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HPLC 2008, BaltimorePage 1
Theoretical and Experimental Comparison of Porous and Superficially-Porous Particles for
High Speed and High Resolution Applications in HPLC
Monika M. Dittmann1; Wu Chen2; Ta-Chen Wei2; Charles Lofton2
1) Agilent Technologies GmbH, Waldbronn, Germany; 2)Agilent Technologies, Inc., Wilmington, DE
HPLC 2008, BaltimorePage 2
Introduction
Superficially porous particles consisting of a solid core and a porous shell have been around since the early days of HPLC. This particle morphology was considered to be mainly useful for separations of compounds with low diffusivity such as peptides or proteins on relatively large particles.
The decrease in intraparticle mass transfer in a partially porous media has already been described by Horvath and Lipsky in 1969.
Superficially porous (Poroshell) particles are commercially available for large molecule separation.
Recently it has been shown that this type of particles can also be useful for separations of small molecules and yield efficiencies comparable to those of smaller fully porous materials.
HPLC 2008, BaltimorePage 3
Introduction
Goal of this study:
Investigate the factors driving the contributions to performance of small superficially porous versus fully porous particles
Use of a general HETP equation to estimate the relative size of the various contributions to the theoretical plate height.
Fit the model to experimental results to determine which of the HETP contributions is driving the particle performance.
HPLC 2008, BaltimorePage 4
Reduced Plate Height vs. Reduced Velocity from a General HETP Equation
CsCmeddyaxtota hhhhh +++=l
1)'(2 −⋅⋅⋅+= em
ssmax kDDγγh ν Knox and Scott (1983)
Knox and Scott (1983)Horvath and Lin (1978)
Horvath and Lin (1978)
)3/1(12
−⋅+=
eωλheddy ν Horvath and Lin (1978)
B-term
A-term
C-term
3/22
)"1("
eCm kkh νκ ⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛+
⋅=
esz
mCs D
Dkksh ν⋅⋅+
⋅= 2)"1("
30
HPLC 2008, BaltimorePage 5
Definition of Reduced Plate Height and Reduced Interstitial Velocity
e
Te uu
εε
⋅= 0
Interstitial solvent velocity
u0 = solvent velocity measured by a t0 marker)
m
pee Dd
u ⋅=ν
Reduced interstitial solvent velocity
pdHh =
Reduced plate heightdiameter Particled
phase mobilein t coefficienDiffusion Dporositycolumn total
porosity alinterstitiparticle ofporosity internal
p
m
i
==
===
T
e
εεε
Diffusion coefficients in this study were determined from an approximation by Carr and Li (1997)
HPLC 2008, BaltimorePage 6
Morphology of Superficially Porous Particles
3
1 ⎟⎟⎠
⎞⎜⎜⎝
⎛−=
p
corePV d
dϕ
The porous volume fraction of a superficially porous particle is given by
Cored
pd
Solid core
Porous shell Vporousporousfullyii ϕεε ⋅= ,
The internal porosity εi of a superficially porous particle is assumed to be
3
653
15951
θθθθ
−−+−
=s pcore dd /=θ
Shape factor (Horvath and Lipsky (1969))
HPLC 2008, BaltimorePage 7
Parameters Depending on Particle Morphology
e
eikε
εε )1("0−⋅
=
Zone retention factor of an unretained compound k0”
Zone retention factor of a retained compound k”
"'"'" 00 kkkkk ⋅++=
)1('
""0
"0 k
DDγkk
kDD
m
sssz
sz
m
+⋅⋅+⋅=
γ
Effective diffusion inside the particle(Knox and Scott, 1983)
phase stationaryfactor n obstructioγphase mobilestagnant in factor n obstructioγ
zonestagnant in t coefficienDiffusion Dpores of surfaceon t coefficienDiffusion D
s
sz
sz
s
===
=
HPLC 2008, BaltimorePage 8
Dependence of Mass Transfer Coefficients Cm and Cson Particle Morphology for k’ = 1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0.4 0.5 0.6 0.7 0.8 0.9 1
porous volume fraction
shape factor s(k"/(1+k"))^2Dm / Dsz
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
0.4 0.5 0.6 0.7 0.8 0.9 1
porous volume fraction
mas
s tra
nsfe
r coe
ffici
ents
CsCm
3/22
)"1("
eCm kkh νκ ⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛+
⋅= esz
mCs D
Dkksh ν⋅⋅+
⋅= 2)"1("
30
Cm Cs
HPLC 2008, BaltimorePage 9
Dependence of Mass Transfer Coefficients Cm and Cson Retention Factor
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0 2 4 6 8 10
