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Theoretical Approaches to Neutral and Charged Polymer Brushes

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Surface-Initiated Polymerization II

Part of the book series: Advances in Polymer Science ((POLYMER,volume 198))

Abstract

Neutral or charged polymers that are densely end-grafted to surfaces form brush-like structures and are highly stretched under good-solvent conditions. We discuss and compare relevant results from scaling models, self-consistent field methods and MD simulations and concentrate on the conceptual simple case of planar substrates. For neutral polymers the main quantity of interest is the brush height and the polymer density profile, which can be well predicted from self-consistent calculations and simulations. Charged polymers (polyelectrolytes) are of practical importance since they are soluble in water. Counterion degrees of freedom determine the brush behavior in a decisive way and lead to a strong and nonlinear swelling of the brush.

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Abbreviations

a :

Kuhn length or effective monomer size

d :

height of counterion layer

f :

fractional charge of the chain 0 < f < 1

F :

free energy in units of k B T (per chain or unit area)

h :

height of brush

k B T :

thermal energy

L :

contour length of a chain

ℓB=e2/(4 πε kBT):

Bjerrum length

N :

polymerization index

R :

end-to-end polymer chain radius

R 0 :

end-to-end radius of an ideal polymer

R F :

Flory radius of a self-avoiding chain

v 2 :

2nd virial coefficient of monomers in solution

κ−1 :

Debye–Hückel screening length

ν:

Flory exponent for the polymer size

Π:

osmotic pressure, rescaled by k B T

ρa :

grafting density of a polymer brush

ρ(z):

monomer density at distance z from grafting surface

σ:

Lennard-Jones diameter in simulation

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Authors and Affiliations

  1. Dept. of Physics, Technical University of Munich, James Franck Str, 85478, Garching, Germany

    Ali Naji & Roland R. Netz

  2. Max-Planck-Institute of Colloids and Interfaces, 14424, Potsdam, Germany

    Christian Seidel

Authors
  1. Ali Naji
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  2. Christian Seidel
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  3. Roland R. Netz
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Correspondence to Roland R. Netz .

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Rainer Jordan

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Naji, A., Seidel, C., Netz, R.R. Theoretical Approaches to Neutral and Charged Polymer Brushes. In: Jordan, R. (eds) Surface-Initiated Polymerization II. Advances in Polymer Science, vol 198. Springer, Berlin, Heidelberg. https://doi.org/10.1007/12_062

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