Magnetic-field-dependent Langmuir adsorption ($b(B)=b(0)\cosh ({\mu }_{\mathrm{B}}B/k_{\mathrm{B}}T)$)

For independent spin-one-half adsorbates whose two spin states are split only at the surface, the one-site partition function contains $2\cosh ({\mu }_{\mathrm{B}}B/k_{\mathrm{B}}T)$. Relative to the unsplit bulk spin degeneracy, this increases the Langmuir adsorption model affinity by a hyperbolic-cosine factor. At fixed temperature and gas pressure, increasing the magnitude of the magnetic field increases surface coverage in this model.