Function Of Penetrant Concentration Research Articles

Gas sorption, diffusion, and permeation in poly(dimethylsiloxane)

The permeability of poly(dimethylsiloxane) [PDMS] to H2, O2, N2, CO2, CH4, C2H6, C3H8, CF4, C2F6, and C3F8, and solubility of these penetrants were determined as a function of pressure at 35 °C. Permeability coefficients of perfluorinated penetrants (CF4, C2F6, and C3F8) are approximately an order of magnitude lower than those of their hydrocarbon analogs (CH4, C2H6, and C3H8), and the perfluorocarbon permeabilities are significantly lower than even permanent gas permeability coefficients. This result is ascribed to very low perfluorocarbon solubilities in hydrocarbon-based PDMS coupled with low diffusion coefficients relative to those of their hydrocarbon analogs. The perfluorocarbons are sparingly soluble in PDMS and exhibit linear sorption isotherms. The Flory–Huggins interaction parameters for perfluorocarbon penetrants are substantially greater than those of their hydrocarbon analogs, indicating less favorable energetics of mixing perfluorocarbons with PDMS. Based on the sorption results and conventional lattice solution theory with a coordination number of 10, the formation of a single C3F8/PDMS segment pair requires 460 J/mol more energy than the formation of a C3H8/PDMS pair. A breakdown in the geometric mean approximation of the interaction energy between fluorocarbons and hydrocarbons was observed. These results are consistent with the solubility behavior of hydrocarbon–fluorocarbon liquid mixtures and hydrocarbon and fluorocarbon gas solubility in hydrocarbon liquids. From the permeability and sorption data, diffusion coefficients were determined as a function of penetrant concentration. Perfluorocarbon diffusion coefficients are lower than those of their hydrocarbon analogs, consistent with the larger size of the fluorocarbons. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 415–434, 2000

Sorption and transport of hydrocarbon and perfluorocarbon gases in poly(1-trimethylsilyl-1-propyne)

Pure gas solubility and permeability of H2, O2, N2, CO2, CH4, C2H6, C3H8, CF4, C2F6, and C3F8 in poly(1-trimethylsilyl-1-propyne) (PTMSP) were determined as a function of pressure at 35°C. Permeability coefficients of the perfluorinated penetrants are approximately an order of magnitude lower than those of their hydrocarbon analogs, and lower even than those of the permanent gases. In striking contrast to hydrocarbon penetrants, PTMSP permeability to fluorocarbon penetrants decreases with increasing penetrant size. This unusual size-sieving behavior in PTMSP is attributed to low perfluorocarbon solubilities in PTMSP coupled with low diffusion coefficients relative to those of their hydrocarbon analogs. In general, perfluorocarbon penetrants are less soluble than their hydrocarbon analogs in PTMSP. The difference in hydrocarbon and perfluorocarbon solubilities in high free volume, hydrocarbon-rich PTMSP is much smaller than in hydrocarbon liquids and liquidlike polydimethylsiloxane. The low solubility of perfluorocarbon penetrants is ascribed to the large size of the fluorocarbons, which inhibits their dissolution into the densified regions of the polymer matrix and reduces the number of penetrant molecules that can be accommodated in Langmuir sites. From the permeability and sorption data, diffusion coefficients were calculated as a function of penetrant concentration. With the exception of H2 and the C3 analogs, all of the penetrants exhibit a maximum in their concentration-dependent diffusion coefficients. Resolution of diffusion coefficients into a mobility factor and a thermodynamic factor reveals that it is the interplay between these two terms that causes the maxima. The mobility of the smaller penetrants (H2, O2, N2, CH4, and CO2) decreases monotonically with increasing penetrant concentration, suggesting that the net free volume of the polymer–penetrant mixture decreases as additional penetrant is added to PTMSP. For larger penetrants mobility either: (1) remains constant at low concentrations and then decreases at higher penetrant concentrations (C2H6, CF4, and C2F6); (2) remains constant for all concentrations examined (C3H8); or (3) increases monotonically with increasing penetrant concentration (C3F8). Presumably these results reflect the varying effects of these penetrants on the net free volume of the polymer–penetrant system. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 273–296, 2000

