Modeling of thermal processes in very high pressure liquid chromatography for column immersed in a water bath: Application of the selected models

Currently, chromatographic analyses are carried out by operating columns packed with sub-2 μm particles under very high pressure gradients, up to 1200 bar for 5 cm long columns. This provides the high flow rates that are necessary for the achievement of high column efficiencies and short analysis times. However, operating columns at high flow rates under such high pressure gradients generate a large amount of heat due to the viscous friction of the mobile phase stream that percolates through a low permeability bed. The evacuation of this heat causes the formation of significant or even large axial and radial gradients of all the physico-chemical parameters characterizing the packing material and the mobile phase, eventually resulting in a loss of column efficiency. We previously developed and successfully applied a model combining the heat and the mass balances of a chromatographic column operated under very high pressure gradients (VHPLC). The use of this model requires accurate estimates of the dispersion coefficients at each applied mobile phase velocity. This work reports on a modification of the mass balance model such that only one measurement is now necessary to accurately predict elution peak profiles in a wide range of mobile phase velocities. The conditions under which the simple equilibrium-dispersive (ED) and transport-dispersive (TD) models are applicable in VHPLC are also discussed. This work proves that the new combination of the heat transfer and the ED model discussed in this work enables the calculation of accurate profiles for peaks eluted under extreme conditions, like when the column is thermostated in a water bath.     

Modeling of thermal processes in high pressure liquid chromatography: II. Thermal heterogeneity at very high pressures

Advanced instruments for liquid chromatography enables the operation of columns packed with sub-2 μm particles at the very high inlet pressures, up to 1000 bar, that are necessary to achieve the high column efficiency and the short analysis times that can be provided by the use of these columns. However, operating rather short columns at high mobile phase velocities, under high pressure gradients causes the production of a large amount of heat due to the viscous friction of the eluent percolating through the column bed. The evacuation of this heat causes the formation of significant axial and radial temperature gradients. Due to these thermal gradients, the retention factors of analytes and the mobile phase velocity are no longer constant throughout the column. The consequence of this heat production is a loss of column efficiency. We previously developed a model combining the heat and mass balance of the column, the equations of flow through porous media, and a linear isotherm model of the analyte. This model was solved and validated for conventional columns operated under moderate pressures. We report here on the results obtained when this model is applied to columns packed with very fine particles, operated under very high pressures. These results prove that our model accounts well for all the experimental results. The same column that elutes symmetrical, nearly Gaussian peaks at low flow rates, under relatively low pressure drops, provides strongly deformed, unsymmetrical peaks when operated at high flow rates, under high pressures, and under different thermal environments. The loss in column efficiency is particularly important when the column wall is kept at constant temperature, by immersing the column in a water bath.     

Prediction of the influence of the heat generated by viscous friction on the efficiency of chromatography columns

The combination of the heat balance in a chromatographic column percolated by a stream of mobile phase and of the model of band migration under linear conditions along such a column permits the calculation of the axial and radial temperature distributions in the column, of the elution band profiles, and of the column efficiency under different sets of experimental conditions. The calculated results are always consistent with the experimental results published by different groups and often in good quantitative agreement. Minor discrepancies arise from difficulties in deriving precise estimates of the heat transfers from the column due to the massive endfittings of the column and to uncontrolled heat transfer from the column tube to ambient air.     

Numerical modeling of elution peak profiles in supercritical fluid chromatography. Part I—Elution of an unretained tracer

