Analysis of the linear tension of two-dimensional droplets on heterogeneous adsorbents

A procedure for analyzing the formation processes of two-dimensional droplets of an adsorbate on a rigid adsorbent support is considered. The molecular theory is based on data on the potential functions between adsorbent atoms and adsorbate molecules. Interactions between nearest neighbors are considered in the quasi-chemical approximation. The internal motions of adsorbent atoms and adsorbate molecules are ignored. Problems of describing the formation of droplets on heterogeneous adsorbents are associated with calculations for binodals (illustrated with the simplest example of two different homogeneous crystal faces) due to the choice of methods for calculating linear tension and the structural model of the region of the liquid–vapor transition. The dependence of the characteristics of droplets in the layered structural model on the method for determining the reference lines of the tension is shown for their metastable and equilibrium states. It is found that for a number of structural parameters, the thermodynamic determination of the line of tensions of metastable droplets can result in nonmonotonic dependences of the linear tension on their radii. The characteristics of two-dimensional liquid–vapor interfaces are compared for two structural models: coordination sphere and layered. It is found that the coordination sphere model allows the exclusion of the structural parameter of the layered model, but both models need refinement at small radii.     

Phase behavior of C60 by computer simulation using ab‐initio interaction potential

A first‐principles intermolecular potential recently proposed by Pacheco and Ramalho [Phys Rev Lett 1997, 79, 3873–3876] has been used with the Gibbs ensemble and Gibbs–Duhem integration Monte Carlo methods to simulate the vapor–liquid and fluid–solid coexistence properties of C₆₀. The critical properties were calculated by fitting the results to the laws of rectilinear diameters and order parameter scaling. The triple‐point properties were determined from the limiting behavior of the Gibbs ensemble vapor–liquid simulations at the lowest temperature range. A stable liquid phase is predicted for temperatures between 1570±20 and 2006±27 K and densities between 0.444±0.003 and 1.05±0.01 nm^?3. The estimated critical and triple‐point pressures are, respectively, 35±6 and 5±16 bars. We show for the first time, to our knowledge, that it is possible, strictly by computer simulation, to estimate a triple point for C₆₀ in accordance with the predictions of theoretical methods and the basic concepts of thermodynamics. The liquid and fluid radial distribution functions indicate the presence of solid or glasslike features. This may support the suggestion of a more cooperative interaction of clusters in C₆₀. A comparison of our results with the data obtained by other authors is presented and discussed. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 375–387, 2001     

On approximate mathematical modeling of the vapor–liquid coexistence curves by the Van der Waals equation of state and non-classical value of the critical exponent

Van der Waals equation of state as well as power laws and critical exponent theories are prototypes to study the cubic shape, asymmetries and “flatness” of the vapor–liquid equilibrium curves near the critical point. In this work we study two similar methods to determine the phase curves in analytical form, which differ from each other by simplicity of mathematical calculation. We analyze temperature dependence of the coexistence curves asymptotically close to the vapor–liquid critical point. We explain the novelty of our method with respect to the standard thermodynamic limit discussed in the literature. Therefore we show that the shape of the coexistence curves can strongly influence the accepted value of the critical exponent. The results of theoretical studies have been compared with the ones obtained by experimental methods.     

Totally inclusive cubic equation of state with five parameters for pure fluids

A totally inclusive cubic equation of state (cubic EOS) is proposed. Although, its form is fairly simple as compared with the present cubic equations, it can include all of them as special cases. The EOS has five parameters. By fitting the experimental critical isothermal for six typical substances combining the critical conditions, the generalized expressions for the five parameters at critical temperature are established. The temperature coefficients of the five parameters for 43 substances are determined by fitting the experimental data of vapor pressure and saturated liquid density. These coefficients are correlated with the critical compressibility factor and acentric factor to obtain the generalized expressions. The predicted saturated vapor pressure, saturated liquid density, critical isothermal and coexistence curve near the critical point show that the equation gives the best results when compared with the Redlich–Kwong–Soave (RKS) and Peng–Robinson (PR) EOS.     

