coating microchannels to improve field-flow fractionation · polymer brush free energy cost...

µ-FFFss-FFF

SimulationsConclusion

Coating microchannelsto improve Field-Flow Fractionation

Tyler ShendrukGary Slater

September 12, 2011

Tyler Shendruk Gary Slater Coating microchannels to improve Field-Flow Fractionation

µ-FFFss-FFF


Normal-mode FFFSteric-mode FFFSelective-mode FFF

Normal-mode Field Flow Fractionation

��

@@ @@ @@ @@ @@ @@ @@ @@

` ` `` ``` `` -〈V〉

?

Field Force f

6Diffusion-

-

-

-

-

- Flow Profile 〈v〉

Figure: Schematic of normal-mode FFF.

Fractionation

λ ≡ kBT

fw

c (y) = c0e−y/λ

〈V〉 =〈cv〉〈c〉

R ≡ 〈V〉〈v〉


µ-FFFss-FFF



Steric-mode Field Flow Fractionation

��

@@ @@ @@ @@ @@ @@ @@ @@

6

?

6

?

``` ```` ``` ` ``` m- ��

--

-

-

-

-

-

Figure: Schematic of steric-mode FFF.

Excluded Region

c (y) =

{c0e

−(y−r)/λ for r < y < 1− r

0 otherwise.


µ-FFFss-FFF



Selective-mode Field Flow Fractionation

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@@ @@ @@ @@ @@ @@ @@

eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee


H6?

ξ

Figure: Schematic of selective-mode FFF.

Polymer Brush

Free energy cost

Hydrodynamicthickness

Brush Model

Alexander Brushstep-function model


µ-FFFss-FFF




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@@ @@ @@ @@ @@ @@ @@



H6?

ξ sss s|


Polymer Brush

Free energy cost


Brush Model



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@@ @@ @@ @@ @@ @@ @@



H6?

ξ 〈V〉 ≈ 0sss s|〈V〉--

--

---


Polymer Brush

Free energy cost


Brush Model



µ-FFFss-FFF


Flow ProfileFree Energy CostRetention

Flow Profile

Brush Model

Alexander Brush

porous: blobsize setspermeability

Brinkman Equation

η∇2v +η

ξ2v = ∇p

0.0 0.2 0.4 0.6 0.8 1.0

y0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

v

H=0

H=0.1 ξ=0.05

H=0.1 ξ=0.005


µ-FFFss-FFF



Modes of Approach

��

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~��

LLLeeeeeeee eeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeee

Figure: Two modes of approach.

Compression Mode

Fcmp = Fint + Fel

≈ F0

(H

h

) 13ν−1

+

(h

H

) 4ν−13ν−1

where F0 = H/ξ.


µ-FFFss-FFF



Modes of Approach

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~��

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Figure: Two modes of approach.

Insertion ModeGenerally,

Fins = Π(φ)V + γ(φ)A

When r > ξ

Fins

kBT∼(

r

ξ

)3 [1 +

ξ

r

]

When r < ξ

Fins

kBT∼(

r

ξ

)3−1/ν


µ-FFFss-FFF



Modes of Approach

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

r/ξ

Fin

s/k

BT

r=ξT r=ξ

ν=3/5

ν=1/2

Insertion ModeGenerally,

Fins = Π(φ)V + γ(φ)A

When r > ξ

Fins

kBT∼(

r

ξ

)3 [1 +

ξ

r

]

When r < ξ

Fins

kBT∼(

r

ξ

)3−1/ν


µ-FFFss-FFF



Concentration Profile

Figure: The piece-wise free energy cost creates abrupt changes in c (y , r)such that the concentration plumets when r < ξ. Forλ = kBT/fw = 0.05, H = 0.1 and ξ = 0.05.


µ-FFFss-FFF



Retention Ratio, R = 〈V〉 / 〈v〉

0.0 0.1 0.2 0.3 0.4 0.5

r0.95

1.00

1.05

1.10

1.15

1.20

1.25

1.30

R

H=0

FFF is nonmonotonic

Brush makes R : r → 1 : 1 overlarger range

Dense brush increases resolution

At this size, retention isindependent of field

0.00 0.05 0.10 0.15 0.20

r

1.0

1.1

1.2

1.3

1.4

1.5

1.6

R

H=0.1 ξ=0.05

0.00 0.05 0.10 0.15 0.20

r

1.0

1.1

1.2

1.3

1.4

1.5

1.6

R

H=0.1 ξ=0.005


µ-FFFss-FFF




0.00 0.05 0.10 0.15 0.20

r0.95

1.00

1.05

1.10

1.15

1.20

1.25

1.30

R

H=0

FFF is nonmonotonic




0.00 0.05 0.10 0.15 0.20

r

1.0

1.1

1.2

1.3

1.4

1.5

1.6

R

H=0.1 ξ=0.05

0.00 0.05 0.10 0.15 0.20

r

1.0

1.1

1.2

1.3

1.4

1.5

1.6

R

H=0.1 ξ=0.005


µ-FFFss-FFF




0.00 0.05 0.10 0.15 0.20

r

1.0

1.1

1.2

1.3

1.4

1.5

1.6

R

H=0

FFF is nonmonotonic




0.00 0.05 0.10 0.15 0.20

r

1.0

1.1

1.2

1.3

1.4

1.5

1.6

R

H=0.1 ξ=0.05

0.00 0.05 0.10 0.15 0.20

r

1.0

1.1

1.2

1.3

1.4

1.5

1.6

R

H=0.1 ξ=0.005


µ-FFFss-FFF


MPC-MD Hybrid

Multi-Particle Collision Dynamics

MPC-MD Hybrid

