Kinetic Model Research Articles

Kinetics of the mechanically induced ibuprofen-nicotinamide co-crystal formation by in situ X-ray diffraction.

Mechanochemistry is drawing attention from the pharmaceutical industry given its potential for sustainable material synthesis and manufacture. Scaling mechanochemical processes to industrial level remains a challenge due to an incomplete understanding of their underlying mechanisms. We here show how time-resolved in situ powder X-ray diffraction data, coupled with analytical kinetic modelling, provides a powerful approach to gain mechanistic insight into mechanochemical reactions. By using the ibuprofen-nicotinamide co-crystal mechanosynthesis as a benchmark system, we investigate the behaviour of the solids involved and identify the factors that promote the reaction. As mechanochemical mechanisms become increasingly clear, it promises to become a breakthrough in the industrial preparation of advanced pharmaceuticals.

Amino-functionalization of PVA/TiO2-CeO2 nanohybrid adsorbent for the removal of selenium ions from aqueous solutions: Equilibrium and kinetics studies

ABSTRACT In this study, a hybrid nanoadsorbent (HnA), (PVA/TiO2-CeO2), was synthesized and amino-functionalized by 3-aminopropyltriethoxysilane (APTES) to produce AHnA, for use in an advanced selenium adsorption study focusing on nonlinear equilibrium and kinetics models. AHnA was characterized using XRD, FTIR spectroscopy, SEM, and EDX elemental analyses, as well as BET-BJH techniques. According to the FTIR results, APTES has successfully cross-linked the PVA chain and introduced amine groups on the surface. Moreover, the modification resulted in an increase in the total pore volume from 0.0061 cm3/g in HnA to 0.021 cm3/g in AHnA. Several adsorption experiments were conducted to determine the impact of varying contact times within a pH range of 1 to 8 and concentrations ranging from 5 to 200 mg/L, using a One-Variable-At-a-Time (OVAT) procedure. Accordingly, a dosage of 2 g/L of modified nanocomposite exhibits optimal performance for removing selenium from a 20 mg/L solution at an acidic pH of 3 during 300 minutes of contact with selenium ions, while conforming to a pseudo-second-order kinetic model. The assessment of various nonlinear isotherm models for analyzing equilibrium data revealed that the experimental data of selenium adsorption conformed to a generalized isotherm, showing a maximum monolayer adsorption capacity of 17.643 mg/g.

Copper leaching from ultrasonically treated milled waste printed circuit boards: investigation of parameters optimization and kinetics.

Waste printed circuit boards (WPCBs) encompass abundant metals (gold, silver, and copper), along with other harmful materials including brominated epoxy resins, plastics, and heavy metals (lead, mercury, and cadmium). Direct burning and landfilling of WPCBs may cause severe health issues and impair the environment. Therefore, sustainable treatment of WPCBs is necessary to recover valuable metals and remove hazardous materials before disposal. The present work investigates the separation of copper-rich metallic fractions from the WPCBs by the combination of hammer milling and ultrasonic irradiation. Initially, discarded mobile phone PCBs are pre-processed and shortened into 1 × 1 cm2. Downscaled WPCBs are fed into the hammer mill to obtain the fine ground powder. The Powdered WPCBs are further processed through ultrasonic treatment to acquire metal-rich fraction. XRD, SEM-EDS, and ICP/AAS analysis revealed that the current technique can efficiently separate the metal-rich fraction without using toxic solvents. Results show the enhancement of copper fraction from 42.73 to 87 wt. % after ultrasonic treatment of WPCBs ground powder. Further, nitric acid leaching has been implemented to metal-rich fractions, and the parameters have been optimized for copper leaching with the assistance of response surface methodology (RSM) of the design of experiments (DOE). Quantitative dissolution (98.96%) of copper occurred using 3.5M nitric acid within 3h at 30°C with 50 GPL pulp density and 500rpm agitation speed. Finally, the kinetics of the leaching process were studied to conform the kinetics model. Moreover, the activation energy for diffusion (19.075kJ/mole) and reaction kinetics model (13.29kJ/mole) has also been calculated. The low energy consumption due to room temperature pre-treatment and effective leaching ensures the industrial feasibility of the proposed process.

All "Roads" Lead to Rocksalt Structure.

