Solution of rate constants in pharmacokinetics local model of nuclear medicine

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Effects of heavy metal ions Cu^(2+)/Pb^(2+)/Zn^(2+)on kinetic rate constants of struvite crystallization

Struvite(MAP)crystallization technology is widely used to treat ammonia nitrogen in waste effluents of its simple operation and good removal efficiency.However,the presence of heavy metal ions in the waste effluents causes problems such as slow crystallization rate and small crystal size,limiting the recovery rate and economic value of the MAP.The present study was conducted to investigate the effects of concentrations of three heavy metal ions(Cu^(2+),Zn^(2+),and Pb^(2+))on the crystal morphology,crystal size,average growth rate,and crystallization kinetics of MAP.A relationship was established between the kinetic rate constant Ktcalculated by the chemical gradient model and the concentrations of heavy metal ions.The results showed that low concentrations of heavy metal ions in the solution created pits on the MAP surface,and high level of heavy metal ions generated flocs on the MAP surface,which were composed of metal hydroxides,thus inhibiting crystal growth.The crystal size,average growth rate,MAP crystallization rate,and kinetic rate constant Ktdecreased with the increase in heavy metal ion concentration.Moreover,the Ktdemonstrated a linear relationship with the heavy metal concentration ln(C/C~*),which provided a reference for the optimization of the MAP crystallization process in the presence of heavy metal ions.

Predicting Rate Constants for Nucleophilic Reactions of Amines with Diarylcarbenium Ions Using an ONIOM Method

The rate constants of the nucleophilic reactions between amines and benzhydrylium ions were calculated using first-principles theoretical methods. Solvation models including PCM, CPCM, and COSMORS, as well as different types of atomic radii including UA0, UAKS, UAHF, Bondi, and UFF, and several single-point energy calculation methods （B3LYP, B3P86, B3PW91, BHANDH, PBEPBE, BMK, M06, MP2, and ONIOM method） were examined. By comparing the correlation between experimental rate constants and the calculated values, the ONIOM（CCSD（T）/6-311＋＋G（2df,2p）：B3LYP/6-311＋＋G（2df,2p））//B3LYP/6- 31G（d）/PCM/UFF） method was found to perform the best. This method was then employed to calculate the rate constants of the reactions between diverse amines and diarylcarbenium ions. The calculated rate constants for 65 reactions of amines with diarylcarbenium ions are in agreement with the experimental values, indicating that it is feasible to predict the rate constant of a reaction between an amine and a diarylcarbenium ion through ab initio calculation.

Temperature dependence of the absolute rate constant for the reaction of ozone with dimethyl sulfide

Absolute rate constants for the reaction of ozone with dimethyl sulfide （DMS） were measured in a 200-L Teflon chamber over the temperature range of 283-353 K. Measurements were carried out using DMS in large excess over ozone of 10 to 1 or greater. Over the indicated temperature range, the data could be fit to the simple Arrhenius expression as kDMS = （9.96 ± 3.61） × 10^-11 exp （-（7309.7 ± 1098.2）/T） cm^3/（molecule.s）. A compared investigation of the reaction between ozone and ethene had a kC2H4 value of （1.35 ± 0.11） × 10^-18 cm^3/（molecule.s） at room temperature.

Kinetic Rate Constant of Liquid Drainage from Colloidal Gas Aphrons

A kinetic model fitted by the empirical equation has been proposed to describe the liquid drainage behavior. Rate constants （kd） of liquid drainage equation could be obtained from the above empirical equation. In this paper, the stability of the colloidal gas aphrons （CGAs）, the effect of concentrations of sodium dodecyl benzene sulphate （SDBS）, dodecyl trimethylammonium bromide （HTAB） and polyoxyethylene sorbitol anhydride monolaurate（Tween-20）, temperature, stirring speed, stirring time, and various kinds of salts on the kd of liquid drainage are further investigated. The results show that the Arrhenius equation can be successfully used to describe the relation between kd arid absolute temperature （T）, and concentrations of surfactants, stirring speed, stirring time and salinities also have great effect on the kd. At last, the CGAs drainage mechanism is explained from analysis of the rate of liquid drainage as a function of time.

QSBR Study on the Biodegradation Rate Constant of Chloro-phenol Compounds

Structural and thermodynamic parameters of 16 chloro-phenol compounds in water solution were calculated and fully optimized by using Onsager model in self-consistent reaction field（SCRF） based on the B3LYP/6-311G＊＊ level.These quantum chemical parameters were used as theoretical descriptors to correlate with the experimental biodegradation rate constant（Kb） of 16 compounds by stepwise multiple linear regression.As a result,a three-parameter model including molecular average polarizability（α）,entropy（Sθ）,and molar heat capacity at constant volume（CVθ） were established for Kb prediction,which was proposed with correlation coefficient R2 = 0.894.α exhibits the most significant effect on Kb.Variance analysis and standard t-value test were applied to validate the model.As expected,this model exhibits good robustness and prediction ability,which can be used in Kb prediction of analogs.

