Simulation of peak profiles in non-linear HPLC

Summary The possibilities and domain of applicability of the ideal chromatography model for calculating peak profiles in non-linear chromatography are analyzed. For this purpose we used the main conclusion of the model of a layer of equilibrium adsorption (LEA model), which determines the difference between ideal and non-ideal chromatography in terms of the relative length of a chromatographic column. It is shown that the experimental data of non-linear high-performance liquid chromatography can be approximated in terms of the elementary analytical relations known in the theory of ideal chromatography.     

构建支持向量机-偏最小二乘法为药物构效关系建模

为研究药物构效关系积累样本数据的过程中,需为小样本建模。此时较易造成过拟合,影响模型的预测性能和稳定性。为此可用偏最小二乘(PLS)法从样本数据中成对地提取最优成分,消除自变量间的复共线性,并有效的降维,然后应用最小二乘支持向量机对成对成分进行非线性回归,并以基于误差修正的策略调整,使之更有效地表达自、因变量间的非线性关系。由此构建为EB-LSSVM-PLS算法,所建模型的预报精度高,稳定性良好。将其应用于新型黄烷酮类衍生物的QSAR建模,效果令人满意,其泛化性能优于其它方法。     

Weak-anchoring effects on a Freedericksz transition in an annulus

This paper investigates the effect of weak anchoring on static orientation patterns in a sample of nematic liquid crystal confined to a cylindrical annular geometry, in the presence of a magnetic field. The particular arrangement considered in detail is that in which a magnetic field is applied in the azimuthal direction to a sample of liquid crystal that is initially uniformly aligned parallel to the cylindrical axis and is weakly anchored at the inner cylinder, but strongly anchored at the outer cylinder. A static solution of the non-linear continuum equations is presented which suggests a possible experiment for evaluating the surface elastic coefficient k₂₄. In addition, a linear stability analysis based on the dynamic theory yields results for critical phenomena in agreement with those derived from the non-linear solution.     

Multivariate monitoring of fermentation processes with non-linear modelling methods

Multiway principal components analysis (MPCA) and parallel factor analysis (PARAFAC) are widely used in exploratory data analysis and multivariate statistical process control (MSPC). These models are linear in nature, thus, limited when non-linear relations are present in the data. Principal component analysis (PCA) can be extended to non-linear principal components analysis using autoassociative neural networks. In this paper, the network’s bottleneck layer outputs (non-linear components) were made orthogonal. A method to estimate confidence limits based on a kernel probability density function was proposed since these limits do not assume that the non-linear scores are normally distributed. A measure for the non-linear scores (D_NL) was presented here to monitor on-line the process replacing the well known Hotelling’s T² statistic. One hundred and two industrial fermentation runs were used to evaluate the performance of a non-linear technique for multivariate process statistical monitoring. Three process runs with faults were used to compare the error detection performance using a statistic for the non-linear scores and the residuals statistic (SPE).     

A convenient electrolytic process for the reduction of aldehydes

We report an efficient electrolytic procedure for the reduction of aldehydes to primary alcohols in the absence of dimeric products. In this promising approach, based on environmentally friendly chemical synthetic methods, a simple electrolytic undivided cell was designed. Two copper plates served as electrodes and recycled water as the medium. A 6-V battery provided the required energy. Although initially the method was intended for the preparation of 2-aryl-3-hydroxymethyl imidazo[1,2-a]azines, it was successfully extended to reduce other aliphatic and aromatic aldehydes. The attractiveness of this procedure includes its operational simplicity, practical viability, inexpensiveness and good yields. In most cases the results were better than those obtained with the standard reduction procedure using sodium borohydride.     