Rocksalt is the most common crystal structure among binary compounds. Moreover, no long-lived, metastable polymorphs are observed in compounds with the rocksalt ground state. We investigate the absence of polymorphism via first-principles random structure sampling and transformation kinetics modeling of three rocksalt compounds: MgO, TaC, and PbTe. Random structure sampling reveals that for all three systems the rocksalt basin of attraction covers much more of configuration space than any other, making it statistically the most significant structure. The kinetics modeling shows that virtually all other relevant structures, including most of the 457 known A1B1 prototypes, transform rapidly to rocksalt, making it the only option at ambient conditions. These results explain the absence of polymorphism in binary rocksalts, answer why rocksalt is the structure of choice for high-entropy ceramics and disordered ternary nitrides, and help understand/predict metastable states in crystalline solids more generally.

Adsorption of acid red 14 from aqueous solutions by ZnO-tyre: kinetics, isotherms, and mechanisms

ABSTRACT This research evaluated the effectiveness of using zinc oxide-waste tyre (ZnO-WT) for the adsorptive removal of the harmful acid red 14 azo dye (AR14 AzD) from polluted water. The synthesised materials were characterised using FT-IR, XRD, FESEM, EDX-map, and pHpzc analyses. Examination of key operational factors confirmed that the adsorptive removal rate of AzD reached 90.09% under the conditions of pH= 3, ZnO-WT= 1 g L− 1, [AR14]₀= 20 mg L− 1, and T= 298 K within 2 hours. The pseudo-second-order (PSO) (R2= 0.9981) and Langmuir (R2= 0.9984) kinetic and isotherm models fitted well with all AzD adsorption data. Notably, the maximum adsorption capacity (qm) of ZnO-WT towards AR14 was found to be 204.082 mg g− 1 at T= 298 K. Moreover, adsorption thermodynamics revealed that the AR14 uptake process was both endothermic (+ΔH ∘ ) and spontaneous (−ΔG ∘ ). Reusability tests demonstrated that the nanocomposites (NCs) were sufficiently stable and reusable. The production cost of the ZnO-WT NCs on a laboratory scale was 0.0886 USD per 8 g, while the cost associated with AR14 adsorptive removal was 0.0576 USD, making it an economical option for large-scale industrial use. These results suggest that waste tyres could be repurposed to produce a new class of carbon materials, with ZnO-WT effectively serving as a low-cost and environmentally friendly adsorbent for removing AR14 dye from aqueous solutions.

Innovative pyrazole–phosphoramidate derivative for effective mercury adsorption and their application for Egyptian industrial waste samples

ABSTRACT Mercury, known for its severe health and environmental impacts even in trace amounts, necessitates effective removal from water systems. This research focuses on preparation of a novel adsorbent of 3,9−bis((4−amino−5−hydroxy−1 H−pyrazol−3−yl)amino)−2,4,8,10−tetraoxa−3,9−diphosphaspiro[5.5] undecane 3, 9−dioxide (PADP) for Hg(II) ions adsorption. To validate functionalization steps and elucidate PADP’s physical and chemical properties, a comprehensive array of assays, including FTIR, surface area, BET, TGA, 13CNMR, Mass spectra, 31PNMR and1HNMR were employed. The study systematically examined several factors controlling mercury sorption, including temperature, adsorbent dosage, pH, interaction time, and mercury concentration using the batch technique. Optimal sorption effectiveness was achieved at pH 5, with an interaction time of 50 min, an 80 mg adsorbent dose, at ambient temperature. The newly devised adsorbent exhibited an impressive adsorption capacity (qe) of 357 mg of Hg(II) per Litre, with empirical data fitting the Langmuir and Dubinin−Radushkevich adsorption isotherm models. The kinetics of mercury sorption followed second-order and Elovich kinetics models. Thermodynamic aspects, including ΔGº, ΔSº, and ΔHº, were also investigated, providing appreciated perceptions into the energetic dynamics of the sorption process. Thermodynamics has shown that the sorption of mercury ions is both endothermic and spontaneous. Additionally, mercury adsorption in the occurrence of other ions was explored, highlighting the selectivity of the modified Pyrazole – Phosphoramidate adsorbent for mercury removal. PADP demonstrates superior performance in removing Hg(II) from wastewater effluents, outshining a range of both natural and synthetic adsorbents previously used for this purpose. This superiority is evident when comparing its adsorption capacity (qo) against those of other adsorbents, showcasing its exceptional efficacy in purifying water from mercury contamination.

