bifurcation of polyelectrolyte brushes subject to normal ... · pdf filebifurcation of...

Bifurcation of Polyelectrolyte BrushesSubject to Normal Electric Fields

Tyler N. ShendrukYu-Fan Ho Gary W. Slater Pai-Yi Hsiao

CAPMay 31, 2013

Stimuli-ResponsiveMaterials

PolyelectrolyteBrushes

PerpendicularFields

Simulations

Low GraftingDensity

IntermediateGraftingDensity

High GraftingDensity

Conclusion

PotentialApplications ofBifurcatingBrushes

Recapitulation

Stimuli-Responsive MEMS Components“Smart” Surfaces

• Biology abounds with mesoscopic systems that dynamically and reversablyrespond to environmental cues

• If structures change radically with environment they can be engineered into

• detectors• gates

←− smart surfaces

Biologicalion-gate

OpenClosed

Biomimetic gate

Schematic of biological and synthetic, mechanically triggered stimuli-responsive surfacesCredit: Wilhelm Huck, Melville Laboratory for Polymer Synthesis



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

Stimuli-Responsive MEMS Components“Smart” Surfaces

• Biology abounds with mesoscopic systems that dynamically and reversablyrespond to environmental cues

• If structures change radically with environment they can be engineered into

• detectors• gates ←− smart surfaces

Biologicalion-gate

OpenClosed

Biomimetic gate

Schematic of biological and synthetic, mechanically triggered stimuli-responsive surfacesCredit: Wilhelm Huck, Melville Laboratory for Polymer Synthesis



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

Charged Soft Matter as “Smart” SurfacesPolyelectrolyte Brushes

• Different than neutral brush due to chain-counterion complex nature

• f is charge fraction of chain, z valency, N number of segments, H brushheight, T counterion cloud thickness and Σ normalized grafting density

• Ideal as stimuli-responsive surfaces becausestructure is hyper-dependent on environmental cues



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation





High Salt Brush

• Salt screens electrostatics so

brush is effectively

electro-neutral• Screening inverse to salt

concentration• H ∼ N• H ∼ Σ1/3

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PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation





Pincus Brush (weakly charged)

• Brush is like a thin charged film

and counterion cloud is

attracted to it• T ∼ [ΣN]−1

• H ∼ N3 — strongdependence

• H ∼ Σ



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation





Osmotic Brush (highly charged)

• Counterions are pulled into

brush (polyelectrolyte /

counterion complex)• T ≈ H• H ∼ N• H does not have Σ

dependence



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation


Osmotic Brushes as “Smart” Surfaces

• Ideal as stimuli-responsive surfaces because structure ishyper-dependent on environmental cues

• Favourable because form electroneutral films when unperturbed

• Easy, reproducible

and fast

control over switching:

• temperature

• pH

• salt

• electric fields



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation


Osmotic Brushes as “Smart” Surfaces

• Ideal as stimuli-responsive surfaces because structure ishyper-dependent on environmental cues

• Favourable because form electroneutral films when unperturbed

• Easy, reproducible and fast control over switching:

• temperature

• pH

• salt

• electric fields



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

Langevin DynamicsSimulations of Polyelectrolyte BrushesSubject to Normal Electric Fields

• Low Grafting Density:Σ = 0.0136

• Intermediate Grafting Density:Σ = 1.11

• High Grafting Density:Σ = 11.1

Modeling the separation of macromolecules: A review of current computer simulation methods.Electrophoresis, 30: 792-818, 2009.



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

Low Grafting Density

Low Grafting Density BrushesSubject to Normal Electric Fields



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

Low Grafting DensityBrush Height

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

0.00

0.05

0.10

0.15

Σ=0.0139

|E|=0.0

|E|=0.01

|E|=0.02

|E|=0.05

|E|=0.10

|E|=0.15

|E|=0.2

Zmax/(Nb

0)

P(Zmax)

Two regimes:

• |E | . 0.02:Height is ratherconstant

• |E | & 0.02:Height increaseswith increased |E |



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation


0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

0.00

0.05

0.10

0.15

Σ=0.0139

|E|=0.0

|E|=0.01

|E|=0.02

|E|=0.05

|E|=0.10

|E|=0.15

|E|=0.2

Zmax/(Nb

0)

P(Zmax) Two regimes:

• |E | . 0.02:Height is ratherconstant

• |E | & 0.02:Height increaseswith increased |E |



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation


Two regimes:

• Why not a steady rise?

• What does “critical” |E∗| arise from?



