Diffusivity
The diffusivity of a solute defines the rate of transfer of the solute in a given fluid under the driving force of a concentration gradient. The mass transfer process is called diffusion. Diffusivity is classically defined as the mass of solute transferred per unit area per unit time under unit concentration gradient. In general, the diffusivity of a solute decreases with its molecular weight, and the molecular weight of the fluid through which it is diffusing, increases with temperature, but decreases with pressure. Diffusion is the method of by which the solutes are transported through the individual phases in chromatography systems but transport through the chromatography column results from fluid flow.
Author: RPW Scott
Book:Dispersion in Chromatography Columns
Section:Dispersion Experimental-Validation
, but the dependence of (Hmin)
on diffusivity is extremely small for the solute benzyl acetate. The slight
slope of the line for the solute hexamethylbenzene might well result from the
fact that either the (A) term is not completely independent of the diffusivity
(Dm) as shown by the results
in figure 21, or the resistance to mass transfer in the stationary phase does
make a small but significant contribution to the value of (H).
The curves
relating the optimum velocity with solute diffusivity are shown in figure 24
and it is seen that the straight lines predicted by the Van Deemter equation
are realized for both solutes. It should be noted that similar treatment of the
Knox equation does not predict that values of Hmin should be independent of the solute diffusivity
neither does it predict that (uopt)
should vary linearly with solute diffusivity. This is strong evidence,
supporting the validity of the Van Deemter equation, as opposed to the Knox
equation.
 
Dispersion Experimental-Validation
Author: RPW Scott
Book:Dispersion in Chromatography Columns
Section:Dispersion Experimental-Validation
mobile phase velocity and the solute diffusivity. The fit of the Van Deemter
equation to the experimental data confirms the former condition and the plot of
the (A) term against solute diffusivity (the data taken from tables 1 and 2 and
shown in figure 20 confirms the latter.
J.Chromatogr.,270(1983)62
Figure 20.
Graph of A Term against Solute Diffusivity for Benzyl Acetate
Figure 20 demonstrates
that the magnitude of the (A) term appears, within experimental error,
independent of the diffusivity of the solute in the mobile phase. Closer
examination, however, indicates that there might be a slight residual
dependence of (A) on diffusivity. This probably indicates that the velocity
range over which the data was taken was not sufficiently high enough to ensure
that the first term of the Giddings equation was reduced to a constant value as
it is in the simple Van Deemter equation.
This can be
examined further by considering the detailed expression for the first term of
the
Dispersion Experimental-Validation
Author: RPW Scott
Book:Dispersion in Chromatography Columns
Section:Dispersion Golay-Equation
Taking a
value of 2.5 x10-5 for Dm (the diffusivity of benzyl acetate in n-heptane)
equation (52) can be employed to calculate the curve relating (H) and (u) for
an uncoated capillary tube. The results are shown in figure 17. It
is seen that the Golay equation produces a curve identical to the Van Deemter
equation but with no contribution from a multipath term. It is also seen that
the value of (H) is solely dependent on the diffusivity of the solute in the
mobile phase and the linear mobile phase velocity. It is clear that the
capillary column can, therefore, provide a simple means of determining the
diffusivity of a solute in any given liquid. The Golay equation (equation (52))
can be put in a simplified form in a similar manner to the equations for packed
columns:-
 
Dispersion Golay-Equation
Author: RPW Scott
Book:Dispersion in Chromatography Columns
Section:Dispersion Experimental-Validation
nbsp;
where (e) is a constant, probably close
to unity.
However that
there are two ways in which the diffusivity of the solute in the mobile phase
can be changed. It can be modified as a result of changing the solute which is
being eluted, in which case the above assumptions are valid as (Ds)
is likely to change linearly with (Dm). The diffusivity can also be
modified by choosing an alternative mobile phase in which case (Dm)
will be changed but (Ds) will remain the same. Under these
circumstances the above assumptions are not likely to be precisely correct.
Nevertheless, if the
Dispersion Experimental-Validation
Author: RPW Scott
Book:Dispersion in Chromatography Columns
Section:Dispersion Van-Deemter-Equation
used. The permeability increases as
the square of the particle diameter but the variance per unit length only
increases linearly with the particle diameter. Thus, doubling the particle
diameter will allow a column four times the length to be used but the number of
plates per unit length will be halved. Consequently, the column
efficiency will be increased by a factor of two. It is also seen that the
higher efficiencies will be obtained with mobile phases of low viscosity and
for solutes of low diffusivity. Solvent viscosity and solute diffusivity tend
to be inversely proportional to each other and so the sensitivity of the
maximum obtainable efficiency to either solvent viscosity or solute diffusivity
will generally not be large. The approximate length of a column that will
provide the maximum column efficiency when operated at optimum velocity is
given by, l = nHmin
Dispersion Van-Deemter-Equation
Author: RPW Scott
Book:Dispersion in Chromatography Columns
Section:Dispersion Compressibility-Effects-GC
Effect of Mobile Phase Compressibility On the HETP Equation for a Packed GC Column
As the pressure falls along the column
length, the velocity changes and, as the solute diffusivity depends on the
pressure, the diffusivity of the solute will also change. The multi-path term,
which contains no velocity or gas pressure dependent parameters, will be
unaffected and the expression that describes it the same. The other terms in
the HETP equation, however, all contain parameters that are affected by
gas pressure (solute diffusivity and mobile phase velocity) and, therefore,
need to be modified to accommodate the compressibility of the mobile phase.
&
Dispersion Compressibility-Effects-GC