Deemter Research Articles

VAN DEEMTER PLOT IN HIGH-SPEED COUNTERCURRENT CHROMATOGRAPHY WITH A FIXED VOLUME OF STATIONARY PHASE

An adaptability of countercurrent chromatographic data to Van Deemter equation (H = A + B/u + Cu) is examined under a fixed volume of the stationary phase. Three test samples, epigallochatechin gallate (EGCG), gallocatechin-gallate (GCG), and epicatechin gallate (ECG) were separated using a two-phase solvent system of n-hexane/ethyl acetate/water (3.5:1:10, v/v/v) at various linear flow rates (u). Our mathematical treatment produced a set of formulae, HEGCG = 6.5 + 1/u + 6u; HGCG = 6.5 + 1.3/u + 7u; and HECG = 6.5 + 2.5/u + 9u, which showed excellent fit to the experimental data for each component. Constants B and C show high correlation with the partition coefficient values of three components. Based on the high correlation between log u and log H when u > 1, the plate height (H) for three components may be expressed by H = Duk, where D is the plate height at u = 1 cm/s and k, the constant for each component.

A new easy-to-prepare homogeneous continuous electrochromatographic bed for enantiomer recognition.

Completely homogeneous polyacrylamide-based gels were used for capillary electrochromatography (CEC) of drug enantiomers. Like continuous beds (also called continuous polymer rods, silica rods, monoliths) they do not require frits to support the bed because it is covalently linked to the capillary wall. A long lifetime is an important feature of the beds. The gel matrices can be prepared in any laboratory and for specific interactions they can be derivatized with appropriate ligands. The application range is, therefore, broad. For chiral electrochromatography, negatively and positively charged polyacrylamide gels copolymerized with 2-hydroxy-3-allyloxy-propyl-beta-cyclodextrin (allyl-beta-CD) were prepared. The latter monomer was synthesized from beta-CD and allylglycidyl ether by a very simple one-step procedure. Eight acidic, neutral and basic drug compounds were resolved into their enantiomers, most of them with baseline separation. Interestingly, the resolution is independent of the electroendosmotic velocity, i.e., rapid analyses will not give low resolution. Upon increasing this velocity, the plate height for the fast enantiomer did not change (or decreased slightly), whereas that for the slow enantiomer increased. Only the last term in the van Deemter equation contributed significantly to the total plate height. The composition of the gel was chosen such that the "pores" became large enough to guarantee a satisfactory electroendosmotic flow (EOF). This open gel structure explains why acetone diffused as in free solution, i.e., independently of the presence of the gel matrix. This finding also indicates that the separation of small molecules in polyacrylamide gels cannot be explained by "molecular-sieving", but rather by some type of adsorption ("aromatic adsorption"?).

Design and optimisation of a simulated moving bed unit: role of deviations from equilibrium theory

The design of a simulated moving bed involves thermodynamic, kinetic and hydrodynamic aspects and requires the optimisation of several variables: plant design variables, such as the column length and diameter, and operating variables, among them four independent flow-rates, the feed concentration and the switch time. In this work we develop an algorithm to design both the unit and its operating conditions, with an overall view on equilibrium properties, efficiency and hydrodynamics, using a simple equilibrium stage model. In this way we determine the parameters leading to the highest possible productivity for a given separation, only requiring the knowledge of the equilibrium isotherms, the Van Deemter equation and a correlation for pressure drop. The algorithm has been used to investigate the effect on the separation performance of some parameters, such as particle size and required product purity, which are not considered by equilibrium theory. The results have been compared with the predictions of equilibrium theory and the observed deviations have been put in evidence and discussed.

Use of equations for the description of experimental dependence of the height equivalent to a theoretical plate on carrier gas velocity in capillary gas–liquid chromatography

Optimal equation for fitting the experimental data on the height equivalent to a theoretical plate (HETP) versus carrier gas velocity in GLC was determined. The data obtained by authors and the literary data by other investigators were used for the comparative study of Van Deemter, Golay and the little known Golay–Guiochon equations. The Golay–Guiochon equation takes into account instrumental contribution and other sources of additional band broadening. Correlation coefficient R and Pirson’s criterion χ 2 were used as a criterion of the data correspondence to the equations. The Golay–Guiochon equation is the best for fitting of the experimental data in 71% considered examples, 19% experimental data may be fitted very precisely by the Van Deemter equation, the Golay equation is preferable for 7% experimental data only. Three percent experimental data may be fitted with the same precision by the Golay and the Van Deemter equations. The results obtained are of theoretical and practical interest. The Golay–Guiochon equation must be used more widely in analytical practice and physicochemical measurements.

