Relations between kinetic parameters of different column models for liquid chromatography applying core-shell particles

This article presents analytical solutions of the general rate model (GRM), the lumped kinetic model (LKM), and the simpler equilibrium dispersive model (EDM) for core-shell particles and linear adsorption isotherms. The solutions in the Laplace domain are applied to derive analytical expressions for the temporal moments of these models. The results provide relations between the model specific kinetic parameters by matching one or more of the temporal moments. Several case studies are considered for illustration. The results show that simpler models are in many cases as good as the most detailed GRM if their kinetic parameters fulfill the matching relations. Thus, it is possible to reliably predict elution profiles using the simpler models. The derived analytical expressions can also be utilized to efficiently estimate model parameters from experimentally observed elution profiles to further optimize core-shell particles and to identify suitable column sizes and operating conditions.     

Dynamic chromatography: A stochastic approach

During the chromatographic separation process, analyte reactions are often observed leading to band broadening and/or elution of peak clusters. For many different chemical compounds the reaction can be reduced to a simple isomerisation kinetic scheme where elution is the result of adsorption–desorption on the surface stationary phase coupled with a flipping two-level reaction system. In this paper, the chromatographic peak shape for a reacting analyte is calculated in frequency domain when the reaction follows a simple reversible first order scheme. Both reaction and dynamic chromatographic systems have been considered. The derived solutions are expressed in closed form in the Fourier domain. Several limit solutions obtained under conditions of very slow and moderately fast kinetics are exploited. The effects of both kinetics rate constants and retention time on the chromatographic peak shape are singled out.     

Nematic-isotropic interfacial tension anisotropy of a calamitic lyotropic liquid crystal

In a planar oriented sample of a calamitic nematic lyotropic system (mixture of sodium lauryl sulphate/water/decanol), isotropic pretransitional domains appear at the nematic to isotropic transition. The domains are oblong in shape with the long axis along the orientational direction. We show experimental evidence that this oblong shape is determined by the nematic-isotropic interfacial tension anisotropy. Two uniparametric models of simple angular dependences for the interfacial tension are tested. Using the differential system obtained from the Young-Laplace condition at the nematic-isotropic interface, the domain shape can be numerically calculated for each value of the interfacial tension anisotropy. By processing the values of the transmitted light through both an isolated isotropic domain and its surrounding nematic zone, we obtain the anisotropy of the interfacial tension as the main fitting parameter. An estimation of the ratio of the extreme values for the interfacial tension is given.     

Estimation of the Moments of the Residence Time and First Passage Time from Experimentally Measurable Permeation Parameters via a New Formulation of the Transmission Matrix

Siegel's analysis on membrane transport in the Laplace domain [J. Phys. Chem. 95 (1991) 2556] in terms of transmission matrix, T(s), has been extended to a more useful formulation. This is achieved by combining uses of the matrix transport equations appropriate for void initial condition, or for saturated equilibrium, or of Dirac delta functional type and the theorem det[T(s)] = 1. This formulation enables us to expand T(s) in power series of the Laplace variable, s, with the expansion coefficients as the algebraic functions of the experimentally measurable transport parameters. Utility of the formulation is illustrated in the estimation of the experimentally inaccessible time moments for the first passage or residence times. It was also applied to the percutaneous drug delivery to obtain from the experimental data. The higher moments of the time lag or time lead using a graphic method.     

Curve fitting to asymmetrical chromatograms by the extended Kalman filter in frequency domain

An algorithm is presented to perform curve fitting on the basis of the Fourier transform of a signal. The curve fitting has been done with the exponentially modified Gaussian model, obtained when convolving a Gaussian distribution and an exponential decay function. The parameter estimation has been carried out by means of the two-dimensional extended Kalman filter. The goodness-of-fit has been characterized by the trace of the covariance matrix of the estimated parameters. The precision of the estimated parameters obtained by fitting either in time or frequency domain is compared.     

The role of the theoretical plate concept and gamma density functions in studies on mass transport and mass loadability of chromatographic columns

Summary The validity of the use of the plate theory in transport processes with non-Gaussian peak shapes is discussed. It is shown that the application of the plate theory implies the assumption of a peak with a gamma density shape which, however, converges rapidly to symmetrical Gaussian shape for large plate numbers. A proposal for an extension of the plate theory, based on a gamma density function is given. This approach results in an extra parameter which characterizes the asymmetry of a peak. Use of the suggested fitting function permits an estimate of the moments of the peak, even without the use of a computer. The proposed model can be used to determine a transfer function for the chromatographic system, allowing a system theoretical approach to determine the influence of, for example, amplifiers, filters and detectors on the peak shape. The exponentially modified Gauss (EMG) is one of the possible peak shapes included in the model.     

