Sequential First-order Reactions Research Articles

General analytical solutions of multispecies advective-dispersive solute transport equations coupled with a complex reaction network

Stepwise reductive dechlorination of tetrachloroethene (PCE) to trichloroethene (TCE), three dichloroethylene (DCE) isomers (1,1-DCE, cis −1,2- DCE, and trans −1,2- DCE), vinyl chloride (VC), and ethane (ETH) may proceed under anaerobic conditions. However, most multispecies transport models for describing the plume migration of a chemical mixture comprising the original chlorinated solvent and its dechlorinated byproducts in the literature are often simplified to a sequential first-order reaction network which cannot account for the divergent reactions from TCE to the three DCE isomers and convergent reactions from the three DCE isomers to VC. In this study, general analytical solutions to multispecies transport equations with a complex reaction network were derived for a combination of semi-infinite and finite systems. The developed analytical solutions were robustly verified against a semi-analytical solution that can consider the same complex reaction network. The verification results indicated that the derived analytical solutions were accurate and robust. The general solutions derived in the present study were also used to investigate the effects of the outlet boundary conditions on solute transport involving a complex reaction network. The results showed that the analytical solution derived for infinite outlet BCs predicted lower concentrations of contaminants near the outlet boundary than those for finite outlet BCs. Moreover, a straight decay chain model may over- or under- estimate the DCE and VC concentrations compared to the multiple branching isomer reaction model. The developed analytical solutions with a complex reaction network provide more realistic and efficient tools for assessing the movement of chlorinated solvents and their degradation-related byproducts in soil–water systems.

Exact analytical solutions with great computational efficiency to three-dimensional multispecies advection-dispersion equations coupled with a sequential first-order reaction network

This study presents novel exact analytical solutions to a set of simultaneous three-dimensional advection-dispersion equations coupled with a sequential first-order degradation reaction network involving distinct retardation factor values among individual species. The analytical solutions to the coupled partial differential equation system subject to both the first - and third -type inlet source boundary conditions are derived by consecutive application of the three integral transformations in combination with sequential substitutions. The correctness of the developed analytical solutions is confirmed through numerical comparisons of three verification examples between our derived exact analytical solutions and a three-dimensional single-species analytical model in a semi-infinite domain, a two-dimensional multispecies exact analytical model in a finite domain and a three-dimensional multispecies semi-analytical model in a semi-infinite domain of the previous studies, respectively. The advantage of the derived analytical solutions is that its computational efficiency is 104 times the computational efficiency of two-dimensional multispecies analytical solutions for a finite domain when two solutions are simultaneously used to solve a two-dimensional multispecies transport problem. The developed analytical solutions are then used to evaluate the performance of the public domain BIOCHLOR model that simulates aquifer remediation by natural attenuation of dissolved multispecies at a chlorinated-solvent contaminated site provided by the Center for Subsurface Modeling Support (CSMoS) of USEPA. Results show that the BIOCHLOR model that was developed based on three-dimensional analytical model assuming a single retardation factor value for all dissolved species would not be suitable for simulating most multispecies plume migration at contaminated sites where each contaminant has its own retardation factor value. The effects of the inlet source boundary conditions on the multispecies plume migration are also investigated. The high computational efficiency of the developed analytical model in this current study renders it a very efficient tool for executing a probabilistic health risk assessment involving a large number of simulations required for problems of multispecies transport of dissolved chlorinated solvent in groundwater at a contaminated site with uncertainties in many different variables.

Comparative analysis of pyrolysis and combustion of bisphenol A polycarbonate and poly(ether ether ketone) using two-dimensional modeling: A relation between thermal transport and the physical structure of the intumescent char

