Application of density functional theory to analysis of energetic heterogeneity and pore size distribution of activated carbons

A new approach based on the nonlocal density functional theory to determine pore size distribution (PSD) of activated carbons and energetic heterogeneity of the pore wall is proposed. The energetic heterogeneity is modeled with an energy distribution function (EDF), describing the distribution of solid-fluid potential well depth (this distribution is a Dirac delta function for an energetic homogeneous surface). The approach allows simultaneous determining of the PSD (assuming slit shape) and EDF from nitrogen or argon isotherms at their respective boiling points by using a set of local isotherms calculated for a range of pore widths and solid-fluid potential well depths. It is found that the structure of the pore wall surface significantly differs from that of graphitized carbon black. This could be attributed to defects in the crystalline structure of the surface, active oxide centers, finite size of the pore walls (in either wall thickness or pore length), and so forth. Those factors depend on the precursor and the process of carbonization and activation and hence provide a fingerprint for each adsorbent. The approach allows very accurate correlation of the experimental adsorption isotherm and leads to PSDs that are simpler and more realistic than those obtained with the original nonlocal density functional theory.

Heterogeneous model for gas transport in carbon molecular sieves

A dual resistance model with distribution of either barrier or pore diffusional activation energy is proposed in this work for gas transport in carbon molecular sieve (CMS) micropores. This is a novel approach in which the equilibrium is homogeneous, but the kinetics is heterogeneous. The model seems to provide a possible explanation for the concentration dependence of the thermodynamically corrected barrier and pore diffusion coefficients observed in previous studies from this laboratory on gas diffusion in CMS.(1.2) The energy distribution is assumed to follow the gamma distribution function. It is shown that the energy distribution model can fully capture the behavior described by the empirical model established in earlier studies to account for the concentration dependence of thermodynamically corrected barrier and pore diffusion coefficients. A methodology is proposed for extracting energy distribution parameters, and it is further shown that the extracted energy distribution parameters can effectively predict integral uptake and column breakthrough profiles over a wide range of operating pressures.

Multicomponent adsorption on activated carbons under supercritical conditions

Adsorption of binary mixtures onto activated carbon Norit R1 for the system nitrogen-methane-carbon dioxide was investigated over the pressure range up to 15 MPa. A new model is proposed to describe the experimental data. It is based on the assumption that an activated carbon can be characterized by the distribution function of elements of adsorption volume (EAV) over the solid-fluid potential. This function may be evaluated from pure component isotherms using the equality of the chemical potentials in the adsorbed phase and in the bulk phase for each EAV. In the case of mixture adsorption a simple combining rule is proposed, which allows determining the adsorbed phase density and its composition in the EAV at given pressure and compositions of the bulk phase. The adsorbed concentration of each adsorbate is the integral of its density over the set of EAV. The comparison with experimental data on binary mixtures has shown that the approach works reasonably well. In the case of high-pressure binary mixture adsorption, when only total amount adsorbed was measured, the proposed model allows reliably determining partial amounts of the adsorbed components. (C) 2004 Elsevier Inc. All rights reserved.

Modelling nucleation in wet granulation

Nucleation is the first stage in any granulation process where binder liquid first comes into contact with the powder. This paper investigates the nucleation process where binder liquid is added to a fine powder with a spray nozzle. The dimensionless spray flux approach of Hapgood et al. (Powder Technol. 141 (2004) 20) is extended to account for nonuniform spray patterns and allow for overlap of nuclei granules rather than spray drops. A dimensionless nuclei distribution function which describes the effects of the design and operating parameters of the nucleation process (binder spray characteristics, the nucleation area ratio between droplets and nuclei and the powder bed velocity) on the fractional surface area coverage of nuclei on a moving powder bed is developed. From this starting point, a Monte Carlo nucleation model that simulates full nuclei size distributions as a function of the design and operating parameters that were implemented in the dimensionless nuclei distribution function is developed. The nucleation model was then used to investigate the effects of the design and operating parameters on the formed nuclei size distributions and to correlate these effects to changes of the dimensionless nuclei distribution function. Model simulations also showed that it is possible to predict nuclei size distributions beyond the drop controlled nucleation regime in Hapgood's nucleation regime map. Qualitative comparison of model simulations and experimental nucleation data showed similar shapes of the nuclei size distributions. In its current form, the nucleation model can replace the nucleation term in one-dimensional population balance models describing wet granulation processes. Implementation of more sophisticated nucleation kinetics can make the model applicable to multi-dimensional population balance models.

The performance of the maximum ratio combining method in correlated Rician-fading channels for antenna-diversity signal combining

The performance of the maximum ratio combining method for the combining of antenna-diversity signals in correlated Rician-fading channels is rigorously studied. The distribution function of the normalized signal-to-noise ratio (SNR) is expanded in terms of a power series and calculated numerically. This power series can easily take into account the signal correlations and antenna gains and can be applied to any number of receiving antennas. An application of the method to dual-antenna diversity systems produces useful distribution curves for the normalized SNR which can be used to find the diversity gain. It is revealed that signal correlation in Rician-fading channels helps to increase the diversity gain rather than to decrease it as in the Rayleigh fading channels. It is also shown that with a relative strong direct signal component, the diversity gain can be much higher than that without a direct signal component.

Recurrence interval statistics of cellular automaton seismicity models

The recurrence interval statistics for regional seismicity follows a universal distribution function, independent of the tectonic setting or average rate of activity (Corral, 2004). The universal function is a modified gamma distribution with power-law scaling of recurrence intervals shorter than the average rate of activity and exponential decay for larger intervals. We employ the method of Corral (2004) to examine the recurrence statistics of a range of cellular automaton earthquake models. The majority of models has an exponential distribution of recurrence intervals, the same as that of a Poisson process. One model, the Olami-Feder-Christensen automaton, has recurrence statistics consistent with regional seismicity for a certain range of the conservation parameter of that model. For conservation parameters in this range, the event size statistics are also consistent with regional seismicity. Models whose dynamics are dominated by characteristic earthquakes do not appear to display universality of recurrence statistics.