Diffusion of organic solvents in isobutylene-based polymers

Diffusion behavior of several organic solvents in polyisobutylene (PIB) and in poly(p-methylstyrene-co-iso-butylene) (PMS-BR) with different monomer ratios has been studied. The experiments have been conducted over a temperature range of 50 to 100°C using a conventional gravimetric Sorption technique. The PMS-BR copolymers contained 2, 7, and 15 weight percent p-methylstyrene, respectively. Although employing temperatures were far above the glass transition temperatures of polymers, the diffusion coefficients are correlated well with the Vrentas-Duda free-volume theory. For all the solvents, the PIB shows the highest diffusivity while the copolymer with the 15% p-methylstyrene gives the lowest value. This behavior can be explained by the amount of fractional free-volume present in a system.     

Preferential adsorption coefficient of polymers

The recent formulation of the preferential adsorption coefficient, λ, which takes into account differences in molecular contact surface and in free volume, is tested by comparing theoretical with experimental values of λ from the literature. Seven different systems containing polystyrene and poly(methyl methacrylate) are considered. Agreement between theory and experiment is reached by treating the contact surface of the polymer as a fitting parameters, s. The adjusted values of s are: (a) systematically higher than the ones calculated from chain geometry; (b) largest in systems containing specific interactions (methanol). The connection between this enhanced apparent contact surface of the polymer and the ternary interaction parameter of the classical theory of λ, is analysed.     

Estimation of densities of ionic liquids using Patel–Teja equation of state and critical properties determined from group contribution method

In this paper, the Valderrama and Robles group contribution model for the critical properties is extended to the prediction of densities of ionic liquids (ILs) at varying temperatures and pressures, where the critical properties of ILs are represented by the modified Lydersen–Joback–Reid group contribution method, and the density is predicted by virtue of the Patel–Teja (PT) equation of state (EOS). The group increments for totally 47 groups with respect to the extended Group Contribution Patel–Teja (GC–PT) model were determined on the basis of experimental density data for 747 pure ILs at atmospheric pressure and ambient temperature. The group increments are suitable for both the GC–PT model and the original Valderrama and Robles model for the density prediction of ILs. The correlation accuracy in terms of overall average absolute relative deviation (AARD) is 4.4% for 918 data points of density at ambient temperature and atmospheric pressure. The applicability of the GC–PT model is justified by predicting the densities of imidazolium-, pyridinium-, and phosphonium-based ILs containing various anions over a wide range of temperatures and pressures and the vapor pressures of five alkylimidazolium-based ILs at varying temperatures, which implied the rationality of the group increments and the critical properties of ILs, as well as the potential uses of the GC–PT model for the thermodynamic modeling of IL-containing systems.     

The use of THz time-domain reflection measurements to investigate solvent diffusion in polymers

Solvent diffusion into polymers is central to their performance, for example as controlled delivery pharmaceutical products. In this work, we present the novel application of terahertz (THz) time-domain reflectance spectroscopy to quantify the ingress of acetone into various polymer materials. Reflections from the top and bottom surfaces of the discs are temporally resolved, as is a reflection from the interface between acetone-wet polymer and dry polymer. These reflections enable both the polymer swelling and more importantly the position of the liquid diffusion front to be quantified as a function of time. Verification of these measurements is provided by equivalent magnetic resonance imaging (MRI) measurements, with which there is excellent agreement.     

Evaluation of the diffusion coefficient of rapeseed oil during solvent extraction with hexane

The diffusion coefficient of rapeseed oil was determined from data obtained during time-varied solvent extraction experiments. The experiments were carried out in a Gülbaran extractor-diffuser with hexane as the solvent. A relationship was found between the slope of the diffusion line and the shape and size of the rapeseed particles. This relation can be used to calculate the diffusion coefficient. A diffusion coefficient of 3.4×10⁻⁸ cm²/s was determined from the experimental data.     