A quantitative understanding of the thermal transport within a growing intumescent char layer remains largely unsolved. The development of improved techniques to analyze charring and intumescent materials is necessary to investigate the physics of heat transfer within the char. To aid in this endeavor, a systematic methodology to parameterize comprehensive pyrolysis models for charring and intumescent materials is presented. Thermogravimetric analysis, differential scanning calorimetry and microscale combustion calorimetry were conducted on 4–7 mg samples to analyze the kinetics and thermodynamics of thermal decomposition and determine heats of complete combustion of gaseous pyrolyzates. A multi-step reaction mechanism, consisting of sequential first-order reactions, was constructed to capture the physical transformations and chemical reactions observed in the milligram-scale experiments. 0.07 m diameter disk-shaped samples were gasified in the Controlled Atmosphere Pyrolysis Apparatus II to characterize the thermal transport within the condensed phase material and evolving char layer. ThermaKin2Ds was employed to interpret the experimental data using inverse analysis techniques. Bisphenol A polycarbonate and poly(ether ether ketone), widely used intumescent materials, were analyzed within this study. The resulting two-dimensional models of bisphenol A polycarbonate and poly(ether ether ketone) were capable of predicting the experimental gasification mass loss rates with a mean error of 17.8% and 16.9%, respectively. An analysis of the char pore structure was also conducted from which quantitative relationships were subsequently developed between relevant thermal transport quantities and physical descriptors of the char's physical structure. Two prominent linear correlations were discovered: the char's effective thermal conductivity increased as a function of increasing volume-weighted mean pore diameter and the product of density and thermal conductivity increased with an increasing char porosity based on image analysis. Finally, a brief sensitivity analysis of the polycarbonate and poly(ether ether ketone) burning rates was conducted to determine which key material properties were responsible for the observed differences in flammability.

A Practical Modeling Framework for Non-Fickian Transport and Multi-Species Sequential First-Order Reaction.

Many studies indicate that small-scale heterogeneity and/or mobile-immobile mass exchange produce transient non-Fickian plume behavior that is not well captured by the use of the standard, deterministic advection-dispersion equation (ADE). An extended ADE modeling framework is presented here that is based on continuous time random walk theory. It can be used to characterize non-Fickian transport coupled with simultaneous sequential first-order reactions (e.g., biodegradation or radioactive decay) for multiple degrading contaminants such as chlorinated solvents, royal demolition explosive, pesticides, and radionuclides. To demonstrate this modeling framework, new transient analytical solutions are derived and are inverted in Laplace space. Closed-form, steady-state, multi-species analytical solutions are also derived for non-Fickian transport in highly heterogeneous aquifers with linear sorption-desorption and matrix diffusion for use in spreadsheets. The solutions are general enough to allow different degradation rates for the mobile and immobile zones. The transient solutions for multi-species transport are applied to examine the effects of source remediation on the natural attenuation of downgradient plumes of both parent and degradation products in highly heterogeneous aquifers. Results for representative settings show that the use of the standard, deterministic ADE can over-estimate cleanup rates and under-predict the cleanup timeframe in comparison to the extended ADE analytical model. The modeling framework and calculations introduced here are also applied for a 30 year groundwater cleanup program at a site in Palm Bay, Florida. The simulated plume concentrations using the extended ADE exhibited agreement with observed long concentration tails of trichloroethene, cis 1,2 DCE, and VC that remained above cleanup goals.

Dependence of the base sequence on the [Cu(2,2′-bipyridine)2(NO3)](NO3)-induced oxidative DNA cleavage probed by linear dichroism

The oxidative DNA cleavage induced by the [Cu(2,2′-bipyridine)2(NO3)]NO3 (Cu(bpy)2) complex was examined using the linear dichroism (LD) technique. Using this method, the oxidative DNA cleavage by the Fenton mechanism was reported to occur through two sequential first-order reactions. As the Cu(bpy)2 concentration increased, the rate constant of both first order reactions increased, as expected. The activation energy of the second step was estimated to be 0.190 kJ mol−1. A similar method was applied for various synthetic polynucleotides. Poly[d(G-C)2], poly(dG)·poly(dC), and poly(dA)·poly(dT) produced a time-dependent decrease in LD, which could be elucidated by a single component exponential decay. This observation is in contrast to Fenton-type oxidative DNA cleavage. On the other hand, poly[d(A-T)2] produced a time-dependent decrease in the LD magnitude, which could be elucidated by two sequential first order reactions.

