Empirical Determination and Calculation of HETP

Key Insight

Column efficiency is empirically characterized using the Height Equivalent to a Theoretical Plate (HETP), H, or the corresponding plate number, N. The reduced HETP, h = H / dp, allows for comparison of stationary phases with varying particle sizes and depends on the reduced velocity, v' = v dp / D0, which indicates the relative significance of dispersive and mass transfer kinetic effects. While v' is typically low for small molecules and particles, it can be quite large for proteins and other biopolymers in process chromatography, leading to vastly different HETPs for different solutes in the same column under identical conditions.

Accurate HETP determination relies on specific experimental conditions during a pulse injection of a test solute under isocratic conditions. First, the injection must be sufficiently small to act as a 'delta function,' meaning the injected volume should not be a substantial fraction of the eluted peak volume, and the detector must provide an adequate signal-to-noise ratio. Second, the adsorption equilibrium between the adsorbed phase (q hat) and the concentration (C) must be strictly linear to ensure that any observed band broadening is due to column efficiency, not non-linear thermodynamics causing tailing or fronting. Achieving a linear isotherm is often challenging for proteins due to their sensitivity to mobile phase composition and potential secondary effects like association or unfolding.

HETP is calculated using statistical moments derived from the peak profile: μ0 for peak area, μ1 for mean elution time, and σ squared for peak variance. The formula is H = σ squared L / μ1 squared, where L is column length. While μ0 and μ1 are generally robust, calculating σ squared is difficult for tailing peaks due to errors at long retention times, often exacerbated by detector signal drift. Extra-column contributions from the injector, detector, and connections must also be accounted for, as their variances are additive and can be significant, especially in high-efficiency columns like 'monoliths'. Approximate Gaussian methods exist, such as the 'area method' (H = (2 pi μ0 squared / Cmax tmax L)), but their accuracy diminishes for asymmetrical peaks with skew greater than approximately 0.7, necessitating the more robust moment-based calculations. For example, for a 20-cm column, calculations based on the width at mid-height are accurate only up to about 300 cm/h, falsely portraying HETP as independent of flow rate at higher velocities when intra-particle mass transfer is controlling.