Retention factor k'
Cm
, Cs fully porous
75% porous50% porous
Cm
Cs
HPLC 2008, BaltimorePage 10
Comparison of the Different Contributions to Reduced Plate Height h
Line Chart
reduced interstitial velocity5 10 15 20 25 30 35 40
0
0.5
1
1.5
2
2.5
3Total hhax
heddy
hCm
hCs
4.14.0)/(
8.04.0
7.25'
==⋅
==
==
λγγγ
μ
mss
m
sz
p
DD
mdk
Con
trib
utio
ns to
redu
ced
plat
e he
ight
HPLC 2008, BaltimorePage 11
interstitial velocity [mm/s]0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
14
16
interstitial velocity [mm/s]0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
14
16
interstitial velocity [mm/s]0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
14
16 scmDm /104.5 210−⋅= scmDm /107.2 210−⋅=
4.14.0)/(
8.04.0
7.25'
==⋅
==
==
λγγγ
μ
mss
m
sz
p
DD
mdk
scmDm /105.1 210−⋅=
Total HHax
Heddy
HCm
HCs
Con
trib
utio
ns to
redu
ced
plat
e he
ight
Plate Height H vs. Linear Velocity for Different Solutes
HPLC 2008, BaltimorePage 12
Experimental Investigation
H – u curves were measured on the 4 porous and 1 superficially porous material
Column A fully porous 1.8 μm Column B fully porous 2.5 μmColumn C fully porous 2.8 μmColumn D fully porous 3.5 μm
Column E superficially porous 2.7 μm (core 1.7 μm), ϕ = 0.75
Conditions:
Solvent: Acetonitrile/water 60:40Temperature : 25 CSample: series of homologous alkylphenones
HPLC 2008, BaltimorePage 13
Reduced van Deemter Curves for Octanophenone and Valerophenone
Scatter Plot
reduced interstitial velocity0 5 10 15 20 25 30 35 40
2
3
4
5
6
7
Scatter Plot
reduced interstitial velocity0 5 10 15 20 25 30 35 40
2
3
4
5
6
7
Column A
Column B
Column C
Column D
Column E
HPLC 2008, BaltimorePage 14
Column A Column B Column C Column D Column E Column Fsz 0.80 0.80 0.80 0.80 0.80 0.80
m 0.50 0.50 0.50 0.50 0.50 0.50
2.40 2.40 2.40 2.40 2.40 2.40
s*Ds/Dm 0.32 0.32 0.36 0.30 0.36 0.27
1.70 1.10 1.20 1.20 1.20 1.00
Fitting the Model to the data
1)'(2 −⋅⋅⋅+= em
ssmax kDDγγh ν
e
m
sssz
Cs
kDDγkk
kkksh ν
γ⋅
+⋅⋅+⋅⋅
+⋅=
)1('
")"1(
"30 "
0"0
2
)3/1(12
−⋅+=
eωλheddy ν
Adjusted parameters
3/22
)"1("
eCm kkh νκ ⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛+
⋅=
HPLC 2008, BaltimorePage 15
Fitting Results for Octanophenone
Line Chart
reduced interstitial velocity5 10 15 20 25
0
1
2
3
4
5
6
Line Chart
reduced interstitial velocity5 10 15 20 25
0
1
2
3
4
5
6
Con
tribu
tions
to h
Column C, totally porous 2.8 μm Column F, superficially porous 2.7 μm
HPLC 2008, BaltimorePage 16
Axial diffusion (hax) contribution for different Columns
Scatter Plot
reduced interstitial velocity0 5 10 15 20 25 30 35 40
0
1
2
3
4
5
6
7
Column A
Column B
Column C
Column D
Column E
HPLC 2008, BaltimorePage 17
Eddy diffusion (heddy) Contribution for Different Columns
Scatter Plot
reduced interstitial velocity0 5 10 15 20 25 30 35 40
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
Column A
Column B
Column C
Column D
Column E
HPLC 2008, BaltimorePage 18
Film diffusion (hCm) Contribution for Different Columns
Scatter Plot
reduced interstitial velocity0 5 10 15 20 25 30 35 40
0.2
0.4
0.6
0.8
1
Column A
Column B
Column C
Column D
Column E
HPLC 2008, BaltimorePage 19
Intraparticle diffusion (hCs) Contribution for Different Columns
Scatter Plot
reduced interstitial velocity0 5 10 15 20 25 30 35 40
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14Column A
Column B
Column C
Column D
Column E
HPLC 2008, BaltimorePage 20
Conclusions
The superficially porous particles investigated show reduced plate heights which are significantly lower than that of fully porous particles in a comparable size range.
Contributions to HETP from intraparticle mass transfer are relatively small compared to contributions from the other HETP terms and there is no clear advantage from the particle morphology.
The increased performance of the superficially porous material can be mainly attributed to a lower eddy-diffusion term and to a lower axial diffusion contribution a low reduced velocities.
The underlying causes for this behavior need to be subject to further investigation.