Estimation of concentration-dependent diffusion coefficient in pressure-decay experiment of heavy oils and bitumen

Molecular diffusion has been considered to be an underlying mechanism for many of oil recovery processes like miscible and immiscible gas injection projects. Reliable estimation of the molecular diffusion coefficient as a transport property is therefore important in studying the performance of such systems. Interpretation of pressure-decay data has been traditionally used to estimate the molecular diffusion coefficient and usually to simplify the interpretation, its concentration dependency has been neglected. A pressure-decay model with concentration-dependent diffusion coefficient leads to a non-linear problem in which an analytical solution is difficult if not impossible to obtain. In this study, we used the Heat Integral Method (HIM) to solve the non-linear diffusion problem as a forward model. Using that forward model, we have developed a simple methodology for estimating the diffusion coefficient regardless of the form of function used for the concentration dependency of the molecular diffusion. Three different forms of functions for diffusion coefficient were considered. In its simplest form, the diffusion coefficient is set to be a constant value. In the two other forms, the diffusion coefficient was evaluated as a concentration-dependent two parameter equation using exponential and power-law functions, respectively. The proposed methodology is verified and tested using direct numerical solutions of the non-linear diffusion problem. Many numerical examples with a wide range of input parameters demonstrate the effectiveness of the proposed approach.     

Bio-convective Darcy-Forchheimer oscillating thermal flow of Eyring-Powell nanofluid subject to exponential heat source/sink and modified Cattaneo–Christov model applications

Nanofluid thermal applications considerably enhanced the heat and mass transfer patterns, which plays novel role in many bio-technological, renewable energy and engineering applications. Many prime applications off nanomaterials have been inspected in solar energy and thermal engineering issues to benefit human society. Furthermore, motile microorganisms, that have applications in petroleum sciences, enzymes biotechnology, biofuels, pharmaceutical, and other fields, greatly improve the stability of nanofluids. The current study examines the Darcy-Forchhiemer accelerating flow of Eyring-Powell nanofluid over an oscillating surface which contains the thermal radiations and gyrotactic microorganisms. The extension in the heat and mass transfer expression is suggested by following the relations of Cattaneo–Christov theory. Furthermore, the non-uniform heat source/sink phenomenon is also being focused to improve the thermal aspect of model. The flow problem model is consisting of non-linear PDEs that are solved by using the homotopy analysis scheme. After highlighting the convergence zone, physical characteristics for parameters are listed.     

Analytical expression of the concentration of species and effectiveness factors in porous catalysts using the Adomian decomposition method

A mathematical model by Hayes et al. [10] of porous catalysts that have non-linear reactions kinetic is discussed. The model involves the non-linear steady-state reaction-diffusion equation. The analytical solution for the concentration of species is obtained using the Adomian decomposition method. Simple and an approximate polynomial expressions for concentration and effectiveness factors are derived for general non-linear Langmiur-Hinshelwood-Haugen-Watson (LHHW) type models which has variety of real rate function. Comparison of the analytical approximation and numerical simulation is also presented. A good agreement between theoretical predictions and numerical results is observed. The concentration and the effectiveness factors are also computed for the limiting cases of LHHW type models.     

Kinetic Analysis of Thermogravimetric Data XXXI. Derivation of a non-linear kinetic compensation law

The kinetic compensation effect observed in heterogeneous non-isothermal kinetics is only an apparent effect. In general, the correlation derived between the kinetic parameters E and log A from TG curves can be described by means of a non-linear compensation law, expressed by Eq. (14). This equation may become approximately linear in certain particular cases, i.e. it may change into an isokinetic relation. The validity of the non-linear compensation law has been tested by using over 1000 sets of kinetic parameters reported earlier. This revised version was published online in July 2006 with corrections to the Cover Date.     

A model for the non-linear viscoelastic response and physical aging in glassy polymers

Constitutive relations are derived for the non-linear viscoelastic behavior of amorphous polymers subjected to physical aging. The model is based on the concept of temporary networks, where a viscoelastic medium is treated as a network of active chains that break and reform due to micro-Brownian motion. With reference to the Adam–Gibbs theory of cooperative relaxation, the breakage and reformation rates are assumed to depend on the current temperature and the configurational entropy, which is determined as a difference between the specific entropies of the equilibrium liquid and glass. Unlike previous studies, the model accounts for the compressibility of polymers below the glass transition temperature. Constitutive equations for viscoelastic media at finite strains are developed using the laws of thermodynamics. For small values of strains, these relationships are simplified and reduced to linear integral equations with some internal time driven by the fictive temperature and the hydrostatic stress (an extension of the KAHR model to non-linear materials). To verify the constitutive model, we determine the adjustable parameters using the data obtained in short-term creep tests and comparing the results of numerical simulation with the observations in long-term tests. Fair agreement is demonstrated for the experimental data of high-density polyethylene and poly(vinyl chloride) with the numerical predictions.     

