Exact analytical expressions for the band broadening in polydisperse 2-D multi-capillary columns with diffusional bridging
Diffusional bridging: the holy grail of chromatography?
Abstract:
The pressure drop required by available chromatography column packings constitutes an operational drawback. Some attempts to solve this problem have been directed toward the use of packings composed of a multiplicity of capillary tubes working in parallel, as a high factor of gain on the pressure drop appears possible. Unfortunately, the small differences in dimensions among individual capillaries have made this solution unpractical. In this study we show that the superimposition of a radial diffusive term between adjacent channels efficiently eliminates this limitation. The behavior becomes that of common particulate packing, with the benefit of a pressure drop that is lower by approximately one order of magnitude for identical characteristic dimensions. The effect is quantified for long retention times by a combination of theoretical, transfer function analysis and simulation studies. The reduced partial height equivalent to a theoretical plate (HETP) of the dispersion phenomena is given quantitatively by the following formula valid for high k when the mass transfer resistance of the stationary phase is negligible:
Dispersion Height Equation
Summary:
François Parmentier, CEO of the Lyon-based startup SEPARATIVE, has just published an important article in the Comptes Rendus Chimie[1] providing the first mathematical demonstration of the efficacy of diffusional bridging, a technology patented by the company in its proprietary universal multicapillary diffusional-bridging (UMDB) columns.
Current liquid chromatography technology is limited by the very high pressure required to pass liquids through the ultrafine powders used for separation in particulate column packings. Efficiency is further hindered by lack of uniformity in stacking the particulate beds causing irregular flow patterns and their lack of long-term stability. As Parmentier points out, “in industrial liquid chromatography (LC), stabilizing and containing large column beds involves levels of complexity and high costs that prohibit the use of this powerful separation method in most chemical processes.”
In an attempt to overcome this difficulty, monolithic packings in polymers or silica gel have been experimented but creating columns large enough for industrial processes has been problematic. While monocapillary columns used in gas chromatography (GC) are highly permeable, their adaptation to liquids is impractical because of the small channel size required (1-10 µm). Multicapillary tubes working in parallel have been studied as an alternative option. “Unfortunately,” notes Parmentier, “the small differences in dimensions between the individual capillaries, the difficulty of coating them evenly with the stationary phase and the differences in their individual aging negatively affect their short- and long-term efficiency and has made this solution very limited in practice.”
Parmentier theorizes that adding diffusional exchange between the independent fluid flow paths in multicapillary columns could greatly improve the technology. The stated goal of his article is thus “to estimate the effect of a diffusional flow, passing through bridges of pores between channels causing the eluting bands in the fast or slow channels to discharge by molecular diffusion in channels flowing with an average velocity.”
Parmentier reviews basic findings regarding expected gains in pressure drop using mutilcapillary rather than particulate packings and estimates the effect of diffusional bridging multicapillary arrays compared with the performance of present state-of-the-art multicapillary chromatography columns. The theoretical study based on Giddings Random Walk model that Parmentier presented at the 17th International Symposium on Preparative and Industrial Chromatography and Allied Techniques (SPICA) in 2018,[2] is also published in this paper. In parallel, he discusses the purely mathematical transfer function of the system. Finally, he presents the results of an ordinary differential equation (ODE) integration simulation, using as its starting point a discretized model based on the method of lines, and compares these to theoretical predictions. These three approaches give numerical results that are in excellent agreement with a deviation of less than 3% from perfect equality.
Parmentier’s analysis and mathematical model suggests that “provided there is suitable diffusional bridging between capillaries, multicapillary packings allow the throughput capacity and efficiency of conventional particulate packings. Given that multicapillary arrays have a pressure drop that is lower by one order of magnitude, they should be a superior candidate for separation applications.”
Parmentier’s theoretical and simulated results show that superimposing a radial diffusive term between adjacent channels, or diffusional bridging, removes the limitation of packing in terms of the number of equivalent theoretical plates (NETP). “In this case, the multicapillary array behaves like particulate packing, with an NETP increasing linearly with packing length. In the case where the multicapillary array has comparable effective diffusivity to classical LC porous stationary phases (i.e. silica gel, PS-DVB gels), this effect is strong enough that the efficiency loss due to inhomogeneity in the capillary diameters, which is catastrophic for a non-diffusive array, becomes negligible for typical standard deviations in the capillary diameter.” Thus, due to the large gain on the pressure drop over conventional packings, even very imperfect arrays that are easier to manufacture will have greater efficiency than current chromatography columns.
What are the practical implications for chromatography and chemical engineering? Multicapillary diffusional bridging columns with reduced pressure requirements should enable liquid chromatography columns to attain 100,000 HETPs, while using existing detectors, injectors and pumps. “In industrial separation,” writes Parmentier, “this approach will allow chromatography to be conducted with high efficiency and with low-pressure pumps, injectors, lines, and other fluid appliances. The investment and cost operation will be reduced by an important factor.”
[1] Parmentier, F. Effect of diffusional bridging in multicapillary packing, Comptes Rendus.Chimie, 2020, 23, no. 6-7, p. 415-431. https://comptes-rendus.academie-sciences.fr/chimie/item/CRCHIM_2020__23_6-7_415_0/
[2] Francois PARMENTIER, OC09 – Improvement of Multicapillary Packing Efficiency by Diffusional Bridging: A Theoretical and Dynamic Simulation Study, SPICA 2018, Darmstadt, Germany, October 7-10, 2018.
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