Micellar catalysis in reactions of some β-lactam antibiotics with p -dimethylaminobenzaldehyde

Kinetic study of the reactions of amoxicillin (I), ampicillin (II) and cephlaxin (III) with p-dimethylaminobenzaldehyde (DAB) in weakly acidic EtOH/H₂O solution has been investigated using spectrophotometric method. Relatively slow reversible reactions of first order with respect to the antibiotic have been found. A derived equation for detecting the existence of reversibility from the linearity has been introduced. The effect of anionic surfactants (sodium dodecyl sulfate, SDS) on the kinetic of these reactions in aqueous solution has been studied. The presence of 0.005 M of SDS increases the rate constants by 4.3, 2 and 3.3 times for I, II and III, respectively. The consequence of the rate constants have a similar order in absence and presence of SDS; III > II > I. The rate constants pass through maxima with increasing SDS concentration followed by a gradual but steady decrease in the rate as the surfactant concentration increases further. Multiple linear regression method has been performed to evaluate the binding constants of each drug and DAB with SDS from the resulted kinetic data. The results suggest using multiple linear correlation method for such calculations, which is more accurate, reliable and less time consuming. The calculated binding constants between these drugs with SDS are following the consequence I > II > III which is related to the differences in their substitutions. The kinetic results were employed for spectrophotometric microdetermination of these drugs (I–III) in aqueous solution. The method was based on the reaction of β-lactam with an excess of DAB in presence of SDS and HCl (pH 2) at a wavelength 410 nm. The results indicate that the presented method is simple, precise and accurate. This method is applied to bulk antibiotics and some of their pharmaceutical preparations.     

Theoretical evaluation of methods for extracting retention factors and kinetic rate constants in liquid chromatography

A three-dimensional stochastic simulation is used to provide a detailed understanding of mass transfer processes in liquid chromatography. In this simulation, the migration of individual molecules is established through diffusion and laminar convection within the mobile phase. The molecules interact with the stationary phase by a partition (absorption) mechanism. For these studies, the column length, linear velocity, stationary-phase diffusion coefficient, interfacial mass transfer coefficient, and equilibrium constant are varied in a system with a homogeneous surface. Heterogeneous surfaces are also investigated by having multiple types of interaction sites that are equally or unequally distributed. For each simulation, the molecular distribution is examined and characterized at specified times or column lengths. Five individual methods are then applied to extract the thermodynamic and kinetic information for transport between the mobile and stationary phases. In the first method, all of the molecules are initially distributed in the mobile phase and the fraction remaining is monitored as a function of time. These simulation data are fit to a single exponential decay by nonlinear regression to determine the "true" retention factors and rate constants. The other methods rely on evaluating the shape of the zone profiles along the column. The statistical moments of the profiles are used to calculate the mean and the variance, which are related to the retention factors and the rate constants, respectively. The profiles are also fit to the exponentially modified Gaussian equation, the Giddings equation, and the Thomas equation. The fitting parameters from these equations are then used to calculate the retention factors and rate constants. Comparisons of the accuracy relative to the "true" retention factors and "true" rate constants, as well as the advantages and limitations of each method are discussed.     

The kinetic compensation effect

On the basis of theoretical TG curves it has been shown that the kinetic compensation effect observed in thermal decomposition reactions is not due to the special form of the Arrhenius equation. Formally, the validity of a linear kinetic compensation law implies the existence of a characteristic temperature at which the rate constants of all reactions have the same value, but this temperature can be higher or lower than the temperatures at which the decomposition takes place.Thermal decomposition processes can be better characterized by means of the compensation parameters than by means of the common kinetic parameters or decomposition temperatures, since the shape and the position of the TG curves and the kinetic parameters derived can be very much influenced by procedural variables, but the compensation parameters are independent of them.     

热动力学对比参量法 --简单级数反应

根据化学反应动力学和热动力学基本理论, 建立了简单级数反应的热动力学对比参量方程, 提出了一种新的热动力学研究法--对比参量法. 利用该法可以从一张热谱图上同时解析出化学反应的速率常数、半衰期和热动力学体系的冷却常数. 实验结果验证了方法的正确性.     

