D.J. Louwerse

Estimating rate constants and pure UV-vis spectra of a two-step reaction using trilinear models

This paper describes the estimation of reaction rate constants and pure species UV‐vis spectra of the consecutive reaction of 3‐chlorophenylhydrazonopropane dinitrile with 2‐mercaptoethanol. The reaction rate constants were estimated from the UV‐vis measurements of the reacting system using the generalized rank annihilation method (GRAM) and the Levenberg–Marquardt/PARAFAC (LM‐PAR) algorithm. Both algorithms can be applied in cases where the contribution of different species in the mixture spectra is of exponentially decaying character. From a single two‐way array, two two‐way datasets are formed by means of splitting such that there is a constant time lag between the two two‐way datasets. By stacking these two two‐way datasets, the reaction rate constants can be estimated very easily from the third dimension. GRAM, which is fast and non‐iterative, decomposes the trilinear structure using a generalized eigenvalue problem (GEP). The iterative algorithm LM‐PAR consists of a combination of the Levenberg–Marquardt algorithm and alternating least squares steps of the PARAFAC model using GRAM results as a set of initial starting values. Pure spectra of the absorbing species were estimated and compared with their measured pure spectra. LM‐PAR performed the best, giving the lowest relative fit error. However, the relative fit error obtained with GRAM was acceptable. Since a lot of measurements are based on exponentially decaying functions, GRAM and LM‐PAR can have many applications in chemistry. Copyright

Cross-validation of multiway component models

Two cross‐validation methods are presented for multiway component models. They are used for choosing the numbers of components to use in Tucker3 models describing three‐way data. The approach is general and can easily be adapted to other three‐way and multiway models. A model is estimated after leaving out a small part of the multiway data array. The predictive residual error sum of squares (PRESS) is calculated for the eliminated part of the data by comparing the model values with the actual data. PRESS of the entire data set can be calculated like this sequentially. The methods are the leave‐bar‐out cross‐validation method, which leaves out data slices in all modes, and the EM cross‐validation method, which handles eliminated data as missing values. A method to calculate the statistical significance of the PRESS reduction for an additional component, the so called W‐statistic, is provided for Tucker3 models. A strategy is proposed to search along an efficient path, to reduce computation time, since the number of feasible models as a function of the total number of components summed over the modes increases fast. Copyright

Rapid estimation of rate constants using on-line SW-NIR and trilinear models

Abstract In this paper, two algorithms are presented to estimate reaction rate constants from on-line short-wavelength near-infrared (SW-NIR) measurements. These can be applied in cases where the contribution of the different species in the mixture spectra is of exponentially decaying character. From a single two-dimensional dataset two two-way datasets are formed by splitting the original dataset such that there is a constant time lag between the two two-way datasets. Next, a trilinear structure is formed by stacking these two two-way datasets into a three-way array. In the first algorithm, based on the generalized rank annihilation method (GRAM), the trilinear structure is decomposed by solving a generalized eigenvalue problem (GEP). Because GRAM is sensitive to noise it leads to rough estimations of reaction rate constants. The second algorithm (LM–PAR) is an iterative algorithm, which consists of a combination of the Levenberg–Marquardt algorithm and alternating least squares steps of the parallel factor analysis (PARAFAC) model using the GRAM results as initial values. Simulations and an application to a real dataset showed that both algorithms can be applied to estimate reaction rate constants in case of extreme spectral overlap of different species involved in the reacting system.

Applications and new developments of the direct exponential curve resolution algorithm (DECRA). Examples of spectra and magnetic resonance images

Recently, a new multivariate analysis tool was developed to resolve mixture data sets, where the contributions (‘concentrations’) have an exponential profile. The new approach is called DECRA (direct exponential curve resolution algorithm). DECRA is based on the generalized rank annihilation method (GRAM). Examples will be given of resolving nuclear magnetic resonance spectra resulting from a diffusion experiment, spectra in the ultraviolet/visible region of a reaction and magnetic resonance images of the human brain. Copyright

PLS discriminant analysis with contribution plots to determine differences between parallel batch reactors in the process industry

Abstract PLS discriminant analysis, applied to a PVC polymerisation batch process, is used to determine performance differences of parallel batch reactors. Weight contribution plots of time points and of variables are used to physically interpret the modelled differences; the main time points in which deviations occur and variables that cause the observed differences are assigned. A simple step-wise procedure is suggested to implement this method in the process industry. It was found that a systematic difference between the polymerisation time of the PVC batch reactors was caused by sensor failure or due to drifting thermocouples.