Preparation of Fe-Modified Diatomite-Based Ceramsite for Efficient Phosphate Adsorption: Utilizing Diatomite’s Distinctive Porous Structure and Surface Silanol Groups

Ceramsites are extensively employed as substrates for adsorbents in studies focused on phosphorus adsorption, leaving ceramsites crafted from diatomite less explored. Diatomite-based ceramsite, with its distinct porous architecture and surface silanol functionalities, is adept at supporting a variety of metal oxides, presenting a distinct advantage over other ceramsite variants. In light of this, the present study embarked on producing diatomite-based ceramsite using diatomite as the foundational material, subsequently enhancing it through the incorporation of Fe, thus yielding an Fe-modified diatomite-based ceramsite. Through adsorption testing, the modified ceramsite demonstrated a significantly improved adsorption capacity of 4.06 mg P/g, marking a substantial enhancement from the initial capacity of 0.9 mg P/g. The process of phosphorus adsorption exhibited a strong alignment with the Langmuir isotherm model and the pseudo-second-order kinetic model. In-depth analyses employing XRD, FTIR, zeta potential, and XPS techniques have revealed that the principal mechanisms driving the adsorption process are centered on interactions involving electrostatic forces, the formation of chemical precipitates, and the exchange of ligands. This investigation not only opens new avenues for the application of diatomite-based ceramsite but also lays down a theoretical foundation for its modification, thereby enriching the spectrum of its utility.

Sulfide-enhanced carboxymethyl cellulose stabilised nano zero-valent iron for chromium(VI) mitigation in water: Evidence from batch and column studies

The primary source of chromium pollution in water is industrial operations such as electroplating, leather tanning, and textile manufacture, which use chromium for its ability to resist corrosion. Hexavalent chromium (Cr(VI)), the most detrimental variant, presents significant health hazards, such as cancer. It is crucial to effectively manage and decrease chromium levels to protect human and environmental health, especially in industrial regions where its presence in water is a persistent issue. This work examined the removal of Cr(VI) by sulfidated carboxymethyl cellulose stabilised nano zerovalent iron (S-CMC-nZVI). S-CMC-nZVI exhibited outstanding uniformity and corrosion resistance. Batch experiments revealed that several factors influenced the degree to which S-CMC-nZVI particles eradicated Cr(VI). The parameters to be considered included pH, initial Cr(VI) concentration, coexisting ions, and S/Fe molar ratio. When the sulfur to iron molar ratio was increased from 0 to 0.4, Cr(VI) removal efficiency increased from 73.89 % to 99 %. A pseudo-second-order kinetic model described Cr(VI) removal, and the Langmuir isotherm model determined the highest adsorptive capacity (311.02 mg/g). The presence of bicarbonate and nitrate anions have minimal inhibitory effects on removal of Cr(VI). Experiments on polluted groundwater showed that synthesised nanoparticles may remove Cr(VI) over a long time. Column investigations showed that increasing S-CMC-NZVI concentration increased Cr(VI) removal. The Adsorption, reduction and coprecipitation were major processes responsible for Cr(VI) removal. The research demonstrates that S-CMC-nZVI is a promising material for the in-situ remediation of Cr(VI)-contaminated groundwater.

N-doped lignin-based activated carbon aerogel derived from bamboo black pulp liquor for efficient removal of malachite green in wastewater.

In this study, a lignin-based aerogel (LA) was prepared through acid precipitation of BPBL, followed by sol-gel method and freeze-drying. Additionally, a one-step activation-carbonization method was used to acquire nitrogen-doped lignin-based activated carbon aerogel (NLACA). The adsorption and catalytic degradation performance for malachite green (MG) were examined. The specific surface area of NLACA after N-doping was 2644.5 m2/g. The adsorption capacity for MG was increased to 3433mg/g with the presence of nitrogenous functional groups on surface of NLACA compared without N-doping. Meanwhile, non-radical singlet oxygen is the primary active substance and degradation efficiency arrives at 91.8% after the catalytic degradation within 20min and it has good stability and reuse. Three possible degradation pathways during degradation were analyzed by LC-MS technique. The adsorption isotherm and kinetic data demonstrated conformity with both the Langmuir model and the pseudo-second-order kinetic model. The primary mechanisms of the adsorption for MG dyes on NLACA include hydrogen bonding, π-π interactions, attraction of electrostatic and pore filling. Hence, NLACA derived from BPBL acts as a cost-effective and high-performance adsorbent and catalyst for removal of MG in dye wastewater. This concept introduces an innovative approach of "treatment of waste with waste" for developing a low-consumption, high-efficiency dye wastewater treatment and provides significant reference to treatment dye wastewater.

