SPME of up to 10%, equilibrium times increases linearly with LDs_SPME for p,p′-DDT and PCB 153. For phenanthrene (LD_SPME<10%), and for lindane and pyrene (1.2% < LD_SPME > 40%), no clear relationships were observed.     

Pedagogic Interest of the H2O2, Cu2+, SCN-, OH- Oscillating Reaction

Chemical reactivity is generally taught by considering the chemical properties of the reacting entities (acid-base, oxidation-reduction, complexation, and precipitation) and the values of the corresponding equilibrium thermodynamic constants (K_a, E⁰ K_d, K_s). This approach, however, is not well-suited to the dynamic chemical systems that are often encountered in industrial and environmental chemistry where nonequilibrium conditions prevail. In this respect, oscillating reactions are a good illustration of the limits of equilibrium thermodynamics and show the need for a complementary dynamic nonequilibrium study. We describe here an oscillating reaction that is easy to carry out in an inorganic chemistry practical class as it uses common reactants (H₂O₂, KSCN, CuSO₄, NaOH). This example should enable students to obtain a more realistic grasp of chemical reactivity based on a comprehension of coupled reaction processes, similar to those encountered in population dynamics or in enzymatic regulation.     

Sorption of Cs,Pu and Am on clay minerals

Performance assessment of radioactive waste disposal requires modeling of long-term migration of radionuclides through the engineered barriers and the geological environment. The chemical complexity of sorption-desorption processes is usually reduced to integrated parameter distribution coefficients (K _d ). There are a great number of publications on K _d determination, however, the existing data on K _d of radionuclides on different geological materials are for general understanding only and are not very useful for performance assessment, since changes of the geological conditions result in variability of K _d values by two orders of magnitude. In order to obtain realistic sorption data sets for safety relevant radionuclides present in a cement/concrete based repository some preliminary studies were carried out. The development of sorption database for the near-surface repository was started with measurements of cesium, plutonium and americium K _d values. Several experiments were performed in order to determine the chemical composition of cement water which could originate from infiltration of precipitation and from contact of groundwater with concrete. More than 100 batch sorption experiments were conducted with two clay samples. Cs, Pu and Am K _d values were determined for rainwater, groundwater and cement-water of different chemical compositions. Cs, Pu, Am K _d values ranged from 450 to 9700, from 15000 to 21000 and 15000 to 80000 ml/g, respectively. Changes in the geochemical conditions resulted in the variability of Cs, Pu and Am K _d values.     

A multitracer Study on the Adsorption of 36 Elements on a Silica: Effects of pH and Fulvic Acid

The distribution coefficients,K _d of 36 elements from Na to Bi on a silica were determined at pH 4, 7, 9 and in the absence and presence of fulvic acid (FA) using a multitracer technique. The multitracer solution was prepared by irradiation of Th(NO₃)₄ with ⁴⁰Ar ion beam. The effects of pH and fulvic acid on the K _d values of 36 elements were studied. It was found that the sequences of the K _d values of alkali elements (Cs>Rb>K>Na) and of alkaline earth elements(Ba>Ca>Mg) in the absence of FA can be qualitatively explained in terms of chemical bond formation and hydration. Various effects of pH and the negative or positive effect of FA on the adsorption of 36 elements were observed and are probably related to the species of 36 elements in the aqueous solutions containing CO₃ ^2–, OH^–, Cl^– and FA. For most of the elements studied here the K _d values are increased with increasing pH and are decreased with adding FA.     

A Highly K+‐Selective Two‐Photon Fluorescent Probe

A highly K⁺‐selective two‐photon fluorescent probe for the in vitro monitoring of physiological K⁺ levels in the range of 1–100 mM is reported. The two‐photon excited fluorescence (TPEF) probe shows a fluorescence enhancement (FE) by a factor of about three in the presence of 160 mM K⁺, independently of one‐photon (OP, 430 nm) or two‐photon (TP, 860 nm) excitation and comparable K⁺‐induced FEs in the presence of competitive Na⁺ ions. The estimated dissociation constant (K_d) values in Na⁺‐free solutions (K_d^OP=(28±5) mM and K_d^TP=(36±6) mM ) and in combined K⁺/Na⁺ solutions (K_d^OP=(38±8) mM and K_d^TP=(46±25) mM ) reflecting the high K⁺/Na⁺ selectivity of the fluorescent probe. The TP absorption cross‐section (σ_2PA) of the TPEF probe+160 mM K⁺ is 26 GM at 860 nm. Therefore, the TPEF probe is a suitable tool for the in vitro determination of K⁺.     

