LJUNGSKILE: a program for assessing uncertainties in speciation calculations

Speciation calculations are often the base upon which further and more important conclusions are drawn, e.g., solubilities and sorption estimates used for retention of hazardous materials. Since speciation calculations are based on experimentally determined stability constants of the relevant chemical reactions, the measurement and experimental uncertainty in these constants will affect the reliability of the simulation output. The present knowledge of the thermodynamic data relevant for predicting the behaviour of a complex chemical system is quite heterogeneous. In order to predict the impact of these uncertainties on the reliability of a simulation output requires sophisticated modelling codes. In this paper, we will present a computer program, LJUNGSKILE, which utilises the thermodynamic equilibrium code PHREEQC to statistically calculate uncertainties in speciation based on uncertainties in stability constants. A short example is included.     

A fresh look at dense hydrogen under pressure. II. Chemical and physical models aiding our understanding of evolving H-H separations

In order to explain the intricate dance of intramolecular (intra-proton-pair) H-H separations observed in a numerical laboratory of calculationally preferred static hydrogen structures under pressure, we examine two effects through discrete molecular models. The first effect, we call it physical, is of simple confinement. We review a salient model already in the literature, that of LeSar and Herschbach, of a hydrogen molecule in a spheroidal cavity. As a complement, we also study a hydrogen molecule confined along a line between two helium atoms. As the size of the cavity/confining distance decreases (a surrogate for increasing pressure), in both models the equilibrium proton separation decreases and the force constant of the stretching vibration increases. The second effect, which is an orbital or chemical factor, emerges from the electronic structure of the known molecular transition metal complexes of dihydrogen. In these the H-H bond is significantly elongated (and the vibron much decreased in frequency) as a result of depopulation of the σ(g) bonding molecular orbital of H(2), and population of the antibonding σ(u)? MO. The general phenomenon, long known in chemistry, is analyzed through a specific molecular model of three hydrogen molecules interacting in a ring, a motif found in some candidate structures for dense hydrogen.     

Uncertainties in Solubility Calculations

Summary.  When considering the possible migration of hazardous elements in groundwater, one has to take into account several phenomena, e.g. solubility, ion exchange, adsorption, matrix diffusion, and transport paths. Here, we focus upon the solubility which in turn depends on several more or less uncertain chemical properties. Uncertainties in the data during laboratory experiments aiming at measurements of thermodynamic constants may cause uncertainties in the amount of some species of several tenths of the relative mass fraction. The thermodynamic data may then be used for solubility calculations under different conditions and water compositions. Clearly, there are several uncertainties associated with solubility calculations in the rock-water system. First, there is the effect of uncertainties in thermodynamic data such as stability and solubility constants, and also enthalpies of reaction if the water is not at room temperature. Furthermore, there are the rock-water interactions which will change the water composition as different minerals come in contact with the water flowing through a system of fractures. Studies in mineralogy to an accuracy good enough for modeling of water evolution are difficult to perform, and therefore the mineral composition of the rock and thus the water composition should be treated as parameters subjected to uncertainties. In addition, there are also conceptual uncertainties with respect to input data. The calculation of a solubility should be an easy task for every chemist, but in fact results differing by orders of magnitude are found even when the modelers have used the same computer program and the same data. In this paper, uncertainties associated with solubility calculations are discussed. The results are exemplified on the calculated solubilities of some actinides in groundwater from crystalline rock. Received August 21, 2000. Accepted (revised) May 18, 2001     

Uses of pH electrodes in nuclear chemistry

The determination and definition of pH is a controversial subject in many areas in chemistry. For these reasons the International Union of Pure and Applied Chemistry (IUPAC) has developed recommendations for pH measurement. These recommendations are currently (winter 2001) under revision - there will be increased emphasis on traceability of uncertainties in pH measurement. Here we describe how glass electrodes designed for measurement of pH are used in nuclear chemistry. The use of pH electrodes is then related to the IUPAC recommendations. In applied chemistry, e.g. nuclear chemistry, a pH is not sought as often as a hydrogen ion concentration or a simple equilibrium point during a titration. Ionic strengths are, moreover, often above the range in which the IUPAC recommendations apply. In these instances uncertainties must be assessed individually.     

