Diffusion of saturated hydrocarbons in low density polyethylene (LDPE) films

The diffusion coefficients at zero penetrant concentration, D₀, of n-heptane, n-heptane, n-octane, n-decane, and 2,2,4-trimethylpentane (TMP) in LDPE were obtained in the range of 25–50°C, using the desorption method. The dependence of D₀ on the size and shape of the penetrant is reported. It was found that D₀ decreases with increasing penetrant molecule size. The activation energies of diffusion in the temperature range of 25–50°C increase with increasing penetrant molecule size and are independent of temperature. The results are interpreted in terms of the free volume theory and semiquantitative estimates of the free volume parameters are reported.     

A Model for the Diffusion of Moisture in Adhesive Joints. Part III: Numerical Simulations

The coupling mechanisms between the diffusion process and the viscoelastic response of an adhesive are explained. A numerical scheme for fully-coupled solutions is proposed and implemented in a two-dimensional finite element code. A number of numerical simulations are presented in order to illustrate the importance of the following features: (1) the bulk viscoelastic behavior, (2) penetrant size, (3) physical aging, (4) the strain dependence of the diffusion coefficient, (5) the concentration dependence of the diffusion coefficient and (6) differential, swelling. The effect of moisture intrusion on the stress (strain) distribution across a butt joint is also presented.     

Diffusion of water vapour in cellulose acetate: 1. Differential transient sorption kinetics and equilibria

The concentration dependence of the diffusion coefficient D, of the cellulose acetate/water vapour system has been investigated: aspects of the non-Fickian behaviour of the system are reported. Kinetic and equilibrium data, were obtained for membranes of different thicknesses from a series of differential sorption experiments along both limbs of the hysteresis loop. The data are treated in alternative ways. It is concluded that we may distinguish two rate-determining molecular relaxation processes: a relatively fast one, prevailing during the initial stages of absorption, which is succeeded by a considerably slower and more drastic reorganization of the polymer structure. During the latter stage the solubility coefficient S is shown to possess a long-term time dependence, which is attributed to penetrant cluster formation. D obtained from desorption kinetics increases with concentration, whereas the apparently concentration-independent D on the absorption side is assumed to be due to partial immobilization of penetrant in regions where penetrant clusters are developed.     

Effects of chain stiffness and penetrant size on penetrant diffusion in simple polymers: deduced relations from simulation and PRISM theory

Molecular dynamics simulations in the NVT ensemble were performed for a repulsive system of bead-spring polymer chains with angle constraints. The diffusion coefficients of spherical penetrants were measured for different size penetrants as the angle constraints were varied. The scaling of the diffusion coefficient with penetrant size varies as a function of chain stiffness from liquid-like behavior to polymeric behavior. Free volume distributions were calculated from both simulation and PRISM theory. It is found that free volume distributions and mean void size are constant with chain stiffness although the diffusion coefficient changes by a factor of two. This suggests that while free volume is necessary for diffusion to occur, binary collisions and chain relaxation also play a role in determining penetrant diffusion. The relative contributions of these factors to the diffusion coefficient may change as a function of chain stiffness.     

Diffusion of organic penetrants through low density polyethylene (LDPE) films: Effect of size and shape of the penetrant molecules

The diffusion coefficient at zero penetrant concentration D₀ of dichloromethane, chloroform, carbon tetrachloride, cyclohexane, benzene, o-xylene, m-xylene, and p-xylene, and n-hexane in LDPE were measured at 25°C, using the desorption method. The D₀ values obtained in this way are correlated with the size, shape, and chemical nature of the penetrant molecules. The temperature dependence of the diffusion coefficients of toluene and n-hexane in LDPE are also reported in the limited temperature range of 25–45°C. It indicates that, in spite of a size larger than that of toluene, n-hexane has a lower activation energy of diffusion.     

