Monte carlo study of the adsorption and aggregation of alkyltrimethylammonium chloride on the montmorillonite-water interface

Organically modified clays exhibit adsorption capacities for cations, anions, and nonpolar organic compounds, which make them valuable for various environmental technical applications. To improve the understanding of the adsorption processes, the molecular-scale characterization of the structures of organic aggregates assembled on the external basal surfaces of clay particles is essential. The focus of this Monte Carlo simulation study was on the effects of the surface coverage and the alkyl chain length n on the structures of alkyltrimethylammonium chloride ((C(n)TMA)Cl) aggregates assembled on the montmorillonite-water interface. We found that the amount of adsorbed C(n)TMA(+) ions is independent of the alkyl chain length and increases with the C(n)TMA(+) surface coverage. The C(n)TMA(+) ions predominantly adsorb as inner-sphere complexes; the fraction of outer-sphere adsorbed ions equals only about 10%. The conformational order of the C(n)TMA(+) alkyl chains substantially decreases with decreasing alkyl chain length. In agreement with previous experiments, the amount of C(n)TMA(+) ions that are aggregated at the mineral surface increases with increasing chain length. The maximum value of 0.66 C(n)TMA(+) adsorption complex per unit cell area of the clay surface considerably exceeds the amount of cations required to compensate the negative charge of the montmorillonite surface. Furthermore, in most of the studied systems, fractions of Na(+) surface cations remain adsorbed on montmorillonite. The resulting interfacial positive charge excess is counterbalanced by coadsorbed chloride ions forming ion pairs with both C(n)TMA(+) and Na(+).     

Cationic Porphyrin-Graphene Oxide Hybrid: Donor-Acceptor Composite for Efficient Photoinduced Electron Transfer

Non-covalent nanohybrids composed of cationic 5,10,15,20-tetra(4-trimethylammoniophenyl)porphyrin tetra(p-toluenesulfonate) (TMAP) and the graphene oxide sheets were prepared under two pH values (6.2 vs. 1.8). The TMAP molecule was positively charged, regardless of the pH value during preparation. However, protonation of the imino nitrogens increased the overall charge of the porphyrin molecule from +4 to +6 (TMAP⁴⁺ and TMAP⁶⁺). It was found that at acidic pH, interaction of TMAP⁶⁺ with GO was largely suppressed. On the other hand, results of FTIR, Raman spectroscopy, thermogravimetric analysis, atomic force microscopy (AFM) and elemental analysis confirmed effective non-covalent functionalization of graphene oxide with cationic porphyrin at pH 6.2. The TMAP⁴⁺-GO hybrids exhibited well defined structure with a monolayer of TMAP⁴⁺ on the GO sheets as confirmed by AFM. Formation of the ground-state TMAP⁴⁺-GO complex in solution was monitored by the red-shift of the porphyrin Soret absorption band. This ground-state interaction between TMAP⁴⁺ and GO is responsible for the static quenching of the porphyrin emission. Fluorescence was not detected for the nanohybrid which indicated that a very fast deactivation process had to take place. Ultrafast time-resolved transient absorption spectroscopy clearly demonstrated the occurrence of electron transfer from the photoexcited TMAP⁴⁺ singlet state to GO sheets, as proven by the formation of a porphyrin radical cation.     

Estimating the pore size distribution of activated carbons from adsorption data of different adsorbates by various methods

Experimental adsorption isotherms of four adsorbates (N2, Ar, C6H6, and CCl4) as well as adsorption enthalpy (C6H6 and CCl4) measured on two strictly microporous carbons are used to evaluate the porosity of adsorbents (i.e., pore size distributions (PSDs) and average pore diameter ( Lav )). The influence of the diameter of adsorbates ( dA) as well as of the temperature ( T ) is analyzed in order to explain the differences or similarities between the above-mentioned quantities for all systems. Proposed previously, the general relationships between the parameters of the Dubinin-Astakhov (DA) isotherm equation (the characteristic energy of adsorption ( E0 ) and the exponent of this equation ( n )) and the average slit-width of carbon micropores are investigated. Moreover, the thermodynamic verification of the Horvath-Kawazoe (HK) theory and the ND model is presented based on data of the adsorption and enthalpy of adsorption of benzene and carbon tetrachloride on two carbons. Finally, the pore diameters calculated from calorimetry data using the Everett and Powl method and those calculated applying the recently developed equations are compared. In our opinion the change of apparent PSD should be monitored by performing a series of isotherm measurements from high (equal and higher than room temperature) to low temperatures (ca. 77.5 K) as was presented in the current study. Moreover, the analysis of the experimental data leads to the conclusion that the entropy of C6H6 and CCl4 can approach to the values characteristic of quasi-solid (a partially ordered structure). Therefore, this behavior of the adsorbate should be taken into consideration in the theoretical assumptions of model and its thermodynamic verification.     

Hausdorff dimension and conformal measures of Feigenbaum Julia sets

We show that contrary to anticipation suggested by the dictionary between rational maps and Kleinian groups and by the ``hairiness phenomenon', there exist many Feigenbaum Julia sets whose Hausdorff dimension is strictly smaller than two. We also prove that for any Feigenbaum Julia set, the Poincaré critical exponent is equal to the hyperbolic dimension . Moreover, if , then . In the stationary case, the last statement can be reversed: if , then . We also give a new construction of conformal measures on that implies that they exist for any , and analyze their scaling and dissipativity/conservativity properties.

     

A Statistical Model for Predicting the Heat Transfer of Solid Particles in Turbulent Flows

The objective of this paper is twofold: (1) to present a statistical model of particle transport and heat transfer in turbulent flows and (2) to examine the performance of this model in various turbulent flows going from a simple flow to a more complicated one. This model is based on a kinetic equation for the probability density function of the particle velocity and temperature distributions in anisotropic turbulent flow. The model predictions compare reasonable well with numerical simulations and properly reproduce the crucial trends of computations performed in various turbulent flows.     

Transport and deposition of colliding particles in turbulent channel flows

The purpose of this paper is twofold: (i) to present statistical models that describe particle–turbulence interactions as well as particle–particle collisions and (ii) to gain a better understanding of the effect of inter-particle collisions on transport, deposition, and preferential concentration of heavy particles in turbulent channel flows. The models presented are based on a kinetic equation for the probability density function of the particle velocity distribution in anisotropic turbulent flow. The model predictions compare reasonable well with numerical simulations and properly reproduce the crucial trends of computations.     

Robust branch-cut-and-price for the Capacitated Minimum Spanning Tree problem over a large extended formulation

This paper presents a robust branch-cut-and-price algorithm for the Capacitated Minimum Spanning Tree Problem (CMST). The variables are associated to q-arbs, a structure that arises from a relaxation of the capacitated prize-collecting arborescence problem in order to make it solvable in pseudo-polynomial time. Traditional inequalities over the arc formulation, like Capacity Cuts, are also used. Moreover, a novel feature is introduced in such kind of algorithms: powerful new cuts expressed over a very large set of variables are added, without increasing the complexity of the pricing subproblem or the size of the LPs that are actually solved. Computational results on benchmark instances from the OR-Library show very significant improvements over previous algorithms. Several open instances could be solved to optimality.