Diffusion coefficient measurements by solvent absorption in concentrated polymer solution

Diffusion coefficient measurements for solvents in concentrated polymer solutions require consideration of both concentration dependence of the diffusion coefficient and surface resistance to mass transport. Solutions to the diffusion equation have been generated where these effects are explored. A method to account for both concentration dependence and surface (absorption) resistance in the experimental determination of diffusion coefficients is given and demonstrated with an example where a multiplying factor of over 300 is required to adjust the apparent diffusion coefficient to the value sought.     

EFFECTS OF MASS TRANSFER ON THE THINNING AND RUPTURE OF A PLANE PARALLEL LIQUID FILM

The effects of mass transfer and physical properties upon the thinning and rupture of adraining plane parallel film are investigated.An equation is derived in which the thinning rate is afunction of bulk properties.surface properties(surface tension,surface viscosities,and the variationof surface tension with surface concentration),intermolecular forces(London-van der Waals forcesand electrostatic double layer forces),adsorption and surface diffusion coefficients,bubble size andfilm thickness.An estimation for the critical thickness at which a film rupture is carried out and thecoalescence time is obtained by integration to the critical thickness,The coalescence time is predictedas a function of bulk and surface properties,London-van der forces,adsorption and surfacediffusion coefficients,and bubble size.     

Determination of Deterrent Profiles in Nitrocellulose Propellant Grains Using Confocal Raman Microscopy

The diffusion profile of dinitrotoluene deterred nitrocellulose based small arms propellants is investigated with Confocal Raman microscopy. The diffusion profile in all samples was found to be non‐Fickian Case II diffusion – a steady concentration with a sharp drop. Diffusion depth from the outside surface was found to be much greater than the interior perforation surface. A strong correlation was found between the perforation size of samples and their inside edge diffusion depth, while the outside surface was found to be more dependent on total diameter and deterrent concentration. Samples were also artificially aged to investigate movement of the deterrent over time.     

INFLUENCE OF RHEOLOGICAL PROPERTIES IN MASS TRANSFER PHENOMENA: SUPER CASE II SORPTION IN GLASSY POLYMERS

The sorption rate of swelling penetrants in glassy polymers has been considered as controlled both by the swelling kinetics and the penetrant diffusion through the swollen layer. The stress exerted on the glassy core at the moving boundary is the driving force for the swelling, and results from an osmotic stress and a differential swelling stress contribution. During the sorption process, the osmotic stress at the moving boundary decreases, due to the increasing diffusion resistance; the differential swelling stress, on the contrary, increases giving rise to an acceleration of the front velocity (Super Case II).

The particular case of negligible diffusion resistance in the swollen region is here considered in more detail. It is shown that the rheological properties of both swollen and glassy phases crucially enter the mass transport problem; thestress relaxation in the swollen region must be taken into account in order to obtain a thickness dependent Super Case 11 effect     

Microscopic spreading of nonreactive perfluoropolyalkylether film on amorphous carbon surfaces

A spreading mechanism of nonfunctional perfluoropolyalkylehter (PFPE) on carbon surfaces is proposed. For the thin thin-film regime, adsorption-desorption is a main driving force for spreading, and the surface diffusion coefficients increase as the film thickness increases. A two-dimensional virial equation is employed to explain the dependency of surface diffusion coefficient on the film thickness. For the thick thin-film regime, the spreading characteristic is determined by the disjoining pressure gradient. We adopt a slip boundary condition to analyze the thick thin-film regime. This modification of the boundary condition reasonably explains the dependence of surface diffusion coefficients on film thickness.     

Effects of film thickness and inhibitor concentration on the sorption and thermal polymerization of acrylic acid in low-density polyethylene

We investigated the effects of hydroquinone monomethyl ether concentration and film thickness upon the thermal polymerization of acrylic acid on low-density polyethylene. The thermal polymerization of acrylic acid on low-density polyethylene depended on the concentration of hydroquinone monomethyl ether inhibitor. It was a free-radical reaction with initiation on the film surface and then proceeding to the bulk matrix. The process was not controlled by monomer diffusion for the range of film thickness of 90–200 μm. It became a diffusion-controlled process at higher film thicknesses ( > 200 μm). A film layer of up to 100 μm was proposed as the limiting thickness for a diffusion-free process. © 1993 John Wiley & Sons, Inc.     