Diffusion of electrolytes across inhomogeneous permselective membranes

Permeability of sulphuric acid through cation-exchange membranes of different inhomogeneity has been investigated. It has been found that the diffusion coefficient of the acid within the membrane D _i is related to that in the aqueous solution D_0,i by the equation: where V is the membrane volume fraction inaccessible for diffusion. This volume was calculated as the sum of the polymer volume fraction V_p and the volume fraction of the internal solution V_G with the local concentration of the ionogenic groups equal or higher than the concentration of the external electrolyte. Introducing the volume V into the equations by Meares, Prager and Yasuda it is possible to find a high correlation between D _i and f(V), which is related to the membrane structure and their inhomogeneity. The best results have been obtained with the equation of Prager; the calculated diffusion coefficients D_0,i for different membranes are then close to the coefficient of H₂SO₄ in a free aqueous solution.     

A free-volume interpretation of the influence of the glass transition on diffusion in amorphous polymers

A new version of the free-volume theory of diffusion is used to describe polymer–solvent diffusion both above and below the glass transition temperature. Expressions are derived for the temperature dependence of the mutual diffusion coefficient and for the effective activation energy in the limit of zero penetrant concentration. The theory also describes the effect of the glass transition on the diffusion process. Predictions of the theory are compared with available diffusivity data for amorphous polymer–solvent systems.     

A principle of equivalent states for liquid transport properties

A principle of equivalent states for liquid transport properties is developed for binary liquid systems. Under the assumption that the activity and viscosity corrected mutual diffusion coefficient is a function of the solution molar volume, working equations are developed for the concentration dependence of the binary mutual diffusion coefficients. The results apply to binary liquid systems for which the coefficient of thermal expansion is independent of composition and for which the difference in activation free energies for viscous flow and diffusion is also independent of composition. The results are tested with available data to show that the binary mutual diffusion coefficient can be predicted from the infinitely dilute values and the solution viscosity and thermodynamics for a large number of liquid systems.     

聚合物-溶剂体系中能量对溶剂扩散的影响

The Vrentas-Duda free-volume theory has been extensively used to correlate or predict the solvent diffusion coefficient of a polymer/solvent system.The energy term in the free volume diffusion equation is difficult to estimate,so the energy term was usually neglected in previous predictive versions of the free volume diffusion coefficient equation.Recent studies show that the energy effect is very important even above the glass transition temperature of the system. In this paper, a new evaluation method of the energy term is proposed,that is the diffusion energy at different solvent concentrations is assumed to be a linear function of the solvent diffusion energy in pure solvents and that in polymers under the condition that the solvent in infinite dilution.By taking consideration of the influence of energy on the solvent diffustion,the prediction of solvent diffusion coefficient was preformed for three polymer/solvent systems over a wide range of concentrations and temperatures.The results show an improvement on the predictive capability of the free volume diffusion theory.     

Concentration Dependence of the Diffusion Coefficients of Disperse Dyes in Polyethylene Terephthalate

Diffusion coefficients of disperse dyes have been calculated by Matano's method from diffusion profiles in polyethylene terephthalate(PET). The diffusion coefficients (D_c) clearly indicate concentration-dependence. It has been found, from the densities of the dyed PET and the dye, that there is no overall change in the volume of the PET and dye in dyeing. The instrinsic diffusion coefficients have been calculated from D_c and the volume fraction (φ₁) of penetrant in the amorphous region. From these values, thermodynamic diffusion coefficients (χ?) were obtained. It has been found that the relation between 1/log (χ?/χo) and 1/φ₁ is a straight line, and it therefore seems reasonable to assume that the diffusion of disperse dyes in PET can be described by Fujita's ‘free volume theory’ for the diffusion of low molecular-weight organic compounds in an amorphous high-polymer.     

