Gas Sorption Isotherms Research Articles

Sorption and diffusion of low molecular weight gases and vapors in glassy polymers at high concentration of sorbate

A theoretical approach has been developed to describe the sorption and diffusion processes of low weight molecular gases and vapors in polymers at wide ranges of sorbate concentration. The equation of an S-shaped gas sorption isotherm in glassy polymer matrix has been derived. The concentration dependence of the sorbate molecule diffusion coefficient has been established. For an S-shaped sorption isotherm, this dependence is nonmonotonous. The conditions of cluster formation of sorbate molecules have been analyzed within the proposed approach, in which it is possible to determine a correlation between these conditions and parameters of sorption isotherm. The comparison of the experimental and theoretical data provides an assessment of the microscopic characteristics of investigated polymer–vapor systems, such as the distances between vapor molecules in a matrix corresponding to intermolecular repulsion and attraction. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2314–2323, 1999

Design and synthesis of metal-carboxylate frameworks with permanent microporosity

Metal-carboxylate clusters are ideally suited as secondary building units (SBU) for the assembly of extended open frameworks. Examples extracted from the chemistry of the multidentate building block 1,4-benzenedicarboxylate (BDC) show that Zn(BDC) clusters lead to the formation of rigid, stable and truly microporous metal-carboxylate networks. Gas sorption isotherms measured for this class of materials show type (I) gas uptake that is analogous to those observed for zeolites and molecular sieves.

Establishing Microporosity in Open Metal−Organic Frameworks: Gas Sorption Isotherms for Zn(BDC) (BDC = 1,4-Benzenedicarboxylate)

Construction of microporous metal-organic frameworks by copolymerization of organic molecules with metal ions has received widespread attention in recent years, with significant strides made toward the development of their synthetic and structural design chemistry.1 Cognizant of the fact that access to the pores and understanding the inclusion chemistry of these materials are essential to their ultimate utility, we prepared rigid frameworks that maintain their structural integrity and porosity during anion-exchange and guest sorption from solution and in the absence of guests.2-4 Although gas sorption isotherm measurements are often used to confirm and study microporosity in crystalline zeolites and related molecular sieves,5 such studies have not been established in the chemistry of open metal-organic frameworks6 thus leaving unanswered vital questions regarding the existence of permanent porosity in this class of materials. Herein, we present the synthesis, structural characterization, and gas sorption isotherm measurements for the Zn(BDC) microporous framework of crystalline Zn(BDC)‚(DMF)(H2O) (BDC ) 1,4benzenedicarboxylate and DMF ) N,N′-dimethylformamide). Slow vapor diffusion at room temperature of triethylamine (0.05 mL) and toluene (5 mL) into a DMF solution (2 mL) containing a mixture of Zn(NO3)2‚6H2O (0.073 g, 0.246 mmol) and the acid form of BDC (0.040 g, 0.241 mmol) diluted with toluene (8 mL) yields colorless prism-shaped crystals that were formulated as Zn(BDC)‚(DMF)(H2O). X-ray single-crystal analysis8 on a sample obtained from the reaction product revealed an extended open-framework structure composed of the building unit shown in Figure 1. A total of four carboxylate units of different, but symmetrically equivalent, BDC building blocks are bonded to two zinc atoms in a di-monodentate fashion. Each zinc is also linked to a terminal water ligand to form an overall arrangement that is reminiscent of the carboxylate bridged M-M bonded molecular complexes. Although the Zn-Zn distance (Zn1-Zn1A ) 2.940 (3) A) is indicative of some M-M interaction, it does not represent an actual bond.9 The structure extends into the (011) crystallographic plane by having identical Zn-Zn units linked to remaining carboxylate functionalities of BDC to yield 2-D microporous layers. These layers are held together along the a axis by hydrogen-bonding interactions between water ligands of one layer and carboxylate oxygens of an adjacent layer as illustrated in a. Stacking of the layers in the

