Environmental Engineering Reference
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has been done in this field in the last decades. Recent developments in sorption in-
strumentation allow for accurate measurements at low-pressure range for various
probe molecules, which are essential for evaluation of the adsorption potential,
micropore and mesopore volume distributions. The adsorption potential distribu-
tion is a model-independent function, which allows for a unique thermodynamic
characterization of gas/solid adsorption systems. This distribution provides in-
formation about possible changes in the Gibbs free energy, which are caused by
the energetic and geometrical heterogeneities of a nanoporous carbon as well as
by the adsorbate-related entropic effects. It appears that in the case of adsorption
of simple gases on nanoporous carbons their energetic heterogeneity does not
change significantly the entropy effects. A general character of the adsorption
potential distribution is clearly visible by its direct relation to the differential en-
thalpy and differential entropy. Also, the average adsorption potential is directly
proportional to the heat of immersion, which through this proportionality can be
estimated on the basis of vapor adsorption isotherms. Another important conclu-
sion concerns the geometrical heterogeneity of nanoporous carbons, which is
characterized by the micropore and mesopore volume distributions. The current
work demonstrates that in terms of the condensation approximation both these
distributions are directly related to the adsorption potential distribution. As shown
the pore volume distribution can be obtained by multiplication of the adsorption
potential distribution by the derivative of the adsorption potential A with respect
to the pore width x . However, the pore volume distribution is a secondary char-
acteristics of a given adsorption system because the derivative dA/dx depends on
the pore geometry and adsorbate. In order to evaluate the pore volume distribution
one needs to assume a model of porous structure, for example, slit-like, cylindri-
cal or spherical pores [1, 2, 133, 145].
A brief review of methods based on the integral adsorption showed that they
are attractive to evaluate the pore volume distribution. The analytical solution of
this integral for subintegral functions represented by the Dubinin-Astakhov equa-
tion and gamma-type distribution is extremely simple (Jaroniec-Choma equation)
and provides a good description of experimental adsorption data on nanoporous
carbons. In particular, application of the gamma distribution leads to simple an-
alytical equations for the adsorption potential distribution and other thermody-
namic functions that characterize the process of the micropore filling and provide
valuable information about structural and surface heterogeneities of nanoporous
carbons. This description can be extended easily to adsorption of organic com-
pounds from dilute solutions on active carbons as well as to adsorption of liquid
mixtures in the whole concentration region. A significant progress has been also
made in modeling adsorption in micropores. Computer simulations including
Monte Carlo and MD simulation and density functional theory calculations have
been recently used to evaluate the structural heterogeneity of nanoporous carbons.
Methods which combine the functional density theory approach and computer
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