Abstract.
In this chapter we review recent advances which have been achieved in the theoretical description and understanding of polyelectrolyte solutions. We will discuss an improved density functional approach to go beyond mean-field theory for the cell model and an integral equation approach to describe stiff and flexible polyelectrolytes in good solvents and compare some of the results to computer simulations. Then we review some recent theoretical and numerical advances in the theory of poor solvent polyelectrolytes. At the end we show how to describe annealed polyelectrolytes in the bulk and discuss their adsorption properties.
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Abbreviations
- DH:
-
Debye-Hückel
- PB:
-
Poisson-Boltzmann
- OCP:
-
One-Component-Plasma
- PRISM:
-
Polymer-Reference-Interaction-Site model
- RLWC:
-
Reference-Laria-Wu-Chandler closure
- Z c :
-
counterion valence
- Z m :
-
monomer valence
- N :
-
polymer chain length, number of repeat units
- h(r):
-
total correlation function
- g(r):
-
pair correlation function
- β=:
-
(k B T)−1
- \(v^{{HC}}_{{ij}} {\left( r \right)}\) :
-
hard core potential
- l :
-
bond length
- l p :
-
persistence length
- b :
-
monomer size
- l B :
-
Bjerrum length
- λ D :
-
Debye (screening) length
- κ :
-
inverse (Debye length)
- ρ :
-
monomer density
- ρ c :
-
counterion density
- R E :
-
ent-to-end distance
- R G :
-
radius of gyration
- f :
-
fraction of charged monomers
- S(q):
-
total structure factor
- S IC :
-
inter-chain structure factor
- S 1 :
-
spherically averaged chain form factor
- ξ :
-
correlation length
- q * :
-
peak in the structure factor S IC (q)
- q m :
-
peak in the total structure factor S(q)
- µ :
-
chemical potential (of charges)
- ξ el :
-
electrostatic blob size
- v :
-
virial coefficient
- τ :
-
reduced temperature
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Holm, C. et al. Polyelectrolyte Theory. In: Schmidt, M. (eds) Polyelectrolytes with Defined Molecular Architecture II. Advances in Polymer Science, vol 166. Springer, Berlin, Heidelberg. https://doi.org/10.1007/b11349
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