Diffusion of Water into Silica Glass at Low Temperature

Diffusion of water into silica glass was measured in the temperature range of 200° to 750° by treating the glass in air containing a constant water vapor pressure and analyzing the concentration profile using a Fourier transform infrared spectrometer. In the short-time diffusion heat treatments, the surface concentration was lower and the apparent diffusion coefficient was higher than the corresponding steady-state values. The temperature dependence of the steady-state diffusion coefficient showed two different activation energies. Above ∼550° the diffusion coefficients were similar to the published results with an activation energy of ∼80 kJ/mol, while below ∼550°, the diffusion coefficient was higher than the value obtained by extrapolation from higher temperatures, and the activation energy was ∼40 kJ/mol. Correspondingly, the water solubility–temperature relation showed a sudden change at around the same temperature: at temperatures above this temperature the solubility increased with decreasing temperature, while at lower temperatures the trend was reversed. It was suggested that this observed peculiarity was caused by the initial nonequilibrium reaction between water and SiO₂ glass and a change in enthalpy of the glass–water reaction.     

Diffusion in polymers

Concentration dependent diffusion coefficients explain Case II type diffusion. Solutions to the diffusion equation yield straight lines for weight gain vs time when the exponential variation of the diffusion coefficient is included. Boundary layer resistance together with concentration dependent diffusion coefficients explain Super Case II type diffusion. The increase in the rate of weight gain after a prolonged period is predictable. The surface concentration rises slowly to its equilibrium value in this case. Boundary layer resistance appears to be quite common, particularly where the penetrant has low affinity (not a true solvent) for the polymer, such as water in most polymers or hexane in polystyrene. Boundary layer resistance is quite significant for coatings (where film thicknesses are usually measured in microns), accounting for the majority of the resistance in some cases. A method to separate diffusional resistance from the surface resistance is suggested, but studies at different film thicknesses appear mandatory.     

Permeation of N-butane,propane and ethane through ethylcellulose

The permeation of n-butane, propane, and ethane in ethylcellulose has been measured over a pressure range from 25 to 200 mm Hg and over the temperature range from 30 to 70°C. The permeation and diffusional time lag of each of the three gases in ethylcellulose is pressure dependent. Transport of the gases through ethylcellulose can be described by the partial immobilization model. It was found that, in general, the Langmuir-mode species diffusion coefficients are lower than the Henry's law species diffusion coefficients. The logarithm of diffusion coefficients at zero penetrant concentration varies linearly with the square of the molecular diameter of n-butane, propane, and ethane permeating through ethylcellulose. This relationship suggests that the diffusion process depends upon the availability of sufficient cross-sectional area for the penetrant to diffuse. An Arrhenius temperature dependence was observed for permeation coefficients and diffusion coefficients for n-butane, propane, and ethane in ethylcellulose. The activation energy of diffusion at zero penetrant concentration is directly proportional to the square of the gas molecular diameter and the entropy of activation. This observation is consistent with the view that the activation energy of diffusion is associated with the energy required to produce a space of sufficient cross-section for the diffusion molecule to pass.     

Diffusion and sorption behavior of glycidyl methacrylate in styrene butadiene rubber

In this study, the diffusion and sorption behavior of glycidyl methacrylate in styrene butadiene rubber (SBR) was investigated as a function of waste tire powder content, sulfur content (i.e., the crosslink density), and temperature by using the gravimetric sorption method. The results indicate that penetrant solubility increases as sulfur and waste tire powder contents decrease, whereas the temperature affects the solubility favorably. The results also indicate that mutual diffusion coefficients decrease as the sulfur and waste tire powder contents increase. This behavior was interpreted in terms of free volume of the polymer and tortuosity. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 2701–2706, 2002     

Diffusion of disperse dye in atactic polystyrene

Sublimative desorption experiments were carried out on atactic polystyrene containing p-nitroaniline, p-aminoazobenzene, or C.I. Disperse Yellow 7 at 114°–170°C (above the T_g of the polymer). The diffusion coefficient of each dye in the polymer increased monotonically with rise in the desorption temperature. The mode of this change was exactly expressed by a WLF relation having the universal parameters given for amorphous polymers. The value of B_d, defined as the ratio of diffusional penetrant volume to that of a segment of the chain molecule, varied from 0.37 to 0.70 for the different dyes used. It is also shown that the B_d value is related to the logarithmic rotational volume of the dye molecule estimated from a molecular model.     