Energetics of gas sorption in glassy polymers

The molar enthalpy for gas sorption in glassy polymers at a fixed concentration, often called the isosteric enthalpy of sorption, exhibits a clearly discernable minimum when plotted as a function of penetrant concentration. This unexpected behaviour has been observed in several glassy polymer systems including poly(ethylene terephthalate), polyacrylonitrile and polycarbonate. The behaviour can be modelled by analysing the temperature dependence of the various equilibrium parameters comprising the so-called dual mode sorption model for gas sorption in glassy polymers. The fundamental significance of the various enthalpies describing the temperature dependence of the Henry's law solubility constant, the Langmuir affinity constant and the Langmuir capacity constant are included in the discussion. Provision is made for non-ideal vapours and gases by introduction of the compressibility factor in the expression for the isosteric enthalpy. Application of relationships for calculating both the isosteric and the isothermal enthalpies of sorption is made to the case of CO 2 in poly(ethylene terephthalate) in the temperature range 35° to 115°C. These results and analyses complement the wealth of equilibrium and transport data which are consistent with the dual mode sorption model for penetrant sorption in glassy polymers.

Diffusion in the Nylon 12 and Water System

Diffusion in a nylon 12 and water system has been measured by means of a quartz microblance and weighing bottle method at penetrant concentrations ranging from about 0.2 to 2 (wt%) and temperatures ranging from 20 to 70°C. The average diffusion coefficient Dav for quenched nylon 12 film and the apparent average diffusion coefficient Dav* for annealed nylon 12 film as a function of penetrant concentration have been determined from the absorption—desorption data. The integral diffusion coefficient Ds as a function of penetrant concentration has been determined from the steady-state behavior and compared with Dav or Dav*. The concentration dependences of Dav and Dav* are somewhat different from each other, but the concentration dependences of Ds for quenched film are the same as those for annealed film when plotted against the weight of water absorbed per unit weight of the amorphous part of the dry polymer. The solubility S and the permeability P in the nylon 12+water system are proportional to the volume fraction Xa of the amorphous phase. The mutual diffusion coefficient at the limit of zero penetrant concentration for this system is compared with those for other polymer+water systems.

Diffusion and viscosity of polyvinyl acetate‐diluent systems

AbstractThe diffusion coefficient of methanol in polyvinyl acetate (PVAc) and the steady flow viscosity of the PVAc‐diethyl phthalate (DEP) system have been studied. In diffusion studies the sorption and permeation of methanol vapor in the polymer were measured over a temperature range above and below Tg of the pure polymer. The mutual diffusion coefficient, D, was estimated from the rates of absorption and desorption from and back to nonzero initial and final concentration, and also from the steady state permeability. The D derived by different methods agreed within experimental error. By using the equation of Frisch, the time lag for permeation was calculated as a function of penetrant concentration from the D data. The calculated values were larger than the observed ones at temperatures slightly above and below Tg, but when the temperature was well above Tg both values agreed with each other. At temperatures below Tg anomalous permeation curves which could not be fully explained at the present stage appeared. In viscosity studies measurements were made over the complete range of DEP composition at temperatures from 10 to 100°C. by using four different experimental techniques. The plot for the logarithm of the viscosity against weight fraction of polymer at a fixed temperature was convex upward at low concentration and then became concave upward at high concentration. In the intermediate region an inflection point appeared. Experimental data for the thermodynamic diffusion coefficient of methanol in PVAc and the isothermal viscosity data for the system PVAc‐DEP have been analyzed in terms of the free volume theory presented previously. It was found that experimental data were well represented by the theory.

The diffusion coefficient for the nylon 6 and water system

The diffusion of water vapor in nylon 6 film has been measured by means of quartz microbalance and weighing bottle methods at penetrant concentrations ranging from about 1 to 8 (wt. %) or (%) and at temperatures ranging from 15° to 60°C. From the sorption-desorption data the average diffusion coefficient D ̄ a as a function of penetrant concentration, and the apparent activation energy for diffusion processes as a function of temperature have been determined. The mutual diffusion coefficient D as a function of penetrant concentration has been determined from the steady-state behavior, and compared with D ̄ a . D ̄ a is almost independent of the penetrant concentration, especially at higher temperatures, whereas D increases with increasing concentration, even at temperatures higher than the transition temperature of the sample. This difference might be attributed to the fact that chain molecules need a long time to change their configurations when the concentration changes.