Van Deemter equation

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Van Deemter graph
Black: H = A + (B / v) + (C · v)
Green: Scattered diffusion A
Red: Longitudinal diffusion : B / v
Blue: Mass transfer: C · v

The Van Deemter equation ( Jan Jozef van Deemter , 1956) describes mathematically / physically the separation performance in gas and liquid chromatography . The floor height H (HETP - height equivalent to a theoretical plate) is described by the following simplified formula:

The smaller H is, the greater the separation efficiency of the system. This follows from the equation:

The H / v hyperbolic function (X = v, Y = HETP) has a minimum at the optimal flow velocity (v), at which the bottom height (H) is lowest and thus the separation efficiency is highest.

  • H : floor level
  • L : length of the column
  • N : number of separation stages
  • v : speed of the mobile phase
  • A : Scattered diffusion / eddy diffusion . In the case of packed columns, the turbulence increases this term. It is independent of the flow velocity. In the case of capillary columns, A. is not applicable. It is a scattered diffusion which is created by the different flow paths of individual sample molecules through the column. These are caused by the changing shape and size of the particles of the carrier material and their irregular packing in the column. Eddy diffusion is particularly small when small particles of uniform size are packed homogeneously in the column. Term A also depends on the particle diameter of the stationary phase: A = 2 λ d (λ = factor, d = particle diameter).
  • B / v : Longitudinal diffusion, diffusion in the longitudinal direction of the column axis. This factor depends on the viscosity and temperature of the mobile phase. It depends on the reciprocal of the flow velocity. The analyte continuously diffuses away from the concentrated center of its sample zone. Term B depends on the diffusion coefficient of the mobile phase (D (M)): B = 2 λ D (M). The higher the flow velocity, the shorter the time spent on the column and the lower the contribution of the longitudinal diffusion.
  • C · v describes the mass transfer between stationary and mobile phases. This term is influenced by the type of mobile phase and the type and thickness of the stationary phase. It is directly proportional to the flow velocity. Term C also depends on the particle diameter, the porosity of the particles, the column length, the column radius and the diffusion coefficient of the stationary phase.

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