Statistical Rate Theory Research Articles

Complete Analytical Solution of the Statistical Rate Theory: Desorption from Solid/Solution Interfaces.

One of the essential steps in the design and regeneration of catalysts is desorption. Kinetics modeling of the desorption process is essential for a better understanding of this process. The statistical rate theory (SRT) method is one of the essential theoretical methods that can be used to study the rate of desorption. For the first time, a complete solution of the SRT equation for desorption from the solid surface to the solution phase (SRT-D) is reported. The new integrated equations are provided as the linear forms, which have been denoted as the SRT-LFD equations. The first complete analytical solution of the SRT-D equation is confirmed using the created data by numerical solution of the SRT-D equation and the experimental data. The perfect agreement between the obtained results of the SRT-LFD equations and the results of the created and experimental data confirms the accuracy of the obtained equations.

Assessment of the statistical rate theory expression for evaporation mass flux

A series of 72 steady-state evaporation experiments in which water evaporated from a spherical liquid-vapor interface have been conducted. In each experiment, the interfacial temperatures, the temperature profile across the liquid-vapor interface, and the pressure in the vapor phase were measured. When the interfacial parameters were used in the statistical rate theory (SRT) expression for evaporation flux, the vapor-phase pressure could be predicted to a reasonable degree of accuracy in all experiments. In all 72 experiments, the interfacial temperature of the vapor was always higher than that of the liquid phase and in certain cases, the difference was measured to be 7.1 K. Measurement of the vapor-phase pressure near the cool liquid-vapor interface and far from the interface did not show a significant difference, indicating that the density (concentration) in the bulk vapor phase may not be uniform.

ChemDyME: Kinetically Steered, Automated Mechanism Generation through Combined Molecular Dynamics and Master Equation Calculations.

In many scientific fields, there is an interest in understanding the way in which chemical networks evolve. The chemical networks which researchers focus upon have become increasingly complex, and this has motivated the development of automated methods for exploring chemical reactivity or conformational change in a "black-box" manner, harnessing modern computing resources to automate mechanism discovery. In this work, we present a new approach to automated mechanism generation which couples molecular dynamics and statistical rate theory to automatically find kinetically important reactions and then solve the time evolution of the species in the evolving network. The key to this chemical network mapping through combined dynamics and ME simulation approach is the concept of "kinetic convergence", whereby the search for new reactions is constrained to those species which are kinetically favorable at the conditions of interest. We demonstrate the capability of the new approach for two systems, a well-studied combustion system and a multiple oxygen addition system relevant to atmospheric aerosol formation.

Thermal Decomposition Kinetics of the Indenyl Radical: A Theoretical Study.

Quantum chemistry and statistical reaction rate theory calculations have been performed to investigate the products and kinetics of indenyl radical decomposition. Three competitive product sets are identified, including formation of a cyclopentadienyl radical (c-C5H5) and diacetylene (C4H2), which has not been included in prior theoretical kinetics investigations. Rate coefficients for indenyl decomposition are determined from master equation simulations at 1800-2400 K and 0.01-100 atm, and temperature- and pressure-dependent rate coefficient expressions are incorporated into a detailed chemical kinetic model for indene pyrolysis. Indenyl is found to predominantly decompose to o-benzyne (o-C6H4) + propargyl (C3H3), with lesser amounts of fulvenallenyl (C7H5) + C2H2 and c-C5H5 + C4H2.

Quantum-Chemical and Theoretical Kinetics Studies on the Gas-Phase Unimolecular Decomposition Reaction of Sulfur Hexafluoride, SF6

The aim of this study is to calculate the unimolecular rate coefficients for the unimolecular decomposition reaction of the industrially important molecule, SF6. The energies of stationary-points involved in the title reaction are calculated by the combination W1 method. Two main reaction paths are considered: SF6 → SF5 + F (R1) and SF6 → SF4 + F2 (R2). Having information on energies and molecular properties of reactants and transition-states, RRKM statistical rate theory is used to compute the rate coefficients as a function of temperature and pressure. For the bond dissociation process R1, special version of RRKM theory, i. e., Variable reaction coordinate-transition state theory (VRC-TST) is employed. Although the reaction R1 is the dominant process over a wide range of pressure and temperature, but the reaction R2 could be significant at high temperatures. The following Arrhenius expressions are obtained for high-pressure limiting rate constants of reaction paths R1 and R2: k∞,1 = 5.71 × 1016 s−1 exp (−429.8 kJ mol−1 /RT) k∞,2 = 2.14 × 1016 s−1 exp (−590.6 kJ mol−1 /RT).