用状态方程改进的高聚物中溶剂扩散系数预测模型

将Simha-Somcynsky状态方程引入Vrentas-Duda自由体积理论模型,提出改进的高聚物-溶剂体系扩散系数模型,计算常压下橡胶态高聚物中有机溶剂扩散系数对浓度和温度的依存关系.利用高聚物结构单元的范德华体积导出高聚物自由体积分数表达式,通过Simha-Somcynsky方程求取高聚物体积以及对溶剂分子扩散有效的自由体积,避免原模型中繁琐的高聚物粘弹性实验测定和回归高聚物自由体积参数,提高了自由体积理论的预测能力.使用改进的模型预测了苯、甲苯、乙苯和三氯甲烷在聚苯乙烯、聚异丁烯和聚醋酸乙烯酯中的自扩散系数和互扩散系数,计算结果表明改进的自由体积模型具有较高的预测精度.     

Effect of glass transition on the concentration dependence of self‐diffusion coefficients

The free‐volume theory of diffusion is used to predict the effect of the glass transition on the concentration dependence of the solvent self‐diffusion coefficient at constant temperature. The theoretical prediction is in agreement with experimental data. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 1682–1684, 2003     

Evidence of dual mobility in sulfur dioxide-polyarylate system: An integral sorption analysis

Integral sorption/desorption measurements were carried out for the sulfur dioxide-glassy polyarylate polymer system at 25°C, 40°C, 55°C, and 63°C. The transport of sulfur dioxide in the glassy polyarylate polymer was governed by Fickian diffusion. The effective diffusion coefficient of sulfur dioxide increased with increasing penetrant concentration. The concentration dependence of the effective diffusion coefficient is explained on the basis of the partial-immobilization model developed by Paul and Koros. The mobility of the molecules sorbed in the Langmuir mode is shown to be significantly lower than the mobility of the molecules in Henry's law dissolution mode. The predictions of permeability values as a function of upstream gas pressure are presented. The equilibrium sorption isotherms for this system are well represented by the dualmode sorption model. The eltergetics and the temperature dependence of the dual-mode parameters are also discussed.     

Numerical simulation of anomalous penetrant diffusion in polymers

This work introduces a new numerical algorithm that can be used to analyze complex problems of penetrant transport. Penetrant transport in polymers often deviates from the predictions of Fick's law because of the coupling between penetrant diffusion and the polymer mechanical behavior. This phenomenon is particularly important in glassy polymers. This leads to a model consisting of two coupled differential equations for penetrant diffusion and polymer stress relaxation, respectively. If the polymer relaxation is the rate-limiting step, both the concentration and stress profiles are very steep. A new algorithm based on a finite difference method is proposed to solve the model equations. It features the development of a tridiagonal iterative method to solve the nonlinear finite difference equations obtained from the finite difference approximation of the differential equations. This method was found to be efficient and accurate. Numerical simulation of penetrant diffusion in glassy polymers was performed, showing that the integral sorption Deborah number is a major parameter affecting the transition from Fickian to anomalous diffusion behavior. © 1993 John Wiley & Sons, Inc.     

Concentration and temperature dependence of diffusional deborah number during dodecane transport in crosslinked polystyrene

The diffusional Deborah number, De, defined as the ratio of characteristic relaxation time to characteristic diffusion time was determined as a function of concentration and temperature in the dodecane transport process in polystyrene. The characteristic relaxation time was obtained from the viscoelastic properties of dodecane/polystyrene systems measured by a dynamic mechanical analyzer. The characteristic diffusion time was obtained from the concentration and temperature dependence of the diffusion coefficient measured by NMR PGSE method. Above the room temperature the Deborah number changed significantly during isothermal transport process; however, the transport mechanism did not deviate from the Fickian transport as the order of De was still greater than 1. Around the room temperature the transport mechanisms represented by the resulting diffusional Deborah number changed significantly as the order of magnitude approached 1 with the temperature decreasing from 50°C to the room temperature. The transport mechanism predicted from the diffusional Deborah number was verified by the diffusional exponent, n, of an exponential time-dependence of the penetrant uptake.