Generalized semi-analytical solutions to multispecies transport equation coupled with sequential first-order reaction network with spatially or temporally variable transport and decay coefficients

This paper presents a semi-analytical procedure for solving coupled the multispecies reactive solute transport equations, with a sequential first-order reaction network on spatially or temporally varying flow velocities and dispersion coefficients involving distinct retardation factors. This proposed approach was developed to overcome the limitation reported by Suk (2013) regarding the identical retardation values for all reactive species, while maintaining the extensive capability of the previous Suk method involving spatially variable or temporally variable coefficients of transport, general initial conditions, and arbitrary temporal variable inlet concentration. The proposed approach sequentially calculates the concentration distributions of each species by employing only the generalized integral transform technique (GITT). Because the proposed solutions for each species’ concentration distributions have separable forms in space and time, the solution for subsequent species (daughter species) can be obtained using only the GITT without the decomposition by change-of-variables method imposing the limitation of identical retardation values for all the reactive species by directly substituting solutions for the preceding species (parent species) into the transport equation of subsequent species (daughter species). The proposed solutions were compared with previously published analytical solutions or numerical solutions of the numerical code of the Two-Dimensional Subsurface Flow, Fate and Transport of Microbes and Chemicals (2DFATMIC) in three verification examples. In these examples, the proposed solutions were well matched with previous analytical solutions and the numerical solutions obtained by 2DFATMIC model. A hypothetical single-well push–pull test example and a scale-dependent dispersion example were designed to demonstrate the practical application of the proposed solution to a real field problem.

An analytical model for simulating two-dimensional multispecies plume migration

Abstract. The two-dimensional advection-dispersion equations coupled with sequential first-order decay reactions involving arbitrary number of species in groundwater system is considered to predict the two-dimensional plume behavior of decaying contaminant such as radionuclide and dissolved chlorinated solvent. Generalized analytical solutions in compact format are derived through the sequential application of the Laplace, finite Fourier cosine, and generalized integral transform to reduce the coupled partial differential equation system to a set of linear algebraic equations. The system of algebraic equations is next solved for each species in the transformed domain, and the solutions in the original domain are then obtained through consecutive integral transform inversions. Explicit form solutions for a special case are derived using the generalized analytical solutions and are compared with the numerical solutions. The analytical results indicate that the analytical solutions are robust, accurate and useful for simulation or screening tools to assess plume behaviors of decaying contaminants.

Effect of Various Intercalators on the Fenton-Type Oxidative Cleavage of Double-Stranded DNA

The intensity of the linear dichroism (LD) in the absorption region of DNA (about 260 nm) decreased with time in the presence of [Fe(EDTA)](2+) (EDTA = ethylenediaminetetraacetic acid), H2O2, and ascorbate. The decrease in the LD signal indicated either an increase in flexibility, a shortening of the DNA stem, or both, owing to oxidative cleavage, and was best described by the difference between the two single-exponential-decay curves, thereby suggesting the involvement of two sequential first-order reactions. The fast reaction was assigned to cleavage of one of two DNA strands, which increased the flexibility of the DNA. The slow reaction corresponded to cleavage at or near the first cleavage site, thereby shortening the DNA stem. The presence of an intercalator, including ethidium, propidium, 9-aminoacridine, and proflavine, inhibited the first step of the cleavage reaction. One of the possible reasons for the observed inhibition might be a change in the DNA conformation near the intercalation site. Intercalation caused an unwinding and elongation of the DNA and resulted in changes in the location of the H atoms of the sugar moiety, which is known to be the main site at which hydroxyl radicals react.

Stochastic modeling analysis of sequential first-order degradation reactions and non-Fickian transport in steady state plumes

Stochastic analyses were performed to examine sequential first-order monomolecular reactions at the microscopic scale and both Fickian and non-Fickian plume reactive transport at the macroscopic scale. An analytical solution was derived for the chemical master equation (CME) for a closed system of irreversible first-order monomolecular reactions. Taking a Lagrangian reference frame of particles migrating from a source, analyses show that the relative concentration of each species in the deterministic analytical solution for 1-D steady state plug flow with first-order sequential degradation is mathematically equivalent to the mean of a multinomial distribution of plume particles moving at constant velocity with sequential transformations described by transition probabilities of a discrete state, continuous-time Markov chain. In order to examine the coupling of reaction and transport terms in subdiffusive-reactive transport equations, a closed-form multispecies analytical solution also was derived for steady state advection, dispersion, and sequential first-order reaction. Using a 1-D continuous-time random walk (CTRW) embedded in Markov chains, computationally efficient Monte Carlo simulations of particle movement were performed to more fully examine effects of subdiffusive-reactive transport with an application to steady state, sequentially degrading multispecies plumes at a site in Palm, Bay, FL. The simulation results indicated that non-Fickian steady state plumes can resemble Fickian plumes because linear reactions truncate the waiting time between particle jumps, which removes lower velocity particles from the broad spectrum of velocities in highly heterogeneous media. Results show that fitting of Fickian models to plume concentration data can lead to inaccurate estimates of rate constants because of the wide distribution of travel times in highly heterogeneous media.