Isotope-specific reactions of acetonitrile (CH3CN) with trapped, translationally cold CCl.

The gas-phase reaction of CCl+ with acetonitrile (CH3CN) is studied using a linear Paul ion trap coupled to a time-of-flight mass spectrometer. This work builds on a previous study of the reaction of CCl+ with acetylene [K. J. Catani et al., J. Chem. Phys. 152, 234310 (2020)] and further explores the reactivity of CCl+ with organic neutral molecules. Both of the reactant species are relevant in observations and models of chemistry in the interstellar medium. Nitriles, in particular, are noted for their relevance in prebiotic chemistry and are found in the atmosphere of Titan, one of Saturn's moons. This work represents one of the first studied reactions of a halogenated carbocation with a nitrile and the first exploration of CCl+ with a nitrile. Reactant isotopologues are used to unambiguously assign ionic primary products from this reaction: HNCCl+ and C2H3 +. Branching ratios are measured, and both primary products are determined to be equally probable. Quantum chemical and statistical reaction rate theory calculations illuminate pertinent information for interpreting the reaction data, including reaction thermodynamics and a potential energy surface for the reaction, as well as rate constants and branching ratios for the observed products. In particular, the reaction products and potential energy surface stimulate questions regarding the strength and role of the nitrile functional group, which can be further explored with more reactions of this class.

The reaction of dimethyl sulfide with the Criegee intermediates CH2OO and (CH3)2COO: Theoretical investigations

In this research, the reactions of two simple Criegee intermediates formaldehyde oxide and acetone oxide with dimethyl sulfide is explored theoretically. The well-tested meta-GGA density functional theory method M11-L is employed to locate the structures of stationary points on the potential energy surface of the title reactions. Statistical rate theories such as transition state theory (TST) and RRKM theory are employed to determine the dominant products of the reactions. It is found that both reactions occur via relatively strong van der Waals complexes leading to CS bonded adducts, IM1C and IM1D. These initial adducts decompose to yield other intermediates and products. According to the present theoretical thermodynamics and kinetics calculations, IM1C adduct could be formed in considerable amount in atmospheric condition. However, the reaction of (CH3)2COO with dimethyl sulfide is not of atmospheric significance.

Atomistic investigation on the kinetic behavior of vapour adsorption and cluster evolution using a statistical rate theory approach.

The kinetic behavior of vapor adsorption on a solid surface in an isobaric-isothermal system is investigated by means of molecular dynamics simulations combined with theoretical studies through a statistical rate theory approach. The molecular insights into the formation and evolution of clusters in the adsorbate are presented. Results show that the argon vapor is adsorbed on the silicon surface as different types of clusters. In the initial stage of adsorption, the empty adsorption sites on the surface decrease, and the adsorbed single-molecule-cluster grows rapidly and dominates the interface. The increasing rate of the adsorbed cluster and the declining rate of the empty adsorption site are dependent on the pressure ratio. For a large pressure ratio, the single-molecule-clusters are aggregated to incubate large clusters, and the fraction of a single-molecule-cluster is decreased with time. When the adsorption isotherm is determined, the chemical potential of the adsorbed cluster is expressed from the zeta isotherm model. Then the adsorption kinetics are analyzed through the statistical rate theory. The molecular exchange rate and the instantaneous driving force are calculated. The higher pressure ratio induces the larger chemical potential difference and accelerates the net adsorption rate. The adsorption kinetics derived from MD simulations are in close agreement with the theoretical analysis of the statistical rate theory.

Thermal decomposition and isomerization of furfural and 2-pyrone: a theoretical kinetic study.