Performance of a monolithic silica column in a capillary under pressure-driven and electrodriven conditions

A continuous macroporous silica gel network was prepared in a fused-silica capillary and evaluated in reversed-phase liquid chromatography. Under pressure-driven conditions, the monolithic silica column derivatized to C18 phase (100 microns in diameter, 25 cm in length, silica skeleton size of approximately 2.2 microns) produced plate heights of about 23 and 81 microns at 0.5 mm/s with a pressure drop of 0.4 kg/cm2, and at 4.0 mm/s with 3.6 kg/cm2, respectively, in 90% acetonitrile for hexylbenzene with a k value of 0.7. The separation impedance, E, calculated for the present monolithic silica column was much smaller at a low flow rate than those for particle-packed columns, although higher E values were obtained at a higher flow rate. Considerable dependence of column efficiency on the linear velocity of the mobile phase was observed despite the small size of the silica skeletons. A major source of band broadening in the HPLC mode was found in the A term of the van Deemter equation. The performance of the continuous silica capillary column in the electrodriven mode was much better than that in the pressure-driven mode. Plate heights of 7-8 microns were obtained for alkylbenzenes at 0.7-1.3 mm/s, although the electroosmotic flow was slow. In HPLC and CEC mode, the dependency of plate height on k values of the solutes was observed as seen in open tube chromatography presumably due to the contribution of the large through-pores. Since monolithic silica capillary columns can provide high permeability, the pressure-driven operation at a very low pressure can afford a separation speed similar to CEC at a high electric field.

Preparation and Chromatographic Application of Macroporous Silicate in a Capillary

Continuous macroporous silica gel networks were prepared in a fused silica capillary, and evaluated in reversed-phase liquid chromatography. Under pressure-driven conditions, considerable dependence of column efficiency on the linear velocity of the mobile phase was observed in spite of the small size of the silica skeletons. A major source of band broadening in the pressure-driven mode was found in the A-term of van Deemter equation. The performance of the continuous silica capillary column in the electro-driven mode was much better than that in the pressure-driven mode.

Capillary columns with in situ formed porous monolithic packing for micro high-performance liquid chromatography and capillary electrochromatography

Capillary columns with monolithic stationary phase were prepared from silanized fused-silica capillaries of 75 μm I.D. by in situ copolymerization of divinylbenzene either with styrene or vinylbenzyl chloride in the presence of a suitable porogen. The porous monolithic support in this study was used either directly or upon functionalization of the surface to obtain a stationary phase that was appropriate for the separation of peptides by capillary electrochromatography (CEC). The main advantages of monolithic columns are as follows. They do not need retaining frits, they do not have charged particles that can get dislodged in high electric field, and they have relatively high permeability and stability. Whereas such columns are designed especially for CEC, they find application in micro high-performance liquid chromatography (μ-HPLC) as well. Five different porogens were employed to prepare the monolithic columns that were examined for permeability and porosity. The flexibility of fused-silica capillaries was not adversely affected by the monolithic packing and the longevity of the columns was satisfactory. This may also be due to the polymerization technique, which resulted in a fluid-impervious outer layer of the monolith that precluded contact between the fused-silica surface and the liquid mobile phase. For the most promising columns, the conductivity ratios and the parameters of the simplified van Deemter equation, both in μ-HPLC and CEC, were evaluated. It was found that the efficiency of the monolithic columns in CEC was significantly higher than in μ-HPLC in the same way as observed with capillary columns having conventional particulate packing. This is attributed to the relaxation of band-broadening with electroosmotic flow (EOF) with respect to that with viscous flow. It follows then that the requirement of high packing uniformity to obtain high efficiency may also be relaxed in CEC. Angiotensin-type peptides were separated by CEC with columns packed with a monolithic stationary phase having fixed n-octyl chains and quaternary ammonium groups at the surface. Plate heights of about 8 μm were routinely obtained. The mechanism of the separation is based on the interplay between EOF, chromatographic retention and electrophoretic migration of the positively charged peptides. The results of the complex migration process, with highly nonlinear dependence of the migration times on the organic modifier and the salt concentration, cannot be interpreted within the framework of classical chromatography or electrophoresis.