A model for estimating the rate constant between CO_2-CO gas and molten slag containing iron oxides using optical basicity

A simple model for estimating the rate constant between CO2-CO gas and molten slag containing iron oxides was developed using optical basicity only. In this model, the temperature dependence of the rate constant can be described by the Arrhenius law, and the activation energy can be expressed with a linear function of the slag＇s optical basicity. The model was applied to some molten slag systems, such as FeO, FeO-CaO, FeO-SiO2, FeO-Na2O, FeO-CaO-SiO2, FeO-SiO2-P2O5, FeO-SiOE-Na2O, and FeO-CaO-SiOE-P2O5. A comparison between the predicted results and measured data showed that the model worked well.

Key Role of Some Specific Occupied Molecular Orbitals of Short Chain n-Alkanes in Their Surface Tension and Reaction Rate Constants with Hydroxyl Radicals: DFT Study

Basing on the DFT calculations we propose the new theoretical model which describes both the surface tension σ of the short chain n-alkanes at their normal boiling points and their reaction rate constants with hydroxyl radicals OH• (at 297 ± 2 K) on the basis of their molecular orbital electronic characteristics. It has been shown that intermolecular dispersion attraction within the surface liquid monolayer of these compounds, as well as their reaction rate constants k with OH• radicals are determined by the energies Eorb of the specific occupied molecular orbitals which are the same in the determination of both the above physico-chemical characteristics of the studied n-alkanes. The received regression equations confirm the theoretically found dependences between the quantities of σ and k and the module |Eorb|. For the compounds under study this fact indicates the key role of their electronic structure particularities in determination of both the physical (surface tension) and the chemical (reaction rate constants) properties.

Theoretical prediction of energy dependence for D+BrO→DBr+O reaction:The rate constant and product rotational polarization

A quasi-classical trajectory（QCT） calculation is used to investigate the vector and scalar properties of the D ＋ Br O → DBr ＋ O reaction based on an ab initio potential energy surface（X1A state） with collision energy ranging from 0.1 kcal/mol to 6 kcal/mol. The reaction probability, the cross section, and the rate constant are studied. The probability and the cross section show decreasing behaviors as the collision energy increases. The distribution of the rate constant indicates that the reaction favorably occurs in a relatively low-temperature region（T 〈 100 K）. Meanwhile, three product angular distributions P（θr）, P（φr）, and P（θr, φr） are presented, which reflect the positive effect on the rotational angular momentum j＇ polarization of the DBr product molecule. In addition, two of the polarization-dependent generalized differential cross sections（PDDCSs）, PDDCS00 and PDDCS20, are computed as well. Our results demonstrate that both vector and scalar properties have strong energy dependence.

Rate Constants for the Reactions of NO_3~.and SO_4^(._) Radicals with Oxalic Acid and Oxalate Anions in Aqueous Solution

Rate constants for the reactions of NO3 and SO4 radicals with oxalic acid and oxalate anions in aqueous solution have been measured using pulse radiolysis and laser flash photolysis.

Apparent 1^st order rate constant of photodegradation of formaldehyde by carbon containing TiO2 nanoparticles

The apparent 1^st order rate constant of photodegradation of formaldehyde by carbon containing TiO2 nanoparticles has been investigated by numerical integration of mass transfer equation with measured degradation degree using a tubular photoreactor. The carbon containing TiO2 nanoparticles are synthesized by the oxidation of TiCl4 in propane/air flame CVD process with futile fraction up to 0.3 and carbon mass fractions up to 0.22, respectively. Thin TiO2 film is coated on the wall of the tubular reactor by sedimentation method. Effects of rutile mass fraction and carbon content have been examined on the apparent 1 ^st order rate constant and results show that, at 570ppm of formaldehyde loaded air stream, 80% relative humidity and about 100nm thin TiOa film, the 1^st order rate constant increases with increasing rutile mass fraction up to 0.3, occurs a maximum at the carbon content of about 5% by weight and is about 2.5 times of that at carbon content about zero or above 10%.

Dependence of Reaction Rate Constants on Density in Supercritical Fluids

A new method,which correlates rate constants of chemical reactions and density or pressure in supercritical fluids,was developed.Based on the transition state theory and thermodynamic principles, the rate constant can be reasonably correlated with the density of the supercritical fluid,and a correlation equation was obtained. Coupled with the equation of state (EOS) of a supercritical solvent,the effect of pressure on reaction rate constant could be represented.Two typical systems were used to test this method.The result indicates that this method is suitable for dilute supercritical fluid solutions.

