A simple method to extract spectral parameters using fractional derivative spectrometry

The nonlinear fitting method, based on the ordinary least squares approach, is one of several methods that have been applied to fit experimental data into well-known profiles and to estimate their spectral parameters. Besides linearization measurement errors, the main drawback of this approach is the high variance of the spectral parameters to be estimated. This is due to the overlapping of individual components, which leads to ambiguous fitting. In this paper, we propose a simple mathematical tool in terms of a fractional derivative (FD) to determine the overlapping band spectral parameters. This is possible because of several positive effects of FD connected with the behavior of its zero-crossing and maximal amplitude. For acquiring a stable and unbiased FD estimate, we utilize the statistical regularization method and the regularized iterative algorithm when a priori constraints on a sought derivative are available. Along with the well-known distributions such as Lorentzian, Gaussian and their linear combinations, the Tsallis distribution is used as a model to correctly assign overlapping bands. To demonstrate the power of the method, we estimate unresolved band spectral parameters of synthetic and experimental infra-red spectra.     

Direct Evaluation of Partial Molar Volumes of Binary Solutions of Dimethyl Sulfoxide with Ethyl Acrylate,Butyl Acrylate,Methyl Methacrylate and Styrene

The Tikhonov regularization is applied to convert specific molar volume data of binary solutions of dimethyl sulfoxide with a number of acrylates and with styrene into their second- and first-partial derivatives with respect to mole fraction under constant temperature and pressure. Generalized Cross Validation is used to guide the selection of the regularization parameter that keeps noise amplification under control. The resulting first derivative is then used to compute the partial molar volumes. These are compared against that obtained by the traditional method of least-squares fitting of excess molar volumes. Some of the advantages of the current approach and possible extension to other partial molar quantities are briefly discussed.     

Interpretation of photon correlation spectroscopy data: A comparison of analysis methods

Properties of solutions and colloidal suspensions such as molecular and particle dynamics, diffusivities, and size distributions may be determined through dynamic light-scattering experiments. Here a number of methods for predicting the details of the linewidth distribution from photon correlation spectroscopy data are reviewed. Their performance on simulated data (with and without noise added) and experimental data from polystyrene latex standards (including a mixture of two standards) is compared. Methods which do not assume a specific form for the distribution are considered. These include cumulants, histograms, exponential sampling, subdistributions, a non-negatively constrained histogram, and Provencher's constrained regularization. Constrained regularization was found to be most robust to noise present in the autocorrelation function and therefore most reliable for analyzing experimental data; however, the method sometimes oversmoothed the distribution. For bimodal distributions the histogram method performed well in our testing, especially when the approximate peak locations were known a priori. Two linear least-squares fitting methods, exponential sampling and the non-negatively constrained histogram, yield accurate values for the overall mean and standard deviation and can be implemented easily on a microcomputer. The linear subdistribution method, although computationally fast, sometimes was not as accurate as other methods.     

Extraction of lifetime distributions from fluorescence decays with application to DNA-base analogues

Several important aspects of fluorescence decay analysis are addressed and tested against new experimental measurements. A simulated-annealing method is described for deconvoluting the instrument response function from a measured fluorescence decay to yield the true decay, which is more convenient for subsequent fitting. The method is shown to perform well against the conventional approach, which is to fit a convoluted fitting function to the experimentally measured decay. The simulated annealing approach is also successfully applied to the determination of an instrument response function using a known true fluorescence decay (for rhodamine 6G). The analysis of true fluorescence decays is considered critically, focusing specifically on how a distribution of decay constants can be incorporated in to a fit. Various fitting functions are applied to the true fluorescence decays of 2-aminopurine in water-dioxane mixtures, in a dinucleotide, and in DNA duplexes. It is shown how a suitable combination of exponential decays and non-exponential decays (based on a Γ distribution of decay constants) can provide fits of equal quality to the conventional multi-exponential fits used in the majority of previous studies, but with fewer fitting parameters. Crucially, the new approach yields decay-constant distributions that are physically more meaningful than those corresponding to the conventional multi-exponential fit. The methods presented here should find wider application, for example to the analysis of transient-current or optical decays and in F?rster resonance energy transfer (FRET).     

