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The chromatographic behavior of a series of racemic benzodiazepines was evaluated under linear and nonlinear conditions on a new hybrid polymeric (DACH-ACR) chiral stationary phase (CSP). Differently substituted benzodiazepines were employed as probes to make hypotheses concerning possible molecular interaction mechanisms originating between target compounds and active sites on the CSP. Hydrogen bonds were found to be pivotal for chromatographic retention and chiral selectivity. The competitive effect from a mobile-phase (MP) modifier able to interact with the CSP through H-bonds was investigated. The performance of the polymeric DACH-ACR CSP for preparative purposes was also evaluated. The competitive adsorption isotherms of two benzodiazepines, lorazepam and temazepam, were measured at different MP compositions through the so-called inverse method. The adsorption data were fitted with a competitive bi-Langmuir adsorption isotherm. Enantiomeric separations under nonlinear conditions were modeled by using the equilibrium dispersive (ED) model of chromatography. Theoretical overloaded band profiles (obtained by solving the system of partial differential equations described by the ED model) matched, in a significantly accurate way, the profiles experimentally measured.

A new method for decoding two-dimensional (2D) multicomponent separations based on the use of the 2D Autocovariance function (2D-ACVF) has been developed. Theoretical models of single component (SC) spot distributions in 2D separations, both random and structured, are developed as the basis for a nonlinear estimation of both sample and separation system parameters from experimental 2D separations. The number of SCs, the average spot size, the spot capacity, and the saturation factor can be evaluated in the case of random SC spot patterns. The procedure was validated by extensive numerical simulation under conditions close to those usually found in GC x GC or 2D-polyacrylamid gel electrophoresis of proteins. The worse precision degree was no greater than 10% in the case of maximum spot density. This imprecision was fully accounted for, and it seems acceptable owing to the intrinsic statistical character of the estimation method. Structured multicomponent 2D separations, where SCs are linked by linear relationships, give rise to specific structured patterns in 2D-ACVF plots from which the parameters (phase and frequency) of the structured SC sequences can be evaluated: the study of 2D-ACVF makes it possible to decode multicomponent 2D separation, that is, to determine the number, relative abundance, and structural similarities of the single components. Pertinent expressions of the theoretical 2D-ACVF were derived for simple cases, and a procedure for decoding cases of structured 2D separations was developed and applied. It was shown that 2D separations containing both random and structured patterns of SC spots give rise to 2D-EACVF, which is the superimposition of the two component parts. This feature allows one, in principle, to decode the two components. The relevance of these results for Giddings sample dimensionality and separation dimensionality and their effective experimental evaluation is discussed.

The Monte Carlo model of chromatography is a description of the chromatographic process from a molecular (microscopic) point of view and it is intrinsically based on the stochastic theory of chromatography originally proposed by Giddings and Eyring. The program was previously validated at infinite dilution (i.e., in linear conditions) by some of the authors of the present paper. In this work, it has been further validated under nonlinear conditions. The correspondence between the Monte Carlo model and the well-known Thomas kinetic model (macroscopic model), for which closed-form solutions are available, is demonstrated by comparing Monte Carlo simulations, performed at different loading factors, with the numerical solutions of the Thomas model calculated under the same conditions. In all the cases investigated, the agreement between Monte Carlo simulations and Thomas model results is very satisfactory. Additionally, the exact correspondence between the Thomas kinetic model and Giddings model, when near-infinite dilution conditions are approached, has been demonstrated by calculating the limit of the Thomas model when the loading factor goes to zero. The model was also validated under limit conditions, corresponding to cases of very slow adsorption-desorption kinetics or very short columns. Different hypotheses about the statistical distributions of the random variables "residence time spent by the molecule in mobile and stationary phase' are investigated with the aim to explain their effect on the peak shape and on the efficiency of the separation.

A stochastic approach to the nonlinear chromatography theory, based on the Monte Carlo simulation method, is presented. A computer program, acting as a "virtual chromatograph" and performing a discrete event simulation, is described. Such a program allows one to choose the column type, operating conditions, sample composition, injection method, mobile-phase dispersion model, and stationary-phase sorption-desorption kinetics. Nonlinearity is accounted for by continuously monitoring and updating both the column and the solute status and by moving individual molecules step by step along the column according to specific random modes. The program has been validated through a series of statistical tests and comparing the results with the well-known achievements of the classical stochastic theory. A first application is presented, referred to a real case benzene elution on a gas solid capillary column, where the Langmuir adsorption isotherm is assumed. The effect of both the sorption modes and the site capacity are investigated. Possible applications to investigate open problems in several fields of separation science are emphasized. In addition, several specific points such as the down-scaling of a real case and the correspondence of specific adsorption dynamics with the equilibrium Langmuir isotherm are described.

