The effect of temperature and pressure on the retention time in series-coupled gas-chromatographic columns

The promising technique of controlling chromatographic selectivity by the adjustment of individual column temperatures in systems of series-coupled columns is investigated by means of a general model incorporating the effects of temperature and mobile phase compressibility. Expressions are derived for the linear flow velocity, the effective partition coefficient and the retention time for a system of n columns assuming an ideal mobile phase gas, under conditions of constant overall pressure drop and neglect of the temperature dependence of the mobile phase viscosity. The results indicate the importance of thermodynamic parameters, relative to parameters influencing the linear flow velocity, in determining the effect of temperature on the chromatographic retention time. Numerical results are illustrated graphically for two-column systems which are discussed in greater detail. Switching of columns is also discussed and it is shown that even if thermodynamic contributions remain unchanged, non-thermodynamic contributions have a notice-able effect.     

Flow of the carrier gas in open-tubular capillary columns in temperature-programmed gas chromatography

A second-order non-linear partial different equation was derived to describe the dependence of carrier gas pressure in the column on the column distance and the time under temperature programmed conditions. This equation was solved numerically by the modified finite difference method for various column parameters. Constant inlet and outlet pressures were used as boundary conditions. The retention times calculated on assumption of a constant pressure profile along the column. Significant differences between retention times of corresponding solutes calculated by the two methods were found, especially when relatively long columns(L>50m) with small internal diameter(d<0.3mm)and high temperature program rates (r>5°/min)are used.     

Modeling of thermal processes in high pressure liquid chromatography: I. Low pressure onset of thermal heterogeneity

Heat due to viscous friction is generated in chromatographic columns. When these columns are operated at high flow rates, under a high inlet pressure, this heat causes the formation of significant axial and radial temperature gradients. Consequently, these columns become heterogeneous and several physico-chemical parameters, including the retention factors and the parameters of the mass transfer kinetics of analytes are no longer constant along and across the columns. A robust modeling of the distributions of the physico-chemical parameters allows the analysis of the impact of the heat generated on column performance. We developed a new model of the coupled heat and mass transfers in chromatographic columns, calculated the axial and radial temperature distributions in a column, and derived the distributions of the viscosity and the density of the mobile phase, hence of the axial and radial mobile phase velocities. The coupling of the mass and the heat balances in chromatographic columns was used to model the migration of a compound band under linear conditions. This process yielded the elution band profiles of analytes, hence the column efficiency under two different sets of experimental conditions: (1) the column is operated under natural convection conditions; (2) the column is dipped in a stream of thermostated fluid. The calculated results show that the column efficiency is remarkably lower in the second than in the first case. The inconvenience of maintaining constant the temperature of the column wall (case 2) is that retention factors and mobile phase velocities vary much more significantly across the column than if the column is kept under natural convection conditions (case 1).     

The effect of the temperature dependence of mobile phase viscosity on the retention time in series-coupled gas chromatographic columns

A previously established model of a system of series-coupled columns, incorporating the effects of temperature and mobile phase compressibility, is generalized to take the temperature dependence of the mobile phase viscosity coefficient into account. Expressions are reported for the linear flow velocity, the effective partition coefficient, and the retention time for both the case of constant mass flow rate and that of constant overall pressure drop. Numerical results indicate that the temperature dependence of the viscosity coefficient affects the retention time and pressure drop while the effective mass distribution coefficient remains essentially unchanged.     

不同操作模式下多环芳烃气相色谱特性的研究

在气相色谱分析萘、联苯、苊、芴、菲、蒽、荧蒽、芘、苯并（ａ）蒽、屈艹、苯并（ａ）芘和匹艹的研究过程中,以有效塔板数（ｎｅｆｆ）作为考察指标对新型色谱操作模式——程序升温升压操作条件进行了优化。通过对Ｋｏｖａｔｓ保留指数体系和Ｌｅｅ 保留指数体系在不同操作模式下的对比实验表明,在脉冲进样和程序升压等新型色谱操作条件下,Ｌｅｅ 保留指数体系仍能够满足对多环芳烃定性分析的要求, 前者则不能。     

Numerical modeling of the elution peak profiles of retained solutes in supercritical fluid chromatography

In supercritical fluid chromatography (SFC), the significant expansion of the mobile phase along the column causes the formation of axial and radial gradients of temperature. Due to these gradients, the mobile phase density, its viscosity, its velocity, its diffusion coefficients, etc. are not constant throughout the column. This results in a nonuniform flow velocity distribution, itself causing a loss of column efficiency in certain cases, even at low flow rates, as they do in HPLC. At high flow rates, an important deformation of the elution profiles of the sample components may occur. The model previously used to account satisfactorily for the retention of an unsorbed solute in SFC is applied to the modeling of the elution peak profiles of retained compounds. The numerical solution of the combined heat and mass balance equations provides the temperature and the pressure profiles inside the column and values of the retention time and the band profiles of retained compounds that are in excellent agreement with independent experimental data for large value of mobile phase reduced density. At low reduced densities, the band profiles can strongly depend on the column axial distribution of porosity.     

