Thesis Bachelor project Chemistry - UvA · 2020. 7. 15. · Thesis Bachelor project Chemistry Liz...

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Miniaturization in asymmetrical flow

field-flow fractionation

Thesis Bachelor project Chemistry

Liz Leenders

Amsterdam 09-06-2014

University of Amsterdam

Analytical Chemistry Group

Supervisors: Dr. W. Th. Kok

J. Králová MSc

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Samenvatting

Asymmetrische flow field-flow fractionatie (asymmetric flow field-flow fractionation, AF4) is een

scheidingstechniek die veel gebruikt wordt in industriële, farmaceutische en biomedische doeleindes.

Deze scheidingstechniek maakt gebruik van het verschil in diffusie coëfficiënt van de te scheiden

proteïnes. Miniaturisatie van AF4 is interessant, omdat het op deze manier, door zijn kleine formaat,

als testmethode buiten het ziekenhuis gebruikt kan worden voor analyse van macromoleculen in

lichaamsstoffen. In dit project zijn één commercieel apparaat en enkele miniaturen van verschillende

vorm getest en geoptimaliseerd. Verschillende hoogtes van scheidingskanalen zijn gebruikt, hoogtes

van 190μm, 250μm, 350μm en 480μm voor het commerciële apparaat en 100μm, 200μm, 300μm,

400μm en 500μm voor de miniaturen. In de eerste stap van het project werd het commerciële apparaat

geoptimaliseerd, hieruit bleek dat grotere (350μm/480μm) scheidingskanalen beter in staat zijn om

een mengsel van proteïnes (BSA, apoferritin en thyroglobulin) te scheiden dan kleinere kanalen

(250μm/190μm). Vervolgens is een miniatuur in dezelfde vorm als het commerciële apparaat getest

en geoptimaliseerd. Ook hieruit bleek dat grotere kanalen (300μm/400μm/500μm) beter werken dan

kleinere (200μm/100μm). Het kanaal met grootte 400μm gaf de beste resultaten. Het scheiden van de

drie proteïnes met een miniatuur van deze vorm (Vorm 1) was mogelijk, maar er zijn een aantal

instrumentele problemen die opgelost moeten worden om de miniaturen optimaal te gebruiken. De

kleinere miniaturen (vorm 2 en 3) zijn niet in staat om het mengsel van proteïnes te scheiden. Analyse

met Blue Dextran wees vervolgens uit dat het kanaal in de miniaturen niet goed op het membraan

wordt gedrukt, wat leidde tot het lekken van het mengsel uit het kanaal in het apparaat. Hierdoor kan

het mengsel niet geanalyseerd worden met UV/Vis. Verder onderzoek naar miniaturisatie van AF4 is

dus nodig.

Abstract

Asymmetrical flow field-flow fractionation (AF4) is a promising separation mechanism that is used in

industrial, pharmaceutical and biomedical applications. In AF4 the separation depends on difference

in diffusion coefficients of the separated proteins. Over the past few years miniaturization of AF4 has

been of great interest, because a miniaturized AF4 device could become a point of care diagnostic

device (POCDD) for analysis of macromolecules in body fluids. During this project one commercial-

and several miniaturized AF4 channels of different shapes were tested and optimized for the

separation of proteins. Several heights of the fractionation channels were tested namely 190μm,

250μm, 350μm and 480μm for the commercial channel and 100μm, 200μm, 300μm, 400μm and

500μm for the miniaturized channels. First step of this project was the optimization of the

commercially available channel. High spacer heights (350μm/480μm) provided better separation of

the mixture of proteins (BSA, apoferritin and thyroglobulin) than small spacer heights

(250μm/190μm). Spacer height 350μm gave the best results. After this optimization, a miniaturized

channel with the same shape as the commercial channel was tested. Also in this case higher channel

heights (300μm/400μm/500μm) were better able to separate the proteins than smaller ones

(200μm/100μm). Channel height 400μm gave the best results. Last step in this project was testing

three different shapes of miniaturized channels. Separation of the three proteins with the largest

miniaturized channel (shape 1) was possible, however there are some instrumental issues that need to

be solved to utilize the full potential of the miniaturized channels. The smaller miniatures (shape 2

and 3) were not able to separate the mixture of three proteins. Analysis with Blue Dextran showed

that the channel was not pressed towards the membrane properly, and therefore part of the mixture

leaked out of the channel into the device. In this way the mixture could not be analyzed properly by

UV/Vis. Further research on miniaturization of AF4 is needed.

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Table of Contents 1. Introduction ......................................................................................................................................... 4

2. Principles of asymmetrical flow field-flow fractionation (AF4) ........................................................ 6

3. Theory ................................................................................................................................................. 7

3.1 Resolution ..................................................................................................................................... 7

3.2 Column efficiency ......................................................................................................................... 7

3.2.1 Number of theoretical plates .................................................................................................. 7

3.2.2 Plate height ............................................................................................................................. 7

3.3 Retention time ............................................................................................................................... 8

3.4 Standard deviation ........................................................................................................................ 8

4. Experimental ....................................................................................................................................... 9

4.1 Reagents and samples ................................................................................................................... 9

4.2 Instruments .................................................................................................................................... 9

4.3 Asymmetrical flow field-flow fractionation ............................................................................... 10

5. Results ............................................................................................................................................... 11

5.1 Commercial channels .................................................................................................................. 11

5.1.1 Comparing commercial channels ......................................................................................... 18

5.2 Miniaturized channels ................................................................................................................. 19

5.2.1 Comparing miniaturized channels with shape 1 .................................................................. 29

5.2.2 Comparing miniaturized channels........................................................................................ 31

6. Conclusion ........................................................................................................................................ 33

7. Discussion and Future Prospects....................................................................................................... 34

Acknowledgements ............................................................................................................................... 35

List of abbreviations ............................................................................................................................. 35

References ............................................................................................................................................. 36

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1. Introduction

Field-flow fractionation (FFF) is a collection of separation techniques suitable for macromolecules or

analytes in the range of nano- and micrometers. FFF has some similarities with liquid chromatography

(LC), but the difference between FFF and LC is in the separation mechanism for elements transported

by the liquid-flow. In LC separation occurs via eluting species with the stationary phase of the

column. In FFF the separation of sample components depends on the interaction with an externally

applied force, which is perpendicular to the axial flow in a channel. The profile of an axial flow can

be identified as a parabola with the highest flow velocity in the middle and a lower velocity on the

channel walls. Because of molecular diffusion, the sample components take different positions across

the parabolic flow-profile under influence of an external force and field. This results in elution with

different velocities, leading to separation of the sample components.

