Modeling and Uncertainty Quantification of Vapor Sorption and Diffusion in Heterogeneous Polymers

A high‐fidelity model of kinetic and equilibrium sorption and diffusion is developed and exercised. The gas‐diffusion model is coupled with a triple‐sorption mechanism: Henry’s law absorption, Langmuir adsorption, and pooling or clustering of molecules at higher partial pressures. Sorption experiments are conducted and span a range of relative humidities (0–95 %) and temperatures (30–60 °C). Kinetic and equilibrium sorption properties and effective diffusivity are determined by minimizing the absolute difference between measured and modeled uptakes. Uncertainty quantification and sensitivity analysis methods are described and exercised herein to demonstrate the capability of this modeling approach. Water uptake in silica‐filled and unfilled poly(dimethylsiloxane) networks is investigated; however, the model is versatile enough to be used with a wide range of materials and vapors.     

Sorption and Diffusion of Propylene and Ethylene in Heterophasic Polypropylene Copolymers

Summary: Sorption experiments of ethylene and propylene in different polypropylene powder samples, both homopolymer and heterophasic copolymers with different rubber content, have been carried out in a high-pressure magnetic suspension balance at 10 bars pressure and 70 °C. The gross solubilities measured can be well correlated with the rubber content of the polymer samples. Solubility of ethylene and propylene in the rubber phase differ from solubility in the amorphous fraction of the homopolymer, especially the concentration ratio of propylene to ethylene differs significantly between rubber phase and amorphous fraction of the homopolymer. From the slope of monomer uptake, information on kinetics of mass-transfer can be gained. No significant differences were observed in terms of mass-transfer for ethylene and propylene. With increasing rubber content, effective diffusion coefficients increased slightly. By combined sorption studies with powder samples and compressed films, information about both effective diffusion coefficients and the effective length scale of diffusion could be gained. It could be shown, that the particle radius is not the characteristic length of diffusion in the studied powder samples. Mass transfer of nearly all samples could be described by a constant diffusion length of 120 to 130 µm, independently on particle size. This indicates that the effective scale of diffusion in polymer particles is in between microparticle and macroparticle scale used in classical particle modeling.     

Sorption and transport of water in nylon-6 films

Sorption and transport properties of water through films of Nylon-6 were obtained at 5, 23, and 40°C. Commercially available films were used and a Cahn electrobalance was employed for measuring the water uptake by the polymer samples. Values of the water sorption isotherms are accurately described by the Langmuir/Flory-Huggins dual-mode sorption model. At water activity values below 0.15, the volume fraction of water described by the Langmuir portion of the model was greater than the Flory-Huggins population. Solubility and diffusion coefficients of water, as well as the diffusion activation energy and enthalpy of dissolution of water for Nylon-6, were determined from the sorption experiments. Values obtained support the hypothesis of a bimodal water sorption mode, and the formation of water clusters. © 1994 John Wiley & Sons, Inc.     

Sorption and diffusion of water vapor in polyimide films

Sorption and diffusion of water vapor are investigated gravimetrically for polyimide films. The activity dependence of the solubility and diffusion coefficients, S and D, respectively, is classified under four types: (1) constant S and D type, (2) dual-mode sorption and transport type, (3) dual-mode type followed by a deviation due to a plasticization effect at high vapor activity, and (4) constant S and D type followed by a deviation due to water cluster formation at high activity. For the dual-mode type, the Henry's law component is much larger than the Langmuir component except at low activity, and therefore deviation in behavior from the first type is small. S is larger for polyimides with higher content of polar groups such as carbonyl, carboxyl, and sulfonyl. D is larger for polyimides with a higher fraction of free space, with some exceptions. The polyimide from 3,3′,4,4′-biphenyltetracarboxylic dianhydride and dimethyl-3,7-diaminodibenzothiophene-5, 5-dioxide belongs to the third type and displays both large S and large D. The polyimide from 2,2-bis(3,4-dicarboxyphenyl) hexafluoropropane dianhydride and 4,4′-oxydianiline belongs to the fourth type, and has the largest D but rather small S because of the hydrophobic C(CF₃)₂ groups. © 1992 John Wiley & Sons, Inc.     