Mathematical modeling of an NMR chemistry problem in ovarian cancer diagnostics

We use mathematical modeling via the fast Padé transform (FPT) with respect to a theoretically-designed problem based on time signals that are similar to NMR data as encoded from benign and malignant ovarian cyst fluid. The FPT reconstructed exactly all the input spectral parameters by using exceedingly small fractions of the full time signals both for those corresponding to the benign, as well as to the malignant case. The converged parametric results remained stable thereafter at longer signal lengths. The Padé absorption spectra yielded clear resolution of all the extracted physical metabolites. The capacity of the FPT to resolve and precisely quantify the physical resonances as encountered in benign versus malignant ovarian cystic fluid is demonstrated. The practical significance of such findings is enhanced by the avoidance of the time signals’ exponential tail which is embedded in the background, leading to problems in quantification. Without any fitting or numerical integration of peak areas, the FPT reliably yields the metabolite concentrations of major importance for distinguishing benign from malignant ovarian lesions. Thus, the FPT provides distinct advantages relative to the standard Fourier methodology, which is also stable, but has a number of drawbacks. These include limited resolution capacity, as well as non-parametric estimation, so that only a shape spectrum is generated and post-processing is necessary via, e.g., fitting or numerical integrations which are not unique. The FPT is also distinguished from other competitive parametric methods, which are generally unstable as a function of signal length N at a fixed bandwidth and, therefore, particularly unsuitable to clinical data. We conclude that these advantages of the FPT could be of definite benefit for ovarian cancer diagnostics via NMR and that this line of investigation should continue with encoded data from benign and malignant ovarian tissue, in vitro and in vivo. This avenue is of clinical urgency for early ovarian cancer detection, a goal which is still elusive and achievement of which would confer a major survival benefit.     

Propagators and related descriptors for non-Markovian asymmetric random walks with and without boundaries

There are many current applications of the continuous-time random walk (CTRW), particularly in describing kinetic and transport processes in different chemical and biophysical phenomena. We derive exact solutions for the Laplace transforms of the propagators for non-Markovian asymmetric one-dimensional CTRW's in an infinite space and in the presence of an absorbing boundary. The former is used to produce exact results for the Laplace transforms of the first two moments of the displacement of the random walker, the asymptotic behavior of the moments as t-->infinity, and the effective diffusion constant. We show that in the infinite space, the propagator satisfies a relation that can be interpreted as a generalized fluctuation theorem since it reduces to the conventional fluctuation theorem at large times. Based on the Laplace transform of the propagator in the presence of an absorbing boundary, we derive the Laplace transform of the survival probability of the random walker, which is then used to find the mean lifetime for terminated trajectories of the random walk.     

基于小波的恒电量瞬态响应信号的滤波处理

利用小波变换的阈值法对恒电量响应信号进行滤波处理, 同时与传统的时域和频域的滤波方法进行分析比较, 并且讨论了小波变换的分解层数对恒电量响应信号滤波效果的影响. 结果表明, 利用小波变换可以在时域和频域同时对恒电量响应信号取得良好的去噪效果. 这不仅能提高时域曲线拟合的精度, 还大大地提高了恒电量频谱解析的可靠性. 在实际应用中, 小波变换的分解层数取5～7层可以收到满意的效果.     

Combined Wavelet Transform with Curve‐fitting for Objective Optimization of the Parameters in Fourier Self‐deconvolution

Fourier self‐deconvolution was the most effective technique in resolving overlapping bands, in which deconvolution function results in deconvolution and apodization smoothes the magnified noise. Yet, the choice of the original half‐width of each component and breaking point for truncation is often very subjective. In this paper, the method of combined wavelet transform with curve fitting was described with the advantages of an enhancement of signal to noise ratio as well as the improved fitting condition, and was applied to objective optimization of the original half‐widths of components in unresolved bands for Fourier self‐deconvolution. Again, a noise was separated from a noisy signal by wavelet transform, therefore, the breaking point of apodization function can be determined directly in frequency domain. Accordingly, some artifacts in Fourier self‐deconvolution were minimized significantly.     

小波变换用于示波信号中有用信息提取的研究

示波分析是近年来在我国发展起来的一个新的电化学分析研究领域［１～４］．它根据阴极射线示波器荧光屏上示波图及其变化进行分析测试,从原理上可以将其分为示波电位法和示波计时电位法;从测定方式上可以将其分为示波滴定和示波测定．关于示波电位法的一些理论问题（如...     

Global fitting without a global model: regularization based on the continuity of the evolution of parameter distributions

We introduce a new approach to global data fitting based on a regularization condition that invokes continuity in the global data coordinate. Stabilization of the data fitting procedure comes from probabilistic constraint of the global solution to physically reasonable behavior rather than to specific models of the system behavior. This method is applicable to the fitting of many types of spectroscopic data including dynamic light scattering, time-correlated single-photon counting (TCSPC), and circular dichroism. We compare our method to traditional approaches to fitting an inverse Laplace transform by examining the evolution of multiple lifetime components in synthetic TCSPC data. The global regularizer recovers features in the data that are not apparent from traditional fitting. We show how our approach allows one to start from an essentially model-free fit and progress to a specific model by moving from probabilistic to deterministic constraints in both Laplace transformed and nontransformed coordinates.     