Diffusion of liquids in molten polymers: Mutual diffusion coefficient dependence on liquid miscibility and polymer molar mass

This paper addresses two important features of the diffusion of liquids into a molten polymer matrix: the dependence of the mutual diffusion coefficient on the liquid miscibility and molar mass of polymers. In addition, a rheological approach is chosen for its capacity to support modeling, and the mutual diffusion coefficient expressed with the free-volume theory, is estimated by an inverse method. For that purpose, the diffusion process of 2,3-epoxypropyl-phenylether (EPPE) and the N-ethylaniline (NEA) in three molten poly(ethylene-co-vinyle acetate) elastomers (EVA) having different molar masses is examined. The NEA is fully miscible with EVA and its diffusion process is not dependent on the molar mass of the polymer. On the other hand, the diffusion process of EPPE, that is partially miscible with EVA, is strongly influenced by the molar mass of the EVA. Furthermore, the evolution of the concentration gradient during the diffusion process of EPPE is driven by the necessity for the mixture to form a two-phase system with an EVA-rich phase and an EPPE-rich phase. In this case, the concentration gradient through the sample is not continuous at a macroscopic scale. Consequently, the calculation procedure is only applied during the early stages of the diffusion. For EPPE, the variation of the mutual diffusion coefficient with the molar mass of EVA is taken into account through the variation of the interaction parameter. Actually, despite the imperfections of the model, our experimental observations and rheological inverse calculation of the diffusion process are in agreement with the findings of the free volume theory of the diffusion.     

Unsteady mass transfer around axisymmetric drops of revolution in variable diffusion coefficient liquids

Unsteady mass transfer in the continuous phase around axisymmetric drops of revolution at high Peclet numbers has been theoretically studied. The liquid is a binary system, having a variable diffusion coefficient, which depends on the solute concentration. The solution to the problem was obtained by extending the theory of Favelukis and Mudunuri, developed for a constant diffusion coefficient liquid. The procedure consists of transforming the differential mass balance, for a binary system, into a partial differential equation which has an analytical solution, and an ordinary differential equation that needs to be solved numerically. Solutions to a large number of problems can be immediately obtained with the only requirements being the shape of the drop, the tangential velocity at the surface of the drop and an expression for the variable diffusion coefficient liquid. An approximate analytical solution is also suggested which is in excellent agreement with the numerical results.     

Atomistic molecular dynamics simulations of gas diffusion and solubility in rubbery amorphous hydrocarbon polymers

Diffusion coefficients D of H₂, He, O₂, N₂, and CO₂ in different rubbery amorphous polymeric matrices were estimated by atomistic molecular dynamics simulations at 298 K using the Einstein relationship, and compared with the relevant experimental values, where available. The simulated diffusion coefficients D of all the gases in all polymers considered almost regularly decreased with increasing molecular gas volumes and increasing polymer glass transition temperature. Further, solubility coefficients and heats of solution were obtained for all gases from Grand Canonical Monte Carlo simulations, which were also used to calculate sorption isotherms. In general, there is a good agreement between experimental and simulated values of diffusion and solubility coefficients for all gases considered.     

用Simha-Somcynsky状态方程改进高分子中溶剂扩散系数模型

将Simha-Somcynsky状态方程和Vrentas-Duda的自由体积理论模型相结合，提出改进的高分子中溶剂扩散系数模型.改进的模型利用状态方程和WLF理论定义的自由体积分数确定扩散过程的有效自由体积，避免原模型中繁琐的黏弹性实验测定.对苯、甲苯、乙苯、氯仿在聚苯乙烯、聚异丁烯和聚醋酸乙烯酯中的扩散系数的计算结果表明，改进模型的预测值与实验值取得较好一致，且自扩散系数的预测精度比原模型高.同时，改进的模型能够反映压力对扩散系数的影响.溶剂扩散系数随外界压强增加而减小，当溶剂浓度较低时，压强的影响非常显著，扩散系数可相差几个数量级.随着溶剂浓度升高，扩散系数接近常压时的扩散系数，压强影响可以忽略.     

