Spectrophotometric determination of acidity constants by two-rank annihilation factor analysis

Annihilation of the contribution of one chemical component from the original data matrix is a general method in rank annihilation factor analysis (RAFA). However, RAFA is not applicable for studying the protonation equilibria of multiprotic acids. In this work, a two-rank annihilation factor analysis (TRAFA) method was proposed for determination of the acidity constants of diprotic acids. After recording the electronic absorbance spectra of the acids at different pH, the contributions of both H₂A and A²⁻ were annihilated from the absorbance data, which made feasible the determination of two successive acidity constants. The method was validated by analysis of simulated data and its application to the determination of the acidity constants of calmagite, as a reference compound. A close agreement was obtained between the resulted values by TRAFA and the declared values. Indeed, the method was used for determination of the acidity constants of two new chromenone derivatives in binary solvents mixtures of methanol and water. The effects of changing solvent composition on acidity constant data were explained by linear solvation free energy relationships (LSFER) utilizing solvatochromic parameters.     

Rank annihilation factor analysis for spectrophotometric study of complex formation equilibria

The use rank annihilation factor analysis (RAFA) for spectrophotometric studies of complex formation equilibria are proposed. One-step complex formation and two successive and mononuclear complex formation systems studied successfully by proposed methods. When the complex stability constant acts as an optimizing object, and simply combined with the pure spectrum of ligand, the rank of original data matrix can be reduced by one by annihilating the information of the ligand from the original data matrix. The residual standard deviation (R.S.D.) of the residual matrix after bilinearization of the background matrix is regarded as the evaluation function. The performance of the method has been evaluated by using synthetic data. For two-step successive complex formation systems, the effects of noise level and equilibrium constants K₁ and K₂ on output of algorithm are investigated. The applicability of method for resolving the two-step successive complex formation systems with full spectral overlapping of two complex species also is shown. Spectrophotometric studies of murexide-calcium, dithiazone-nickel and methyl thymol blue (MTB)-copper are used as experimental model systems with different complexation stoichiometries and spectral overlapping of involved components.     

Rank annihilation factor analysis method for spectrophotometric study of second-order reaction kinetics

In this study several methods are described to determine the rate constant of a second-order reaction in the form of A+B→C. These approaches allow circumventing a rank deficiency inherent of a second-order reaction when the spectroscopic data is influenced by additional source of variance. Classically, to determine the unknown rate constant in this kind of systems, one needs to have extra knowledge about the system, including the spectra of the reactants or product and the exact kinetics. In the case of the presence of an unknown phenomenon in the data set that cannot be explained by the model, such as baseline drift, the estimated rate constant might be erroneous. Present work is a modification of the rank annihilation factor analysis (RAFA) algorithm by inclusion of I) pure spectra of reactants, or IIA) mean centering step, or IIB) mean spectrum. The proposed methods can interestingly be applied on a single kinetic run. The performances of the new methods have been evaluated by applying them to analysis of simulated and experimental data.     

Simultaneous determination of reaction order and rate constant by rank annihilation factor analysis from kinetic-spectral data

Rank annihilation factor analysis combined with the optimization of kinetic parameter is adopted to resolve the two-way kinetic-spectral data measured online from chemical reactions. To a multi-step reaction whose intermediate process is complicated and reaction order is fractional, the reaction order and rate constant of the first step can be determined without the knowledge of the kinetic model of the reaction. Taken a three-step reaction as an example, the synthetic data has been resolved and its effectiveness was proved. When the approach is applied to the analysis of practical reaction systems such as alkaline hydrolysis of phenyl benzoate, oxidization of sodium bromide by potassium permanganate and electro-degradation of sunset yellow, reliable results are obtained.     