We have studied the decomposition and isomerization of furfural in the gas phase using quantum chemical and statistical reaction rate theory techniques. This work uncovers a variety of new reaction channels in furfural pyrolysis that lead to formation of the experimentally observed products, including CO2, which was previously unexplained. In addition to the known mechanism for furan + CO production, furfural is shown to isomerize directly to 2-pyrone, with a barrier height of 69 kcal mol-1, from where it can decompose to vinylketene + CO (highest barrier of 65 kcal mol-1) or to CO2 + 1,3-cyclobutadiene (highest barrier of 66 kcal mol-1). Alternative pathways to vinylketene + CO and 4-pyrone are also described. An RRKM theory/master equation model is developed to describe reactions on the C5O2H4 surface and used to simulate the decomposition kinetics of furfural and 2-pyrone. For both molecules, decomposition at 1400-2100 K is dominated by the formation of furan + CO, which represents around 75% of the total products, compared to around 19% and 6% for vinylketene + CO and total CO2, respectively. The model also predicts significant formation of stabilized 2-pyrone under these conditions. Rate coefficient expressions are reported as a function of both temperature and pressure for the main decomposition and isomerization channels identified in the pyrolysis of furfural and 2-pyrone, to facilitate detailed chemical kinetic modelling of these important oxygenated hydrocarbons.

Collisional stabilization of ion-molecule association complexes in He, H2, or N2 buffer gases

The role of collisional energy transfer in ion-molecule association reactions is analyzed. Rate constants for the formation of adducts between HCl and NO3−(HNO3)x (H2SO4)y or HSO4−(HNO3)x (H2SO4)y (with x = 0–2 and y = 0–2) in the buffer gases H2, He, and N2 and at temperatures between 150 and 300 K are considered. Quantum-chemical calculations of molecular parameters and statistical unimolecular rate theory are combined to model low-pressure rate constants whereas ion-molecule capture theory provides high-pressure rate constants. The comparison with experimental results indicates that energy transfer is dominated by overall collision numbers while weak-collision effects are only of minor importance. On the other hand, often neglected falloff effects between termolecular and bimolecular reaction behavior have to be taken into account.

A theoretical kinetic study on the reaction of atomic bromine with toluene

AbstractThe reaction of Br atoms with toluene was investigated by employing various quantum chemical methods and statistical rate theory calculations. Various composite methods such as CBS‐QB3, G3, and G4 were used to obtain the energy profiles of the Br + toluene reaction. Further single‐point calculations of the stationary points were performed at the CCSD(T)/cc‐pV(D,T)Z level of theory using B3LYP/cc‐pVTZ and MP2/aug‐cc‐pVDZ optimized geometries. Our calculations revealed several reaction pathways in the potential energy surface of the Br + toluene reaction. However, the reaction pathway that abstracts hydrogen atoms from the methyl site of toluene was found to be energetically the most favorable. This reaction pathway appears to proceed via a complex forming mechanism, similar to that seen in the reactions of cyclic ethers with Br atoms. Our calculations reveal that the reaction of a Br atom with toluene proceeds exclusively via intermediate complexes in an overall endothermic addition‐elimination mechanism. Based on the ab initio results, the standard enthalpies of formation of the product radicals and the rate coefficients for the relevant reaction pathways are computed. The calculated values of the enthalpy of formation are found to match excellently with the available literature data. Lowering the barrier height of hydrogen abstraction reaction at the methyl site by less than 4 kJ/mol, the calculated rate coefficients, kov(T) = 1.36 × 10–23 T3.687 exp(−4.57 K/T) cm3 molecule–1 s–1, reproduced the experimental data excellently from 200 to 500 K.

On the influence of water on urea condensation reactions: a theoretical study

Abstract The influence of water molecules on the kinetics of urea condensation reactions was studied with high-level quantum chemical methods and statistical rate theory. The study focuses on the production of biuret, triuret, and cyanuric acid from urea because of their relevance as unwanted byproducts in the urea-based selective catalytic reduction (urea-SCR) exhaust after treatment of Diesel engines. In order to characterize the potential energy surfaces and molecular reaction pathways, calculations with explicitly-correlated coupled-cluster methods were performed. It turned out that the reactions proceed via pre-reactive complexes and the inclusion of one or two water molecules into the condensation mechanisms leads to a decrease of the energy barriers. This effect is particularly pronounced in the production of biuret. Due to the pre-reactive equilibria, the rates of the overall reactions can increase or decrease by incorporating water into the mechanism, depending on the temperature and water concentration. Under the conditions of urea-SCR, the studied reactions are too slow to contribute to the observed byproduct formation.

Prediction of Rate Coefficients for the H2CO + OH → HCO + H2O Reaction at Combustion, Atmospheric and Interstellar Medium Conditions.