Sorption and diffusion measurements in ternary polymer-solvent-solvent systems by means of a magnetic suspension balance—Experimental methods and correlations with a modified Flory-Huggins and free-volume theory

Diffusion and sorption data of methanol and toluene in the ternary system methanol-toluene-poly(vinylacetate) (pvac) were measured by means of a magnetic suspension balance (MSB). Ternary diffusion coefficients were determined from sorption kinetics with a method of Crank [1975. The Mathematics of Diffusion, second ed. Claredon Press, Oxford] classically used for binary polymer solvent systems. Assumptions and limitations for this method are discussed. Sorption data of methanol and toluene in the ternary system were correlated with a modified Flory-Huggins theory taking four instead of three interaction parameters into account and compared with predictions of UNIFAC-FV. All four binary Flory-Huggins interaction parameters were correlated as a function of concentration, determined from binary polymer-solvent sorption measurements and from solvent-solvent equilibrium data. The modified Flory-Huggins approach for ternary systems predicts the two limiting cases for the binary polymer-solvent as well the two solvent-solvent equilibria. Diffusion coefficients determined from sorption kinetics measurements were correlated with free-volume theory predictions of Vrentas et al. [1984. Self diffusion in polymer-solvent-solvent systems. Journal of Polymer Science, Polymer Physics Edition, 22, 459-469] and compared with a few available literature data from Surana et al. [1998. Diffusion and equilibrium measurements in ternary polymer-solvent-solvent systems using inverse gas chromatography. Industrial and Engineering Chemistry Research, 37, 3203-3207]. Cross diffusion terms are not taken into account. Diffusion and sorption data, determined with this gravimetric method, were used in model simulations with modified Flory-Huggins and free-volume theory to predict drying curves of ternary methanol-toluene-pvac solutions. The results were compared with previously published experimental results performed by means of Inverse-Micro-Raman-Spectroscopy (IMRS) from Schabel [2004. Trocknung von Polymerfilmen - Messung von Konzentrationsprofilen mit der Inversen-Mikro-Raman-Spektroskopie. Ph.D. Thesis, Universität Karlsruhe (TH), Germany].     

基团贡献法确定简化空穴理论状态方程的分子参数

本文对作者开发的简化空穴理论状态方程的纯物质参数做了基团贡献处理，得到了１４个基团参数，可以比较好地预测正构烷烃、异构烷烃、环烷烃、芳香烃及部分聚合物的热力学性质。     

Determination of chloride diffusion coefficient of concrete using open-circuit potential measurements

The rate of chloride ion ingress into concrete is of great importance for the performance of reinforced concrete structures exposed to chloride-contaminated environments. The service life of reinforced concrete structures subjected to such exposure conditions is closely related to the rate of chloride ion diffusion through the concrete. This paper presents the determination of the apparent chloride diffusion coefficient of concrete using open-circuit potential measurements. The chloride diffusion coefficients obtained are in the range of 6.4×10⁻⁸ to 12.4×10⁻⁸ cm²/s for a simulated seawater tidal condition, which is quite consistent with those reported in the literature. This indicates that open-circuit potential measurements can be considered as an approximate but simple method of assessing the diffusivity of chloride through concrete. Limited with the testing conditions and the characteristics of concrete used, results indicated that the time necessary for corrosion initiation of concrete with a cover depth of 7 cm ranges from 3 to 6 years for the seawater exposure, whereas it is only 1.5 years for a 3% sodium chloride exposure.     

Analysis of the solvent diffusion in glassy polymer films using a set inversion method

Within the framework of solvent diffusion in glassy polymers, this paper concerns an experimental study of toluene sorption and desorption in P(MMA/nBMA) copolymer films. Gravimetric experiments (quartz microbalance) are performed in a pressure and temperature controlled chamber. Coupling between solvent diffusion and viscoelastic relaxation is taken into account through the time-dependent solubility model, based on the Fick diffusion equation inside the film and a time variable boundary condition at the film/vapor interface. Viscoelastic relaxation is described by a first order model or by a stretched exponential. In the present paper, a special focus is given on the set inversion method used to analyze the data and to derive well-defined uncertainty intervals upon each determined quantity, taking all the uncertainties on the weight measurements into account. We find that the mutual diffusion coefficient strongly decreases in the glassy state, of about two orders of magnitude for a 0.05 decrease in the solvent weight fraction.     

Biochemical reaction and diffusion in seafloor gas hydrate capillaries: Implications for gas hydrate stability

A one-dimensional mathematical model is presented to describe biochemical reactions and diffusion occurring within massive seafloor gas hydrates. Methanogenesis and anaerobic methane oxidation coupled with sulfate reduction are the two reactions analyzed with emphasis on gas hydrate stability. Many numerical simulations are being developed to predict gas hydrate formation, dissociation, and stability. The model complements these simulations as a subunit by incorporating the consequences of kinetic and transport processes occurring within seafloor gas hydrate capillaries. Better predictions of gas hydrate stability will assist in understanding the role of gas hydrates in the global carbon cycle, particularly as pertaining to global warming.     