Structural Destabilization of DNA Duplexes Containing Single-Base Lesions Investigated by Nanopore Measurements

The influence of DNA duplex structural destabilization introduced by a single base-pair modification was investigated by nanopore measurements. A series of 11 modified base pairs were introduced into the context of an otherwise complementary DNA duplex formed by a 17-mer and a 65-mer such that the overhanging ends comprised poly(dT)23 tails, generating a representative set of duplexes that display a range of unzipping mechanistic behaviors and kinetic stabilities. The guanine oxidation products 8-oxo-7,8-dihydroguanine (OG), guanidinohydantoin (Gh), and spiroiminodihydantoin (Sp) were paired with either cytosine (C), adenine (A), or 2,6-diaminopurine (D) to form modified base pairs. The mechanism and kinetic rate constants of duplex dissociation were determined by threading either the 3' or 5' overhangs into an α-hemolysin (α-HL) channel under an electrical field and measuring the distributions of unzipping times at constant force. In order of decreasing thermodynamic stability (as measured by duplex melting points), the rate of duplex dissociation increases, and the mechanism evolves from a first-order reaction to two sequential first-order reactions. These measurements allow us to rank the kinetic stability of lesion-containing duplexes relative to the canonical G:C base pair in which the OG:C, Gh:C, and Sp:C base pairs are, respectively, 3-200 times less stable. The rate constants also depend on whether unzipping was initiated from the 3' versus 5' side of the duplex. The kinetic stability of these duplexes was interpreted in terms of the structural destabilization introduced by the single base-pair modification. Specifically, a large distortion of the duplex backbone introduced by the presence of the highly oxidized guanine products Sp and Gh leads to a rapid two-step unzipping. The number of hydrogen bonds in the modified base pair plays a lesser role in determining the kinetics of duplex dissociation.

Unzipping Kinetics of Duplex DNA Containing Oxidized Lesions in an α-Hemolysin Nanopore

The unzipping kinetics for lesion-containing DNA duplexes was studied in an α-hemolysin (α-HL) nanopore. The lesion of focus was the guanine two-electron oxidation product, 8-oxo-7,8-dihydroguanine (OG), and its further oxidation products, the hydantoins guanidinohydantoin (Gh) and spiroiminodihydantoin (Sp). The voltage-driven unzipping of individual duplex DNA molecules with symmetrical overhangs was carried out by pulling one strand of the duplex through the α-HL channel using an electrical field. Entry from the 3' or 5' end produced distinct current blockages, allowing directional effects on unzipping kinetics to be investigated. We find that the strand dissociation of complementary duplexes or duplexes containing the slightly destabilizing lesion OG follows a first-order kinetic model, while opening of duplexes that contain the highly destabilizing lesions Gh or Sp is described by two sequential first-order reactions, in which the intermediate state is proposed to correspond to the duplex unzipped to the lesion site within the channel. The rate constants for strand separation of the duplexes containing single lesions were obtained from kinetic model fits to histograms of unzipping duration. For all duplexes, the rate constants for strand separation displayed a significant dependence on the direction of entry into the nanopore. For duplexes containing Gh, truncated duplexes were used to assign the measured rate constants for the first and second unzipping steps of symmetrically designed duplexes.

Analytical Solution for Multi-Species Contaminant Transport in Finite Media with Time-Varying Boundary Conditions

Most analytical solutions available for the equations governing the advective–dispersive transport of multiple solutes undergoing sequential first-order decay reactions have been developed for infinite or semi-infinite spatial domains and steady-state boundary conditions. In this study, we present an analytical solution for a finite domain and a time-varying boundary condition. The solution was found using the Classic Integral Transform Technique (CITT) in combination with a filter function having separable space and time dependencies, implementation of the superposition principle, and using an algebraic transformation that changes the advection–dispersion equation for each species into a diffusion equation. The analytical solution was evaluated using a test case from the literature involving a four radionuclide decay chain. Results show that convergence is slower for advection-dominated transport problems. In all cases, the converged results were identical to those obtained with the previous solution for a semi-infinite domain, except near the exit boundary where differences were expected. Among other applications, the new solution should be useful for benchmarking numerical solutions because of the adoption of a finite spatial domain.