When chromatography is carried out with high-density carbon dioxide as the main component of the mobile phase (a method generally known as “supercritical fluid chromatography” or SFC), the required pressure gradient along the column is moderate. However, this mobile phase is highly compressible and, under certain experimental conditions, its density may decrease significantly along the column. Such an expansion absorbs heat, cooling the column, which absorbs heat from the outside. The resulting heat transfer causes the formation of axial and radial gradients of temperature that may become large under certain conditions. Due to these gradients, the mobile phase velocity and most physico-chemical parameters of the system (viscosity, diffusion coefficients, etc.) are no longer constant throughout the column, resulting in a loss of column efficiency, even at low flow rates. At high flow rates and in serious cases, systematic variations of the retention factors and the separation factors with increasing flow rates and important deformations of the elution profiles of all sample components may occur. The model previously used to account satisfactorily for the effects of the viscous friction heating of the mobile phase in HPLC is adapted here to account for the expansion cooling of the mobile phase in SFC and is applied to the modeling of the elution peak profiles of an unretained compound in SFC. The numerical solution of the combined heat and mass balance equations provides temperature and pressure profiles inside the column, and values of the retention time and efficiency for elution of this unretained compound that are in excellent agreement with independent experimental data.     

Linearized non-equilibrium and non-isothermal two-dimensional model of liquid chromatography for studying thermal effects in cylindrical columns

A non-equilibrium and non-isothermal two-dimensional lumped kinetic model (2?D-LKM) is formulated and analytically solved to study the influence of temperature variations along the axial and radial coordinates of a liquid chromatographic column. The model includes convection-diffusion partial differential equations for mass and energy balances in the mobile phase coupled with differential equations for mass and energy in the stationary phase. The solutions are derived analytically through sequential implementation of finite Hankel and Laplace transformations using the Dirichlet inlet boundary conditions. The coupling between the thermal waves and concentration fronts is demonstrated through numerical simulations and important parameters are recognized that influence the column performance. For a more comprehensive study of the considered model, numerical temporal moments are obtained from the derived solutions. Several case studies are conducted and validity ranges of the derived analytical solutions are identified. The current analytical results will play a major role in the improvements of non-equilibrium and non-isothermal liquid chromatographic processes.     

Measurement of the axial and radial temperature profiles of a chromatographic column. Influence of thermal insulation on column efficiency

The temperatures of the metal wall along a chromatographic column (longitudinal temperature gradients) and of the liquid phase across the outlet section of the column (radial temperature gradients) were measured at different flow rates with the same chromatographic column (250 mm x 4.6 mm). The column was packed with 5 microm C18-bonded silica particles. The measurements were carried out with surface and immersion thermocouples (all junction Type T, +/-0.1 K) that measure the local temperature. The column was either left in a still-air bath (ambient temperature, T(ext) = 295-296 K) or insulated in a packing foam to avoid air convection around its surface. The temperature profiles were measured at several values of the inlet pressure (approximately = 100, 200, 300 and 350 bar) and with two mobile phases, pure methanol and a 2.5:97.5 (v/v, %) methanol:water solution. The experimental results show that the longitudinal temperature gradients never exceeded 8 K for a pressure drop of 350 bars. In the presence of the insulating foam, the longitudinal temperature gradients become quasi-linear and the column temperature increases by +1 and +3 K with a water-rich (heat conductivity approximately = 0.6 W/m/K) and pure methanol (heat conductivity approximately = 0.2 W/m/K), respectively. The radial temperature gradients are maximum with methanol (+1.5 K at 290 bar inlet pressure) and minimum with water (+0.8 K at 290 bar), as predicted by the solution of the heat transfer balance in a chromatographic column. The profile remains parabolic all along the column. Combining the results of these measurements (determination of the boundary conditions on the wall, at column inlet and at column outlet) with calculations using a realistic model of heat dispersion in a porous medium, the temperature inside the column could be assessed for any radial and axial position.     

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.     