Highly accurate biomolecular electrostatics in continuum dielectric environments

Implicit solvent models based on the Poisson-Boltzmann (PB) equation are frequently used to describe the interactions of a biomolecule with its dielectric continuum environment. A novel, highly accurate Poisson-Boltzmann solver is developed based on the matched interface and boundary (MIB) method, which rigorously enforces the continuity conditions of both the electrostatic potential and its flux at the molecular surface. The MIB based PB solver attains much better convergence rates as a function of mesh size compared to conventional finite difference and finite element based PB solvers. Consequently, highly accurate electrostatic potentials and solvation energies are obtained at coarse mesh sizes. In the context of biomolecular electrostatic calculations it is demonstrated that the MIB method generates substantially more accurate solutions of the PB equation than other established methods, thus providing a new level of reference values for such models. Initial results also indicate that the MIB method can significantly improve the quality of electrostatic surface potentials of biomolecules that are frequently used in the study of biomolecular interactions based on experimental structures.     

Current-potential curves with an EE mechanism

The dc polarographic response for the EE mechanism both in the expanding plane electrode and in the expanding sphere electrode is examined. Explicit equations for the current-potential curves when all species are initially added to the solution and without using the steady-state approximation have been derived. The situation obtained in some particular cases (reversible steps, one reversible and the other irreversible, totally irreversible steps and well-separated steps) is also discussed.     

Der nichtlineare Ausgleich in der Röntgenspektrometrie

The hyperbolic approximation of non-linear relationships between intensities and concentrations can be reduced to a linear regression for two constants, being carried out with a modern non-programmable scientific desk or pocket calculator. The approximation is independent on dead-time losses and ensures good results also in cases of unknown background.     

Study on the retention behaviour of low-molar-mass polystyrenes and polyesters in reversed-phase liquid chromatography by evaluation of thermodynamic parameters

Polymers can be characterized under sorption conditions, to obtain information on molar mass and chemical composition. In order to get a better understanding of their retention behaviour under such conditions, the evaluation of thermodynamic parameters obtained from van't Hoff analyses on low-molar-mass polystyrenes (PS) and polyesters (PE) in various THF–water mixtures on a C₁₈ column is described in this study. Linear van't Hoff behaviour was observed in almost all cases. Negative values for both ΔH and ΔS were found for both PS and PE oligomers, which increase with increasing %THF. For ΔS this is explained from multi-site attachment effects. For PS, the non-linear relations between ΔH and ΔS, and degree of polymerization (p) could be properly described by the Stockmayer–Fixman equation. Although less clear, similar trends were found for PE. For PS, evidence for penetration effects of oligomer chains into the bonded chains was obtained. Martin plots for both PS and PE were shown to be non-linear in all investigated eluent compositions. The extent of non-linearity is suggested to depend on the conformation of a polymer in solution. No distinct enthalpy–entropy-compensation temperature (EECT) independent of p was found for PS, thus confirming the findings of an earlier study in which no exact molar mass independence was found under critical conditions. Further evaluation of EECT for PS oligomers revealed a retention mechanism independent of the binary eluent composition. This indicates that conclusions from this study can also be used for a qualitative understanding of sorption mechanisms in the gradient elution mode. Finally, for PS it was shown that ΔG equals zero under critical conditions, thus confirming theoretical predictions.     

Modeling and simulation of IEF in 2-D microgeometries

A 2-D finite-volume model is developed to simulate nonlinear IEF in complex microgeometries. This mathematical model is formulated based on the mass conservation and ionic dissociation relations of amphoteric macromolecules, charge conservation, and the electroneutrality condition. Based on the 2-D model, three different separation cases are studied: an IPG in a planar channel, an ampholyte-based pH gradient in a planar channel, and an ampholyte-based pH gradient in a contraction-expansion channel. In the IPG case, cacodylic acid (pK(1) = 6.21) and Tris (pK(1) = 8.3) are used as the acid and base, respectively, to validate the 2-D IEF model. In the ampholyte-based pH gradient cases, IEF is performed in the pH range, 6.21-8.3 using 10 ampholytes in the planar channel and 20 ampholytes in the contraction-expansion channel. The numerical results reveal different focusing efficiencies and resolution in the narrow and wide sections of the contraction-expansion channel. To explain this, the expressions for separation resolution and peak concentrations of separands in the contraction-expansion channel are presented in terms of the channel shape factor. In a 2-D planar channel, a focused band remains straight all the time. However, in a contraction-expansion channel, initially straight bands take on a crescent profile as they pass through the trapezoidal sections joining the contraction and expansion sections.     