Efficient removal of polycyclic aromatic hydrocarbons from aqueous solutions using green cyclodextrin-maltodextrin nanosponge incorporated polyvinyl alcohol cryogel

Developing efficient adsorbents for removing polycyclic aromatic hydrocarbons (PAHs) from aqueous solutions is a significant and worthwhile approach. In this study, we showcase a method for fabricating β-cyclodextrin-maltodextrin nanosponges (βCD-MD) incorporated polyvinyl alcohol (PVA) cryogel for removing PAHs from aqueous solutions. The composite nanosponges enhanced the adsorption efficiency of PAHs such as Naphthalene, Acenaphthene, Fluorene, Phenanthrene, Anthracene, Fluoranthene, Pyrene, and Benzo[a]pyrene from water samples and the porous PVA cryogel helped to entrap and prevent the loss of the adsorbent. This efficacy was attributed to the strong affinities of PAHs toward βCD-MD nanosponges, facilitated by hydrophobic interactions between the analytes and the hydrophobic inner region present in both dextrins. The removal efficiency of the prepared βCD-MD/PVA composite cryogel was more than 95 % for all 8 PAHs (C0 = 5.0 mg/L) in less than 30 min, and the experimental data were well described by the Freundlich isotherm and the pseudo-second-order kinetic model. Additionally, the βCD-MD/PVA composite cryogel exhibited a maximum adsorption capacity ranging from 16.34 to 18.49 mg/g for eight PAHs. Moreover, the thermodynamic study revealed that the adsorption of PAHs was an endothermic and spontaneous process. The βCD-MD/PVA composite cryogel exhibited an abundance of polar functional groups along with numerous hydrophobic cavities and regions. It demonstrated high mechanical and thermal stability and maintained high removal efficiency even after seven adsorption–desorption cycles. Overall, it was concluded that βCD-MD/PVA composite cryogel can be utilized as a high-performance, eco-friendly, and sustainable alternative for PAH removal.

Curing kinetics and mechanical properties of the epoxy vitrimer based on transesterification and its composite laminates

AbstractThe resin is a fundamental factor in determining the performance and usage conditions of its composites. The epoxy vitrimer, which combines both thermoplastic and thermosetting properties, shows significant potential in extending the service life of material. The curing process significantly affects the macroscopic properties of the vitrimer and the resulting carbon fiber reinforced plastics (CFRP). Effective control of curing parameters constitutes the critical factor for the assurance of product quality. In the study, a differential scanning calorimetry (DSC) was utilized to establish a curing kinetics model for a modified, self‐healable epoxy vitrimer based on transesterification. Then the molecular structure, thermodynamic, and mechanical properties of the cured vitrimer were analyzed. Next vitrimeric CFRP (vCFRP) laminates were fabricated, and the tensile and bending properties of the vCFRP laminates were investigated. The results showed the curing process was obtained: 95°C/1 h + 150°C/2 h + 170°C/2 h. The thermodynamic and mechanical properties of cured vitrimer could meet practical requirements. The minimal differences observed in the stress–strain curves of the specimens indicated that the curing process was appropriately configured. The prepared laminates exhibited performance comparable to that of commercial thermosetting composites.

Fugacity and kinetic models reveal specific-fate of geosmin in air-water-fish microcosm and channel catfish (Ictalurus punctatus)