Concentration dependence,boundary layer resistance,and the “time-lag” diffusion coefficient

Diffusion coefficient measurements have been shown to be strongly influenced by boundary layer resistance and concentration dependence. When half-times for desorption or absorption are used to find diffusion coefficients from the equation for a constant coefficient (T_½ = Dt/L² = 0.049), the values so obtained require correction. Diffusion coefficients found by the “time-lag” method are also influenced strongly by surface resistance and concentration dependence. The usual equation for a constant diffusion coefficient gives a break-through curve with an extrapolation to the time-lag, T_L = Dt/L² = 1/6. This factor can rise to ½ for concentration dependence. Where boundary layer resistance is encountered, (a situation which appears to be quite common), T_L is significantly increased and the slope at steady state is decreased.     

铂盐溶液浸渍Nafion膜的外扩散

以Nemst-Planck方程为基础,对铂盐溶液浸渍Nation膜过程建立了非稳态的外扩散过程数学模型,采用预测-校正方法对模型求解,经Powell法搜索寻优,获得了液膜扩散系数及液膜厚度,计算值与实测值吻合较好。     

Sorption and diffusion of alcohols in amorphous polymers

The effects of polymer composition and penetrant molecular size on the solubility and diffusivity of alcohol vapors in a series of well characterized isoprene-methyl methacrylate copolymers and their corresponding homopolymers has been investigated at room temperature. The rate of sorption behavior changes progressively from Fickian to non-Fickian, to Case II to “Super Case II” transport with increasing methyl methacrylate (MMA) content in the polymers. The equilibrium solubility of the alcohols increases linearly with increasing penetrant molecular size for polymers which are above their glass transition temperature and decreases for polymers which are below their T_g. The solubility also initially increases as an approximately linear function of MMA content in the copolymers. At about 55 mole percent MMA, the sorbed concentration either levels off or passes through a maximum depending on the size of the penetrant. The apparent “diffusion coefficients” (D) decrease with increasing molecular volume of the penetrants. An exponential dependence was found between these two variables for PMMA. These “diffusion coefficients” also decrease exponentially with increasing MMA content in these polymers. However, at 55 mole percent MMA the copolymer undergoes a rubber to glass transition at the temperature of the experiments. On this basis, it is suggested that the hindered chain segmental motion contributes to the sorption process in addition to strictly thermodynamic considerations. Free volume theory can be used to explain the mechanism of diffusion through the rubbery polymers while the “hole” theory can be applied to explain the transport of the penetrants through the glassy polymers.     

A study on desorption resistance in pervaporation of single component through dense membranes

Desorption resistance taking place between a membrane surface and a permeate vapor phase, which had not accounted for an overall mass transfer resistance in pervaporation, was studied. The resistance-in-series concept and Flory-Huggins thermodynamics were used to establish model equations for evaluating the desorption resistance in the permeation of a single component. In order to exclude any possible concentration polarization of permeants occurring in feed adjacent to a membrane surface, the permeations of pure water through polyether imide membranes with various thicknesses were observed at different permeate pressures. From the permeation data of pure water through the membranes with help of the model equations, both the permeability coefficient based on a general flux equation expressed in terms of the chemical potential driving force and the desorption resistance were determined quantitatively. According to the model equations, the desorption resistance could be affected by two factors: membrane thickness and permeate pressure. The magnitude of the desorption resistance was dependent mainly on permeate pressure, and the importance of the resistance relative to diffusion resistance in the membrane for the overall process became more significant with decreasing membrane thickness at a given permeate pressure. As the membrane thickness decreased and/or the permeate pressure increased, the desorption resistance was observed to be more significant, causing higher chemical activity and a higher concentration of the permeant at the downstream interface of the membrane. In some cases, the desorption resistance was predominant over the diffusion resistance in very thin membrane thicknesses. This study seeks to emphasize the importance of the desorption resistance on the transport of components at small membrane thicknesses or high permeate pressure. © 1997 John Wiley & Sons, Inc.     

Diffusion of disperse dyes into microfibres and conventional polyester fibres

The dyeing properties of polyester microfibres are quite different from those of conventional polyester fibres. In this paper, the sorption isotherms, the diffusion coefficients and the amount and rate of dye uptake into the fibres are compared for both conventional fibres and microfibres. Shibusawa's approximation of Hill's equation is used to compute the diffusion coefficient, which depends on the initial dye concentration, the time and the fibre count for a fixed temperature (130 °C). The kinetic properties are analysed only under infinite bath conditions. The sorption isotherms and diffusion coefficients as functions of time for conventional polyester fibres and microfibres are compared by considering the surface area and the diffusional boundary layer influence.     

