Comparison of Theories SCFT and Variational Formalism

Self-Consistent Field Theory for Single Chain 

The theoretical description presented above for multichain polyelectrolyte solutions can be easily adapted to study a single flexible polyelectrolyte chain confined in a spherical cavity of volume Q = 4jtl /3. For a single flexible polyelectrolyte chain with a fixed degree of ionization (=/) in the presence of salt ions and solvent molecules, the Hamiltonian can be written as 

Defining the dimensionless Flory parameter for chemical mismatch, Xps by Eq. (6.71) after using Wpp, w ss, and Wps as the excluded volume parameters characterizing the short-range excluded volume interactions of type monomer-monomer. 

using the methods of collective variables (cf. Section 6.4.2.1) for decoupling all the interactions except the electrostatics and the Hubbard-Stratonovich transformation [14, 55] (cf. Section 6.4.2.2) for the electrostatic part in Eq. (6.124), the partition function can be written as integrals over the collective densities and corresponding fields so that Eq. (6.124) becomes 

Wg are the collective fields experienced by the monomers and solvent, respectively, and Qp,Qg represent their respective collective densities. All charged species (excluding the ion-pairs formed due to adsorption of counterions) experience a field t ) (which is equivalent to the electrostatic potential), t) and u are Lagrange s multipliers corresponding to, respectively, the incompressibility and net charge constraints in the partition function. 

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Comparison of Theories SCFT and Variational Formalism 325 Table 6.2 Comparison of contributions to Ff in SCFT and variational formalism. 

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