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ANALYSIS OF ADSORBENTS POROSITY - METHODS AND MODELS Faculty of Energy and Fuels Department of Fuels Technology Azerbaijan, Baku; 23rd may 2013 Magda Ziółkowska Janina Milewska-Duda Jan T. Duda

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Methods of analysis microporous materials Nonadsorptive methods: Mercury porosimetry X-ray diffraction Microscopic methods Adsorptive methods: Adsorption isotherms models. Widely used adsorption models: BET LBET DFT (NL, QS)

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uniBET model - introduction Adsorption system is viewed as: an aggregation of adsorbate molecules (clu- sterization) limited by pore geometry consisting of a number of a subsystems (clu- sters), each satisfying equilibrium condition: R - gas constant - relative fugacity of adsorbate (P, T) H, S - total enthalpy and entropy change respectively m pa - amount of adsorbate in a-th subsystem [mol/g] [1]

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uniBET model - assumptions first layer (n=1) adsorption is localized at only one site enabling molecules to be held by adhesive forces further layers (n>1, n=2,..,k) are formed due to the adhesive and cohesive forces between molecules clusters enlarging doesn’t affect creation of other ones (configurational independence) clusters can be grouped into classes with the same adsorption energy profile and number of layers k Mechanism of molecule clusterization in micropores dendrite-like cluster stuck-like cluster [1]

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LBET model - assumptions primary adsorption sites are the same energy Q A adsorption energy of further layers is the same Q C > Q A, Q C 0 adsorption energy at the k-th and (k-1)-th layers results the same coverage ratio simple stack like clusters are dominant number of primary sites m Ak capable to start stack-like cluster is exponentially distributed: m A - total number of primary sites - geometrical restrictions for multilayer adsorption parameter [1]

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LBET model - formula Uniformly heterogeneous surfaces adsorption capacity LBET formula is expressed: Amax, C - effective adsorbate-pore contact surface ratio on primary sites on pores at 1st and further layers - average coverage ratio of the 2nd and higher layers - cluster branching ratio - parameter of porous structure, - relative adsorbate fugacity (P, T) R - gas constant, T - temperature B A, B f - adsorption energy parameter for 1st (Q A ) and further (Q sC ) layers [1], [3]

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Non-local DFT model Adsorption system is viewed as: corresponding to the grand canonical ensemble (, V, T) grand potential ( f ) is a functional of the density f (r) of adsorbed fluid solid-fluid interactions are neglected, and modeled instead with an effective spatially distributed external potential V ext (r) r - position vector inside the pore F - Helmholtz free energy of the fluid F - chemical potential of the fluid [2]

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Non-local DFT assumptions Helmholtz free energy is the sum of the kinetic energy of the ideal gas F id [ f (r)], hard spheres repulsion forces F ex [ f (r)] and attra- ctive term u ff - attractive fluid-fluid potential solid-fluid interactions corresponds to the L-J potential for a given geometry (ignoring the real molecular structure) FF, F interactions are modeled with the APPs [2]

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Complementary study Complementary study of microporous carbon samples, CS1 (carbon molecular sieve, Supleco) and ACF10 (an activated carbon fiber, Nippon Kynol, Japan): two incomparable models NLDFT and LBET calculations fit relatively well the experimental adsorption data [2]

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Conclusions insight into the modeling of adsorption process fitting experimental data and predicting adsorption isotherms incomparable models describes relatively well experimental data crucial problem is the predicting material adsorptivity further LBET researches yielded a model, which can be employed as a support in analysis and prediction of cheap adsorbents porous structures properties. [1], [2], [3]

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Bibliography [1] Milewska-Duda, J.; Duda, J. T.; Appl. Surf. Sci.; 2002; 196; [2] Duda, J. T.; Jagiełło, L.; Jagiełło, J.; Milewska-Duda, J.; Appl. Surf. Sci.; 2007; 253, [3] Duda, J. T.; Milewska-Duda, J.; Kwiatkowski, M.; Ziółkowska, M.; Adsorption; 2013; 19,

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ANALYSIS OF ADSORBENTS POROSITY - METHODS AND MODELS Faculty of Energy and Fuels Department of Fuels Technology Azerbaijan, Baku; 23rd may 2013 Magda Ziółkowska Janina Milewska-Duda Jan T. Duda

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