Estimation of the dead times of gas-chromatographic systems under different temperature conditions with the use of recurrence relations

A new procedure for evaluating the retention time of an unsorbed gas (t ₀), which is applicable to any temperature conditions of gas-chromatographic analysis, is proposed. The procedure is based on the extrapolation of the absolute retention times of homologs (n-alkanes) with the estimation of the retention time of a hypothetical homolog with the zero number of carbon atoms in the molecule using recurrence relations. A consequence of this approximation is the modification of a known formula for the estimation of t ₀ from the retention times of three sequential homologs (the Peterson and Hirsch method), which consists in the replacement of absolute retention times by their squares. This modification makes this method applicable to not only isothermal conditions but also temperature programming conditions.     

Extrapolation of isothermal retention data in gas chromatography for chiral recognition studies

Summary The calculation of capacity factors, k, from net retention times, t_R, and the corresponding dead times, t_M, at different temperatures suffers from the limited accuracy of the t_M values. If the temperature coefficient racy of the t_M values. If the temperature coefficient d ln k/d (1/T) only is required, it is sufficient to determine net retention times (t_R)_p at constant inlet pressure p_i for different temperatures, since the temperature dependence of (t_M)_p can be assumed as (t_M)_p=A·e^B/T, with B being approximately independent of the column inlet pressure and of the nature of the carrier gas. The extrapolation and interpolation of (t_R)_p may be either performed by linear regression or graphically with a nomogram for ln (t_R)_p versus 1/T. The resolution factor, , of two components, e.g. enantiomers which are resolved on a chiral stationary phase, can be treated in a similar way. Examples are given for the resolution of enantiomers of two non-proteinogenic amino acids on the new polysiloxane phase L-Chirasil-CPG.     

Effect of Temperature on the Variation of Retention Time of Unretained Compound and Retention Indices of Some Explosives and Related Compounds Calculated Using a Multiparametric Method in RP-LC

In reversed phase liquid chromatography (RP-LC), a multiparametric non-linear least-squares regression iterative method has been evaluated at different column temperatures (ranging from 30 to 60 °C in 5 °C steps) for calculating the retention time of the unretained compound t _M and the regression parameter (slope b), based on the use of alkan-2-ones, alkyl aryl ketones and 1-nitroalkanes homologous series on two different columns: Spherisorb-ODS2 C₁₈ and Nucleosil C₈. The calculated parameters t _M and b by the multiparametric method (MP) were compared with those obtained by using the iterative method of Guardino’s. The influence of the number of subsets of homologues used for the calculation of t _M and b values was investigated. The retention indices (RI) of some neutral and acidic explosives and related compounds (nitramines, nitroaromatics, aminonitroaromatics and nitrophenols) based on the alkan-2-ones retention index standards have been determined and compared at various temperatures by the MP method. Good agreement was observed between retention data calculated by the MP and GU methods.     

Trilinearity deviation ratio: A new metric for chemometric analysis of comprehensive two-dimensional gas chromatography time-of-flight mass spectrometry data

Comprehensive two-dimensional gas chromatography coupled with time-of-flight mass spectrometry (GC × GC–TOFMS) is a well-established instrumental platform for complex samples. However, chemometric data analysis is often required to fully extract useful information from the data. We demonstrate that retention time shifting from one modulation to the next, Δ²t_R, is not sufficient alone to quantitatively describe the trilinearity of a single GC × GC–TOFMS run for the purpose of predicting the performance of the chemometric method parallel factor analysis (PARAFAC). We hypothesize that analyte peak width on second dimension separations, ²W_b, also impacts trilinearity, along with Δ²t_R. The term trilinearity deviation ratio, TDR, which is Δ²t_R normalized by ²W_b, is introduced as a quantitative metric to assess accuracy for PARAFAC of a GC × GC–TOFMS data cube. We explore how modulation ratio, M_R, modulation period, P_M, temperature programming rate, T_ramp, sampling phase (in-phase and out-of-phase), and signal-to-noise ratio, S/N, all play a role in PARAFAC performance in the context of TDR. Use of a P_M in the 1–2 s range provides an optimized peak capacity for the first dimension separation (500–600) for a 30 min run, with an adequate peak capacity for the second dimension separation (12–15), concurrent with an optimized two-dimensional peak capacity (6000–7500), combined with sufficiently low TDR values (0–0.05) to facilitate low quantitative errors with PARAFAC (0–0.5%). In contrast, use of a P_M in the 5 s or greater range provides a higher peak capacity on the second dimension (30–35), concurrent with a lower peak capacity on the first dimension (100–150) for a 30 min run, and a slightly reduced two-dimensional peak capacity (3000–4500), and furthermore, the data are not sufficiently trilinear for the more retained second dimension peaks in order to directly use PARAFAC with confidence.     

