Handbook of Size Exclusion Chromatography and Related ...

Experimental efficiency vs. velocity data can be fitted to any of anumber of h–v
equations, of which the Knox equation (34) is the most widely used.
h¼ B
v þAv0:33 þCv (3)
The A, B, and Cterms of Eq. (3) symbolize contributions to sample dispersion
from the interparticle flow structure A, axial diffusion B, and finite rate of
equilibration of the solute between mobile and stationary phases C. Thevalues of
thecoefficientsA,B,andCareobtainedfromcurvefittingofexperimentaldatato
Eq. (3) for asufficiently wide velocity range. For very good columns, A¼0:5,
B¼2, and C’0:05 (35). Independent of particle size and solute molecular
weight, hreaches an optimal value of 2–3for a“well-packed” column, when vis
in the range 3–5. For agiven solute, the linear velocity at this optimum increases
withdecreasingparticlesize.Forexample,forasolutewithamolecular weightof
200(Dm’1 10 5 cm 2 /s),acolumnfilledwith5-mmparticlesprovidesthebest
efficiency when operated at alinear velocity of 0.6–1.0 mm/s.
The definition of linear velocity is based on the retention time for the first
eluting component. In interactive modes of chromatography, linear velocity is
calculated by dividing the length of the column by the retention time of an
unretained (small) molecule that can freely access the total available pore
structure. In SEC, linear velocity is based on the retention time of atotally
excluded solute. Because the interparticle volume is about as large as the pore
volume,thelinearvelocityinSECkvl SEC isroughlytwicethatininteractivemodes
when operating the column at the same flow rate. In other words, as in the
preceding example, an SEC column filled with 5-mm particles provides the best
efficiencyfora200daltonmolecularweightsolutewhenkvl SEC is1.2–2.0 mm/s.
Similarly,for aprotein with amolecular weight of 100,000 dalton and adiffusion
coefficient of 3 10 7 cm 2 /s, the column efficiency is optimal when kvl SEC is in
the range 0.036–0.060 mm/s. In the remainder of this chapter kvl represents
kvl SEC.
The analysis time in SEC is given by the retention time for an unretained
smallmolecularweightsolute.Thus,theoptimalanalysistimeforanalysingsmall
molecular weight solutes on awell-packed 30 cm (5 mm) column is5–8minutes.
Forproteins,theoptimalanalysistimeis3–5h,whichnecessitatestheuseofvery
low flow rates. These approximations are in agreement with the calculations of
Guiochon and Martin (36), who predicted an optimum analysis time of 1.6 hat a
reduced velocity of 10. Sjodahl first put this principle into practice for SEC of
proteins by operating a30 cm 7.5 mm inner diameter (ID), 10 mm, TSKgel
G3000SWcolumnataflowrateof50 mL/min,asshowninFig.1(37).Although
excellent resolution is obtained during the 12-h analysis time, most users prefer to
work at linear velocities of 0.4–1.0 mm/s to keep the analysis time below
30 minutes.
© 2004 by Marcel Dekker, Inc.