Page 6 - BR20828_E Accucore 0713S

Theory of solid-core particles
The general resolution equation relates the
separation power of the chromatographic
support to its efficiency, selectivity and
retention capacity, which are dependant on
particle size and quality of the packing,
bonded phase chemistry and surface area
respectively. Efficiency is solute independent
(i.e. is an inherent function of the physical
properties of the column), whereas retention
factor and selectivity are not.
Equation 1
R s – resolution
N – efficiency
α – selectivity factor
k’ – retention factor
Equation 2
HETP – height equivalent to a
theoretical plate
µ - Linear velocity of mobile phase
A – Eddy diffusion constant
B – Longitudinal diffusion constant
C m – Resistance to mass transfer in the
mobile phase
C s - Resistance to mass transfer in the
stationary phase
The height equivalent to a theoretical plate
(HETP) is generally used as a measure of
efficiency when comparing columns. HETP is
related to linear velocity through the column
via the van Deemter equation. In this
equation A, B and C (both components) are
constants that describe contributions to
band broadening through Eddy diffusion,
longitudinal diffusion and resistance to mass
transfer respectively. Peak or band
broadening is the consequence of several
mass transfer processes that occur as the
analyte molecules migrate down the column.
The A-term, Eddy diffusion, is dependent on
particle size and the homogeneity of the
packed bed. Smaller particles reduce the A-
term and therefore improve efficiency. The
average particle size distribution of a
spherical chromatographic medium is
generally defined through the ratio d90/10;
the closer this value is to 1 the less spread
there is on the average diameter of the
particles. The Accucore material has a d90/10
of 1.12 whereas most fully porous particles
have a d90/10 around 1.50. The schematic on
Figure 2 illustrates the effect of the average
particle size distribution on the homogeneity
of the chromatographic packed bed.
Whereas the A-term is independent of the
linear velocity of the mobile phase through
the column, the C-term, resistance to mass
transfer, is proportional to it and therefore an
important consideration when working with
fast separations. The C-term has two
contributors:
• resistance to the mass transfer in the
stationary phase Cs
• resistance to the mass transfer in the
mobile phase Cm.
The first occurs when the analyte molecule
diffuses in and out of the pores of the
stationary phase particle. With solid-core
particles the diffusional path of the analytes
is limited by the depth of the outer porous
layer, and therefore analytes do not have the
propensity to have greater diffusional lengths
within the more limited pore structure of the
solid-core material. This results in less band
broadening and more efficient peaks. The
resistance to mass transfer in the mobile
phase is caused by the fact that the liquid is
flowing in the channels between particles
and analytes have to diffuse through the
liquid to reach the stationary phase. This
effect is equivalent to the longitudinal
diffusion, however whereas with the
longitudinal diffusion increasing the flow
reduces the band broadening, increasing the
flow will have an adverse effect on the
homogeneity of the flow in a radial direction.
Analytes that are in the centre of the flow will
have a longer diffusional path to the particle
than analytes that are at the edge nearer to
the particle. Better packing and smaller
particles result in a more uniform diffusional
path in the liquid mobile phase.
From the discussion above we may expect
solid-core particle packed columns to be
more efficient than fully porous particle
packed columns of the same average particle
diameter. Both the A and C-terms are
reduced, and therefore H is reduced which
equates to higher efficiencies. It would also
be expected that the drop off in efficiency
that is seen with increasing flow rates will be
less with solid-core material than with fully
porous material due to a lesser contribution
form the resistance to mass transfer terms.
The next section will investigate the
experimental findings found when
comparing porous and solid-core particles.
Benefits of solid-core particles
Figure 3 compares the experimentally
determined separation efficiency (measured
as HETP) of fully porous 5 and 3 and sub-2µm
with that of the solid-core Accucore 2.6 µm
material. The van Deemter curves have a very
definite minimum HETP, which is where
minimal band broadening occurs, and
therefore a very definite maximum in term of
chromatographic efficiency. This means that
for a chromatographic support there is a
maximum chromatographic efficiency
delivered at a very definitive flow through the
column. Deviation from that flow will severely
impact chromatographic efficiency which in
turn may compromise assay performance. As
the particle size is decreased, HETP becomes
smaller and therefore the chromatographic
efficiency increases; also, for smaller particles
the flow rate that provides the best efficiency
Rs = N ( )
1 α-1
α √
4
B
µ
( )k’
1+k’
HETP = A Cm µ Cs µ
+ + +
Figure 2: Representation of the effect of average particle size distribution (D90/10) on the packed bed
homogeneity and band broadening through Eddy diffusion. Top - D90/10 ~ 1.5; Bottom - D90/10 ~ 1.1.