Effects of thermal heterogeneity in hydrophobic interaction chromatography

Manipulating temperature and salt concentration can have a powerful effect on the separation effectiveness in hydrophobic interaction chromatography (HIC). However, use of temperature as an operating variable in large-scale applications may involve undesirable consequences such as radial heterogeneity of the column temperature. In this study non-ideal effects of heat transfer in HIC columns were analyzed. The radial temperature gradients were measured by thermocouples immersed in a bed packed into a preparative column. The column wall was either thermostatted by a water jacket or left under ambient conditions. The influence of ineffective column thermostatting and of heat losses on the radial temperature profiles was demonstrated and predicted by a model of heat dispersion in a packed bed. To analyze possible positive or negative effects of thermal heterogeneity on band propagation, non-isothermal chromatographic elution of a model protein (α-chymotrypsinogen A) was recorded under salt gradient conditions as well as at constant salt concentration. To predict temperature and concentration profiles a model of the column dynamics was used. The model accounted for kinetics of mass and heat transfer. A good agreement between experimental and simulated profiles was achieved. It was shown that by proper selection of the process conditions undesirable temperature effects can be avoided or controlled.     

Efficiency for unretained solutes in packed column supercritical fluid chromatography II. Experimental results for elution of methane using large pressure drops

At near-critical temperatures and pressures, experimental results for elution of methane with neat carbon dioxide on a 150 mm x 2.0 mm I.D. column packed with 5 microm porous silica with a bonded octylsilica stationary phase show much greater efficiency losses than predicted by theory if isothermal conditions are assumed. Experiments with insulated, air- and water-thermostatted columns demonstrate that significant axial and radial temperature gradients are produced by Joule-Thomson cooling of the mobile phase, and that radial temperature gradients can be a major cause of band spreading at low temperatures and pressures. The use of thermal insulation on the column can greatly improve efficiency under these conditions.     

CEC with monolithic poly(styrene-divinylbenzene-vinylsulfonic acid) as the stationary phase

In this study, poly(styrene-divinylbenzene-vinylsulfonic acid) monolithic columns, prepared by singlestep in situ polymerization, were first used as separation columns for CEC in which vinylsulfonic acid was employed as the charge-bearing monomer. The effects of the polymerization conditions (compositions of monomer and porogenic solvent, and polymerization time) on the chromatographic property of the polystyrene-based monolithic column were examined. Furthermore, an increase in water content of the porogenic solvent markedly altered the retention behaviors of these analytes, where the monolithic column was able to be produced in a higher ratio of vinylsulfonic acid. Finally, the study demonstrated that acidic analytes could be successfully separated by the polystyrene-based monolithic column under an acidic mobile phase.     

Column radial homogeneity in high-performance liquid chromatography

The radial distribution of analyte molecules within an elution band in HPLC was determined by local, on-column, fluorescence detection at the column outlet. Several optical fiber assemblies were implanted in the exit frit at different points over the column cross-section and the fluorescence of a laser-dye analyte was measured. The individual elements of a diode array were used as independent detectors. The distribution of the mobile phase velocity across the column was measured for a number of standard size analytical HPLC columns of different efficiencies, operated at different mobile phase linear velocities. The dependence of the column efficiency on these profiles is discussed.     

Effect of the carrier gas pressure on the dynamic and separation characteristics of divinylbenzene-based monolithic capillary columns for gas chromatography

The efficiency and dynamic characteristics of divinylbenzene-based monolithic capillary columns for gas chromatography were analyzed using a test mixture composed of five light hydrocarbons. The chromatographic properties of these columns were evaluated within the framework of two varieties of the van Deemter equation, the classical one and that proposed by Giddings (with consideration given to the pressure drop across the column). An analysis of the van Deemter curves demonstrated that the main contribution to peak smearing comes from the diffusion processes in the mobile phase. The contribution from the resistance to mass transfer between the mobile and stationary phases is less important. Negative values obtained for A in the van Deemter equation and for C _s in the Giddings model, parameters that characterize the stationary phase structure and mass transfer kinetics in the stationary phase, have no physical meaning, a result calling for further studies of this type of monolithic capillary columns since the classical theory supposed these parameters to be strictly positive. Under optimal conditions, the HETP of the monolithic columns was found to be 3 to 4 times smaller than that typical of open capillary columns of the same diameter.     