Various types of external fields have been used in FFF, such as electrical fields (electrical FFF)1,

temperature gradients (thermal FFF)2 and cross-flow (flow FFF)

3. In all subclasses of FFF, the

channel does not contain a stationary phase. Various solvents can be used as a mobile phase,

including water and buffers. The physiochemical properties and applications of various FFF subtypes

are listed in table 1.4 The focus in this thesis is on asymmetrical flow FFF and its strength in

characterizing macromolecules, such as proteins or polymers, by difference in diffusion coefficients

and size.

Table 1: Physiochemical properties and applications for various field-flow fractionation systems

FFF subtype Physiochemical properties Applications

Electrical

Size, electrophoretic mobility

Cells and organelles, bacteria and

viral separations, characterization

of emulsions, liposomes, protein

adsorption

Thermal Size, thermal diffusion

coefficient

Separation of dissolved and

suspended polymers, polymer and

silica nanoparticle analysis

Cyclical electrical Electrophoretic

mobility

Biopolymer separations and zeta

potential measurements

Dielectrophoresis Dielectric permittivity,

size

Cell separation and dielectric

property measurements and cancer

cell separation

(Asymmetrical) flow Diffusion, size Proteins, DNA, polymers, cells,

micro and nanoparticles

Flow field-flow fractionation (FlFFF) was discovered by J.C. Giddings in late 1970’s3 and has

become the most often used subtype of FFF. In FlFFF the field applied to the channel is a second flow

which pushes the flowing components to a membrane on top of the wall of a thin rectangular channel.

This membrane is permeable to carrier liquid, but does not permit the sample components to pass

through. Diffusion of the sample components acts as a withstanding force, and therefore all of the

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components take different locations in the channel. Separation occurs via differences in diffusion

coefficients of the eluting elements. Particles with large diffusion coefficients (or smaller sizes) elute

first; and particles with small diffusion coefficients elute later due to the parabolic profile of the

channel flow.

FlFFF can be classified into three different variants based on the geometry of the channel. Firstly, the

symmetric FlFFF, which has a flat channel having both upper and lower walls permeable, secondly,

an asymmetric FlFFF (AF4) channel, which contains only one permeable wall on top of the channel.

Thirdly a hollow fiber FlFFF, which is a relatively new technique, its channel is based on ceramic

hollow fiber having a porous cylindrical wall.5

AF4 is the most often used technique, because of its promising features. Especially its possibility to

separate particles with a wide range of sizes using variable cross-flow programs is promising. Today,

AF4 is used in industrial, pharmaceutical and biomedical applications, as an alternative to size-

exclusion chromatography.6

The principles of AF4 are discussed in detail in chapter 2. In short, the part of the axial flow which is

pumped out through the membrane, acts as cross-flow. During sample injection a mobile phase flows

in from both inlet and outlet of the channel and meets at a focusing point. The sample is introduced in

the channel at the focusing point where it is focused for a short period. After the focusing step, the

flow is introduced in the channel to start the elution, the sample components are separated in the

channel and then detected by the UV-Vis detector.

Over the past few years miniaturization of separation techniques has been of great interest since it has

many advantages as a sample volume reduction, a lower mobile phase consumption and a faster

analysis.4 A miniaturized AF4 device could become a point of care diagnostic device (POCDD) for

analysis of macromolecules in body fluids. POCDD measurements provide results rapidly and near

the patient. This leads to major time savings because the samples do not travel to a laboratory and

results can be collected immediately. During this project one commercial- and several miniaturized

AF4 channels were tested for the separation of proteins. Obtained results were compared. The goal of

this thesis is to examine the possibility of using miniaturized AF4 channels for the separation of

macromolecules without losing the performance of a commercially available channel.

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2. Principles of asymmetrical flow field-flow fractionation (AF4)

In FFF the separation is executed with a carrier liquid pumped through a flat channel. The channel is

formed by a spacer between two walls (Figure 1)7. In a symmetric system the walls are both porous

(Figure 1a). A second pump is used to flow the same carrier liquid in the perpendicular direction,

through both walls of the channel. The macromolecular components of the sample stay inside the

channel by a semi-permeable membrane on top of one of the porous walls.

Wahlund and Giddings8 proposed an easier system in 1987. This asymmetrical system (Figure 1b)

contains only one porous wall. The in-going flow (Fin) in AF4 is split in two parts with help of flow

regulators or an extra pump. One part is flushed through the channel in the axial direction towards the

detection side outlet, called the channel flow (Fout). The other part passes through the membrane and

the porous wall, called the cross-flow (Fc). The advantage of AF4 is the fact that the set-up requires

one pump or flow regulator less than a symmetrical system. All commercial instruments use the AF4

method.

Figure 1: Experimental set-up for (a) symmetrical and (b) asymmetrical FlFFF (Qureshi, R. N.; Kok, W. T7)

Separation in AF4 contains three different steps (Figure 2)7. The first step is called the injection

(Figure 2a), in which a specific volume of the sample is introduced in the channel. This is done

through an extra inlet port close to the channel inlet.

After this injection, a part of the in-going flow enters the channel through the channel inlet, and part is

pumped into the channel from the channel outlet. This step is called focusing. In this way the sample

components are concentrated on top of the membrane in a thin layer and focused close to the inlet port

in a thin band.

The final step is the elution (Figure 2b). The carrier liquid enters the channel from the inlet side. A

part of the liquid leaves the channel through the porous wall and the rest flows through the detector.

The velocity profile of the channel flow is a parabola, velocity is high in the middle of the channel

and low at the walls. The sample components are all concentrated in a thin layer on top of the

membrane by the cross-flow, and then flushed towards the detector with the channel flow with

different velocities, dependent on the position of the sample in the channel. Retention time of sample

components only depend on differences in diffusion constant, and consequently on differences in

molecular size.