Reaction-path Dynamics and Theoretical Rate Constants for the Reaction of CH_3CH_2OCF_3 with HOOO Radical

A dynamic method is employed to study the reaction mechanisms of CH3CH2OCF3 with the hydrogen trioxy （HOOO） radical. In our paper, the geometries and harmonic vibrational frequencies of all the stationary points and minimum energy paths （MEPs） are calculated at the MPW1K/6-31＋G（d,p） level of theory, and the energetic information along MEPs is further refined by the CCSD/6-31＋G（df, p） level of theory. The rate constants are evaluated with the conventional transition-state theory （TST）, the canonical variational transition-state theory （CVT）, the microcanonical variational transition-state theory （μVT）, the CVT coupled with the small-curvature tunneling （SCT） correction （CVT/SCT）, and the μVT coupled with the Eckart tunneling correction μVT/Eckart） based on the ab initio calculations in the temperature range of 200-3000 K. The theoretical results are important in determining the atmospheric lifetime and the feasible pathways for the loss of HFEs.

Estimation of rate constants for polymerization based on Monte Carlo simulation

The application of Monte Carlo method in estimating rate constants for polymerization was described, A general program for Monte Carlo simulation was determined first according to the elementary reactions, after which the rate constants could be automatically adjusted and optimized through comparing of experimental and simulated data with an error expression that meeted a given minimum criterion. Such a process made the rate constants to be estimated without kinetic model in advance. The technique was applied to estimate the rate constants of the bulk polymerization of styrene catalyzed by the rare earth catalyst. The esthnated results showed the Monte Carlo method was feasible and effective for estimating rate constants in polymerization engineering.

Calculation of the Canonical Rate Constant for the Nonadiabatic Trapping Model Based on Unified Statistical Theory:A Test on The Exchange Reaction H_2+H

A new approach was employed to calculate the canonical (thermal) rate constant basedon unified statistical theory. All information for the calculation was obtained from ab initio meth-ods. The flux integral for any point of reaction coordinate was calculated by counting the numberof quantum states and applied to determine the dividing surfaces along the intrinsic reaction coor-dinate (IRC). The classical exchange reaction H2+H, as an example, was investigated. The IRC forthe reaction has been traced and detailed information of IRC was carried out at the QCISD/6-311 G** level .The calculated rate constants are well consistent with the experimental results.

THE CALCULATION OF RATE CONSTANT OF ELECTRON TRANSFER REACTION AT ELECTRODES

After the electron transfers from the metal electrode to the Fe3+(H2O)(6) ion, the free energy of activation of this electron transfer reaction is calculated, then using the transition probability which is calculated by the perturbed degeneration theory and the Fermi golden rule,, the rate constant is gotten. Compared with the experimental results, it is satisfactory.

Molecular Orbital Nature of Solubility of Shot Chain n-Alkanes in Water and Their Reaction Rate Constants with Nitronium Cations: A DFT Study

The new theoretical models describe both the solubility S of the shot chain n-alkanes in water at 298.15 K, and their reaction rate constants k with nitronium cation NO2+ at 293.15 K on the basis of their molecular orbital characteristics. It is shown that both the quantities S and k are determined by the energies Eorb of the specific virtual (for S) and occupied (for k) molecular orbitals of these n-alkanes. The obtained regression equations confirm the theoretically found dependences of S and k on the absolute value of Eorb. This fact demonstrates that the electronic structure particularities of the studied n-alkanes play a crucial role in both their above-mentioned physicochemical properties.

MCSCF STUDIES ON THE IRC AND REACTION RATE CONSTANTS FOR THE DEHYDROGENATION REACTION OF VINYL RADICAL

The transition state(TS) and Intrinsic Reaction Coordinate (IRC) for the titled reaction were traced by means of MCSCF/6-31G (210 configurations). The reaction activation energy of this reaction is 140.2KJ/mol. The reaction rate constants of five temperetures were calculated by CVT involving the tunneling effects.

FLOTATION RATE CONSTANT MODE FOR FINE COAL

The density of fine coal has a major effect on the value of its flotation rate constant. The collector dose can increase the flotation rate of fine coal, especially for low ash coal, but the effect for gangue is not notable. The flotation rate of gangue is mainly governed by the water entrainment. A coal flotation rate constant model has been developed.

Electrochemical Determination of Rate Constants for Reactions of OH and its Application in the Evaluation of Anti-Oxidant Actions of Rheum

A single-sweep oscillopolarographic procedure is descrital which allows detethenahon of rateconstants for reachons of oH. For a wide range of compounds, the results fit well with rate constantspreviously obtained with other methods. Rate constants for reactions of six kinds of active compoundscontalned in rheum, a tradihonal Chinese herb, have been deteboned by this method. Rcationmechanism ha5 also been discussed.