Stopped flow kinetic studies on reductive half-reaction of histamine dehydrogenase from Nocardioides simplex with histamine

Histamine dehydrogenase from Nocardioides simplex (HmDH) which catalyzes the oxidative deamination of histamine is an iron-sulphur-containing flavoprotein. For our further understanding on the intramolecular electron transfer process, the reductive half reaction of HmDH with histamine has been studied by stopped flow spectrophotometry at pH 7.5 and 10. The reaction at pH 7.5 is found to be analysed on a kinetic model composed of three sequential first-order reactions. The first fast phase, of which the rate constant shows a hyperbolic dependence on the histamine concentration, is assigned to a direct two-electron reduction of the oxidized flavin (CFMN(O)) by histamine with no involvement of the semiquinone form of the flavin (CFMN(S)). The second moderate process is the substrate-independent intramolecular single-electron transfer from the reduced flavin to the oxidized iron-sulphur cluster. The third slow process is considered to reflect the second binding of histamine to CFMN(S), which is responsible for the substrate inhibition. At pH 10, the reaction is analysed with one pseudo-first-order reaction phase which is substrate-dependent two-electron reduction of CFMN(O) coupled with the subsequent fast intersubunit single-electron transfer. The UV-vis spectroscopy of HmDH suggests the deprotonation of Tyr residues, which seems to cause the switching of the electron transfer property.

Kinetics of Anthocyanin Degradation and Browning in Reconstituted Blackberry Juice Treated at High Temperatures (100−180 °C)

Monomeric anthocyanin degradation and nonenzymatic browning (NEB) index have been determined in reconstituted blackberry juice heated at high temperature in a hermetically sealed cell. Statistical analysis demonstrated that, when the temperature range (100-180 degrees C) was divided into two subranges (100-140 and 140-180 degrees C) for anthocyanin degradation, reaction kinetics were well represented by two sequential first-order reactions. The activation energy for NEB from 100 to 180 degrees C (106 kJxmol(-1)) was slightly higher than the anthocyanin value at the lower temperature range (92 kJxmol(-1)), but was more than twice the value for the higher range (44 kJxmol(-1)). The reaction rate constant at 140 degrees C for anthocyanin degradation (3.5 x 10(-3) s(-1)) was two times that for the NEB index (1.6 x 10(-3) s(-1)). Hence, anthocyanin degradation was faster than the appearance of NEB products. The non-isothermal method developed allows estimating kinetic parameters and thereby generating temperature profiles of heat processes that would help preserve the nutritional properties of foods during high-temperature processes.

Thermal stability of bioactive enzymatic papers

The thermal stability of two enzymes adsorbed on paper, alkaline phosphatase (ALP) and horseradish peroxidase (HRP), was measured using a colorimetric technique quantifying the intensity of the product complex. The enzymes adsorbed on paper retained their functionality and selectivity. Adsorption on paper increased the enzyme thermal stability by 2–3 orders of magnitude compared to the same enzyme in solution. ALP and HRP enzymatic papers had half-lives of 533 h and 239 h at 23 °C, respectively. The thermal degradation of adsorbed enzyme was found to follow two sequential first-order reactions, indication of a reaction system. A complex pattern of enzyme was printed on paper using a thermal inkjet printer. Paper and inkjet printing are ideal material and process to manufacture low-cost–high volume bioactive surfaces.

Analytical Solution for Multi-Species Contaminant Transport Subject to Sequential First-Order Decay Reactions in Finite Media

Transport equations governing the movement of multiple solutes undergoing sequential first-order decay reactions have relevance in analyzing a variety of subsurface contaminant transport problems. In this study, a one-dimensional analytical solution for multi-species transport is obtained for finite porous media and constant boundary conditions. The solution permits different retardation factors for the various species. The solution procedure involves a classic algebraic substitution that transforms the advection-dispersion partial differential equation for each species into an equation that is purely diffusive. The new system of partial differential equations is solved analytically using the Classic Integral Transform Technique (CITT). Results for a classic test case involving a three-species nitrification chain are shown to agree with previously reported literature values. Because the new solution was obtained for a finite domain, it should be especially useful for testing numerical solution procedures.