Despite the relevance of the H2CO + OH → HCO + H2O reaction for combustion, atmospheric, and interstellar medium conditions, a large discrepancy on energetic and kinetic data for this reaction is still observed in the previous literature. In this work, this hydrogen abstraction reaction has been investigated at the CCSD(T)/CBS level of theory, suggesting that both the prebarrier complex and saddle point are stabilized in relation to the reactants by 3.31 and 1.35 kcal mol-1, respectively. Moreover, from the Gibbs free energy profile of the reaction coordinate, it has been verified that the formation of the prebarrier complex is endergonic, for temperatures above 550 K. Hence, for temperatures lower than 550 K, the reaction is described by a mechanism consisting of three elementary steps, while for higher temperatures it can be assumed to be an elementary reaction. Finally, the prediction of rate coefficients suggests that unified statistical rate theory best applies to the low temperature regime, while canonical variational rate coefficients better fit experimental data at the high temperature regime.

The reaction of OH radical with the Criegee intermediate propanone oxide: Theoretical investigations

The mechanism and kinetics of reaction of the Criegee intermediate (CH3)2CO(O) with OH radicals is investigated by theoretical methods. The stationary point on the potential energy surface of the reaction and their corresponding molecular properties are calculated by quantum-chemical methods. The significant product channel is found to be CH3COCH3 + HO2 (P1). The product CH3CO(O)CH2 + H2O (P3) is also predicted to be formed effectively at low temperatures. The reaction path (CH3)2CO(O) + OH → CH3COCH2 + 2 OH which is an auto-catalytic pathway for degradation of the Criegee intermediate has been of special interest. The rate constants for all important product channels including the latter auto-catalytic pathway are computed by statistical rate theories. It is found that the latter auto-catalytic process is not of importance in the kinetics of the title reaction.

Clean technology for synchronous sequestration of charged organic micro-pollutant onto microwave-assisted hybrid clay materials.

The Sustainable Development Goal 6 (SDG #6) of the United Nations (UN) is hinged on the provision, availability, and sustainability of water for the global populace by 2030. In a bid to achieve this goal, the quest to seek for ubiquitous and low-cost adsorbents to treat effluents laden with industrial dyes, such as methylene blue (MB), is on the increase in recent years. Acute exposure of humans to (MB) dye causes cyanosis, necrosis, and jaundice and even leads to death. In this research, zinc-modified hybrid clay composite adsorbent (materials from kaolinite and biomass (crushedCarica papaya seeds and/or plantain peel)) was developed via microwave route. This adsorbent was characterized using field emission scanning electron microscopy (FE-SEM), Fourier transform infrared (FTIR) spectroscopy, energy-dispersive X-ray (EDX), and high-resolution transmission electron microscopy (HR-TEM). These characterization techniques confirmed the success achieved in doping hybrid clay with Zn. These adsorbents were used to sequester cationic dye (MB) from aqueous solutions and textile effluent under various experimental conditions. The adsorption and desorption data obtained were analyzed using various kinetic models, which are two-step kinetics, pseudo-first order, pseudo-second order, fractal kinetics, first-order desorption, second-order desorption, and modified statistical rate theory (MSRT) desorption models. Results showed that the adsorption of the dye occurred via several chemical interactions, while the latter models (for desorption) indicated that desorption occurred in two different desorption sites on the adsorbent surfaces, which showed that the adsorption of MB dyeonto the adsorbents was stable without the emergence of any secondary pollution. Adsorption of MB was achieved within 15min for aqueous solutions and 900min for textile effluent, which is an improvement on previous results from other studies. The three adsorption-desorption cycles for MB uptake by the adsorbents showed that it is pragmatically applicable to treat textile effluents. Hence, low-cost composite adsorbents have a potential for the effective remediation of MB dyefrom textile effluents as this study confirmed.

