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.     

Empirical method for preparing a plutonium predominance-region diagram

An empirical method for preparing a plutonium predominance-region diagram is illustrated by an example. The method estimates the boundaries of the forbidden, unique, and ambiguous regions as defined by the equilibrium fraction of hexavalent plutonium and the plutonium oxidation number.     

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.     

Plutonium and intrinsic predominance-region diagrams

Four intrinsic predominance-region diagrams for aqueous plutonium are described. They are easily prepared from an existing diagram by changing the oxidation-state fractions on the axes of the diagram and renaming the predominance regions. Not all combinations of oxidation-state fractions can be used to prepare the diagrams.     

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.     

Plutonium Predominance-Region Diagram

The oxidation number and the pH are used to construct a predominance-region diagram for soluble plutonium. Features of the diagram can be verified by means of rearrangement equations for plutonium.     

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.     

Triple points and plutonium equilibrium

Summary Equilibrium prevails at all points in plutonium predominance region diagrams. Triple points combine equilibrium with equal fractions of three Pu oxidation states. A rearrangement equation can be used to describe plutonium at a triple point. Two-reaction-product disproportionation equations are not satisfactory for that purpose.     

Oxidation-state maxima in plutonium chemistry

Maxima in the fractions of the trivalent and hexavalent oxidation states of plutonium are inherent in the algebra of its disproportionation reactions. The maxima do not support overall disproportionation equations as satisfactory representations of aqueous plutonium.     

A graphical approach to redox titrations

Summary A method for drawing a logarithmic diagram which gives a correct representation of the equilibrium concentrations of the various species taking part in a redox titration is described. The use of this kind of diagrams for evaluating the titration error and for calculating the titration curve is illustrated. The symmetry properties of titration curves and the linearity range of Gran plots are also discussed on the basis of the logarithmic diagrams.

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Graphische Behandlung von Redox-Titrationen

Zusammenfassung Ein Verfahren wird beschrieben zur Aufstellung eines logarithmischen Diagramms, das eine korrekte Darstellung der Gleichgewichtskonzentrationen der verschiedenen Teilnehmer an einer Redoxtitration bietet. Der Gebrauch eines solchen Diagramms zur Auswertung des Titrationsfehlers und zur Berechnung der Titrationskurve wird gezeigt. Aufgrund der logarithmischen Diagramme werden auch die Symmetrieeigenschaften von Titrationskurven und der Linearitätsbereich von Gran-Diagrammen diskutiert.

     

物理化学课程中相平衡理论的教学策略

针对物理化学相平衡章节体系多变、知识点繁多、相图抽象等问题提出了一套系统的教学策略。首先对相平衡中的基本概念和定律进行论述,并强调重、难点;随后对章节知识点进行总结归纳,通过表格系统罗列相图的体系、相律、应用和术语;最后提出相图解读通行方法,并结合具体例子讲解这些方法、相律以及杠杆规则如何使用。     

Plutonium disproportionation: maxima in the fractions of two oxidation states

The equilibrium fractions of soluble tri- and hexavalent Pu depend on the pH and the Pu oxidation number. Both fractions can exhibit maxima as the pH changes at constant N. A fraction at maximum can be used to estimate the equilibrium constant of the first hydrolysis reaction of tetravalent Pu. A new formula that renders least-squares estimates of this constant is illustrated.     

Interfacial properties and equilibria in the apatite-aqueous solution system

Thermodynamic calculations of the solubility of hydroxyapatite have been carried out and the results are presented in different types of equilibrium diagrams in order to interpret observed interfacial behavior in this system. For predicting the electrical double-layer properties, especially the conditions for zero surface charge, diagram with activities of predominant calcium and phosphorous species as the axes and pH as the third independent variable have been found to be most useful. Conditions for zero charge at the surface are predicted based on the assumption that the affinity for the surface of all the lattice ions in solution is nearly equal. The different kinds of equilibrium diagrams have been found useful to explain some hitherto unexplained observations in the literature. Calculations have also been made to determine the effect of fluoride ions on the thermodynamic properties of the system. Experimental data are presented to support the calculations.     

Three-dimensional PTx phase diagrams through interactive computer graphics

Interactive computer graphic techniques have been developed for the display of binary mixture phase diagrams. The diagrams are defined in temperature-pressure-composition space, and are portrayed as wireframe objects with depth perception in order to provide a three-dimensional effect. The displays used were vectro refresh workstations whose transformation hardware allows real-time rotation, rescaling, and translation of the diagrams, while software allows the extraction of constant property Px, Tx, PT and x - y plots. The equilibrium surfaces and the critical lines were calculated using the Redlich-Kwong equation of state and its Soave modification.     

