Van Deemter Equation

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Chi Ruan - One of the best experts on this subject based on the ideXlab platform.

  • optimisation of mass transfer in column elution of rare earths from low grade weathered crust elution deposited rare earth ore
    Hydrometallurgy, 2010
    Co-Authors: Yin Jingqun, Chen Kaihong, Rao Guohua, Jiang Mintao, Chi Ruan
    Abstract:

    An investigation was carried out to optimize the leaching and mass transfer of rare earth metals with ammonium sulfate solution during the column elution of a low grade weathered crust elution-deposited rare earth ore. The effects of flow rate, concentration of leach reagent and ore grade on the leaching performance were examined. The experimental data was analyzed using chromatographic non-equilibrium plate theory in order to elucidate the mass transfer phenomena. It was found that the relationship between the height equivalent to a theoretical plate (HETP) and the leaching flow rate can be described by the Van Deemter Equation and there is an optimum flow rate in the leaching process. Compared with similar higher grade ores which have a sharp peak followed by a short tail, the leach curve of low grade ores has a long tail following a broader peak.

A. A. Kurganov - One of the best experts on this subject based on the ideXlab platform.

  • Impact of a pressure drop on a monolithic capillary column on the efficiency and separation ability of the column
    Russian Journal of Physical Chemistry A, 2011
    Co-Authors: V. E. Shiryaeva, A. A. Korolev, T. P. Popova, A. A. Kurganov
    Abstract:

    The impact of inlet and outlet column pressures on column separation properties was investigated for monolithic capillary column in gas chromatography. It was demonstrated that the classical Van Deemter Equation does not allow us to make a clear choice of the optimal separation conditions. More releVant data can be obtained from the dependence of the height equivalent to a theoretical plate (HETP) on the inlet and outlet column pressures. The dependence ensures that the minimum HETP value can be achieved at high values of inlet and outlet column pressures, but the ratio of the pressures must approach 1. The efficiency of the column under these optimal conditions can exceed by 25–35% the column efficiency under the optimal conditions found using the classical Van Deemter plot. It was shown that a decrease in inlet and outlet column pressures even at a relative pressure close to 1 leads to an increase in HETP and the loss of column separation ability.

  • Porous structure of the monolithic sorbent and separation properties of monolithic capillary columns in gas and liquid chromatography
    Russian Chemical Bulletin, 2010
    Co-Authors: A. A. Korolev, V. E. Shiryaeva, T. P. Popova, E. N. Viktorova, A. A. Kurganov
    Abstract:

    Macroporous polymer based on polydivinylbenzene was used for the preparation of monolithic capillary columns with the diameter from 0.01 to 0.53 mm for separations by gas and liquid chromatography. The separation properties of the columns were studied by analysis of model systems of aromatic (in liquid chromatography) and light (in gas chromatography) hydrocarbons. The permeability was determined and the C parameter of the Van-Deemter Equation was found for each column. The permeability of the majority of columns determined by gas chromatography is independent of the column diameter. The permeability of the same columns in liquid chromatography is also almost constant for the columns 0.53–0.1 mm in diameter; however, the permeability decreases sharply on going to columns of smaller diameter. In gas chromatography the value of the C parameter reflecting the effect of the mass transfer of the sorbate between the mobile and stationary phases on the smearing of a chromatographic peak in the column approximately the same for all columns. In liquid chromatography the value of the C coefficient in the Van-Deemter Equation for the same capillary columns changes with a change in the column diameter and reaches a minimum for the columns 0.1 mm in diameter. The differences observed for the characteristics of the columns in gas and liquid chromatography are due to different structures of the macroporous monolith formed in columns of different diameter and to the effect of solvation of the monolith by the mobile phase under the conditions of liquid chromatography.

  • Influence of the diameter of monolithic capillary columns on their gas chromatography characteristics
    Russian Journal of Physical Chemistry A, 2010
    Co-Authors: A. A. Korolev, V. E. Shiryaeva, T. P. Popova, E. N. Viktorova, A. A. Kurganov
    Abstract:

    Divinylbenzene polymer monolithic capillary columns were prepared on the basis of capillaries 0.01 to 0.53 mm in diameter. Separation properties of the columns were investigated with the use of a test mixture of light hydrocarbons. The permeability and C parameter in the Van Deemter Equation were determined for all the columns. For the most part, the columns had similar characteristics: permeability was in the range (2.2 ± 0.2) × 10^−9 cm^2, with parameter C in the range (0.7 ± 0.2) × 10^−3 s (with n -butane as a sorbate). It was thus established that capillary diameter has only a slight effect on the efficiency of monolithic capillary columns (unlike packed capillary columns and microcolumns, whose properties, according to the literature data, depend strongly on the column diameter). The difference in properties between the narrowest monolithic column (capillary diameter 0.01 mm) and the others is explained by column overloading.