Characteristics and application of an electrochemical concentration modulator in correlation chromatography Part 1. Characterization

Abstract An electrochemical concentration modulator is tested for its applicability as an injection device in correlation chromatography. The use of conventional signals to control the potential of the working electrode in the modulator cell produces ghost peaks in the correlogram. The effects of the modulation interval, the time scale of the control signal and the concentration of an electroactive model compound (hydroquinone) on the pattern of the ghost-peak intensities are described. A simple model, based on the combined action of a charging-current time constant and the relative position of the half-wave potential in the modulation interval, is used to describe the result on the concentration profile of the analyte. The mechanisms responsible for ghost peak generation are described.

Single-sequence correlation chromatography. A novel technique to decrease detection limits

Abstract A new method, being an intermediate between single-injection chromatography and conventional correlation chromatography, is described. With respect to single-injection chromatography, the injection volume can be significantly enlarged. However, the rectangular input function is modulated with a finestructure. A deconvolution procedure makes it possible to preserve a good peak resolution for the fast eluting narrow peaks, while other more broadened peaks can be treated in a conventional way. In both cases the signal-to-noise ratio is improved, and the detection limit is decreased. The theoretical background is presented, and the feasibility of the method is confirmed by simulation studies and experiments. Potentially, gradient elution liquid chromatography or programmed-temperature gas chromatography is still applicable, in contrast to conventional correlation and multiplex techniques.

Monitoring time-varying concentrations in sample streams by multiple input chromatography

Abstract The possibility of monitoring time-varying concentrations with conventional chromatography or correlation chromatography (CC) is restricted. The highers frequency that can be monitored is, due to Shannon, limited for conventional chromatography to (2 x chromatogram length) −1 , and for CC, due to a moving average effect, to (sequence lenght) − . A method is presented in which considerable higher frequencies can be monitored. Theoretically the power spectral density of the chromatographical peak shape limits the upper frequency that can be monitored. The method originates from CC. A pseudo-random binary sequence (PRBS) is used as injection pattern. The detector signal however is not correlated or deconvoluted with a PRBS as in CC. The time-varying concentrations of the components are described as functions of time and a number of parameters, e.g. parameters of a Fourier series. These parameters then are optimised in a non-linear fitting procedure. A detector signal is calculated using the parameters, the known PRBS and known peak shapes; and the squared differences with the real detector signal are minimised. The results from simulated experiments and practical experiments are shown.

Characteristics and application of an electrochemical concentration modulator in correlation chromatography: Part 2. Computational aspects, modelling and application

Abstract An electrochemical cell was used as an injection device in correlation chromatography. The use of a conventional injection control signal combined with a conventional deconvolution method leads to the appearance of ghost peaks in the correlogram. Several methods to suppress or correct for the presence of ghost peaks in the correlogram were studied, taking into account the electrochemical cell characteristics determined in the first part of this paper. An overview is given of existing time-domain deconvolution methods with emphasis on the shape of the virtual injection. Fourier-domain deconvolution methods are discussed and compared with time-domain methods. An improved model for the modulation process taking place in the electrochemical cell is used to calculate the real injection pattern. Three alternative methods to diminish the ghost peak phenomenon have been compared. First, deconvolution of the detector signal with a calculated or experimentally determined input pattern was examined. Secondly, intrinsic correction properties of correlation chromatography were used to remove the ghost peaks. Finally, the effect of adjusting the signal used to control the potentiostat was tested. The latter method proved to be the best solution. Calibration curves were measured to test the linearity of the method.