Multivariate standard addition method solved by net analyte signal calculation and rank annihilation factor analysis

This article describes the use of the net analyte signal (NAS) concept and rank annihilation factor analysis (RAFA) for building two different multivariate standard addition models called “SANAS” and “SARAF.” In the former, by the definition of a new subspace, the NAS vector of the analyte of interest in an unknown sample as well as the NAS vectors of samples spiked with various amounts of the standard solutions are calculated and then their Euclidean norms are plotted against the concentration of added standard. In this way, a simple linear standard addition graph similar to that in univariate calibration is obtained, from which the concentration of the analyte in the unknown sample and the analytical figures of merit are readily calculated. In the SARAF method, the concentration of the analyte in the unknown sample is varied iteratively until the contribution of the analyte in the response data matrix is completely annihilated. The proposed methods were evaluated by analyzing simulated absorbance data as well as by the analysis of two indicators in synthetic matrices as experimental data. The resultant predicted concentrations of unknown samples showed that the SANAS and SARAF methods both produced accurate results with relative errors of prediction lower than 5% in most cases.     

Investigation of oxidation and tautomerization of a recently synthesized Schiff base in micellar media using multivariate curve resolution alternative least squares and rank annihilation factor analysis methods

The oxidation of the recently synthesized Schiff base 3,6-bis((2-aminoethyl-5-Br-salicyliden)thio)pyridazine (PABST) with hydrogen peroxide was investigated using spectrophotometric studies. The reaction rate order and observed rate constant of the oxidation reaction was obtained in the mixture of N,N-dimethylformamide (DMF):water (30:70, v/v) at pH 10 using multivariate cure resolution alternative least squares (MCR-ALS) method and rank annihilation factor analysis (RAFA). The effective parameters on the oxidation rate constant such as percents of DMF, the effect of transition metals like Cu²⁺, Zn²⁺, Mn²⁺ and Hg²⁺ and the presence of surfactants were investigated. The keto-enol equilibria in DMF:water (30:70, v/v) solution at pH 7.6 was also investigated in the presence of surfactants. At concentrations above critical micelle concentration (cmc) of cationic surfactant cetyltrimethylammonium bromide (CTAB), the keto form was the predominant species, while at concentrations above cmc of anionic surfactant sodium dodecyl sulfate (SDS), the enol form was the predominant species. The kinetic reaction order and the rate constant of tautomerization in micellar medium were obtained using MCR-ALS and RAFA. The results obtained by both the methods were in a good agreement with each other. Also the effect of different volume percents of DMF on the rate constant of tautomerization was investigated. The neutral surfactant (Triton X-100) had no effect on tautomerization equilibrium.     

Determination of Sudan I in chilli powder from solvent components gradual change-visible spectra data using second order calibration algorithms

It was discovered that a second order spectra data matrix of Sudan I produced from the solvent components gradual change-visible absorption spectra can be expressed as the combination of two bilinear data matrices. Based on this discovery, a new method for the determination of Sudan I in gray systems using second order calibration algorithms has been developed. The second order calibration algorithms were based on the popular parallel factor analysis (PARAFAC) and rank annihilation factor analysis (RAFA), respectively. In the method described here, the components of the solvent were changed gradually by adding ethanol into cyclohexane, the absorption spectra of Sudan I and chilli samples in a series of cyclohexane-ethanol mixed solvents with various ethanol volume fractions were recorded, and then the second order data were obtained from the solvent components gradual change-visible absorption spectra. Thus, the concentration of Sudan I in a gray system could be determined from the spectra matrices using second order calibration algorithms. This method is simple, convenient and dependable. The method has been used to determine Sudan I in chilli powder with satisfactory results.     

Simultaneous quantitative analysis of overlapping spectrophotometric signals using wavelet multiresolution analysis and partial least squares

The mathematical bases and program algorithms of discrete wavelet transform (DWT), multiresolution and Mallat’s pyramid algorithm were described. The multiresolution analysis (MRA) based on Daubechies orthogonal wavelet basis was studied as a tool for removing noise and irrelevant information from spectrophotometric spectra. After wavelet MRA pre-treatment, eight error functions were calculated for deducing the number of factors. A partial least squares based on wavelet MRA (WPLS) method was developed to perform simultaneous spectrophotometric determination of Fe(II) and Fe(III) with overlapping peaks. Data reduction was performed using wavelet MRA and principal component analysis (PCA) algorithm. Two programs, SPWMRA and SPWPLS, were designed to perform wavelet MRA and simultaneous multicomponent determination. Experimental results showed the WPLS method to be successful even where there was severe overlap of spectra.     

