Charge balance vs. charge conservation for plutonium

A recent paper about plutonium disproportionation confuses charge balance with charge conservation. To explain disproportionation, impossible solutions in which the charges do not balance were proposed.Mound is operated for the U. S. Department of Energy by EG & G Mound Applied Technologies Incorporated under Contract NO. DE-AC04-88DP43495.     

Rearrangement equations for plutonium

The percents of all oxidation states produced by Pu disproportionation, including unreacted starting material, can be obtained by new equations that are easy to apply. The equations are useful for quantifying the extent and the stoichiometry of disproportionation, the consequences of complexation, and the effects of temperature changes on the composition of the oxidation-state mixture.     

General disproportionation equations for plutonium

Disproportionation equations are illustrated for two oxidation numbers (N) and for the general case of any N. The new method illustrates the effect of N on the coefficients in disproportionation equations. An estimate of the equilibrium constant for the first hydrolysis reaction of tetravalent plutonium is obtained by a new approach. The estimated value agrees with many previous results.     

Charge conservation applied to experimental data for plutonium solutions

The principle of charge conservation in isolated systems is used to analyze data recorded for an academic thesis. The analysis reveals a gradual chemical reduction of the plutonium during studies of its behavior in dilute aqueous acids. The reduction effect is reproduced in several different studies. The effect was apparently unnoticed by the author.     

Time-property least-squares spectral method for population balance equations

In multiphase chemical reactor analysis the dispersed phase distribution plays a major role in obtaining reliable predictions. The population balance equation is a well established equation for describing the evolution of the dispersed phase. However, the numerical solution of this type of equations is computationally intensive. In this work, a time-property least squares spectral method is presented for solving the population balance equation including breakage and coalescence processes. In this problem, both property and time are coupled in the least squares minimization procedure. Spectral convergence of the L ² least squares functional and L ² error norms in time-property is verified using a smooth solution to the population balance equation.     

Acidity changes in plutonium solutions: Generalized proportional equations method

Summary Disproportionation reactions change the pH of a plutonium solution. The method of generalized proportional equations is used to estimate the magnitude of the change. It is illustrated by examples and it is easy to apply.     

Problems in plutonium chemistry: Generalized proportional equations and polymer formation

Summary This paper illustrates a generalized form of the method of proportional equations. It permits equilibrium calculations for Pu disproportionation reactions at any oxidation number and any pH by means of combining arbitrary proportions of tri- and hexavalent plutonium. Two methods for estimating the work of Pu polymer formation are illustrated. One method uses the work of disproportionation of tetravalent plutonium. The other method suggests the transition between hydrous Pu(IV) oxide and polymer is accompanied by a small change in free energy.     

Work integrals for plutonium

Free energy changes in Pu disproportionation reactions can be measured by integrating the reaction isotherm with respect to one of the reaction products. Separate integrations can be made for the isotherms of the component reactions contributing to the equilibrium.Mound is operated for the U.S. Department of Energy by EG&G Mound Applied Technologies Incorporated under contract No. DE-AC04-88DP43495.     

Numerical and similarity solutions for reversible population balance equations with size-dependent rates

Population balance equations (PBEs) for reversible aggregation-fragmentation processes are important to particle agglomeration and dissolution, polymerization and degradation, liquid droplet coalescence and breakup, and floc coagulation and disintegration. Moment solutions provide convenient solutions to the PBEs, including steady state and similarity solutions, but may not be feasible for complex forms of size-dependent rate coefficients and stoichiometric kernels. Numeric solutions are thus necessary not only for applications, but also for the study of the mathematics of PBEs. Here we propose a numerical method to solve PBEs and compare the results to moment solutions. The numeric results are consistent with known steady state and asymptotic long-time similarity solutions and show how processes can be approximated by self-similar formulations.     

Two predominance-region diagrams for plutonium

Two predominance-region diagrams for plutonium are illustrated. One diagram plots the pH vs. the equilibrium fraction of hexavalent plutonium. The other diagram plots the equilibrium fraction of tetravalent plutonium vs. the plutonium oxidation number. Both diagrams define the boundaries of the regions where tri-, tetra-, penta-, and hexavalent plutonium are the predominant species. In each diagram, the two principal triple points are located at the intersections of three predominance-region boundary lines.Los Alamos National Laboratory is operated by the University of California for the U.S. Department of Energy under Contract No. W-7405-ENG-36.     

Triangular predominance-region diagrams for plutonium

Two predominance region diagrams can be prepared by plotting the equilibrium fractions of hexavalent vs. trivalent plutonium. The diagrams are differentiated by the species that predominate near their origins. Both diagrams have a curved boundary that separates permissible from forbidden oxidation-state combinations.     