Kubische Berechnung der Retentionsindices ohne Kenntnis der Totzeit tm

Zusammenfassung In der vorliegenden Arbeit wird eine Methode zur Retentionsindex-Bestimmung beschrieben, die von einem kubischen Zusammenhang zwischen Bruttoretentionszeit-Differenzen der Referenzhomologen und der Kohlenstoffzahl ausgeht. Hieraus ergeben sich direkt die Nettoretentionszeiten. Der Fehler der Totzeitbestimmung entfällt bei dieser Methode. Mit den so gewonnenen Nettoretentionszeiten erhält man über einen kubischen Zusammenhang zwischen 1g t_s=f(C) die Retentionsindices. Extrapolationen und Interpolationen sind über 300 Retentionsindexeinheiten mit einem mittleren Fehler von ±0,02 Retentionsindexeinheiten möglich. Das Verfahren bietet sich für eine automatische Berechnung der I-Werte mittels on-line-Datenverarbeitung an.

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Cubic calculation of retention indices without determining the dead-time t_m

Summary The method for the calculation of retention indices described here is based on a third order relationship between the logarithm of differences of unadjusted retention times of homologues and the carbon number. From this adjusted retention times are directly calculated. A determination of the dead-time is not necessary thus avoiding the errors connected with this factor. A cubic equation for the logarithm of the adjusted retention time lg t_s as a function of carbon number C_n is used for the retention index calculation. Extrapolations and interpolations can be done over a range of 300 index units with an average deviation of ±0.02 i.u.. The method offers the possibility of an automated on-line calculation of retention indices by computer merely on the basis of unadjusted retention times.

     

Berechnung von Retentionsindices auf der Grundlage eines nichtlinearen Zusammenhanges zwischen Nettoretentionszeit und Kohlenstoffzahl von n-Alkanen

Zusammenfassung Die bisher in der Literatur beschriebenen Verfahren zur Retentionsindex-Bestimmung beruhen auf einem linearen Zusammenhang zwischen dem Logarithmus der Nettoretentionszeit lg t_s und der Kohlenstoffzahl C der n-Alkane. Wie genaue Meßwerte für Retentionszeiten zeigen, ist die Funkton lg t_s=f(C) nicht streng linear. Die Krümmung des Funktionsbildes bedingt, daß lineare Regressionsmethoden, sowie auch die Methode nach Kovats, es nicht erlauben, extrapolativ sowie über weite Retentionsbereiche interpolativ I-Werte zu berechnen. In dieser Arbeit werden Retentionsindices aufgrund eines kubischen Zusammenhanges zwischen lg t_s und der Kohlenstoffzahl ermittelt. Die hierzu notwendige Totzeit t_m wird aus den Differenzen der Bruttoretentionszeiten der Referenzhomologen ermittelt.

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Retention index calculation based on a non-linear relationship between net retention time and carbon number of n-alkanes

Summary Methods of retention index calculation described in the literature have been based on a linear relationship between the logarithm of the adjusted retention times lg t_s and the carbon numbers C of n-alkanes. Exact measurements of the retention times of n-alkanes show that the relationship lg t_s=f(C) is in fact not strictly linear. Correct extrapolative or interpolative calculations of retention indices over a wide retention range are therefore impossible when using the original formula as given by Kovats or methods based on a linear regression concept. The method of retention index calculation presented here is based on a cubic relationship between lg t_s and carbon number allowing extrapolative or interpolative calculations. The hold-up time (t_m) is calculated on the basis of differences of retention times of the reference homologues.

