Fundamental chromatographic equations designed for columns packed with very fine particles and operated at very high pressures

On physical meaning of van't Hoff equation and its applicability in chromatography

The van't Hoff equation is a widely used tool to study adsorption thermodynamics in chromatography. Recent experimental data and some theoretical arguments questioned the accuracy of thermodynamic characteristics determined by using this equation. The present report addresses these concerns and shows that if certain requirements are satisfied, the van't Hoff analysis provide reliable results. These requirements include isothermality of the column not perturbed by the percolation of the mobile phase, mass transfer kinetics allowing sufficient proximity to equilibrium, pressure below 200 bar for low molecular weight compounds and below 50 bar for macromolecules, and knowledge of the phase ratio at all experimental temperatures to allow accurate conversion of the retention factor to the equilibrium constant. Physical meaning of adsorption enthalpy and entropy obtained by means of the van't Hoff analysis particularly in the case of heterogeneous adsorbents is discussed and recommendations on how to perform experiments to obtain reliable results are given.

Repeatability of gradient ultrahigh pressure liquid chromatography-tandem mass spectrometry methods in instrument-controlled thermal environments

The impact of viscous friction on eluent temperature and column efficiency in liquid chromatography is of renewed interest as the need for pressures exceeding 1000bar to use with columns packed with sub-2μm particles has grown. One way the development of axial and radial temperature gradients that arise due to viscous friction can be affected is by the thermal environment the column is placed in. In this study, a new column oven integrated into an ultrahigh pressure liquid chromatograph that enables both still-air and forced-air operating modes is investigated to find the magnitude of the effect of the axial thermal gradient that forms in 2.1×100mm columns packed with sub-2μm particles in these modes. Temperature increases of nearly 30K were observed when the generated power of the column exceeded 25W/m. The impact of the heating due to viscous friction on the repeatability of peak capacity, elution time, and peak area ratio to an internal standard for a gradient UHPLC-MS/MS method to analyze neurotransmitters was found to be limited. This result indicates that high speed UHPLC-MS/MS gradient methods under conditions of high viscous friction may be possible without the negative effects typically observed with isocratic separations under similar conditions.

The rationale for the optimum efficiency of columns packed with new 1.9μm fully porous Titan-C18 particles-a detailed investigation of the intra-particle diffusivity

In a previous report, it was reported that columns packed with fully porous 1.9μm Titan-C18 particles provided a minimum reduced plate height as small as 1.7 for the most retained compound (n-octanophenone) under RPLC conditions. These particles are characterized by a relatively narrow size distribution with a relative standard deviation (RSD) of only 10%. A column packed with classical 5μm Symmetry-C18 particles, used as a reference RPLC column, generated a minimum reduced plate height of 2.1 for the same retained compound. This work demonstrates that this was due to an unusually low intra-particle diffusivity across these particles, which leads to a small longitudinal diffusion coefficient along the column. The demonstration is based on the combination of accurate measurements of the height equivalent to a theoretical plate (HETP), inverse size exclusion chromatography (ISEC), peak parking (PP), and minor disturbance method (MDM) experiments. The experimental results show that the reduced eddy dispersion HETP term (A=0.8 for a reduced velocity of 5), the internal particle porosity (ϵp=0.35), and the enrichment of acetonitrile in the pore volume (75% acetonitrile in the bulk, 85% inside the mesoporous volume) are identical on both the Titan-C18 and Symmetry-C18 columns. The difference between the internal structures of these two brands of RPLC-C18 fully porous particles lies in the values of the internal obstruction factor γp, which is 0.42 for the Symmetry-C18 but only 0.26 for the Titan-C18 particles. This is in part related to the diffusion hindrance due to the small average pore size of the Titan-C18 particles, around 59Å versus 77Å for Symmetry-C18 particles. A simple model of constriction along diffusion paths having the shape of a truncated cone suggests that the width of the pore size distribution (RSD of 30% and 20% for Titan-C18 and Symmetry-C18 particles) is mostly responsible for the difference in their obstruction factors.

