Half-order Kinetics Research Articles

Transition from Sequential to Concerted Proton-Coupled Electron Transfer of Water Oxidation on Semiconductor Photoanodes.

Accelerating proton transfer has been demonstrated as key to boosting water oxidation on semiconductor photoanodes. Herein, we study proton-coupled electron transfer (PCET) of water oxidation on five typical photoanodes [i.e., α-Fe2O3, BiVO4, TiO2, plasmonic Au/TiO2, and nickel-iron oxyhydroxide (Ni1-xFexOOH)-modified silicon (Si)] by combining the rate law analysis of H2O molecules with the H/D kinetic isotope effect (KIE) and operando spectroscopic studies. An unexpected and universal half-order kinetics is observed for the rate law analysis of H2O, referring to a sequential proton-electron transfer pathway, which is the rate-limiting factor that causes the sluggish water oxidation performance. Surface modification of the Ni1-xFexOOH electrocatalyst is observed to break this limitation and exhibits a normal first-order kinetics accompanied by much enhanced H/D KIE values, facilitating the turnover frequency of water oxidation by 1 order of magnitude. It is the first time that Ni1-xFexOOH is found to be a PCET modulator. The rate law analysis illustrates an effective strategy for modulating PCET kinetics of water oxidation on semiconductor surfaces.

Iridium-Catalyzed Enantioselective Hydrogenation of Oxocarbenium Ions: A Case of Ionic Hydrogenation.

Ionic hydrogenation has not been extensively explored, but is advantageous for challenging substrates such as unsaturated intermediates. Reported here is an iridium-catalyzed hydrogenation of oxocarbenium ions to afford chiral isochromans with high enantioselectivities. A variety of functionalities are compatible with this catalytic system. In the presence of a catalytic amount of the Brønsted acid HCl, an α-chloroether is generated in situ and subsequentially reduced. Kinetic studies suggest first-order kinetics in the substrate and half-order kinetics in the catalyst. A positive nonlinear effect, together with the half kinetic order, revealed a dimerization of the catalyst. Possible reaction pathways based on the monomeric iridium catalyst were proposed and DFT computational studies revealed an ionic hydrogenation pathway. Chloride abstraction and the cleavage of dihydrogen occur in the same step.

Impact of defect-driven surface inhomogeneity and minimal island formation on temperature-programmed desorption spectra: A kinetic Monte Carlo study

Inhomogeneity often manifests itself on surfaces with pre-adsorbed adsorbates in which islands have widely-disparate sizes due to the presence of distinct morphological features or perhaps even impurities, or defects. In this kinetic Monte Carlo study, we developed a model in which these defects are in the form of vacancy clusters or chains and grow progressively longer with each repeated adsorption-desorption cycle owing to repeated stress that a substrate is subjected to with each cycle. We then explored different simulation-imposed conditions – vacancy or defect concentration as well as maximum vacancy chain length – and noted their impact on the resulting temperature-programmed desorption spectra. We found that growing chains can induce single desorption peak to progressively shift, then split into two closely-overlapping ones over a course of several such cycles. Interestingly, such evolving peaks may hide the true desorption kinetics since calculation of desorption order may yield unconventional, non-integer values – neither zero, first or second-order. We also observed that for the same vacancy concentration, peak-splitting becomes more pronounced with increasing maximum chain length. Analysis of simulation data also revealed that unlike bigger and more compact islands, small ones follow first-order desorption kinetics rather than half-order kinetics.

Nutrient removal through pyrrhotite autotrophic denitrification: Implications for eutrophication control

This study investigated nutrient removal kinetics and main influencing factors of natural pyrrhotite autotrophic denitrification (PAD), and nutrient removal performance and the microbial community in the PAD biofilter (PADB). Results demonstrated that both NO3− and PO43− in wastewater were nearly completely removed, and biological N removal and chemical P removal took place simultaneously in the PAD process. NO3− removal kinetics of the PAD can be described with half-order kinetics. The PAD was effective across a wide temperature range of 11–34 °C, initial NO3−-N range of 13–52 mg·L−1 and PO43−-P below 60 mg·L−1. Both NO3− and PO43− decreased gradually with wastewater flowing along the PADB. The PADB operation results show that at 12 h HRT, when the PADB treated wastewater containing 30.95 ± 0.97 mg·L−1 of NO3− and 3.02 ± 0.10 mg·L−1 of PO43−-P, the effluent contained 1.15 ± 2.08 and 0.09 ± 0.11 mg·L−1 of NO3−-N and PO43−-P on average, respectively. In the PADB the dominant bacteria were Thiobacillus and Sulfurimonas, which used pyrrhotite as the electron donor to reduce NO3−. The relative abundance of Thiobacillus at the bottom of the PADB increased from 0.81% to 58.65% and that of Sulfurimonas decreased from 97.22% to 12.30%, with exposure to pyrrhotite. From the bottom to the top of the PADB, the relative abundance of Thiobacillus increased from 58.65% to 86.23% and Sulfurimonas decreased from 12.30% to 0.52%. Technologies based on the PAD are promising ways to control eutrophication.