Modeling migration of strontium in sand and gravel aquifer in the candidate VLLW disposal site

Study of fine-particle media, because of their high sorption capacities, is of particular importance for the use as backfill materials in waste repository design, and because argillaceous formations are particularly suitable as host rock formations. In this study, sorption and retardation characteristics of strontium in fine-particle media were studied to evaluate the distribution coefficient (K _d ) and retardation factor (R _d ) of this radioactive element in fine-particle media, which was comprised of selected particles with a diameter less than 1 mm from a candidate site to dispose very low level waste (VLLW). The results indicated that K _d values of strontium under different initial concentrations ranged between 20 and 110. Values of strontium R _d measured from column experiments ranged between 36 and 102, with the corresponding K _d values, determined from solving the inverse problem of R _d calculating formula, ranging between 5 and 20. In conclusion, the K _d value of Sr from the batch tests was found to be higher than these from the column experiments.     

Vertical random variability of the distribution coefficient in the soil and its effect on the migration of fallout radionuclides

In the field, the distribution coefficient, K _d, for the sorption of a radionuclide by the soil cannot be expected to be constant. Even in a well defined soil horizon, K _d will vary stochastically in horizontal as well as in vertical direction around a mean value. The horizontal random variability of K _d produce a pronounced tailing effect in the concentration depth profile of a fallout radionuclide, much less is known on the corresponding effect of the vertical random variability. To analyze this effect theoretically, the classical convection-dispersion model in combination with the random-walk particle method was applied. The concentration depth profile of a radionuclide was calculated one year after deposition assuming (1) constant values of the pore water velocity, the diffusion/dispersion coefficient, and the distribution coefficient (K _d = 100 cm^3.g^-1), and (2) exhibiting a vertical variability for K _d according to a log-normal distribution with a geometric mean of 100 cm^3.g^-1 and a coefficient of variation of CV = 0.53. The results show that these two concentration depth profiles are only slightly different, the location of the peak is shifted somewhat upwards, and the dispersion of the concentration depth profile is slightly larger. A substantial tailing effect of the concentration depth profile is not perceivable. Especially with respect to the location of the peak, a very good approximation of the concentration depth profile is obtained if the arithmetic mean of the K _d-values (K _d = 113 cm^3.g^-1) and a slightly increased dispersion coefficient are used in the analytical solution of the classical convection-dispersion equation with constant K _d. The evaluation of the observed concentration depth profile with the analytical solution of the classical convection-dispersion equation with constant parameters will, within the usual experimental limits, hardly reveal the presence of a log-normal random distribution of K _d in the vertical direction in contrast to the horizontal direction.     

Sorption behavior of selenide on montmorillonite

Batch sorption experiments were performed to investigate the sorption mechanism of Se on montmorillonite under reducing conditions in deep geological environments. Based on E_h–pH diagrams and ultraviolet–visible spectra, Se was dissolved as selenide (Se(–II)) anions under the experimental conditions. The distribution coefficients (K_d; m³ kg^?1) of Se(–II) indicated ionic strength independence and slight pH dependence. The K_d values of Se(–II) were higher than those of Se(IV), which also exists as an anionic species. X-ray absorption near edge spectroscopy showed that the oxidation state of Se-sorbed on montmorillonite was zero even though selenide remained in the solution. These results suggest that Se(–II) was oxidized and precipitated on the montmorillonite surface. Therefore, it is implied that a redox reaction on the montmorillonite surface contributed to high K_d values for Se(–II).

     

Quantification of thorium and uranium sorption to contaminated sediments

Desorption tests, using a sequential extraction method, were used to characterize and quantify thorium and uranium sorption to contaminated wetland sediments collected from the Department of Energy's Savannah River Site located in South Carolina. In situ distribution coefficients, or K _d values (K _d = C _solid/C _liquid), were determined. Sequential extraction data were used to assign solid-phase radionuclide concentrations (C _solid) that, by definition, should represent only the reversibly sorbed fraction. A series of selective and sequential extractions was used to determine desorption K _d values. Thorium K _d values ranged from 115 to 2255 ml/g. Uranium K _d values ranged from 170 to 6493 ml/g. Compared to sorption K _d values, these desorption K _d values were appreciably greater because they captured the aging process of the radionuclides with the sediment, making the radionuclide more refractory. Compared to nonsite-specific data, these in situ K _d values improved accuracy, were more defensible, and removed unnecessary conservatism for subsequent transport and risk calculations. Additional tests were conducted to provide geochemical information relevant for selecting appropriate remediation technologies for the contaminated site. Thorium and uranium were associated with labile fractions and were not concentrated with the smaller sediment particles. These findings suggest that phytoremediation or heap leaching, and not soil washing, are viable remediation approaches for this site.     