Correction of Gel Chromatograms for Instrumental Broadening

The Tikhonov regularization method was proposed for correction of gel chromatograms for instrumental broadening. The results obtained in solving the Tung equation by approximation and regularization methods and also in using the Gauss and Pearson distributions as a function of instrumental broadening were compared.     

Solution of inverse problem of light beating spectroscopy using Tikhonov method of regularization for analyzing polydisperse suspensions of nanoparticles

The results of a numerical solution of the inverse problem of light beating spectroscopy using the Tikhonov regularization method are presented. The developed algorithm takes into account the positivity of the solution and the constant background signal. The regularization parameter of the method is determined based on the a priori information on the noise amplitude of the input signal. The results of the reconstruction of model uni-, bi-, and multimodal distributions are presented. For examples of numerically generated spectra, the effects of the measured spectrum noise, background signal, and frequency bandwidth of the signal measurement on the characteristics of the reconstructed distributions are studied.     

Spectral density analysis of nuclear spin—spin coupling: II. Hartree-Fock LCAO studies for homonuclear coupling constants

A spectral density function has been calculated for the indirect nuclear spin—spin coupling constant for homonuclear coupling. The ground state wavefunction is obtained with a normal ab-initio calculation. The sum over states approach for calculating the reduced coupling constant K is replaced by an integration over a spectral density function where the integration variable is the orbital exponent of a “scanning molecular orbital”. This results in a stable method for calculating K with reasonable accuracy. The spectral density function also gives information about which excited states give important contributions to K.Furthermore a residual spectral density function is defined that can be used as a test for the completeness of a set of virtual orbitals in a sum over states calculation.     

The Effective Permittivity of Reacting Mixture Solutions for Multiphysics Calculations

Huang and Yang (PIER Lett. 5: 99?C107, 2008) proposed a method based on experimental results to calculate the effective permittivity of liquid reacting mixture solutions. The method cannot be directly applied to multiphysics calculations for microwave heating on chemical reactions, because the derived formula of effective permittivity is a function of the reaction time. In this paper, we improve the method to obtain the effective permittivity as a function of the reactants?? concentrations and temperature by numerical fitting. Thus, the formula can be directly used for multiphysics calculation. Three measured effective permittivity curves for the iodination of acetone reaction under constant temperature were used to calculate the corresponding coefficients of the method at both 915?C2,450?MHz. The results calculated by the coefficients are in satisfactory agreement and approach the measured results.     

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.     

Molecular Architecture of Non-Linear Polymers: Kinetic Modeling and Experimental Characterization of the System Methyl Methacrylate + Ethylene Glycol Dimethacrylate

A general kinetic approach allowing the prediction of the molecular architecture of non-linear polymers is applied to the study of the copolymerization of methyl methacrylate (MMA) with ethylene glycol dimethacrylate (EGDMA). Dynamic predictions of molecular weight distributions, sequence length distributions and mean square radius of gyration are possible before and after gelation. A set of experiments concerning the copolymerization of MMA and EGDMA was carried out in toluene solution at 60 °C for which classic radical kinetics is a good approximation. The time evolution of key polymer properties was followed using a SEC system with a refractive index detector coupled with MALLS allowing the determination of absolute weight average molecular weight and apparent molecular size distributions as well as z-average radius of gyration. Special focus was given to assess the influence of the initial amount of cross-linker on the dynamics of the non-linear structure build-up of these products. A kinetic scheme comprising 23 different chemical species and 76 chemical reactions was used in the modeling studies of this chemical system. Most of the kinetic parameters used in the simulations have been collected from previous studies. For experiments at low monomer conversion (up to about 0.5) a good agreement between predictions and experimental measurements is observed for molecular weights and z-average radius of gyration by fitting a small number of parameters describing gel effect (with a conversion dependent but chain length independent termination rate parameter) and the relative propagation on pendant double bonds. However, predicted values of weight-average molecular weights and z-average radius of gyration before gelation are too low at higher monomer conversions with non-linear systems. The likely cause is the presence of intramolecular reactions which should not be neglected in these circumstances.     

