The Electrophoretic Mobility of a Polyelectrolyte within a Radially Confining Potential Well

Size: px

Start display at page:

Download "The Electrophoretic Mobility of a Polyelectrolyte within a Radially Confining Potential Well"

Marshall James
5 years ago
Views:

1 The Electrophoretic of a Polyelectrolyte within a Radially Confining Potential Well Tyler N. Shendruk Martin Bertrand Gary W. Slater University of Ottawa March 18, 2013

ConfinementBased NanoEngineering Gels Confinement in nanochannels, nanoslits or capillaries modifies electrophoretic mobility with walls can cause the Electrohydrodynamic Equivalence Principle to

2 ConfinementBased NanoEngineering Gels Confinement in nanochannels, nanoslits or capillaries modifies electrophoretic mobility with walls can cause the Electrohydrodynamic Equivalence Principle to apply. Cross, Strychalski and Craighead, J. Appl. Phys. (2007) has been observed to increase with confinement. Liao, Watari, Wang, Hu, Larson and Lee, (2010) Strong dependence on salt concentration. Stein, Deurvorst, van der Heyden, Koopmans, Gabel and Dekker, NanoLetters (2010)

3 Capillary Reduced System System We consider radial confinement No walls

4 Capillary Reduced System System We consider radial confinement No walls A radial harmonic well acts on only the monomers Simplified polyelectrolyte FreelyJointed MD chain

5 CoarseGrained Electrohydrodynamics MeanField MPCDMD DebyeHückel Algorithm Hydrodynamics Use a coarsegrained, particlebased NavierStokes solver MultiParticle Collision Dynamics or Disipative Particle Dynamics Coupled to Molecular Dynamics chain Slater, Holm, Chubynsky, de Haan, Dubé, Grass, Hickey, Kingsburry, Sean, Shendruk and Zhan, (2009)

6 monomers UDH (r) = r e r/λ D, r < rcut particles based on counterion density ρe (r) UDH. counterion cloud equals the charge of the monomer CoarseGrained Electrohydrodynamics MeanField MPCDMD DebyeHückel Algorithm Electrostatics Counterions are included implicitly DebyeHückel potential between { λb q 2 0, r > rcut Fractional charge given to the fluid The total charge given to the

7 CoarseGrained Electrohydrodynamics MeanField MPCDMD DebyeHückel Algorithm Electrostatics Counterions are included implicitly DebyeHückel potential between monomers U DH (r) = { λb q 2 r e r/λ D, r < r cut 0, r > r cut Fractional charge given to the fluid particles based on counterion density ρ e (r) U DH. The total charge given to the counterion cloud equals the charge of the monomer

8 CoarseGrained Electrohydrodynamics MeanField MPCDMD DebyeHückel Algorithm Parameters Used: σ LJ = 0.5a MPCD λ D = 1a MPCD λ B = 1.5 MPCD r cut = 5a MPCD q = 1 Hickey, Shendruk, Harden, and Slater, PRL (2012).

9 FreeSolution Electrohydrodynamic Screening Stokes Flow

10 FreeSolution Electrohydrodynamic Screening Stokes Flow EOF

11 FreeSolution Electrohydrodynamic Screening Stokes Flow EOF No Flow Beyond λd Shendruk, Hickey, Slater and Harden, Current Opinion in Colloid & Interface Science (2012)

12 CoarseGrained Electrohydrodynamics FreeSolution Oligomer 1.5 µ / µ FD Experiment (NMR) Experiment (CE) Simulation (Explicit Ions) MPCD without Charge Condensation 1 MPCD Coupling Scheme MPCD with Charge Condensation N 1.1 Hickey, Shendruk, Harden, and Slater, PRL (2012).

05 Experiment (NMR) Experiment (CE) Simulation (Explicit Ions) MPCD without Charge

13 CoarseGrained Electrohydrodynamics FreeSolution Oligomer 1.5 Freedraining Polymer µ / µ FD Experiment (NMR) Experiment (CE) Simulation (Explicit Ions) MPCD without Charge Condensation 1 MPCD Coupling Scheme MPCD with Charge Condensation N 1.1 Hickey, Shendruk, Harden, and Slater, PRL (2012).