Estimation of distribution coefficient of polonium in geological matrices around uranium mining site

In case of ground (groundwater) contamination or contaminants release from the disposal modules (facilities) to the geo-environment, the fate of contaminant transport is mainly governed by the parameter called distribution (partition) coefficient, K _d. It is a measure of sorption of contaminants to soils. For that the sorption of polonium in soil were carried out using laboratory batch method in different soil samples collected from different places around Turamdih uranium mining site. The kinetics of polonium sorption were also carried out at different time intervals which clearly indicates that sorption equilibrium for polonium achieved at around 72 h. The K _d for polonium varies from 1,443 to 7,501.3 L/kg in soil samples. Chemical characterization of soil and ground water samples were carried out to know the effect of various chemical parameters with distribution coefficient of polonium.     

Iranian clinoptilolite-rich tuffs for radionuclide removal from water

Three Iranian natural zeolites were characterized and evaluated for their abilities to take up Ba⁺², Ca⁺², K⁺ and Na⁺ from radioactive waste waters. The distribution coefficient values (K _d ) of the cations were measured and investigated as a function of pH. Four different cationic forms (Na, K, NH₄, and Ca) were also prepared and theirK _d values were determined. Some cations such as potassium presented highK _d values both in natural and exchanged zeolites. In sodium and ammonium exchanged forms theK _d values increased between 7 to 100 times with respect to the untreated zeolite.     

Resorcinol - formaldehyde adsorption of cesium from Hanford waste solutions

Batch equilibrium measurements were conducted at 25±2 °C with a granular resorcinol-formaldehyde (RF) resin to determine the distribution coefficients (K _d ) for cesium. In the tests, Hanford Site actual waste sample containing radioactive cesium (¹³⁷Cs) and a pretreated waste sample that was spiked with non-radioactive ¹³³Cs were used. Initial concentrations of non-radioactive cesium in the waste sample were varied to generate an equilibrium isotherm for cesium. Majority of the tests were conducted at 25±2 °C using a liquid to solid phase ratio of 100 ml/g and at a contact time of 72 hours. Two additional tests were conducted at a liquid to solid phase ratio of 10 and at contact time of 120 hours. The measured distribution coefficient (K _d ) for radioactive cesium (¹³⁷Cs) was 948 ml/g, the K _d for non-radioactive cesium (¹³³Cs) was 1039 ml/g. The K _d for nonradioactive cesium decreased from 1039 to 691 ml/g with increased initial cesium concentration from 8 to 64 g/ml. Very little change of the K _d was observed at initial cesium concentration above 64 g/ml. The maximum sorption capacity for cesium on granular RF resin was 1.17 mmole/g dry resin. This value was calculated from the fit of the equilibrium isotherm data to the Dubinin-Radushkevich equation. Previously, a total capacity of 2.84 mmole/g was calculated by Bibler and Wallace for air-dried RF resin.This work was conducted at the Savannah River Technology Center in Aiken, SC, which is operated for the U. S. Department of Energy (DOE) by Westinghouse Savannah River Company under Contract DE-AC09-96SR18500. The Hanford River Protection Project-Waste Treatment Plant (RPP-WTP) funded this work. The authors are very grateful to Karen Palmer, Betty Mealer, and Yvonne Simpkins for their assistance in the experimental work.     