Dynamics of capillary electrochromatography: II. Comparison of column efficiency parameters in microscale high-performance liquid chromatography and capillary electrochromatography

In capillary electrochromatography (CEC) the flow of the mobile phase is generated by electrosmotic means in high electric field. This work compares band spreading measured experimentally in several packed capillaries with electrosmotic flow (EOF) and viscous flow under otherwise identical conditions. The data were fitted to the simplified van Deemter equation for the theoretical plate height, H= A+ B/ u+ Cu, in order to evaluate parameters A and C in each mode of flow in the different columns. The ratio of these two parameters obtained with the same column in microscale HPLC (μ-HPLC) and CEC was used to quantify the attenuation of their contribution to band spreading upon changing from viscous flow (in μ-HPLC) to electrosmotic flow (in CEC). The capillary columns used in this study were packed with stationary phases of different pore sizes as well as retentive properties and measurements were carried out under different mobile phase conditions to examine the effects of the retention factor and buffer concentration. In the CEC mode, the value of both column parameters A and C was invariably by a factor of two to four lower than in the μ-HPLC mode. This effect may be attributed to the peculiarities of the EOF flow profile in the interstitial space and to the generation of intraparticle EOF inside the porous particles of the column packing. Thus, band spreading due to flow maldistribution and mass transfer resistances is significantly lower when the mobile phase flow is driven by voltage as in CEC, rather than by pressure as in μ-HPLC.

Detailed study of the mass transfer kinetics of Tröger's base on cellulose triacetate

The adsorption isotherm of S-Tröger'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.

Comparison of diffusion and diffusion–convection matrices for use in ion-exchange separations of proteins

A comprehensive study has been undertaken to characterise a range of chromatographic properties for a series of modified polystyrene–divinylbenzene (PS–DVB) chromatography matrices. The matrices studied included diffusion matrices and matrices that allowed convective mass transfer of liquid into the particles at high flow-rates, so-called “perfusion” matrices. The matrices tested included the following: CG1000sd 20–50 μm (TosoHaas), PLRP4000s 15–25 μm, 50–70 μm (Polymer Labs.), Source 15RPC and 30RPC, 15S, 30S, (Pharmacia Biotech), POROS 20SP type 1 matrix and OH activated POROS 20 type 2 matrix (PerSeptive Biosystems) and SP Sepharose Fast Flow (Pharmacia Biotech). A Van Deemter equation was used to determine bead tortuosities and split ratios. Frontal analysis, resolution studies, ionic capacities and isotherms were measured. It was found that diffusion–convection chromatographic particles had smaller plate heights to comparable diffusion particles. The smallest diffusion bead, Source 15, had the lowest plate heights at low superficial velocities, but the small particle size resulted in a high back pressure at high flow-rates. The equilibrium binding capacities for lysozyme and IgG on the diffusion–convection matrices were substantially lower than the equilibrium binding capacities on the diffusion matrices. The dynamic capacities for these proteins were also lower on the diffusion–convection particles, compared to the diffusion particles, over the tested flow-rates. At high protein loading, resolution between proteins was higher on diffusion particles than on diffusion–convection particles. Diffusion–convection particles showed low or no resolution at high protein loading. At analytical level loadings, the diffusion–convection particles achieved a high resolution over the whole flow-rate range tested and were more suitable for this application than diffusion particles.