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Development of a novel RP‐HPLC method for the efficient separation of aripiprazole and its nine impurities

The development of an RP‐HPLC method for the separation of aripiprazole and its nine impurities was performed with the use of partial least squares regression, response surface plot methodology, and chromatographic response function. The HPLC retention times and computed molecular parameters of the aripiprazole and its nine impurities were further used for the quantitative structure–retention relationship (QSRR) study. The QSRR model, R²: 0.899, Q²: 0.832, root mean square error of estimation: 4.761, root mean square error of prediction: 6.614, was developed. Very good agreement between the predicted and observed retention times (t_R) for three additional aripiprazole impurities (TC1–TC3) indicated the high prediction potential of the QSRR model for t_R evaluation of other aripiprazole impurities and metabolites. The developed HPLC method is the first reported method for the efficient separation of aripiprazole and its nine impurities, which could be used for the analysis of an additional three aripiprazole impurities (TC1–TC3).     

Probability of failure of the watershed algorithm for peak detection in comprehensive two-dimensional chromatography

The watershed algorithm is the most common method used for peak detection and integration in two-dimensional chromatography. However, the retention time variability in the second dimension may render the algorithm to fail. A study calculating the probabilities of failure of the watershed algorithm was performed. The main objective was to calculate the maximum second-dimension retention time variability, Δ²t_R,crit, above which the algorithm fails. Several models to calculate Δ²t_R,crit were developed and evaluated: (a) exact model; (b) simplified model and (c) simple-modified model. Model (c) gave the best performance and allowed to deduce an analytical expression for the probability of failure of the watershed algorithm as a function of experimental Δ²t_R, modulation time and peak width in the first and second dimensions. It could be demonstrated that the probability of failure of the watershed algorithm under normal conditions in GC × GC is around 15–20%. Small changes of Δ²t_R, modulation time and/or peak width in the first and second dimension could induce subtle changes in the probability of failure of the watershed algorithm. Theoretical equations were verified with experimental results from a diesel sample injected in GC × GC and were found to be in good agreement with the experiments.     

Determination of Zero Retention Times (t0) by Temperature Dependent Reversed Phase High Perfomance Liquid Chromatography

Abstract

For a given reversed phase HPLC system the zero retention time (t₀) can be determined by measuring brutto retention times at different temperatures. For calculation of t₀ value temperature intervals must be equidistant in 1/T. If at least two compounds are separated on the column having almost the same sorption enthalpies a more simple intersecting point method can be practised. In this case only two temperature points are necessary for graphic evaluation. The presented methods for determination of t₀ values are proved for noradrenaline and adrenaline under selected experimental conditions using aqueous solutions of alkaline perchlorates as mobile phases. Thus t₀ values can be determined with an accuracy and a precision of less than ± 3%.     

手性有机酸薄层色谱保留指数的拓扑模型

基于Kier的分子连接性指数及邻接矩阵提出新型分子连接性指数（^mG_t^v）;引入手性指数（w_j）并建立了手性连接性指数（^mG_t^v）：^mG_t^v=^mG_t^v×w_j。^mG_t^v适用于手性分子、非手性分子及内消旋异构体的结构差异表征。用多元统计回归研究18种手性羟酸和氨基酸的薄层色谱保留指数（R_M）与^mG_t^v的定量构效关系,经最佳变量子集回归建立其四元数学模型,传统的判定系数（R²）为0.973,逐一剔除法（leave-one-out,LOO）的交互验证系数（Q²）为0.950,结果证明具有良好的稳健性及预测能力。根据进入该模型的4个手性连接性指数（⁰C_p^v、²C_p^v、C_ch^v、⁵C_p^v）可知,影响手性有机酸保留指数的主要因素是分子的二维结构特征和分子的手性特征以及柔韧性、折叠程度等三维结构因素。从上可见,新建手性连接性指数对手性有机酸的保留指数表征具有合理性与有效性,为预测手性有机酸的保留指数提供了一种有效方法。     

