  A weakly charged flexible polyelectrolyte chain in a neutral spherical cavity
is analyzed using self-consistent field theory (SCFT) within an explicit
solvent model. Assuming the radial symmetry for the system, it is found that
the confinement of the chain leads to creation of a charge density wave along
with the development of a potential difference across the center of cavity and
the surface. We show that the solvent entropy plays an important role in the
free energy of the confined system. For a given radius of the spherical cavity
and fixed charge density along the backbone of the chain, solvent and small ion
entropies dominate over all other contributions when chain lengths are small.
However, with the increase in chain length, chain conformational entropy and
polymer-solvent interaction energy also become important. Our calculations
reveal that energy due to electrostatic interactions plays a minor role in the
free energy. Furthermore, we show that the total free energy under spherical
confinement is not extensive in the number of monomers. Results for the osmotic
pressure and mean activity coefficient for monovalent salt are presented. We
demonstrate that fluctuations at one-loop level lower the free energy and
corrections to the osmotic pressure and mean activity coefficient of the salt
are discussed. Finite size corrections are shown to widen the range of validity
of the fluctuation analysis.
