Handbook of Size Exclusion Chromatography and Related ...

described the partitioning of hard-sphere solutes in a random pore system
described as a “porous network.” Also unique to this study was an attempt to
express SEC partitioning as a function of both complex pore and solute
contributions. Furthermore, the authors treated the distribution of solutes of
various shapes (spherical, thin rod, dumb-bell, and capsular shaped) in pores
described as cylinders, slabs, spheres, and rectangular pockets. Giddings
concluded that SEC partitioning may best be defined as
( sL=2)
K ¼ e
where K is the SEC equilibrium constant for a random plane pore model and sL is
the product of the mean external molecular length, L, and the effective pore
radius, s. The equilibrium partitioning of rigid solutes in a random-fiber pore
model was also proposed by Giddings (32). Here the SEC equilibrium constant
was defined as
K ¼ e Ah
where A is the projection of the molecular dimension, Ax, averaged over all
directions in space and h is the fiber length per unit volume. The fiber diameter is
assumed similar to the size of the solute molecule.
Further contributions to SEC theory were made by Glandt (33) for the
description of the spatial density distribution for “crowded pores.” This work
contrasts earlier with studies based solely on dilute solutions of solutes where
solute-wall effects are primarily considered.
3.2.2 Proteins as SEC Solutes
It is noteworthy that the field of SEC elution theory turned largely to the
description of partitioning of random-coil polymers during the late 1960s and
throughout the following decade. Contributions from Cassassa and Tagami (34),
based on Flory theory (35), served to further the understanding of high polymer
SEC. This work focused on new descriptions of flexible solutes. When considering
the elution of proteins as SEC solutes, the treatment of solution conformation
becomes somewhat simplified when viewed from the perspective of the statistical
mechanical arguments needed to describe high polymers. The hard shell or rigid
sphere solute models described above are probably adequate for proteins. This
approach was used by Squire (30) to extend Eq. (4) to
© 2004 by Marcel Dekker, Inc.
Ve
V0
¼ 1 þ g 1
M 1=3
C 1=3
3
(5)
(6)
(7)