Derivation of Pseudo-First-Order, Pseudo-Second-Order and Modified Pseudo-First-Order rate equations from Langmuir and Freundlich isotherms for adsorption

• Kinetics study of Langmuir and Freundlich isotherms by Statistical Rate Theory. • Derivation of Pseudo-First-Order and Pseudo-Second-Order models. • Derivation of Modified Pseudo-First-Order model. • Derivation of a new kinetics model for adsorption. • Simulation of Humic Acid adsorption on Hematite and Kaolinite adsorbents. The kinetics of adsorption for Langmuir and Freundlich isotherms has been explored theoretically on the basis of Statistical Rate Theory (SRT). The Modified Pseudo-First-Order (MPFO) and Pseudo-First-Order (PFO) models were derived from Freundlich isotherm on the basis of Statistical Rate Theory at c 0 ≫ c e and at close to equilibrium respectively. Also, for a Langmuirian adsorption MPFO was derived at initial times of adsorption under condition c 0 ≫ c e and also Pseudo-First-Order (at close to equilibrium) and Pseudo-Second-Order (PSO) model (at close to equilibrium for c 0 ≫ c e and θ e ≅ 1 ) were obtained based on SRT. It has been proven that from Freundlich and Langmuir isotherms the fractional coverage is a linear function of t at very short initial times of adsorption. Also an useful rate equation was derived at condition c 0 ≅ c e from Freundlich isotherm. The theoretical obtained equations from Freundlich and Langmuir isotherms have been examined by several set of experimental data selected from literature.

KinBot: Automated stationary point search on potential energy surfaces

KinBot is a Python code that automatically characterizes kinetically important stationary points on reactive potential energy surfaces and arranges the results into a form that lends itself easily to master equation calculations. This version of KinBot tackles C, H, O and S atom containing species and unimolecular (isomerization or dissociation) reactions. KinBot iteratively changes the geometry of the reactant to obtain initial guesses for reactive saddle points defined by KinBot’s reaction types, which are then optimized by a third-party quantum chemistry package. KinBot verifies the connectivity of the saddle points with the reactant and identifies the products through intrinsic reaction coordinate calculations. New calculations can be automatically spawned from the products to obtain complete potential energy surfaces. The utilities of KinBot include conformer searches, projected frequency and hindered rotor calculations, and the automatic determination of the rotational symmetry numbers. Input files for popular RRKM master equation codes are automatically built, enabling an automated workflow all the way to the calculation of pressure and temperature dependent rate coefficients. Four examples are included. (i) [1,3]-sigmatropic H-migration reactions of unsaturated hydrocarbons and oxygenates are calculated to assess the relative importance of suprafacial and antrafacial reactions. (ii) Saddle points on three products of gamma-valerolactone thermal decomposition are studied and compared to literature potential energy surfaces. (iii) The previously published propene+OH reaction is reproduced to show the capability of building an entire potential energy surface. (iv) All species up to C4 in the Aramco Mech 2.0 are subjected to a KinBot search. Program summaryProgram title: KinBotProgram files doi:http://dx.doi.org/10.17632/hsh6dvv2zj.1Licensing provisions: BSD 3-ClauseProgramming language: PythonSupplementary material:1. A static version of the source code (KinBot.tar),2. The manual for the static version (KinBot_Manual.pdf)3. Geometries and energies of the stationary points on the potential energy surface of the sigmatropic reaction search (sigmatropic_H_shift.out)4. Geometries and energies of the stationary points on the potential energy surface of the propene+ OH central and terminal addition reaction (propene+oh central addition.out, propene+oh terminal addition.out)5. Geometries and energies of the stationary points on the potential energy surface of gamma valerolactone, 4-pentenoic acid and 3-pentenoic acid (GVL energies and geometries.out, 4PA energies and geometries.out, 3PA energies and geometries.out)6. Example runs including all input and output files for a one-well search for propanol radical, full PES search for the n-pentyl radical, a search for all homolytic scission in propanol, and the reaction searches for GVL (output.zip)7. Results of symmetry calculations for a literature benchmark dataset (Symmetry_correct.pdf, Symmetry_wrong.pdf)Nature of problem: Automatic discovery of unimolecular reaction pathways (isomerization and dissociation) for molecules and radicals relevant in gas-phase combustion and atmospheric chemistry, including oxidation and pyrolytic processes for structures including carbon, oxygen, sulfur and hydrogen atoms. The reactants, products, and transition states are characterized using a suite of tools coupled to electronic structure codes, and the results are provided in a format that lends itself easily to calculating rate coefficients based on statistical rate theories with other external codes.Solution method: Reaction pathways are identified using heuristic searches starting from a reactant by iteratively altering its geometry toward a good guess for a transition state for reactions with barriers. The transition state is identified as a first-order saddle point on the potential energy surface, which is located using local optimization methods of third-party quantum chemistry codes. We use intrinsic reaction coordinate calculations to verify the direct connectivity of the saddle point to the reactant and to identify the product species. Conformational searches, hindered rotor potentials, frequency calculations, and high-level optimizations yield the necessary data for RRKM master equation calculations.Additional comments including restrictions and unusual features: KinBot is designed to run on Unix clusters, and is written in Python, compatible with versions 2.7 and 3. It communicates with a PBS or SLURM workload manager to submit quantum chemistry calculations to third-party software. It makes use of a modified fork of ASE for the input writing, calling and output parsing of the quantum chemistry software which has been tested with Gaussian (G09RevD.01). OpenBabel (2.4.1) and RDKit (2018.09.01) are used to convert smiles to internal species representations and for species comparison and results visualization. The output of KinBot can be visualized with the PESViewer script, and graph structures are drawn using NetworkX. The master equation solvers MESS or MESMER are needed to calculate rate coefficients at the end of a given run. This version of KinBot can handle H, C, S, and O atom-containing molecules, and searches for isomerization and dissociation pathways.