The kinetic study of isothermal solid state decompositions: a combined numerical and experimental approach

This paper identifies and makes quantitative allowance for experimental errors in isothermal weight change data. For experiments which involve a purge gas to remove decomposition products, attention is directed to errors due to variations in the gas flow rate and the need to heat the sample initially to the temperature of study. For experiments carried out at reduced pressure, importance is also attached to the undesirable influence of draughting, buoyancy, pressure and conventional effects. An experimental procedure which minimises the errors due to some of these factors is discussed. The paper also examines how the non-linear least squares method employed to analyse the kinetic data may be extended to allow for error produced by the initial temperature change. This extended method is used to analyse weight change data which are consistent with a contracting-interface mechanism, and the results clearly demonstrate the improved accuracy of the kinetic parameter estimates.     

Accounting for Poisson noise in the multivariate analysis of ToF‐SIMS spectrum images

Recent years have seen the introduction of many surface characterization instruments and other spectral imaging systems that are capable of generating data in truly prodigious quantities. The challenge faced by the analyst, then, is to extract the essential chemical information from this overwhelming volume of spectral data. Multivariate statistical techniques such as principal component analysis (PCA) and other forms of factor analysis promise to be among the most important and powerful tools for accomplishing this task. In order to benefit fully from multivariate methods, the nature of the noise specific to each measurement technique must be taken into account. For spectroscopic techniques that rely upon counting particles (photons, electrons, etc.), the observed noise is typically dominated by ‘counting statistics’ and is Poisson in nature. This implies that the absolute uncertainty in any given data point is not constant, rather, it increases with the number of counts represented by that point. Performing PCA, for instance, directly on the raw data leads to less than satisfactory results in such cases. This paper will present a simple method for weighting the data to account for Poisson noise. Using a simple time‐of‐flight secondary ion mass spectrometry spectrum image as an example, it will be demonstrated that PCA, when applied to the weighted data, leads to results that are more interpretable, provide greater noise rejection and are more robust than standard PCA. The weighting presented here is also shown to be an optimal approach to scaling data as a pretreatment prior to multivariate statistical analysis. Published in 2004 by John Wiley & Sons, Ltd.     

The second and third order non-linear optical properties of liquid crystalline polymers

The second and third order non-linear optical susceptibilities of several donoracceptor substituted side chain polymers, some of which exhibit mesophases, will be reported. The susceptibilities were measured by harmonic generation from thin films, typically 0·5 μm thick, at a fundamental wavelength of 1064 nm and 1579 nm. For second harmonic generation, the spin coated films were contact poled on a glass substrate with an interdigited electrode pattern. Typical values obtained were χ⁽²⁾₃₁ = 1 × 10^-9 esu and χ⁽²⁾₃₃ = 3 × 10^-9 esu, the largest value was χ⁽²⁾₃₃ = 6·3 × 10^-9 esu. The difficulty in deriving reliable second order structure-property relations because of the large effect which the contact poling process has on the non-linear optical susceptibility of the films will be highlighted. The highest χ⁽³⁾ value of 5·8 × 10^-12 esu obtained from an amorphous film of a polymer with an asymmetrically substituted azo side group is comparable with the susceptibility of more typical third order non-linear materials such as the main chain polymers polyphenylacetylene and poly-p-phenylenebenzobisthiazole.     

沸石的表面酸、碱性与甲醇、甲苯侧链烷基化反应

以TPD和质谱检测的TPSR、IR及微型反应器等手段探讨了X型沸石的表面酸、碱性质对甲醇、甲苯侧链烷基化反应的作用及可能的反应历程。