The adsorption behavior of four perfluoroalkyl acids, including the environmentally relevant perfluorooctanoic acid, has been investigated on a straight-chain perfluorohexyl adsorbent. The aim of this study was to probe the potential of perfluorinated materials for the analysis and enrichment of perfluoroalkyl analytes. Water/acetonitrile mixtures, to which formic acid had been added (generally, 0.1%), were employed as mobile phases. For all perfluorinated acids, a U-shaped retention profile was observed by changing the amount of acetonitrile in the mobile phase. This behavior has been correlated to the excess adsorption of the organic component on the adsorbent surface. The concept of perfluoromethylene selectivity has been defined as the ability of a chromatographic system to discriminate between molecules that differ by a single perfluoromethylene group. The contribution to the Gibbs free energy of phase transfer for the passage of a perfluoroalkyl carbon from the mobile to the stationary phase has been evaluated. This information, in addition to the traditional van't Hoff analysis, has also been used to estimate the analogous contribution for the transfer of a carboxylic unit. Finally, insights into the retention mechanisms of perfluoroalkyl acids on straight-chain perfluorohexyl sorbents are discussed.

On the basis of only the assumptions of the independence between peak heights and peak position and of stationary retention time distribution and under the hypothesis of constant peak shape, Fourier analysis is applied to analyze the structure of multicomponent chromatograms. In essence analysis is made of the properties of the chromatographic response covariance as a function of time distance and of its Fourier transform which is the power spectrum (PS)

The paper describes a method for determining homologous classes of compounds in a multicomponent complex chromatogram obtained under programming elution conditions. The method is based on the computation of the autocovariance function of the experimental chromatogram (EACVF). The EACVF plot, if properly interpreted, can be regarded as a "class chromatogram" i.e., a virtual chromatogram formed by peaks whose positions and heights allow identification and quantification of the different homologous series, even if they are embedded in a random complex chromatogram. Theoretical models were developed to describe complex chromatograms displaying random retention pattern, ordered sequences or a combination of them. On the basis of theoretical autocovariance function, the properties of the chromatogram can be experimentally evaluated, under well-defined conditions: in particular, the two components of the chromatogram, ordered and random, can be identified. Moreover, the total number of single components (SCs) and the separated number of the SCs belonging to the random and ordered components can be determined, when the two components display the same concentration. If the mixture contains several homologous series with common frequency and different phase values, the number and identity of the different homologous series as well as the number of SCs belonging to each of them can be evaluated. Moreover, the power of the EACVF method can be magnified by applying it to the single ion monitoring (SIM) signals to selectively detect specific compound classes in order to identify the different homologous series. By this way, a full "decoding" of the complex multicomponent chromatogram is achieved. The method was validated on synthetic mixtures containing known amount of SCs belonging to homologous series of hydrocarbon, alcohols, ketones, and aromatic compounds in addition to other not structurally related SCs. The method was applied to both the total ion monitoring (TIC) and the SIM signals, to describe step by step the essence of the procedure. Moreover, the systematic use of both SIM and TIC can simplify the decoding procedure of complex chromatograms by singling out only specific compound classes or by confirming the identification of the different homologous series. The method was further applied to a sample containing unknown number of compounds and homologous series (a petroleum benzin, bp 140-160 degrees C): the results obtained were meaningful in terms of both the identified number of components and identified homologous series.

A renewed stochastic model of chromatography is proposed able to establish a conceptual link between the single-molecule dynamics observations in a given chromatographic system and chromatographic experiment results in the same media. The chromatographic peak is expressed through its Fourier transform as a function of the experimental sorption time distribution. The pertinent numerical procedure necessary for obtaining the chromatographic peak is described, and the numerical programming code is given. Two types of cases were considered, the first one where the sole discrete sorption time distribution is available, and the second one where the adsorption mechanism is made of a mixture of continuous and discrete sorption time distributions. The method is applied to experimental data found in the literature by determining typical chromatographic peak shapes on the basis of the experimental interface adsorption data. This renewed stochastic approach is based on the so-called Levy canonical description of stochastic processes and appears to be the most general basis for handling separation processes from a stochastic point of view.