Prediction of retention indices. VI: Isothermal and temperature-programmed retention indices,methylene value,functionality constant,electronic and steric effects

The Kováts retention index system with n-alkanes as reference standards has properties not fully explored when single, isolated or stand-alone analytes are analyzed by isothermal gas chromatography. When a homologous series of analytes are analyzed by either linear or non-linear temperature-programmed gas chromatography, the retention data of the entire series can be treated systematically to produce an I vs. Z plot that is linear, thereby giving insight into the relationship between chemical structure and retention index. Dead time t_M is both instrument and temperature dependent. With no dead time t_M adjustment, the retention indices of analytes calculated from experimental retention times by the method of either linear or logarithmic interpolation give statistically identical values. Linear regression analysis of the data shows the slope as methylene value (A) and intercept as functionality constant or group retention factor (GRF) of the homologous series. The A and (GRF) values vary with chemical structures, intermolecular electronic and steric interactions, and polarity of column liquid phases, and can link gas chromatographic retention index to chemical structure. Examples of the influence of molecular electronic effects and steric effects on retention index are given and discussed.     

Calculations of Jahn-Teller coupling constants in the weak-field basis via the angular overlap model: a simple operator equivalent technique

Within the framework of the angular overlap model the matrix elements of the linear Jahn-Teller operator may easily be calculated in the weak-field basis in terms of simple operator equivalents. The method is applied to the calculation of the 〈M_J|?V/?Q|M_j〉 matrix elements for the |LSJMj〉 ground states of t^x species (x = 1) ? 13) in )^* symmetry.     

Ordre local dans quelques verres fluores du systeme PbF2MIItF2MIIItF3 par EXAFS

The local environment of transition metal (M_t) and lead has been studied by EXAFS for some fluoride glasses in the system PbF₂M^II_tF₂M^III_tF₃ (M^II_t = Mn²⁺, Zn²⁺; M^III_t = Fe³⁺, Ga³⁺). Theoretical phase shifts and backscattering amplitude are used after testing with crystallized fluorides of various structures. Transition metals are sixfold coordinated and M_tF distances are very close to those known in crystallized compounds. Lead has eight to nine fluorine neighbors forming a very distorted polyhedra. Radial distributions, partially corrected for phase shifts, show a very weak second peak but the second neighbors nature and the distances cannot be determined without ambiguity.     

Synthesis and Characterization of Tris(oxazolinyl)borato Copper(II) and Copper(I) Complexes

The reaction of To^MTl (To^M=tris(4,4-dimethyl-2-oxazolinyl)phenylborate) and CuBr₂ in benzene at 60 °C provides To^MCuBr ( 1 ) as an entry-point into tris(oxazolinyl)phenylborato copper chemistry. To^MCuO^tBu ( 2 ) and To^MCuOAc ( 3 ) are prepared by the reactions of To^MCuBr with KO^tBu and NaOAc, respectively. To^MCuO^tBu is transformed into (To^MCuOH)₂ ( 4 ) through hydrolysis. NMR, FT-IR, and EPR spectroscopies are used to determine the electronic and structural properties of these copper(II) compounds, and the solid-state structures were characterized by X-ray crystallography. Reduction of copper is observed upon treatment of To^MCuO^tBu with phenylsilane in an attempt to synthesize monomeric copper(II) hydride. To^MCu ( 5 ) and To^M₂Cu ( 6 ) were independently synthesized and characterized for comparison.     

