Dynamics of Chromatography. Part I. Principles and Theory

Abstract

Building upon the micromachined column idea proposed by the group of Regnier in 1998, we report on the first high-resolution reversed-phase separations in microma-chined pillar array columns under pressure-driven LC conditions. A three component mixture could be separated in 3 s using arrays of nonporous silicon pillars with a diameter of approximately 4.3 µm and an external porosity of 55%. Under slightly retained component conditions (retention factor k′) 0.65-1.2), plate heights of about H) 4 µm were obtained at a mobile phase velocity around u) 0.5 mm/s. In reduced terms, such plate heights are as low as h min) 1. Also, since the flow resistance of the column is much smaller than in a packed column (mainly because of the higher external porosity of the pillar array), the separation impedance of the array was as small as E) 150, i.e., of the same order as the best currently existing monolithic columns. At pH) 3, yielding very low retention factors (k′) 0.13 and 0.23), plate heights as low as H) 2 µm were realized, yielding a separation of the three component mixture with an efficiency of N) 4000-5000 plates over a column length of 1 cm. At higher retention factors, significantly larger plate heights were obtained. More experimental work is needed to investigate this more in depth. The study is completed with a discussion of the performance limits of the pillar array column concept in the frame of the current state-of-the-art in microfabrication precision. As a radical solution to the tedious problem of column-to-column packing reproducibility of HPLC columns, Regnier 1 proposed in 1998 to leave the conventional approach to slurry pack HPLC columns with micrometer sized-spherical particles for the high-precision etching technologies of the microelectronics industry. 2 Given that these techniques also offer a perfect control over the position of each individual "particle", this novel manufacturing approach should also allow eliminating all possible sources of eddy-diffusion. The advantage of the latter can be assessed from, among others, the work of John Knox. 3,4 Building further upon Giddings's coupling theory, 5 he postulated that the major fraction of the band broadening in a packed column is due to the mobile zone and more particularly to the irregularity of the flow in the interstitial space (eddy-dispersion). He guessed that these flow irregularities are responsible for about one-half of the widely accepted "theoreti-cal" minimum of h min) 2 (h) reduced plate height) H/d p). He derived this from the fact that in packed bed electrochromatog-raphy (CEC), where the flow is much less sensitive to irregularities of the bed structure, minimal reduced plate heights on the order of h min) 1 can be obtained. 4,6,7 Reduced plate heights as low as h min) 1 have also been obtained under pressure-driven conditions in beds of very large particles (on the order of 1 / 2 mm). 4 Such large particles can be made much more monodisperse than the micrometer size beads currently used in HPLC and can hence also be assumed to pack more easily into a highly regular bed. Tallarek et al. showed experimentally using in situ pulsed field gradient NMR that the part of the minimal plate height value in excess of h min) 1 is due to large scale inhomogeneities variations in packing density (long range and transcolumn coupling). 8 The advantage of ordered packings to obtain lower degrees of axial dispersion was also already recognized a long time ago in the field of chemical engineering. 9 A computational fluid dynamics study of chromatographic beds with various degrees of packing heterogeneity 10,11 found that the minimal reduced plate height in a perfectly ordered packing of porous pillars grouped in an array with an external porosity of) 40% can be expected to be equal to h min) 0.91 (retained component with retention factor k) 1.25), i.e., very close to Knox's prediction. The decrease in plate height obtained by going from the most heterogeneous packing case to a perfectly ordered