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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 q.wang@colostate.edu Qiang (David) Wang Laboratory of Computational Soft Materials

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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)

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Why Layer-by-Layer (LbL) Assembly ? Simple, fast, cheap Self-healing Versatile Synthetic 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

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“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.

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Model System for PE Adsorption 0x A + + + + + + l A,b c s,b b 0 solvent molecule (S) cation ( ) anion ( ) Parameters in the model: SF substrate charge density; d 1 for short-range interactions between substrate and PE, >0 for repulsive and <0 for attractive substrates; pdegree of ionization of PE, smeared (or annealed); Flory-Huggins parameter between PE and solvent; A,b bulk polymer concentration; c s,b bulk salt concentration; lsystem 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.

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H 0 entropic contribution from Gaussian chains, S, , and ; H 1 short-range interaction energy described by the parameter; H 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) N 0 : (arbitrary) chain length chosen for normalization

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ParametersDimensionless ValuesValues in Real Units T300 K a ( 0 a 3 ) 5 Å 0.34380 l7~17542~1050 nm A,b 1~100 10 0.133~13.3 mM c s,b 0~0.10~1.33 M SF 0~0.2 0~5.22×10 C m 2 p0~1 d1d1 10~∞

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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. SF 0.01, c s,b 0.05, 1 RepulsiveAttractive d 1 0, SF 0.1, c s,b 0.1 p 0.5, A,b 1.25×10 Conditions for Strong Charge Inversion RepulsiveAttractive p 0.5, A,b 1.25×10

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PE at High c s,b ≈ Neutral Polymers in Good Solvent

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GSDA vs. SCFT d 1 0, SF 0.01, 1, p 0.5, c s,b 0.05, A,b 1.25×10 c ≥1.25 Q. Wang, MM, 38, 8911 (2005).

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Layer Profiles – Symmetric, Smeared PE p 1 p 2 0.5, c s,b1 c s,b2 0.05 (0.667M), 1S 2S 1 Q. Wang, JPC B, 110, 5825 (2006). SF 0.1 (2.61mC/m 2 ), v 1 v 2 , A,b 7.5×10 4 (10mM) (with a 0.5nm and 0 a 3 )

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x w (1) Layer Profiles – Symmetric, Smeared PE Q. Wang, JPC B, 110, 5825 (2006). p 1 p 2 0.5, c s,b1 c s,b2 0.05, 1S 2S 1

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Layer Profiles – Symmetric, Smeared PE Q. Wang, JPC B, 110, 5825 (2006). p 1 p 2 0.5, c s,b1 c s,b2 0.05, 1S 2S 1

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Layer Profiles – Symmetric, Smeared PE Q. Wang, JPC B, 110, 5825 (2006). p 1 p 2 0.5, c s,b1 c s,b2 0.05, 1S 2S 1

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Three-Zone Structure – Symmetric, Smeared PE Q. Wang, JPC B, 110, 5825 (2006). p 1 p 2 0.5, c s,b1 c s,b2 0.05, 1S 2S 1

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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. p 1 p 2 0.5, c s,b1 c s,b2 0.05, 1S 2S PS

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Charge Compensation – Smeared PE c s,b1 c s,b2 0.05, 1S 2S 1

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Charge Compensation – Asymmetric, Smeared PE p 1 p 2 0.5

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Charge Density Profiles – Asymmetric, Smeared PE p 1 p 2 0.5, c s,b1 c s,b2 0.05, 1S 1, 2S 0.6 1S 2S 1

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Annealed vs. Smeared PE – 1 st Layer p 1 0.5, c s,b1 0.05, 1S 1

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Charge Fractions in Multilayer – Symmetric, Annealed PE p 1 p 2 0.5, c s,b1 c s,b2 0.05, 1S 2S 1 Each deposition changes 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 i th deposition. (i) : amount of PE adsorbed in the i th deposition.

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Annealed vs. Smeared PE – Polymer Density in Zone II p 1 p 2 0.5, c s,b1 c s,b2 0.05, 1S 2S 1

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p 1 p 2 0.5, c s,b1 c s,b2 0.05, 1S 2S 0.5, 1,b 2,b 7.5×10 4 Non-Equilibrium & Solvent Effects – Symmetric, Smeared PE Multilayer does not form in or good solvent. Q. Wang, Soft Matter, 5, 413 (2009).

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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@colostate.edu Q. Wang, MM, 38, 8911 (2005). Q. Wang, JPC B, 110, 5825 (2006). Q. Wang, Soft Matter, 5, 413 (2009).

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AB =0 Layer Thickness SF =0.1, c s,b =0.05 D (59) a (A) D (60) a (B) p A =p B =0.44.174.18 p A =0.4, p B =12.821.10 p A =1, p B =0.41.112.81 p A =p B =10.27

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AB 0 Layer Thickness

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