Experimental studies of pressure/temperature dependence of protein adsorption equilibrium in reversed-phase high-performance liquid chromatography

The effect of the average pressure and temperature of the column on the adsorption equilibrium of insulin variants on a C₈ bonded silica was studied in isocratic reversed-phase HPLC. Analytical injections of samples of four different insulins (bovine, porcine, Lys–Pro and human recombinant) were carried out at constant flow-rate but under increased average pressure. The temperature dependence of the retention parameters over the range 25–50 °C was studied under two different average column pressures (47 and 147 bar). Substantial increases of the retention time (up to 300%) were observed when the pressure and/or the temperature were increased. Similar adsorption-induced changes in the partial molar volume at constant temperature (ΔV_m≈102 ml/mol) were found for all the variants studied. Furthermore, ΔV_m was revealed to be practically independent of the temperature, which suggests that the temperature has no or very little influence on the mechanism of the pressure induced perturbations in the molecular structure of the solute. This conclusion was also derived from the observed temperature dependence of the logarithm of the retention factor (k) measured under different pressures. The relation between the temperature and ln k was nonlinear with a parabolic shape. Moreover, the shapes of the plots corresponding to the low and high pressures were found to be exactly the same, except that the curves were vertically shifted, due to the difference between the two average column pressures. These results indicate that pressure and temperature affect the retention behavior of insulins in a different and separate way.     

Fundamental chromatographic equations designed for columns packed with very fine particles and operated at very high pressures. Applications to the prediction of elution times and the column efficiencies

The wall temperatures of three Acquity-BEH-C18columns (2.1 mm x 50, 100, and 150 mm) and the temperature of the incoming eluent were maintained constant at 289 K, using a circulating water heat exchanger. The retention times and the band broadening of naphtho[2,3-a]pyrene were measured for each column as a function of the flow rate applied. Pure acetonitrile was used as the eluent. The flow rate dependence of neither elution volumes nor bandwidths can be accounted for by classical models of retention and HETP, respectively, since these models assume columns to be isothermal. Because the heat generated by friction of the eluent against the column bed increases with increasing flow rate, the column bed cannot remain isothermal at high flow rates. This heat is evacuated radially and/or longitudinally by convection, conduction, and radiation. Radial and axial temperature gradients are formed, which are maximum and minimum, respectively, when the temperature of the column wall is kept uniform and constant. The retention times that we measured match well with the values predicted based on the temperature distribution along and across the column, which we calculated and on the temperature dependence of the retention for the same column operated isothermally (i.e., at very low flow rate). The rate of band spreading varies along non-isothermal columns, so the HETP can only be defined locally. It is a function of the axial coordinate. A new contribution is needed to account for the radial thermal heterogeneity of the column, hence the radial distribution of the flow velocities, which warps the elution band. A new model, based on the general dispersion theory of Aris, allows a successful prediction of the unusually large bandwidths observed with columns packed with fine particles, operated at high flow rates, hence high inlet pressures.     

Use of isopycnic plots in designing operations of supercritical fluid chromatography: I. The critical role of density in determining the characteristics of the mobile phase in supercritical fluid chromatography

In Supercritical Fluid Chromatography (SFC), the key chromatographic parameters of any compound, its retention and efficiency, are known to strongly depend on the density of the mobile phase. This indicates that iso-density, also called isopycnic, plots drawn on the pressure-temperature plane can provide an effective tool to analyze how SFC systems may operate under different combinations of inlet and outlet pressures and column temperature. To effectively use these isopycnic plots in designing the operations of SFC systems, however, a deeper understanding of the factors behind the dependence of the performance of these systems on the mobile phase density is required. The nature of this density dependence is explored with reference to the key physical properties of the mobile phase, its viscosity, diffusivity and solubility. This study is focused on the use of pure carbon dioxide as the mobile phase, but this method of investigation is applicable for other mobile phase combinations as well.     

