Apparent Anomalous Temperature Dependence of Self-Diffusion Studied by Pulsed-Field Gradient Nuclear Magnetic Resonance and Thermodynamic Modeling.

The self-diffusivity of cyclohexane and n-octane adsorbed in hierarchical zeolite monoliths has been investigated by using PFG-NMR. In these samples, the intrinsic FAU-X zeolite microporosity combines with a complex macroporous network composed of aggregated zeolite nanocrystals. As temperature is increased, cyclohexane self-diffusivity apparently decreases, reaches a minimum, and then starts increasing upon further increasing the temperature. Such striking, i.e., non-Arrhenius, temperature dependence is not observed for n-octane in the same samples and for cyclohexane adsorbed in purely microporous FAU-X. Through thermodynamic modeling, we show that this anomalous behavior can be rationalized by considering the evolution in the adsorbate populations when changing the temperature. In more detail, we show that the slow and fast diffusing species present in the microporosity and secondary porosity arising from the packing of zeolite nanocrystals vary significantly with a strong impact on the effective diffusivity. Applying the temperature evolution of their relative fractions to a simple two-phase diffusion model helps obtain insights into the physicochemical factors responsible for the complex behavior of effective self-diffusivity in hierarchical zeolites.

Impact of surface diffusion on transport through porous materials.

The peak parking method was applied to evaluate the surface diffusivity Ds of polystyrenes dissolved in a THF/heptane mixture and transported through porous silica materials with various morphologies. With this method, the overall effective diffusivity D is measured experimentally with coarse-grained models like Maxwell equation allowing one to infer the particle diffusivity Dpz. Such particle diffusivity has two main contributions: in-pore diffusivity Dp and surface diffusivity Ds. The diffusion within the pores is determined experimentally using either non-adsorbing conditions or calculated from particle porosity, particle tortuosity, and hydrodynamic hindrance. The surface diffusion coefficient Ds is usually determined using models considering parallel diffusion in the pores and at the surface but this assumption is rather crude. In this paper, to address this problem, another approach is proposed using the Brownian motion of molecules in the pore space. These two approaches lead to similar equations relating the effective diffusion coefficient D, the in-pore diffusion Dp and surface diffusion Ds. The surface diffusion is analyzed as a function of the surface affinity of the probes considered here (polystyrenes of different molecular weights/lengths). Such surface affinity depends both on the probe chain length and surface chemistry of the host solid (the latter being characterized here through the silanol surface density). For short chain lengths, a non-monotonic change in the surface diffusion with affinity (i.e. retention factor) is observed in some cases. Yet, generally, as expected, surface diffusion decreases upon increasing the surface affinity. In contrast to short chain lengths, the longest chain lengths are less sensitive to the silanol surface density.

Effect of the polydispersity on the dispersion of polymers through silicas having different morphologies (fully porous and core-shell particles and monoliths).

The effect of the polydispersity of polystyrenes on the dispersion through silicas having different morphologies (fully porous, core-shell particles and monoliths) was investigated. The heights equivalent to a theoretical plate (HETP) of those columns were measured for a small molecule (toluene) and a series of polystyrenes of different sizes in non-adsorbing conditions. The different contributions to the total HETP including polydispersity were determined experimentally. The longitudinal diffusion and the mass transfer resistance term were obtained from peak parking experiments. The eddy dispersion was obtained from models and experiments. The effect of polydispersity on the HETP values (Hpoly) can thus be calculated from the total HETP by substraction of the other contributions. The results were compared to the Knox model which surestimates the Hpoly values for porous and core-shell particles which is usually explained by an overestimation of the polydispersity index (PDI) given by the manufacturer. The PDI of two polymers (P02, Mw= 690 g.mol-1 and P03, Mw=1380 g.mol-1) was verified by liquid chromatography by separating each fraction of the polymer on the silica columns by using adsorbing conditions which are obtained with a mixture of heptane and THF. The PDI obtained are comparable to the PDI given by the manufacturer meaning that the assumptions made by Knox are not entirely valid. A direct method is proposed in this paper in order to determine Hpoly. In this method the excess of spreading as compared with a polymer with only one size corresponding to the average size is studied assuming the polymer size distribution is gaussian. The Hpoly values obtained by the direct method are comparable to the experimental values.

Impact of the solute exclusion on the bed longitudinal diffusion coefficient and particle intra-tortuosity determined by ISEC.

