Generalized HVL Models

The Generalized HVL Model Template

The generalized Haarhoff VanderLinde (HVL) models use the basic HVL (one term slope of adsorption isotherm) in the following template:

a₀ = area of the overall model

a₁ = the center value used in the density and cumulatives

a₂ = the width value used in the density and cumulatives

a₃ = HVL chromatographic distortion parameter (fronted for a₃<0, tailed for a₃>0)

Density = PDF for the specified ZDD (zero distortion density), area=1

Cumulative = CDF for the specified ZDD, magnitude=1

RevCumulative = CDF complement for the ZDD, magnitude=1

The a₃ distortion only appears in the the template and nowhere in the density and cumulative terms.

For user-defined peak models, the MHVL(a0,a1,a2,a3,Density,Cumulative,RevCumulative) built-in function implements the above template.

Parameter Description

In general, the following applies:

a₀ = the area or zeroth moment parameter

a₁ = parameter related to first moment, the center value (this will be model specific)

a₂ = parameter related to the square root of the second moment, the width value (this will be model specific)

a₃ = the HVL chromatographic distortion parameter (fronted for a₃<0, tailed for a₃>0) (identical across all GenHVL models)

a₄ = for 5 parameter models, the parameter relating to the skew or third moment; for 6 parameter models, the parameter relating to the kurtosis or fourth moment

a₅ = for 6 parameter models, the parameter relating to the skew or third moment

The Generalized HVL Models

HVL (Full Range)

GenHVL - Generalized Normal ZDD

Gen2HVL - Generalized Error Model ZDD

GenHVL[Z] - [Z] Generalized Normal ZDD

GenHVL[Y] - [Y] Generalized Error Model ZDD

GenHVL[G] - [G] Half-Gaussian Modified Gaussian (GMG)

GenHVL[E] - [E] Exponentially-Modified Gaussian (EMG)

GenHVL[Q] - [Q] Error Model (Symmetric)

GenHVL[S] - [S] Student's t (Symmetric)

GenHVL[T] - [T] Generalized Student's t (Asymmetric)

GenHVL[V] - [V] Generalized GMG

GenHVL[Yp] - [Yp] Asymmetric Error Model (High Overload Shapes Only)

GenHVL[YpE] - [YpE] Generalized Laplace (High Overload Shapes Only)
GenHVL[Yp2] - [Yp2] Asymmetric Error Model Two-Width (High Overload Shapes Only)

GenHVL[Yp2E] - [Yp2E] Generalized Laplace Two-Width (High Overload Shapes Only)

GenHVL[K] - [K] Generalized Two-Sided Kinetic Orders 0,1 (High Overload Shapes Only)

GenHVL[W] - [W] Generalized Error Model, Linear Gradient (Gradient HPLC Only)