Effects of cis‐trans‐configurations of the main chains of poly(trimethylsilyl norbornene) on its transport and sorption properties as well as free volume

Samples of poly(trimetylsilyl norbornene) having different content of cis configurations of double bonds in the main chains were prepared by ring opening metathesis polymerization in the presence of the catalysts characterized by different stereoselectivity (Re2O7, RuCI3, WCI6). It was shown that the polymer obtained in the presence of the WCI6 catalysts having the closest content of the cis-and trans-configurations is distinguished by the largest gas permeability, diffusion, and solubility coefficients. Determination of the parameters of gas sorption isotherms and estimation of free volume using group contribution and positron annihilation methods allowed to conclude that microstructure of this polymer (cis/trans ratio) affects its free volume and, therfore, its transport and thermodynamic properties. © 1996 John Wiley & Sons, Inc.

Effects of cis-trans-configurations of the main chains of poly(trimethylsilyl norbornene) on its transport and sorption properties as well as free volume

Samples of poly(trimetylsilyl norbornene) having different content of cis configurations of double bonds in the main chains were prepared by ring opening metathesis polymerization in the presence of the catalysts characterized by different stereoselectivity (Re2O7, RuCI3, WCI6). It was shown that the polymer obtained in the presence of the WCI6 catalysts having the closest content of the cis-and trans-configurations is distinguished by the largest gas permeability, diffusion, and solubility coefficients. Determination of the parameters of gas sorption isotherms and estimation of free volume using group contribution and positron annihilation methods allowed to conclude that microstructure of this polymer (cis/trans ratio) affects its free volume and, therfore, its transport and thermodynamic properties. © 1996 John Wiley & Sons, Inc.

Nonequilibrium Lattice Fluids: A Predictive Model for the Solubility in Glassy Polymers

The calculation of sorption isotherms for gases and vapors in glassy polymers is approached through a nonequilibrium equation of state procedure. The basic peculiar feature of the system, represented by the nonequilibrium structure of the mixture, is accounted for by introducing an order parameter for an isotropic glass. By revisiting the lattice fluid model by Sanchez and Lacombe (Macromolecules 1978, 11, 1145.), an expression for the Gibbs free energy of nonequilibrium lattice fluids is obtained in which the polymer species density in the solid mixture is considered as an order parameter and it is thermodynamically treated as an internal state variable. The absence of adjustable parameters makes the resulting model entirely predictive for the solubility, once the pseudoequilibrium volumetric data are available. The comparison of the predicted isotherms with the data for CO2−poly(carbonate) systems at 35 °C, obtained by Fleming and Koros (Macromolecules 1990, 23, 1353.) under different polymer prehistori...

Mixed gas sorption in elastic solids

The thermodynamic changes that accompany mixed gas sorption in glassy polymeric materials are examined. The solid polymer is treated as an elastic solid in the analysis. Two contributions are identified: deformation of the solid to accommodate the penetrant and mixing of the deformed solid and penetrant. Equating the chemical potential of the penetrant in the gas phase to that in the solid yields sorption isotherms. By estimating two material parameters, the penetrant partial molar volume and interaction parameter, from pure gas sorption measurements, a priori predictions of mixed gas sorption are possible. The resulting sorption isotherms are compared to two sets of experimental measurements: carbon dioxide, ethylene, methane and nitrous oxide sorption in poly (methyl methacrylate) and carbon dioxide and methane sorption in poly(phenylene oxide) and carboxylated poly(phenylene oxide). The predicted mixed gas sorption isotherms are in good agreement with experimental data.