Prediction of the resolution of capillary columns in different conditions of inlet pressure and temperature

A procedure previously described for the prediction of the plate height of capillary columns operated at different inlet pressure of the carrier gas and at various column temperatures by using few retention data measured under isobaric conditions was modified and improved in order to permit the prediction of the retention times and of the peak widths at various heights. It is therefore possible to calculate the ratio, delta, between the peak width at different heights and the peak width at half height, whose value is used to predict the resolution at different height of two closely eluting peaks. It was found that the delta values do not depend on temperature and inlet pressure and are a characteristic of the used column; they can therefore be used in order to calculate the resolution in any temperature and inlet pressure condition. The method was used to predict the retention time, the peak width and the resolution of polar and non-polar compounds (alkanes, alkenes, chloroalkanes, alcohols, ketones) on capillary columns of different length and polarity by using as the starting data retention and width values measured in three isobaric runs only.     

On retentivity tuning by flow in the second column of different comprehensive two dimensional gas chromatographic configurations

Retentivity tuning in comprehensive two dimensional GC separations of aliphatics (linear and cyclic hydrocarbons) and aromatics in gasoline by changing the carrier gas flows in the column series at constant working temperature parameters of both columns is discussed. Comprehensive 2D techniques studied include GC×GC with cryogenic and differential flow modulation and non-modulated transfer (NMT). In all configurations, the first dimension was a non-polar column and the second dimension a polar column. Using three different flows (0.6, 1.0 and 1.4mL/min) of helium carrier gas in cryogenic modulated GC×GC illustrated that, as expected, retention of the solutes on the (1)D and (2)D columns increased but the separation quality was nearly constant. A change of carrier gas pressure (p(m)=175-125kPa) on the (1)D and (2)D columns joint point at constant inlet pressure (p(i)=525kPa) in NMT, induces an increase of the carrier gas flow rate on the (1)D and a decrease on the (2)D column, respectively. The higher retentivity of the (2)D column improved the group type separation of aliphatic/cyclic hydrocarbons and aromatics and a higher distribution of aromatics on the 2D retention plane was noted. Retentivity tuning was also performed in flow modulated GC×GC by operating the (1)D column at 0.8mL/min and the (2)D column at 20 and 26mL/min. The higher retentivity at 20mL/min improved the group type separation of aliphatic/cyclic hydrocarbons and aromatics in the 2D retention plane.     

Extrathermodynamic Study of Retention Equilibrium in RP-LC Using a C18-Silica Monolithic Stationary Phase

This study is concerned with the explanation of some thermodynamic properties of the retention equilibrium on a C₁₈-silica monolithic column. Pulse response experiments were carried out in a reversed-phase liquid chromatography system using a methanol/water mixture (70/30, v/v) and n-alkylbenzene homologs as the mobile phase and sample compounds, respectively, in the temperature range between 278 and 318 K. The retention equilibrium constant (K _a) was calculated from the first absolute moment of elution peaks. The dependence of K _a on the column temperature was analyzed using the modified van??t Hoff plot proposed by Krug et al. to derive the changes of the Gibbs free energy, the enthalpy and the entropy concerning the retention behavior. First, the presence of a real enthalpy?Centropy compensation (EEC) for the retention equilibrium was demonstrated. Then, a thermodynamic model based on the real EEC was developed to explain the temperature dependence of the linear free energy relationship (LFER) of the retention equilibrium. The model indicates how the slope and intercept of the LFER are correlated with the compensation temperatures and several molecular thermodynamic parameters. The model was effective for explaining the thermodynamic properties of the retention equilibrium of the C₁₈-silica monolithic stationary phase.     

Effect of extra-column volume on practical chromatographic parameters of sub-2-μm particle-packed columns in ultra-high pressure liquid chromatography

Effects of extra-column volume on apparent separation parameters were studied in ultra-high pressure liquid chromatography with columns and inlet connection tubings of various internal diameters (id) using 50-mm long columns packed with 1.8-μm particles under isocratic conditions. The results showed that apparent retention factors were on average 5, 11, 18, and 41% lower than those corrected with extra-column volumes for 4.6-, 3.0-, 2.1-, and 1.0-mm id columns, respectively, when the extra-column volume (11.3 μL) was kept constant. Also, apparent pressures were 31, 16, 12, and 10% higher than those corrected with pressures from extra-column volumes for 4.6-, 3.0-, 2.1-, and 1.0-mm id columns at the respective optimum flow rate for a typical ultra-high pressure liquid chromatography system. The loss in apparent efficiency increased dramatically from 4.6- to 3.0- to 2.1- to 1.0-mm id columns, less significantly as retention factors increased. The column efficiency was significantly improved as the inlet tubing id was decreased for a given column. The results suggest that maximum ratio of extra-column volume to column void volume should be approximately 1:10 for column porosity more than 0.6 and a retention factor more than 5, where 80% or higher of theoretically predicted efficiency could be achieved.     

