Binary Composite Media Research Articles

Mass transfer mechanism in hydrophilic interaction chromatography

The mass transfer mechanism in HILIC was investigated in depth. The reduced heights equivalent to a theoretical plate (HETP) of five low molecular weigh compounds with retention factors of −0.05 (slight exclusion from the surface due to the presence of a water-rich layer in which naphthalene is insoluble) to 3.64 were measured at room temperature for a 4.6mm×100mm column packed with 3.5μm 140Å XBridge HILIC particles in a wide range of flow velocities. The mobile phase was a buffered acetonitrile–water mixture (92.5/7.5, v/v). Using a physically reliable model of effective diffusion in binary composite media (Torquato's model), the longitudinal diffusion and solid–liquid mass transfer resistance reduced HETP terms were measured. The reduced short-range eddy dispersion HETP was taken from the literature data. The long-range reduced HETP was directly measured from the subtraction of these HETP terms to the overall HETP measured from moment analysis. In contrast to RPLC, the plots of the reduced HETP versus the reduced velocity depend weakly on the retention factor, due to the constant, low intra-particle diffusivity observed in HILIC. So, the reduced longitudinal diffusion HETP is smaller and the reduced solid–liquid mass transfer resistance HETP is larger in HILIC than in RPLC. Whereas border effects can be concealed in RPLC for retained analytes due to fast radial equilibration across the column diameter, a residual long-range eddy dispersion term persists in 4.6mm I.D. HILIC columns, even at very slow flow rates. Experiments show that the minor differences in the long-range eddy dispersion term between analytes having different retention factors is directly correlated to the reciprocal of their bulk diffusion coefficient. The performance of HILIC columns packed with fine particles is then more sensitive to the inlet sample distribution and to the outlet sample collection than RPLC columns due to the relatively poor radial mixing controlled by lateral diffusion.

Comparison between the intra-particle diffusivity in the hydrophilic interaction chromatography and reversed phase liquid chromatography modes. Impact on the column efficiency

The effective diffusion coefficients of five low molecular weigh compounds (naphthalene, uracil, uridine, adenosine, and cytosine) were measured at room temperature in a 4.6mm×100mm column packed with 3.5μm XBridge HILIC particles. The mobile phase was an acetonitrile–water mixture (92.5/7.5, v/v) containing 10mM ammonium acetate and 0.02% acetic acid. Using a physically reliable model of effective diffusion in binary composite media (Torquato's model), accurate estimates of the intra-particle diffusivities in the HILIC particles were obtained as a function of the retention of these analytes. The HILIC diffusion coefficients were compared to those previously obtained for endcapped RPLC-C18 particles (5.0μm Gemini-C18). The experimental results confirm that adsorption sites are not localized in RPLC whereas they are so in the HILIC mode. In contrast to RPLC columns, HILIC columns provide longitudinal diffusion B/u terms that increase very little with increasing retention factors. This confirms the absence of surface diffusion in HILIC. The impact of intra-particle diffusivity on the column efficiency was projected in HILIC and RPLC on the basis of the measured intra-particle diffusivities and on the well established theory of band broadening in particulate columns. Accordingly, RPLC columns generate short-range eddy dispersion and solid–liquid mass transfer resistance Cu terms that increase less than do HILIC column with increasing retention factors. The HETP contribution caused by the trans-column structure heterogeneity is smaller in the HILIC than in the RPLC modes because the transverse excursion length is smaller in HILIC. Even though the overall column efficiencies are comparable in HILIC and RPLC, this study shows that the individual mass transfer phenomena are inherently different in the HILIC and the RPLC retention modes.

The Ising model and critical behavior of transport in binary composite media

We present a general theory for critical behavior of transport in binary composite media. The theory holds for lattice and continuum percolation models in both the static case with real parameters and the quasi–static case (frequency dependent) with complex parameters. Through a direct, analytic correspondence between the magnetization of the Ising model and the effective parameter problem of two phase random media, we show that the critical exponents of the transport coefficients satisfy the standard scaling relations for phase transitions in statistical mechanics. Our work also shows that delta components form in the underlying spectral measures at the spectral endpoints precisely at the percolation threshold pc and at 1 − pc. This is analogous to the Lee-Yang-Ruelle characterization of the Ising model phase transition, and identifies these transport transitions with the collapse of spectral gaps in these measures.

Importance of sample intraparticle diffusivity in investigations of the mass transfer mechanism in liquid chromatography

AbstractThe effective diffusivity of a nonretained (thiourea) and of a strongly retained (phenol) compounds were measured with the peak parking method in two different columns (both 150 × 4.6 mm) packed with two types of porous particles having different mesopore sizes [5 μm Jupiter‐C18, 320 Å and Luna(2)‐C18, 100 Å]. The eluent was a methanol–water mixture (10/90 v/v) and the temperature 294 K. The effective diffusivity data acquired were used to determine the intraparticle diffusivity, Dp, based on two different diffusion models. The first one assumes that the diffusion fluxes across the particles and in the interparticle volume are additive (parallel diffusion model). The second model was rigorously derived on the basis of the effective medium theory of diffusion (diffusion model) in a binary composite medium (particles + interparticle volume). In both models, it was assumed that the rate of equilibrium between the liquid and the solid phases was infinitely faster than the rate of axial diffusion along the column at zero flow rate. Both models provide physically meaningful intraparticle diffusivity coefficients that take into account the average mesopore size of the particles, their specific surface area, and the retention factor of the analyte. Although the actual effective intraparticle diffusivity remains unknown, these result confirm that the mass transfer resistance due to diffusion through the porous particles has almost negligible effects in reversed phase liquid chromatography due to the importance of surface diffusion. Combining the results of the peak parking method with the h data measured at high linear velocities allows the unambiguous measurement of the film mass transfer and the surface diffusion coefficients. © 2010 American Institute of Chemical Engineers AIChE J, 2011

An electrical model circuit that reproduces the behaviour of conducting polymer electrodes in electrolyte solutions

An electrical model circuit is proposed that can reproduce, with high accuracy, the small-amplitude impedance behaviour of conducting polymer electrodes in electrolyte solutions. In its most general form, the model consists of a diagonally connected discrete ladder network characterized by three impedances x, y and z. However, some special cases are considered in which x, y and z are replaced by passive circuit elements, such as resistors and capacitors, in arrangements corresponding to particular processes in real polymers. The resulting responses are analysed in the complex plane. One case is explored in detail. In it, a conducting polymer electrode in an electrolyte solution is assumed to be porous, with the pores behaving as simple resistors while the mass of the polymer behaves as a binary composite medium. Concurrently, at the cylindrical walls of the pores, the interfacial electrochemistry is modelled as a Debye-type charging process in which the capacitance depends inversely on frequency. Two semicircles are predicted in the complex plane of impedance, with diameters which have opposite dependences on polymer thickness.