Geosmin (GSM) is a ubiquitous odorant found in aquatic environments and organisms, with significant impacts on drinking water and aquaculture. However, its transfer from contaminated water to fish tissues is poorly investigated, resulting in limited information on its bioconcentration and environmental behavior. Fugacity and one-compartment models were developed to describe the fate, transformation, and transport of GSM in an air-water-fish system and analyze its uptake, distribution, and elimination kinetics in channel catfish (Ictalurus punctatus). The results showed that the fugacity model calculations indicated that 81.3 % of GSM was found in water for all microcosm. The primary mass transfer processes from water were water-air diffusion process (T21v) and that from water to fish (T2 f), with values of 67.3 and 22.54 μg/h, respectively. The emission rate (E2) and area (A2) in water parameters are most sensitive to GSM concentration, impacting the distribution and variance of contaminant concentration. Kinetic studies in fish revealed that GSM primarily accumulate in the muscle and skin, with the earthy-odor burden of fish contributed by the former, reaching 86.59 %. The uptake rate constant (kup), depuration rate constant (kde), and half-lives (t1/2) fell within the ranges of 0.737–3.534 L/(kg·h), 0.024–0.097 1/h, and 7.1–28.9 h, respectively. Bioaccumulation factors (BAFs) for GSM in fish skin, muscle, and liver tissues were 105.79, 61.71, and 51.22 L/kg, respectively. GSM was effectively depurated by other tissues within 72 h, while 18.16 % remained in skin. The liver demonstrated the most accurate curve (R2=0.97), followed by skin and muscle, with the gill showing the worst simulation. This work offers insights into understanding the fate and mass transfer flux of trace odorants in environmental and biological phases.

Optimization and Kinetic Study of Manganese Leaching from Pyrolusite Ore in Hydrochloric Acid Solutions with Oxalic Acid

AbstractThe leaching behavior of pyrolusite minerals was examined in hydrochloric acid solutions, including oxalic acid, to evaluate the influence of various experimental conditions. The optimum parameters for the leaching process were found in the first stage, and the process's kinetics were assessed in the second. The concentrations of oxalic acid, hydrochloric acid, and temperature were chosen as independent variables in the optimization experiments, with the central composite design used to analyze the experimental data. The optimum concentrations for oxalic acid, hydrochloric acid, and temperature were determined to be 0.75 mol/L, 1.2 mol/L, and 60 °C, respectively. The leaching rate was determined to be 97.4% for 120 min of response time in optimum situations. The kinetic assessment experiments studied the effects of solid/liquid ratio, particle size, stirring speed, and temperature on the manganese leaching rate from pyrolusite. In the studies, the leaching rate was shown to rise with increasing temperature and stirring speed, as well as with decreasing particle size and solid/liquid ratio. The kinetic analysis revealed that the leaching kinetics matched the mixed kinetic model, and a mathematical model for the leaching process was developed. This process's activation energy was determined to be 29.05 kJ/mol. Graphical Abstract

A Kinetic Model for Catalytic N-Butane Oxidative Dehydrogenation under Oxygen-Free Reaction Conditions in a Fluidized CREC Riser Simulator

This study considers the development of a kinetic model for the n-butane oxidative dehydrogenation (ODH) to C4-olefins using a VOx/MgO−γAl2O3 catalyst. The prepared catalyst contained 5 wt% V on an MgO modified γAl2O3 support. The developed catalyst exhibited both weak and medium acid sites, as revealed by NH3-temperature-programmed desorption. TPR/TPO analyses also indicated that 73% of the loaded VOx was reducible. Kinetic experiments were conducted in a fluidized CREC Riser Simulator at temperatures ranging from 475–550 °C and residence times of 5–20 s. An optimal C4-olefin selectivity of 86% was achieved at 500 °C and 10 s, with this selectivity then decreasing at higher temperatures and longer residence times. The kinetic model developed involved a Langmuir–Hinshelwood-type of kinetics that incorporated cracking, oxydehydrogenation, and complete oxidation reactions. Model parameters were determined by fitting experimental data with kinetic parameters established with narrow 95% confidence intervals and low cross-correlation.

Adsorption of Bichromate and Arsenate Anions by a Sorbent Based on Bentonite Clay Modified with Polyhydroxocations of Iron and Aluminum by the “Co-Precipitation” Method

