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.     

Migration of low molecular weight components from polymers: 1. Methodology and diffusion of straight-chain octadecane in polyolefins

The migration kinetics of monomers, oligomers and antioxidants from several polymers into various solvents at different temperatures has been studied by radioactive tracer techniques. This paper describes in detail the methodology used for observing the migration and for reducing the data. Examples of the migration that follows strictly the Fickian diffusion behaviour with a constant diffusion coefficient are shown. These examples were obtained by first saturating the polyolefin test plaques with a labelled oligomer and then extracting the labelled species from the polymer with identical, but unlabelled, oligomer as the solvent. The polyolefin test plaques were made from linear and branched polyethylene, as well as from isotactic polypropylene. The migrating oligomer was straight-chain octadecane. The diffusion coefficients observed range from 2 to 5 μm²s^?1 at 30°C and 7–22 μm²s^?1 at 60°C. The activation energies range from 35 to 53 kJ mol^?1 for the three polymers.     

Association between polyether–polyamine block-copolymers and low molecular weight polyacids in solution

An ABA block-copolymer in which A is a poly(N-tert-butylimino-ethylene) segment and B a poly(oxytetramethylene) segment has been prepared. The salt form of this polymer, obtained with low molecular weight polycarboxylic acids such as citric acid or benzene-1,3,5-tricarboxylic acid, was found to form ionic networks in organic solvents of low or medium polarity, when the concentration of the polymeric salt exceeded a critical concentration, between 2 and 4wt%. The viscosities of the polymeric salt solutions were strongly pseudoplastic, showing a yield point and thixotropic behaviour.     

A study of the low molecular weight components of furfuryl alcohol polymers

Low molecular weight components of both an acid-polymerized and a γ-alumina polymerized furfuryl alcohol polymer were separated by gas chromatography utilizing a Porapak type P-S column packing. The identities of the separated polymer components were established by infrared spectroscopy, mass spectrometry, and nuclear magnetic resonance analysis. Volatile constituents found to be common to both furfuryl alcohol resin types were: furfuryl alcohol, water, difurylmethane, difurfuryl ether, and 2,5-difurfurylfuran. Also, 5-furfurylfurfuryl alcohol was found to be present only in the acid-polymerized resin, and 4-furfuryl-2-pentenoic acid γ-lactone was a constituent only of the γ-alumina-polymerized resin. Contrary to expectation, no esters of levulinic acid were found among the low molecular weight components of the γ-alumina-polymerized furfuryl alcohol polymer.     

Concentration dependence of the diffusion coefficient in polymer solution and molecular weight distribution determined by the diffusion method

The effects of the concentration dependence of the diffusion coefficient of a polymer solution (polystyrene in benzene and cyclohexane) in determining molecular weight distribution by the diffusion method are briefly discussed. The value of the ratio D_m0/D_A0 in a good solvent was found to be close to 1.0 for a polydisperse polymer and less than 1.0 for monodisperse polymers. Molecular weight distribution curves of the polydisperse sample were obtained by the diffusion method in cyclohexane and benzene, respectively. The molecular weight distribution curve obtained for the polymer used in benzene solution looked as if the polymer had a narrow molecular weight distribution. The phenomena cited above were interpreted in the light of the concentration dependence of the diffusion coefficient of polymer solutions.     

The Diffusion of Deterrents into Propellants Observed by FTIR microspectroscopy — Quantification of the diffusion process

The interior ballistic performance of propellants can be significantly improved by the application of deterrents. However the diffusion of the deterrents from the surface into the propellant grains during long-time storage may significantly reduce the propellants shelf life. The diffusion of different types of deterrents into single- and double-base propellants was investigated by Fourier Transform Infrared (FTIR) Microspectroscopy. The observed diffusion phenomena were explained sufficiently well by the 2nd Fickian diffusion equation. The determined diffusion coefficient values ranged between 10⁻¹⁷ m²/s and 10⁻¹⁴ m²/s at 71 °C. Polymeric deterrents were found to diffuse about one order of magnitude slower than deterrents of small molecular weight in the same propellant matrix. The diffusion velocities of the deterrents investigated increased by about 2 orders of magnitude between single and double base propellants. The changes in the interior ballistic behaviour caused by long-time storage could be correlated with the obtained deterrent diffusion coefficient values. The results of this study are in good agreement with the very few data about the solventless diffusion process of deterrents published before.     