Figure 2: Flow regimes in AF4 during (a) sample injection and focusing and (b) elution (Qureshi, R. N.; Kok, W. T7)

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3. Theory

3.1 Resolution

The resolution is referred to the separation ability of the system. It is the degree of overlap of two

peaks. It is agreed that a resolution index Rs of more than 1.5 indicates a baseline separation between

the peaks, and a resolution less than 1.5 indicates some degree of co-elution. A resolution of zero

indicates that the peaks are completely overlapped. The resolution can be described mathematically

by9:

(1)

In which Δtr is the retention time difference between the peaks and σ1 and σ2 are the standard

deviations of two peaks. The standard deviations in case of Gaussian peaks can be calculated using

equation 2.9

√ (2)

3.2 Column efficiency

The number of theoretical plates and the plate height are mathematical concepts to predict column

efficiency, these concepts are related to each other.

3.2.1 Number of theoretical plates

The number of theoretical plates N is an indirect measure of the width of the peak at a specific

retention time, and can be calculated by10

:

(

)

(3)

Where tr is the elution time of the peak and w1/2 is the width of the sample peak at half height.

3.2.2 Plate height

Another concept to predict column efficiency is the height equivalent of the theoretical plate H. In

plate theory the plate height is given by the length of the column L divided by the number of

theoretical plates N, as shown in equation 4.11

(4)

The plate height represents the length of the separation column that is necessary to generate a

separation between two particles. The goal for an efficient column is to minimize H and maximize N.

This is because the shorter each theoretical plate is, the more theoretical plates will fit in the length of

the column. This translates to more plates per meter, which leads to higher column efficiency.

The total plate height contains several factors, such as instrumental effects Hi, non-equilibrium effects

Hn, polydispersity Hp and diffusion Hd, as shown in equation 5.11

(5)

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The diffusion coefficients for the particles used in this project are small because the particles have

high molecular weights. The flow velocity is high, so the contribution of the diffusion to plate height

can be neglected. The polydispersity is also negligible, because we are working in this project with

fairly monodisperse macromolecules. The only effects to the total plate height taken into

consideration are the instrumental and non-equilibrium effects, when optimizing the instrument.

Instrumental plate height

The instrumental component of the plate height in field-flow fractionation systems depends on the

channel geometry, the post-column volumes, the sample injection size, method, the instrument set-up

and the fluidic connections. All of these elements are not easily expressed in a comprehensive theory,

so they have not been mathematically examined. The instrumental plate height is usually measured

experimentally.11

Non-equilibrium plate height

The non-equilibrium component of the plate height in field-flow fractionation systems depends on the

channel thickness, the diffusion D and the flow velocity v, as shown in the complex equation 6.11

⟨ ⟩

(6)

The function χ(λ) is traditionally represented by:

(7)

The non-equilibrium term is the main contributor to the measured plate height. This effect is due to

the differential axial movement of the zone components, as a result these components are located in

different velocity streamlines across the channel thickness.11

3.3 Retention time

The relation of the retention of a compound and its molecular size in AF4 relies only on liquid flows

and molecular diffusion. The retention time of a compound can be calculated using the simplified

equation 8.7

(

) (8)

In which w is the thickness of the spacer (or height of the channel). Di is the diffusion coefficient of

the compound, and can be calculated using the Stokes-Einstein equation.

3.4 Standard deviation

The standard deviation of a peak of a compound with an adequate amount of retention can be

calculated by the simplified equation 9.7

{ (

)}

(9)

In which uC is the cross-flow velocity (the cross-flow rate divided by the area of the porous channel),

and w is the real spacer height of the channel. This equation does not take into account the

instrumental parameters, but only the non-equilibrium plate height. In a specific fractionation the

compounds are eluted as peaks with the same width.

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4. Experimental

4.1 Reagents and samples

In this project three different proteins were used for the analysis, BSA, apoferritin and thyroglobulin,

all provided by Sigma Aldrich. Phosphate Saline Buffer (PBS) (15mM) was used as mobile phase. In

distilled water, 8.00g/L NaCl, 2.76g/L Na2HPO4∙2H2O and 0.63g/L NaH2PO4∙H2O were dissolved.

The pH of this buffer was adjusted to 7.4 with NaOH.

4.2 Instruments

All samples were analyzed with an Applied Biosystems 757 Absorbance detector (220/280nm

wavelength used) equipped with an Agilent Technologies 1100/1200 series Isocratic LC system, Iso

Pump, Degasser and a Wyatt Technology Europe GmbH Eclipse 2 separation system.

For the commercial channel measurements an Eclipse AF4 mini-channel was used.

Data processing was achieved with software Clarity Lite Chromatography Station.

For the final data treatment Microsoft Excel version 2010 was used.

The miniaturized channels are not commercially available, but are costum-made. In figure 3 the

miniaturized channels are shown.

Figure 3: Miniaturized channel. Left: a. channel inlet, b. injection port, c. channel outlet. Right:

Different parts of the device, membrane is placed on top of the black ring on the bottom part.

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4.3 Asymmetrical flow field-flow fractionation

For the AF4 experiments 15µL of sample was injected with a concentration of approximately 1

mg/mL. For all experiments a blank was injected as well. The blank was PBS, which was the solvent

for preparation of sample solutions.

Figure 4 shows a typical fractogram of BSA, apoferritin and thyroglobulin. As said in chapter 2, an

AF4 run has three different steps. The first part of the fractogram shows the focusing part and sample

injection, after a few minutes (in this case 5 min) the elution starts and the proteins are detected by the

UV/Vis detector. BSA elutes first, because this is the smallest protein (66kDa). Apoferritin (444kDa)

and thyroglobulin (660kDa) elute later. BSA and thyroglobulin have dimers, which are also shown in

the fractogram. In the last part of the run there is no crossflow, so the amount of sample that is

absorbed on the membrane elutes in this part.

Figure 4: Fractogram of BSA, apoferritin and thyroglobulin

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5. Results All results are obtained with UV-Vis detector at wavelength 280nm, except miniature of shape 1 with

spacer height 100µm is obtained at wavelength 220nm. Resolution and number of theoretical plates

are calculated using equation 1 and 3. The theoretical fractograms (figure 7,9,12,17,19,21 and 24)

were made using equation 8 and 9, to calculate the retention time of the proteins and width of their

peaks in the fractogram.

