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.     

Toluene and n-heptane sorption in Matrimid asymmetric hollow fiber membranes

Equilibrium and transient sorption isotherms were obtained for toluene and n-heptane in both annealed and non-annealed Matrimid^® asymmetric hollow fiber membranes at 35 °C. Equilibrium sorption follows the dual mode model except for toluene sorption into annealed fibers above a pressure of 0.5 psia. Except at the highest toluene exposure pressure, the equilibrium uptake of penetrant in annealed fibers was signigicantly less than in non-annealed fibers at a given pressure due to the significant reduction of excess free volume. Changes in the dual mode model parameters for the annealed samples may reflect not only reductions in sample free volume, but also charge transfer formation. The Berens-Hopfenberg model successfully describes all of the various transient sorption behaviors observed for toluene and n-heptane in Matrimid^® with a significant relaxation-controlled contribution to the overall mass uptake over much of the experimental range explored. Purely diffusion-controlled (Fickian) uptake was seen only for toluene sorption in annealed fibers for a change in activity from 0 to 0.05, while purely relaxation-controlled (non-Fickian) uptake was observed for n-heptane sorption in non-annealed fibers for a change in activity from 0 to 0.09. A reduced value of D_A/L², the effective Fickian diffusion time, in non-annealed fibers for toluene at a low activity level provides evidence of antiplasticization, while at intermediate to high activity, the value of D_A/L² increases with activity for all of the systems studied in this work indicating plasticization.     

The effect of styrene grafting on the diffusion and solubility of organic liquids in polyethylene

The effect of grafting styrene onto low-density polyethylene on the diffusion and solubility of benzene and n-hexane in the graft copolymer has been investigated. The diffusion coefficient at zero concentration D_{c = 0} for both benzene and n-hexane decreased with the amount of styrene grafting in the polyethylene–styrene graft copolymer membrane. The free volume parameters of the polyethylene–styrene graft copolymer were calculated using benzene and n-hexane as the diffusing species. Results show that there is a large decrease in free volume as grafting proceeds and the effect is more pronounced at low levels of grafting. Solubility was found to be a function of the per cent grafting, there being a 50%–90% increase in benzene solubility in a 26% graft compared to polyethylene. The increase in solubility for n-hexane was considerably lower. The effect of crystallinity on the free volume parameters has also been calculated.     

Sorption and diffusion of water into melamine–formaldehyde‐incorporated poly(vinyl acetate)–polyester nonwoven fabric composites

A series of composites were fabricated by impregnating a polyester nonwoven fabric with melamine–formol (MF)‐incorporated poly(vinyl acetate) (PVAc) latex. The effect of different weight ratios of MF/PVAc, i.e. 0/100, 5/100, 10, 100, 15/100 and 20/100 (dry, wt/wt), on the water sorption and diffusion into the composites was evaluated. Water sorption studies were carried out at different temperatures, i.e. 30, 50 and 70 °C, based on the immersion weight gain method. From the sorption results, the diffusion (D) and permeation (P) coefficients of water penetrant were calculated. A significant increase in the diffusion and permeation coefficients was observed with an increase in the temperature of sorption. Drastic reductions in diffusion and permeation coefficients were noticed with increasing MF content in the composites. Attempts were made to estimate the empirical parameters like n, which suggests the mode of transport, and K, a constant which depends on the structural characteristics of the composite in addition to its interaction with water. The temperature dependence of the transport coefficients was used to estimate the activation energy parameters for diffusion (E_D) and permeation (E_p) processes from Arrhenius plots. Copyright © 2006 Society of Chemical Industry     

Sorption kinetics and diffusion of alkanes into tetrafluoroethylene/propylene copolymer membranes

Sorption kinetics and diffusion of hexane, heptane, octane, nonane, decane, cyclohexane, and 2,2,4-trimethylpentane through tetrafluoroethylene/propylene copolymer membranes were studied using the gravimetric sorption method at 30, 45, and 60°C. Coefficients of diffusion were calculated from Fick's equation. From these data, the permeability coefficients were obtained. Analytical solutions of Fick's relations were used to estimate the liquid concentration profiles into the polymeric membranes at different times. The profiles of liquid concentrations were also simulated for the polymer–solvent systems using the numerical simulation method. Activation parameters for diffusion and sorption were evaluated and these results are discussed in terms of the molecular sizes and geometries of liquids (i.e., shape) as well as temperature. The diffusion coefficients follow a systematic decrease with increasing size of the penetrant molecules. The activation energies i.e., E_D values, increase with increasing size of n-alkanes. © 1996 John Wiley & Sons, Inc.     