14 Globally Deformed

15 Globally Deformed

16 Globally Deformed

17 Globally Deformed Asymmetry, φ Asymmetry Ratio Const. Polymerization N = 200 N = 100 N = 80 N = 60 N = 40 Asymmetry φ = R G,x /R G,r continuously increases with confinement depends on length R eff = k B T/k

18 The polyelectrolyte is deformed but if it is freedraining, we expect an unaltered mobility.

19 , µx/µ Const. Polymerization N = 200 N = 100 N = 80 N = 60 N = 40 suddenly increases with confinement independent of length R eff = k B T/k

20 Why does the mobility change? There is no obvious force antiparallel to the electric field. The chain is was freedraining in freesolution. Yet the mobility increases above it s freesolution value. The mobility for of a chain of given length increases as the conformation becomes more asymmetric. Since the mobility is no longer the freedraining value is the chain still freedraining? The transition for a Rousianlike drag to a Zimmianlike drag would allow for the observed conformationally dependent mobility. This would require hydrodynamic entrainment of fluid within the chain and longrange perturbation to the surrounding flow field.

21 Radial Position, r Axial Flow Velocity vx (x, r) /µxe R eff = Axial Position, x

Radial Position, r 6 5 4 3 2 Axial Flow Velocity 0.000 0.008 0.016 0.024 0.032 0.

22 Radial Position, r Axial Flow Velocity vx (x, r) /µxe R eff = Axial Position, x

Unconfined Radial Position, r 6 5 4 3 2 Axial Flow Velocity 0.000 0.008 0.016 0.

23 Unconfined Radial Position, r Axial Flow Velocity vx (x, r) /µxe Axial Position, x

24 Unconfined Radial Position, r Axial Flow Velocity vx (x, r) /µxe Axial Position, x

25 Unconfined Radial Position, r Axial Flow Velocity vx (x, r) /µxe Axial Position, x

26 Unconfined Radial Position, r Axial Flow Velocity vx (x, r) /µxe Axial Position, x

27 Unconfined Radial Position, r Axial Flow Velocity vx (x, r) /µxe Axial Position, x

28 Unconfined Radial Position, r Axial Flow Velocity vx (x, r) /µxe Axial Position, x

29 Unconfined Radial Position, r Axial Flow Velocity vx (x, r) /µxe Axial Position, x

Unconfined Radial Position, r 6 5 4 3 2 Axial Flow Velocity 0.080 0.160 0.040 0.000 0.008 0.

30 Unconfined Radial Position, r Axial Flow Velocity vx (x, r) /µxe Axial Position, x

31 Both Unconfined and are The polyelectrolyte is not perfectly freedraining This is because λ D is finite. But it is freedraining in the sense that drag is local. Both the unconfined and confined chains have the same draining quality. has no length dependence but conformation does. The polyelectrolyte is not any more hydrodynamically coupled when confined. Freedraining means the polyelectrolyte does not depend on the global asymmetry.

32 Local Local orientation sets mobility

33 Local Local orientation sets mobility S = 3 cos 2 θ 1 / Const. Polymerization N = 200 N = 100 N = R eff = k B T/k

34 Local Local orientation sets mobility S = 3 cos 2 θ 1 / Const. Polymerization N = 200 N = 100 N = 80, µx/µ Const. Polymerization N = 200 N = 100 N = 80 N = 60 N = R eff = k B T/k R eff = k B T/k

35 Local Local orientation sets mobility, µx VS. k N , S

36 Free Solution λd defines length scale of hydrodynamic interactions in free solution. λhi = λd 2σLJ Local λd. Mechanism for Setting Local and Hydrodynamic Interaction Layer HI Screened

37 Free Solution λd defines length scale of hydrodynamic interactions in free solution. λhi = λd 2σLJ Local λd. Mechanism for Setting Local and Hydrodynamic Interaction Layer HI Unscreened

38 Weakly Within λhi = λd 2σLJ the environment appears unconfined. Local λd. λhi Reff. Mechanism for Setting Local and Hydrodynamic Interaction Layer

39 Weakly Within λhi = λd 2σLJ the environment appears unconfined. Local λd. λhi Reff. Mechanism for Setting Local and Hydrodynamic Interaction Layer

40 Weakly Within λhi = λd 2σLJ the environment appears unconfined. Local λd. λhi Reff. Mechanism for Setting Local and Hydrodynamic Interaction Layer

41 Weakly Within λhi = λd 2σLJ the environment appears unconfined. Local λd. λhi Reff. Mechanism for Setting Local and Hydrodynamic Interaction Layer