5.1 Commercial channels

First step in this project was to optimize the commercially available channels. Four different channels

were tested, channels with spacer height 190µm, 250µm, 350µm and 480µm. All fractograms

containing the best conditions for each channel were also compared to their theoretical fractogram.

Commercial channel with spacer height 350μm

The channel with spacer height 350μm was optimized first. Several measurements with different

crossflows were tested, and resolutions and number of theoretical plates were calculated using

equations 1 and 3. The peaks used for these calculations were the peaks of apoferritin and

thyroglobulin, because BSA always elutes quite fast and is well separated from apoferritin and

thyroglobulin. Crossflow 2.0ml/min gave a resolution of 1.49, which is almost baseline separation

(resolution 1.5), as shown in table 2 and figure 5.

Table 2: Resolution and number of theoretical plates for various flow-conditions

Crossflow Fc

(ml/min)

Detectorflow Fout

(ml/min)

Resolution Rs Theoretical plates N

2.0 1.0 1.49 204

1.5 1.0 1.26 158

1.1 1.0 0.87 65

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Figure 5: Fractogram of BSA + apoferritin + thyroglobulin. Experimental conditions: inj. vol. 15µL, mobile phase

PBS, spacer height 350µm

In order to examine the effect of detectorflow on resolution, different detectorflows were tested and

resolutions were calculated, as shown in table 3 and figure 6. Higher detectorflow led to lower

number of theoretical plates and lower resolution, so crossflow 2.0ml/min and detectorflow 1.0ml/min

are the optimum conditions for the 350μm spacer. The detectorflow was kept constant in every

measurement, because this made it easier to compare the spacer height in chapter 5.1.1.


Crossflow Fc

(ml/min)

Detectorflow Fout

(ml/min)


2.0

2.0

1.0

1.5

1.49

1.47

204

196

2.0 2.0 1.42 154

0,0

0,1

0,2

0,3

0,4

0,5

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min) 0,0

0,1

0,2

0,3

0,4

0,5

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min)

0,0

0,1

0,2

0,3

0,4

0,5

0 10 20 30

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nsi

ty (

mV

)

tR (min)

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Figure 6: Fractogram of BSA + apoferritin + thyroglobulin. Experimental conditions: inj. vol. 15µL,

mobile phase PBS, spacer height 350µm

The fractogram of the measurement with the best conditions was compared to the theoretical

fractogram, as shown in figure 7. The theoretical fractogram doesn’t take dimers into account, so

these peaks are not shown in the theoretical fractogram. The BSA-peak of the real fractogram appears

to be similar to the theoretical one, the apoferritin and thyroglobulin elute slightly later than theory.

This is due to the fact that the equations used for calculating the theoretical fractogram, only takes the

non-equilibrium plate height (chapter 3.2.2) into account, not the instrumental plate height. In this

case the peaks elute later than should be according to the theoretical fractogram, also their width is

larger. This could be because of the fact that the instrumental plate height is quite large.

0,0

0,1

0,2

0,3

0,4

0,5

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min) 0,0

0,1

0,2

0,3

0,4

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min)

0,0

0,1

0,2

0,3

0,4

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min)

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Figure 7: Theoretical fractogram of BSA + apoferritin + thyroglobulin. Experimental conditions: inj. vol.

15µL, mobile phase PBS, real spacer height 263µm, Fc=2.0mL/min, Fout=1.0mL/min


The conditions used for the first measurement with the channel with spacer height 250μm were the

same as the optimum conditions for the 350μm. This measurement resulted in a resolution of 0.89, so

there was still some degree of co-elution. In order to push the sample to the bottom of the channel

more, more runs with higher crossflow were measured. After calculating the resolution, as shown in

table 4, crossflow 3.0 ml/min seemed to be the best condition for this spacer height. The resolution for

these conditions is 1.22, so there is still some degree of co-elution, as shown in figure 8, but this was

the best result possible with detectorflow 1.0ml/min.


Crossflow Fc

(ml/min)

Detectorflow Fout

(ml/min)


2.0 1.0 0.89 102

3.0 1.0 1.22 208

3.5 1.0 1.17 226

4.0 1.0 1.15 211

0,0

0,1

0,2

0,3

0,4

0,5

0 5 10 15 20 25 30

Inte

nsi

ty (

mV

)

tR (min)

Theoretical fractogram

Real fractogram

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fractogram, as shown in figure 9. The peaks coming from the dimers are not shown in the theoretical

fractogram, because these dimers were not taken into account. The experimental fractogram of the

250μm spacer looks very similar to the theoretical fractogram. Still the width of the peaks is larger

than theory, but this is again due to the instrumental plate height.

0,0

0,5

1,0

1,5

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min)

crossflow 2detectorflow 1

0,0

0,5

1,0

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min)


0,0

0,5

1,0

1,5

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min)

crossflow 3.5detectorflow 1

0,0

0,5

1,0

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min)


0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

0 5 10 15 20 25 30

Inte

nsi

ty (

mV

)

tR (min)


Real fractogram

Figure 9: Theoretical fractogram of BSA + apoferritin + thyroglobulin. Experimental conditions: inj. vol. 15µL,

mobile phase PBS, real spacer height 182µm, Fc=3.0mL/min, Fout=1.0mL/min

16


The first conditions used for the measurements with the channel with spacer height 190μm were the

best conditions for the 250μm spacer. The fractogram didn’t show any peaks of the proteins, and the

peak after focusing+elution (without crossflow) at the end of the fractogram was extremely large.

Lower detectorflows were tested, and with detectorflow 0.5ml/min a peak in the fractogram appeared,

but the proteins were not separated, as shown in figure 10. After this measurement higher crossflows

were tested, but all of them gave a similar result, only the amount of sample left after the

focusing+elution step (the large peak at the end of the fractogram) became larger. This is due to the

fact that the sample components are pushed harder onto the membrane by a higher crossflow, and they

might get stuck in the membrane. The channel with spacer height 190μm is not able to separate this

mixture of proteins.




The channel with spacer height 480μm is closest in size to the 350μm spacer, so the optimum

conditions for this spacer were tested on the 480μm spacer first. The resolution for this measurement

was immediately above 1.5, so there was baseline separation already. Lower crossflows were tested in

order to make the analysis as quick as possible. The crossflow 1.8ml/min also gave a resolution higher

than 1.5, and the measurement was a lot faster than the measurement with crossflow 2.0ml/min and

had a higher number of theoretical plates, as shown in table 5 and figure 11.

