Effects of film thickness on density and gas permeation parameters of glassy polymers

Dense films of poly(vinyltrimethyl silane) (PVTMS) and poly(trimethylsilyl norbornene) (PTMSNB) having different thicknesses in the range l = 5–150 μm were cast from hydrocarbon solutions. It was shown that a density is inversely proportional to the film thickness. The following equation holds for the density ?: 1/? = 1/?⁰ − b/l. Permeability and diffusion coefficients were determined using the time lag method in respect to different gases. For all the gases, diffusion coefficients decrease when film thickness decreases and film density increases. A correlation of diffusion coefficients with fractional free volume were demonstrated. On the other hand, permeability coefficients are nearly independent of the thickness and density. Possible mechanisms of this behavior are discussed.     

Direct measurement of gas solubility and diffusivity in poly(vinylidene fluoride) with a high-pressure microbalance

We present solubility and diffusion data for the gases methane and carbon dioxide in the polymer poly(vinylidene fluoride). The polymer was cut from extruded piping intended for use in offshore oil and gas applications. Measurements were carried out using a purpose-built high-pressure microbalance. These properties were determined in the temperature range 80-120 °C and in the pressure range 50-150 bar for methane and 20-40 bar for carbon dioxide. In general, good agreement was obtained for similar measurements reported in the literature. Solubility follows a Henry’s law (linear) dependence with pressure. Diffusion coefficients for each of the gases in the polymer were also measured using the balance. Activation energies for diffusion and heats of solution for the two gases in the polymer were also determined.     

Activity coefficients and diffusion coefficients of dilute aqueous solutions of lithium,sodium, and potassium hydroxides

A simplified version of Harned's conductimetric technique has been used to measure binary diffusion coefficients of aqueous lithium, sodium, and potassium hydroxides at 25°C from 0.002 to 0.14 mol-dm^–3. Because of the large difference in mobility between OH^– and the cations, the electrophoretic effect tends to reduce the rate of diffusion of the alkali metal hydroxides; the largest effect is observed for LiOH solutions. The measured diffusion coefficients are in excellent agreement with predictions of the Onsager-Fuoss theory of ion transport. Precise activity coefficients determined from the diffusion measurements are compared with activity coefficients obtained previously by emf methods.     

Sorption,diffusion, and partial molar volumes of C4 hydrocarbons in rubbery polymers

Sorption and dilation isotherms and diffusion coefficients for seven hydrocarbons (n-butane, isobutane, 1-butene, cis-2-butene, trans-2-butene, isobutylene, and 1,3-butadiene) in two rubbery polymers, 1,2-polybutadiene (PB) and poly(ethylene-co-vinyl acetate) (EVAc), were measured at 25°C. Dissolution parameters (Henry's law coefficient and Flory-Huggins interaction parameter), partial molar volumes, and diffusion coefficients were determined. PB exhibited greater affinity and lower diffusivity than EVAc to the C₄ gases, although the gases showed nearly the same partial molar volumes in the two polymers. The diffusivity of such elongated molecules as trans-2-butene in both polymers was higher than that of bulky molecules with similar partial molar volume, such as cis-2-butene and isobutylene. Pressure-dependent permeabilities of PB and EVAc films to the hydrocarbons were predicted and discussed based on the dissolution parameters and the diffusivities. © 1995 John Wiley & Sons, Inc.     

The diffusion of CO2, CH4, C2H4, and C3H8 in polyethylene at elevated pressures

Diffusion and solubility coefficients have been determined for the CO₂^?, CH₄^?, C₂H₄^?, and C₃H₈-polyethylene systems at temperatures of 5, 20, and 35°C and at gas pressures up to 40 atm. Diffusion coefficients were obtained from rates of gas absorption in polyethylene rods under isothermal-isobaric conditions by means of a new diffusivity apparatus. The concentration dependence of the diffusion coefficients was represented satisfactorily by Fujita's free-volume model, modified for semicrystalline polymers, while the solubility of all the penetrants in polyethylene was within the limit of Henry's law. Semiempirical correlations were found for the free-volume parameters in terms of physicochemical properties of the penetrant gases and the penetrant-polymer systems. These correlations, if confirmed, should permit the prediction of diffusion and permeability coefficients of other gases and of gas mixtures in polyethylene as functions of pressure and temperature.     

Heterogeneous catalysis on solids of gases diffusing through a liquid layer,studied by inverse gas chromatography

Physicochemical parameters for heterogeneous catalytic reactions when the catalytic bed was under a liquid phase have been determined, using a non-linear adsorption isotherm by the reversed-flow version of inverse gas chromatography (RF-GC). The mathematical analysis developed in heterogeneous catalysis, mass transfer across gas-liquid boundaries, and diffusion coefficients of gases in liquids was associated with a non-linear adsorption isotherm to find the relevant equations pertaining to the problem. These equations were then used to calculate the adsorption/desorption rate constant, the rate constant for the first-order catalytic reaction and the equilibrium constant for the non-linear adsorption isotherm. The diffusion coefficients of the reactant in the liquid and gaseous phases and the partition coefficients for the distribution of the reactant between the gaseous and liquid phase were also determined.     