An approximate expression for the minimum plate height produced by Knox's equation

The van Deemter (h=A+B/v+Cv) and the Knox equations (h=av1/3+b/v+cv) are the most widely accepted equations for describing the dependence of the plate height on mobile phase linear velocity. The simple form of the analytical solution for the minimum plate height obtained from van Deemter's equation allows one to locate the optimum velocity and minimum plate height and to obtain insight into the contribution of A, B, and C terms to the minimum plate height. Although Knox's equation provides better fit s to liquid chromatography data than van Deemter's equation, the exact solution of the minimum plate height based on Knox equation is too complicated to be informative. In this work, we describe a simple approach to estimating the minimum plate height based on Knox's equation. For typical HPLC conditions, the relative error of the estimates is generally less than 3%. The approximate analytical solution for the minimum plate height based on Knox's equation indicates the important contribution of the column packing term to the minimum plate height. © 1998 John Wiley & Sons, Inc. J Micro Sep10: 149–152, 1998

Theory of fast capillary gas chromatography. Part 1: Column efficiency

AbstractTypically, fast GC requires high column pressure drop. Under that condition, known relations do not provide a complete description of dependence of [apparent] plate height, ĥ, on average velocity, u, of carrier gas.A complete descriptions for ĥ vs. u is derived and analyzed. It is shown that, under the high pressure drop, ĥ = B/u2 + C1 u2 + C2 u. This is substantially different from the Van Deemter equation ĥ = B/u + Cu for the low pressure drop. Analytical expressions for the minimum plate height and for the respective optimum u under the high pressure drop are derived and analyzed.

Permeable packings and perfusion chromatography in protein separation

The use of permeable packings in perfusion chromatography for protein separation is reviewed. Mass transport mechanisms in large-pore materials include forced convection in addition to diffusive transport. The key concept in perfusion chromatography is the “augmented” diffusivity by convection which explains the improved efficiency of perfusive packings compared with conventional supports. An extended Van Deemter equation has t be appplied when calculating the height equivalent to a theoretical plate (HETP) of chromatographic columns with flow-through particles. It is shown that the effect of forced convective flow in pores is to drive the separation performance between diffusion-controlled and equilibrium limits. A methodology to understand mass transfer mechanisms in permeable packings is proposed. Experimental results for protein separation by high-performance liquid chromatography in new packing media are discussed. Simulated moving bed technology is addressed.

Stochastic theory of two-site adsorption chromatography by the characteristic function method

The problem of two-site adsorption chromatography under linear conditions is considered by using the molecular dynamic theory of chromatography originally developed by Giddings and Eyring. The probabilistic description is made by using the characteristic function method, and the solution is obtained under the most general conditions of both stationary phase entry process and site desorption process. Relevant chromatographic attributes such as the C term of van Deemter equation and the peak skewness and excess are investigated with reference to column heterogeneity. © 1997 John Wiley & Sons, Inc. J Micro Sep 9: 295–302, 1997

Elevated temperature liquid chromatography using reversed-phase packed capillary columns

Reversed-phase packed capillary column liquid chromatography (LC) was investigated at column temperatures of 24°C, 40°C, 60°C, and 80°C. For a mixed mobile phase containing acetonitrile and water (72:28, v/v), the viscosity of the mobile phase decreased 2.2 times and the diffusion rate of the solute increased 2.6 times in the range of temperatures investigated. The faster diffusion rate of naphthalene in the mobile phase at 80°C resulted in a 2.6-fold faster optimum linear velocity and a 2.5-fold decrease in the C term of the van Deemter equation compared to values obtained at 24°C. Better efficiencies were obtained at faster than optimum linear velocities at elevated temperatures, while at the same time retention times were much shorter than at room temperature. It was also found that temperature could have a better or worse effect on selectivity, depending on the retention factors, enthalpies, and entropies of the compounds analyzed. The pressure drop decreased by one half at an elevated temperature of 80°C compared with that at room temperature for the mobile phase investigated. It is estimated that smaller particles or longer columns could be used at elevated temperatures in an LC system to obtain even higher total plate numbers. © 1997 John Wiley & Sons, Inc. J. Micro Sep 9: 63–72, 1997

Stochastic theory of two‐site adsorption chromatography by the characteristic function method