Numerical solution of hydraulic models based on the axially-dispersed plug flow model by Laplace transforms

The problem of solving hydraulic models based on the axially-dispersed plug flow model which are applicable for the mathematical modelling of different flow-through systems both in chemical analysis (e.g., chromatography, flow injection analysis) and chemical industry (e.g., different tubular reactors) is discussed. Methods for numerical inversion of the model solution in the Laplace domain by expanding it into series of orthogonal functions are compared. Best results with respect to precision and consumption of computation time are given by the methods employing Chebyshov polynomials of the first kind and Fourier sine series. These methods were found to be better in these respects than some other frequently used numerical inversion methods.     

小波变换用于二次微分交流示波计时电位信号中有用信息的提取

小波分析是８０年代发展起来的一种新的数学分支。由于小波变换具有许多其它的信号处理手段所不具备的优良特性，如正交性，可变的时－频分辨率和可调节的局部支持等，使它成为信号处理的一种强有力的工具。     

Statistical theory of linear adsorption capillary chromatography with porous-layer stationary phase

A set of accurate expressions of elution-curve moments are derived from the moments of residence time and displacement in a step based on probability theory. Then the problems about residence time and displacement in a step of a solute molecule in the porous layer of capillary columns and in the moving mobile phase are described by a set of mass-balance equations respectively. The set of equations are solved in Fourier-Laplace domain, and the characteristic functions of residence time of a step, as well as the moments, are obtained by means of computing software Mathematica. At last, using numerical inverse Laplace transform, the elution curves for various conditions are calculated. In the case of large desorption constant the results entirely coincide with those of mass-balance-equation theory and in the case of small desorption constant they are equivalent to those of stochastic theory.     

Dechaos — A program for automatic or interactive analysis of gamma-ray spectra

DECHAOS is a gamma-ray spectral analysis program for personal computers. The program offers two modes of operation, automatic or interactive. The spectra to be analyzed can be acquired using any pulse height analyzer. The program includes routines for energy calibration, peak shape and efficiency calibration. Complex multiplets can be resolved automatically with the peak areas being determined using least-squares fitting techniques. Output tables include all data used in the calculation and peak information. The program is public domain software.     

Propagation, beam geometry, and detection distortions of peak shapes in two-dimensional Fourier transform spectra

Using a solution of Maxwell's equations in the three-dimensional frequency domain, femtosecond two-dimensional Fourier transform (2DFT) spectra that include distortions due to phase matching, absorption, dispersion, and noncollinear excitation and detection of the signal are calculated for Bloch, Kubo, and Brownian oscillator relaxation models. For sample solutions longer than a wavelength, the resonant propagation distortions are larger than resonant local field distortions by a factor of approximately L/lambda, where L is the sample thickness and lambda is the optical wavelength. For the square boxcars geometry, the phase-matching distortion is usually least important, and depends on the dimensionless parameter, L sin(2)(beta)Deltaomega/(nc), where beta is the half angle between beams, n is the refractive index, c is the speed of light, and Deltaomega is the width of the spectrum. Directional filtering distortions depend on the dimensionless parameter, [(Deltaomega)w(0) sin(beta)/c](2), where w(0) is the beam waist at the focus. Qualitatively, the directional filter discriminates against off diagonal amplitude. Resonant absorption and dispersion can distort 2D spectra by 10% (20%) at a peak optical density of 0.1 (0.2). Complicated distortions of the 2DFT peak shape due to absorption and dispersion can be corrected to within 10% (15%) by simple operations that require knowledge only of the linear optical properties of the sample and the distorted two-dimensional spectrum measured at a peak optical density of up to 0.5 (1).     

Thermal lens spectroscopy in cryogenic solutions: Analysis and comparison of intensities in CH4-N2 and CH4-Ar liquid solutions

The C-H (Delta upsilon = 6) absorption spectrum of methane has been obtained in liquid nitrogen and argon solutions using thermal lens spectroscopy. Mathematical models for continuous and periodic excitation were used to describe the concentration dependence of thermal lens intensities. Better fitting of the experimental results was accomplished by taking into account the periodic nature of the excitation. Comparison of thermal lens intensities in nitrogen and argon allowed calculation of relative enhancement factors. In dilute solutions, the intensity in liquid nitrogen was 1.39 +/- 0.08 times higher than that in argon. The literature estimation of this ratio is 1.49 +/- 0.61. In contrast to the estimated value, our result confidently shows actual variation in enhancement factors. This article not only shows the applicability of thermal lensing to cryosamples but also demonstrates that accurate measurements at low temperature are possible.     

An object-oriented approach to evaluating multiple spectral models

A versatile, spectroscopy analysis engine has been developed by using object-oriented design and analysis techniques coupled with an object-oriented language, C++. This engine provides the spectroscopist with the choice of several different peak shape models that are tailored to the type of spectroscopy being performed. It also allows ease of development in adapting the engine to other analytical methods requiring more complex peak fitting in the future. This results in a program that can currently be used across a wide range of spectroscopy applications and anticipates inclusion of future advances in the field.