The mathematical origins of the kinetic compensation effect: 1. The effect of random experimental errors

The kinetic compensation effect states that there is a linear relationship between Arrhenius parameters ln A and E for a family of related processes. It is a widely observed phenomenon in many areas of science, notably heterogeneous catalysis. This paper explores one of the mathematical, rather than physicochemical, explanations for the compensation effect and for the isokinetic relationship. It is demonstrated, both theoretically and by numerical simulations, that random errors in kinetic data generate an apparent compensation effect (sometimes termed the statistical compensation effect) when the true Arrhenius parameters are constant. Expressions for the gradient of data points on a plot of ln A against E are derived when experimental kinetic data are analysed by linear regression, by non-linear regression and by weighted linear regression. It is shown that the most appropriate analysis technique depends critically on the error structure of the kinetic data. Whenever data points on a plot of ln A against E are in a straight line with a gradient close to 1/RT, then confidence ellipses should be calculated for each data point to investigate whether the apparent compensation effect arises from random errors in the kinetic measurements or has some other origin.     

Significance of Non-isothermal Kinetic Data. A statistical study

Arrhenius parameters values, in non-isothermal kinetic vaporisation processes for a series of compounds with related structures, have been calculated. This was made using a method of calculation that allows to find the most probable vaporisation mechanisms. According to this method DTG curves were compared with some theoretical ones reported in literature, whose shape results to be only a function of the mechanisms. In this way the choice of the mathematical functions which can be inserted in the kinetic equations, was influenced by the shape of the DTG plots and other thermal analysis signals thus allowing to choose the most probable mechanisms. The kinetic parameters derived from these mechanisms were compared, using statistical analysis, with those obtained from another method of calculation based on ‘a priori’ vaporisation mechanism chosen for the investigated liquid–gas transition. The standard deviations of the slope and of the intercept, together with the standard deviation and the square correlation coefficient (r ²) of the linear regression equations related to the mechanisms of the two methods were calculated. Student t-test, Fisher F-test, confidence intervals (c.i.) and residuals valueswere also given. Statistical analysis shows that the mechanisms obtained with the former method (diffusive and geometrical models) and the related Arrhenius parameters result to be more significant (in terms of probability) than the corresponding quantities of the latter for which a first-order model was chosen. This revised version was published online in August 2006 with corrections to the Cover Date.     

Continuum mesoscopic framework for multiple interacting species and processes on multiple site types and/or crystallographic planes

While recently derived continuum mesoscopic equations successfully bridge the gap between microscopic and macroscopic physics, so far they have been derived only for simple lattice models. In this paper, general deterministic continuum mesoscopic equations are derived rigorously via nonequilibrium statistical mechanics to account for multiple interacting surface species and multiple processes on multiple site types and/or different crystallographic planes. Adsorption, desorption, reaction, and surface diffusion are modeled. It is demonstrated that contrary to conventional phenomenological continuum models, microscopic physics, such as the interaction potential, determines the final form of the mesoscopic equation. Models of single component diffusion and binary diffusion of interacting particles on single-type site lattice and of single component diffusion on complex microporous materials' lattices consisting of two types of sites are derived, as illustrations of the mesoscopic framework. Simplification of the diffusion mesoscopic model illustrates the relation to phenomenological models, such as the Fickian and Maxwell-Stefan transport models. It is demonstrated that the mesoscopic equations are in good agreement with lattice kinetic Monte Carlo simulations for several prototype examples studied.     

On the method of bae for the determination of kinetic parameters from DTA curves

The mathematical error in the method proposed by Bae for the determination of kinetic parameters from DTA curves has been corrected. The proposed equation does not contain thermal constants of the apparatus, and can be applied to DTA curves by an iterative method. The results obtained by the application of this equation to experimental DTA curves for the decomposition of sodium bicarbonate compared well with those from isothermal measurements, even when the DTA sample holder assembly was of the isolated cup-type instead of the block-type assembly recommended by Bae.     