Work surface for soluble plutonium

Summary A three-dimensional work surface for aqueous plutonium is illustrated. It is constructed by means of estimating work as a function of the ambient pH and redox potential in a plutonium solution. The surface is useful for illustrating the chemistry of disproportionation reactions. Work expressions are easier to use than work integrals.     

Two predominance-region diagrams for plutonium

Two predominance-region diagrams for plutonium are illustrated. One diagram plots the pH vs. the equilibrium fraction of hexavalent plutonium. The other diagram plots the equilibrium fraction of tetravalent plutonium vs. the plutonium oxidation number. Both diagrams define the boundaries of the regions where tri-, tetra-, penta-, and hexavalent plutonium are the predominant species. In each diagram, the two principal triple points are located at the intersections of three predominance-region boundary lines.Los Alamos National Laboratory is operated by the University of California for the U.S. Department of Energy under Contract No. W-7405-ENG-36.     

Alpha coefficients for tetravalent plutonium

The complexation of tetravalent plutonium in aqueous solutions derives from several sources including counterions, hydrolysis, additives, and impurities. A quantitative tool accounting for all such effects, known and unknown, is the alpha coefficient. It can be expressed in six ways by means of the equilibrium fractions of two Pu oxidation states.     

Surprising coordination for plutonium in the first plutonium(III) borate

The first plutonium(III) borate, Pu(2)[B(12)O(18)(OH)(4)Br(2)(H(2)O)(3)]·0.5H(2)O, has been prepared by reacting plutonium(III) with molten boric acid under strictly anaerobic conditions. This compound contains a three-dimensional polyborate network with triangular holes that house the plutonium(III) sites. The plutonium sites in this compound are 9- and 10-coordinate and display atypical geometries.     

Advances in numerical methods for the solution of population balance equations for disperse phase systems

Accurate prediction of the evolution of particle size distribution is critical to determining the dynamic flow structure of a disperse phase system. A population balance equation (PBE), a non-linear hyperbolic equation of the number density function, is usually employed to describe the micro-behavior (aggregation, breakage, growth, etc.) of a disperse phase and its effect on particle size distribution. Numerical solution is the only choice in most cases. In this paper, three different numerical methods (direct discretization methods, Monte Carlo methods, and moment methods) for the solution of a PBE are evaluated with regard to their ease of implementation, computational load and numerical accuracy. Special attention is paid to the relatively new and superior moment methods including quadrature method of moments (QMOM), direct quadrature method of moments (DQMOM), modified quadrature method of moments (M-QMOM), adaptive direct quadrature method of moments (ADQMOM), fixed pivot quadrature method of moments (FPQMOM), moving particle ensemble method (MPEM) and local fixed pivot quadrature method of moments (LFPQMOM). The prospects of these methods are discussed in the final section, based on their individual merits and current state of development of the field. Supported by the National Basic Research Program of China (Grant No. 2004CB720208), the National Natural Science Foundation of China (Grant Nos. 40675011 & 10872159), and the Key Laboratory of Mechanics on Disaster and Environment in Western China     

Intrinsic predominance region diagram for plutonium

Summary A predominance-region diagram for aqueous plutonium can be prepared by plotting the equilibrium fractions of tetra- and hexavalent plutonium. An example illustrates how the triple points can be used to estimate hydrolysis constants.     

New fecal method for plutonium and americium

A new fecal analysis method that dissolves plutonium oxide was developedat the Westinghouse Savannah River Site. Diphonix Resin . (Eichrom Technologies),is used to pre-concentrate the actinides from digested fecal samples. A rapidmicrowave digestion technique is used to remove the actinides from the DiphonixResin ., which effectively extracts plutonium and americium from acidic solutionscontaining hydrofluoric acid. After resin digestion, the plutonium and americiumare recovered in a small volume of nitric acid that is loaded onto small extractionchromatography columns, TEVA Resin and TRU Resin (Eichrom Technologies). Themethod enables complete dissolution of plutonium oxide and provides high recoveryof plutonium and americium with good removal of thorium isotopes such as ²²⁸Th.     

Sources of misinterpretation for environmental plutonium measurements

Analytical and statistical uncertainties associated with low-level measurements may lead to spurious conclusions regarding the behavior of some plutonium isotopes. The general aspect of the methodology used in sample collection, preparation, radiochemical separation and alpha spectroscopy analysis of plutonium is considered. Biases and experimental artifacts that may produce inaccurate results and improper conclusions are discussed with examples from our research and from the open literature.