Open spaces and molecular motions in carbon‐black‐ and silica‐loaded SBR investigated using positron annihilation

Lifetime spectra of positrons were measured for styrene–butadiene rubber (SBR) vulcanizates filled with carbon black (CB) or silica. At temperatures between 10 and 420 K, no large difference between the size of the open spaces in the CB/SBR vulcanizate and that in the specimen without the filler was observed. Above the glass‐transition temperature (T_g = 230 K), the same was true for the silica/SBR vulcanizate. Below T_g, however, the size of the open spaces was reduced by the incorporation of silica as a result of the suppression of local molecular motions in the SBR. The density of the open spaces was reduced by the incorporation of the fillers. However, above 400 K it started to increase in the silica/SBR vulcanizate. For the CB/SBR vulcanizate, the introduction of open spaces was well suppressed, even at 420 K. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 835–842, 2001     

A study on free volume of acrylonitrile‐styrene copolymer and methyl methacrylate‐styrene copolymer by using positron annihilation

The o‐Ps lifetime τ₃ and the intensity I₃ of ST‐AN copolymers and ST‐MMA copolymers have been determined by using the positron annihilation technique. The average free volume hole radius R is estimated according to Tao's and Eldrup's model. The result shows that the average free volume hole size mainly attributes to lateral group volume and polarity of macromolecular chain as well as polymerizing temperature, and the o‐Ps intensity I₃ to the effect of the lateral group volume and the polarity. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 465–472, 1999     

Acetylacetone-formaldehyde reagent for the spectrophotometric determination of some sulfa drugs in pure and dosage forms

A new simple and sensitive spectrophotometric procedure for the determination of sulfacetamide sodium (I), sulfadiazine (II), sulfadimidine (III) and sulfathiazole (IV) is based on the reaction of the drug with acetylacetone-formaldehyde reagent to give a yellow product having _max at 400 nm. Optimization of the reaction conditions has been investigated. A linear correlation was obtained between absorbance at _max and the concentration. The Beer's law limits of I, II, III and IV are 4–80, 4–72, 4–60 and 4–80 g/ml, respectively. For more accurate results, Ringbom optimum concentration ranges were evaluated to be 6–76, 8–66, 6–56 and 8–75 g/ml for I, II, III and IV, respectively. The molar absorptivities and Sandell sensitivities for all sulfa drugs under consideration were evaluated. Relative standard deviations of 0.98, 1.07, 0.86 and 0.79% were obtained for I, II, III and IV, respectively. The method has been compared to the official method and found to be simple, accurate (t-test) and reproducible (F-test). The developed procedures were applied for bulk sulfa drugs and some of their dosage forms without interferences from additive and common prescribed drugs.     

Parallel vector analysis based soft resolution of spectral data from pH‐metric titration using symmetry constraint

In this study, a soft method is proposed to calculate concentration and spectral profiles for the two‐way spectral data from dissociation equilibria of polyprotic acids (H_nA). This method has four main distinct steps: (i) a fixed size moving window evolving factor analysis (FSMWEFA) was used to identify the local rank map, (ii) WFA was applied to calculate the concentration profiles of H_nA and Aⁿ⁻ (selection of the window for application of WFA was performed using EFA), (iii) PVA was used to calculate H_{n − 1}A to HA spectral profiles, and (iv) a symmetry constraint, in addition to the non‐negativity constraint, was utilized to obtain the unique concentration and spectral profiles from different acceptable sets of profiles. In the absence of any selective region in the spectral data, the proposed soft method resulted in unique solution without rotational ambiguity. This study is the first application of symmetry constraint on concentration profiles. The rotational ambiguity drastically decreased on considering the constraint of symmetry of the H_{n − 1}A and HA concentration profiles, in addition to non‐negativity of profiles. Simulated examples were used to confirm these approaches. Effect of closeness of dissociation constants on the estimated values of constants was investigated. The results showed that when the difference between pK_a values is more than 1.2, the obtained errors in the estimation of pK_a values are less than about 6.5%. The considered real data were from pH‐metric titration of fluorescein. The obtained spectral and concentration profiles and the estimated pK_a values for fluorescein were in good agreement with the previously reported data. Copyright © 2009 John Wiley & Sons, Ltd.     