Systematic investigation of global phase behavior of polymer mixtures in the pressure-temperature plane

We investigate the critical lines of polymer mixtures in the presence of their vapor phase at the mathematical double point, where two critical lines meet and exchange branches, and its environment. The model used combines the lattice gas model of Schouten, ten Seldam and Trappeniers with the Flory-Huggins theory. The critical line structure is displayed for various combinations of the chain length and system parameters in the pressure (P)-temperature (T) plane, as is usually done with experimental results. This type of work sheds light on the essential transition mechanism involved in the phase diagram's change of character, such as multi-critical points and mathematical double points, which are of great practical importance in supercritical fluid extraction processes. The P, T diagrams are discussed in accordance with the Scott and van Konynenburg binary phase diagram classification. We found that our P, T plots were in agreement with type II, type III, or type IV phase diagram behaviors. We also found that some of our phase diagrams represent the liquid-liquid equilibria in polymer solutions and mixtures.     

Correlation energy contribution to the ammonia inversion barrier

Diagrammatic many-body double-perturbation theory is used to study the correlation contribution to the inversion barrier in ammonia. With a one-center solution as the zero-order function, the perturbation energy diagrams are shown to be of three types: Hartree-Fock diagrams (geometry dependent), atom-like correlation diagrams (geometry independent) and non-atom-like correlation diagrams (geometry dependent). Only the third class of diagrams enter into the correlation correction to the barrier. These diagrams, which appear first in third order, contribute a small fraction (1%) of the total correlation energy. We estimate from them that the correlation energy contribution to the barrier is small (less than 10% of the total barrier), although the bond length dependence of the correlation correction is such that it is difficult to obtain an exact value for it.     

Role of hydroxyl concentrations in solvatochromic measures of solvent polarity of alcohols and alcohol-water mixtures-evidence that preferential solvation effects may be overestimated

For single solvents, primary alcohols and water, there is a good linear correlation (r = 0.994) between the solvent polarity index ET(30) and the molar concentration of OH groups (or 1000/Vm, where Vm is the solvent molar volume). The corresponding correlations for alcohol-water mixtures are plots vs. the sum of molar concentrations of alcohol and water, alternatively expressed as plots of ET(30)vs. volume fraction. Our quantitative treatment is an extension of recent theoretical and experimental results. In contrast, previous studies of alcohol-water mixtures have relied on plots of ET(30)vs. mole fraction, and have overestimated the effect of preferential solvation of solvatochromic dyes by the more hydrophobic alcohols.     

Phase Equilibria of Quaternary System NaCl-NaBr-Na2B4O7-H2O at 348 K

The phase equilibria of quaternary system NaCl-NaBr-Na₂B₄O₇-H₂O at 348 K were studied by the isothermal equilibrium method. The solubilities and densities of the equilibrium solution were determined. According to the experimental data, the phase diagram, density-composition diagrams and water content diagram of the quaternary system at 348 K were plotted respectively. And the phase diagram consists of one univariant curve, two crystallization fields and without any invariant point of the quaternary system. The equilibrium solid phases of the two crysta- llization fields were Na(Cl, Br) and Na₂B₄O₇·5H₂O. The experimental results show that the quaternary system contained solid solution. The densities of the solution decrease with increasing NaCl concentration and increase with increasing NaBr concentration.     

Phase behaviour of ordered polymer solutions

Rules for equilibrium phase behaviour, laid down long ago on the basis of the two laws of thermodynamics, appear to be valid also for many polymer systems in which aggregates of various topology occur. The phase rule offers a useful tool for the construction and understanding of phase diagrams for systems in which order of some kind is prevalent in certain ranges in the diagram. ‘Double sickle’ type phase diagrams, found for surfactant solutions, microemulsions as well as block-copolymer solutions can be traced back to the considerable loss of translational entropy which accompanies aggregation.     

Phase diagrams of blends of azide-containing polyoxetanes

The mutual solubility of polymers based on the azide-containing oxetane monomers 3,3-bis(azidomethyl)oxetane and 3-azidomethyl-3-methyloxetane is studied. The temperatures of melting, crystallization, glass transition; the upper critical solution temperature; and the compositions of coexisting phases for blends of polymers with different molecular masses are determined via differential scanning calorimetry and multiple-beam microinterferometry. On the basis of these data, the phase diagrams of blends are constructed. The melting regions and the metastable and heterogeneous states are determined. The studied systems are shown to have a complex amorphous-crystalline equilibrium and to differ in the location of boundary curves on the phase diagram, depending on the molecular mass of the components. Amorphous separation below the liquidus line in the metastable region with respect to the crystalline equilibrium is experimentally detected. The motion of the figurative point in different regions of the diagram is thoroughly considered. The specifics of structural and morphological organization of systems are examined via electron microscopy.