The physicochemical properties of natural bentonite and its sorbents were studied. It has been established the modification of natural bentonites using polyhydroxoxides of iron (III) (mod.1_Fe_5-c) and aluminum (III) (mod.1_Al_5-c) by the “co-precipitation” method led to changes in their chemical composition, structure, and sorption properties. It was shown that modified sorbents based on natural bentonite are finely porous (nanostructured) objects with a predominance of pores of 1.5–8.0 nm in size. The modification of bentonite with iron (III) and aluminum compounds by the “co-precipitation” method also leads to an increase in the sorption capacity of the obtained sorbents with respect to bichromate and arsenate anions. A kinetic analysis showed that, at the initial stage, the sorption process was controlled by an external diffusion factor, that is, the diffusion of the sorbent from the solution to the liquid film on the surface of the sorbent. The sorption process then began to proceed in a mixed diffusion mode when it limited both the external diffusion factor and the intra-diffusion factor (diffusion of the sorbent to the active centers through the system of pores and capillaries). To clarify the contribution of the chemical stage to the rate of adsorption of bichromate and arsenate anions by the sorbents under study, kinetic curves were processed using equations of chemical kinetics (pseudo-first-order, pseudo-second-order, and Elovich models). It was found that the adsorption of the studied anions by the modified sorbents based on natural bentonite was best described by a pseudo-second-order kinetic model. The high value of the correlation coefficient for the Elovich model (R2 > 0.9) allows us to conclude that there are structural disorders in the porous system of the studied sorbents, and their surfaces can be considered heterogeneous. Considering that heterogeneous processes occur on the surface of the sorbent, it is natural that all surface properties (structure, chemical composition of the surface layer, etc.) play an important role in anion adsorption.

A novel kinetic model to demonstrate the independent effects of ATP and ADP/Pi concentrations on sarcomere function.

Understanding muscle contraction mechanisms is a standing challenge, and one of the approaches has been to create models of the sarcomere-the basic contractile unit of striated muscle. While these models have been successful in elucidating many aspects of muscle contraction, they fall short in explaining the energetics of functional phenomena, such as rigor, and in particular, their dependence on the concentrations of the biomolecules involved in the cross-bridge cycle. Our hypothesis posits that the stochastic time delay between ATP adsorption and ADP/Pi release in the cross-bridge cycle necessitates a modeling approach where the rates of these two reaction steps are controlled by two independent parts of the total free energy change of the hydrolysis reaction. To test this hypothesis, we built a two-filament, stochastic-mechanical half-sarcomere model that separates the energetic roles of ATP and ADP/Pi in the cross-bridge cycle's free energy landscape. Our results clearly demonstrate that there is a nontrivial dependence of the cross-bridge cycle's kinetics on the independent concentrations of ATP, ADP, and Pi. The simplicity of the proposed model allows for analytical solutions of the more basic systems, which provide novel insight into the dominant mechanisms driving some of the experimentally observed contractile phenomena.

Enhanced removal of tetrabromobisphenolA (TBBPA) from e-waste by Fe–S nanoparticles and Fe–S/CuS nanocomposite with response surface methodology (RSM)

TetrabromobisphenolA is a well-known member of the brominated flame retardant group and is widely used as a highly effective fire-retardant additive in electronic and electrical equipment. TBBPA is commonly found in various environmental sources and can be harmful to human health. This study presents a simple approach to preparing a magnetic nanocomposite, offering a straightforward method that results in consistent quality and low resource consumption. The nanocomposite has a high surface-to-volume ratio for the removal of tetrabromobisphenolA. Various characterization techniques, including XRD, FTIR, EDX, FESEM, VSM, TEM, and BET analyses were used to characterize the Fe–S nanoparticles and Fe–S/CuS. The results showed that Fe–S/CuS nanocomposite successfully removed over 97% of the initial TBBPA (15 mg L−1) under optimized conditions determined by RSM, such as a contact time of 15 min, pH of 7, Fe–S/CuS nanocomposite dosage of 0.69 g L−1, and salt concentration of 0.10%. The RSM analysis provided a second-order polynomial model with a confidence level of 93% (F = 29.58; p < 0.0001) to predict the TBBPA removal efficiency at various concentrations. In the adsorption kinetic studies, the second-order kinetic model provided the best fit for the experimental data. Additionally, Fe–S/CuS nanocomposite shows great potential for practical applications and environmental remediation efforts, making it a valuable asset for real-sample use in environmental settings.

Mathematical Modeling of Tumor Growth in Preclinical Mouse Models with Applications in Biomarker Discovery and Drug Mechanism Studies.