Properties of hydrophobically modified polyacrylamide with low molecular weight and interaction with surfactant in aqueous solution

Hydrophobically modified polyacrylamide (HMPAM), with a molecular weight of 10⁴ g/mol, was studied using a range of rheological methods and dynamic light scattering (DLS). DLS measurements indicate that the association of the modified polymer begins at low concentration. The modified polymer with high substitution forms transient networks below the critical concentration, but the networks are disrupted by the micelles formed by the polymer itself, and the networks do not contribute to viscosity enhancement. The modified polymers exhibited surface activity, and so they may be regarded as nonionic polymeric surfactants rather than thickeners. On the other hand, HMPAM is shown to interact with the surfactant SDS while PAM is inert to SDS. In the hydrophobic domains, it undergoes a surfactant‐induced association process; in the hydrophobe‐surfactant transition regions, the surfactant binds to the polymer in a noncooperative way and forms a polymer–surfactant complex. Contracted polymer chains begin to extend because of electrostatic repulsion, which can overcome the association at surfactant domains. The conformation of HMPAM polymer chains could be controlled by adding a specific amount of surfactant. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 4348–4360, 2006     

Viscometric determination of the molecular weight of polymers in the low molecular weight region

In order to overcome the difficulty of the determination of the molecular weight of a polymer in the low molecular weight region by viscometry using the Mark–Houwink–Sakurada (MHS) equation, we have proposed the Dondos–Benoit relationship [η]^?1 = A₂ + AM^?1/2, for a number of polymer–solvent systems, for which we give the numerical values of the parameters A₁ and A₂. Furthermore, we suggest a method for the determination of the above parameters using the MHS constants a and k.     

Absorption of low molecular weight solutes into polyurethane in supercritical carbon dioxide

Absorption of a series of low molecular weight solutes into polyurethane was investigated in supercritical carbon dioxide with different conditions. The effect on the amount of solutes absorbed in polyurethane due to these factors such as pressure, temperature, absorption time, decompression time, the character of solutes, and the amount of cosolvent was examined by a gravimetric method. The absorption mechanism was discussed. The desorption of solutes in polyurethane showed a dependence on the logarithm of time. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 3162–3168, 2000     

The synthesis of low molecular weight hydroxy-tipped polyethylene and polypropylene by the intermediacy of Ziegler—Natta catalysts

The use of diethylzinc in conjunction with conventional and supported Ziegler—Natta catalysts permits the synthesis of polypropylene and polyethylene samples with g.p.c. $\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}$ values as low as 4000 and 3000 respectively. At high diethylzinc concentrations the number of metal—polymer bonds appears to be 40% for polypropylene and 50% for polyethylene respectively, as measured by a tritium-quench radiotracer method. The metal-bound macromolecules can be efficiently oxidized with molecular oxygen at 60°C, and subsequently hydrolysed to give hydroxy-tipped polymers. The oxidation efficiency appears to be variable and to be lower at high diethylzinc concentrations.     

Characterization and modelling of diffusion and reaction of low molecular weight reactants in molten polymer

A model reactive system was defined for studying experimentally and by simulation the competition between reaction and diffusion of two low molecular weight reactants, 2,3-epoxypropyl-phenylether (EPPE) and dipentylamine (DPA). Both reactants are miscible in a high-viscous molten polymer, poly(ethylene-co-vinyl acetate) (EVA). The comparison of the experimental rates of reaction for initially homogeneous samples and bi-layer unpremixed samples proved that the reaction was diffusion controlled. A kinetic model of the epoxy-amine reaction was coupled to mutual diffusion coefficients of reacting species in a transport model and the simulations were compared with experimental results. The diffusion/reaction process was finally related to typical mixing conditions encountered in reactive polymer processes. For the model reactive system, the simulations have established that actual mixing conditions with shear rate values encountered in polymer processing machines, were able to homogenize the system in less than 10 s. In other words, the reaction should no longer be controlled by molecular diffusion as soon as a relatively low intensity mixing is applied (shear rate > 10 s⁻¹).     

Thermal conductivity of high polymers—the influence of molecular weight

Some earlier observations on the influence of molecular weight, plasticizer, and irradiation on the thermal conductivity of polymers is reviewed. Also some new data on polystyrene and some new calculations based on the theory of Hansen and Ho are presented. These data show almost a two fold increase in the thermal conductivity of polystyrene as the molecular weight goes from 900 to 100,000. Data on the moleculer weight effect on thermal conductivity appear to be consistent with the theoretical calculations.     

