  The elastic properties of a self-assembled bilayer membrane are studied using
the self-consistent field theory, applied to a model system composed of
flexible amphiphilic chains dissolved in hydrophilic polymeric solvents.
Examining the free energy of bilayer membranes with different geometries allows
us to calculate their bending modulus, Gaussian modulus, two fourth-order
membrane moduli, and the line tension. The dependence of these parameters on
the microscopic characteristics of the amphiphilic chain, characterized by the
volume fraction of the hydrophilic component, is systematically studied. The
theoretical predictions are compared with the results from a simple monolayer
model, which approximates a bilayer membrane by two monolayers. Finally the
region of validity of the linear elasticity theory is analyzed by examining the
higher-order contributions.
