Equilibrium adsorption in cylindrical mesopores: A modified Broekhoff and de boer theory versus density functional theory

This paper presents a thermodynamic analysis of capillary condensation phenomena in cylindrical pores. Here, we modified the Broekhoff and de Boer (BdB) model for cylindrical pores accounting for the effect of the pore radius on the potential exerted by the pore walls. The new approach incorporates the recently published standard nitrogen and argon adsorption isotherm on nonporous silica LiChrospher Si-1000. The developed model is tested against the nonlocal density functional theory (NLDFT), and the criterion for this comparison is the condensation/evaporation pressure versus the pore diameter. The quantitative agreement between the NLDFT and the refined version of the BdB theory is ascertained for pores larger than 2 nm. The modified BdB theory was applied to the experimental adsorption branch of adsorption isotherms of a number of MCM-41 samples to determine their pore size distributions (PSDs). It was found that the PSDs determined with the new BdB approach coincide with those determined with the NLDFT (also using the experimental adsorption branch). As opposed to the NLDFT, the modified BdB theory is very simple in its utilization and therefore can be used as a convenient tool to obtain PSDs of all mesoporous solids from the analysis of the adsorption branch of adsorption isotherms of any subcritical fluids.

Equilibrium swelling measurements of network and semicrystalline polymers in supercritical carbon dioxide using high-pressure NMR

The extent of swelling of cross-linked poly(dimethylsiloxane) and linear low-density poly(ethylene) in supercritical CO2 has been investigated using high-pressure NMR spectroscopy and microscopy. Poly(dimethylsiloxane) was cross-linked to four different cross-link densities and swollen in supercritical CO2. The Flory-Huggins interaction parameter, x, was found to be 0.62 at 300 bar and 45 degrees C, indicating that supercritical CO2 is a relatively poor solvent compared to toluene or benzene. Linear low-density poly(ethylene) was shown to exhibit negligible swelling upon exposure to supercritical CO2 up to 300 bar. The effect Of CO2 pressure on the amorphous region of the poly(ethylene) was investigated by observing changes in the H-1 T-2 relaxation times of the polymer. These relaxation times decreased with increasing pressure, which was attributed to a decrease in mobility of the polymer chains as a result of compressive pressure.

Effects of Al2O3 on phase equilibria in the olivine primary phase field of the MgO-"FeO"-SiO2-Al2O3 system in equilibrium with metallic iron

Liquidus temperatures and phase equilibria have been determined in the olivine primary phase field of the MgO-FeO-SiO2-Al2O3 system. Liquidus isotherms have been determined in the temperature range from 1748 to 1873K. The results are presented in the form of pseudo-ternary sections of the MgO-FeO-SiO2 with 2 and 3wt% Al2O3 in the liquid. The study enables the liquidus to be described for a range of SiO2/MgO ratios. It was found that liquidus temperatures in the olivine primary phase field decrease with the addition of Al2O3.

Effect of Al2O3 and Cr2O3 on loquidus temperatures in the cristobalite and tridymite primary phase fields of the MgO-"FeO"-SiO2 ststem in equilibrium with metallic iron

The effects of alumina and chromite impurities on the liquidus temperatures in the cristobalite/tridymite (SiO2) primary phase fields in the MgO-FeO-SiO, system in equilibrium with metallic iron have been investigated experimentally. Using high temperature equilibration and quenching followed by electron probe X-ray microanalysis (EPMA), liquiclus isotherms have been determined in the temperatures range 1 673 to 1 898 K. The results are presented in the form of pseudo-ternary sections of the MgO-FeO-SiO, system at 2, 3 and 5 wt% Al2O3, 2 wt% Cr2O3, and 2 wt% Cr2O3+2 wt% Al2O3. The study enables the liquidus to be described for a range of SiO2/MgO and MgO/FeO ratios. It was found that liquiclus temperatures in the cristobalite and tridymite primary phase fields, decrease significantly with the addition of Al2O3 and Cr2O3.

Capital market equilibrium with moral hazard and flexible technology

(Magill, M., Quinzii, M., 2002. Capital market equilibrium with moral hazard. Journal of Mathematical Economics 38, 149-190) showed that, in a stockmarket economy with private information, the moral hazard problem may be resolved provided that a spanning overlap condition is satisfed. This result depends on the assumption that the technology is given by a stochastic production function with a single scalar input. The object of the present paper is to extend the analysis of Magill and Quinzii to the case of multiple inputs. We show that their main result extends to this general case if and only if, for each firm, the number of linearly independent combinations of securities having payoffs correlated with, but not dependent on, the firms output is equal to the number of degrees of freedom in the firm's production technology.