A study of the effects of temperature and pressure on the retention time in series-coupled columns under conditions of constant mass flow rate

The technique of controlling chromatographic selectivity by the adjustment of 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. In a previous article the performance of series-coupled columns was investigated under conditions of constant overall pressure drop. The present paper, on the other hand, considers systems in which a constant mass flow rate is maintained at all temperatures. The expressions derived for the effective partition coefficient and the retention time are compared with those of the previous paper. The numerical results for two-column systems exhibit the same major trends as those for constant pressure drop. It is shown that the effective partition coefficient is slightly dependent on the mass flow rate.     

Comparison of different types of stationary phases for the analysis of soy isoflavones by HPLC

Nowadays, there are new technologies in high-performance liquid chromatography columns available enabling faster and more efficient separations. In this work, we compared three different types of columns for the analysis of main soy isoflavones. The evaluated columns were a conventional reverse phase particle column, a fused-core particle column, and a monolithic column. The comparison was in terms of chromatographic parameters such as resolution, asymmetry, number of theoretical plates, variability of retention time, and peak width. The lower column pressure was provided by the monolithic column, although lower chromatographic performance was achieved. Conventional and fused-core particle columns presented similar pressure. Results also indicate that direct transfer between particle and monolithic columns is not possible requiring adjustment of conditions and a different method optimization strategy. The best chromatographic performance and separation speed were observed for the fused-core particle column. Also, the effect of sample solvent on the separation and peak shape was evaluated and indicated that monolithic column is the most affected especially when using higher concentrations of acetonitrile or ethanol. Sample solvent that showed the lowest effect on the chromatographic performance of the columns was methanol. Overall evaluation of methanol and acetonitrile as mobile phase for the separation of isoflavones indicated higher chromatographic performance of acetonitrile, although methanol may be an attractive alternative. Using acetonitrile as mobile phase resulted in faster, higher resolution, narrower, and more symmetric peaks than methanol with all columns. It also generated the lower column pressure and flatter pressure profile due to mobile phase changes, and therefore, it presents a higher potential to be explored for the development of faster separation methods.     

Preparation of a novel carboxyl stationary phase by “thiol‐ene” click chemistry for hydrophilic interaction chromatography

A novel carboxyl‐bonded silica stationary phase was prepared by “thiol‐ene” click chemistry. The resultant Thiol‐Click‐COOH phase was evaluated under hydrophilic interaction liquid chromatography (HILIC) mobile phase conditions. A comparison of the chromatographic performance of Thiol‐Click‐COOH and pure silica columns was performed according to the retention behaviors of analytes and the charged state of the stationary phases. The results indicated that the newly developed Thiol‐Click‐COOH column has a higher surface charge and stronger hydrophilicity than the pure silica column. Furthermore, the chromatographic behaviors of five nucleosides on the Thiol‐Click‐COOH phase were investigated in detail. Finally, a good separation of 13 nucleosides and bases, and four water‐soluble vitamins was achieved.     

Peak tailing and column radial heterogeneity in linear chromatography

The correlation between the radial heterogeneity of a column and the tailing of the elution profiles of chromatographic peaks was studied using a numerical method. A parabolic distribution of the linear flow velocity of the mobile phase and of the column efficiency in the radial direction were assumed. Moment analysis showed that peak tailing takes place under such experimental conditions and that it increases with increasing range of radial variations of the flow velocity and the column efficiency. It was also found that the higher the column efficiency, the larger the effect of a given degree of radial heterogeneity on the extent of peak tailing. Peak tailing behavior of columns having different efficiencies could be correlated with each other by an equation. Some characteristic features of tailing peaks were analyzed in connection with the column radial heterogeneity.     

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.     

Capillary electrochromatography with macroporous particles.