On a nonelementary progress curve equation and its application in enzyme kinetics

The analytical equation describing progress curves of an enzyme catalyzed reaction acting upon the Michaelis-Menten mechanism has been known for the case in which only the free enzyme incurs a loss of its activity, either spontaneously or as a result of an irreversible inhibitor action. The solution of differential equations which defines the rates of enzyme inactivation and substrate utilization is expressed by a nonelementary function in equation of an implicit type that precludes direct calculation of the extent of reaction at any time. Previously, the implicit equations have been rearranged to the alternative formulas and solved by the Newton-Raphson method, but this procedure may fail when used upon the presented equation. For this reason the other root-finding numerical method was applied, and the enzyme kinetic parameters of such numerically solved implicit equation for the reaction mechanism of irreversibly inhibited acetylcholinesterase were fitted to the experimental data by a nonlinear regression computer program.     

Closed form numerical approach for a kinetic interpretation of high-cis polybutadiene rubber vulcanization with sulphur

A novel mathematical approach to predict the vulcanization degree of high-cis polybutadiene rubber vulcanized with sulphur is presented. The model has kinetic base, it is constituted by four reactions occurring in series and parallel and takes contemporarily into consideration, within a simplified but reliable scheme, the actual reactions occurring during polybutadiene sulphur curing, namely primary crosslinking and possible de-vulcanization. The first order differential equation system obtained is suitably rearranged and a closed form expression for the vulcanization degree is derived, depending the four kinetic constants characterizing the chemistry describing reactions. Instead of using classic least-squares optimization routines to characterize kinetic constants on experimental data, a simplified but reliable approach is proposed, where a system of four non-linear equations is solved with a recursive strategy, allowing estimating kinetic constants that proved to fit well normalized experimental data. The procedure is fast and its reliability is tested on a number of experimental data available, relying into a high-cis polybutadiene rubber cured under different temperatures and accelerators concentrations. Very good approximations of experimental data are obtained, also in comparison with a heuristic numerical approach where optimization is obtained interactively.     

A computer simulation — Statistical procedure for predicting complexation equilibrium constants

The complexing properties of macrocyclic ligands have been quantitatively studied by the combined use of molecular mechanics, molecular dynamics, and multiple linear regression. The dependent variables in the regression equations are experimental equilibrium constants for known macrocycle complexes in various solvents. The independent variables are theoretical simulation results on the solvent-free ligand and its complex and additional physically motivated empirical variables to describe solvent and other important effects.The systems studied were: (a) 314 metal ion-macrocycle-solvent (including 3 mixed solvents) combinations; (b) 88 ammonium ion-crown ether-solvent (including 1 mixed solvent) combinations; (c) 24 hydrogen ion-crown ether-H₂O combinations; (d) 26 Na⁺ ion-spherand-CDCl₃ combinations; (e) 78 ammonium ion-spherand-CDCl₃ combinations; and (f) 73 complicated host-guest-solvent (including 1 mixed solvent) combinations.For each system, we report the best regression equation obtained using the AMBER force field. The standard errors in logK range from 1.42 in the largest system to 0.36 in the smallest. Regression equations were determined for several of the systems using the MMP2 force field as well, and the equations are shown to be relatively insensitive to the force field.The predictive ability of the method was tested by predicting logK for 20% of the cases chosen at random using equations derived from the remaining 80%. The errors in the predicted values are shown to be consistent with the statistical assumptions of the model.Regression equations obtained with this method can be used to predict the equilibrium constants for new complexes involving some combination of new, possibly unknown macrocycle, new host and, in certain cases new solvent. No X-ray or other structural data for the macrocycle is needed.     

Removal of Cr(VI) from wastewater using rice bran

The novel biosorbent rice bran has been successfully utilized for the removal of Cr(VI) from wastewater. The maximum removal of Cr(VI) was found to be 99.4% at pH 2.0, initial Cr(VI) concentration of 200 mg l(-1), and temperature 20 degrees C. The effect of different parameters such as contact time, adsorbate concentration, pH of the medium, and temperature was investigated. The adsorption kinetics was tested for first-order reversible, pseudo-first-order, and pseudo-second-order; reaction and the rate constants of kinetic models were calculated. Mass transfer of Cr(VI) from the bulk to the solid phase (rice bran) was studied at different temperatures. Different thermodynamic parameters, viz., changes in standard free energy, enthalpy, and entropy, have also been evaluated and it has been found that the reaction was spontaneous and endothermic in nature. The Langmuir and Freundlich equations for describing adsorption equilibrium were applied to data. The constants and correlation coefficients of these isotherm models were calculated and compared. Desorption studies was also carried out and found that complete desorption of Cr(VI) took place at pH of 9.5. The data were also subjected to multiple regression analysis and a model was developed to predict the removal of Cr(VI) from wastewater.     