Volumetric behavior and micelle formation of aqueous surfactant mixtures

A thermodynamic treatment of the volumetric behavior of surfactant mixtures in water have been developed on the basis of the thermodynamic treatment of mixed micelle by Motomura et al. Densities of aqueous solutions of mixtures of decyltrimethylammonium bromide (DeTAB) and dodecyltrimethylammonium bromide (DTAB) have been measured as a function of total molality at constant compositions. The apparent molar volumes of the mixtures have been derived from the density data and the mean partial molar volume of monomeric surfactant mixture V _t ^w , the molar volume of mixed micelle V^M/N _t ^M , the voluem of formation of mixed micelle _W ^M V, and the composition of surfactant in the mixed micelle have been evaluated. The V _t ^W , V^M/N _t ^M , and _W ^M V have been observed to depend on the composition. The linear dependence of V _t ^W and V^M/N _t ^M on the composition indicates that the mixing of DeTAB and DTAB is ideal both in the monomeric and micellar states. This has been confirmed further by the shape of the critical micelle concentration vs. composition curves.     

Computer-assisted peak recognition for polychlorinated dibenzo-p-dioxins (PCDD) and polychlorinated dibenzofurans (PCDF) in environmental samples

A software has been developed for the peak recognition of 136 polychlorinated dibenzo-p-dioxins (PCDD) and polychlorinated dibenzofurans (PCDF) after high resolution gas chromatography coupled with mass spectrometry (HRGC/HRMS). Based on the retention times of ¹³C labelled 2,3,7,8-substituted PCDD/F internal standards, the retention times of all PCDD and PCDF can be calibrated automatically and accurately. Therefore, it is very convenient to identify the peaks by comparing the retention of samples and the calibrated retention times of their chromatograms. Hence, this approach is very significant because it is impossible to obtain always a standard chromatogram and PCDD/F analysis are very expensive and time consuming. The calibration results can be transferred to Excel for calculation. The approach is a first step to store costly and environmentally relevant data for future application.     

Relaxation spectra of concentrated polystyrene solutions

The relaxation modulus G(t) and the stress decay after cessation of steady shear flow were measured on concentrated solutions of polystyrenes in diethyl phthalate. Ranges of concentration c and molecular weight M of the polymer were from 0.112 to 0.329 g/ml and from 1.23 × 10⁶ to 7.62 × 10⁶, respectively. The relaxation spectrum H(τ) as calculated from G(t) for the solution of very high M was found to be composed of two parts. One, at relatively short times, was a broad distribution (plateau zone) with height proportional to c². The second, at the long-time end, was very sensitive to concentration and gave rise to a maximum in H(τ) for very high concentrations. The behavior of H(τ) at long times was examined quantitatively by evaluating the longest relaxation time τ₁⁰ and the corresponding relaxation strength G₁⁰ from G(t) and from the stress decay function, on the assumption of a discrete distribution of relaxation times at long times. The longest relaxation time was approximately proportional to M^3.5, even at relatively low concentrations where the zero-shear viscosity was not proportional to M^3.5. The strengths of relaxation modes with the longest few relaxation times are proportional to the third power of concentration.     

Retention Time of Unretained Compound Calculation and Determination of Retention Indices of Some Monosubstituted Benzenes Using a Multiparametric Method in Binary, Ternary and Quaternary Solvent RP-LC Systems

In reversed phase liquid chromatography (RP-LC), the validity of a multiparametric (MP) non-linear least-squares regression iterative method has been evaluated for 14 different aqueous mobile phases modified with one, two or three organic solvents [acetonitrile (ACN), methanol (MeOH), or tetrahydrofuran (THF)] for calculating the retention time of unretained compound t _M and the regression parameter (slope b), based on the use of alkan-2-ones and alkyl aryl ketones homologous series. The determination of t _M and b has been studied for eight binary (ACN?CH₂O or MeOH?CH₂O), 3 ternary (ACN?CMeOH?CH₂O) and 3 quaternary (ACN?CMeOH?CTHF?CH₂O) mobile phase systems on an Omnispher C₁₈ column. The multiparametric calculated t _M and b values were compared with those obtained by Guardino??s, and Grobler??s methods. The MP retention indices (RI) of ten monosubstituted benzenes with different functionality (hydroxyl, carbonyl, nitro, etc.) based on the alkan-2-ones retention index standards have been determined and compared for the different mobile phase compositions studied. The influence of organic modifier type, the nature of mobile phase system and water content on the variation of retention parameter studied in this work were discussed.