  • The influence of pressure on the separating properties of columns in gas chromatography
    Russian Journal of Physical Chemistry A, 2010
    Co-Authors: A. A. Korolev, V. E. Shiryaeva, T. P. Popova, A. A. Kurganov
    Abstract:

    The Giddings model taking into account the dependence of the coefficients of the Van Deemter Equation on pressure was used to study changes in the efficiency of a hollow capillary column as the inlet and outlet carrier gas pressures changed. The observed dependence of height equivalent to a theoretical plate (HETP) in the coordinates of inlet and outlet pressures can be approximated by a surface having the shape of a folded sheet of paper, when minimum HETP values are situated along the bend line. Any surface section is actually a Van Deemter curve in the corresponding coordinates. The dependence of the minimum HETP on inlet and outlet pressures, which determines the optimum parameters of column service, is of the greatest interest. It was shown that, over the range of pressures studied, the minimum HETP should monotonically decrease as the pressure increases. Experimental model verification showed close correspondence between the inlet and outlet pressures and the values predicted by the model. At the same time, the experimentally found improvement of the efficiency of the column was smaller than that predicted theoretically. Possible reasons for the discrepancy between theory and experiment are considered.

  • Effect of the carrier gas pressure on the dynamic and separation characteristics of divinylbenzene-based monolithic capillary columns for gas chromatography
    Russian Journal of Physical Chemistry A, 2007
    Co-Authors: A. V. Kozin, A. A. Korolev, V. E. Shiryaeva, T. P. Popova, A. A. Kurganov
    Abstract:

    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.

Jonathan J Schroden - One of the best experts on this subject based on the ideXlab platform.

  • effects of pressure drop particle size and thermal conditions on retention and efficiency in supercritical fluid chromatography
    Journal of Chromatography A, 2009
    Co-Authors: Jonathan J Schroden
    Abstract:

    Abstract The effects of particle size and thermal insulation on retention and efficiency in packed-column supercritical fluid chromatography with large pressure drops are described for the separation of a series of model n-alkane solutes. The columns were 2.0 mm i.d. × 150 mm long and were packed with 3, 5, or 10-μm porous octylsilica particles. Separations were performed with pure carbon dioxide at 50 °C at average mobile phase densities of 0.47 g/mL (107 bar) and 0.70 g/mL (151 bar). The three principal causes of band broadening were the normal dispersion processes described by the Van Deemter Equation, changes in the retention factor due to the axial density gradient, and radial temperature gradients associated with expansion of the mobile phase. At the lower density the use of thermal insulation resulted in significant improvements in efficiency and decreased retention times at large pressure drops. The effects are attributed to the elimination of radial temperature gradients and the concurrent enhancement of the axial temperature gradient. Thermal insulation had no significant effect on chromatographic performance at the higher density. A simple expression to predict the onset of excess efficiency loss due to the radial temperature gradient is proposed.

A. A. Korolev - One of the best experts on this subject based on the ideXlab platform.

  • Impact of a pressure drop on a monolithic capillary column on the efficiency and separation ability of the column
    Russian Journal of Physical Chemistry A, 2011
    Co-Authors: V. E. Shiryaeva, A. A. Korolev, T. P. Popova, A. A. Kurganov
    Abstract:

    The impact of inlet and outlet column pressures on column separation properties was investigated for monolithic capillary column in gas chromatography. It was demonstrated that the classical Van Deemter Equation does not allow us to make a clear choice of the optimal separation conditions. More releVant data can be obtained from the dependence of the height equivalent to a theoretical plate (HETP) on the inlet and outlet column pressures. The dependence ensures that the minimum HETP value can be achieved at high values of inlet and outlet column pressures, but the ratio of the pressures must approach 1. The efficiency of the column under these optimal conditions can exceed by 25–35% the column efficiency under the optimal conditions found using the classical Van Deemter plot. It was shown that a decrease in inlet and outlet column pressures even at a relative pressure close to 1 leads to an increase in HETP and the loss of column separation ability.