0,0

0,5

1,0

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min) 0,0

0,5

1,0

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min)

0,0

0,5

1,0

0 10 20 30

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nsi

ty (

mV

)

tR (min)

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Crossflow Fc

(ml/min)

Detectorflow Fout

(ml/min)


2.0

1.8

1.0

1.0

1.68

1.58

111

228

1.6 1.0 1.43 52




fractogram, as shown in figure 12. The width of the peaks in the real fractogram is much bigger than it

should be, according to the theory. The width of the peaks is also larger than was the case in the

250μm and 350μm spacer fractograms, so the instrumental plate height of the 480μm spacer will be

bigger than in case of the other two spacer heights.

0,0

0,1

0,2

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min) 0,0

0,1

0,2

0 10 20 30In

ten

sity

(m

V)

tR (min)

0,0

0,1

0,2

0,3

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min)

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Figure 12: Theoretical fractogram of BSA + apoferritin + thyroglobulin. Experimental conditions: inj.

vol. 15µL, mobile phase PBS, real spacer height 398µm, Fc=1.8mL/min, Fout=1.0mL/min

5.1.1 Comparing commercial channels

As shown in table 6, the resolution for the channel with spacer height 480µm is the highest, there is

baseline separation. Also the channel with spacer height 350µm has a resolution higher than 1.5, so

also in this case there is baseline separation. The number of theoretical plates is highest for the

channel with spacer height 480µm, which indicates more plates per meter in a separation column,

which leads to higher column efficiency.

Table 6: Resolution and number of theoretical plates for various spacer heights

Spacer height w

(µm)

Crossflow Fc

(ml/min)

Detectorflow

Fout (ml/min)

Resolution Rs Theoretical

plates N

190 3.5 0.5 - -

250 3.0 1.0 1.22 208

350 2.0 1.0 1.49 204

480 1.8 1.0 1.58 228

In figure 13 all fractograms for the different spacers are shown. The channel with spacer height

190µm is not able to separate the proteins. Table 6 indicates that the channel with spacer height

480µm is the best, but the fractogram shows that the separation takes almost 25 minutes. Compared to

the channel with spacer height 350µm, which also had high resolution and number of theoretical

plates, this is a very long separation. In order to use AF4 as a POC technique, the analysis should be

as short as possible. The separation in channel with spacer height 350µm only takes 15 minutes, so

this is the best spacer height for separation in the commercial channels.

0,0

0,1

0,2

0,3

0,4

0 5 10 15 20 25 30

Inte

nsi

ty (

mV

)

tR (min)


Real fractogram

19

Figure 13: Fractogram of BSA + apoferritin + thyroglobulin, best conditions for every spacer.

Experimental conditions: inj. vol. 15µL, mobile phase PBS, spacer height 190-480µm

5.2 Miniaturized channels

During the second part of the project several miniaturized channels of different shapes and

dimensions (figure 14) were optimized and compared to the commercial channels. Five different

miniaturized channels of shape 1 were tested, varying in channel height (100, 200, 300, 400 and 500

µm). In the optimization of the commercial channels, the channels with spacer height 350 and 480µm

showed the best separation of the proteins. Because of that when testing the miniatures, the channel

with height 400µm was tested first. For shape 2 and 3 only channel height 400μm was tested.

Figure 14: Shapes and dimensions of the different miniatures

-0,1

0,4

0,9

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min)

190um

-0,1

0,4

0,9

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min)

250um

-0,1

0,4

0,9

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min)

350um

-0,1

0,4

0,9

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min)

480um

20

Miniaturized channel shape 1 with channel height 400μm

Since the miniature is smaller in size than the commercial channel, the conditions for the

measurements also need to be reduced. First a measurement was done with the same ratio in

crossflow/detectorflow 2:1 as the best conditions for the commercial channel with spacer height

350μm. The resolution for these conditions was only 0.48, so lower crossflows were tested to make

sure the sample is pushed to the membrane more. The resolution became higher (as shown in table 7

and figure 15), but there was still no baseline separation.


Crossflow Fc

(ml/min)

Detectorflow Fout

(ml/min)


0.8

0.9

0.5

0.5

0.98

1.12

92

126

1.0 0.5 0.48 68


mobile phase PBS, channel height 400µm

Crossflow 0.9ml/min gave the highest resolution with detectorflow 0.5ml/min, but to make sure this

was the best resolution possible, lower detectorflows were tested, as shown in table 8. Although the

run with detectorflow 0.5ml/min was shorter than the other ones (figure 16), detectorflow 0.2ml/min

gave a much higher resolution and number of theoretical plates, so crossflow 0.9ml/min and

detectorflow 0.2ml/min were the best conditions for channel height 400μm. The detectorflow was

kept the same in every measurement, because this made it easier to compare the channel height in

chapter 5.2.1 and 5.2.2.

0,0

0,1

0,2

0,3

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min) 0,0

0,1

0,2

0,3

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min)

0,0

0,1

0,2

0,3

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min)

21


Crossflow Fc

(ml/min)

Detectorflow Fout

(ml/min)


0.9

0.9

0.2

0.3

1.28

1.25

228

204

0.9 0.5 1.12 126




fractogram, as shown in figure 17. The width of the peaks is extremely large in the real fractogram,

the proteins elute later than should according to the theory. The equation used for calculating the

retention times in the theoretical fractogram was equation 8, which takes only into account the non-

equilibrium plate height. In this case the instrumental plate height is large because the width of the

peaks is large, larger than was the case in the commercial channels.

-0,1

0,0

0,1

0,2

0,3

0,4

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min)

-0,1

0,0

0,1

0,2

0,3

0,4

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min)

0,0

0,1

0,2

0,3

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min)

22


vol. 15µL, mobile phase PBS, real channel height 331µm, Fc=0.9mL/min, Fout=0.2mL/min


The channel height of this miniature is smaller than 400μm, therefore the crossflow should be higher

than 0.9ml/min, as seen before with the commercial channels. First crossflow 1.0ml/min was tested,

but the resolution was only 1.00. Higher crossflow was needed to make the resolution higher, and

crossflow 1.3ml/min got the highest resolution possible (as shown in table 9 and figure 18), only there

was still some degree of co-elution. Because the miniaturized channel is a small channel compared to

the commercial channels, higher crossflows were not used. When using high crossflows, the channel

could be leaking because the pressure in the channel becomes too high.