Oncology drug efficacy is evaluated in mouse models by continuously monitoring tumor volumes, which can be mathematically described by growth kinetic models. While past studies have investigated various growth models, their reliance on small datasets raises concerns about whether their findings are truly representative of tumor growth in diverse mouse models under different vehicle or drug treatments. Here, we systematically evaluated six parametric models (exponential, exponential quadratic, monomolecular, logistic, Gompertz, and von Bertalanffy) and the semi-parametric generalized additive model (GAM) on fitting tumor volume data from over 30,000 mice in 930 experiments conducted in patient-derived xenografts, cell line-derived xenografts, and syngeneic models. We found that the exponential quadratic model is the best parametric model and can adequately model 87% studies, higher than other models including von Bertalanffy (82%) and Gompertz (80%) models, the latter is often considered the standard growth model. On the mouse group level, 7.5% of growth data could not be fit by any parametric model and were fitted by GAM. We show that eGaIT, a GAM derived efficacy metric, is equivalent to eGR, a metric we previously proposed and conveniently calculated by simple algebra. Using five studies on Paclitaxel, anti-PD-1 antibody, Cetuximab, Irinotecan, and Sorafenib, we show that exponential and exponential quadratic models achieve similar performance in uncovering drug mechanism and biomarkers. We also compared eGR-based association analysis and exponential modeling approach in biomarker discovery and found they complement each other. Modeling methods herein are implemented in an open-source R package freely available at https://github.com/hjzhou988/TuGroMix.

A kinetic modelling approach to explore mechanism of Cr(VI) detoxification by a novel strain Pseudochrobactrum saccharolyticum NBRI-CRB 13 using response surface methodology.

A novel Pseudochrobactrum saccharolyticum strain NBRI-CRB 13, isolated from tannery sludge, was studied to grow up to 500 mgL-1 of Cr(VI) and showed Cr(VI) detoxification by reducing > 90% of Cr(VI) at different concentrations 25, 50 and 100 mgL-1. Kinetic studies showed that first-order models were fitted (R2 = 0.998) to the time-dependent Cr(VI) reduction with degradation rate constant (k) (1.03-0.429h-1). Cr(VI) detoxification was primarily related to the extracellular fraction of microbial cells, which showed a maximum extracellular reductase enzyme activity led to 94.6% reduction of Cr(VI). Moreover, the strain showed maximum extracellular polymeric substances (EPS) production at 100 mgL-1 Cr(VI), which is presumably the reason for Cr(VI) removal as EPS serves as the metal binding site for Cr(VI) ions. Further, an optimization study using Box-Behnken design was conducted considering parameters viz., pH, temperature, and initial concentration of Cr(VI). The maximum percent reduction of Cr(VI) was obtained at pH 6.5, temperature 30°C with 62.5 mgL-1Cr(VI) concentration. Further, the Cr(VI) reduction and adsorption ability of strain P. saccharolyticum NBRI-CRB13 were confirmed by SEM-EDS, FTIR, and XRD analyses. FTIR analysis confirmed the presence of functional groups (-OH, -COOH, -PO4) on bacterial cell walls, which were more likely to interact with positively charged chromium ions. The study elucidated the reduction of Cr(VI) by the novel bacterium within 24h using the response surface methodology approach and advocated its application in real-time situations.

Discovery of Molecular Intermediates and Nonclassical Nanoparticle Formation Mechanisms by Liquid Phase Electron Microscopy and Reaction Throughput Analysis

Formation kinetics of metal nanoparticles are generally described via mass transport and thermodynamics‐based models, such as diffusion‐limited growth and classical nucleation theory (CNT). However, metal monomers are commonly assumed as precursors, leaving the identity of molecular intermediates and their contribution to nanoparticle formation unclear. Herein, liquid phase transmission electron microscopy (LPTEM) and reaction kinetic modeling are utilized to establish the nucleation and growth mechanisms and discover molecular intermediates during silver nanoparticle formation. Quantitative LPTEM measurements show that their nucleation rate decreases while growth rate is nearly invariant with electron dose rate. Reaction kinetic simulations show that Ag4 and Ag− follow a statistically similar dose rate dependence as the experimentally determined growth rate. We show that experimental growth rates are consistent with diffusion‐limited growth via the attachment of these species to nanoparticles. The dose rate dependence of nucleation rate is inconsistent with CNT. A reaction‐limited nucleation mechanism is proposed and it is demonstrated that experimental nucleation kinetics are consistent with Ag42+ aggregation rates at millisecond time scales. Reaction throughput analysis of the kinetic simulations uncovered formation and decay pathways mediating intermediate concentrations. We demonstrate the power of quantitative LPTEM combined with kinetic modeling for establishing nanoparticle formation mechanisms and principal intermediates.