Equation (10) shows that k is always in the range 0 to 1.
Figure 2. Tracer Distortion-simulation
The same value of KD is used for both curves of Figure 2, so we can extract some useful information. First, we note that skewness becomes increasingly
severe as TD/Tv becomes large relative to the time required for solute to pass a particle. Next we see that the definitions of N and H are ambiguous, and no single measure is sufficient. Moreover the mean residence time is no longer the same as that for appearance
of the concentration peak.
Figure 3. Tracer Distortion — Effect of Experimental Conditions Column: 1.6 × 8.8 cm ToyoPearl SP 650M. Linear velocity: 200
cm/hr. Mobile Phase: 150mM Citrate, Solute Pulses: 500 mL of 10 mg/mL globular protein, 500 mL of 5% acetone.
A low-molecular weight tracer is commonly used to characterize a chromatographic column. Frequently, a low-molecular weight
tracer will show less skewness that a larger solute. This is shown in Figure 3 for actual effluent curves. The acetone tracer
has a sharper peak than for the desired product, a globular protein. Even the acetone tracer distribution is appreciably skewed,
and this skewness shows a fundamental difference between the effluent curves of this figure and the intra-column profiles
of Figure 2. The later bits of acetone to appear have been in the column longer and have therefore had more opportunity to
disperse. In summary, no effluent curves are truly Gaussian, and the plate concept as defined earlier represents an ideal
case that can only be approached as a limit for very large N.
Measures of Column Efficiency
There is no simple way to resolve this ambiguity, but it is clear that we now need at least two measures of tracer shape —
one for the extent of dispersion about the mean residence time and another for skewness. In our experience, these have generally
proved sufficient, and we recommend the use of statistical moments.These moments are described in Equations (11), (12), and
Anurag S. Rathore, PhD, is a consultant, Biotech CMC Issues, and a member of the faculty in the department of chemical engineering at the Indian Institute of Technology. Rathore is also a member of BioPharm International's Editorial Advisory Board.
Articles by Anurag S. Rathore, PhD
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