热动力学特征对比参量法及其应用研究

基于简单级数反应的积分和微分热动力学方程，建立了热动力学特征对比参量 法的数学模型，提出了一种由特征时间参量计算特征对比参量的方法，通过几种不 同级数模型反应的热动力学研究证明了方法的正确性，并利用该法研究了过氧化氢 在磷酸盐缓冲液中氧化对苯醌反应的动力学特征，实验结果表明该反应动力学方程 可以表示为：dC(醌)/dt=kC(醌)C(H_2O_2)~0.5C(H~+)~(-0.5)     

N-苄氧甲酰基-α-氨基膦酸二苯酯有机磷化合物高效液相 色谱保留和手性识别 机理的研究

在正相条件下,首次对一系列N-苄氧甲酰基-α-氨基膦酸二苯酯化合物在环糊精类固定相CYCLOBONDISN和Pirkle型固定相SumichiralOA4700上实现了高效液相色谱手性折分,探索运用定量结构-对映异构体选择性保留关系的方法,将对映异构体的色谱保留和溶质分子描述参数相关性联系建立定量方程,结比研究了这二种不同类型的手性固定相对该系列有机磷化合物的色谱保留和手性识别机理,结果表明：对该系列化合物而言,Pirkle型手性因定相SumichiralOA4700的色谱手性折分能力明显优于在β-环糊精上衍生引入了额外的与前者类同的Pirkle型不对称中心的环糊精类固定相CYCLOBONDISN;环糊精类固定相CYCLOBONDISN在正相色谱条件下,包结机理不起主要作用,其作用方式更接近"Pirkle"型手性固定相;虽然二者具有类同的Pirkle型不对称中心,但是,手性识别机理差异显著,在CYCLOBONDISN手性固定相上,对N-苄氧甲酰基-α-氨基膦酸二苯酯化合物色谱折分贡献较大的是其logP和Angle参数相应的相互作用,环糊精提供的不对称性环境对手性识别有重要影响;而SumichiralOA4700对该系列化合物的手性识别与locD和TE相应的作用力相关。     

Curing degree prediction for S-TBBS-DPG natural rubber by means of a simple numerical model accounting for reversion and linear interaction

The paper presents a simple numerical model able to provide directly kinetic constants and reliable numerical rheometer curves for S-TBBS-DPG natural rubber. The approach is suitable to calculate the kinetic constants and maximum torque (MH) at any S-TBBS-DPG concentration, following a 3D mathematical interpolation/extrapolation procedure, when kinetic constants on few grid points of S-TBBS-DPG concentrations are available. In particular, the possibility to estimate with sufficient accuracy the behavior of natural rubber at any intermediate concentration of S-TBBS-DPG having engineering relevance has been proved, calibrating the model by means of simple closed form standard best fitting on few experimental data. The model used is a three kinetic parameters one, derived from the well known Han's and co-workers approach, where constants have been evaluated normalizing experimental rheometers curves following the commonly accepted Sun and Isayev method. The procedure has been validated against experimentally obtained rheometer curves by means of inverse analysis, exhibiting excellent prediction capabilities. The approach may be used for practical purposes in order to avoid expensive and cumbersome experimental investigations.     

Generalized composite degradation kinetics for polymeric systems under isothermal and nonisothermal conditions

A composite degradation methodology is extended to the conversion-dependence function in order to explain the importance of multiple reaction mechanisms which might be considered to be involved in degradation processes. Based on two elementary reaction mechanisms, a specific form of the model equation is derived, which is capable of describing various types of degradation behavior showing sigmoidal rate as well as deceleratory rate. The conversion-dependence function is derived to be independent of the Arrhenius-type reaction constant or temperature, and thus the kinetic parameters are determined by analytic methods that have been developed for isothermal and dynamic-heating experiments without any modification or additional assumptions. The developed model equation is tested by predicting the isothermal master curve of polyether-ether-ketone (PEEK), which is used as a model system in this study. The activation energies of the model system are analyzed using comparable methods for isothermal and dynamic experiments, which compare favorably in terms of the activation energy as a function of conversion. The resulting model equation, based on the kinetic parameters determined by isothermal experiments, can accurately predict both isothermal and dynamic-heating thermogravimetry utilizing the same constants and identical reaction mechanisms without additional assumption.     

