  Structure and thermodynamics in restricted primitive model electrolytes are
examined using three recently developed versions of a linear form of the
modified Poisson-Boltzmann equation. Analytical expressions for the osmotic
coefficient and the electrical part of the mean activity coefficient are
obtained and the results for the osmotic and the mean activity coefficients are
compared with that from the more established mean spherical approximation,
symmetric Poisson-Boltzmann, modified Poisson-Boltzmann theories, and available
Monte Carlo simulation results. The linear theories predict the thermodynamics
to a remarkable degree of accuracy relative to the simulations and are
consistent with the mean spherical approximation and modified Poisson-Boltzmann
results. The predicted structure in the form of the radial distribution
functions and the mean electrostatic potential also compare well with the
corresponding results from the formal theories. The excess internal energy and
the electrical part of the mean activity coefficient are shown to be identical
analytically for the mean spherical approximation and the linear modified
Poisson-Boltzmann theories.