NMR Study of the Kinetics of Butane and Hexane Adsorption from Vapor Phase by Porous Glasses

The kinetics of butane and hexane sorption from vapor phase by porous glasses is studied by the pulsed NMR technique. The sorption process is revealed to proceed in two stages: monomolecular adsorption and capillary condensation. The rate of adsorption is limited by the rate of adsorbate transfer to the adsorbent surface, with the latter rate being described by the classical diffusion flux. It is shown that ultramicropores are filled simultaneously with the formation of a monolayer. The relative content of molecules in such pores is estimated. At the stage of monomolecular adsorption and at the initial stage of capillary condensation, when the adsorption proceeds from the vapor phase of butane-hexane or butane-deuterated hexane mixtures, butane molecules are predominantly sorbed and followed by their partial displacement by hexane molecules. The rate of the capillary condensation of butane from the mixture is 15–18-fold lower than that from the vapor phase of butane alone which is explained by a decrease in the gradient of chemical potential. It is shown that, when adsorption occurs from a nonequilibrium butane-hexane mixture, anomalous kinetic curves are observed because the driving force of adsorption changes in the course of establishing equilibrium in the liquid phase.     

Unveiling the Molecular Origin of Vapor-Liquid Phase Transition of Bulk and Confined Fluids

At temperatures below the critical temperature, discontinuities in the isotherms are one critical issue in the design and construction of separation units, affecting the level of confidence for a prediction of vapor–liquid equilibriums and phase transitions. In this work, we study the molecular mechanisms of fluids that involve the vapor–liquid phase transition in bulk and confinement, utilizing grand canonical (GCE) and meso-canonical (MCE) ensembles of the Monte Carlo simulation. Different geometries of the mesopores, including slit, cylindrical, and spherical, were studied. During phase transitions, condensation/evaporation hysteretic isotherms can be detected by GCE simulation, whereas employing MCE simulation allows us to investigate van der Waals (vdW) loop with a vapor spinodal point, intermediate states, and a liquid spinodal point in the isotherms. Depending on the system, the size of the simulation box, and the MCE method, we are able to identify three distinct groups of vdW-type isotherms for the first time: (1) a smooth S-shaped loop, (2) a stepwise S-shaped loop, and (3) a stepwise S-shaped loop with just a vertical segment. The first isotherm type is noticed in the bulk and pores having small box sizes, in which vapor and liquid phases are close and not clearly identified. The second and the third types occurred in the bulk, cylindrical, and slit mesopores with sufficiently large spaces, where vapor and liquid phases are distinctly separated. Results from our studies provide an insight analysis into vapor–liquid phase transitions, elucidating the effect of the confinement of fluid behaviors in a visual manner.     

Atomic-Scale Insights into Electrode Surface Dynamics by High-Speed Scanning Probe Microscopy

Atomic-scale processes at electrode surfaces in liquid electrolytes are central elemental steps of electrochemical reactions. Detailed insights into the structure of these interfaces can be obtained with in situ scanning tunnelling and atomic force microscopy. By increasing the time resolution of these methods into the millisecond range, highly dynamic processes at electrode surfaces become directly observable. This review gives an overview of in situ studies with video-rate scanning probe microscopy techniques. Firstly, quantitative investigations into the dynamic behaviour of individual adsorbed atoms and molecules are described. These reveal a complex dependence of adsorbate surface diffusion on potential and co-adsorbed species and provide data on adsorbate–adsorbate and adsorbate–substrate interactions in a liquid environment. Secondly, results on collective dynamic phenomena are discussed, such as molecular self-assembly, the dynamics of nanoscale structures, nucleation and growth, and surface restructuring due to phase-formation processes.     

The special features of molecular transport in nanosized channels

The molecular theory of the transport of pure substances and mixtures of molecules of different shapes in narrow slit-like pores, in which the potential of surface forces creates a strongly anisotropic distribution of molecules across pores and thereby makes the hydrodynamics equation inapplicable, is considered. The new microhydrodynamic approach is based on the lattice gas model, which takes into account the intrinsic volume of molecules and intermolecular interactions in the quasi-chemical approximation. Self-consistent calculations of dissipative coefficients taking nonlocal fluid properties into account were performed on the basis of the transition state model including information about equilibrium adsorbate distribution. Changes in fluid concentrations from the gaseous to liquid state and a broad temperature range, including the critical region, are analyzed. This allows vapor, liquid, and vapor-liquid fluid flows to be considered in the presence of capillary condensation. An increase in the size of pores transforms the equations of the theory into hydrodynamic transfer equations for gas or liquid flows, while preserving the relation of transfer coefficients to intermolecular potentials. The use of microhydrodynamic approach equations in numerical calculations and the possibility of applying this approach are discussed.     

