Justification of statistical overlap theory in programmed temperature gas chromatography: thermodynamic origin of random distribution of retention times

A specific distribution of compounds' standard-state changes of enthalpy and entropy between mobile and stationary phases in programmed temperature gas chromatography (PTGC) is shown to produce the Poisson distribution of retention times often postulated in statistical-overlap theory (SOT). A three-part model is proposed, in which the enthalpy change is Poisson distributed, the average entropy change depends on the enthalpy change, and the actual entropy change varies in a uniformly random manner about the average entropy change. To test the model, the entropy and enthalpy changes of 350 aliphatic and aromatic hydrocarbons in petroleum were calculated with commercial GC software. These changes are shown to follow the three-part model. The model then was used with Monte Carlo methods to mimic the enthalpy and entropy changes. The substitution of the mimicked enthalpy and entropy changes into an equation for the retention temperature in PTGC is shown to produce a Poisson distribution of retention times that is statistically significant. This finding establishes a scientific link between the thermodynamics governing retention in PTGC and the superficially ad hoc assumption of the Poisson retention time distribution in SOT. Similar thermodynamic distributions are found for flavors and fragrances and for tetrachlorodibenzo-p-dioxins and furans, which follow SOT based on the Poisson distribution, but not for polychloronaphthalenes, which do not follow that SOT.     

Combination of column temperature gradient and mobile phase flow gradient in microcolumn and capillary column high-performance liquid chromatography

The combination of several gradient modes (solvent, temperature, and flow programming) is rarely used in HPLC analysis. In this work, the separations obtained utilizing simultaneous flow and temperature gradient in capillary column and microcolumn HPLC were compared with the separations performed under isocratic, isothermal, and isorheic (constant flow) conditions. When the mobile phase flow rate and the column temperature were changed simultaneously during the separation run, the analysis time was shortened up to 50%, while the separation efficiency was preserved. The separations obtained with combined temperature and flow gradients show high reproducibility (relative standard deviation <2.0%), comparable to the reproducibility normally seen with a mobile phase gradient. For capillary HPLC, simultaneous temperature and flow programming is the method of choice because of the great technical difficulties involved in performing solvent gradient elution.     

Capillary ion chromatography at high pressure and temperature

The application of high pressure and temperature in ion chromatography (IC) can significantly improve the efficiency and reduce the analysis time. In this work, the kinetic-performance limits of capillary IC columns with inner diameters of 400 μm packed with 4 and 7 μm macroporous anion-exchange particles were investigated employing a capillary ion-exchange instrument allowing column pressures up to 34 MPa and column temperatures up to 80 °C. Plate heights below 10 μm could be realized using capillary columns packed with 4 μm particles. Compared to conventional IC using 7 μm particles and pressures up to 21 MPa, a 40% improvement in plate number could be achieved when working at the kinetic performance limits at 34 MPa and using columns packed with 4 μm particles. Using coupled columns with a total length of 400 mm, a mixture of seven anions was separated within 7.5 min while yielding 20?000 plates. Increasing the temperature improved the performance limits when operating in the C-term region (for fast IC separation using columns <75 cm). Temperature also affected the retention properties and hence the selectivity. At higher temperature, retention for monovalent ions was mainly governed by ion diameter. An increase in retention with temperature was observed for small ions, and there was a decrease for ions having a larger diameter. The retention factor for divalent and trivalent anions increased with temperature.     

Modeling retention and selectivity as a function of pH and column temperature in liquid chromatography

In reversed-phase liquid chromatography (RPLC), the retention of weak acids and bases is a sigmoidal function of the mobile-phase pH. Therefore, pH is a key chromatographic variable to optimize retention and selectivity. Furthermore, at an eluent pH close to the pKa of the solute, the dependence of ionization of the buffer and solute on temperature can be used to improve chromatographic separations involving ionizable solutes by an adequate handling of column temperature. In this paper, we derive a general equation for the prediction of the retentive behavior of ionizable compounds upon simultaneous changes in mobile-phase pH and column temperature. Four experiments, two limiting pH values and two temperatures, provide the input data that allow predictions in the whole range of these two variables, based on the thermodynamic fundamentals of the involved equilibria. Also, the study demonstrates the significant role that the choice of the buffer compound would have on selectivity factors in RPLC at temperatures higher than 25 degrees C.     