Correlating the solubility of supercritical gases in high‐molecular weight substances using a density‐dependent equation

Chrastil (1982) established that the solubility of a substance in a supercritical fluid can be correlated with the density of the pure supercritical gas. Recently, the solubility of supercritical fluids in different organic liquids was successfully correlated as a function solely of the supercritical fluid density, since we demonstrated that the supercritical fluid density also defines the solubility of the gas in the liquid phase. In this work, the solubility of supercritical carbon dioxide in high‐molecular weight substances, such as high‐molecular weight paraffins, alcohols, fatty acids, fatty acid methyl and ethyl esters, has been correlated and constants provided. More than 20 binary systems comprising around 1000 solubility data points were correlated, obtaining regression coefficients greater than 0.96 and confirming the goodness of the density‐dependent equation previously reported. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Molecular weight and molecular weight distribution control in HDPE with VOCl3-based Ziegler—Natta catalysts

Some characteristics of alkoxylated catalysts derived from VOCl₃ and trialkylaluminum compounds have been examined for ethylene polymerization. Specifically studied were catalysts resulting from reaction of VOCl₃ with either an alcohol or an alkylaluminum alkoxide, or both, prior to reduction with a trialkylaluminum compound (R₃Al). Although the two methods of preparing alkoxylated catalysts did not give identical results, certain overall generalizations can be drawn. In general, as the alkoxide content was increased, the molecular weight distribution was narrowed (by a simultaneous increase in M?_n and decrease in M?_w), polymerization rate was decreased, and the polymer melt index increased at a constant hydrogen level. Alkoxides had a negative effect on rate which could largely be overcome by raising the R₃Al/V ratio or using continuous addition of R₃Al. By suitably adjusting the alkoxide and hydrogen amounts, the complete range of molecular weights and molecular weight distribution of current commercial HDPE products can be made.     

A molecular dynamics study of siloxane diffusion in a polyester-melamine solution

This study examines the diffusion of small methylated and hydroxylated siloxanes through solutions of polymer and crosslinker molecules. The diffusivity of the siloxanes was calculated for bulk diffusion and for surface segregation. Our simulations demonstrate that there is significant interaction between 3,3-dimethylhexahydroxytrisiloxane (hexa-OH-TS) and the polar solvent components of the paint matrix at 298 K. The nature of these associations is largely due to hydrogen bonding between the siloxane and the polar solvent molecules. At 573 K the diffusivity of solvent molecules is sufficiently high to disrupt interactions. The smaller number of hydroxyl groups in 1,5-dihydroxyhexamethyltrisiloxane (hexa-Me-TS) results in a weaker interaction with the polar solvent. Surface segregation studies indicate that there is a slight increase in the concentration of hexa-OH-TS in the surface layer of the system as a result of curing and relaxation processes. However, for hexa-Me-TS there is in fact a decrease in the surface concentration of the siloxane relative to the bulk concentration.     

Diffusion of deterrents into a nitrocellulose matrix. An example of diffusion with interaction

The diffusion of various concentrations of a deterrent (di-n-butyl phthalate) into a spherical, nitroglycerin-containing nitrocellulose matrix was studied. It was concluded that the final concentration profile could best be explained by a diffusion with interaction mechanism. Based on this mechanism, a method for calculating the depth of deterrent penetration is presented.     

Time-dependent shear flow of artificial slurries in coaxial cylinder viscometer with a wide gap

An experimental method was developed for characterizing time-dependent slurries of elongated particles in a coaxial cylinder viscometer which has a wide gap between the inner rotating cylinder and the stationary cup. A model slurry system was studied; it consisted of a dispersed phase of regularly sized nylon fibres and a dispersing medium of an aqueous solution of polyethylene glycol with dextrose and sodium chloride, each of whose effects on the time-dependent nature of the slurry could be examined. It was found that only a part of the gap between the cylinders of the viscometer flows under shear, and that the thickness of the flowing layer increases with time and approaches an equilibrium value. An empirical reaction-rate type model was constructed for the time-variation of the thickness of the flowing layer. A second order-zero order reversible reaction model fitted the experimental data well. The fitting parameters of the model were correlated with slurry variables.     

Diffusion of an acid dye in nylon—in relation to sorption and diffusion of a gas in glassy polymers

The steady-state permeation rate data of an acid dye in a nylon film were analyzed via dual-mode sorption and mobility model based on gradients of concentration. The model used incorporates diffusion in a porelike region, unlike diffusion of a gas in a glassy polymer. There was some possibilities of the Nernst to the Langmuir mode diffusion jump, and the diffusivity was estimated.     

含吡啶小分子胶凝剂研究进展

简述了含吡啶结构的小分子胶凝剂的研究进展，介绍了这类胶凝剂的结构特点、胶凝行为和凝胶性能。