基于毛细管电泳的苦参碱转运过程中的血清白蛋白行为成像

利用毛细管电泳（CE）技术在体外条件下建立了苦参碱（MT）与血清白蛋白（SA）相互作用的分析方法。生理条件下通过淌度移动法和前沿分析法（FA）研究苦参碱与血清白蛋白的结合状况，构建配体（MT）-受体（SA）相互作用模型。其中，淌度移动法采用非线性拟合方法获得苦参碱与人血清白蛋白（HSA）结合参数；FA运用非线性回归方程、Scatchard方程、Klotz方程3种方程获得苦参碱与人血清白蛋白结合参数，分析其相互作用状况进而分析模型适用度。利用淌度移动法可知，人血清白蛋白与苦参碱表观结合常数K_B为8.072×10³ mol/L；利用FA法可知，采用非线性回归方程、Scatchard方程、Klotz方程3种方程获得苦参碱与人血清白蛋白表观结合常数K_B分别为1.434×10³、1.781×10³和2.133×10³ mol/L，且二者结合位点数在1.0左右，说明苦参碱与人血清白蛋白作用只有单一类型的结合位点。通过计算分析得到3个方程的相关系数（r），关系为r_Klotz > r_非线性 > r_Scatchard。结果表明：淌度移动法和FA法均适用于分析MT-HSA体系的结合状况；由于FA法可以计算出表观结合常数的同时又能计算出结合位点数，因而更适合MT-HSA体系的分析研究；分析比较得出3种方程之中Klotz方程为最适理论模型。结合参数表明，MT-HSA相互作用体系之间发生的结合反应为单一类型的结合位点且结合稳定。相关工作阐明了典型生物碱与血清白蛋白的相互作用机制，可为生物碱的血液输运机制的深入研究提供有益参考。     

Simulations for evaluation of kinetic methods in differential scanning calorimetry. Part 1. Application to single-peak methods: Freeman-Carroll, Ellerstein, Achar-Brindley-Sharp and multiple linear regression methods

In order to simplify the choice between different kinetic methods used in differential scanning calorimetry, an interesting way for testing kinetic treatments is proposed, using simulated thermoanalytical curves computed from given kinetic parameters. Applied to the study of a polymerization, we tested the Freeman-Carroll, Ellerstein, multiple linear regression (reaction-order model) and Achar-Brindley-Sharp methods. The test of the validity of the methods is performed using the LSM parameter that represents the fit between the mathematical treatment used in the kinetic model and known data. The study reveals the importance of the number of points used, i.e. the resolution, in the thermoanalytical curve recording, especially for the Freeman-Carroll and Ellerstein methods, there being an increase in the relative error on all the kinetic parameters when the number of points is decreased. Maximum relative errors are reported for the pre-exponential factor calculations. Evaluation of the enthalpy error on the determination of the kinetic parameters has been performed. Simulations obtained with various enthalpies indicate the necessity in such cases of computing a relative dimensionless LSM parameter (relative to the amplitude of the phenomena) in order to compare different thermal effects.     

Nonequilibrium thermodynamics of transport processes on membrane surfaces

Nonequilibrium processes have been considered on interfaces between media, with one medium being a permeable membrane. The nonequilibrium processes have been described in terms of nonequilibrium thermodynamics combined with the Fokker?Planck kinetic equation. Phenomenological equations derived within the framework of the combined approach have been discussed. It has been shown that the formal use of linear equations of nonequilibrium thermodynamics may be, in some cases, reduced to nonlinear equations for heat and mass transfer through an interface. It has been noted that the asymmetry of transport characteristics of asymmetric membranes may be explained in terms of the derived relations.