numerical modeling of polyelectrolyte adsorption and layer-by-layer assembly department of chemical...
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Numerical Modeling of Polyelectrolyte Adsorption and Layer-by-Layer Assembly
Department of Chemical & Biological Engineering
and School of Biomedical Engineering
Colorado State University
Qiang (David) Wang
Laboratory of Computational Soft Materials
Laboratory of Computational Soft Materials
PE are important materials
• Can be soluble in water
• Can be adsorbed onto charged surfaces
PE are difficult to study
PE are charged polymers
• Both long-range (Coulomb) and short-range (excluded volume) interactions present in the system
Decher, Science, 277, 1232 (1997)
PE Layer-by-Layer (LbL) Assembly
Polyelectrolytes (PE)
Why Layer-by-Layer (LbL) Assembly ?• Simple, fast, cheap• Self-healing• VersatileSynthetic PE: conducting &
light-emitting polymers, reactive polymers, polymeric complexes, polymeric dyes, …
Natural PE: DNA, RNA, proteins, viruses, …
Charged nano-particles and platelets, …
Peyratout and Dahne, Angew. Chem. Int. Ed., 43, 3762 (2004)
surface modification, enzyme immobilization, gene transfection, separation membranes, conducting or light-emitting devices, batteries, optical data storage, controlled particle and catalyst preparation, …
• Potential Applications
“Fuzzy Nanoassemblies:Toward Layered Polymeric Multicomposites”
Decher, Science, 277, 1232 (1997)
Black curve: Concentration profile of each layer.
Blue (Red) dots: Total concentration profile of anionic (cationic) groups from all layers.
Green dots: Concentration profile of a labeling group applied to every fourth layer.
Model System for PE Adsorption
0 x
A++++++
l
A,b
cs,b
b0
solvent molecule (S)cation ()anion ()
Parameters in the model:
SF substrate charge density;
d1 for short-range interactions between substrate and PE, >0 for repulsive and <0 for attractive substrates;
p degree of ionization of PE,
smeared (or annealed);
Flory-Huggins parameter between PE and solvent;
A,b bulk polymer concentration;
cs,b bulk salt concentration;
l system size;
(uniform) dielectric constant.
• Monovalent, 1D system;• Ions from salt counterions from
PE and substrate;• Ions have no volume and short-rang
interactions;• Polymer segments have the same
density 0 as solvent molecules;• All polymer segments have the same
statistical segment length a.
0 1 2Hamiltonian: H H H H
0 entropic contribution from Gaussian chains, S, , and ;
1 short-range interaction energy described by the parameter;
2 pure Coulomb interaction energy.
Canonical ensemble
Incompressibility Constraint: A(x) S(x) 1 for x ≥ 0.
Self-Consistent Field Theory (SCFT)Self-Consistent Field Theory (SCFT) &Ground-State Dominance Approximation (GSDA)
20
A , A, ,2
2A,A
0 A A, A2A
0AA SF
1
A
d
d
1dln 2
d 1
d d At 0: , ;
d d
d d At : 0, 0.
d d
s b b s b
bb
Np c p e c e
x
N px
Nx
x x
xx
d
lx
PB Eq. :
GSDA
B.C.s :
N0: (arbitrary) chain length chosen for normalization
Parameters Dimensionless Values Values in Real Units
T 300 K
a (0a3) 5 Å
0.343 80
l 7~175 42~1050 nm
A,b 1~100 10 0.133~13.3 mM
cs,b 0~0.1 0~1.33 M
SF 0~0.2 0~5.22×10 Cm2
p 0~1
0~1
d1 10~∞
Poor solvent for polymers, high salt concentrations, attractive or indifferent surface for polymers, and oppositely charged surface and polyelectrolytes are all needed to obtain strong charge inversion.
SF0.01, cs,b0.05, 1
RepulsiveAttractive
d10, SF0.1, cs,b0.1
p0.5, A,b1.25×10
Conditions for Strong Charge Inversion
RepulsiveAttractive
p0.5, A,b1.25×10
SF S
0
F
A A,0 ( 0 : Depletion; 0 : Adsorption)
( 0 : Charge inversion; 1: Strong charge inversio
(
n)
) dl
bN x x
p
PE at High cs,b ≈ Neutral Polymers in Good Solvent
A, 0A A,
A
22
A0 A A,0
21
A, 1
0 A, 0 A,
A
1ln exp 0
1
d1d 0
d
Assume , , and
, then
2 1 1 1
2 2
effbeff
eff eff b ef
bb
b
D
b
b
f
b
N cx
pN v x
dd
v N v N
c x
v
GSDA
0
20 SF1 1 1 2
with and , where .eff effb b
N ppv v d d
c cv
SF 0A A,
A
, A,
AAssume and , then
( ) 1 that ( ) dec
exp , wher
ay
e .2
s much faster than ( )
bb
bb
b s b bc c pN c p
xc
x x
c
x
PB Eq.