Crossflow Fc

(ml/min)

Detectorflow Fout

(ml/min)


1.0

1.1

1.2

0.2

0.2

0.2

1.00

1.04

1.00

170

173

205

1.3 0.2 1.15 209

-0,1

0,0

0,1

0,2

0,3

0,4

0 5 10 15 20 25 30

Inte

nsi

ty (

mV

)

tR (min)


Real fractogram

23




fractogram, as shown in figure 19. Same as was the case in the fractogram of the 400μm spacer, the

width of the peaks in the real fractogram is much bigger than should be according to theory, also the

retention time is later than in the theoretical fractogram. This is again due to the instrumental plate

height, which is in this case even larger than in the channel with height 400μm.

-0,1

0,0

0,1

0,2

0,3

0,4

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min)

crossflow 1detectorflow 0.2

-0,1

0,0

0,1

0,2

0,3

0,4

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min)

crossflow 1.1detectorflow 0.2

-0,1

0,0

0,1

0,2

0,3

0,4

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min)


-0,1

0,0

0,1

0,2

0,3

0,4

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min)


24




As said in the previous part, the crossflow for this channel height needed to be higher than for channel

height 300μm. Crossflow 1.5ml/min was tested first, but the resolution was only 1.04, so there was

some degree of co-elution. The number of theoretical plates was quite high already. Higher crossflows

were tested, but this resulted in resolutions almost equal to 1.04, as shown in table 10 and figure 20.

The reason for these similarities was the fact that the actual crossflow and detectorflow differed from

the numbers set in the program during analysis, so the crossflows and detectorflows were almost

similar in every measurement. In order to make the miniaturized channel a POCDD, the analysis

should be short and the amount of mobile phase used should be as low as possible. Because the

resolutions were all almost the same and the number of theoretical plates was high for every

crossflow, the crossflow 1.5ml/min was the best condition for channel height 200μm.


Crossflow Fc

(ml/min)

Detectorflow Fout

(ml/min)


1.5

1.7

2.0

0.2

0.2

0.2

1.04

1.05

1.07

249

236

253

-0,1

0,2

0,4

0,6

0,8

1,0

0 5 10 15 20 25 30

Inte

nsi

ty (

mV

)

tR (min)


Real fractogram

25




fractogram, as shown in figure 21. In this case the width of the peaks is still bigger than theory, but

the width of the peaks is smaller than the width of the peaks in the fractograms of the 300 and 400μm

spacer height. Also the retention times are faster, but still not fast enough according to theory. In this

case the instrumental plate height is still quite large, but not as large as was the case in the 300 and

400μm channel height.

-0,1

0,0

0,1

0,2

0 10 20 30Inte

nsi

ty (

mV

)

tR (min) -0,1

0,0

0,1

0,2

0 10 20 30

Inte

nsi

ty (

mV

)

tR (min)

-0,1

0,0

0,1

0,2

0 10 20 30Inte

nsi

ty (

mV

)

tR (min)

26




Channel height 100μm is extremely small when compared to the other channels, so it is harder to

separate the proteins, as seen before in the commercial channels. Proteins absorb UV light at 220nm

due to the presence of double bonds within the carbonyl groups. Most proteins also absorb light at

280nm, which shows less impurities in the fractogram. In order to show higher signals (but possibly

also more impurities), the UV/Vis detector was switched to 220nm. Crossflow 1.5ml/min was tested

first, but this crossflow was too low and there was no separation of the proteins (as shown in figure

22). Higher crossflow did not change the rate of separation, so this miniature is not able to separate

the proteins.

-0,1

0,1

0,2

0,3

0,4

0 5 10 15 20 25 30

Inte

nsi

ty (

mV

)

tR (min)


Real fractogram

27




The best conditions for the 400μm were crossflow 0.9ml/min and detectorflow 0.2ml/min, so these

conditions were tested first. After a measurement of 45 minutes the proteins were still not detected by

the UV/Vis detector. In order to make the run as short as possible, this takes too long. Lower

crossflows were tested, and crossflow 0.6ml/min was the only condition in which the proteins were all

detected after 45 minutes, as shown in figure 23. Lower crossflows gave the same results as crossflow

0.6ml/min, because the actual crossflow and detectorflow were similar to crossflow 0.6ml/min and

detectorflow 0.2ml/min. The actual crossflow and detectorflow differed from the numbers set in the

program during analysis. The resolution was 1.37 (as shown in table 11) which is quite good, almost

baseline separation. Although the measurement takes too long, crossflow 0.6ml/min is the best

condition possible for spacer height 500μm.


Crossflow Fc

(ml/min)

Detectorflow Fout

(ml/min)


0.9

0.8

0.7

0.2

0.2

0.2

-

-

-

-

-

-

0.6 0.2 1.37 180

-0,1

0,9

1,9

2,9

3,9

4,9

5,9

6,9

7,9

0 5 10 15 20 25 30

Inte

nsi

ty (

mV

)

tR (min)



28




fractogram, as shown in figure 24. Same as in the fractogram of the 300 and 400μm spacer, the width

of the peaks is much bigger than theory, also the retention time is much later than is the case in the

theoretical fractogram. In this case the instrumental plate height is even larger than was the case with

channel height 400μm.

-0,1

0,4

0,9

0 50

Inte

nsi

ty (

mV

)

tR (min)


-0,1

0,4

0,9

0 50

Inte

nsi

ty (

mV

)

tR (min)


-0,1

0,4

0,9

0 50

Inte

nsi

ty (

mV

)

tR (min)


-0,1

0,4

0,9

1,4

0 50

Inte

nsi

ty (

mV

)

tR (min)


-0,1

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0 10 20 30 40

Inte

nsi

ty (

mV

)

tR (min)


Real fractogram

Figure 24: Theoretical fractogram of BSA + apoferritin + thyroglobulin. Experimental conditions: inj. vol.