Coupling effect of phase change heat transfer on free surface in pure steam environment and thermocapillary convection in annular pool

In order to reveal the coupling effect between surface phase change heat transfer in pure steam environment and thermocapillary convection in annular pool, we performed a series of three-dimensional numerical simulations by using the finite volume method based on the statistical evaporation rate theory. The inner and the outer radii of the annular pool are respectively 20 mm and 40 mm, the depth ranges from 1 mm to 20 mm. The selected working fluid is water with Prandtl number of 6.13. Results show that the radial temperature gradient on the free surface near the cylinders increases due to the latent heat absorbed and/or released as a result of phase change heat transfer, which leads to the increase of the thermocapillary force near the cylinders and the enhancement of the flow. Therefore, the isotherms converge to the cylinders. The axial velocity on the free surface caused by surface phase change is much less than the inward radial velocity. Flow pattern depends slightly on Marangoni number. But with the increase of Marangoni number, the flow is enhanced and the flow cells near the cylinders gradually expand to the middle of the annular pool. With the increase of the aspect ratio, thermocapillary convection is enhanced and the evaporation strengthens. With the increase of ambient steam temperature and pressure, the condensation mass flux near the inner cylinder increases, the radial temperature gradient rises, and thermocapillary convection strengthens. However, near the outer cylinder, it is the opposite.

The mechanism and kinetics of the gas-phase reactions of OH radicals with O,O-diethyl methylphosphonothioate, (C2H5O)2P(S)CH3: Theoretical investigations

In this research, the kinetics of bimolecular reaction of O,O-diethyl methylphosphonothioate (DEMPT) with OH radical is investigated theoretically. First, the mechanism of the reaction of OH radical with DEMPT is explored some by well-tested density functional methods. Next, the rate constants for different reaction pathways are calculated by statistical rate theories. The results are compared with available experimental data. The present calculations reveal that in the most favorable reaction pathway, the reaction proceed through a relatively deep complex due to the hemi-bond between OH radical and sulphur atom of DEMPT leading to the product (C2H5O)(OH)P(S)CH3+C2H5O. Other product channels have minor contribution to overall reaction rate. The present theoretical rate coefficients are in accord with the available empirical data. Based on the predicted rate coefficients, the tropospheric lifetime of DEMPT is estimated to be about 50 min.

Binary Adsorption of Two Textile Dyes onto Diatomite: Kinetic and Isotherm Study

Nowadays, many studies focus only on the removal of dyes from water in single solution. In real applications the colored effluents contain more than one component to eliminate. In this study, the adsorption of two textile dyes – Red Bemacid-ETL (RB-ETL) and Bezaktiv Turquoise Blue-VG (BTB-VG) – was investigated in a binary mixture. The derivative spectrophotometry was used to determine the specific wavelength for each dye. The effect of pH, contact time and initial dye concentrations was considered. The results show that diatomite has a good potential to eliminate both of dyes simultaneously. The competitive statistical rate theory model fits the adsorption kinetic data of the binary system well. The adsorption isotherm data for both dyes is well described by multicomponent Langmuir isotherm model. A high competition effect was observed, but BTB-VG dye was more selectively adsorbed by heat treated diatomite than RB-ETL dye.