Distribution analysis for single molecule FRET measurement

A new numerical analysis method for experimental single-pair fluorescence resonance energy transfer (sp-FRET) data is proposed. In this method, every single data point was plotted in a style of a cumulative distribution function and dedicated to curve-fitting analysis, so that the analysis does not depend on bin size. A series of numerical simulations showed that this analysis has a more efficient and accurate resolvability of components than a fitting method based on Gaussian functions to a histogram plot. A simulated data based on experimental FRET distributions were also used to discuss the fitting errors of this method. The proposed method was applied to sp-FRET experiments of doubly dye-labeled double-strand DNA with a short sequence. Mixtures of up to three species were analyzed, and the contributions up to four subpopulations were successfully resolved.     

1H multiple-quantum nuclear magnetic resonance investigations of molecular order in polymer networks. II. Intensity decay and restricted slow dynamics

We present an approach towards the analysis of the intensity decay in proton multiple-quantum experiments on polymeric networks in terms of slow fluctuations of the residual dipole-dipole coupling tensor. Solutions for individual spin pairs as well as the three-spin system of methyl groups are derived, and the influence of the cycle time of the multiple-quantum pulse sequence is evaluated. The multiple-quantum strategy discussed herein features the advantage that the magnitude of the fluctuating part of the residual dipole-dipole coupling constant and the correlation time of the slow process can be determined independently of the integral residual coupling constant as well as its distribution. The theory is applied to experiments on end-linked poly(dimethylsiloxane) model networks with mono- and bimodal chain length distributions, where it is found that, for all samples, correlation times of the slow processes average to about 1 ms, and that the magnitude of the fluctuating part of the dipole-dipole coupling is significantly smaller than the average dipole-dipole coupling constant. This observation is interpreted in terms of considerably restricted reorientations of topological constraints.     

The use of Tikhonov regularization method for calculating the distribution function of relaxation times in impedance spectroscopy

The state-of-the-art in realization of the method of distribution of relaxation times (DRT) as applied to the analysis of data of electrochemical impedance spectroscopy is briefly surveyed. The theoretical fundamentals of the DRT method are described, the methods of solving the Fredholm equation of the 1st order with respect to the unknown DRT function are considered as an ill-defined problem. The Tikhonov regularization method presently considered as the most suitable for solving this equation is discussed. For several numerical experiments, the high resolution of the DRT method and its stability with respect to noise in impedance spectra are demonstrated. Among the problems and limitations of the DRT methods, the choice of the optimal regularization coefficient is considered as the most significant. Particularly, it is shown that in those cases where several relaxation processes with the constant phase angle appear in the response of objects under study to ac disturbances, different regularization coefficients should be selected for each of these elements in order to obtain adequate results.     

Combined effect of temperature and organic modifier concentration on the retention under single mode gradient conditions in reversed-phase HPLC

The combined effect of temperature, T, and organic modifier concentration, phi, on the retention under gradient conditions in RPLC is studied by considering, both theoretically and experimentally gradients, of phi at constant T and gradients of T at constant phi. Two approaches are examined: in the first approach the prediction of the elution time of a sample solute is based on the isocratic/isothermal properties of this solute. The second approach is based on a direct fitting procedure of a proper retention model to 2-D isocratic/T-gradient or isothermal/phi-gradient retention data. These approaches were tested using alkylbenzes in eluting systems modified by ACN. We found that both approaches can give excellent predictions under certain prerequisites. However, the first approach exhibits the notable advantage that it can be used effectively to predict retention times under any kind of phi-gradients at constant T or T-gradients at constant phi. The second approach has the advantage that it is relatively simple but its applicability is very restricted since its predictions are satisfactory only if the gradients are of the same kind with those used in the fitting procedure and the conditions lie within those used for fitting.     