GSDA vs. SCFT
d10, SF0.01, 1,
p0.5, cs,b0.05,
A,b1.25×10
c≥1.25
Q. Wang, MM, 38, 8911 (2005).
Layer Profiles – Symmetric, Smeared PEp1p20.5, cs,b1cs,b20.05 (0.667M), 1S2S1
2
for layer A
for eve l
1 odd
ay r n e
i
i
Q. Wang, JPC B, 110, 5825 (2006).
SF0.1 (2.61mC/m2), v1v2,
A,b7.5×104 (10mM) (with a0.5nm and 0a3)
xw(1)
Layer Profiles – Symmetric, Smeared PE
2
for layer A
for eve l
1 odd
ay r n e
i
i
Q. Wang, JPC B, 110, 5825 (2006).
p1p20.5, cs,b1cs,b20.05, 1S2S1
2
for layer A
for eve l
1 odd
ay r n e
i
i
Layer Profiles – Symmetric, Smeared PE
Q. Wang, JPC B, 110, 5825 (2006).
p1p20.5, cs,b1cs,b20.05, 1S2S1
Layer Profiles – Symmetric, Smeared PE
Q. Wang, JPC B, 110, 5825 (2006).
p1p20.5, cs,b1cs,b20.05, 1S2S1
Three-Zone Structure – Symmetric, Smeared PE
Q. Wang, JPC B, 110, 5825 (2006).
p1p20.5, cs,b1cs,b20.05, 1S2S1
P
For a homogeneous system such as Zone II, SCFT reduces to the Flory-Huggins
theory modified for PE, i.e., the free energy (of mixing) per polymer segment or
solvent molecule is given by
ln 12
fN
2
PS 12
1 2
P , PP , P
P
ln 1 14
where
22 ln
2 2 , 2
.
s bs b
cp
N
pc
Polymer Density in Zone II – Symmetric, Smeared PE
• Zone II is not in phase equilibrium with a bulk solution.
• The total polymer density in Zone II, PEM, does not depend on electrostatic interactions.
p1p20.5, cs,b1cs,b20.05, 1S2SPS
Charge Compensation – Smeared PE
( )( )SF A A
1
( )
th
: amount of PE adsorbed
in the deposition.
At steady state,
iji
j
j
v p
j
( )
( )
0 for odd
0 for even
i
i
i
i
cs,b1cs,b20.05, 1S2S1
( )( ) ( 1) ( 1)A A 2
ii i iv p
( ) ( 1)( ) ( 2)A A A A
i ii i v p v p
( )( )SF A A
1
( ) ( 1)( ) ( 2)A A A A
At steady state,
iji
j
i ii i
v p
v p v p
Charge Compensation – Asymmetric, Smeared PEp1p20.5
Charge Density Profiles – Asymmetric, Smeared PEp1p20.5, cs,b1cs,b20.05, 1S1, 2S0.6
1S2S1
Annealed vs. Smeared PE – 1st Layerp10.5, cs,b10.05, 1S1
Charge Fractions in Multilayer – Symmetric, Annealed PEp1p20.5, cs,b1cs,b20.05, 1S2S1
Each depositionchanges the charges carried by the PE in a few previously deposited layers, of which the density profiles are fixed in our modeling. Thus,
(i): charges carried by PE adsorbed in the ith deposition.
(i): amount of PE adsorbed in the ith deposition.
( ) ( 1) ( ).i i i
Annealed vs. Smeared PE – Polymer Density in Zone II
Smeared PEM
AnnealedPEM
0.805 0.004
0.816 0.010
p1p20.5, cs,b1cs,b20.05, 1S2S1
p1p20.5, cs,b1cs,b20.05, 1S2S0.5, 1,b2,b7.5×104
Non-Equilibrium & Solvent Effects – Symmetric, Smeared PE
Multilayer does not form in or good solvent.
Q. Wang, Soft Matter, 5, 413 (2009).
• We have used a self-consistent field theory to model the layer-by-layer assembly process of flexible polyelectrolytes (PE) on flat surfaces as a series of kinetically trapped states.
• Our modeling, particularly for asymmetric PE having different charge fractions, bulk salt concentrations, or solvent qualities, reveals the internal structure and charge compensation of PE multilayers. We have also compared multilayers formed by strongly and weakly dissociating PE.
• Our results qualitatively agree with most experimental findings.
Summary
Q. Wang, MM, 38, 8911 (2005).Q. Wang, JPC B, 110, 5825 (2006).Q. Wang, Soft Matter, 5, 413 (2009).