Application of consistency checking to evaluation of uncertainty in multiple replicate measurements

Use of repeated measurements in quantitative chemical analysis is common but leads to the problem of how to combine the measurement values and produce a result with an uncertainty following the GUM. There is often confusion between repeated indications or observations of an input quantity, for whose uncertainty the GUM prescribes a type A evaluation, and complete measurements repeated on multiple sub-samples, as considered here. A solution for combining repeated measurement results and their individual uncertainties based on simple interval logic is proposed here. The individual measurement values and their uncertainties are compared with the calculated average value to see if this implies that another, possibly unknown, source of uncertainty is present. The model of the individual results is modified for this possible between-replicate effect so that the repeated measurements are consistent. Lack of consistency is a strong indication that the measurement is not fully under control and needs further development or investigation. This is not always possible, however and the method given here is proposed to ensure that the values of the repeated measurements agree with each other. A simple numerical example is given showing how the method can be implemented in practice.     

Scoring Functions – the First 100 Years

The use of simple linear mathematical models to estimate chemical properties is not a new idea. Albert Einstein used very simple ‘gravity-like' forces to explain the capillarity of different liquids in 1900–1901. Today such models are used in more complicated situations, and a great many have been developed to analyse interactions between proteins and their ligands. This is not surprising, since proteins are too complicated to model accurately without lengthy numerical analysis, and simple models often do at least as good a job in predicting binding constants as much more computationally expensive methods. One hundred years after Einstein’s ‘miraculous year’ in which he transformed physics, it is instructive to recall some of his even earlier work. As approximations, ‘scoring functions’ are excellent, but it is dangerous to read too much into them. A few cautionary tales are presented for the beginner to the field of ligand affinity prediction by linear models.     

Chemistry in Compressed Solutions

Contrary to “common sense” impression, modest pressures often have quite large effects on reactions in solution.—The volume profile of a chemical reaction in solution is easily measurable with considerable precision by means of the effect of pressure on the rate and equilibrium constant. The factors that govern the magnitude of these pressure effects are similar to those that affect the entropy changes and there is a rough correlation between them; however, the volume parameters are much less subject to apparently random fluctuations, have much greater appeal to the solution chemist's intuition, and most important, the activation volume is the only transition state property that can readily be determined in absolute terms (rather than as a difference value). In this paper we outline the experimental approach to the measurement of volume changes in wet chemical reactions, interpret the volume quantities, discuss a number of simple model equilibria and reactions, point out a number of contributions in both mechanistic and synthetic chemistry, and make an attempt to foresee future developments.     

A time-dependent quantal analysis of vibronic excitation via charge transfer in ion-molecule collisions

A semi-classical multiple state model describing charge transfer in ion-molecule system is presented. Analytical expressions for the state-to-state transition probabilities are given for both the weak-coupling and the high-velocity limits. The expressions are compared to a two-state model describing charge transfer in ion-atom systems. Some numerical calculations are presented to illustrate the various phenomena which can occur in multiple state charge transfer processes. These numerical calculations will be based upon a simple system derived from the system (Ar + N₂)⁺.     

Introduction to Chemical Oscillations Using a Modified Lotka Model

In teaching chemical kinetics most textbooks use the Lotka-Volterra Model to introduce the concept of chemical oscillations. Unfortunately, the Lotka-Volterra Model yields neutrally stable limit cycles for any initial conditions, which is a nonphysical property not observed in chemical kinetics. A more physical, two-variable model with simple linear stability analysis is, therefore, desirable. Here, we consider a Modified Lotka-Volterra Model that shows multiple physical steady states and both damped and stable oscillations. We can also study a stable node bifurcation to a saddle point and a stable node bifurcation to a stable limit cycle. This dynamically richer model can be analyzed through a simple linear stability analysis and numerical integration of the system of ordinary differential equations. Both methods, in particular the analytical analysis, are accessible to undergraduate students.     

Model uncertainty and bias in the evaluation of nuclear spectra

Unbiased analysis of γ-ray and X-ray spectra is impossible in the absence of a complete physical or mathematical model. Partial model knowledge may be supplemented by simple assumptions or by various heuristic schemes in order to effect a solution. Assessment of limits for bias, based upon the properties of the surrogate model and physical-chemical knowledge of the measurement system, is the principal target of this work. The Smoothest Consistent Baseline (SCB) approach has been introduced in an attempt to reduce assumptions and minimize bias in the extraction of a spectral peak from a baseline of uncertain shape. The bias matrix, which results directly from the numerical analysis, permits limiting baseline profiles to be simply converted into bounds for systematic model error. Contribution of the National Bureau of Standards; not subject to copyright.     