Diffusion of Organic Vapors in Materials for Gas Sensing Application

Mass-variation measurements were carried out on carbon black (CB)-poly(vinyl chloride) (PVC) composite film with 40% by weight of di(2-ethylhexyl)-phthalate (DOP), cast on resonant piezo-layer (RPL) elements of lead zirconat titanate (PZT). Even if anomalous diffusion is predicted by fitting the data with M_t/M_∞=kt^α, the fractional uptake M_t/M_∞ is linear with the square root of the time up to M_t/M_∞=0.6, suggesting Fickian behavour. The anomalous values of α are probably due to experimental time lag. A dependence of the diffusion on the morphology of the material and the penetrant shape and flexibility has been found.     

Phase Transitions of MBBA Confined in Porous Solids

The diffusive and dynamic mechanical behaviour of an epoxy system containing tetraglycidyl-4,4′-diaminodiphenylmethane and a multifunctional Novolac glycidyl ether cured with 4,4′-diaminodiphenylsulfone was studied after water sorption. The diffusion of water was performed at 100% relative humidity, by immersion of specimens in water at 20, 40, 70 and 100°C. In all sorption experiments, the water diffusion followed Fick's law. Diffusion coefficients and saturated water concentrations were estimated for these temperatures. The activation energy for diffusion was determined from the relationship linking the diffusion coefficient and the reciprocal of the absolute temperature. The value obtained was 45.7 kJ mol^-1. Dynamic mechanical analysis of samples immersed in water at 25 and 100°C, and with various water contents, showed a shift in T_g> (defined by the tanδ peak) to lower temperatures over the glass transition region, and a slight decrease in the dynamic storage modulus in the presence of water as a result of a plasticization effect. This revised version was published online in July 2006 with corrections to the Cover Date.     

Sorption of water and organic solutes in polyimide films and its effects on dielectric properties

The effect of structure on the sorption kinetics of water and of various organic solutes into polyimide (PMDA-ODA) thin films was studied. The major techniques employed include measurements of sorption kinetics, density, and dielectric relaxation. More solute uptake, lower densities and higher diffusivities were observed for films cured at lower temperatures. By measuring both changes of mass and of density, the volume expansion of the polymer due to each solute was obtained; this was found to be proportional to the molar volume of the solute. The two dielectric relaxation peaks (denoted by γ₁ and γ₂) due to water (and other solutes) were studied in detail to obtain the relevant activation energies and the separate dipole moments. While water and methylene chloride appear in both γ₁ and γ₂ configurations, methyl and ethyl alcohol appear mainly as γ₂, while acetic acid is primarily γ₁. It was concluded that the γ₁ configurations are relatively homogeneously distributed throughout the polymer, involving loose bonding to the polymer structure, while the γ₂ configurations involve small clusters, probably chains of molecules. © 1993 John Wiley & Sons, Inc.     

Sorption and diffusion of gases in a polyimide

Sorption and diffusion of gases (CO₂, N₂, and He) in a polyimide (PI2080) film were measured by using an apparatus which gives the sorption rate curves from the initial state to the equilibrium state. Nonlinear isotherms observed for CO₂ sorption were interpreted successfully in terms of the dual-mode model for sorption in glassy polymers. Linear isotherms observed for N₂ and He seemed to obey Henry's law. Two diffusion coefficients (D_I and D_E) were obtained using the short-time method and the long-time method for a Fickian diffusion model, together with the equilibrium solubility (C_e) from each experiment. The initial sorption rate curves agreed with the calculated curves using D_I, however near sorption equilibrium the curves are in accord with the calculated curves using D_E. These observations suggest that some relaxation process is superimposed on the diffusion process. The non-Fickian transport data were correlated successfully with a model that combines time-dependent diffusion and the Fickian model.     

A New Kinetic Model for Water Sorption Isotherms of Cellulosic Materials

Summary: Some natural fibres like flax, hemp and others show excellent mechanical properties which make them a promising choice for the reinforcement of polymers. For natural fibre reinforced composites, hydrophilicity is a problem with respect to dimensional changes, fibre to matrix adhesion and long term stability. The interaction of differently prepared and modified fibres with water vapour has been investigated by dynamic vapour sorption. It has been found that the sorption and desorption kinetics of cellulosic fibres can be excellently fitted by assuming two parallel, independent first order processes. This empirical model, defined here as the “Parallel Exponential Kinetics” model (PEK-model), reveals two distinct mechanisms with slow and fast exchange of water vapour respectively, related to different sorption sites. The specific sorption mechanisms are represented by individual sorption-desorption isotherms as components of the total isotherms. The results suggest a relation to the differing types of amorphous regions in the fibres and/or to the different states of “bound” or “free” water, discussed for hydrophilic materials. The PEK-model proved to be consistently applicable for sorption and desorption over the whole humidity range, and also for all tested cellulose fibres. It is especially useful for a clearer distinction of different fibre types or modifications and can be successfully used for an extended fibre characterization.     