  • Porous structure of the monolithic sorbent and separation properties of monolithic capillary columns in gas and liquid chromatography
    Russian Chemical Bulletin, 2010
    Co-Authors: A. A. Korolev, V. E. Shiryaeva, T. P. Popova, E. N. Viktorova, A. A. Kurganov
    Abstract:

    Macroporous polymer based on polydivinylbenzene was used for the preparation of monolithic capillary columns with the diameter from 0.01 to 0.53 mm for separations by gas and liquid chromatography. The separation properties of the columns were studied by analysis of model systems of aromatic (in liquid chromatography) and light (in gas chromatography) hydrocarbons. The permeability was determined and the C parameter of the Van-Deemter Equation was found for each column. The permeability of the majority of columns determined by gas chromatography is independent of the column diameter. The permeability of the same columns in liquid chromatography is also almost constant for the columns 0.53–0.1 mm in diameter; however, the permeability decreases sharply on going to columns of smaller diameter. In gas chromatography the value of the C parameter reflecting the effect of the mass transfer of the sorbate between the mobile and stationary phases on the smearing of a chromatographic peak in the column approximately the same for all columns. In liquid chromatography the value of the C coefficient in the Van-Deemter Equation for the same capillary columns changes with a change in the column diameter and reaches a minimum for the columns 0.1 mm in diameter. The differences observed for the characteristics of the columns in gas and liquid chromatography are due to different structures of the macroporous monolith formed in columns of different diameter and to the effect of solvation of the monolith by the mobile phase under the conditions of liquid chromatography.

  • Influence of the diameter of monolithic capillary columns on their gas chromatography characteristics
    Russian Journal of Physical Chemistry A, 2010
    Co-Authors: A. A. Korolev, V. E. Shiryaeva, T. P. Popova, E. N. Viktorova, A. A. Kurganov
    Abstract:

    Divinylbenzene polymer monolithic capillary columns were prepared on the basis of capillaries 0.01 to 0.53 mm in diameter. Separation properties of the columns were investigated with the use of a test mixture of light hydrocarbons. The permeability and C parameter in the Van Deemter Equation were determined for all the columns. For the most part, the columns had similar characteristics: permeability was in the range (2.2 ± 0.2) × 10^−9 cm^2, with parameter C in the range (0.7 ± 0.2) × 10^−3 s (with n -butane as a sorbate). It was thus established that capillary diameter has only a slight effect on the efficiency of monolithic capillary columns (unlike packed capillary columns and microcolumns, whose properties, according to the literature data, depend strongly on the column diameter). The difference in properties between the narrowest monolithic column (capillary diameter 0.01 mm) and the others is explained by column overloading.

  • The influence of pressure on the separating properties of columns in gas chromatography
    Russian Journal of Physical Chemistry A, 2010
    Co-Authors: A. A. Korolev, V. E. Shiryaeva, T. P. Popova, A. A. Kurganov
    Abstract:

    The Giddings model taking into account the dependence of the coefficients of the Van Deemter Equation on pressure was used to study changes in the efficiency of a hollow capillary column as the inlet and outlet carrier gas pressures changed. The observed dependence of height equivalent to a theoretical plate (HETP) in the coordinates of inlet and outlet pressures can be approximated by a surface having the shape of a folded sheet of paper, when minimum HETP values are situated along the bend line. Any surface section is actually a Van Deemter curve in the corresponding coordinates. The dependence of the minimum HETP on inlet and outlet pressures, which determines the optimum parameters of column service, is of the greatest interest. It was shown that, over the range of pressures studied, the minimum HETP should monotonically decrease as the pressure increases. Experimental model verification showed close correspondence between the inlet and outlet pressures and the values predicted by the model. At the same time, the experimentally found improvement of the efficiency of the column was smaller than that predicted theoretically. Possible reasons for the discrepancy between theory and experiment are considered.

  • Effect of the carrier gas pressure on the dynamic and separation characteristics of divinylbenzene-based monolithic capillary columns for gas chromatography
    Russian Journal of Physical Chemistry A, 2007
    Co-Authors: A. V. Kozin, A. A. Korolev, V. E. Shiryaeva, T. P. Popova, A. A. Kurganov
    Abstract:

    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.

