High performance capillary electrophoresis - T.E.A.M.

Under ideal conditions (that is, small injection plug length,
no solute-wall interactions, and so on) the sole contribution
to solute-zone broadening in CE can be considered to be
longitudinal diffusion (along the capillary). Radial diffusion
(across the capillary) is unimportant due to the plug flow
profile. Similarly, convective broadening is unimportant due
to the anticonvective properties of the capillary. Thus, the
efficiency can be related to the molecular diffusion term in
chromatography. That is:
2DlL
s 2 = 2 Dt = (13)
m e
V
where D= diffusion coefficient of the solute.
Substituting equation (13) into equation (11) yields a fundamental
electrophoretic expression for plate number
Principles
m
N = e
Vl m
= e
El
(14)
2DL 2D
D (× 10 -5 cm 2 /s)
HCl 3.05
NaCl 1.48
Glycine 1.06
Citrate 0.66
Cytochrome C 0.11
Hemoglobin (human) 0.069
Tobacco mosaic virus 0.0046
Table 2
Diffusion coefficients of selected
molecules (in water, 25 °C)
From equation (13), the reason for the application of high
fields is evident. This follows simply because the solute
spends less time in the capillary at high field and has less
time to diffuse. In addition, this equation shows that large
molecules such as proteins and DNA, which have low
diffusion coefficients, will exhibit less dispersion than small
molecules. The wide range of possible diffusion coefficients
is illustrated in table 2.
The theoretical plate number can be determined directly
from an electropherogram, using, for example,
( )
2
t
N = 5.54 (15)
w 1/2
where: t = migration time
w 1/2
= temporal peak width at half height
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