Dissolved Ozone Decomposition in Presence of Activated Carbon at Low pH: How Experimental Parameters Affect Observed Kinetics of the Process

ABSTRACTPlenty of controversies have recently surrounded the mechanism and kinetics of ozone decomposition process in presence of activated carbon. We have decided to study and explain the source of these controversies, or at least identify it correctly. Several series of experiments were conducted and various parameters (activated carbon amount and grain size, initial ozone concentration, agitation speed) were modified over their course. It was found that widely accepted (pseudo)first-order kinetics cannot explain some observations, and the best fitting was found for half-order kinetics. Ozone decomposition mechanism explaining these results was proposed.

Effect of Sulfur to Quartz Sand Ratios on the Removal of High-Concentration Perchlorate in Packed-Bed Reactors

Three autotrophic packed-bed reactors, each with a different sulfur/quartz sand ratio(R1, 2:1; R2, 1:1; R3, 1:2,)were used to remove high-concentration perchlorate from contaminated water. The perchlorate removal efficiency, kinetics, and biofilm of the reactors were studied using different perchlorate concentrations and hydraulic retention times (HRTs). The perchlorate removal efficiency decreased with higher perchlorate concentration and shorter HRT, and the removal efficiency of R1 was higher than of R2 and R3. The maximum removal loading of R1 was 2.18 kg·(m3·d)-1at an HRT of 3.2 h and perchlorate concentration of 300 mg·L-1. The half-order kinetics model fit the reactors' experimental data well; the reaction rate constants of R1, R2, and R3 were 8.036, 6.596, and 4.212 mg1/2·(L1/2·h)-1. The yield of SO42- was greater than the stoichiometric yield of sulfur autotrophic reduction owing to sulfur disproportionation. The disproportionation was inhibited with a higher perchlorate concentration or shorter HRT. Moreover, disproportionation of R3 was the weakest because the SO42- yield of R3 was lower than of R1 and R2. The pH and alkalinity of the effluent increased with lower perchlorate concentration and shorter HRT. The development of biofilm in R2 and R3 was better than in R1. The secretion of extracellular polymeric substances can promote the formation of biofilm.

Simultaneous bio-autotrophic reduction of perchlorate and nitrate in a sulfur packed bed reactor: Kinetics and bacterial community structure

This study investigated the simultaneous removal of perchlorate and nitrate from aqueous solution in an up-flow sulfur autotrophic reduction reactor. A nitrate and perchlorate containing pollution solution was treated with a remarkable removal efficiency greater than 97%. The concentration of nitrate was 22.03 ± 1.07 mg-N/L coexisting with perchlorate either 21.87 ± 1.03 mg/L or 471.7 ± 50.3 μg/L, in this case the reactor could be operated at a hydraulic retention time (HRT) ranging from 12.00 h to 0.75 h. Half-order kinetics model fit the experimental data well; this indicates that diffusion in the biofilm was the limiting step. Perchlorate reduction required a longer reaction time than the coexisting nitrate, regardless of the perchlorate concentration. Sulfur (S) disproportionation was inhibited when nitrate was not completely removed; whereas it was accelerated when perchlorate decreased to low concentrations. This process therefore generated excessive sulfate and consumed much more alkalinity. High-throughput sequencing method was used to analyze bacterial community spatial distribution in the reactor under different operational conditions. The reduction of the two contaminants was accompanied by a decrease in biodiversity. The results indicated that Sulfuricella, Sulfuritalea Thiobacillus, and Sulfurimonas are effective DB (denitrification bacteria)/PRB (perchlorate reduction bacteria). The Chlorobaculum genus was the dominant bacteria associated with S disproportionation.