Sorption and transport of linear alkane hydrocarbons in biaxially oriented polyethylene terephthalate

Equilibrium sorption and uptake kinetics of n‐butane and n‐pentane in uniform, biaxially oriented, semicrystalline polyethylene terephthalate films were examined at 35 °C and for pressures ranging from 0 to approximately 76 cmHg. Sorption isotherms were well described by the dual‐mode sorption model. Sorption kinetics were described either by Fickian diffusion or a two‐stage model incorporating Fickian diffusion at short times and protracted polymer structural relaxation at long times. Diffusion coefficients increased with increasing penetrant concentration. n‐Butane solubility was lower than that of n‐pentane, consistent with the more condensable nature of n‐pentane. However, n‐butane diffusion coefficients were higher than those of n‐pentane. Infinite‐dilution, estimated amorphous phase diffusion and solubility coefficients were well correlated with penetrant critical volume and critical temperature, respectively. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 1160–1172, 2001     

Robust Atomistic Modeling of Materials,Organometallic, and Biochemical Systems

Modern chemistry seems to be unlimited in molecular size and elemental composition. Metal-organic frameworks or biological macromolecules involve complex architectures and a large variety of elements. Yet, a general and broadly applicable theoretical method to describe the structures and interactions of molecules beyond the 1000-atom size regime semi-quantitatively is not self-evident. For this purpose, a generic force field named GFN-FF is presented, which is completely newly developed to enable fast structure optimizations and molecular-dynamics simulations for basically any chemical structure consisting of elements up to radon. The freely available computer program requires only starting coordinates and elemental composition as input from which, fully automatically, all potential-energy terms are constructed. GFN-FF outperforms other force fields in terms of generality and accuracy, approaching the performance of much more elaborate quantum-mechanical methods in many cases.     

Robust Atomistic Modeling of Materials,Organometallic, and Biochemical Systems

Modern chemistry seems to be unlimited in molecular size and elemental composition. Metal‐organic frameworks or biological macromolecules involve complex architectures and a large variety of elements. Yet, a general and broadly applicable theoretical method to describe the structures and interactions of molecules beyond the 1000‐atom size regime semi‐quantitatively is not self‐evident. For this purpose, a generic force field named GFN‐FF is presented, which is completely newly developed to enable fast structure optimizations and molecular‐dynamics simulations for basically any chemical structure consisting of elements up to radon. The freely available computer program requires only starting coordinates and elemental composition as input from which, fully automatically, all potential‐energy terms are constructed. GFN‐FF outperforms other force fields in terms of generality and accuracy, approaching the performance of much more elaborate quantum‐mechanical methods in many cases.     

Sorption and diffusion of water vapour on edible films

Two types of films consisting of sodium salt of carboxymethyl cellulose (NaCMC) and hydroxypropyl cellulose (HPC) as film forming materials and glycerin as plasticizer were prepared, characterized and their water vapour sorption properties were determined. The water sorption isotherms of the films were measured using a magnetic suspension balance. Results show that diffusion of water vapour in NaCMC based film is faster than that in HPC based films, due to the heterogeneous structure and larger pore dimensions of the NaCMC films.     