Interpretation of the temperature dependence of equilibrium and rate constants

The objective of this review is to draw attention to potential pitfalls in attempts to glean mechanistic information from the magnitudes of standard enthalpies and entropies derived from the temperature dependence of equilibrium and rate constants for protein interactions. Problems arise because the minimalist model that suffices to describe the energy differences between initial and final states usually comprises a set of linked equilibria, each of which is characterized by its own energetics. For example, because the overall standard enthalpy is a composite of those individual values, a positive magnitude for AHO can still arise despite all reactions within the subset being characterized by negative enthalpy changes: designation of the reaction as being entropy driven is thus equivocal. An experimenter must always bear in mind the fact that any mechanistic interpretation of the magnitudes of thermodynamic parameters refers to the reaction model rather than the experimental system For the same reason there is little point in subjecting the temperature dependence of rate constants for protein interactions to transition-state analysis. If comparisons with reported values of standard enthalpy and entropy of activation are needed, they are readily calculated from the empirical Arrhenius parameters. Copyright (c) 2006 John Wiley & Sons, Ltd.

Negative second virial coefficients as predictors of protein crystal growth: Evidence from sedimentation equilibrium studies that refutes the designation of those light scattering parameters as osmotic virial coefficients

The effects of ammonium sulphate concentration on the osmotic second virial coefficient (B-AA/M-A) for equine serum albumin (pH 5.6, 20 degrees C) have been examined by sedimentation equilibrium. After an initial steep decrease with increasing ammonium sulphate concentration, B-AA/M-A assumes an essentially concentration-independent magnitude of 8-9 ml/g. Such behaviour conforms with the statistical-mechanical prediction that a sufficient increase in ionic strength should effectively eliminate the contributions of charge interactions to B-AA/M-A but have no effect on the covolume contribution (8.4 ml/g for serum albumin). A similar situation is shown to apply to published sedimentation equilibrium data for lysozyme (pH 4.5). Although termed osmotic second virial coefficients and designated as such (B-22), the negative values obtained in published light scattering studies of both systems have been described incorrectly because of the concomitant inclusion of the protein-salt contribution to thermodynamic nonideality of the protein. Those negative values are still valid predictors of conditions conducive to crystal growth inasmuch as they do reflect situations in which there is net attraction between protein molecules. However, the source of attraction responsible for the negative virial coefficient stems from the protein-salt rather than the protein-protein contribution, which is necessarily positive. (c) 2005 Elsevier B.V. All rights reserved.

On the equilibrium and dynamic behavior of alcohol vapors in activated carbon

As alcohol molecules such as methanol and ethanol have both polar and non-polar groups, their adsorption behavior is governed by the contributions of dispersion interaction (alkyl group) and hydrogen bonding (OH group). In this paper, the adsorption behavior of alcohol molecules and its effect on transport processes are elucidated. From the total permeability (B-T) of alcohol molecules in activated carbon, an adsorption mechanism is proposed, describing well the experimental data, by taking combination effects of clustering, entering micropores, layering and pore filling processes. Unlike the case of non-polar compounds, it was found that at low pressures there are two rises in the BT of alcohol molecules in activated carbon. The first rise is due to the major contribution of surface diffusion to the transport (which is the case of non-polar molecules) and the second one may be associated with cluster formation at the edge of micropores and entering micropores when the clusters are sufficiently large enough to induce a dispersive energy. In addition the clusters formed may enhance surface diffusion at low pressures and hinder gas phase diffusion and flow in meso/macropores. (c) 2006 Elsevier Ltd. All fights reserved.

Stability for parametric implicit vector equilibrium problems

In this paper, we consider a class of parametric implicit vector equilibrium problems in Hausdorff topological vector spaces where a mapping f and a set K are perturbed by parameters is an element of and lambda respectively. We establish sufficient conditions for the upper semicontinuity and lower semicontinuity of the solution set mapping S : Lambda(1) x A(2) -> 2(X) for such parametric implicit vector equilibrium problems. (c) 2005 Elsevier Ltd. All rights reserved.

Varieties of algebras arising from K-perfect m-cycle systems

A class of algebras forms a variety if it is characterised by a collection of identities. There is a well-known method, often called the standard construction, which gives rise to algebras from m-cycle systems. It is known that the algebras arising from {1}-perfect m-cycle systems form a variety for m is an element of {3, 5} only, and that the algebras arising from {1, 2}-perfect m-cycle systems form a variety for m is an element of {3, 5, 7} only. Here we give, for any set K of positive integers, necessary and sufficient conditions under which the algebras arising from K-perfect m-cycle systems form a variety. (c) 2006 Elsevier B.V. All rights reserved.