The problem of two-site adsorption chromatography under linear conditions is considered by using the molecular dynamic theory of chromatography originally developed by Giddings and Eyring. The probabilistic description is made by using the characteristic function method, and the solution is obtained under the most general conditions of both stationary phase entry process and site desorption process. Relevant chromatographic attributes such as the C term of van Deemter equation and the peak skewness and excess are investigated with reference to column heterogeneity. © 1997 John Wiley & Sons, Inc. J Micro Sep 9: 295–302, 1997

Optimization of the Flow Rate in High Pressure Liquid Chromatography of explosives

AbstractThe height of a theoretical plate of 7 nitroaromatic substances and 2 aliphatic explosives was determined in dependence on the flow rate. The optimal flow rate for the maximum of the number of theoretical plates is in the area of 0.4 to 0.6 ml/min. For difficult separations this should be considered, since most HPLC instruments are used in the area of 0.7 to 1.0 ml/min. The amount of theoretical plates was calculated and presented in dependence of the flow rate. The height of a theoretical plate was plotted against the retention time and the capacity factor. The optimal area for the separation of the substances was at a capacity factor of 2 to 10. The van Deemter equation and the Knox equation were adjusted using 2,4‐dinitrotoluene. The data were fitted iteratively and the constants were determined. The equation for the conversion of the flow rate for other column diameters was shown, and using an example, the dependence of the flow rate on the column inner diameter and the flow rate was presented graphically.

Perfusion chromatography — characterization of column packings for chromatography of proteins

A Van Deemter equation modeling columns packed with spherical monodisperse perfusive media was utilized to calculate the predicted values of the effective pore diffusivity ( D p) and split ratio (α) of columns packed with POROS® and Oligo R3™ media. The validity of the model was established by calculating consistent values of D p and α for lysozyme, α-chymotrypsinogen A and IgG using columns packed with POROS ion-exchange media. The split ratio was shown to be dependent on the pore structure of the media and not the eluite. The technique allows quantitative measurements of α and D p, and is applicable for both perfusive and diffusive media.

Protein separation by liquid chromatography using permeable POROS Q/M particles

Elution chromatography under non-retained conditions and frontal chromatography in retained conditions using various proteins (bovine serum albumin, myoglobin and ovalbumin) and POROS Q/M large-particles (PerSeptive Biosystems, Cambridge, MA, USA) were studied. Elution experiments show that the mass transfer mechanism which allows improved performance of perfusion chromatography is intraparticle convection. Convection enhances intraparticle diffusivity; the concept of “augmented” effective diffusivity was used to explain both peak sharpening and the modified Van Deemter equation for large-pore particles. Experimental adsorption isotherms were measured from experimental breakthrough curves. In the high concentration range (above 1 mg ml −1) the isotherm is rectangular; however, data in the low concentration region show that the Langmuir equation better represents the whole isotherm. A simple fixed-bed model based on a rectangular adsorption isotherm was used in the simulation of breakthrough curves and augmented effective diffusivities were calculated. The dependence of the augmented effective diffusivity on the superficial velocity agrees well with the relationship derived by Rodrigues et al. (A.E. Rodrigues, B. Ahn and A. Zoulalian, AIChE J., 28 (1982) 541). Similar results were obtained by using the Langmuir isotherm in a more detailed modelling of the chromatographic column.

Performance of a parallel passage adsorbent contactor

Results of an experimental and theoretical study of a parallel passage adsorbent contactor are reported. Theoretical considerations suggest that such an adsorber should be preferable to the traditional packed bed for applications in which pressure drop is important. An expression for the HETP (height equivalent to a theoretical plate) for a parallel passage contactor, analogous to the van Deemter equation for the packed bed, is derived and verified experimentally for the adsorption of several light gases from a helium carrier in an adsorber consisting of parallel sheets of activated carbon fibre adsorbent. The extension to a multiple passage system and the effect of moisture in the feed gas were also investigated. A high selectivity ratio ( αCO 2 N 2 ) and a diffusion time constant of about 10 ms for adsorption of CO 2 and N 2 on activated carbon fibre (ACF) adsorbent confirm that such a parallelsided duct coated with ACF sheets would be well suited to a dual piston rapid pressure swing adsorption system for large throughput and low value added applications such as CO 2 removal from stack gas.