Gas sorption and permeation in poly(ethyl methacrylate)

Gas sorption isotherms for N 2, Ar, CH 4, and CO 2 have been measured at various temperatures for poly(ethyl methacrylate) (PEMA) below its T g. For the three low solubility gases, N 2, Ar and CH 4, the sorption isotherms are concave as predicted for glassy polymers but the amount of sorption in PEMA is much lower than that in high T g polymers. For the higher solubility gas CO 2, however, the amount of sorption is the same as that in high T g polymers. The CO 2 isotherms changed from concave at low pressures to a straight line at high pressures, which can be extrapolated to the origin of the coordinates, indicating the PEMA is plasticized by CO 2 from the glassy to the rubbery state. The sorption parameters for CO 2 are derived from a modified dual mode sorption equation which considers the plasticizing effect. New findings about these parameters and the derived enthalpy change on sorption are reported. Gas permeability coefficients for PEMA to He, H 2, O 2, Ar, N 2, and CH 4 measured at 35°C are observed to be independent of pressure. On the other hand, the CO 2 permeability coefficients increase with pressure. Appropriate models are used to describe this transport behavior. Evidence from gas sorption and DSC thermograms show that PEMA can sub- T g anneal under CO 2 plasticization. However, when the T g is depressed by plasticization below the observation temperature, the annealing effect is erased. This leads to complex behavior as described.

Gas and vapor sorption in polymers just below Tg

AbstractGenerally, sorption isotherms for gases like CO2 in glassy polymers are concave to the pressure axis, whereas in the rubbery state these isotherms are linear for gases or sometimes convex to the pressure axis for more condensable vapors. Examples of CO2 isotherms are reported here that show at low pressure the curvature characteristic of glasses and then become linear at higher pressures. This is observed when the glass transition temperature Tg is not much greater than the observation temperature T, and plasticization of the polymer by sorbed CO2 causes Tg to become equal to T within the range of pressures employed in the isotherm measurement. For the sorption of vapors in glassy polymers, this can lead to sigmoidal isotherms, as discussed using an illustration from the literature.

Pure and mixed gas sorption of carbon dioxide and ethylene in poly(methyl methacrylate)

The sorption of CO 2, C 2 H 4 and mixtures of these gases in poly(methyl methacrylate) at 35°C has been characterized at pressures up to 6.5 atm. The pure gas sorption isotherms exhibit significant concave curvature to the pressure axis and are described well by the dual mode sorption model. The mixed gas sorption data indicate that significant decrements in the solubility of each component in the mixture occur relative to the pure component case at equivalent partial pressures. This phenomenon is predicted accurately by the dual mode sorption model, which accounts for competition between mixture components for sorption in the polymer. The model requires only pure component sorption parameters to describe the mixture behaviour over the full range of composition. The mixture data reveal that the model should be formulated in terms of the gas phase fugacity rather than the partial pressures of the gases at high pressures where non-ideal gas mixture behavior may occur. Deviations between mixed gas sorption data and model predictions based on pure component dual mode parameters are small (± 2.1%) and probably negligible for most purposes for the pressure range studied.

A Multilayer Theory for Gas Sorption

A multilayer model is proposed which predicts the equilibrium sorption isotherms for pure gases in Part I and for binary gas mixtures in Part II. This first part deals with the sorption of a pure gas or vapor, particularly by polymers. The model and equations are significantly different from those presently most used. The model gives good fits to the data against which it has been tested, particularly when used with sigmoidal isotherms. It allows the thermodynamic parameters to be calculated and gives important knowledge about the distribution and location of sorbed species.

Hysteresis in gas sorption isotherms

Hysteresis in the nitrogen sorption isotherm for a system containing slit-shaped pores has been shown to conform to the “open-pore” theory suggested by Foster [ Trans. Faraday Soc. 28, 645 (1932)]. Adsorption takes place largely by the development of multilayers on the surfaces of the plate-shaped crystals and ceases when opposite films merge thus filling the pore. Desorption is then governed by the curvature of the semicylindrical meniscus formed. Hysteresis thus arises essentially from a delay in the formation of a meniscus during the adsorption process. In a system containing cylindrical capillaries capillary condensation occurs during both the adsorption and desorption processes. Neither process appears thermodynamically reversible with a delay in adsorption resulting from the presence of cylindrical menisci in open-ended pores being followed by a delay in desorption due to the retention of liquid behind narrow restrictions.