Models of the boundary conditions for the Boltzmann equation were constructed systematically in a recent paper by the present authors (K. Aoki et al., in: Phys. Rev. E 106:035306, 2022) using an iteration scheme for the half-space problem of a linear kinetic equation describing the behavior of gas and physisorbed molecules in a thin layer adjacent to a solid surface (physisorbate layer). In the present paper, special attention is focused on the model based on the second iteration that was only touched on in the above reference. The model is presented in an explicit form, and its properties are investigated numerically. In particular, it is shown by the comparison with the numerical solution of the half-space problem that the model is a significant improvement compared with the model based on the first iteration and is accurate and useful.