Page 284 - Chiral Separation Techniques

10.3 SMB as a Development Tool 263
K ⋅ N C
⋅
˜
C =⋅ λ C + A A
A A ˜ ˜
1 + K ⋅ C + K ⋅ C
A A B B
(5)
⋅
K ⋅ N C
˜
C =⋅ λ C + B B
A B ˜ ˜
1 + K ⋅ C + K ⋅ C B
B
A
A
Using this model, the initial slopes of the adsorption isotherms are given by:
K = λ + K ⋅ N and K = λ + K ⋅ N
˜
˜
A A B B
If adsorption data are not available and/or if a quick evaluation is required, the
parameters of the isotherms can be set to:
λ is set to about 0.5 (internal porosity)
–
–
K and K derived from the knowledge analytical retention times 1
–
B
A
N, the saturation capacity, taken in the range:
–1
100–300 g L in the case of silica
–1
50–200 g L in the case of C or related stationary phases.
18
–1
25–50 g L in the case of bulk polymeric chiral phases.
10–20 g L –1 in the case of silica-based chiral stationary phases (cellulosic,
amylosic)
–1
1–5 g L for other silica-based chiral stationary phases
Column efficiency (number of theoretical plates): As in batch chromatography,
one needs to determine the efficiency of the column in order to evaluate the disper-
sion of the fronts due to hydrodynamics dispersion or kinetics limitations. The rela-
tionship of N proportional to L can be expressed in terms of the equation for height
equivalent to a theoretical plate (HETP) as:
H = L (6)
N
where L is the column length and N is the number of theoretical plates.
HETP can be related to the experimental parameters through the Van Deemter
[59] or Knox [60] equations. It is possible to describe the dependence of H on u since
H is a function of the interstitial mobile phase velocity u. In the case of preparative
chromatography, where relatively high velocities are used, these equations can very
often be simplified into a linear relation [61, 62].
H = a + b · u (7)
Parameters a and b are related to the diffusion coefficient of solutes in the mobile
phase, bed porosity, and mass transfer coefficients. They can be determined from the
knowledge of two chromatograms obtained at different velocities. If H is unknown,
b can be estimated as 3 to 5 times of the mean particle size, where a is highly depen-
dent on the packing and solutes. Then, the parameters can be derived from a single
analytical chromatogram.