The
microscopic pressure tensor plays an important role in understanding
the mechanical stability, transport, and high-pressure phenomena of
confined phases. The lack of an exact formulation to account for the
long-range Coulombic contribution to the local pressure tensor in
cylindrical geometries prevents the characterization of molecular
fluids confined in cylindrical pores. To address this problem, we
first derive the local cylindrical pressure tensor for Lennard-Jones
fluids based on the Harasima (H) definition, which is expected to
be compatible with the Ewald summation method. The test of the H-definition
pressure equations in a homogeneous system shows that the radial and
azimuthal pressure have unphysical radial dependence near the origin,
while the axial pressure gives physically meaningful values. We propose
an alternative contour definition that is more appropriate for cylindrical
geometry and show that it leads to physically realistic results for
all three pressure tensor components. With this definition, the radial
and azimuthal pressures are of Irving–Kirkwood (IK) type, and
the axial pressure is of Harasima type. Because of the practical interest
in the axial pressure, we develop a Harasima/Ewald (H/E) method for
calculating the long-range Coulombic contribution to the local axial
pressure for rigid molecules. As an application, the axial pressure
profile of water inside and outside a (20, 20) single-wall carbon
nanotube is determined. The H/E method is compared to the IK method,
which assumes a spherically truncated Coulombic potential. Detailed
analysis of the pressure profile by both methods shows that the water
confined in the nanotube is in a stretched state overall in the axial
direction.