15µL, mobile phase PBS, real channel height 462µm, Fc=0.6mL/min, Fout=0.2mL/min

29

5.2.1 Comparing miniaturized channels with shape 1

As shown in table 12, all resolutions are lower than 1.5, so there is some degree of co-elution in every

measurement. The resolution for the channel with height 500µm is the highest, this means there is

almost baseline separation. Also the channel with height 400µm has a relatively good resolution. The

number of theoretical plates is highest for the channel with height 400µm, which indicates that the

length of the separation column that is necessary to generate a separation between two particles is as

short as possible in this channel height, if compared to the other spacer heights.

Table 12: Resolution and number of theoretical plates for various spacer heights

Spacer height w

(µm)

Crossflow Fc

(ml/min)

Detectorflow

Fout (ml/min)

Resolution Rs Theoretical

plates N

200 1.5 0.2 1.04 249

300 1.3 0.2 1.15 209

400 0.9 0.2 1.28 228

500 0.6 0.2 1.37 180

Figure 25 shows the fractograms of all different channel heights. Channel height 100μm was not able

to separate the proteins and therefore is not included in the figure. The 500μm channel height gave the

highest resolution, but the measurement takes 45 minutes. In order use AF4 as a POCDD, a

measurement should be as short as possible. The measurement of the 500μm channel height takes too

long, so the 400μm channel height (which takes only 30 minutes) is the best spacer for the miniature

with shape 1.

Figure 25: Fractogram of BSA + apoferritin + thyroglobulin, best conditions for every spacer.

Experimental conditions: inj. vol. 15µL, mobile phase PBS, channel height 200-500µm

-0,1

0,0

0,1

0,2

0 20 40Inte

nsi

ty (

mV

)

tR (min)

200um

-0,1

0,0

0,1

0,2

0 20 40Inte

nsi

ty (

mV

)

tR (min)

300um

-0,1

0,0

0,1

0,2

0 20 40

Inte

nsi

ty (

mV

)

tR (min)

400um

-0,1

0,0

0,1

0,2

0 20 40

Inte

nsi

ty (

mV

)

tR (min)

500um

30


The best spacer height for the miniature with shape 1 was the spacer height 400μm. The best

conditions for this miniature were crossflow 0.9ml/min and detectorflow 0.2ml/min, so these

conditions were tested first on the miniature with shape 2. As shown in figure 26, the proteins were

not separated. The peak after focusing+elution (after 30min) is large, which indicates all sample

components are pushed onto the membrane by the crossflow and got stuck in the membrane. The

sample components stay inside the channel until the crossflow is stopped. Lower and higher crossflow

were tested, but all of them gave the same results, no separation of the proteins.




Because the channel with shape 3 is very small, the flows also need to be low, otherwise the pressure

inside the device will be too high. A few crossflows were tested (figure 27), but all of them gave

fractograms with no signals for the proteins. In this case the peak after focusing+elution is quite small,

so there is not much mixture stuck in the membrane. Blue Dextran (chapter 5.2.2) showed a large part

of the mixture leaks out of the channel, leading to no signal from the UV-Vis detector.

-2,0

0,0

2,0

4,0

6,0

8,0

10,0

0 20 40

Inte

nsi

ty (

mV

)

tR (min) -2,0

0,0

2,0

4,0

6,0

8,0

10,0

0 20 40

Inte

nsi

ty (

mV

)

tR (min)

-2,0

0,0

2,0

4,0

6,0

8,0

10,0

0 20 40

Inte

nsi

ty (

mV

)

tR (min)

31



5.2.2 Comparing miniaturized channels

The miniature with shape 1 was able to separate the proteins and channel height 400μm was the

height with the best conditions possible, although the miniature did not give results as good as the

commercial channel. Miniatures with shape 2 and 3 cannot be used for separation of the mixture of

three proteins. A single run with only BSA and another run with only apoferritin were tested, and the

results are shown in figure 28 and 29. Instead of just one peak expected, both proteins showed two

peaks in the fractogram.

After this observation, a single run with Blue Dextran was measured, to see if all of the sample stayed

inside of the channel and to see if the focusing in the channel went well. The Blue Dextran focused in

almost half of the channel, so the sample is in fact insufficiently focused. Also the Blue Dextran

leaked out of the channel (but stayed in the device), so this could be an explanation why the

miniaturized channels were not able to separate the proteins properly.

0,0

10,0

20,0

30,0

40,0

50,0

0 10 20 30 40

Inte

nsi

ty (

mV

)

tR (min)

crossflow 0.1 detectorflow 0.1

crossflow 0.3 detectorflow 0.2

32

Figure 28: Fractogram of Apoferritin. Experimental conditions: inj. vol. 15μl, mobile phase PBS, channel

height 400μm

Figure 29: Fractogram of BSA. Experimental conditions: inj. vol. 15μl, mobile phase PBS, channel height

400μm

-0,2

0,4

0 5 10 15 20 25 30

Inte

nsi

ty (

mV

)

tR (min)

Apoferritin crossflow0.5 detectorflow 0.2

-0,2

0,4

0 5 10 15 20

Inte

nsi

ty (

mV

)

tR (min)

BSA crossflow 0.3detectorflow 0.3

33

6. Conclusion

The commercial channel was optimized for separation of three proteins (BSA, apoferritin and

thyroglobulin). For the fastest analysis close to baseline separation, the optimal spacer height and

separation method were found. The best spacer height for the commercial channel is 350μm, the best

conditions for this spacer are crossflow 2.0ml/min and detectorflow 1.0ml/min. The 480μm spacer

gave a higher resolution than the 350μm spacer (respectively resolution 1.58 and 1.49) and a higher

number of theoretical plates (respectively 228 and 204), but both resolutions show that there is

baseline separation in the measurements and both spacer heights have a large number of theoretical

plates. A single measurement with the 350μm spacer also takes 10 minutes less than a measurement

with the 480μm spacer. In order to make an analysis faster and with lower mobile phase consumption

to become a POCDD, the 350μm spacer is the best spacer height for the commercially available

channels.