Effect of sample size on solvent extraction for detecting cocontinuity in polymer blends

The effect of sample size on the results of solvent extraction measurements for detecting cocontinuity in polymer blends was investigated. Poly(ethylene oxide)/polystyrene (PEO/PS) blend samples of several thicknesses were analyzed by removing the PEO phase using water extraction. The experimental degree of continuity was shown to have a linear dependence on the reciprocal of sample thickness. A model is proposed to explain this dependence and to allow the bulk or true degree of continuity to be determined. Measurement of the bulk degree of continuity is useful for understanding properties of cocontinuous polymer blends such as electrical conductivity, impact strength, or tensile strength.     

FTIR-ATR studies of the sorption and diffusion of acetone/water mixtures in poly(vinyl alcohol)

The diffusion kinetics of water and acetone into dried PVOH polymer films have been measured simultaneously using the FTIR-ATR technique. The data have been fitted to a pseudo-Fickian model, along with allowance for a ‘lag’ time which lengthens considerably when the water mole fraction is low. It has been found that a case II model is viable at short times when the polymer is ‘glassy’ (<T_g). However, as water enters the polymer (unzipping the chain-chain hydrogen bonding), conversion to a ‘gel’ is rapid and the crystallinity drops concurrently. A Fickian-like model then becomes viable at intermediate times. FTIR-ATR is an excellent technique with which to study sorption from solvent mixtures. In this case, for example, we have demonstrated that acetone does not enter a dry polymer film and that the micro-crystallinity of the PVOH returns at longer times. Neither of these two potentially important results could have been obtained using gravimetric methods.     

Quantitative modeling of scratch-induced deformation in amorphous polymers

In order to predict scratch performance of polymers, the present study focuses on quantitative assessment of various scratch-induced deformation mechanisms based on a set of model amorphous polymers via numerical modeling. A modification of Ree-Eyring theory is used to account for the rate dependent behavior of the model polymers at high strain rates using the experimental data obtained at low strain rates. By incorporating the rate and pressure dependent constitutive and frictional behaviors in the finite element methods (FEM) model, good agreement has been found between FEM simulation and experimental observations. The results suggest that, by including appropriate constitutive relationship and frictional model in the numerical analysis, the scratch behavior of polymers can be quantitatively predicted with reasonable success. Usefulness of the present numerical modeling for designing scratch resistant polymers is discussed.     

Modeling diffusion limitation in solid-oxide fuel cells

Effect of surface diffusion on the performance of solid-oxide fuel cell is investigated. A methodical approach for the evaluation of surface diffusion coefficients of various adsorbed species based on bond-order conservation Morse potential (BOC-MP) method is presented. The surface diffusion fluxes are used for the evaluation of temporal changes in surface coverages. Our analysis shows that surface diffusion does not lead to the concentration losses in solid oxide fuel cells. Further analysis is carried out and results are presented to substantiate the significance of interface diffusion on the behavior of voltage at limiting current.     

Development of a predictive model for polymer/solvent diffusion coefficient calculations

A new calculation procedure for free‐volume parameters is considered in this work by using viscosity prediction methods and the Levenberg‐Marquardt calculation scheme. All parameters used in the Vrentas–Duda free‐volume theory can be estimated from pure component properties. The prediction results are compared with experimental data for some polymer/solvent systems. The diffusion coefficient calculated by Vrentas–Duda theory can be used in the modeling of membrane separation processes. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Estimation of concentration-dependent diffusion coefficient in drying process from the space-averaged concentration versus time with experimental data

The estimation of a concentration-dependent diffusion coefficient in a drying process is known as an inverse coefficient problem. The solution is sought wherein the space-average concentration is known as function of time (mass loss monitoring). The problem is stated as the minimization of a functional and gradient-based algorithms are used to solve it. Many numerical and experimental examples that demonstrate the effectiveness of the proposed approach are presented. Thin slab drying was carried out in an isothermal drying chamber built in our laboratory. The diffusion coefficients of fructose obtained with the present method are compared with existing literature results.