42 Strongly λd defines length scale of hydrodynamic coupling along the axis HI λ = λd 2σLJ but Reff breaks the symmetry within the Debye cloud. λ HI = Reff The local ensemble of monomers is asymmetric and so has a different average effective friction coefficient. Mechanism for Setting Local and Hydrodynamic Interaction Layer

43 Strongly λd defines length scale of hydrodynamic coupling along the axis HI λ = λd 2σLJ but Reff breaks the symmetry within the Debye cloud. λ HI = Reff The local ensemble of monomers is asymmetric and so has a different average effective friction coefficient. Mechanism for Setting Local and Hydrodynamic Interaction Layer

44 Strongly λd defines length scale of hydrodynamic coupling along the axis HI λ = λd 2σLJ but Reff breaks the symmetry within the Debye cloud. λ HI = Reff The local ensemble of monomers is asymmetric and so has a different average effective friction coefficient. Mechanism for Setting Local and Hydrodynamic Interaction Layer

45 Strongly λd defines length scale of hydrodynamic coupling along the axis HI λ = λd 2σLJ but Reff breaks the symmetry within the Debye cloud. λ HI = Reff The local ensemble of monomers is asymmetric and so has a different average effective friction coefficient. Mechanism for Setting Local and Hydrodynamic Interaction Layer

46 Strongly λd defines length scale of hydrodynamic coupling along the axis HI λ = λd 2σLJ but Reff breaks the symmetry within the Debye cloud. λ HI = Reff The local ensemble of monomers is asymmetric and so has a different average effective friction coefficient. Mechanism for Setting Local and Hydrodynamic Interaction Layer

47 Transition in Local S = 3 cos 2 θ 1 /2 Transition from constant unconfined value to steep increase with confinement at Const. Polymerization R eff λ HI = 2σ λ D = 2 N = 200 N = 100 N = 80, µx/µ Const. Polymerization N = 200 N = 100 N = 80 N = 60 N = R eff = k BT/k R eff = k BT/k

48 Transition in Local Transition from constant unconfined value to steep increase with confinement at R eff λ HI = 2σ λ D = 2

49 Transition in Local Transition from constant unconfined value to steep increase with confinement at R eff λ HI = 2σ λ D = 2

50 s to Estimate ξ Coefficient Asymmetry within the Debye layer reduces effective friction, ξ

51 s to Estimate ξ By doing full hydroynamics interaction calculation for ensemble. Coefficient Asymmetry within the Debye layer reduces effective friction, ξ

52 Coefficient Asymmetry within the Debye layer reduces effective friction, ξ s to Estimate ξ By doing full hydroynamics interaction calculation for ensemble. By replacing whole HI coupled ensemble with an effective solid spheroid.

53 VS, µx/µ VS Model Inverse Coefficient, ξ 1 ellipsoid (λ HI, R eff ) Model λ 2 HI λ 2 HI ξ eff 2λ 2 HI λ 2 HI S 2λ HI λ HI R eff < λ HI R eff λ HI k N S = 2 λ 2 2 1/2 HI λ HI ln ξ eff ξ ellipsoid (λ HI, λ HI µ = Q eff ξ eff λ HI λ HI 2 λ 2 1/2 HI λ HI )

54 VS, µx/µ VS Model Inverse Coefficient, ξ 1 ellipsoid (λ HI, R eff ) Model λ 2 HI λ 2 HI ξ eff 2λ 2 HI λ 2 HI S 2λ HI λ HI R eff < λ HI R eff λ HI k N S = 2 λ 2 2 1/2 HI λ HI ln ξ eff ξ ellipsoid (λ HI, λ HI µ = Q eff ξ eff λ HI λ HI 2 λ 2 1/2 HI λ HI )

55 changes via antiparallel force are not equivalent to perpendicular force mobility independent of conformation (while R eff > λ HI = λ D ) varies in strong confinement even in the absence of walls requires finite λ D strong confinement increases subλ HI asymmetry which decreases each monomer s effective friction coefficient Future work: improved simple models of effective friction coefficient vary Debye length steeper confining potential fluid impenetrable walls

56 Thank you, Owen Hickey Mykyta Chubynsky Henk de Haan David Sean Yuguo Tao Zheng Ma

Electrophoretic Mobility within a Confining Well

Electrophoretic Mobility within a Confining Well Tyler N. Shendruk Martin Bertrand Gary W. Slater University of Ottawa December 5, 2013 Free-Solution Electrophoresis: free-draining polyelectrolytes Free-Draining