The statistical theory of linear capillary chromatography with uniform stationary phase

Diffusion and Equilibrium Adsorption Coefficients of Aromatic Hydrocarbon Species in Capillary Columns

This study focuses on a mathematical description of elution of aromatic species in a 30 m×0.25 mm×0.25 μm BPX5 capillary column. Experimental studies involve the detection of chemical species at the capillary column outlet. Using the recorded peaks, statistical moments of different orders are calculated for both toluene and naphthalene. Modeling studies involve a laminar flow model with an equilibrium coefficient (Ks) and a solute diffusion coefficient in the stationary phase (Ds). Model validation is developed by performing experiments at different carrier gas velocities and GC oven temperatures. Under the conditions, neither the first statistical moment (M1) nor the second statistical moment (M2) is affected by the carrier gas velocity. Thus, the interface equilibrium coefficients (Ks) and the diffusion coefficients (Ds) solely depend on the solute and the capillary column polymer coating properties. Furthermore, the statistical moments of different orders show that the proposed interface equilibrium based model in the “narrow bore” 30 m×0.25 mm×0.25 μm BPX5 capillary column is adequate for aromatic species such as toluene and naphthalene.

New Moment Equations for Chromatography Using Various Stationary Phases of Different Structural Characteristics

New moment equations were systematically developed for chromatography using various types of separation media having different structural characteristics, i.e., shape (spherical particle, cylindrical fiber, flat plate) and porous structure (full-porous, partially porous (pellicular), nonporous). First, a set of basic equations of the general rate model of chromatography representing the mass balance and the mass-transfer kinetics were analytically solved in the Laplace domain. Then, the moment equations in the real-time domain of the first absolute moment and the second central moment were derived from the analytical solution in the Laplace domain. The new moment equations were used for predicting the chromatographic behaviors of benzene in the hypothetical RPLC systems using the full-porous, partially porous (pellicular), and nonporous spherical particles as packing materials. The influence of the difference in their structure on the total performance of the three types of spherical particles as the separation media for the fast HPLC with a high efficiency was quantitatively evaluated from the viewpoints of the column efficiency, column back pressure, and sample retention strength. The framework of the new moment equations can provide not only the qualitative but also the quantitative information about the intrinsic characteristics of the chromatographic behaviors of various separation media having the different shapes and structures. This study is devoted to demonstrating the important advantage of the moment analysis strategy over the conventional plate theory and rate models of chromatography.