Gas sorption in mesoscopic slit-pores

Prom a theoretical perspective, the Thommes Findenegg experiment [31] can be represented by the equation 

42) cannot be solved explicitly for pp in terms of pb and T, we must have recourse to a numerical method, which is detailed below. In the remainder of this section, we express all quantities in the customary dimensionless (i.e., reduced ) units, where length is given in units of Tf and energy in unite of ejf. In addition, for simplicity we set at — and d = Ts/ /2 assuming the (100) configuration of the face-centered cubic lattice for substrate atoms. Then in dimensionless units we have Ob = 87t/3 and Pb = 1 

To solve Eq. (4.42) for subcritical bulk isodiorcs in the temperature range Tch T Txb, we need to determine T b first by solving (see Eq. (4.29)] 

As only the gas density /Jb = Pb i fixed, and the density of coexisting liquid and the coexistence temperature are unknown, we must solve Eqs. (4.43) and (4.45) simultaneously for Txb and pj,. We accomplish this numerically by a procedure also detailed in Appendix D.1.3. 

Equation (4.42) can now be solved under experimentally relevant conditions [31], that is, for bulk isochoric paths (pb = const) and T — T. Again wc defer a detailed description of the numerical procedure to Appendix D.1.3. Once the numerical solution has been found, we are in a position to calculate the excess coverage for the thermodynamically stable pore phase via 

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