  The Canham--Helfrich free-energy density for a lipid bilayer has drawn
considerable attention. Aside from the mean and Gaussian curvatures, this
free-energy density involves a spontaneous mean-curvature that encompasses
information regarding the preferred, natural shape of the lipid bilayer. We use
a straightforward microphysical argument to derive the Canham--Helfrich
free-energy density. Our derivation (i) provides a justification for the common
assertion that spontaneous curvature originates primarily from asymmetry
between the leaflets comprising a bilayer and (ii) furnishes expressions for
the splay and saddle-splay moduli in terms of derivatives of the underlying
potential.
