Structure and Thermodynamics of Polyelectrolyte Complexes

  • Johannes FruehEmail author
  • Meiyu Gai
  • Simon Halstead
  • Qiang HeEmail author
Part of the Engineering Materials book series (ENG.MAT.)


Polyelectrolytes (PEs) find applications in many fields of modern life starting from food additives to flocculation and solubility enhancers, down to viscosity adjusting agents in cosmetics and subterranean gelling or drug delivery agents. Most of these properties are related to the PE charge density, structure, counterions, temperature or counter PE. This book chapter gives an overview of the current state of understanding of the thermodynamical properties of PEs in solution. The theoretical predictions and results are compared with current state of the art computer simulations (with a focus on molecular dynamics) as well as experiments on PE structure, complex formation and viscosity properties.


Counterion Condensation Zimm Model Entanglement Concentration Polyampholytes Charged Monomers 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Valence of PE monomer group

\(k_{B} T\)

Thermal energy


Boltzmann constant


Dielectric constant


Local dielectric constant


Debye length


Inverse Debye length


Persistence length


Bjerrum length


Length between two monomers


Length of dipole


Length of fully elongated PE


Length of collapsed PE

\(L_{\xi }\)

Correlation length


Distance between 2 PE chain centers


Length of string between globules

\(L_{\xi }\)

Size of a globule/bead


Salt concentration


PE concentration


Crossover concentration


Local concentration of counterions next to PE


Fraction of charged monomers


Monomer length/diameter


Reduced coupling constant (Based on thermal energy)


Reduced coupling constant (based on excluded volume)


Excluded volume per monomer


Local volume close to monomer


Elongation per monomer


Size of electrostatic blob

\(V_{\zeta }\)

Volume of electrostatic blob


Total length of PE


Hydrodynamic radius


Number of monomers


Number of charged groups in PE


Number of monomers in the diameter D of a rodlike molecule


Number of monomers in string


Number of monomers in a bead


Number of monomers in entangled region


Number of P-bonds in strong PE


Amount of PE molecules


Amount of solvent molecules


Amount of solvent molecules inside \(v_{0}\)


Amount of solvent molecules outside \(v_{0}\)


Number of counter ions

\(n_{\Psi }\)

Number of ψ bindings


Effective diameter of the rod-like molecule


Degree of dissociated charges






Charge density


Valence of counterions


Reaction constant


Volume fraction of solvent


Volume fraction of PE


Volume fraction of counterion


Molecular volume of solvent


Molecular volume of counterion


Molecular volume of PE


Molar volume of solvent


Molar volume of PE


Number of gratings used in Flory lattice

\(\Delta H\)

Free enthalpy


Electrostatic enthalpy

\(\Delta S\)

Free entropy


Entropy of mixing


Kuhn entropy


Counter ion entropy


Free energy of electrolyte


Free energy of ionic atmosphere


Non electrostatic part of free energy


Free energy


Flory Huggins solution parameter


Electrostatic based energies


Debye electrostatic energy of the PE chain


Energy of the counterion adsorbed on the PE

\(E_{{_{ela} }}\)

Elastic energy of the stretched, charged PE


Fraction of free counter ions


Fraction of condensed counter ions


Charge density parameter


Constant related to \(k_{2}\)


Concentration parameter ~\(- \log c_{P}\)


Charge density parameter


Euler number ex


Electron charge


Effective expansion factor


Strength parameter for short ranged effects



\(V_{ + }\)

Positive ion cloud scaling factor

\(V_{ - }\)

Negative ion cloud scaling factor


Ideal gas constant


Entropy of condensed counterions


Translational entropy of ions


Fluctuations between PE and ions


Ion pair energy


Free energy term for partly charged PE


Correlation term (ion pair PE)


Viscosity of the solvent


Viscosity of the solution

\(\tau_{RZ} , \tau_{RR}\)

Zimm and Rouse relaxation time




Diffusion coefficient

\(D_{Z} , D_{R}\)

Zimm and Rouse diffusion coefficient

\({\rm Z}_{P}\)

Friction coefficient of the polymer

\({\rm Z}_{B}\)

Friction coefficient of the beads


Shear stress

\(\dot{\gamma }\)

Shear rate


Reduced shear rate


Volume fraction


Tube diameter


Reduced temperature


Theta temperature of solvent/PE


Concentration dependent parameter, which depends on concentration (values used for X are shown below the equations)



Acknowledgments: This work was supported by the National Nature Science Foundation of China (91027045), 100-talent Program of HIT, China Postdoctoral Science Foundation (2013M531019) and New Century Excellent Talent Program (NCET-11-0800) and Harbin Institute of Technology.


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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Key Laboratory of Microsystems and Microstructures Manufacturing, Ministry of Education, Micro/Nano Technology Research CentreHarbin Institute of TechnologyHarbinChina
  2. 2.School of Chemical Engineering and TechnologyHarbin Institute of TechnologyHarbinChina

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