We present a unified approach to pore size characterization of microporous carbonaceous materials such as activated carbon and carbon fibers by nitrogen, argon, and carbon dioxide adsorption at standard temperatures, 77 K for N2 and Ar and 273 K for CO2. Reference isotherms of N2, Ar, and CO2 in a series of model slit-shaped carbon pores in the range from 0.3 to 36 nm have been calculated from the nonlocal density functional theory (NLDFT) using validated parameters of intermolecular interactions. Carbon dioxide isotherms have also been generated by the grand canonical Monte Carlo (GCMC) method based on the 3-center model of Harris and Yung. The validation of model parameters includes three steps: (1) prediction of vapor-liquid equilibrium data in the bulk system, (2) prediction of adsorption isotherm on graphite surface, (3) comparison of the NLDFT adsorption isotherms in pores to those of GCMC simulations, performed with the parameters of fluid-fluid interactions, which accurately reproduce vapor-liquid equilibrium data of the bulk fluid. Pore size distributions are calculated by an adaptable procedure of deconvolution of the integral adsorption equation using regularization methods. The deconvolution procedure implies the same grid of pore sizes and relative pressures for all adsorbates and the intelligent choice of regularization parameters. We demonstrate the consistency of our approach on examples of pore structure characterization of activated carbons from adsorption isotherms of different gases and from different models (NLDFT and GCMC). Since the CO2 isotherms measured up to 1 atm are not sensitive to pores wider then 1 nm, the NLDFT method for CO2 has been extended to high-pressure CO2 adsorption up to 34 atm. The methods developed are suggested as a practical alternative to traditional phenomenological approaches such as DR, HK, and BJH methods.

Grand canonical MonteCarlo simulations in conjunction with high-resolution low-pressure argon adsorption experiments were employed to study adsorption mechanisms on the copper(II) benzene-1,3,5-tricarboxylate metal-organic framework (Cu−BTC). We constructed a molecular structural model of Cu−BTC. The pore network of Cu−BTC has a simple cubic symmetry. It consists of main channels of a square crosssection of ca. 0.9 nm diameter and tetrahedral side pockets of ca. 0.5 nm, which are connected to the main channels by triangular windows of ca. 0.35 nm diameter. Using a parameterized united-atom force field, we have determined the preferential adsorption sites and the sequence of adsorption mechanisms from a gradual filling of the side pockets to a stepwise adsorption and condensation in the main channels. The simulation results agree quantitatively with the experimental isotherm of argon up to almost complete filling of the pore network.

Capillary condensation hysteresis in nanopores is studied by Monte Carlo simulations and the nonlocal density functional theory. Comparing the theoretical results with the experimental data on low temperature sorption of nitrogen and argon in cylindrical channels of mesoporous siliceous molecular sieves of MCM-41 type, we have revealed four qualitatively different sorption regimes depending on the temperature and pore size. As the pore size increases at a given temperature, or as the temperature decreases at a given pore size, the following regimes are consequently observed: volume filling without phase separation, reversible stepwise capillary condensation, irreversible capillary condensation with developing hysteresis, and capillary condensation with developed hysteresis. We show that, in the regime of developed hysteresis (pores wider than 5 nm in the case of nitrogen sorption at 77 K), condensation occurs spontaneously at the vaporlike spinodal while desorption takes place at the equilibrium. A quantitative agreement is found between the modeling results and the experimental hysteresis loops formed by the adsorption-desorption isotherms. The results obtained provide a better understanding of the general behavior of confined fluids and the specifics of sorption and phase transitions in nanomaterials.

The microphase segregation in the Nafion (DuPont trademark) perfluorinated membrane at different water contents was studied using molecular dynamics simulations. As the degree of solvation increased, we observed the formation of water clusters containing up to ca. 100 water molecules. In contrast to the conventional network models, the water clusters do not form a continuous hydrophilic subphase. The cluster size distribution is rather wide and evolves in time due to formation and break-up of temporary bridges between the clusters. This dynamic behavior of the cluster system allows for the macroscopic transfer of water and counterion. The calculated diffusion coefficients of water were found to be on the same order as the experimental ones.

The nonlocal density functional theory (NLDFT) of confined fluids is tested against Monte Carlo simulations by using the example of Lennard-Jones (LJ) fluid sorption in slit-shaped and cylindrical nanopores ranging from 0.3 to 10 nm in width. The fluid-fluid and solid-fluid parameters of the LJ potentials were chosen to represent several experimentally important adsorption systems: nitrogen and carbon dioxide in activated carbons, zeolites, and mesoporous molecular sieves of the MCM-41 type. Freezing in nanopores is discussed using the example of methane sorption in carbon at 111 K. Comparison with reference experiments is given when available. Two versions of NLDFT, the smoothed density approximation and the fundamental measure theory, are considered. It is shown that NLDFT approaches with properly chosen parameters provide quantitative agreement with the results of Monte Carlo simulations and reference experiments. Appreciable deviations are found in extremely narrow pores of less than two molecular diameters in width. In wider pores, NLDFT models can be used for quantitative predictions of reversible and hysteretic adsorption isotherms and analyses of the specifics of phase transformations, including the equilibrium and spinodal phase transitions.