Georges Guiochon - One of the best experts on this subject based on the ideXlab platform.

  • The Van Deemter Equation: Assumptions, limits, and adjustment to modern high performance liquid chromatography
    Journal of Chromatography A, 2013
    Co-Authors: Fabrice Gritti, Georges Guiochon
    Abstract:

    The fundamental assumptions of the Van Deemter height equivalent to a theoretical plate (HETP) Equation were formulated nearly 60 years ago in its rigorous final mathematical derivation in 1956. The limit of applicability of this classical theory of band broadening in chromatographic columns is discussed on the basis of accurate measurements of diffusion coefficients (in the bulk, in particles, and in column beds), of peak moments in both RPLC and HILIC, on the recent numerical solution of the Navier-Stokes Equation and on the results of the simulation of the advection-diffusion transport in the bulk region of computer-generated random packed beds. A result of this discussion is that serious errors are made in the interpretations of the mass transfer mechanism in HILIC and RPLC that are based on the use of the original Van Deemter expressions of the longitudinal diffusion coefficient through packed bed, of the mass transfer resistance in the mobile phase, and of the mass transfer resistance in the stationary phase. These errors are discussed and quantitatively assessed. Physically acceptable and releVant expressions are proposed to account for the true mass transfer mechanism in packed columns.

  • Mass transfer mechanism in liquid chromatography columns packed with shell particles: would there be an optimum shell structure?
    Journal of Chromatography A, 2010
    Co-Authors: Fabrice Gritti, Georges Guiochon
    Abstract:

    Abstract The mass transfer mechanisms in columns packed with old (55 μm Zipax and 5 μm Poroshell) and recently commercialized shell particles (2.7 μm Halo-C 18 and Kinetex-C 18 ) were investigated from a physico-chemical point of view. Combining a model of diffusion in heterogeneous packed beds (effective medium theory) with values of the heights equivalent to a theoretical plate (HETPs derived from the first and second central moments of the elution profiles) and of the peak variances provided by the peak parking method, we demonstrate that columns packed with current shell particles perform better than those packed with fully porous particles in resolving low molecular weight compounds because the eddy diffusion term of the Van Deemter Equation of the former is markedly smaller. The calculation of eddy diffusion in column beds suggests that the smaller A terms are due to smaller trans-column velocity bias in columns packed with shell particles. We also show that the mass transfer of large molecules (e.g., proteins) is faster when the internal volume accessible to the analyte increases. Therefore, it is suggested that shell particles made of concentric layers with average pore sizes increasing with increasing diameter would provide columns with higher efficiency.

  • Moment analysis of mass-transfer kinetics in C18-silica monolithic columns.
    Analytical Chemistry, 2003
    Co-Authors: Kanji Miyabe, Marianna Kele, Fabrice Gritti, Alberto Cavazzini, Georges Guiochon
    Abstract:

    The moment analysis of elution peak profiles based on new moment Equations provides information on the mass-transfer characteristics of C18-silica monolithic columns. The flow rate dependence of the HETP data was analyzed using the generalized Van Deemter Equation, after correction of these data by subtraction of the external mass-transfer contribution to band broadening. Kinetic parameters and diffusion coefficients related to the mass-transfer processes in monolithic columns were derived by taking adVantage of the different flow velocity dependence of their contributions to band broadening. At high flow rates, axial dispersion and diffusive migration across the monolithic C18-silica skeleton contribute much to band broadening, suggesting that it remains important to reduce the influence of eddy diffusion and the mass-transfer resistance in the stationary phase to achieve fast separations and a high efficiency. Surface diffusion plays a predominant role for molecular migration in the monolithic stationar...

  • Detailed study of the mass transfer kinetics of Tröger's base on cellulose triacetate
    Journal of Chromatography A, 1998
    Co-Authors: Preshious Rearden, Peter Sajonz, Georges Guiochon
    Abstract:

    Abstract The adsorption isotherm of S -Troger's base on microcrystalline cellulose triacetate was measured by frontal analysis at several flow-rates between 0.2 and 1.2 ml/min. Two chromatographic models were used in order to study the kinetics of mass transfer between the two phases and to derive plate height values, the equilibrium–dispersive model and the transport model of chromatography. The dependence of the plate height on the flow velocity and on the solute concentration was studied. A modified Van Deemter Equation was used to separate the contributions due to slow mass transfer and to axial dispersion.