Electrophoretic Mobility within a Confining Well
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1 Electrophoretic Mobility within a Confining Well Tyler N. Shendruk Martin Bertrand Gary W. Slater University of Ottawa December 5, 2013
2 Free-Solution Electrophoresis: free-draining polyelectrolytes Free-Draining Free-solution electrophoretic mobility (µ 0 = Q/ξ) is independent of length and conformation ~E = Monomer (-) = Cloud of counterions (+)
3 Free-Solution Electrophoresis: free-draining polyelectrolytes ~E Free-Draining Free-solution electrophoretic mobility (µ 0 = Q/ξ) is independent of length and conformation Drag is local and effective friction (ξ) increases with length (N), just like effective charge (Q) = Monomer (-) = Cloud of counterions (+)
4 Free-Solution Electrophoresis: free-draining polyelectrolytes ~E Free-Draining Free-solution electrophoretic mobility (µ 0 = Q/ξ) is independent of length and conformation Drag is local and effective friction (ξ) increases with length (N), just like effective charge (Q) Counterion clouds (λ D ) screen both electrostatic and hydrodynamic interactions = Monomer (-) = Cloud of counterions (+) Mobility, µ/µ Experiment (NMR) Experiment (CE) Explicit Ions MPCD thin Debye layer MD-MPCD Debye-Hückel Degree of Polymerization, N
5 Separation via electrophoresis: breaking friction s extensivity Many systems subvert mobility s size independence by simultaneously applying both an electric field E and a mechanical force f Examples: Gels, end-labeled free-solution electrophoresis, collisions with posts, translocation through nanopores, etc. a Balducci, Mao, Han and Doyle, Macromolecules, 39(18), Cross, Strychalski and Craighead, J. Appl. Phys., 102(2), Salieb-Beugelaar, et.al., Nano Letters, 8(7), b Campbell, et.al., Lab Chip, 4(3), 2004.
6 Separation via electrophoresis: breaking friction s extensivity Many systems subvert mobility s size independence by simultaneously applying both an electric field E and a mechanical force f Examples: Gels, end-labeled free-solution electrophoresis, collisions with posts, translocation through nanopores, etc. Confinement in nanofluidic channels is observed to modify mobility but ~E = Monomer (-) = Cloud of counterions (+) a Balducci, Mao, Han and Doyle, Macromolecules, 39(18), Cross, Strychalski and Craighead, J. Appl. Phys., 102(2), Salieb-Beugelaar, et.al., Nano Letters, 8(7), b Campbell, et.al., Lab Chip, 4(3), 2004.
7 Separation via electrophoresis: breaking friction s extensivity Many systems subvert mobility s size independence by simultaneously applying both an electric field E and a mechanical force f Examples: Gels, end-labeled free-solution electrophoresis, collisions with posts, translocation through nanopores, etc. Confinement in nanofluidic channels is observed to modify mobility but conflicting experimental results have been reported. a,b ~E = Monomer (-) = Cloud of counterions (+) a Balducci, Mao, Han and Doyle, Macromolecules, 39(18), Cross, Strychalski and Craighead, J. Appl. Phys., 102(2), Salieb-Beugelaar, et.al., Nano Letters, 8(7), b Campbell, et.al., Lab Chip, 4(3), 2004.
8 Simulate a Simple System: remove walls entirely! ~E Harmonic well s k BT D e 2 k sp = Monomer (-) = Cloud of counterions (+) Radially confining potential well no walls harmonic well (spring constant k) acts on monomers transparent to fluid
9 Simulate a Simple System: remove walls entirely! ~E Harmonic well s k BT D e 2 k sp = Monomer (-) = Cloud of counterions (+) Radially confining potential well no walls harmonic well (spring constant k) acts on monomers transparent to fluid Simplified polyelectrolyte freely-jointed MD chain
10 Simulate a Simple System: remove walls entirely! ~E Harmonic well s k BT D e 2 k sp = Monomer (-) = Cloud of counterions (+) Radially confining potential Coarse-Grained Electrohydrodynamics: Mean-Field MPCD-MD Debye-Hückel Algorithm well no walls harmonic well (spring constant k) acts on monomers transparent to fluid Simplified polyelectrolyte freely-jointed MD chain
11 Simulate a Simple System: remove walls entirely! ~E Harmonic well s k BT D e 2 k sp = Monomer (-) = Cloud of counterions (+) Radially confining potential well no walls harmonic well (spring constant k) acts on monomers transparent to fluid Simplified polyelectrolyte freely-jointed MD chain Coarse-Grained Electrohydrodynamics: Mean-Field MPCD-MD Debye-Hückel Algorithm q(r) / e r/ D r Q = Q X i r qi(ri) r cut D FE
12 Mobility: of confined and deformed polyelectrolytes Asymmetry ratio 10 2 Asymmetry, ϕ N = 120 N = 80 N = Effective Radius, R eff = k B T/k where ϕ = R g,x /R g,r
13 Mobility: of confined and deformed polyelectrolytes Asymmetry ratio Electrophoretic Mobility 10 2 N = 120 N = 80 N = 40 Asymmetry, ϕ Mobility, µ/µ N = 120 N = 80 N = Effective Radius, R eff = k B T/k Effective Radius, R eff = k B T/k where ϕ = R g,x /R g,r The conformation has N dependence and continues to increases at strong confinement The mobility is N-independent and saturates at strong confinement
14 Free-draining: far-field fluid speed remains zero 4 (a) (c) Radial Position, r (b) Axial Position, z uz (z, r) /µ0e
15 Free-draining: far-field fluid speed remains zero 4 (a) (c) Radial Position, r (b) Axial Position, z uz (z, r) /µ0e Together with the asymmetry ratio, the flow profiles suggest that hydrodynamic interactions remain screened.
16 Why Does Mobility Increase? local hydrodynamic coupling Monomers within a given λ D are hydrodynamically coupled. Segments are locally rod-like
17 Why Does Mobility Increase? local hydrodynamic coupling Monomers within a given λ D are hydrodynamically coupled. Segments are locally rod-like Confinement orients the segments, lowering their local friction
18 Why Does Mobility Increase? local hydrodynamic coupling log (µ/µ0) N = 120 N = 80 N = 40 MPCD-MD oriented rods point-charges log ( ) R eff Monomers within a given λ D are hydrodynamically coupled. Segments are locally rod-like Confinement orients the segments, lowering their local friction
19 Conclusion Conformation changes via antiparallel force are not equivalent to perpendicular force mobility independent of conformation (while R eff > λ D ) Mobility varies in strong confinement even in the absence of walls requires finite λ D strong confinement decreases each segment s effective friction coefficient Future work: improved simple models of effective friction coefficient vary Debye length steeper confining potential fluid impenetrable walls
20 Thank you, Owen Hickey Mykyta Chubynsky Henk de Haan David Sean Zheng Ma
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