Determination of the diffusion coefficient of CO2 in the ionic liquid EMIM NTf2 using online FTIR measurements

Physical data concerning the absorption kinetics like the diffusion coefficients are important values for designing an economically working gas separation processes. Considering ionic liquids, which emerged in recent years as interesting alternative solvent media for versatile industrial purposes, usually only solubility data for gases are available if at all. Therefore in order to gain additional information such as diffusion coefficients of gases in ionic liquids, we established an efficient and easily assembled set-up based on time-resolved FTIR measurements. Applying this methodology, the diffusion coefficient of carbon dioxide in 1-ethyl-3-methyl-imidizolium bis[(trifluoromethyl)sulfonyl]amide (EMIM NTf₂) was determined at a temperature of 303 K.     

Synthesis and Gas-Transport Properties of Iron- and Zirconium-Containing Polydimethylsiloxanes

Novel membrane materials—three-dimensional polydimethylsiloxane networks with nonaggregated metal atoms (Fe, Zr)—have been synthesized using commercial siloxane rubber SKTN and polyfunctional metallosiloxane as a crosslinking agent. For the resulting composites, the permeability, diffusion, and solubility coefficients for a wide range of gases have been determined. It has been found that the permeability coefficients for most of the gases are close to values previously obtained for linear siloxanes; however, the permeability and Р(С₄Н₁₀)/Р(СН₄) selectivity for n-butane are significantly higher. It has been shown that the differences in the permeability coefficients are attributed to higher solubility coefficients of gases in the synthesized composites.     

气体在无定型聚异戊二烯中扩散的分子动力学模拟

采用分子动力学模拟方法研究了多个温度下氧气、氮气及甲烷在无定型顺式1,4-聚异戊二烯中的扩散系数。在模拟过程中,使用COMPASS力场作为分子力场。应用COMPASS力场的势能函数,聚合物的密度及玻璃化转变温度的计算结果与实验值有较好吻合。在278-378 K的温度范围内,通过3或1.5 ns时长的正则系综动力学模拟,计算了不同温度下氧气、氮气及甲烷的扩散系数。结果表明,根据爱因斯坦关系式计算得到的扩散系数与实验结果比较接近。对气体扩散系数与温度的关系进一步研究,发现在278-378 K温度范围内,甲烷的扩散系数随温度变化的半对数曲线图是非线性的,而氧气和氮气的扩散系数随温度变化的半对数曲线图是线性的。本文研究结果有助于理解温度对气体扩散的影响机制,并为高温下气体在天然橡胶中扩散系数的测定及天然橡胶热氧老化建模分析提供依据。     

Ion chromatographic measurement of sulfide, methanethiolate, sulfite and sulfate in aqueous and air samples

Simultaneous measurement of sulfur species was investigated using ion chromatography. Sulfide, methanethiolate, sulfite and sulfate are representative of sulfur species. The aqueous sulfur species were simultaneously measured using a two-detector system: suppressor-type conductivity detector for sulfite and sulfate, and fluorometric or electrochemical detector for the reduced sulfur compounds. The major sulfur-containing gases, hydrogen sulfide, methyl mercaptan and sulfur dioxide are collected into aqueous solution as the species listed above. Collection of sulfur gases using a membrane-based cylindrical diffusion scrubber was investigated. Atmospheric hydrogen sulfide and sulfur dioxide are measured by the diffusion scrubber collection and subsequent measurement by ion chromatography without an enrichment column. In addition to the two gases, methyl mercaptan was also determined using a dual scrubber system.     

Determination of diffusion coefficients by gas chromatography

Gas chromatography (GC), apart from the qualitative and quantitative analysis of gaseous mixtures, offers many possibilities for physicochemical measurements, among which the most important is the determination of diffusion coefficients of gases in gases and liquids and on solids. The gas chromatographic techniques used for the measurement of diffusion coefficients, namely the methods based on the broadening of the chromatographic elution peaks, and those based on the perturbation of the carrier gas flow-rate, are reviewed from the GC viewpoint, considering their running though the history, the experimental arrangement and procedure, the appropriate mathematical analysis and the main results with brief discussions. The experimental data on diffusion coefficients, determined by the various gas chromatographic techniques, are compared with those quoted in the literature or estimated by the known empirical equations predicting diffusion coefficients. This comparison permits the calculation of the precision and accuracy of the techniques applied to the measurement of diffusion coefficients.     