Sulfide and methane production in sewer sediments

Recent studies have demonstrated significant sulfide and methane production by sewer biofilms, particularly in rising mains. Sewer sediments in gravity sewers are also biologically active; however, their contribution to biological transformations in sewers is poorly understood at present. In this study, sediments collected from a gravity sewer were cultivated in a laboratory reactor fed with real wastewater for more than one year to obtain intact sediments. Batch test results show significant sulfide production with an average rate of 9.20 ± 0.39 g S/m2·d from the sediments, which is significantly higher than the areal rate of sewer biofilms. In contrast, the average methane production rate is 1.56 ± 0.14 g CH4/m2·d at 20 °C, which is comparable to the areal rate of sewer biofilms. These results clearly show that the contributions of sewer sediments to sulfide and methane production cannot be ignored when evaluating sewer emissions. Microsensor and pore water measurements of sulfide, sulfate and methane in the sediments, microbial profiling along the depth of the sediments and mathematical modelling reveal that sulfide production takes place near the sediment surface due to the limited penetration of sulfate. In comparison, methane production occurs in a much deeper zone below the surface likely due to the better penetration of soluble organic carbon. Modelling results illustrate the dependency of sulfide and methane productions on the bulk sulfate and soluble organic carbon concentrations can be well described with half-order kinetics.

Application of half-order kinetics to sulfur-utilizing autotrophic denitrification for groundwater remediation

The kinetics of sulfur-utilized autotrophic denitrification of groundwater was evaluated in batch tests to obtain kinetic parameters. Experiments were performed in media bottles containing varying NO3 −-N concentrations (20, 44, and 77 mg/L) with 4.0–4.75 mm-sized sulfur particles. Alkalinity was set as a constant in all experimental containers at 850 mg/L as CaCO3. The half-order kinetic model was found to adequately describe the process efficiently, yielding denitrification rate constants of 4.36, 5.51, and 6.91 mg-N1/2/L1/2 · h in the presence of NO3 −-N at 20, 44, and 77 mg/L, respectively. The rate of denitrification increased with the increasing initial NO3 −-N concentrations.

RpoS Regulates a Novel Type of Plasmid DNA Transfer in Escherichia coli

Spontaneous plasmid transformation of Escherichia coli is independent of the DNA uptake machinery for single-stranded DNA (ssDNA) entry. The one-hit kinetic pattern of plasmid transformation indicates that double-stranded DNA (dsDNA) enters E. coli cells on agar plates. However, DNA uptake and transformation regulation remain unclear in this new type of plasmid transformation. In this study, we developed our previous plasmid transformation system and induced competence at early stationary phase. Despite of inoculum size, the development of competence was determined by optical cell density. DNase I interruption experiment showed that DNA was taken up exponentially within the initial 2 minutes and most transforming DNA entered E. coli cells within 10 minutes on LB-agar plates. A half-order kinetics between recipient cells and transformants was identified when cell density was high on plates. To determine whether the stationary phase master regulator RpoS plays roles in plasmid transformation, we investigated the effects of inactivating and over-expressing its encoding gene rpoS on plasmid transformation. The inactivation of rpoS systematically reduced transformation frequency, while over-expressing rpoS increased plasmid transformation. Normally, RpoS recognizes promoters by its lysine 173 (K173). We found that the K173E mutation caused RpoS unable to promote plasmid transformation, further confirming a role of RpoS in regulating plasmid transformation. In classical transformation, DNA was transferred across membranes by DNA uptake proteins and integrated by DNA processing proteins. At stationary growth phase, RpoS regulates some genes encoding membrane/periplasmic proteins and DNA processing proteins. We quantified transcription of 22 of them and found that transcription of only 4 genes (osmC, yqjC, ygiW and ugpC) encoding membrane/periplasmic proteins showed significant differential expression when wildtype RpoS and RpoSK173E mutant were expressed. Further investigation showed that inactivation of any one of these genes did not significantly reduce transformation, suggesting that RpoS may regulate plasmid transformation through other/multiple target genes.

Photocatalytic Activity of Magnetically Separable TiO2/SiO2/Fe3O4 Composite for Dye Degradation

In the present study, a magnetically separable photocatalyst (TiO2/SiO2/Fe3O4) has been prepared and used for the photooxidation of methyl orange (MO) dye. The effects of various reaction conditions such as dye concentration, catalyst dose, and pH on the reaction rate were investigated to enhance the photooxidation process. Thephotocatalytic oxidation of MO was found to follow half-order kinetics. The optimum reaction conditions were found to be a 2000 ppm TiO2 catalyst dose in an acidic medium. A higher catalyst load had no effect on the degradation rate. The dye concentration negatively affected the reaction rate because of the reduced light transmittance inside the photoreactor. The catalyst could be reused several times with nearly the same activity and thus the final cost of the treatment process could be reduced.