环境化工中微弱溶解度测定的新方法

将激光透射原理与化工中溶解度测定方法相结合,提出了一种激光法测定固体在液体中微弱溶解度的新方法.由于激光的稳定性、单向性和灵敏性,使得该种溶解度的测定比传统的目测法更加客观准确.这种新型测定方法除了可以解决传统化工中的数据测定问题,还可以应用于新兴的交叉学科——环境化工领域,尤其适用于环境化工中水溶解度方面的测定.例如,可针对环境保护中有毒有害腐蚀性物质的微弱水溶解度做准确测定.以对苯二甲酸分别在水和醋酸中的溶解为例,测定了300到 445 K温度范围内的微弱溶解度,并采用Wilson和Wilson-T模型关联.后者精度较好,可以作数据内插使用.     

How accurate is your two-dimensional numerical simulation? Part 1. An introduction

Numerical simulations of the diffusion processes at electrode surfaces are subject to three sources of error: those arising in the calculation of the concentration values, those arising in the numerical approximation of the flux at the electrode surface, and those arising from the integration of the flux over the electrode surface. In this paper we investigate the effects of each type of error on the accuracy of numerical simulation at the microdisc electrode by solving the steady state problem (for which the analytical solution is known). We are able to show that the major source of error is due to the boundary singularity at the electrode edge. By introducing a simple model problem, we demonstrate that the theoretical rates of convergence of the standard finite difference schemes can be attained in the absence of a boundary singularity, but these rates are destroyed by the presence of the singularity when solving for the electrode problem. Finally, we show that it is not possible to recover accuracy using n-point flux calculations or spline functions at the electrode edge.     

Chemistry of star-forming regions

The space between stars is not empty but contains gas-phase and particulate matter under varying conditions. Neutral matter is found mainly in large regions of the interstellar medium known as "clouds", the largest of which, termed "giant molecular clouds", are essentially molecular in nature. Stars and planetary systems form inside these giant clouds when portions collapse and heat up. The details of the collapse can be followed by observation of the chemical changes in the molecular composition of the gas and dust particles. Moreover, an understanding of the chemical processes yields much information on the time scales and histories of the assorted stages. Among the most recent additions to our chemical knowledge of star formation are a deeper understanding of isotopic fractionation, especially involving deuterium, and a realization that the role of neutral-neutral reactions is more salient than once thought possible.     

Uncertainty analysis of correlated stability constants

Every attempt of using a computer to model reality has two main uncertainties: the conceptual uncertainty and the data uncertainty. The conceptual uncertainty deals with the choice of model selected for the simulation and the data uncertainty is about the precision and accuracy of the input data. They are often determined experimentally and may thus be encumbered by a number of uncertainties. Normally when treating uncertainties in input data these data are treated as independent variables. However, since many of these parameters are determined together they are actually correlated. This paper focuses on chemical stability constants, a most important parameter for chemical calculations based on speciation. Commonly in the literature they are at best given with an uncertainty interval. We propose to also give the covariance matrix thus giving the opportunity to really assess correlations. In addition we discuss the effect of these correlations on speciations.     

Quantum hydrodynamics: capturing a reactive scattering resonance

The hydrodynamic equations of motion associated with the de Broglie-Bohm formulation of quantum mechanics are solved using a meshless method based upon a moving least-squares approach. An arbitrary Lagrangian-Eulerian frame of reference and a regridding algorithm which adds and deletes computational points are used to maintain a uniform and nearly constant interparticle spacing. The methodology also uses averaged fields to maintain unitary time evolution. The numerical instabilities associated with the formation of nodes in the reflected portion of the wave packet are avoided by adding artificial viscosity to the equations of motion. A new and more robust artificial viscosity algorithm is presented which gives accurate scattering results and is capable of capturing quantum resonances. The methodology is applied to a one-dimensional model chemical reaction that is known to exhibit a quantum resonance. The correlation function approach is used to compute the reactive scattering matrix, reaction probability, and time delay as a function of energy. Excellent agreement is obtained between the scattering results based upon the quantum hydrodynamic approach and those based upon standard quantum mechanics. This is the first clear demonstration of the ability of moving grid approaches to accurately and robustly reproduce resonance structures in a scattering system.     