Ideal for Pe≈ 1

0.0 0.2 0.4 0.6 0.8 1.0 1.2

1/R

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

D

0 5 10 15 20y

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

φ

N=20,σ=0.20

N=20,σ=0.40

x

5

10

15

y

10

20

30

40

~ v

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0 5 10 15 20

y0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

v

H=0

σ=0.20 N=20

σ=0.40 N=20


µ-FFFss-FFF


Conclusions

Selective Steric-mode Field Flow Fractionation

Polymer brush alters FFF by

screening flow within the brushenacting free energy cost to enter

Polymer brush leads to

increased monotonic rangeincreased resolutionsignificantly increased resolution of solutes smaller than blobs

Simple model to be corroborated by MPC-MD simulations


µ-FFFss-FFF


Thank you,

Thank you to the U. of O. Polymer Physics Group members

Mykyta Chubynsky

Yugou Tau

Henk DeHaan

David Sean

Owen Hickey


µ-FFFss-FFF


Steric-mode FFF

0.0 0.1 0.2 0.3 0.4 0.5

r0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

R

λ

100

20

10

2

1

0.5

0.2

0.1

0.02

0.01

0.002

0.0 0.1 0.2 0.3 0.4 0.50.0

0.1

0.2

0.3

0.4

⟨ y⟩

Figure: Retentionratios for fixedretention parameters,λ.

0.0 0.1 0.2 0.3 0.4 0.5

r0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

R

Λ

0.2

0.1

0.05

0.02

0.01

0.005

0.002

0.001

0.0005

0.0002

0.0 0.1 0.2 0.3 0.4 0.50.0

0.1

0.2

0.3

0.4

⟨ y⟩

Figure: Retentionratios when forcevaries with particlesize λ = Λr−α.

λ =kBT

fw

=kBT

µrαw

= Λr−α


µ-FFFss-FFF


Snug-mode FFF

��

@@ @@ @@ @@ @@ @@ @@ @@ @@

&%'$

��

-

-

-

-

-

-

Flow Profile

Figure: Schematic of snug-mode FFF.


µ-FFFss-FFF


Snug-mode FFF

0.0 0.1 0.2 0.3 0.4 0.5

r0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

R

λ

100

20

10

2

1

0.5

0.2

0.1

0.02

0.01

0.002

0.0 0.1 0.2 0.3 0.4 0.50.0

0.1

0.2

0.3

0.4

⟨ y⟩

Figure: Retentionratios for fixedretention parameters,λ.

0.0 0.1 0.2 0.3 0.4 0.5

r0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

R

Λ

0.2

0.1

0.05

0.02

0.01

0.005

0.002

0.001

0.0005

0.0002

0.0 0.1 0.2 0.3 0.4 0.50.0

0.1

0.2

0.3

0.4

⟨ y⟩

Figure: Retentionratios when forcevaries with particlesize λ = Λr−α.

0.0 0.1 0.2 0.3 0.4 0.5

r0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

R

Λ

0.0020.0040.0060.0080.010.0120.0140.0160.018

Figure: Retentionratios when velocityprofile average oversurface area.


µ-FFFss-FFF


Snug-mode FFF

0 1 2 3 4 5 6 7 8r [µm]

0

5

10

15

20

w[µm

]

GoldSilicaPolystyrene


µ-FFFss-FFF


Flow ProfileBrinkman equation:

η∇2v +η

ξ2v = ∇p

where ξ is the hydrodynamic penetration depth which acts as the typical pore size and corresponds to thecorrelation length of the chains.

Alexander Brush - step function density

ξ =b

φν/(3ν−1)

L. Miao, H. Guo, M.J. Zuckermann. Conformation of polymer brushes under shear. Macromolecules,29(6):22892297, 1996.Parabolic Brush - density falls linearly at extremity

ξ =b

φ

S. T. Milner. Hydrodynamic penetration into parabolic brushes. Macromolecules, 24(12):37043705, 1991.


µ-FFFss-FFF


Free Energy Coefficients

∆F

kBT∼

F0

[(Hh

)1/(3ν−1)+(hH

)(1−4ν)/(1−3ν) − 1]

r � H(rξ

)3H � r � ξ(

rξ

)3 [1 + ξ

r

]r ≥ ξ(

rξ

)3−1/νξ > r > ξT

rξid

ξT > r > b


µ-FFFss-FFF



∆F

kBT∼

F0

[(Hh

)1/(3ν−1)+(hH

)(1−4ν)/(1−3ν) − 1]

r ≥ H(rξ

)3 [1 + ξ

r

]ξ ≤ r ≤ H(

rξ

)3−1/νr ≤ ξ


µ-FFFss-FFF



∆F

kBT=

a1F0

[(Hh

)1/(3ν−1)+(hH

)(1−4ν)/(1−3ν) − 1]

r ≥ H

a2

(rξ

)3 [1 + ξ

r

]ξ ≤ r ≤ H

a3

(rξ

)3−1/νr ≤ ξ


µ-FFFss-FFF



∆F

kBT=

a1F0

[(Hh

)1/(3ν−1)+(hH

)(1−4ν)/(1−3ν) − 1]

r ≥ H

a2

(rξ

)3 [1 + ξ

r

]ξ ≤ r ≤ H

a3

(rξ

)3−1/νr ≤ ξ

Recalling F0 = H/ξ. At r = H, F1 = F2 such that

a1 = a2

(H

ξ

)2 [1 +

ξ

H

]At r = ξ, F2 = F3 and we see

a3 = 2a2

We choose a2 = 1.Tyler Shendruk Gary Slater Coating microchannels to improve Field-Flow Fractionation

coating microchannels to improve field-flow fractionation · polymer brush free energy cost...

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