ChemInform Abstract: Kinetic Study of Ethylene Hydrogenation

Abstract Turnover frequencies and kinetic reaction orders were determined for ethylene hydrogenation over platinum catalysts at temperatures from 223 to 336 K, hydrogen pressures between 50 and 650 Torr, and ethylene pressures from 5 to 600 Torr. The hydrogen kinetic order was observed to decrease continuously from first order at 336 K to half order at 248 K. Zero-order ethylene kinetics were found at ethylene pressures above 75 Torr, and the ethylene order became negative at lower ethylene pressures. The half-order hydrogen kinetics at low temperatures and the observed zero-order ethylene kinetics at higher ethylene pressures can be explained by a Horiuti-Polanyi mechanism in which hydrogen is adsorbed noncompetitively on a surface essentially covered with adsorbed hydrocarbon species. Hydrogen competes with ethylene adsorption at higher temperatures and lower ethylene pressures. A combination of the noncompetitive and competitive pathways explains the steady-state kinetics over the entire range of temperatures and pressures studied.

Heterotrophic denitrification kinetics in a pressurized sewer biofilm reactor

Nitrate dosage in sewers is a well documented method for odor and corrosion control. However, the knowledge of anoxic sewer processes kinetics is limited. 17 experiments were conducted in a lab scale sewer biofilm reactor, under steady state conditions, to study the kinetics of heterotrophic denitrification in a sewer pressure main, under 3 different temperatures (20, 25 and 30°C). Experimental results show that heterotrophic denitrification in the biofilm phase can be described by half order kinetics due to decreasing biofilm biomass concentration along the reactor. The temperature coefficient for heterotrophic denitrification is calculated and an empirical temperature dependent equation is developed to predict the biofilm phase denitrification rate in any pressure main.

Decomposition of Harmful Organic Compounds with Ultrasound Wave

The water pollution by harmful organic compounds is one of the most important environmental problems now. We focused on sonochemistry which is a method of decomposing and removing these pollutants. In this study, relationship between reaction rate of sonochemistry and operational parameters (sound pressure, initial concentration and hydrophilicity of organic compounds) was investigated. Reaction rate was found to be increased with increasing sound pressure. The decomposition rates of compounds were found to increase but their pseudo first order rate constants were found to decrease with their increasing initial concentration, which suggests around half order kinetics. Finally, their reaction rates were found to increase when the smaller the hydrophilicity of decomposed compound (the greater the hydrophobicity of compound) becomes.

Adsorption and Desorption of Stilbene from the Ag/Ge(111)-√3 Surface

The adsorption and desorption of stilbene on Ag/Ge(111)-(√3 × √3)R30° (Ag/Ge(111)-√3) were investigated using low-energy electron diffraction (LEED), scanning tunneling microscopy (STM), temperature-programmed desorption (TPD), and density functional theory (DFT). Both trans- and cis-stilbenes form a (2 × 1) overlayer structure on Ag/Ge(111)-√3 at a coverage of ∼1 ML. The STM images show parallel strips with three equivalent directions, indicating a self-ordered molecular structure. At a coverage of less than 1 ML, the TPD of cis-stilbene shows only one peak, attributed to submonolayer desorption. The TPD peaks are indistinguishable for desorption of trans-stilbene from the surface submonolayer and multilayer. This is due to the simultaneous desorption and/or thinning of adsorbed multilayers during the TPD process, as determined from the STM analysis of adsorbed trans-stilbene structures before and after annealing. The TPD traces fit the half-order kinetics for molecular desorption of stilbene from Ag/Ge(111)-√3 with desorption energies of 20.1 (cis-) and 21.3 kcal/mol (trans-), which are comparable with the calculated values using the DFT method. A plausible explanation for the stilbene desorption process on Ag/Ge(111)-√3 is proposed and discussed.

Using the combined bioelectrochemical and sulfur autotrophic denitrification system for groundwater denitrification

A combined bioelectrochemical and sulfur autotrophic denitrification system (CBSAD) was evaluated to treat a groundwater with nitrate contamination (20.9–22.0 mg NO 3 - -N/L). The reactor was operated continuously for several months with groundwater to maximize treatment efficiency under different hydraulic retention times (HRT) and electric currents. The denitrification rate of sulfur autotrophic part followed a half-order kinetics model. Moreover, the removal efficiency of bioelectrochemical part depended on the electric current. The reactor could be operated efficiently at the HRT ranged from 4.2 to 2.1 h (corresponding nitrogen volume-loading rates varied from 0.12 to 0.24 kg N/m 3 d; and optimum current ranged from 30 to 1000 mA), and the NO 3 - -N removal rate ranged from 95% to 100% without NO 3 - -N accumulation. The pH of effluent was satisfactorily adjusted by bioelectrochemical part, and the sulfate concentration of effluent was lower than 250 mg /L, meeting the drinking water standard of China EPA.