Calculation of the adsorption-desorption hysteresis curves in narrow-pore systems

The gas and liquid spinodal branches for an adsorbate located in narrow slit-shaped, cylindrical, and spherocylindrical pores were calculated. The adsorbate is modeled by Lennard-Jones spherical particles. The calculation was based on the lattice gas model taking into account the intermolecular interactions of nearest neighbors in the quasichemical approximation. The density-temperature diagrams for the gas and liquid spinodal branches in the pores are similar to the equilibrium vapor-liquid phase diagrams: they have a common critical point; the dense-phase branches are shifted to lower pore fillings, while the rarefied-phase branches are shifted toward higher pore fillings. The width of adsorption-desorption hysteresis loop in the adsorption isotherms for Lennard-Jones particles was analyzed as a function of the pore size and the interaction potential of the adsorbate with the pore walls. The effect of pore wall roughness and the accuracy of isotherm calculation on the width of the adsorption-desorption hysteresis loop in cylindrical pores is discussed Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 813–823, May, 2007.     

Parachors of liquid/vapor systems: A set of critical amplitudes

In light of the available experimental data and of our current understanding of liquid–vapor critical phenomena, we examine the values of the parachors and of the parachor exponent, which are commonly used to estimate surface tension from the density difference between coexisting liquid and vapor phases. This is a controversial issue, as values for the parachor exponent ranging from 3.5 to 4 have been proposed in the literature. The parachor exponent and parachors can be viewed as a critical exponent and critical amplitudes, respectively. The Ising value, equal to 3.88, should be observed for the exponent “close enough” to the liquid/vapor critical point, i.e., for “low enough” tensions and densities. However, a review of experimental data for several fluids suggests an effective value in the range of 3.6, in line with the effective values observed for the exponents that describe the vanishing of the density difference and capillary length with the distance to the critical temperature. In fact, the asymptotic Ising regime is not reached experimentally, as confirmed by an estimation of the parachors very near the critical point. Those (Ising) parachors can be inferred from other critical amplitudes corresponding to bulk properties by using two-scale factor universality. Their values exceed those deduced from off-critical tension and density data by more than 10%, corresponding to surface tension differences larger than 50%. We argue that effective parachors (i.e., corresponding to an exponent in the range of 3.6) can be utilized in combination with two-scale-factor universality for determining the critical behavior of fluid systems in an extended range around their liquid/vapor critical point.     

Characteristic features of phase diagrams describing condensation of adsorbate in narrow pores

The phase diagrams describing condensation of adsorbate in micro- and mesoporous adsorbents having slit-shaped and cylindrical pores whose size varied from 1 to 20 monolayers were constructed. The study was performed using the lattice-gas model in the quasichemical approximation to take into account the intermolecular interactions. The phase diagrams for various values of the potential arising from different types of adsorbate--adsorbent interaction were analyzed for adsorption of helium, neon, methane, and carbon tetrachloride in graphite pores. Other adsorption systems are considered and the relationship between the pressure and temperature of adsorbate condensation is discussed. A nonmonotonic variation of the critical densities for pore widths from 3 to 10 molecular diameters was found. The pattern of this variation depends on the ratio of the energy of lateral interactions of the adsorbate molecules to the energy of interaction of the adsorbate molecules with pore walls. The critical temperature decreases monotonically with a decrease in the pore width. The stronger the adsorbate interaction with the pore walls, the greater the decrease in the critical temperature.     

金属有机骨架薄膜用于小分子和离子的高效分离

综述了近几年金属有机骨架（MOF）薄膜在小分子和离子高效分离应用中的研究进展.MOF膜材料因具有结晶度良好、结构可设计、孔径可调和可功能化等特点,在分离领域展现出极大的潜在应用价值而受到广泛关注.鉴于近年来MOF膜材料在分离领域取得的巨大进展,对这一领域的前沿进展进行及时系统的总结,并对未来的发展趋势进行展望,具有重要的学术价值,也为科研工作者对MOF膜材料的研究提供了参考.本文首先总结了MOF膜的4种制备方法,包括LBL自组装法（液相外延和Langmuir-Blodgett沉积）、真空制备法（化学气相沉积和原子层沉积）、电化学沉积法和粉末沉积法;而后,详述了MOF膜在气体分离、液体分离及离子/质子传导等方面的应用;最后,总结了MOF膜材料领域当前存在的挑战及潜在解决途径,并对该领域的未来发展方向进行了展望.     