The best channel height for the miniature of shape 1 is 400μm, the best conditions for this channel are

crossflow 0.9ml/min and detectorflow 0.2ml/min. All resolutions were lower than 1.5, so in every

measurement there is some degree of co-elution. The 500μm channel height gave a higher resolution

than the 400μm channel (respectively 1.37 and 1.28), but the number of theoretical plates was higher

for the 400μm channel (228 and 180). A single measurement with the 500μm channel takes 45

minutes, which is 15 minutes longer than the 400μm channel. In order to make a measurement as

short as possible this is too long, therefore the 400μm channel height (which takes only 30 minutes) is

the best height for the miniaturized channel with shape 1.

The design of miniaturized channels with shape 2 and 3 at this stage of the research is not suited for

separation of the mixture of three proteins.

In both the commercial channels and miniatures, the larger spacer/channel heights are best in

separating the mixture of three proteins. The instrumental plate height for larger spacer/channel

heights are also larger, so the peaks have a larger width than should be according to the theory. The

smaller heights (190μm commercial and 100μm miniature) were not able to separate the chosen

mixture of proteins. These spacer/channel heights are probably too small, so the focusing part will

take place in a larger part of the channel and the separation doesn’t work well. In the miniaturized

devices the channel is not pressed properly towards the membrane, so part of the mixture of proteins

leaks out of the channel in the device. This way the proteins cannot be detected by the UV/Vis

detector.

34

7. Discussion and Future Prospects

The miniaturized channels were not able to separate the proteins as properly as the commercial

channels, and some of the miniaturized channels were not able to separate the proteins at all. After

injecting Blue Dextran in the miniature channel, it leaked out of the channel but stayed in the device.

More specifically, the Blue Dextran leaked outside the separation channel but it stayed inside the o-

ring, which is used to seal the miniaturized channel. This is an explanation for the fact why the

miniatures did not give good results, because the protein-sample probably also leaked out of the

channel. There should be more pressure on the channel, to push the channel more towards the

membrane. A solution could be some kind of glue, to make sure the membrane is attached to the

channel and the sample stays inside the channel.

The focusing of the sample takes up almost half of the channel, so in fact the sample is not focused.

The mixture of proteins is also not properly pushed towards the membrane (because of leakage). In all

of the measurements in this project the focusing took at most 5-6 minutes, so e a longer focusing time

(in the range of 10-20 minutes) could be a solution. In order to use AF4 as a POCDD it is not ideal to

use long focusing times, because the analysis will take a lot longer.

A third solution in making the miniatures more efficient, is the use of another type of FFF. Frit-Inlet

AF412

uses the frit-inlet injection technique with an AF4 channel. The AF4 method used in this

project uses a channel flow that is divided in two parts, the crossflow and the axial flow. The driving

force in bringing the sample towards the membrane, where the separation takes place, is created by

the crossflow. Frit-Inlet AF4 is promising because of the fact that it utilizes a stopless sample

injection technique with the conventional asymmetrical channel by implementing an inlet frit nearby

the channel inlet, which reduces possible flow imperfections caused by the porous wall.12

Frit-Inlet

AF4 does not require sample focusing and relaxation steps which are time consuming. This way it

does not interrupt sample migration and valve switching, and thus could be a promising new method

for protein separation.

35

Acknowledgements

Here I would like to thank Peter Schoenmakers for the opportunity to work on my project in his

research group. Also very special thanks to Jana Králová and Wim Kok for supervising and helping

me over the course of this project. Last but not least, a thank you note for the entire analytical

chemistry group for all sociability and helping me out with anything.

List of abbreviations

FFF field-flow fractionation

FlFFF flow field-flow fractionation

AF4 asymmetrical flow field-flow fractionation

LC liquid chromatography

POCDD point of care diagnostic device

BSA Bovine Serum Albumin

PBS phosphate buffered saline

36

References

1. Caldwell, K. D.; Kesner, L. F.; Myers, M. N.; Giddings, J. C. Electrical Field-Flow Fractionation of

Proteins. Science 1972, 176, 296-298.

2. Giddings, J. C.; Smith, L. K.; Myers, M. N. Thermal field-flow fractionation. Extension to lower

molecular weight separations by increasing the liquid temperature range using a pressurized system.

Anal. Chem. 1975, 47, 2389-2394.

3. Giddings, J.; Yang, F.; Myers, M. Flow-field-flow fractionation: a versatile new separation method.

Science 1976, 193, 1244-1245.

4. Sant, H. J.; Gale, B. K. Chapter 12: Microscale Field-Flow Fractionation: Theory and Practice. In

Microfluidic Technologies for Miniaturized Analysis Systems. Hardt, S.; Schönfeld, F. Eds.; Springer

US: New York, 2007; 471-521.

5. Lee, W.J.; Min, B; Moon, M.H. Improvement in Particle Separation by Hollow Fiber Flow Field-

Flow Fractionation and the Potential Use in Obtaining Particle Size Distribution. Anal. Chem. 1999,

71, 3446-3452.

6. Qureshi, R. N.; Kok, W. T. Application of flow field-flow fractionation for the characterization of

macromolecules of biological interest: a review. ABC, 2011, 399(4), 1401-1411.

7. Qureshi, R. N.; Kok, W. T. Optimization of Asymmetrical Flow Field-flow Fractionation (AF4).

LC-GC Europe 2010, 23, 18-25.

8. Wahlund, K. G.; Giddings, J. C. Properties of an asymmetrical flow field-flow fractionation

channel having one permeable wall. Anal. Chem. 1987, 59, 1332-1339.

9. Inczédy, J.; Lengyel, T.; Ure, A. M. Compendium of Analytical Nomenclature [Online], Third

edition; IUPAC, 1997; Chapter 9: Separations.

http://old.iupac.org/publications/analytical_compendium/TOC_cha9.html (accessed May 18,2014).

10. SHIMADZU (Shimadzu Corporation). Formula for Calculating the Number of Theoretical Plates.

http://www.shimadzu.com/an/hplc/support/lib/lctalk/34/34tec.html (accessed May 18, 2014).

11. Sant, H. J.; Gale, B. K. Geometric scaling effects on instrumental plate height in field flow

fractionation. Journal of Chromatography A 2006, 1104, 282-290.

12. Moon, M. H. FFF: Frit-Inlet Asymmetrical Flow. In Encyclopedia of Chromatography, Third

edition. Cazes, J. Eds.; CRC Press: Boca Raton, Fl., USA, 2009; Volume 2; 860-861.

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