Theoretical analysis of vibrational spectra and scaling‐factor of 2‐aryl‐1,3,4‐oxadiazole derivatives

In this study, the direct molecular structure implementations for calculating vibrational spectra and scaling factors, and infrared intensities at both the Hartree–Fock (HF) and density functional (B3LYP) levels of theory with 6‐31G(d), 6‐311G(d), 6‐31++G(d,p), and 6‐311++G(d,p) basis sets are presented. Also, vibrational frequencies have been investigated as dependence on the choice of method and basis set. The parameters of molecular geometry and vibrational frequencies values of 2‐aryl‐1,3,4‐oxadiazoles 5a–g in the ground state have been calculated. Theoretical determination of vibrational frequencies is quite useful both in understanding the relationship between the molecular structures and scaling factor. The data of 2‐aryl‐1,3,4‐oxadiazoles 5a–g display significant electronic properties provide the basis for future design of efficient materials having the oxadiazole core and theoretical IR studies. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

“Parallel factor analysis of multi-excitation ultraviolet resonance Raman spectra for protein secondary structure determination”

Protein secondary structural analysis is important for understanding the relationship between protein structure and function, or more importantly how changes in structure relate to loss of function. The structurally sensitive protein vibrational modes (amide I, II, III and S) in deep-ultraviolet resonance Raman (DUVRR) spectra resulting from the backbone C–O and N–H vibrations make DUVRR a potentially powerful tool for studying secondary structure changes. Experimental studies reveal that the position and intensity of the four amide modes in DUVRR spectra of proteins are largely correlated with the varying fractions of α-helix, β-sheet and disordered structural content of proteins. Employing multivariate calibration methods and DUVRR spectra of globular proteins with varying structural compositions, the secondary structure of a protein with unknown structure can be predicted. A disadvantage of multivariate calibration methods is the requirement of known concentration or spectral profiles. Second-order curve resolution methods, such as parallel factor analysis (PARAFAC), do not have such a requirement due to the “second-order advantage.” An exceptional feature of DUVRR spectroscopy is that DUVRR spectra are linearly dependent on both excitation wavelength and secondary structure composition. Thus, higher order data can be created by combining protein DUVRR spectra of several proteins collected at multiple excitation wavelengths to give multi-excitation ultraviolet resonance Raman data (ME-UVRR). PARAFAC has been used to analyze ME-UVRR data of nine proteins to resolve the pure spectral, excitation and compositional profiles. A three factor model with non-negativity constraints produced three unique factors that were correlated with the relative abundance of helical, β-sheet and poly-proline II dihedral angles. This is the first empirical evidence that the typically resolved “disordered” spectrum represents the better defined poly-proline II type structure.     

Flow injection kinetic spectrophotometric method for the determination of trace amounts of nitrite

In this work, a new, simple and sensitive flow injection catalytic kinetic spectrophotometric determination of nitrite is reported based on catalytic effect of nitrite on the redox reaction between sulfonazo III and potassium bromate in acidic media. The reaction was monitored by measuring the decrease in the absorbance of sulfunazo III at 570 nm. Various chemical (such as the effect of acidity, reagents concentrations) and instrumental parameters (flow rate, reaction coil length, injection volume and temperature) were studied and were optimized. Under the optimum conditions calibration graph was linear in the nitrite concentration ranges of 8.00 × 10⁻³-3.00 × 10⁻¹ μg/ml (with slope of 2.40) and 3.50 × 10⁻¹-1.80 μg/ml (with slope of 0.42). The detection limit was 6.00 × 10⁻³ μg/ml of nitrite, the relative standard deviation (n = 10) was 1.25% and 0.88% for 5.00 × 10⁻² and 2.00 × 10⁻¹ μg/ml of nitrite respectively. About 60 samples in 1 h can be analyzed. The interfering effects of various chemical species were studied. The method was successfully applied in the determination of nitrite in food and environmental samples.     

