Handbook of Size Exclusion Chromatography and Related ...

information regarding appropriate Mark–Houwink coefficients and/or the
inability to perform intrinsic viscosity measurements.
Balke, Hamielec et al. described a computer method to determine a
calibration curve expressed by
Ve ¼ C1 C2 log 10 M (15)
where Ve is the elution (or retention) volume and M is the molecular weight (16).
Their original method involved a cumbersome, simultaneous search for the constants
C1 and C2, which was prone to false convergence. Revised methods featured
a sequential, single-parameter search (17,18). These methods rely on the fact that
the dispersity, D, is a function of the slope, C2, alone. Arbitrary values are first
assigned to the two constants. The resulting calibration equation is iteratively
applied to the time slice data while the slope value is optimized to minimize the
difference between the true and computed dispersities. Once the slope has been
determined it is fixed and the intercept, C1, is optimized to minimize the difference
between the true and computed moments (either individually or their sum).
3.4 Universal Calibration
Benoit and co-workers demonstrated that it is possible to use a set of narrow
polymer standards of one chemical type to provide absolute molecular weight
calibration to a sample of a different chemical type (19,20). In order to understand
how this is possible, one must first consider the relationship between molecular
weight, intrinsic viscosity and hydrodynamic volume, the volume of a random,
freely jointed polymer chain in solution. This relationship has been described by
both the Einstein–Simha viscosity law for spherical particles in suspension
[h] ¼ C Vh
M
and the Flory–Fox equation for linear polymers in solution
[h] ¼ F ks2l 3=2
!
M
(16)
(17)
where [h] is the intrinsic viscosity, Vh, is the hydrodynamic volume, ks 2 l 1=2 is
the root-mean-square radius of gyration of the polymer chain, and C and F are
constants (21). If either equation is multiplied by M, the molecular weight,
the resulting product, [h]M, is seen as proportional to hydrodynamic volume.
(Note that the cube of the root-mean-square radius of gyration is also proportional
to volume.) Benoit and co-workers plotted this product versus elution volume for a
number of chemically different polymers investigated under identical SEC
© 2004 by Marcel Dekker, Inc.