Path dependence of surface–tension scaling in binary mixtures

A mean-field free-energy functional for an n-component mixture with an integral non-local interaction is introduced and then written explicitly for a binary mixture. We use this functional to calculate the liquid–vapor surface tension with parameters chosen to model CO₂/n–C₄H₁₀ and CO₂/n–C₁₀H₂₂, and we examine the scaling of the surface tension as a function of the difference in density between the liquid and vapor phases as various critical points are approached. Each critical point is approached on either a constant-temperature or constant-pressure path; we investigate the path dependence of the scaling behavior. For the constant-temperature paths in the CO₂/n–C₄H₁₀ mixture, we compare our calculated results with experimental data. We find no significant dependence of the scaling on the path to the critical point. We note that the asymptotic scaling holds for a larger range of densities the higher the temperature of the critical point.     

Highly Selective Water Adsorption in a Lanthanum Metal–Organic Framework

We present a new metal–organic framework (MOF) built from lanthanum and pyrazine‐2,5‐dicarboxylate (pyzdc) ions. This MOF, [La(pyzdc)_1.5(H₂O)₂] ? 2 H₂O, is microporous, with 1D channels that easily accommodate water molecules. Its framework is highly robust to dehydration/hydration cycles. Unusually for a MOF, it also features a high hydrothermal stability. This makes it an ideal candidate for air drying as well as for separating water/alcohol mixtures. The ability of the activated MOF to adsorb water selectively was evaluated by means of thermogravimetric analysis, powder and single‐crystal X‐ray diffraction and adsorption studies, indicating a maximum uptake of 1.2 mmol g^?1 MOF. These results are in agreement with the microporous structure, which permits only water molecules to enter the channels (alcohols, including methanol, are simply too large). Transient breakthrough simulations using water/methanol mixtures confirm that such mixtures can be separated cleanly using this new MOF.     

The interaction of water with MOF-5 simulated by molecular dynamics

Force field parameters for use with metal-organic framework-5 (MOF-5 or IRMOF-1) are presented. Flexibility within the framework is included in this model, so that structural changes upon interaction with adsorbate molecules can be observed and quantified. The model was validated by comparing simulated lattice parameters of pure MOF-5 with X-ray diffraction results. For the first time, molecular dynamics simulations have been performed that show how water interacts with MOF-5. The framework is stable at water contents up to 2.3% by mass, but distortion in the lattice structure is already evident. At water contents of 3.9% and higher, the framework collapses because of the replacement of MOF O atoms by water O atoms in the Zn coordination shells. As a result, inorganic MOF O atoms are no longer coordinated by four Zn ions, and benzene dicarboxylate linkers are no longer tethered to Zn centers.     

Multi-stage Transformations of a Cluster-Based Metal-Organic Framework: Perturbing Crystals to Glass-Forming Liquids that Re-Crystallize at High Temperature

Glassy and liquid state metal–organic frameworks (MOFs) are emerging type of materials subjected to intense research for their rich physical and chemical properties. In this report, we obtained the first glassy MOF that involves metal-carboxylate cluster building units via multi-stage structural transformations. This MOF is composed of linear [Mn₃(COO)₆] node and flexible pyridyl-ethenylbenzoic linker. The crystalline MOF was first perturbed by vapor hydration and thermal dehydration to give an amorphous state, which can go through a glass transition at 505 K into a super-cooled liquid. The super-cooled liquid state is stable through a wide temperature range of 40 K and has the largest fragility index of 105, giving a broad processing window. Remarkably, the super-cooled liquid can not only be quenched into glass, but also recrystallize into the initial MOF when heated to a higher temperature above 558 K. The mechanism of the multi-stage structural transformations was studied by systematic characterizations of in situ X-ray diffraction, calorimetry, rheological, spectroscopic and pair-distribution function analysis. These multi-stage transformations not only represent a rare example of high temperature coordinative recognition and self-assembly, but also provide new MOF processing strategy through crystal-amorphous-liquid-crystal transformations.     