Polymerization of isoprene in n-heptane with triethylaluminum–titanium tetrachloride catalyst. I. Effect of Al/Ti ratio on stereoregularity,conversion, molecular weight,and molecular weight distribution

The influence of the Al/Ti ratio of the heterogeneous Ziegler–Natta catalyst system AlEt₃–TiCl₄ on the isoprene polymerization in n-heptane at 30°C in a bench scale reactor was investigated. Each batch run consisted of 50 mL isoprene, 200 mL n-heptane with 0.45 and 0.5g catalyst. Conversion of isoprene and molecular weights of polyisoprene increased with increasing Al/Ti ratio, reaching their maxima values at 1.0 and 1.2, respectively. Conversion and molecular weights decreased remarkably at a higher ratio of Al/Ti. As this ratio decreases from the value of 1.2 to 0.4, the cis1,4 content in polyisoprene decreased from 97 to 25%. When the ratio of Al/Ti increased from 1.2 to 2.2 the cis-1,4 structure of polyisoprene decreased from 97 to 85%.     

Role of Sulfur and Its Diffusion in Silicate Glass Melts

Sulfur diffusion D_S is reported on a technical alkali-poor barium alumoborosilicate glass melt at 900–1400°C and on three further Na₂O-modified glass melts at 900°C, using a radioactive tracer method. Whereas D_S for the base glass melt amounts to ≈1 × 10⁻¹⁵m²/s at 900°C, it increases nearly exponentially with increasing Na₂O content from 0 to 15 mol% by almost three orders of magnitude. Similar to other glass melts, the sulfur diffusion obtained in these melts is also closely related to the Eyring diffusivity D_n derived from viscosity. The diffusion controlling species in oxidized melts seems to be SO₄²⁻, in reduced melts S²⁻. SO₃²⁻ does obviously not play any role in this transport process.     

Gas transport in poly(vinylidene fluoride): Effects of uniaxial drawing and processing temperature

This paper reports on the gas sorption and transport properties of poly(vinylidene fluoride) (PVF₂) and on the effects uniaxial drawing and processing temperature have on these properties. Sorption and transport were first examined for “as-received” commercial Kynar PVF₂ film at 35°C. This film was 54% crystalline by weight. Solubility, diffusion, and permeability coefficients were measured for He, H₂, Ar, O₂, N₂, CH₄, and CO₂. The solubility coefficient and the diffusion coefficient D were correlated with the Lennard–Jones potential and mean molecular diameter of the gas, respectively. Uniaxial drawing of PVF₂ films was performed up to a draw ratio of 3.7 and over the temperature range 75–140°C. Transport properties were correlated with the extent of draw and drawing temperature. The permeability P and D were found to significantly decline with uniaxial drawing; the magnitude of this effect was dependent on both the drawing temperature and the molecular size of the penetrant considered. Roduetions in P and D became progressively more pronounced with increasing molecular diameter and with decreasing drawing temperature (down to a limit of about 75°C), which reflects an increase in effectiveness of drawing at low temperatures. PVF₂ films annealed above 75°C showed an increase in P and D as opposed to the effect of drawing. The solubility of various gases in PVF₂ was not found to be sensitive to processing treatments such as drawing and annealing, in agreement with the relatively small changes observed in free volume. PVF₂ films subjected to various treatments were characterized by DSC, density, birefringence, and dynamic mechanical measurements. Gas transport measurements appear to provide a more sensitive and hence more viable measure of the effectiveness of drawing than these other techniques. Drawing PVF₂ in the melt state was found to increase P and D, in contrast with the effects observed for solid-state drawing. The results have been interpreted in terms of existing theories on morphology and microstructure in semicrystalline polymers.     

