Estimation of diffusion coefficients for multiple penetrant/polyolefin systems based on sorption data

Abstract

The binary and ternary diffusion coefficients for gas/polymer systems can be estimated from solubility data and an equation of state to the free volume of penetrant/polymer systems. The system free volume can be calculated by the Sanchez Lacombe equation-of-state (SL-EoS), eliminating the need for viscoelastic data in determination of free volume parameters. Furthermore, this approach accounts for polymer swelling. The model gives reliable predictions for both binary and ternary systems of alkanes and alkenes in polyolefins.

A Single Particle Model to Predict the Impact of Induced Condensing Agents on Polymerizing Particles During the Gas Phase Polymerization of Ethylene

“…The 𝜉 i3 parameter is the ratio of polymer and solvent molar jumping units, [40] defined as follows: [32,38]…”

Diffusivity of Multicomponent Gas Mixtures in Polyethylene

“…However, if one knows the diffusivity in question, then the sorption experiments can be used to solve the inverse problem using the sorption curves to estimate the parameters of the substructural size distribution. In this case we used the model and parameters of Alves et al [7] to calculated the diffusivity of ethylene in LLDPE. Their diffusivity values of ethylene in LLDPE should be comparable to those of the LLDPE powders used here as the they used a polymer with a crystallinity of 48.6% for Alves et al [1] The values used in the present work are shown in Table 1.…”

“…The experimental sorbed weight were therefore fitted to Crank's diffusion equation to estimate the average size of Table 1. Diffusivity data were taken from Alves et al [7] at 70 °C. particles, r m , and the standard deviation, 𝜎, in Equation ( 3).…”

“…[2][3][4] However, one significant point that emerges from a perusal of the references in the review articles just cited is that there is a significant lack of data concerning both solubility and diffusivity of multicomponent gas phase mixtures. [5][6][7][8] This information is crucial, particularly in terms of understanding mass transfer and the evolution of the concentrations of reactive species in the growing polymer particles under realistic polymerization conditions. Typical polymerization recipes contain not only ethylene, hydrogen, and nitrogen, but DOI: 10.1002/macp.202100406 also co-monomers and inert alkanes that help to improve the control of the reactor temperature by increasing the heat capacity of the gas phase, and, when liquefied, through the latent heat of evaporation.…”

“…They showed that the diffusivity of the ternary mixture is higher than the diffusivity of the pure components. In terms of diffusion in PE, Alves et al [7] studied the diffusion of ethylene/n-hexane/PE and ethylene/n-pentane/PE by employing the free volume theory of Vrentas and Duda. They showed that, as expected, the ternary diffusivity of ethylene in presence of a heavier species is higher than its binary diffusivity due to the co-solubility effect increasing ethylene concentration in the amorphous phase of the polymer.…”