A new gas chromatographic methodology for the estimation of the composition of binary gas mixtures

The relatively new technique of reversed-flow gas chromatography (RFGC) is used to determine the diffusion coefficients of pure gases into gas mixtures (D(mix)(exp)). The pure gases are CO and CO(2), and the mixtures consist of H(2) and He in various volume percentage compositions. A linear regression analysis of D(mix)(exp) of CO and CO(2) in various mixtures of H(2) and He against the percentage composition (X(H2) or X(He)) of the mixtures at different temperatures results in an empirical equation relating D(mix)(exp) to the corresponding theoretical values of the diffusion coefficients of CO and CO(2) in the pure gases H(2) and He, as they are calculated from the Fuller-Schettler-Giddings equation. The empirical equation shows that the diffusion coefficient of an analyte gas in a gas mixture is the partial sum of its diffusion coefficients in the component gases, therefore making possible the determination of the mole fractions of the components of the mixture. The found percentage volume compositions are very close to those determined independently by routine gas chromatography, indicating that the proposed RFGC methodology could be successfully applied to the accurate determination of the volume composition of binary gas mixtures.     

Effects of substituent groups of polyimides on sorption and diffusion of gases

Sorption rate curves of CO₂, N₂, and He gases below 1 atm were measured for polyimide films prepared from benzophenone tetracarboxylic dianhydride (BTDA) with 3,5-diaminotoluene trifluoride (DATF), 2,4-diaminotoluene (DAT), m-phenylenediamine (MPD), and diaminobenzoic acid (DABA). The molecular structures of these four polyimides differ only in the substituent groups of the diamine structure. These polyimides exhibit dualmode type sorption isotherms for carbon dioxide that are concave to the pressure axis, typical of glassy polymer/gas system. The apparent diffusion coefficients below 1 atm pressure of carbon dioxide for this series of compounds decrease in the order: BTDA-DATF > BTDA-DAT > BTDA-MPD > BTDA-DABA. A linear relation between the logarithm of the apparent diffusion coefficient and the reciprocal of free volume, calculated by the method of Bondi using density data, is found for these polyimides. However, this tendency is not observed for the other two gases. The activation energies of the apparent diffusion coefficients at 20 cmHg pressure of carbon dioxide increase with increasing cohesive energy density of the polyimides. The energy per mole of free volume elements in a liquidlike structure in each cohesive energy density may be equated to the activation energy and used to calculate the free volume. The values from the activation energy are almost the same as those from Bondi's method.     

Nuclear magnetic resonance diffusion with surface relaxation in porous media

Nuclear magnetic resonance (NMR) diffusion simulations with surface relaxation were performed numerically in unconsolidated and consolidated porous media by a random walk technique. Two uniform and nonuniform models of surface relaxation were proposed and compared. The apparent diffusion coefficient and extinction function were determined and studied in the fast, slow and intermediate diffusion regimes of relaxation. According to theoretical predictions, it was observed that the extinction function does not depend on surface relaxivity parameter rho 2 in the slow diffusion regime. The apparent diffusion coefficients are independent of rho 2 in the fast diffusion regime and tend to be superposed onto a single curve in the slow one. The evolution of the apparent diffusion coefficients is gathered by a reduced representation in the fast diffusion regime.     

Measurements of partition,diffusion coefficients of solvents in polymer membranes using rectangular thin-channel column inverse gas chromatography (RTCCIGC)

Rectangular thin-channel columns were designed to determine partition and diffusion coefficients of small molecular weight solvents in polymer membranes based on the inverse gas chromatography (IGC) technique. The advantage of using this novel column was analyzed in terms of uniform distribution of polymer thickness, ease of preparation of stationary phase (thin polymer layer), and repeated use of the column. A mathematical model was developed to describe the velocity profile of the carrier gas, and both the time- and location-dependent concentration profiles of solvent in the column. By using the moment analysis method, the partition coefficient and diffusion coefficient were related to the dimensionless first moment and dimensionless second central moment of the elution curve of the solvent, respectively.The first dimensionless moment of the elution curve was found to be independent of the carrier gas velocity, while the second central moment increased with the increase of the carrier gas velocity. Both these behaviors support the theoretical predictions. The diffusion and partition coefficients of ethanol were obtained on polymers of cellulose diacetate (CDA) and sulfonated poly(ether ether ketone) (SPEEK) with a sulfonation degree of 79% over different temperature ranges. Based on the Arrhenius formula, the diffusion activation energies and the solvent dissolution enthalpies in both polymers were also obtained. The diffusion coefficients of 1-propanol were also obtained using two different lengths of columns.     