Effect of aluminum hydroxide on low‐molecular‐weight siloxane distribution and microstructure of high‐temperature vulcanized silicone rubber

This paper investigates the effect of aluminum hydroxide (ATH) content on the free volume and surface recovery property of polydimethylsiloxane (PDMS)–based silicone rubber containing low‐molecular‐weight siloxanes. With increasing ratio of ATH up to 43.1 wt %, the concentration of cyclic siloxanes (D_n = [(CH₃)₂SiO]_n, n = 4–12) in the PDMS matrix increases remarkably, indicative of a spacing effect of ATH particles on the crosslinking of PDMS chains. When more ATH is added, the concentration of D₄–D₁₂ began to decrease. PDMS network variation is verified by free volume size corresponding to τ₃ in positron annihilation lifetime spectroscopy. The o‐Ps intensity decreases linearly with ATH content. Data obtained from X‐ray photoelectron spectroscopy suggest the surface recovery property is weakened by ATH. This process is dominated by the amount of free volume holes in the sample. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018 , 135, 45803.     

Diffusion of additives in polyolefins

A simple radio-tracer method based on ¹⁴C is described for determining the diffusion coefficient of an additive in a polymer. Two theoretical models representing extreme cases for the diffusion system are discussed and shown to yield the same solution to within 10%. The diffusion coefficients of didodecyl 3,3′-thiodipropionate, N-octadecyldiethanolamine, and 1,1,3-tri(2-methyl-4-hydroxy-5-tert-butylphenyl)butane migrating in polyethylene, polypropylene, and poly-4-methylpentene-1 have been measured over temperature ranges of 50–80°C., within the range 20–200°C. In each case the variation of the diffusion coefficient D with temperature T can be represented by an Arrhenius equation D = D₀ exp {-E/RT}, where the activation energy E is virtually independent of the size and shape of the diffusing molecule. The activation energy depends upon the polymer and is about 12.5, 21, and 14.5 kcal./mole for polyethylene, polypropylene, and poly-4-methylpentene-1, respectively.     

Effect of tensile strain,time, and temperature on gas transport in biaxially oriented polystyrene

The permeability and diffusion coefficients (P and D) for gases in a biaxially oriented polystyrene film have been found to increase when a specimen is stretched in simple tension and to decrease with time when the strain is held constant. These effects are attributed, respectively, to an increase in free volume with strain and to the continuous volume recovery (densification) at constant strain. The strain dependence, at small strains, of P and D for Ar, Kr, N₂, CO₂, and Xe at 1 atm pressure and 50°C indicates that the size distribution of free-volume elements is not distorted when a specimen is stretched. At a constant strain of 1.8 percent at 50°C, P and D for xenon decrease about 13.8 and 11.8 percent, respectively, per decade of time—two to threefold faster than for carbon dioxide. These results and those obtained with argon, whose molecular diameter is significantly smaller than that for xenon, suggest that the larger free-volume elements decrease in size faster than the smaller ones as volume recovery progresses.     

Diffusivity and solubility of organic vapors in modified polyethylene films. II. Diffusivity studies

The diffusion coefficient at zero concentration and the free volume parameters in Fujita's free volume theory were measured for benzene, hexane, and heptane in modified polyethylene films using an unsteady-state absorption technique. Films were modified by gamma irradiation, solvent conditioning, and post- and preirradiation conditioning. D_c=0 was found to drop with irradiation, the drop being larger the larger the molecular size of the diffusing molecule. A relationship for the dependance of D_c=0 on the crosslink density is proposed. Solvent conditioning led to an increase in D_c=0 directly proportional to the swelling power of the conditioning agent and to the molecular size of the diffusant molecule. In most cases, combined treatment resulted in an increase in D_c=0, the extent of which was dependent upon the relative effect of the swellant and the irradiation dose. In all cases, postirradiation conditioning led to values of D_c=0 higher than those obtained by preirradiation conditioning. The fractional free volume of the polymer was found to decrease with irradiation, showing a marked drop at low doses when reaching a state where the dose was of small effect. Changes in f(0,T) with conditioning and with combined treatment followed the same general pattern as D_c=0. β(T) was unaffected by any kind of treatment studied. B_d changed in practically the same manner as f(0,T) but in the opposite direction. A method is proposed for the optimum choice of a membrane modification procedure based on solubility and diffusivity results.     

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 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.     