The effective diffusion coefficient of non retained toluene and polystyrenes compounds was measured by the peak parking method for two columns packed with mesoporous silica. Different models used to predict the effective diffusion are compared. These models include the conventional Knox time-averaged model and some effective medium theory models such as Maxwell, Landauer, Garnett or Torquato models. In all these models the effective intraparticle diffusion coefficient is needed. It is derived here, in non-adsorbing conditions, from internal porosity, hindrance factor, which can be estimated with the Renkin correlation, and internal tortuosity, which can be considered as either constant or calculated by the Weissberg equation τ=1-plnɛ, where ɛ is the accessible particle porosity and p a parameter characteristic of the topology. The experimental effective diffusion coefficients of toluene and polystyrenes were found to be in good agreement with the values predicted by the Maxwell, or Torquato models, provided the internal tortuosity is calculated by using the Weissberg equation.

Carbon nanofiber mesoporous films: efficient platforms for bio-hydrogen oxidation in biofuel cells.

The discovery of oxygen and carbon monoxide tolerant [NiFe] hydrogenases was the first necessary step toward the definition of a novel generation of hydrogen fed biofuel cells. The next important milestone is now to identify and overcome bottlenecks limiting the current densities, hence the power densities. In the present work we report for the first time a comprehensive study of herringbone carbon nanofiber mesoporous films as platforms for enhanced biooxidation of hydrogen. The 3D network allows mediatorless hydrogen oxidation by the membrane-bound hydrogenase from the hyperthermophilic bacterium Aquifex aeolicus. We investigate the key physico-chemical parameters that enhance the catalytic efficiency, including surface chemistry and hierarchical porosity of the biohybrid film. We also emphasize that the catalytic current is limited by mass transport inside the mesoporous carbon nanofiber film. Provided hydrogen is supplied inside the carbon film, the combination of the hierarchical porosity of the carbon nanofiber film with the hydrophobicity of the treated carbon material results in very high efficiency of the bioelectrode. By optimization of the whole procedure, current densities as high as 4.5 mA cm(-2) are reached with a turnover frequency of 48 s(-1). This current density is almost 100 times higher than when hydrogenase is simply adsorbed at a bare graphite electrode, and more than 5 times higher than the average of the previous reported current densities at carbon nanotube modified electrodes, suggesting that carbon nanofibers can be efficiently used in future sustainable H2/O2 biofuel cells.

Influence of molecule size on its transport properties through a porous medium.

The mass transfer kinetics of toluene and polystyrenes (of which the M(w) varies from 162 to 1.85 x 10(6) g mol(-1)) through columns filled with silica porous spheres were studied by inverse size exclusion chromatography. The mass transfer parameters were measured by modeling the band broadening of the chromatograms. The experimental height equivalent to a theoretical plate (HETP) data were analyzed using the general rate model in order to determine the effective diffusion coefficient in porous particles as a function of molecular size. The bulk molecular diffusion coefficients were experimentally determined by dynamic light scattering (DLS) and Taylor dispersion analysis (TDA). The topological tortuosity of the porous particles was determined by electrical measurements. The effective molecular diffusion coefficient through porous particles was modeled taking into account exclusion, friction, and at last tortuosity effects. A phenomenological law is proposed to model the evolution of the tortuosity experienced by a molecule in a porous particle as a function of its size. It gives a good prediction of the evolution of effective diffusion coefficient with the molecule/pore size ratio.

Adsorption of the uremic toxin p-cresol onto hemodialysis membranes and microporous adsorbent zeolite silicalite.

Para-cresol CH3C6H4OH is a protein-bound solute which is not eliminated efficiently by hemodialysis systems. In this study, we present adsorption of p-cresol as a complementary process to hemodialysis. The kinetics and isotherms of adsorption onto cellulose-based membranes (cellulose diacetate and triacetate), synthetic membranes (polyamide, polysulfone, polyacrylonitrile and polymethylmethacrylate) and microporous zeolite silicalite (MFI), have been evaluated in static conditions. The results indicate that p-cresol has a low affinity to all membranes but polysulfone and polyamide and that the times to reach equilibrium conditions are slow. In contrast, equilibration time on silicalite is fast (2 min to eliminate 90%) while adsorption levels are high (maximum adsorption about 106 mg g(-1)). Adsorption onto microporous adsorbents could be a novel way to eliminate uremic toxins from blood.