Blind separation of fluorescence spectra using sparse non‐negative matrix factorization on right hand factor

Sparse non‐negative matrix factorization on right side factor (SNMF/R) has better performance in feature extraction than non‐negative matrix factorization. In this work, SNMF/R was first used to separate the overlapped three‐dimensional fluorescence spectra of polycyclic aromatic hydrocarbons mixtures in pure water, lake water, and river water, respectively. It is found that the similarity coefficients between the acquired three‐dimensional spectra and the corresponding reference spectra with random initials are all above 0.80; the recognition rate of SNMF/R is higher than that of PARAFAC and non‐negative matrix factorization algorithms, especially in the case of lake water and river water samples. In addition, SNMF/R does not need any initialization scheme designing during spectra separation. These results demonstrate that SNMF/R is an appropriate algorithm to separate the overlapped fluorescence spectra of polycyclic aromatic hydrocarbons in aquatic environment accurately and effectively. Copyright © 2015 John Wiley & Sons, Ltd.     

Parallel column liquid chromatography with a single multi-wavelength absorbance detector for enhanced selectivity using chemometric analysis

The selectivity of high performance liquid chromatography (HPLC) separations is increased using a parallel column configuration. In this system, an injected sample is first split between two HPLC columns that provide complementary separations. The effluent from the two columns is recombined prior to detection with a single multiwavelength absorbance detector. Complementary stationary phases are used so that each chemical component produces a detected concentration profile consisting of two peaks. A parallel column configuration, when coupled with multivariate detection, provides increased chemical selectivity relative to a single column configuration with the same multivariate detection. This enhanced selectivity is achieved by doubling the number of peaks in the chromatographic dimension while keeping the run time constant. Unlike traditional single column separation methodology, the parallel column system sacrifices chromatographic resolution while actually increasing the chemical selectivity, thus allowing chemometric data analysis methods to mathematically resolve the multivariate chromatographic data. The parallel column system can be used to reduce analysis times for partially resolved peaks and simplify initial method development as well as provide a more robust methodology if and when subsequent changes in the sample matrix occur (such as when new interferences show up in subsequent samples). Here, a mixture of common aromatic compounds were separated with this system and analyzed using the generalized rank annihilation method (GRAM). Analytes that were significantly overlapped on both stationary phases applied, ZirChrom PBD and CARB phases, when used in traditional single column format, were successfully quantified with a R.S.D.% of typically 2% when the same stationary phases were used in the parallel column format. These results indicate that a parallel column system should substantially improve the chemical selectivity and quantitative precision of the analysis relative to a single-column instrument.     

The spectrophotometric multicomponent analysis of a ternary mixture of ascorbic acid, acetylsalicylic acid and paracetamol by the double divisor-ratio spectra derivative and ratio spectra-zero crossing methods

The double divisor–ratio spectra derivative and ratio spectra–zero crossing methods were applied to the analysis of an effervescent tablet containing the title compounds without using a chemical separation procedure. In the use of both methods, the calibration graphs were linear in the range of 8–28 μg ml⁻¹ for three compounds. Comparison of the results obtained by the two methods indicates that both methods gives the best results.     

Mean centering of ratio spectra as a new spectrophotometric method for the analysis of binary and ternary mixtures

In this paper a new and very simple method was developed for the simultaneous determination of binary and ternary mixtures, without prior separation steps. This method is based on the mean centering of ratio spectra. The mathematical explanation of the procedure is illustrated. After modeling procedure, the method has been successfully applied to the simultaneous analysis of binary mixtures of mefnamic acid and paracetamol and ternary mixtures of acetylsalysilic acid, ascorbic acid and paracetamol. The analytical characteristics of the method such as detection limit, accuracy, precision, relative standard deviation (R.S.D.) and relative standard error (R.S.E.) was calculated. The results showed that the proposed method is simple, rapid, accurate and precise method for analysis of binary and ternary mixtures.