  The effect of line tension on the axisymmetric nanoscale capillary bridge
between two identical substrates with convex, concave and flat geometry at the
liquid-vapor equilibrium is theoretically studied. The modified Young's
equation for the contact angle, which takes into account the effect of line
tension is derived on a general axisymmetric curved surface using the
variational method. Even without the effect of line tension, the parameter
space where the bridge can exist is limited simply by the geometry of
substrates. The modified Young's equation further restricts the space where the
bridge can exist when the line tension is positive because the equilibrium
contact angle always remain finite and the wetting state near the zero contact
angle cannot be realized. It is shown that the interplay of the geometry and
the positive line tension restricts the formation of capillary bridge.