Shrinking-core modeling of binary chromatographic breakthrough

Most chromatographic processes involve separation of two or more species, so development of a simple, accurate multicomponent chromatographic model can be valuable for improving process efficiency and yield. We consider the case of breakthrough chromatography, which has been considered in great depth for single-component modeling but to a much more limited degree for multicomponent breakthrough. We use the shrinking core model, which provides a reasonable approximation of particle uptake for proteins under strong binding conditions. Analytical column solutions for single-component systems are extended here to predict binary breakthrough chromatographic behavior for conditions under which the external transport resistance is negligible. Analytical results for the location and profile of displacement effects and expected breakthrough curves are derived for limiting cases. More generally, straightforward numerical results have also been obtained through simultaneous solution of a set of simple ordinary differential equations. Exploration of the model parameter space yields results consistent with theoretical expectations. Additionally, both analytical and numerical predictions compare favorably with experimental column breakthrough data for lysozyme-cytochrome c mixtures on the strong cation exchanger SP Sepharose FF. Especially significant is the ability of the model to predict experimentally observed displacement profiles of the more weakly adsorbed species (in this case cytochrome c). The ability to model displacement behavior using simple analytical and numerical techniques is a significant improvement over current methods.     

The behaviour of Sal'nikov's reaction, P --> A --> B, in a spherical batch reactor with the diffusion of heat and matter

The behaviour of a simple chemical reaction, occurring with the release of heat in a closed batch reactor, is considered for the situation when matter and heat are transported only by diffusive processes; thus, the reacting fluid has negligible velocity, so that heat transfer is by thermal conduction. The reaction is Sal'nikov's, which consists of two, consecutive first-order steps, producing a product B, from a precursor P, via an active intermediate A, in P --> A --> B. The first of these steps is assumed to be thermoneutral, with zero activation energy, whilst the second is exothermic, with an appreciable activation energy. These features make Sal'nikov's reaction the simplest to display thermokinetic oscillations that characterise many, more complex schemes, e.g. cool flames in hydrocarbon combustion. This study involves identifying the regions of parameter space, in which these oscillations in the temperature and the concentration of the intermediate A occur, by means of numerical simulation. These regions are compared with previous analytical stability analyses in one-dimensional systems. It was found that oscillations occur over a much larger range of conditions in the case considered here, i.e. a reactor with spherical symmetry, than in the simple 1-D case, previously studied by Gray and Scott (P. Gray and S. K. Scott, Chemical Oscillations and Instabilities, Clarendon Press, Oxford, 1990, pp. 264-291). In addition, approximate analytical solutions for the temperature and concentration of A are presented for two limiting cases of non-oscillatory behaviour. These analytical solutions have been verified by comparison with full numerical solutions of the governing equations.     

Speculations about future trends in the field of ecotoxicology

Although much is known about the effects of toxicants on single species, not much is known about the effects upon ecosystems that are more than assemblages of individual species. This situation must be addressed because past exponential growth of human populations and continuing exponential growth of national economies will put Earth's natural resources under stresses unprecedented in human history. The mission of ecotoxicologists is to see that no imbalance in the technological and ecological life support system happens, thus facilitating sustainable use of the planet. Ecosystem services will be more dependable if ecosystems are healthy. Both functional and structural attributes are as important for determining the ecosystem's health as they are for human health. Ecotoxicological assessments will be characterized by increases in both temporal and spatial scales. However, laboratory toxicological tests will remain extremely important and essential. Ecotoxicologists must become even more adept at interacting with policymakers who are responsible for societal decisions.     

Numerical Methods for a Quantum Drift–diffusion Equation in Semiconductor Physics

We present the numerical methods and simulations used to solve a charge transport problem in semiconductor physics. The problem is described by a Wigner–Poisson kinetic system we have recently proposed and whose results are in good agreement with known experiments. In this model, we consider doped semiconductor superlattices in which electrons are supposed to occupy the lowest miniband, exchange of lateral momentum is ignored, the electron–electron interaction is treated in the Hartree approximation and elastic and inelastic collisions are taken into account. Nonlocal drift-diffusion equations derived systematically elsewhere from the hyperbolic limit of a kinetic Wigner–Poisson model are solved. The nonlocality of the original quantum kinetic model equations implies that the derived drift-diffusion equations contain spatial averages over one or more superlattice periods. Numerical methods are based upon prior knowledge on physical properties of the phenomenon and have shown to be effective in validating our formulation. Numerical solutions of the equations show self-sustained oscillations of the current through a voltage biased superlattice, in good agreement with known experiments.