Statistical-overlap theory of column switching in gas chromatography: applications to flavor and fragrance compounds

First-column gas chromatograms (GCs) of hundreds of flavor and fragrance compounds, and second-column GCs of specific regions of these GCs, are predicted using thermodynamic databases in commercial software. A statistical-overlap theory of column switching with cryogenic focusing then is developed by mimicking the predicted GCs by two kinds of Monte Carlo simulations. In the first kind, a probability distribution is calculated for the number of compounds in a region of the first-column GC, based on the number of observed peaks in the region, the number of observed peaks in the second-column GC, and the retention-time distributions and breadths of single-component peaks in both GCs. In the second kind, criteria are established for the theory's application. The theory is applied to 12 regions of first-column GCs. The theory predicts the number of compounds in all of them and shows that separation rarely is complete in second-column GCs, when 10 or more compounds are transferred between columns. The theory also rationalizes the tedious search required to find good separation conditions by showing that column-switching gas chromatography with cryogenic focusing is inherently statistical. The number of peaks in the second-column GC can be greater than, less than, or equal to the number of peaks in the relevant region of the first-column GC, and the good conditions sought by researchers to substantially improve separation correspond to favorable "rolls of the dice" found only by trial and error.     

Comprehensive two-dimensional supercritical fluid and gas chromatography with independent fast programmed heating of the gas chromatographic column

With comprehensive two-dimensional supercritical fluid and fast, independent temperature-programmed gas chromatography (SFCxGC), a polar column was used in the first dimension to achieve group-type analysis. The eluent of this separation was repetitively sampled and transferred to a fast, resistively heated gas chromatograph to obtain the boiling point distribution over the entire polarity separation. The SFC was operated isothermally with stopped flow to provide a sufficient time span for the GC analysis. The GC analysis had a typical cycle time of 1 min for the system demonstrated here. During this time, the GC column was independently heated at a rate of 450 degrees C/min to 250 degrees C and actively cooled again to -50 degrees C before the next GC injection took place. The analysis of petrochemical samples is presented to illustrate the technique.     

Generating multiple independent retention index data in dual-secondary column comprehensive two-dimensional gas chromatography

A method producing simultaneously three retention indexes for compounds has been developed for comprehensive two-dimensional gas chromatography by using a dual secondary column approach (GC x 2GC). For this purpose, the primary flow of the first dimension column was equally diverted into two secondary microbore columns of identical geometry by means of a three-way flow splitter positioned after the longitudinally modulated cryogenic system. This configuration produced a pair of comprehensive two-dimensional chromatograms and generated retention data on three different stationary phases in a single run. First dimension retention indexes were determined on a polar SolGel-Wax column under linear programmed-temperature conditions according to the van den Dool approach using primary alcohol homologues as the reference scale. Calculation of pseudoisothermal retention indexes in both second dimensions was performed on low-polarity 5% phenyl equivalent polysilphenylene/siloxane (BPX5) and 14% cyanopropylphenyl/86% dimethylpolysiloxane (BP10) columns. To construct a retention correlation map in the second dimension separation space upon which KovAts indexes can be derived, two methods exploiting "isovolatility" relationships of alkanes were developed. The first involved 15 sequential headspace samplings of selected n-alkanes by solid-phase microextraction (SPME), with each sampling followed by their injection into the GC at predetermined times during the chromatographic run. The second method extended the second dimension retention map and consisted of repetitive introduction of SPME-sampled alkane mixtures at various isothermal conditions incremented over the temperature program range. Calculated second dimension retention indexes were compared with experimental values obtained in conventional one-dimensional GC. A case study mixture including 24 suspected allergens (i.e., fragrance ingredients) was used to demonstrate the feasibility and potential of retention index information in comprehensive 2D-GC.     

