Diffusion multivariate

A solvent free, fast and environmentally friendly near infrared-based methodology was developed for the determination and quality control of 11 pesticides in commercially available formulations. This methodology was based on the direct measurement of the diffuse reflectance spectra of solid samples inside glass vials and a multivariate calibration model to determine the active principle concentration in agrochemicals. The proposed PLS model was made using 11 known commercial and 22 doped samples (11 under and 11 over dosed) for calibration and 22 different formulations as the validation set. For Buprofezin, Chlorsulfuron, Cyromazine, Daminozide, Diuron and Iprodione determination, the information in the spectral range between 1618 and 2630 nm of the reflectance spectra was employed. On the other hand, for Bensulfuron, Fenoxycarb, Metalaxyl, Procymidone and Tricyclazole determination, the first order derivative spectra in the range between 1618 and 2630 nm was used. In both cases, a linear remove correction was applied. Mean accuracy errors between 0.5 and 3.1% were obtained for the validation set. 

DOSY is a technique that may prove successful in the determination of additives in mixtures [279]. Using different field gradients it is possible to distinguish components in a mixture on the basis of their diffusion coefficients. Morris and Johnson [271] have developed diffusion-ordered 2D NMR experiments for the analysis of mixtures. PFG-NMR can thus be used to identify those components in a mixture that have similar (or overlapping) chemical shifts but different diffusional properties. Multivariate curve resolution (MCR) analysis of DOSY data allows generation of pure spectra of the individual components for identification. The pure spin-echo diffusion decays that are obtained for the individual components may be used to determine the diffusion coefficient/distribution [281]. Mixtures of molecules of very similar sizes can readily be analysed by DOSY. Diffusion-ordered spectroscopy [273,282], which does not require prior separation, is a viable competitor for techniques such as HPLC-NMR that are based on chemical separation. 

Intensified metabolic control, especially in case of diabetes, demands minimal-invasive or non-invasive methods of analytical measurement. For this goal, a method has been developed to measure the blood glucose content in vivo, in direct contact with the skin, by means of diffuse reflection near infrared (NIR) spectroscopy on the basis of multivariate calibration and neural networks (Muller et al. [1997] Fischbacher et al. [1997] Danzer et al. [1998]). Because no patients with any standard blood glucose value are available in principle, a method of indirect calibration has... 

Rieckmann and Volker fitted their kinetic and mass transport data with simultaneous evaluation of experiments under different reaction conditions according to the multivariate regression technique [116], The multivariate regression enforces the identity of kinetics and diffusivities for all experiments included in the evaluation. With this constraint, model selection is facilitated and the evaluation results in one set of parameters which are valid for all of the conditions investigated. Therefore, kinetic and mass transfer data determined by multivariate regression should provide a more reliable data basis for design and scale-up. 

A stepwise multivariate LR analysis of the log PS values of the 23 diffusion compounds and 50 descriptors yielded a linear equation that consisted of 10 descriptors. After considering the relevance in physical meaning of each descriptor and statistical significance, the 10-descriptor model was reduced to a 3-descriptor model (Eq. 68) ... 

II) Chakraborty and Ganguly, 1992 diffusion experiments (12) Koziol, 1990 phase equilibration (13) Ganguly and Cheng, 1994 multivariate analysis (14) Berman, 1990 multivariate analysis (15) Ganguly, 1995 personal communication (16) Ottonello et al. (in prep.) structure-energy calculations. 

Dyrstad, K., Veggeland, J., and Thomassen, C. (1999), A multivariate method to predict the water vapour diffusion rate through polypropylene packaging, Int. J. Pharm., 188,... 

So far we only considered transport of particles by diffusion. As mentioned in 1 the continuous description was not strictly necessary, because diffusion can be described as jumps between cells and therefore incorporated in the multivariate master equation. Now consider particles that move freely and should therefore be described by their velocity v as well as by their position r. The cells A are six-dimensional cells in the one-particle phase space. As long as no reaction occurs v is constant but r changes continuously. As a result the probability distribution varies in a way which cannot be described as a succession of jumps but only in terms of a differential operator. Hence the continuous description is indispensable, but the method of compounding moments can again be used. 

The feasibility of diffuse reflectance NIR, Fourier transform mid-IR and FT-Raman spectroscopy in combination with multivariate data analysis for in/ on-line compositional analysis of binary polymer blends found in household and industrial recyclates has been reported [121, 122]. In addition, a thorough chemometric analysis of the Raman spectral data was performed. 

Schultz TP, Glasser WG (1986) Quantitative structural analysis of lignin by diffuse reflectance Fourier transform infrared spectromety Holzforschung 40 (Suppl) 37-44 Schultz TP, Nicholas DD (1987) Fourier transform infrared spectrometry Detection of incipient brown rot decay in wood Int Analyst 41 35-39 Sjostrom M, Wold, S, Lindberg W, Persson J-A, Martens H (1983) A multivariate calibration problem in analytical chemistry solved by partial least-squares models in latent variables Anal Chim Acta 150 61-70... 

C. Hofmann, H. Michel, M. van Heel, J. Kohler, Multivariate analysis of single-molecule spectra Surpassing spectral diffusion. Phys. Rev. Lett. 94, 195501 (2005)... 

Because a diffuse reflectance spectrum is scatter-dependent, information on mean particle sizes is also obtainable, which is a parameter of great importance in powder technology. An approach using near-infrared spectrometry combined with multivariate calibration has been presented by Ilary, Martens, and Isaksson. Included was a spectrum standardization by multiplicative scatter correction (see later). 

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