Size dependence of protein diffusion very close to membrane surfaces: measurement by total internal reflection with fluorescence correlation spectroscopy

The diffusion coefficients of nine fluorescently labeled antibodies, antibody fragments, and antibody complexes have been measured in solution very close to supported planar membranes by using total internal reflection with fluorescence correlation spectroscopy (TIR-FCS). The hydrodynamic radii (3-24 nm) of the nine antibody types were determined by comparing literature values with bulk diffusion coefficients measured by spot FCS. The diffusion coefficients very near membranes decreased significantly with molecular size, and the size dependence was greater than that predicted to occur in bulk solution. The observation that membrane surfaces slow the local diffusion coefficient of proteins in a size-dependent manner suggests that the primary effect is hydrodynamic as predicted for simple spheres diffusing close to planar walls. The TIR-FCS data are consistent with predictions derived from hydrodynamic theory. This work illustrates one factor that could contribute to previously observed nonideal ligand-receptor kinetics at model and natural cell membranes.     

Solubility and diffusion of CO2 and H2S in the ionic liquid 1-ethyl-3-methylimidazolium ethylsulfate

The solubility and diffusion coefficient were determined for carbon dioxide and hydrogen sulfide gases in the ionic liquid 1-ethyl-3-methylimidazolium ethylsulfate ([emim][EtSO₄]) at temperatures ranging from (303.15 to 353.15) K and pressures up to 1.6 MPa. The Krichevsky–Kasarnovsky equation was used to correlate solubility data and Henry’s law constants at different temperatures were obtained. The partial molar thermodynamic functions of solution such as Gibbs free energy, enthalpy, and entropy were calculated using the solubility data. A semi-infinite volume approach is used to obtain the diffusion coefficients for CO₂ and H₂S and a correlation equation with temperature is presented for each gas. Comparison showed that H₂S is more soluble than CO₂ and its diffusion coefficient is about two orders of magnitude as that of CO₂ in the ionic liquid studied in this work.     

Comparison of three models for permeation of CO2/CH4 mixtures in poly(phenylene oxide)

Two models for the permeability of pure gases have been extended to include binary gas mixtures. The first is an extension of a pure gas permeability model, proposed by Petropoulos, which is based on gradients of chemical potential. This model predicts the permeability of components in a gas mixture solely on the basis of competition for sorption sites within the polymer matrix. The second mixed gas model follows an earlier analysis by Barrer for pure gases which includes the effects of saturation of Langmuir sites on the diffusion as well as the sorption processes responsible for permeation. This generalized “competitive sorption/diffusion” model includes the effect of each gas component on the sorption and diffusion of the other component in the mixture. The flux equations from these two models have been solved numerically to predict the permeability of gas mixtures on the basis of pure gas sorption and transport parameters. Both the mixed gas Petropoulos and competitive sorption/diffusion model predictions are compared with predictions from the earlier simple competitive sorption model based on gradients of concentration. An analysis of all three models is presented for the case of CO₂/CH₄ permeability in poly(phenylene oxide) (PPO). As expected, the competitive sorption/diffusion model predicts lower permeability than either of the models which consider only competitive sorption effects. The permeability depression of both CO₂ and CH₄ predicted by the competitive sorption/diffusion model is roughly twice that predicted by the competitive sorption model, whereas the mixed gas Petropoulos model predictions for both gases lie between the other two model predictions. For the PPO/CO₂/CH₄ system, the methane permeability data lie above the predictions of all three models, whereas CO₂ data lie below the predictions of all models. Consequently, the competitive sorption/diffusion model gives the most accurate prediction for CO₂, while the simple competitive sorption model is best for methane. The effects of mixed gas sorption, fugacity, and CO₂-induced dilation were considered and do not explain the inaccuracies of any of the models. The relatively small errors in mixed gas permeability predictions using either of the three models are likely to be related to “transport plasticization” of PPO owing to high levels of CO₂ sorption and its effect on polymer segmental motions and gas diffusivity.     

An investigation of the high gas permeability of poly (1-Trimethylsilyl-1-Propyne)

The permeability of poly (1–trimethylsilyl–1−propyne), PMSP, to light gases is higher than that of any other nonporous synthetic polymer at ambient temperatures. PMSP is in the glassy polymer state at these temperatures. Permeability, diffusion, and solubility coefficients were determined for N₂, O₂, CH₄, and CO₂ in PMSP, and are compared with values reported for these gases in poly (dimethyl siloxane). The higher gas permeability of PMSP results primarily from a substantial gas solubility, which appears to be due, in turn, to a large “excess” free volume in the unrelaxed (Langmuir) domains of this glassy polymer. The structure of PMSP, which consists of relatively rigid backbone chains separated by bulky trimethylsilyl side groups, probably is responsible for this large free volume.