Analysis of Primary Degradation and Decolourization of Dyes in Water by an H2O2/UV Advanced Oxidation Process

AbstractSynthetic dyes are extensively used in textile dyeing, paper printing, colour photography, pharmaceuticals, food, cosmetics and other industries. In spite of their diversity there are a certain number of properties common to many dye compounds, such as aromatic constitution, chromophore groups and others. Similarly to other dyes and due to the formation of colour intermediates, in the case of Rhodamine 6G colour capacity is maintained in the initial steps of dye degradation. For this reason in the degradation of a dye it is necessary to distinguish between two processes that take place simultaneously: dye removal and decolourization. This study was conducted by using a water solution of 50 mg/L of Rhodamine 6G (Rh-6G), as a model of a dye wastewater, in the hydrogen peroxide/UV system. The kinetic model proposed in this paper for the removing of Rh- 6G is a sequential first-order reaction. This model describes acceptably the changes in two kinds of compound for a wide interval of H

Analytical solutions for sequentially coupled one-dimensional reactive transport problems – Part I: Mathematical derivations

Multi-species reactive transport equations coupled through sorption and sequential first-order reactions are commonly used to model sites contaminated with radioactive wastes, chlorinated solvents and nitrogenous species. Although researchers have been attempting to solve various forms of these reactive transport equations for over 50 years, a general closed-form analytical solution to this problem is not available in the published literature. In Part I of this two-part article, we derive a closed-form analytical solution to this problem for spatially-varying initial conditions. The proposed solution procedure employs a combination of Laplace and linear transform methods to uncouple and solve the system of partial differential equations. Two distinct solutions are derived for Dirichlet and Cauchy boundary conditions each with Bateman-type source terms. We organize and present the final solutions in a common format that represents the solutions to both boundary conditions. In addition, we provide the mathematical concepts for deriving the solution within a generic framework that can be used for solving similar transport problems.

Analytical solutions for sequentially coupled one-dimensional reactive transport problems – Part II: Special cases, implementation and testing

This is Part-II of a two-part article that presents analytical solutions to multi-species reactive transport equations coupled through sorption and sequential first-order reactions. In Part-I, we provide the mathematical derivations and in this article we discuss the computational techniques for implementing these solutions. We adopt these techniques to develop a general computer code and use it to verify the solutions. We also simplify the general solutions for various special-case transport scenarios involving zero initial condition, identical retardation factors and zero advection. In addition to this, we derive specialized solution expressions for zero dispersion and steady-state conditions. Whereever possible, we compare these special-case solutions against previously published analytical solutions to establish the validity of the new solution. Finally, we test the new solution against other published analytical and semi-analytical solutions using a set of example problems.

Simulation of Regulated Exocytosis of Amylase from Salivary Parotid Acinar Cells by a Consecutive Reaction Model Comprising Two Sequential First-order Reactions

Amylase secretion from parotid acinar cells results from stimulus-regulated fusion of apical membrane and secretory granules that contain amylase. The time course of amylase secretion induced by various secretagogues has been reported. Calcium-mobilizing agonists such as carbamylcholine and substance P induce rapid and transient secretion while cAMP-mobilizing agonists such as isoproterenol cause long-term secretion. Combination of these two types of agonists results in a rapid and high rate of secretion. To explain the various time courses of these stimulations, it was assumed that amylase secretion is a consecutive reaction that consists of two first-order reactions. It was postulated that secretory granules were classified into three states: (A) pre-docked, (B) docked, and (C) fusion. The simple simulation could explain the time course of amylase secretion induced by various secretagogues by simply changing the rate constants for docking (reaction A to B) and fusion (reaction B to C) steps. It was also found that calcium mainly enhances the last fusion step and that cAMP activates the docking step. The amount of docked granules is estimated to be quite small, which accounts for why amylase secretion is regulated mainly by cAMP. The effects of the two types of secretagogues were synergistic, meaning that their intracellular signaling pathways are independent. At the same time, this also suggests that basal and enhanced secretion induced by two types of agonists have the same exocytotic process and that two stimuli independently activate the same machinery that mediates docking or fusion. This simulation is useful in analysis of the effects of secretion modulators and the molecular mechanism of amylase secretion.