Resorcinol - formaldehyde adsorption of cesium from Hanford waste solutions

Batch equilibrium measurements were conducted at 25±2 °C with a granular resorcinol-formaldehyde (RF) resin to determine the distribution coefficients (K _d ) for cesium. In the tests, Hanford Site actual waste sample containing radioactive cesium (¹³⁷Cs) and a pretreated waste sample that was spiked with non-radioactive ¹³³Cs were used. Initial concentrations of non-radioactive cesium in the waste sample were varied to generate an equilibrium isotherm for cesium. Majority of the tests were conducted at 25±2 °C using a liquid to solid phase ratio of 100 ml/g and at a contact time of 72 hours. Two additional tests were conducted at a liquid to solid phase ratio of 10 and at contact time of 120 hours. The measured distribution coefficient (K _d ) for radioactive cesium (¹³⁷Cs) was 948 ml/g, the K _d for non-radioactive cesium (¹³³Cs) was 1039 ml/g. The K _d for nonradioactive cesium decreased from 1039 to 691 ml/g with increased initial cesium concentration from 8 to 64 g/ml. Very little change of the K _d was observed at initial cesium concentration above 64 g/ml. The maximum sorption capacity for cesium on granular RF resin was 1.17 mmole/g dry resin. This value was calculated from the fit of the equilibrium isotherm data to the Dubinin-Radushkevich equation. Previously, a total capacity of 2.84 mmole/g was calculated by Bibler and Wallace for air-dried RF resin.This work was conducted at the Savannah River Technology Center in Aiken, SC, which is operated for the U. S. Department of Energy (DOE) by Westinghouse Savannah River Company under Contract DE-AC09-96SR18500. The Hanford River Protection Project-Waste Treatment Plant (RPP-WTP) funded this work. The authors are very grateful to Karen Palmer, Betty Mealer, and Yvonne Simpkins for their assistance in the experimental work.     

A Highly K+‐Selective Fluorescent Probe – Tuning the K+‐Complex Stability and the K+/Na+ Selectivity by Varying the Lariat‐Alkoxy Unit of a Phenylaza[18]crown‐6 Ionophore

A desirable goal is to synthesize easily accessible and highly K⁺/Na⁺‐selective fluoroionophores to monitor physiological K⁺ levels in vitro and in vivo. Therefore, highly K⁺/Na⁺‐selective ionophores have to be developed. Herein, we obtained in a sequence of only four synthetic steps a set of K⁺‐responsive fluorescent probes 4 , 5 and 6 . In a systematic study, we investigated the influence of the alkoxy substitution in ortho position of the aniline moiety in π‐conjugated aniline‐1,2,3‐triazole‐coumarin‐fluoroionophores 4 , 5 and 6 [R=MeO ( 4 ), EtO ( 5 ) and iPrO ( 6 )] towards the K⁺‐complex stability and K⁺/Na⁺ selectivity. The highest K⁺‐complex stability showed fluoroionophore 4 with a dissociation constant K_d of 19 mm , but the K_d value increases to 31 mm in combined K⁺/Na⁺ solutions, indicating a poor K⁺/Na⁺ selectivity. By contrast, 6 showed even in the presence of competitive Na⁺ ions equal K_d values (K_d^K+=45 mm and K_d^K+/Na+=45 mm ) and equal K⁺‐induced fluorescence enhancement factors (FEFs=2.3). Thus, the fluorescent probe 6 showed an outstanding K⁺/Na⁺ selectivity and is a suitable fluorescent tool to measure physiological K⁺ levels in the range of 10–80 mm in vitro. Further, the isopropoxy‐substituted N‐phenylaza[18]crown‐6 ionophore in 6 is a highly K⁺‐selective building block with a feasible synthetic route.     

On the interpretation of solubilization results obtained from semi-equilibrium dialysis experiments

The interpretation of intramicellar solubilization data obtained from semi-equilibrium dialysis (SED) experiments is described, and methods are presented for determining equilibrium constants for the solubilization of organic species by aqueous surfactant solutions as well as activity coefficients of both the organic solute and the surfactant within the micelle. The solubilization equilibrium constant of an organic solute in an aqueous micellar solution (K) is defined as the ratio of the mole fraction of organic solute in the micellar pseudophase (X) to the concentration of the unsolubilized monomeric organic solute in the aqueous phase (c ₀). Expressions compatible with the Gibbs-Duhem equation are used to represent the concentration dependence of activity coefficients of both the solubilizate and surfactant in the micellar pseudophase; the analysis leads to calculated values of the concentrations of free and intramicellar surfactant and organic solute in both compartments of the equilibrium dialysis cell. Solubilization equilibrium constants for many amphiphiles are well correlated by the simple expressionK=K ₀(1-BX)², whereB is an empirical constant andK ₀ is the limiting value ofK asX approaches 0.