Ohmic contacts to semiconducting diamond using a Ti/Pt/Au trilayer metallization scheme

Ohmic contacts have been fabricated on a naturally occurring type IIb diamond crystal using an annealed Ti/Pt/Au trilayer metallization where the Pt served successfully as a barrier to Ti diffusion into the Au capping layer. However, a specific contact resistance could not be reliably determined using transmission line model measurements. Auger microanalysis revealed the presence of Ti on the diamond surface near the ohmic contact pads. The most likely origin of the Ti on the diamond surface was determined to be lateral diffusion from beneath the contact pads. This would have produced a nonuniform concentration of Ti across the diamond surface which, in turn, would have affected the diamond sheet resistance in a complicated way.     

Diffusion of low molecular weight substances into a laminar film. I: Rigorous solution of the diffusion equation in a composite film of multiple layers

A rigorous solution of the diffusion of penetrant into a laminar film comprised of multilayers of m components is presented by an orthogonal-expansion method. As the simplest practical cases of m ? 2 and m ? 3, with stepwise distribution of both diffusion coefficients and solubility coefficients at the boundary between respective layers, the diffusion properties in the transient state are analyzed in detail. That is, changes in the penetrant concentration distribution within the laminar film and the total amount of penetrant sorbed within the film both with time after exposing the film to an atmosphere of fixed penetrant concentration are calculated for A–B as well as A–B–A type layer arrangements. The calculation is performed while keeping (L₂/L₁) at a constant value of 2.0 but varying the diffusion coefficient ratio of (D₁/D₂) from 10² to 10^?2, and/or varying the solubility coefficient ratio of (S₁/S₂) from 1 to 10, where L₁ and (L₂ ? L₁) are the thickness D₁ and D₂ are the diffusion coefficients of penetrant, and S₁ and S₂ are the solubility coefficients in the A-component and B-component, respectively. The sorption curves deviate considerably from those of Fickian curves of homogeneous film with (D₁/D₂) ? 1 in their respective ways. The results obtained here can be applied to the diffusion in a single component polymer film having a surface layer with different diffusion properties from that of the inner side of the film caused by differing distributions in molecular orientation or degrees of crystallinity.     

Modeling of backwash cleaning methods for RO membranes

A new comprehensive and time-dependent 2D model using finite element method (FEM) was developed to account for different versions of the backwash (BW) cleaning method for RO membranes. Two distinct cases of backwash were identified: Case 1, which has no applied pressures and velocities; and Case 2, where inlet velocity and pressure are applied in the feed channel, and in some cases pressure is also applied in the permeate channel. The model was verified by comparing it to existing BW data from both cases. The current 2D model is accurate enough to describe the actual 3D time-dependent BW process. Case 1 reduces to a 1D model agrees with the existing 1D analytical model and was found to be fully predictive. Case 2 deals with reported studies in a 2D format, and is suited to an industrial interest of keeping desalination setup unchanged while activating BW membrane cleaning. Water and salt diffusion coefficients were determined and found to be dependent on feed concentration and applied pressures. Dynamic change of concentration profiles of feed and permeate channels were illustrated. The resulting profiles reveal that in Case 2, changes in feed concentration profiles are negligible, while all other profiles of both cases change substantially with time.     

Sorption and diffusion of water vapor in poly(ethylene terephthalate) film

The sorption and diffusion of water vapor in poly(ethylene terephthalate) (PET) film were measured by applying a thermogravimetric analyzer (TG‐DTA), which customarily has been used to detect the weight loss of a sample with the increase of temperature under a given atmosphere. In this case, we detected the weight gain of PET film by sorption of water vapor under a given humidity at a constant temperature. Sorption‐rate curves were successfully obtained in spite of the low solubility of PET film and the presence of Fickian‐type curves. The solubility was better described according to the dual‐mode sorption model. The diffusion coefficients were determined in their initial slopes by the short‐time method. We found that the diffusion coefficient depended on vapor pressure. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 76: 67–74, 2000     

Influence of interfacial resistance on kinetics of sorption

A model for sorption influenced by rate of transfer to the surface layer of polymeric sheets has been examined. The rate of uptake into the surface layer has been taken to be proportional to the degree of unsaturation of the surface layer. The predicted sorption behaviour has been compared with experimentally observed data which shows a reasonable agreement. A method for calculating diffusion coefficients has been demonstrated. It has been shown that sorption rates could be affected by factors like pressure of the penetrant in the vapour phase and the structure of the surface vis-á-vis that of the bulk. Extension of the model qualitatively, to systems with diffusion coefficients strongly dependent on concentration, indicates the possibility of larger uptake of the penetrant in thinner sheets in an initial time interval. This supports some experimental observations reported earlier. The model supports the experimental work of Long and Richman who observed the time dependence of surface concentrations during sorption.     