General strategy for performing temperature programming in high performance liquid chromatography: prediction of linear temperature gradients

This paper describes how an empirical retention model is transferred from temperature-programmed gas chromatography (GC) to high temperature liquid chromatography (HT-HPLC). In order to evaluate the retention prediction, a temperature range from 50 to 180 °C was investigated using two test mixtures consisting of steroids and polycyclic aromatic hydrocarbons. In this temperature range, heating rates from 1.5 °C min(-1) up to 30 °C min(-1) were applied using four different high temperature stable HPLC columns with inner diameters of 1.0, 2.1, 3.0, and 4.6 mm. Temperature lag phenomena in the HPLC column as well as in the column oven are discussed, and it is shown that the linear elution strength (LES) model can be applied without any mathematical extension in order to take a temperature-dependent delay time into account. On the basis of this approximation, it is possible to perform a systematic method development using linear temperature gradients in liquid chromatography. Furthermore, it is shown that only two initial temperature gradient runs are necessary to predict the retention times of the analytes with a maximal relative error of less than 2%.     

Effect of particle size on gas holdup in three-phase reactors

Gas holdups were measured in a batch three-phase cocurrent column in which glass beads ranging from 17 to 5000μm were suspended up to 20 vol %. The effect of particle size on gas holdup was found to be different in three types of reactors such as the gas-sparged slurry reactors, three-phase bubble columns and three-phase fluidized beds. An increase of particle size reduced gas holdup in three-phase bubble columns, while raising it in gas-sparged slurry reactors and three-phase fluidized beds. The maximum and minimum gas holdup were observed respectively for particle size of about 88–250μm and 500μm, but the values of particle size were dependent on solid content and gas velocity. This paper is dedicated to Dr L K Doraiswamy on his sixtieth birthday.     

Transient flow in response to a pressure pulse in gas chromatography

The analysis of flow through a gas chromatography column has traditionally assumed the presence of steady-state conditions. However, when rapid changes in inlet pressure are introduced, a significant transient period is observed, leading to a failure of the steady-state model. Through the introduction of a one-dimensional continuity equation into the basic set of equations, a nonlinear partial differential equation is derived to describe the evolution of pressure profiles in a capillary gas chromatography column. A numerical solution is used to solve the differential equation for the case of a pulse injection under isothermal conditions, and comparisons with experimental holdup and retention times show very good agreement.     

毛细管白酒专用柱气相色谱法测定白酒中甲醇含量

氢火焰检测器测定,外标法定量。实验结果表明,采用毛细管白酒专用色谱柱程序升温直接进样的气相色谱方法测定白酒中甲醇含量,准确度高、分离效果好、精密度高、重复性好、分析速度快。     

Comparison of inlet geometry in microfluidic cell affinity chromatography

Cell separation based on microfluidic affinity chromatography is a widely used methodology in cell analysis research when rapid separations with high purity are needed. Several successful examples have been reported with high separation efficiency and purity; however, cell capture at the inlet area and inlet design have not been extensively described or studied. The most common inlets-used to connect the microfluidic chip to pumps, tubing, etc.-are vertical (top-loading) inlets and parallel (in-line) inlets. In this work, we investigated the cell capture behavior near the affinity chip inlet area and compared the different performances of vertical inlet devices and parallel inlet devices. Vertical inlet devices showed significant cell capture capability near the inlet area, which led to the formation of cell blockages as the separation progressed. Cell density near the inlet area was much higher than that in the remaining channel, whereas for parallel inlet chips cell density at the inlet area was similar to that in the rest of the channel. In this paper, we discuss the effects of inlet type on chip fabrication, nonspecific binding, cell capture efficiency, and separation purity. We also discuss the possibility of using vertical inlets in negative-selection separations. Our findings show that inlet design is critical and must be considered when fabricating cell affinity microfluidic devices.     

Stabilization of temperature and pressure of a real gas in a stopped pipe

Nonisothermal unsteady flow of a real gas in a pipe is studied. A numerical method is given for solving a system of quasi-linear differential equations that describe the flow of a real gas in a stopped pipe. The calculated results are discussed.