Morphological characterization and kinetics study of polyaniline film formation by emulsion polymerization

The kinetics and morphology of polyaniline film prepared by using ammonium persulfate (APS) as oxidant and dodecylbenzoyl sulfonic acid (DBSA) as both emulsifier and dopant were studied in this paper. The kinetics of the formation of polyaniline film was determined by using the quartz crystal microbalance (QCM), and the film morphology was characterized by scanning electron microscopy (SEM). The reaction exhibited half-order kinetics with respect to APS concentration and first-order kinetics with respect to aniline concentration. The activation energy is 41.15 kJ/mol, and the growth rate of PANI film increased with increasing temperature and decreased with increasing concentration of DBSA.

High biofilm activity under increased oxygen concentrations in a pressurised biofilm system

A new pressurised biofilm reactor (PBR) process with a patented disc system that enables constant biofilm control has been developed to treat concentrated wastewater with respect to easily degradable organic matter under pressures of up to 6 bar. The pressurisation enables a six-fold increase of the O2 saturation level and aeration capacity, which potentially increases the reaction rate of COD as long as O2 is limiting the reaction rate. Experiments performed in a pilot-scale PBR-reactor fed by synthetic wastewater were conducted to verify the potential and kinetics of heterotrophic conversion of O2 and acetate. Under O2-limited conditions the maximum removal rate of O2 and CODf was measured to rA,O2=60 g O2/m2/d and rA,CODf=150 g CODf/m2/d at 70 mg O2/l. Experiments verified that half-order kinetics could be applied but liquid film diffusion apparently influenced the reaction rate considerably. The observed half-order rate constant was experimentally determined to K½A,O2=7.0 (g O2)1/2m−1/2d−1 but this value is underestimated by 15% due to the observed liquid film diffusion. Based on this the intrinsic zero-order reaction rate was estimated at k0f,O2=190 kg O2/m3 biofilm/d when both liquid film and biofilm diffusion were taken into account.

Photocatalytic degradation of herbicide fluroxypyr in aqueous suspension of TiO 2

The photocatalytic degradation of fluroxypyr (FLX) was studied using Degussa P-25 Titania as a catalyst. The disappearance of FLX was proved to follow a half-order kinetics. This implies that two active sites are involved in the adsorption of one molecule of fluroxypyr. In our conditions, complete mineralization of 40 ppm of pure fluroxypyr occurred within ca. 240 min of UV-radiation. Some reaction intermediates were identified by HPLC–MS (ESI+) and a tentative degradation pathway was proposed. The presence of HCl (pH 2) seemed to have an inhibiting effect on the initial rate, whereas degradation of FLX was accelerated at basic pH values (pH 8 or 10, achieved with CaCO 3 or NaOH, respectively). Photocatalysis proved to be an excellent new advanced oxidation technology (AOT) to eliminate fluroxypyr residues present in surface and ground waters.

Modeling biofilm and floc diffusion processes based on analytical solution of reaction-diffusion equations

Biofilm modeling is often considered as a complex mathematical subject. This paper evaluates simple equations to describe the basic processes in a biofilm system with the main aim to show several interesting applications. To avoid mathematical complexity the simulations are carried out in a simple spreadsheet. Frequently, only the solution for zero-order reaction kinetics of the reaction-diffusion equation is used (better known as half-order kinetics). A weighted average of the analytical solutions for zero- and first-order reactions is proposed as basic and useful model to describe steady-state (in biofilm composition) biofilm reactors. This approach is compared with several modeling approaches, such as the simple solution for zero-order reaction and more complex ones (i) direct numerical solution for the diffusion equations, (ii) 1-D AQUASIM and (iii) 2-D modeling. The systems evaluated are single and multiple species biofilms. It is shown that for describing conversions in biofilm reactors, the zero-order solution is generally sufficient; however, for design purposes large deviations of the correct solution can occur. Additionally, the role of diffusion in flocculated and granular sludge systems is discussed. The relation between the measured (apparent) substrate affinity constant and diffusion processes is outlined.