A kinetic model of diamond nucleation and silicon carbide interlayer formation during chemical vapor deposition

The presence of thin silicon carbide intermediate layers on silicon substrates during nucleation and the early stages of diamond deposition have been frequently reported. It is generally accepted that the intermediate layer is formed by the bulk diffusion of carbon atoms into the silicon carbide layer and the morphology and orientation of the diamond film subsequently grown on the intermediate layer are strongly affected by that layer. While there have been considerable attempts to explain the mechanism for intermediate layer formation, limited quantitative data are available for the layer formation under the operating conditions conducive to diamond nucleation.This study employs a kinetic model to predict the time evolution of a β-SiC intermediate layer under the operating conditions typical of diamond nucleation in hot filament chemical vapor deposition reactors. The evolution of the layer is calculated by accounting for gas-phase and surface reactions, surface and bulk diffusions, the mechanism for intermediate layer formation, and heterogeneous diamond nucleation kinetics and of its dependence on the operating conditions such as substrate temperature and inlet gas composition. A comparison between the time scales for intermediate layer growth and diamond nuclei growth is also performed. Discrepancies in published adsorption energies of gaseous hydrocarbon precursors on the intermediate layer—ranging from 1.43 to 4.61 eV—are examined to determine the most reasonable value of the adsorption energy consistent with observed saturated thicknesses, 1–10 nm, of the intermediate layer reported in the literature. The operating conditions that lead to intermediate layer growth followed by diamond deposition vs. those that yield heteroepitaxial diamond nucleation without intermediate layer formation are discerned quantitatively. The calculations show that higher adsorption energies, 3.45 and 4.61 eV, lead to larger surface number densities of carbon atoms, lower saturated nucleation densities, and larger intermediate layer thicknesses. The observed saturated thicknesses of the intermediate layer may be reproduced if the true adsorption energy is in the range of 3.7–4.5 eV. The intermediate layer thickness increases by increasing substrate temperature and inlet hydrocarbon concentration and the dependence of the thickness on substrate temperature is especially significant. Heteroepitaxial diamond nucleation without intermediate layer formation reported in experimental results can be readily explained by the significant decrease of the intermediate layer thickness at lower substrate temperatures and at higher diamond nucleation densities. Further, the present model results indicate that the intermediate layer thickness becomes saturated when growing diamond nuclei cover a very small surface area of that layer.     

MICROSCOPIC SPREADING CHARACTERISTICS OF NONPOLAR PERFLUOROPOLYETHER FILMS

The surface diffusion characteristics of nonpolar perfluoropolyether (PFPE) Z on carbon surfaces are investigated in two regimes, submonolayer and multilayer, for nano-thin films. For the submonolayer regime, the two-dimensional, cubic van der Waals equation of state is applied to determine the dependence of the surface diffusion coefficient on the film thickness, as experimental surface diffusion coefficients increase with increasing film thickness. For the multilayer regime, a conventional fluid mechanics analysis with position dependent viscosity and a van der Waals disjoining pressure gradient is applied to investigate the surface diffusion characteristics. The present theoretical analysis qualitatively agrees with the experimental results.     

Semi-empirical model of toluene transport in polyethylene membranes based on the data using a new type of apparatus for determining gas permeability, diffusivity and solubility

Solubility, diffusivity and permeability of toluene vapors in low-density polyethylene (LDPE) membranes of various thicknesses (approximately 48, 93, 138 and 187 μm) at different temperatures 30, 40 and 50 °C in the range of relative vapor pressure p/p⁰=(0.05; 0.95) were measured using new type of permeation apparatus. Moreover, special construction of the new cell enables determination of the permeant amount sorbed in the membrane in the steady state operation of vapor permeation.The simple semi-empirical model of toluene transport in a polyethylene membrane based on relation between experimentally obtained effective diffusion coefficients and concentration dependent diffusion coefficients evaluated from experiments on a new permeation apparatus was proposed. The model enables estimation of toluene fluxes, sorption in the steady state of vapor permeation and concentration profiles in a polyethylene membrane from equilibrium sorption isotherms and effective diffusion coefficients. Very good agreement between experimental and calculated values from the proposed model was obtained.