The performance of macro-porous particles in capillary electrochromatography is studied. Three reversed-phase stationary phases with pore diameters between 500 A and 4000 A have been tested for separation efficiency and mobile phase velocity. With these stationary phases, a large portion of the total flow appears to be through the pores of particles, thereby increasing the separation efficiency through a further decrease of the flow inhomogeneity and through enhancement of the mass transfer kinetics. The effects of pore size and mobile phase composition on the plate height and mobile phase velocity have been studied. With increasing buffer concentrations and larger pore diameters, higher mobile phase velocities and higher separation efficiencies have been obtained. Columns packed with 7 microns particles containing pores with a diameter of 4000 A generated up to 430,000 theoretical plates/m for retained compounds. Reduced plate heights as low as 0.34 have been observed, clearly demonstrating that a significant portion of the flow is through the pores. For the particles containing 4000 A pores no minimum was observed in the H-u plot up to linear velocities of 3.3 mm/s, suggesting that the separation efficiency is dominated by axial diffusion. On relatively long (72 cm) columns, efficiencies of up to 230,000 theoretical plates/column have been obtained under non-optimal running conditions. On short (8.3 cm) columns fast separations could be performed with approximately 15,000 theoretical plates generated in less than 30 s.     

Characterization of High‐Pressure Liquid Chromatography Columns using Chromatographic Methods

Abstract

A great variety of columns for liquid chromatography (LC) are available in dimensions ranging from industrial scale to micro‐bore, nano‐bore, and capillary size, and on‐chip columns. The columns may be used in various liquid chromatography modes or in capillary electrochromatography, depending on the support materials and stationary phase chemistry. Every year many new column types are introduced on the market, with improved selectivity and efficiency, long lifetime, and mobile phase compatibility, intended for general use, for liquid chromatography/mass spectrometry (LC/MS) applications, proteomic research, or for the analysis of other specific sample types. Considerable improvement in pH, high‐temperature, and high‐pressure stability of new column types, together with advances in the instrumentation, enabled introduction of capillary, high‐temperature, and ultra‐high‐pressure HPLC into routine practice. Even though reversed‐phase mode is still by the most widely used in contemporary LC, applications of other separation modes (such as ion, normal‐phase, or high‐interaction liquid chromatography (HILC)) have become more frequent recently, because of unique separation selectivity for certain sample types.

Characterization of column quality is not a simple task, because a number of factors should be taken into account, that affect the selectivity, efficiency and resolution of sample separation and the reproducibility of chromatographic data. These include the type of the support, the arrangement and density of the stationary phase on the adsorbent surface, the homogeneity of the chromatographic bed, etc. Various physicochemical techniques are used for characterization of the properties of column packings however, most of them are suitable for bulk materials only and cannot be directly applied for commercial columns without damaging them. Not to destroy the columns, often precious and expensive, practicing chromatographers can apply chromatographic methods to characterize columns and evaluate their analytical suitability under real‐life conditions, where the intermolecular interactions between the analytes, the stationary phase, and the mobile phases affect the retention. The present review reports various chromatographic tests and strategies available for column evaluation.     

Comparison of the chromatographic behavior of tricyclic neuroleptics on calixarene-bonded, monolithic and conventional RP-HPLC columns

The effect of different chromatographic conditions, such as buffer concentration and type of organic modifier, on the retention behavior of nine tricyclic neuroleptics on three different RP-HPLC columns was investigated. Two recently developed columns, calixarene-bonded (CALTREX) AIII) and monolithic (Chromolith) Performance RP-18e) columns, were compared with a conventional RP-C18 HPLC column (LiChrospher). The results showed how the mobile phase conditions had different effects on the analyte retention on these three columns. For example, the elution order of some analytes and the initiation of separation of the geometric isomers of the three analytes--which have E/Z-isomers (cis/trans-isomers)--could be altered by changing the conditions and the column type. Under identical conditions, a calixarene-bonded phase was the best for this separation, a monolithic phase gave comparable results and the conventional RP-column was the least effective. Concerning the geometric isomers separation, the Chromolith Performance RP-18e was superior.