Reversed-phase ion-pair liquid chromatographic method for determination of reaction equilibria involving ionic species: exemplification of the method using ligand substitution reactions of ethylenediaminetetraacetatochromium(III) ion with acetate and phosphate ions

A reversed-phase ion-pair liquid chromatographic method is presented for the determination of reaction equilibria involving ionic species of the same charge sign as reactant and product compounds. It has been demonstrated that ion-exchange chromatography or reversed-phase ion-pair chromatography is a useful tool for the determination of equilibrium constants of chemical reactions involving ionic species such as metal complexation reactions. Previous work with these methods has been based on the assumption that the limiting retention factors of the reactant and product species are constant independent of concentration of the chemical species (X) in the mobile phase, which reacts with the analyte compound. However, when all the reactant and product species are ions of the same charge sign as that of the species X, it is virtually impossible to apply these methods to the equilibrium constant determination because the retention factors of both the reactant and product species may depend on the concentration of X. In this study, an alternative approach was developed that estimates the limiting retention factors of ionic species from the dependence of the retention factor on the ionic strength of the mobile phase. Ligand substitution reactions of ethylenediaminetetraacetatochromium(III) ion with acetate and phosphate ions were used as model reactions to test this method. The equilibrium constants determined by this method are in good agreement with those obtained by a UV-visible spectrophotometric method.     

New pressure regulating system for constant mass flow supercritical-fluid chromatography and physico-chemical analysis of mass-flow reduction in pressure programming by analogous circuit model

Summary The newly developed regulating valve is based on high-speed flow switching, and is capable of controlling the column outlet pressure independent of the mass flow-rate of the fluid. The reproducibility of retention times in pressure-programming elution on a 4.6 mm i.d. ×250mm long silica gel column was better than 1% with supercritical carbon dioxide as the mobile phase. The outlet mass flow-rate decreased while the pressure was increasing, keeping the input flow to the system constant; this was due to the compressibility of the fluid. The amount of decrease in the outlet flow was calculated by introducing an analogous circuit model and new parameters, instrumental and column capacitances. The result agreed with the measured value within 30% error.     

Effect of the flow rate on the measurement of adsorption data by dynamic frontal analysis

The adsorption data of propyl benzoate were acquired by frontal analysis (FA) on a Symmetry-C18 column, using a mixture of methanol (65%, v/v) and water as the mobile phase, at three different flow rates, 0.5, 1.0 and 2.0 mL/min. The exact flow rates Fv were measured by collecting the mobile phase in volumetric glasses (deltaFv / Fv < or = 0.2%). The extra-column volumes and the column hold-up volume were accurately measured at each flow rate by tracer injections. The detailed effect of the flow rate on the value of the amount adsorbed was investigated. The best isotherm model accounting for the adsorption data was the same BET isotherm model at all three flow rates. Only slight differences (always less than 5%) were found between the three different sets of isotherm parameters (saturation capacity, q(s), equilibrium constant on the adsorbent, b(s) and equilibrium constant on successive layers of propyl benzoate, bL). The reproducibility of the same isotherm parameters measured by the inverse method (IM) is less satisfactory, leading to R.S.D.s of up to 10%. A flow rate increase is systematically accompanied by a slight increase of the amount adsorbed. This phenomenon is consistent with the influence of the pressure on the equilibrium constant of adsorption due to the difference between the partial molar volumes of the solute and the adsorbate. The larger average pressure along the column that is required to achieve a larger flow rate causes a larger amount of solute to be adsorbed on the column at equilibrium. This result comforts the high sensitivity and versatility of the FA method for isotherm determination under any kind of situation.     