The current revolution in column technology: how it began, where is it going?

This work revisits the exceptionally rapid evolution of the technology of chromatographic columns and the important progress in speed of analysis and resolution power that was achieved over the last ten years. Whereas columns packed with 10 and 5 μm fully porous particles dominated the field for nearly thirty years (1975-2000), it took barely six years to see the commercialization of monolithic silica rods (2000), their raise to fame and decay to oblivion, the development of finer fully porous particles with size down to 1.7 μm (2006), and of sub-3 μm superficially porous particles (2006). Analysis times and plate heights delivered by columns packed with these recent packing materials have then been improved by more than one order of magnitude in this short period of time. This progress has rendered practically obsolete the age-old design of LC instruments. For low molecular weight compounds, analysts can now achieve peak capacities of 40 peaks in about 15s with a hold-up time of the order of 1.5s , in gradient elution, by operating columns packed with sub-3 μm shell particles at elevated temperatures, provided that they use optimized high pressure liquid chromatographs. This is the ultimate limit allowed by modern instruments, which have an extra-column band broadening contribution of 7 μL² at 4.0 mL/min and data acquisition rate of 160 Hz. The best 2.1 mm × 50 mm narrow-bore columns packed with 1.7 μm silica core-shell particles provide peaks that have a variance of 2.1 μL² for k=1. Finally, this work discusses possible ways to accelerate separations and, in the same time perform these separations at the same level of efficiency as they have today. It seems possible to pack columns with smaller particles, probably down to 1 μm and operate them with current vHPLC equipments for separations of biochemicals. Analyses of low molecular weight compounds will require new micro-HPLC systems able to operate 1mm I.D. columns at pressures up to 5 kbar, which would eliminate the heat friction problems, and providing extra-column band broadening contributions smaller than 0.1 μL². Alternatively, a new generation of vHPLC systems with minimal extra-column contributions of less than 0.5 μL² could run 2.1mm I.D. columns if these latter were to be packed with high heat conductivity materials such as core-shell particles made with an alumina or gold core.

Mass transfer equation for proteins in very high-pressure liquid chromatography

The mass transfer kinetics of human insulin was investigated on a 50 mm x 2.1 mm column packed with 1.7 microm BEH-C(18) particles, eluted with a water/acetonitrile/trifluoroacetic acid (TFA) (68/32/0.1, v/v/v) solution. The different contributions to the mass transfer kinetics, e.g., those of longitudinal diffusion, eddy dispersion, the film mass transfer resistance, cross-particle diffusivity, adsorption-desorption kinetics, and transcolumn differential sorption, were incorporated into a general mass transfer equation designed to account for the mass transfer kinetics of proteins under high pressure. More specifically, this equation includes the effects of pore size exclusion, pressure, and temperature on the band broadening of a protein. The flow rate was first increased from 0.001 to 0.250 mL/min, the pressure drop increasing from 2 to 298 bar, and the column being placed in stagnant air at 296.5 K, in order to determine the effective diffusivity of insulin through the porous particles, the mass transfer rate constants, and the adsorption equilibrium constant in the low-pressure range. Then, the column inlet pressure was increased by using capillary flow restrictors downstream the column, at the constant flow rate of 0.03 mL/min. The column temperature was kept uniform by immersing the column in a circulating water bath thermostatted at 298.7 and 323.15 K, successively. The results showed that the surface diffusion coefficient of insulin decreases faster than its bulk diffusion coefficient with increasing average column pressure. This is consistent with the adsorption energy of insulin onto the BEH-C(18) surface increasing strongly with increasing pressure. In contrast, given the precision of the height equivalent to a theoretical plate (HETP) measurement (+/-12%), the adsorption kinetics of insulin appears to be rather independent of the pressure. On average, the adsorption rate constant of insulin is doubled from about 40 to 80 s(-1) when the temperature increases from 298.7 to 323.15 K.