The chemical potential of metal atoms, μ
M
, in supported metal
nanoparticles is
an important descriptor related to both the catalytic activity and
the stability of the nanoparticles. Here, we derive an expression
relating μ
M
to
the radius of the particle’s contact area with the support
and the adhesion energy at the metal/support interface (Eadh
) that assumes the particles have the shape of
spherical caps but of arbitrary contact angle with the support (θ
c
) and includes an empirical
correction for the increase in metal surface energy and adhesion energy
with decreasing radius of curvature. We then show that, at any assumed
contact angle, we can simultaneously fit previously reported measurements
of both calorimetric μ
M
(from heats of metal vapor adsorption during nanoparticle
growth by vapor deposition) versus metal coverage data and the He+ low-energy ion scattering (LEIS) intensities for the metal
and/or support versus metal coverage (using our recently developed
spherical cap model for quantitative LEIS intensities), to determine
the particle size versus coverage and E
adh
. Only one choice of contact angle gives a pair
of values for contact angle and E
adh
, which is consistent with the Young–Dupré equation
for the equilibrium shape of a spherical particle. At this equilibrium
shape, we then applied this spherical cap model (SCM) to reanalyze
microcalorimetric metal chemical potentials and LEIS signals versus
coverage data for nine metal/support combinations that were previously
analyzed by assuming that the particles had the shape of hemispherical
caps, i.e., with a contact angle of 90°. We show that this revised
approach gives close agreement with the calorimetric and LEIS data;
the best-fit contact angles vary from 64 to 84°, correcting the
earlier assumption of 90°. These results provide significant
accuracy improvements in particle size versus coverage, metal chemical
potential versus size and coverage, metal/support adhesion energies
and contact angles for Cu, Ag and Au on CeO2(111), Ni on
MgO(100), Ag on Fe3O4(111) and TiO2(100), and Ag, Ni and Pd on Ni-supported graphene. This revised approach
is much more broadly applicable than the earlier hemispherical cap
model (HCM).