Measurement of emulsion droplet sizes using PFG NMR and regularization methods

The droplet size distributions of emulsions have been measured using pulsed field gradient (PFG) nuclear magnetic resonance (NMR) for many years. This technique finds particular application with emulsions that are concentrated and/or opaque, since such emulsion systems are difficult to characterize by other methods. Most studies employing PFG techniques assume a lognormal form when extracting the droplet size distribution from the experimental data. It is clearly desirable to retrieve a droplet size distribution from the experimental data without assuming such a functional form. This is achieved for the first time using regularization techniques. Regularization based on the distribution area and on its second derivative are compared and assessed along with the following techniques for selecting the optimal regularization parameter: the L-curve method, generalized cross validation (GCV), and the discrepancy principle. Regularization is applied to both simulated data sets and experimental data. It is found that when the experimental error can be estimated accurately, the discrepancy principle with area regularization is the best approach. When the error is not known the GCV method, with second derivative regularization and allowing only nonnegative values, is most effective.     

Putting error bars on the ab initio theoretical estimates of the magnetic coupling constants: the parent compounds of superconducting cuprates as a case study

The influence of the basis set size and computational method in the calculation of the magnetic coupling constant J is evaluated using a series of cuprate superconductor parent compounds as a case study. The variational DDCI method and an iterative modification, the IDDCI method, are tested, as well as the perturbative CASPT2 method, with two different reference wave functions. Results show that the DDCI magnetic coupling constant is in rather good agreement with the experiment, although it shows a moderate basis set dependency. The IDDCI results are less dependent on the size of the basis set, but slightly overestimate the magnetic coupling constant. CASPT2 results are nearly independent of the chosen basis set. With a minimal active space values are obtained that are about 20% smaller than the DDCI results. The experimental coupling constant can be reproduced when an extended reference wave function is used.     

Tailor-made thermoplastic elastomers: customisable materials via modulation of molecular weight distributions

The ability to change polymer properties has in the past largely been a factor of modulating the molecular weight, molecular weight distribution breadth, crosslinking, or branching. The use of controlled MWD shape has recently emerged as a promising avenue towards modifying polymer properties. Taking advantage of molecular weight distribution shape, we report a simple and efficient approach for tuning material properties in polystyrene-block-polyisoprene-block-polystyrene (SIS) thermoplastic elastomers (TPEs). We find that the skew of the MWD function governs tensile properties and can be used as a handle to predictably vary polymer toughness while reducing energy dissipation.

Taking advantage of molecular weight distributions shape, we report a simple and efficient approach for predictably tuning material properties for thermoplastic elastomers.     

Semi‐supervised kernel partial least squares fault detection and identification approach with application to HGPWLTP

In this paper, fault detection and identification methods based on semi‐supervised Laplacian regularization kernel partial least squares (LRKPLS) are proposed. In Laplacian regularization learning framework, unlabeled and labeled samples are used to improve estimate of data manifold so that one can establish a more robust data model. We show that LRKPLS can avoid the over‐fitting problem which may be caused by sample insufficient and outliers present. Moreover, the proposed LRKPLS approach has no special restriction on data distribution, in other words, it can be used in the case of nonlinear or non‐Gaussian data. On the basis of LRKPLS, corresponding fault detection and identification methods are proposed. Those methods are used to monitor a numerical example and Hot Galvanizing Pickling Waste Liquor Treatment Process (HGPWLTP), and the cases study show effeteness of the proposed approaches. Copyright © 2016 John Wiley & Sons, Ltd.     

The density distributions of the counterions and the coions confined in two similarly charged plates

By using the field-theoretic method, we established a unified systematic formulation of a model of counterions and coions confined in two similarly charged plates, and calculated the density distributions of counterions and coions with various coupling parameters by the two methods: Poisson-Boltzmann (PB) approach and the strong coupling (SC) theory, respectively. We also performed Monte Carlo simulations, and obtained the density distributions of counterions and coions with several different coupling parameters. Comparing our theoretical results with those from Monte Carlo simulation, we find that the PB approach is valid when the coupling parameter Xi is smaller than 1, but, as Xi > or = 1, the results by the PB approach deviate from the corresponding Monte Carlo simulation data, and the deviation gets larger with the coupling parameter increasing. This shows that the PB approach is completely invalid when the coupling parameter is equal to 1 or larger than 1. For the latter case, the development trend of the distribution curve calculated by SC theory agrees with that from Monte Carlo simulation as the coupling parameter increases. This demonstrates that the SC theory can give a qualitative available explanation on the density distribution of the counterions in the system in which the coupling parameters are strictly confined.