theoretical and experimental comparison of porous … and... · hplc 2008, baltimore page 1...

HPLC 2008, Baltimore

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


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.


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.


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


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)


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))


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

===

=


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("


⎠

⎞⎜⎜⎝

⎛+

⋅= esz

mCs D

Dkksh ν⋅⋅+

⋅= 2)"1("

30

Cm Cs


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


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


interstitial velocity [mm/s]0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

14

16


0

2

4

6

8

10

12

14

16


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


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


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


2

3

4

5

6

7

Column A

Column B

Column C

Column D

Column E


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("


⎠

⎞⎜⎜⎝

⎛+

⋅=


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


Axial diffusion (hax) contribution for different Columns

Scatter Plot


0

1

2

3

4

5

6

7

Column A

Column B

Column C

Column D

Column E


Eddy diffusion (heddy) Contribution for Different Columns

Scatter Plot


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


Film diffusion (hCm) Contribution for Different Columns

Scatter Plot


0.2

0.4

0.6

0.8

1

Column A

Column B

Column C

Column D

Column E


Intraparticle diffusion (hCs) Contribution for Different Columns

Scatter Plot


0

0.02

0.04

0.06

0.08

0.1

0.12

0.14Column A

Column B

Column C

Column D

Column E


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.


Acknowledgements

Prof. Pete Carr

Prof. Gert DesmetKen BroekhovenJeroen BillenDeirdre Cabooter

Konstantin ChoikhetBill Barber

theoretical and experimental comparison of porous … and... · hplc 2008, baltimore page 1...

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