STUDIES ON THE DYNAMIC COMPETITIVE ADSORPTION OF ORGANIC VAPORS ON THE ACTIVATED CARBON FIBERS ACTIVATED WITH PHOSPHORIC ACID

The dynamic competititve adsorption behaviors of different binary organic vapor mixtures on ACF-Ps under different operation conditons were investigated by gas chromatography in this paper,The studied mixtrues included benzene/toluene,toluene/xylene,benzene/isopropylbenzene ethly acetate/toluene and benzene/ethyl acetate.Experimental results show that various ACF-Ps,as with ACF-W,can remove both vapors in binary vapor mixtures with over 99% of removal efficiency before the breakthrough point of the more weakly adsorbed vapor,In dynamic competitive adsorption,the more weakly weakle adsorbed vapor noe only penetrates early,but also will be displaced and desorbed consequently by stronger adsorbate and therefore produces a rolling up in the breakthrough curve,The ACF-Ps prepared at different temperatuers have somewhat different adsorption selectivity,The feed concentration ratio of vapros,the length/diameter ratio and the thick of bed have effect on competitive adsorption.The competitive adsorption ability of a vapor is mainly related to its boiling point.Usually,the higher the boiling point ,the stronger the vapor adsorbed on ACF-P.     

The use of two-phase molecular dynamics simulations to determine the phase behavior and critical point of propane molecular models

Molecular dynamics simulations were performed to determine two-phase configurations of model propane molecules below the critical point and in the near-critical, two-phase region. A postprocessor that uses a Monte Carlo method for determination of volumes attributable to each molecule was used to obtain density histograms of the particles from which the bulk coexisting equilibrium vapor and liquid densities were determined. This method of analyzing coexisting densities in a two-phase simulation is straightforward and can be easily implemented for complex, multisite models. Various degrees of internal flexibility in the propane models have little effect on the coexisting densities at temperatures 40 K or more below the critical point, but internal flexibility (angle bending and bond vibrations) does affect the saturated liquid densities in the near-critical region, changing the critical temperature by approximately 20 K. Shorter cutoffs were also found to affect the phase dome and the location of the critical point.     

High-pressure phase equilibria for the carbon dioxide–2-methyl-1-butanol,carbon dioxide–2-methyl-2-butanol,carbon dioxide–2-methyl-1-butanol–water,and carbon dioxide–2-methyl-2-butanol–water systems

High-pressure vapor–liquid equilibria for the binary carbon dioxide–2-methyl-1-butanol and carbon dioxide–2-methyl-2-butanol systems were measured at 313.2 K. The phase equilibrium apparatus used in this work is of the circulation type in which the coexisting phases are recirculated, on-line sampled, and analyzed. The critical pressure and corresponding mole fraction of carbon dioxide for the binary carbon dioxide–2-methyl-1-butanol system at 313.2 K were found to be 8.36 MPa and 0.980, respectively. The critical point of the binary carbon dioxide–2-methyl-2-butanol was also found 8.15 MPa and 0.970 mole fraction of carbon dioxide. In addition, the phase equilibria of the ternary carbon dioxide–2-methyl-1-butanol–water and carbon dioxide–2-methyl-2-butanol–water systems were measured at 313.2 K and several pressures. These ternary systems showed the liquid–liquid–vapor phase behavior over the range of pressure up to their critical point. The binary equilibrium data were all reasonably well correlated with the Redlich–Kwong (RK), Soave–Redlich–Kwong (SRK), Peng–Robinson (PR), and Patel–Teja (PT) equations of state with eight different mixing rules the van der Waals, Panagiotopoulos–Reid (P&R), and six Huron–Vidal type mixing rules with UNIQUAC parameters.     

Molecular distribution at the interface in an aqueous triethylamine solution. <Superscript>1</Superscript>H NMR

The ¹H NMR spectra in a binary aqueous triethylamine solution are recorded with a lower critical point of the liquid–liquid phase transition. It is found that, above the critical temperature the ¹H NMR spectra of water and triethylamine molecules in the phase with a predominant content of triethylamine molecules are characterized by an inhomogeneous broadening. It can be supposed that the found broadening is due to the features of the molecular distribution at the interface.