Pressure dependence of viscosity

We reanalyze the pressure dependence of viscosity of liquids of constant composition under isothermal conditions. Based exclusively on very general considerations concerning the relationship between viscosity and "free volume," we show that, at moderate values of pressure, viscosity increases, as a rule, with increasing pressure, provided the liquid is in stable or metastable (undercooled) equilibrium states. However, even if the behavior of the viscosity is governed by free volume effects, deviations from a positive pressure dependence are possible, when the liquid's thermal expansion coefficient is negative. We derive an equation that allows one to quantitatively determine the pressure dependence of viscosity, which requires, in the simplest case, only the knowledge of the temperature dependence of viscosity at constant pressure, the thermal expansion coefficient, and the isothermal compressibility of the liquid. As an example, the negative pressure dependence of water in the range of temperatures 0-4 degrees C and of several silicate liquids, such as albite, jadeite, dacite, basalts, etc., could be explained in such a way. Other glass-forming liquids initially (for moderate pressures) show a positive pressure dependence of viscosity that changes to a negative one when subjected to high (approximately GPa) isostatic pressure. A detailed analysis of water and already mentioned silicate melts at GPa pressures shows that, in addition to free volume effects, other pressure induced structural transformations may have to be accounted for in a variety of cases. By this reason, the theoretical analysis is extended (i) in order to describe the pressure dependence of viscosity for systems that are in frozen-in thermodynamic nonequilibrium states (glasses, i.e., undercooled liquids below the glass transition temperature Tg) and (ii) to systems which undergo, in addition to variations of the free volume, pressure induced changes of other structural parameters. In such cases a decrease of viscosity with increasing pressure may occur, in principle, even if the thermal expansion coefficient is positive. In this way, the present analysis grants a general tool to estimate the pressure dependence of viscosity and supposedly settles the controversy in the current literature.     

Determination of retention indices in constant inlet pressure mode and conversion among different column temperature conditions in comprehensive two-dimensional gas chromatography

A method to determine the second dimensional real retention time, dead times on both dimensions and retention indices in constant inlet pressure mode was developed in comprehensive two-dimensional gas chromatography. At the same time, the conversion of GC x GC retention indices among different column temperature conditions were also conducted based on some thermodynamics parameters. The calculation accuracies are better than 1.0 retention index unit. Furthermore, a retention index database was developed and used to identify the compounds in a cigarette essential oil sample. It showed that identification by the database was of close agreement with by time-of-flight mass spectrometry, and some isomers could also be distinguished based on the retention index database.     

Kinetic behaviour in supercritical fluid chromatography with modified mobile phase for 5 μm particle size and varied flow rates

After much development of stationary phase chemistry, in recent years the focus of many studies in HPLC has shifted to increase the efficiency and analysis speed. Ultra high pressure liquid chromatography (UHPLC) using sub-2 μm particles, and high temperature liquid chromatography (HTLC), using temperatures above 100°C have received much attention. These new approaches allow the use of flow rates higher than those classically used in HPLC, reducing the analysis duration. Due to the low viscosity of supercritical fluids, high velocities, i.e. high flow rates, can be achieved with classical pumping systems typically used in supercritical fluid chromatography (SFC). The effects of the flow rate increase with CO(2)/methanol mobile phase was studied on the inlet pressure, t(0), the retention factor of the compounds, and on the efficiency. Simple comparisons of efficiencies obtained at varied temperature between SFC and HPLC, with a packed column containing 5 μm particles, show the greater kinetic performances achieved with the CO(2)/methanol fluid, and underline specific behaviours of SFC, occurring for high flow rates and sub-ambient temperature. Some values (N/t(0)) are also compared to UHPLC data, showing that good performance can be achieved in SFC without applying drastic analytical conditions. Finally, simple kinetic plots (t(0) vs N) at constant column length are used to select combinations of temperature and flow rate necessary to achieve a required theoretical plate number.     

Modelling of n-alkane retention and optimization of the conditions for analysis in gas adsorption chromatography with temperature programming

Summary The possibility of constructing a mathematical model of n-alkanes retention upon their separation by gas solid chromatography with temperature programming has been studied. The functional dependence between the number of the carbon atoms in n-alkane molecules, their retention in isothermal conditions and temperature of chromatographic column was used for constructing this mathematical model. It showed necessary to take into account the variance in the process temperature programming of both the carrier gas volume velocity and the column inlet pressure to obtain the adequate mathematical model of the chromatographic retention. With the use of the specific retention parameters of substances i.e. relative to the surface or the mass of sorbents the proposed model can be used not only for Silochrom C-80 but for the whole class of macroporous silica sorbents.