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

Low Grafting DensityMonomer/Counterion Distributions — Low Fields

0 10 20 30 40 50 600.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

|E|=0.005

Σ=0.0139

Log10(σ

xz)

Monomer density distributionz/(Nb0)

x/Rg,0

-6.00

-5.00

-4.00

-3.00

-2.00

-1.00

0 10 20 30 40 50 600.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

x/Rg,0

Counterion density distribution

• Counterion distribution corresponds to monomer distribution

• Not perfectly electroneutral — background probability

• Low grafting density brush not quite ideal osmotic brush



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

Low Grafting DensityCounterion Confinement and Condensation

In weak field limit, 82% ofcounterions confined to brushregion (z ≤ Zmax)

• 56% condensed (closer than λB to a chain)

• Manning theory for free chain predictsχion = 1− b0/λB = 61%

Although not perfect, screening is effective for fields . |E∗| ' 0.02• When |E | �

∣∣E∗∣∣, counterion and monomer distributions correspond

• When |E | &∣∣E∗∣∣, counterions forced down thus superimposing exponential/Boltzmann distribution

• When |E | �∣∣E∗∣∣, positive monomers hardly perturb exponential distribution



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation





Although not perfect, screening is effective for fields . |E∗| ' 0.02

• When |E | �∣∣E∗∣∣, counterion and monomer distributions correspond





PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation





Although not perfect, screening is effective for fields . |E∗| ' 0.02• When |E | �

∣∣E∗∣∣, counterion and monomer distributions correspond





PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

Low Grafting DensityCritical Field

Scaling ArgumentChain stretches once energy gained bymoving charge a characteristic distance,`, is greater than kBT

E∗e` ∼ kBT → E∗ ∼kBT

e

1

`

But what is the characteristic distance?

• In mean-field sense, ` is averagedistance between charges

` ∼(

Hσ−1g

N

)1/3



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

Low Grafting DensityCritical Field

Scaling Result

E∗ ∼kBT

e

(Nσg

H

)1/3

∼ Σ1/3

• If H = H (Σ) (asobserved) thenE∗ ∼ Σ0.341.



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

Low Grafting DensityConclusion

Conclusion About Low Grafting Density:

• There are two regimes:• |E | < |E∗|: brush height is constant• |E | > |E∗|: brush height increases

• E ∗ ∼ Σ1/3

Structure of polyelectrolyte brushes subject to normal electric fields.Langmuir, 29(7): 2359-2370, 2013.



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

Intermediate Grafting Density

Intermediate Grafting Density BrushesSubject to Normal Electric Fields



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

Intermediate Grafting DensityBrush Height

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

0.00

0.02

0.04

0.06

0.08

Σ=1.11

Zmax/(Nb

0)

P(Zmax)

|E|=0.0

|E|=0.05

|E|=0.09

|E|=0.2

|E|=0.3

|E|=0.35

|E|=0.5

|E|=0.7

Three regimes:

• Height constantat low fields|E∗| ' 0.09

• Height increasesat intermediatefields

• Splitting at secondcritical field|E∗∗| ' 0.35



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

Intermediate Grafting DensityMonomer/Counterion Distributions — Low Fields

0 1 2 3 4 5 6 70.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

|E|=0.01

Σ=1.11

Log10(σ

xz)

Monomer density distributionz/(Nb0)

x/Rg,0

-4.00

-3.00

-2.00

-1.00

0

0 1 2 3 4 5 6 70.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

x/Rg,0

Counterion density distribution

• At intermediate densities brush is closer to ideally osmotic

• Most (97% in zero field) counterions reside within brush

• More homogeneous and effectively electroneutral



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

Intermediate Grafting DensityMonomer/Counterion Distributions — Low Fields

0 1 2 3 4 5 6 70

1

2

3

4

5

6

|E|=0.01

Σ=1.11

Log10

(σxy

mon)

Monomer density distribution

y/R

g,0

x/Rg,0

-4.00

-3.00

-2.00

-1.00

0

1.00

• At intermediate densities brush is closer to ideally osmotic

• Most (97% in zero field) counterions reside within brush

• More homogeneous and effectively electroneutral



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

Intermediate Grafting DensityMonomer/Counterion Distributions — High Fields

0 1 2 3 4 5 6 70

1

2

3

4

5

6

|E|=1.0

Σ=1.11

Log10

(σxy

mon)

Monomer density distribution

y/R

g,0

x/Rg,0

-4.00

-3.00

-2.00

-1.00

0

1.00

• The population bifurcates into

• few unstretched chains• many highly stretched chains



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

Intermediate Grafting DensityBrush Height – Bifurcation

• Why does bifurcation occur at |E∗∗|?



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

Intermediate Grafting DensityCritical Field

Scaling ArgumentSecond critical field |E∗∗| is the minimum for which

Felectro = zqE on segmentthat has fluctuated out of the protective counterion cloud is greater than theelastic restoring force Fspring = H/Na2

zqE∗∗ ∼H

Na2

E∗∗ ∼1

qa

(f

z3

)1/2

= const.

since H ' Na (f /z)1/2 in an osmotic brush.

• E∗∗ is not predicted to scale with Σ,nor N



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation


Scaling ArgumentSecond critical field |E∗∗| is the minimum for which Felectro = zqE on segmentthat has fluctuated out of the protective counterion cloud

is greater than theelastic restoring force Fspring = H/Na2

zqE∗∗ ∼H

Na2

E∗∗ ∼1

qa

(f

z3

)1/2

= const.



barefluctuation



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation


Scaling ArgumentSecond critical field |E∗∗| is the minimum for which Felectro = zqE on segmentthat has fluctuated out of the protective counterion cloud is greater than theelastic restoring force Fspring = H/Na2

zqE∗∗ ∼H

Na2

E∗∗ ∼1

qa

(f

z3

)1/2

= const.





PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

Intermediate Grafting DensityConclusion

Conclusion About Intermediate Grafting Density:

• There are three regimes:• |E∗| < |E |: brush height is constant• |E∗| < |E | < |E∗∗|: brush height increases• |E∗∗| < |E |: brush bifurcates

• |E ∗∗| ∼ Σ0




PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

High Grafting Density

High Grafting Density BrushesSubject to Normal Electric Fields



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

High Grafting DensityImmediate Bifurcation

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

0.00

0.01

0.02

0.03

0.04

Σ=11.1

|E|=0.0

|E|=0.1

|E|=0.2

|E|=0.3

|E|=0.5

|E|=0.7

Zmax/(Nb

0)

P(Zmax)

Bifurcates but . . .E∗ (Σ) = E∗∗ at high Σ

• Increasing Σ increasesE∗

• but E∗∗ nearlyconstant

• Therefore, immediatebifurcation at high Σ

Fully stretched chains nowthe minority



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

High Grafting DensityMinority

• When |E | > |E∗∗|:Majority stretched if Σ = 1.11 but minority stretched if Σ = 11.1

• Why are more relaxed and unstretched compared to intermediate Σ?



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

High Grafting DensityIncreased Counterion Confinement and Condensation

• In weak fields and low graftingdensity, 82% of counterionsconfined to brush

• Jumps to 97% when Σ = 1.11 and99% when Σ = 11.1

• In weak fields and low graftingdensity, 56% of counterionscondensed

• Increases to 78% when Σ = 1.11and 84% when Σ = 11.1

Assuming local neutrality becomes more accurate at higher grafting densities.

Less chains bare and liable to be fully stretched.



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation


10-310

-210

-10.75

0.80

0.85

0.90

0.95

1.00

10-310

-210

-110

010

-310

-210

-110

0

Σ=0.0139

κion

field intensity |E|

Σ=1.11

Σ=11.1









PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation


10-310

-210

-10.75

0.80

0.85

0.90

0.95

1.00

10-310

-210

-110

010

-310

-210

-110

0

Σ=0.0139

κion

field intensity |E|

Σ=1.11

Σ=11.1



10-3

10-2

10-1

100

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

χion

Σ=11.1

Σ=5.54

Σ=1.11

Σ=0.554

Σ=0.0139

field intensity |E|







PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

High Grafting DensityConclusion

Conclusion About High Grafting Density:

• At high grafting densities, |E ∗| = |E ∗∗|• Fully stretched population becomes minority




PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

ConclusionPotential Applications of Bifurcating Brushes

Original Motivation:Polyelectrolyte brushes as field controlled gates

but bifurcation suggests an array of unexpected possiblities.

Novel MEMS Components:

• Control flow resistance

• Filtration by number of rods

• Control the surface friction

• Utilizing polyampholytes or end-labeled chains may allowchoosing which chains stretch

• Fishing – the tethering and subsequent trapping within theinterior of the brush of analytes by alternating fields

Can slip walls improve field-flow fractionation or hydrodynamic chromatography?Journal of Chromatography A, 1256: 206-212, 2012.



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

ConclusionPotential Applications of Bifurcating Brushes

Original Motivation:Polyelectrolyte brushes as field controlled gatesbut bifurcation suggests an array of unexpected possiblities.

Novel MEMS Components:

• Control flow resistance

• Filtration by number of rods

• Control the surface friction

• Utilizing polyampholytes or end-labeled chains may allowchoosing which chains stretch

• Fishing – the tethering and subsequent trapping within theinterior of the brush of analytes by alternating fields

Can slip walls improve field-flow fractionation or hydrodynamic chromatography?Journal of Chromatography A, 1256: 206-212, 2012.



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

Nat. Tsing Hua Uni.

Pai-Yi Hsiao• Yu-Fan Ho

University of Ottawa

Gary Slater• Mykyta Chubynsky

• Henk de Haan

• Martin Bertrand

• Yuguo Tao

• David Sean

• Zheng Ma

Webpages

• Gary Slater:www.science.uottawa.

ca/~gslater

• Tyler Shendruk:www.tnshendruk.com


www.science.uottawa.ca/~gslater

www.science.uottawa.ca/~gslater

www.tnshendruk.com



PerpendicularFields

Simulations

Low GraftingDensity



Conclusion


Recapitulation

RecapitulationStructure of highly charged polyelectrolyte brushes in the no-salt limit,subject to normal electric fields:

1.0

1 phase

2 phases

1 phase|E|

2 phases

1 phase (predicted)

1.11 11.1

0.01

0.1

0.35

0.0139 0.554 5.54Σ

+z

+y+x

1 phase

Low Intermediate High grafting density

1 phase0.15 0.2


bifurcation of polyelectrolyte brushes subject to normal ... · pdf filebifurcation of...

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