Diffusion of stabilizers in polymers. IV. 2,4-dihydroxybenzophenone in plasticized poly(vinyl chloride)

The diffusion of the radioactively labeled ultraviolet stabilizer 2,4-dihydroxybenzophenone in compression-molded sheets of plasticized poly(vinyl chloride) was studied over the temperature range of 30°C–75°C. No detectable diffusion occurred in the 0% and 10% plasticized poly(vinyl chloride) when the diffusion temperature was below the glass transition temperatures of the polymers. Diffusion coefficients have been measured for plasticizer concentrations of 20, 30, 40, and 50 wt%. In each case, the variation of the diffusion coefficient D with temperature T can be represented by an Arrhenius expression D = D₀ exp(?E/RT). The linear relation log D₀ = ?7.1 + 0.20E/T was obtained as an empirical expression of the results.     

Molecular transport of n‐alkanes into PU/PBMA interpenetrating polymer network systems

The methylene diisocyanate (MDI) and toluene diisocyanate (TDI) based polyurethane/polybutyl methacrylate (PU/PBMA‐50/50) interpenetrating polymer network (IPN) membranes have been prepared. The molecular migration of n‐alkane penetrants such as hexane, heptane, octane, nonane, and decane through PU/PBMA (50/50) membranes has been studied at 25, 40, and 60°C using a weight gain method. From the sorption results, diffusion (D) and permeation (P) coefficients of n‐alkane penetrants have been calculated. Molecular migration depends on membrane‐solvent interactions, size of the penetrants, temperature, and availability of free volume within the membrane matrix. Attempts have been made to estimate the parameters of an empirical equation and these data suggest that molecular transport follows Fickian mode. From a study of temperature dependence of transport parameters, activation energy for diffusion (E_D) and permeation (E_P) have been estimated from the Arrhenius relation. Furthermore, sorption results have been interpreted in terms of enthalpy (ΔH) and entropy (ΔS) of sorption. The liquid concentration profiles have been computed using Fick's equation with appropriate initial and boundary conditions. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 739–746, 2003     

Diffusion of m-nitroaniline into polyacylonitrile

The diffusion of nonionic penetrant, m-nitroaniline, into polyacrylonitrile was studied in detail on a range of temperature from 50.6°C to 95.0°C. The penetrant distribution in polymer is Fickian, which is different from that of cationic dye, Malachite Green reported earlier. The diffusion coefficient D increases with the rise of temperature. The sharp inflection point (72°C) of the Arrhenius plot, log D versus 1/T, corresponds to T_g of polyacrylonitrile in the presence of water, which is lower than that measured in the dry state by a dynamic mechanical testing method. The activation energy is constant below T_g (ca. 10 kcal/mole), suddenly reaches a maximum at T_g and then gradually decreases with increasing temperature. General trends of Arrhenius plot for different polymer–penetrant systems are discussed. The temperature dependence of penetrant diffusion above T_g can be described by a general form of the WLF equation, log a_T = log (D_Tg/D_T) = ? C₁^g(T ? T_g)/(C₂^g + T ? T_g), where the values of C₁^g and C₂^g were calculated to be 4.03 and 24.54, respectively. A comparison was made between m-nitroaniline and Malachite Green. The difference in the respective T_g and the constants C₁^g and C₂^g of the WLF equation in polyacrylonitrile is attributed to the size of the penetrants and their ionic character. The surface concentration increases below T_g and decreases above T_g with rise in temperature.     

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.     

Water absorption behavior of acrylonitrile‐butadiene (NBR) latex impregnated jute nonwoven fabric composites

Composites were fabricated by impregnating the jute nonwoven fabric in acrylonitrile–butadiene (NBR) latex. The effect of different pickup ratio (dry, wt/wt) of NBR latex to jute nonwoven fabric, viz., 0.5 : 1, 1 : 1.5, 1.5 : 1, 2 : 1, and 2.5 : 1 on the water absorption behavior of the composites were evaluated. Water absorption studies were carried out at different temperatures, viz. 30, 50, and 70°C, based on immersion weight gain method. From the sorption result, the diffusion (D) and permeation (P) coefficients of water penetrant have been calculated. Significant increase in the diffusion and permeation coefficients was observed with increase in the temperature of sorption experiments. Drastic reductions in diffusion and permeation coefficients were noticed with increase in the pickup ratio of NBR on to jute nonwoven fabric. Attempts were made to estimate the empirical parameters like n, which suggests the mode of transport, and K is a constant that depends on the structural characteristics of the composite in addition to its interaction with water. The temperature dependence of the transport coefficients has been used to estimate the activation energy parameter for diffusion (E_D) and permeation processes (E_p) from Arrhenius plots. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 2045–2050, 2006