Study of the peak variance in isocratic and gradient liquid chromatography using the transport model

• A general plate height equation for gradient elution is proposed.
• This equation is suited for any type of solvent strength model.
• This equation is suited for any type of gradient profile.
• This equation is suited for varied plate height with mobile phase composition.
• This equation takes the effects of dwelling time into consideration.

The expressions accounting for the peak variance in isocratic and gradient liquid chromatography is derived from the transport model. In mathematical treatments, the dwelling time is taken into account, and the type of solvent strength, gradient profile and the variation of plate height (H) with mobile phase composition (φ) is not specified. By applying a coordinate transformation, the transport model is solved by using the Laplace transform approach. A plate height equation that is suited for both isocratic and gradient elution is obtained. Based on this equation, the plate height equations for any combination of stepwise and linear gradients are derived. These equations will be algebraic when the solvent strength is linear and the H–φ plot is parabolic. The plate height equations for single stepwise, single linear and the ladder-like gradients are also given.