Sorption and diffusion of organic vapors in amorphous Teflon AF2400

Vapor sorption in amorphous Teflon AF2400 of various organic solutes was studied in a wide range of activity at 25 °C by means of the gravimetric technique. The sorption isotherms of hexane, toluene, and chloroform were shown to be concave to the pressure axis and are consistent with the dual mode sorption model (DMS). The parameters of the DMS model k_D and b reveal a linear correlation with squared critical temperature of solutes T. The third model parameter, the Langmuir sorption capacity C′_H decreases when the size of solutes (critical volume) increases. Sorption isotherms of methanol and ethanol were shown to be convex to the pressure axis and are consistent with cluster formation in this strongly hydrophobic polymer. Concentration‐dependent diffusion coefficients D were determined using a linear implicit difference scheme in analysis of sorption kinetics. It was shown that D values increase exponentially with concentration for all the solutes, except alcohols for which exponential reduction of D(C) was observed. The partitioning of the thermodynamic and mobility contributions in D indicated that the reduction of D values of alcohols is consistent with clustering phenomena in AF2400. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 832–844, 2006     

Calorimetric Studies and Structural Aspects of Ionic Liquids in Designing Sorption Materials for Thermal Energy Storage

The thermal properties of a series of twenty‐four ionic liquids (ILs) have been determined by isothermal titration calorimetry (ITC) with the aim of simulating processes involving water sorption. For eleven water‐free ILs, the molecular structures have been determined by X‐ray crystallography in the solid state, which have been used to derive the molecular volumes of the ionic components of the ILs. Moreover, the structures reveal a high prevalence of hydrogen bonding in these compounds. A relationship between the molecular volumes and the experimentally determined energies of dilution could be established. The highest energies of dilution observed in this series were obtained for the acetate‐based ILs, which underlines their potential as working fluids in sorption‐based thermal energy storage systems.     

Sorption of Hydrophobic Organic Compounds by Aqueous Latexes

Summary: Optical absorption measurements are used for the first time to investigate the uptake of pure organic solvents or solutions by latex particles. Sorption into glassy polymer particles is a two‐stage process with distinctly different characteristic times, which reflects that an initial softening of the outer particle layer facilitates further uptake. The sorption of solutions containing highly water‐insoluble compounds allows the preparation of composite nanoparticles, which are hardly accessible by other routes.

Photograph of the neat 100 nm latex (right) particles and the particles after dying by sorption with the hydrophobic pigment Sudan IV (left).     

碳化多孔有机骨架制备氮掺杂多孔碳及其气体吸附研究

通过简单的一步碳化方法, 以含氮的多孔有机骨架JUC-Z2为碳前驱物制备出氮掺杂多孔碳材料. 与原始JUC-Z2材料相比, 制备的多孔碳材料显示出明显提高的气体吸附量和增强的吸附焓. 其中JUC-Z2-900的CO₂吸附量高达113 cm³·g^-1, H₂吸附量也达到246 cm³·g^-1, 超过了大部分报道的多孔材料. 尤其是JUC-Z2-900的CH₄吸附量在273 K, 1 bar下高达60 cm³·g^-1, 据我们所知, 这一值为目前报道材料的最高值. 除此之外, 样品还显示出选择性吸附CO₂的能力, 273 K下, JUC-Z2-900的CO₂/N₂的选择性高达10, CO₂/H₂的选择性也高达66. 另外, 样品具有很高的热稳定性, 有望应用在碳捕获和清洁能源储存等领域.     

The Design of an Automatic System for the Gravimetric Measurement of Water Sorption

An understanding of the mechanisms by which water molecules are held within a substance or at its surface, either by physical or chemical processes, is of importance in the formulation, preparation and storage of a wide variety of substances. The traditional experimental techniques which have been used to make measurements on samples exposed to specific levels of relative humidity, (e.g. using desiccators containing saturated salt solutions), are slow, laborious, inaccurate, and provide a limited amount of data. This paper describes the conception, operation, and facilities of a new system which by employing recently developed electronic components and transducers, significantly advances the performance capability for moisture sorption analysis. This revised version was published online in July 2006 with corrections to the Cover Date.     

Diffusion of Solvents and Cations in Porous Sol-Gel Glass

Diffusion coefficients for water, cyclohexane, toluene, chloroform, acetone and acetonitrile in porous sol-gel glass were determined using the diaphragm and radioactive tracer techniques. Polar solvents were found to diffuse faster than nonpolar solvent within porous sol-gel glass. The diffusion coefficients of Nd³⁺ and Er³⁺ inside porous sol-gel glass were determined from concentration profiles within monoliths impregnated by 1.6 M rare earth salts dissolved in either acetone or water. To study the effects of ligands on the diffusion, four different erbium salts were used: nitrate, chloride, bromide, and perchloride. It was found that the diffusion rate increases with decreasing radius of rare earth coordination sphere.