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Modelling solubility and permeability in polymers

Keywords: solubility, glassy polymers, non equilibrium, thermodynamics, polymer solutions.
Fig.1 CH4 solubility in Polystyrene-Tetramethyl Polycarbonate (PS-TMPC) blends at 35°C, lines are NELF model predictions. (Author M. Minelli)
Fig.2 Infinite dilution solubility coefficient of CO2 in polysulfone: experimental data and SAFT and NE-SAFT model predictions. (Author M. Minelli)
Fig.3 CO2 permeability in BCPC-PMMA blends at 35°C, lines are model predictions. (Author M. Minelli)

The solubility and transport behavior of fluids in polymers is relevant in many industrial applications such as membrane separations and packaging, as well as polymer processing and technology (desolventization, CO2 and solvent foaming). Starting from mid-1990s, the group has developed a model specifically devoted to the prediction of solubility in glassy polymers named Non Equilibrium Thermodynamics for Glassy Polymers (NET-GP) and the relative versions NELF, NE-SAFT, NE-PHSC, which adopt the concepts of the Lattice Fluid (LF), SAFT and PHSC equations of state (EoS), respectively. The NET-GP approach uses the density of the glassy phase to identify univocally the out-of-equilibrium state of the system, extending usual EoS models available for polymeric systems to nonequilibrium domains. Model parameters can be retrieved from the literature, experimental data or molecular simulations.

The NET-GP model is able to predict in wide T and p ranges the solubility of pure and mixed gas, vapor and liquid in glassy polymers, such as homopolymers, polyblends or block copolymers, as well as composite materials. The approach can also account for the effects of history and processing conditions on the sorption properties, and it has been recently implemented by molecular techniques to obtain the parameters of poorly characterized systems.

The model is downloadable from the group website and is interfaced to a user-friendly Excel spreadsheet, containing also a large database with the parameters of several fluids and polymers. Furthermore, the thermodynamic approach is readily implemented in a fundamental diffusional scheme for the evaluation of penetrant permeability and diffusivity. The model is able to describe accurately all permeability behaviors with penetrant upstream pressure, temperature or composition.

Main publications

Minelli M., Sarti G.C. (2016). Gas permeability in glassy polymers: A thermodynamic approach, Fluid Phase Equilibria, 424, pp. 44-51

Minelli M., De Angelis M.G., Giacinti Baschetti B., Doghieri F., Sarti G.C., Ribeiro C.P., Freeman B.D. (2015), Equation of state modeling of the solubility of CO2/C2H6 mixtures in cross-linked poly(ethylene oxide), Industrial & Engineering Chemistry Research, 54, pp 1142–1152.

Ansaloni, L., Minelli, M., Giacinti Baschetti, M., Sarti, G. C. (2014). Effect of relative humidity and temperature on gas transport in Matrimid: Experimental study and modeling. Journal of Membrane Science, 471, pp 392–401.

Minelli M., Sarti G.C. (2013). Permeability and diffusivity of CO2 in glassy polymers with and without plasticization, Journal of Membrane Sci-ence, 435, pp. 176–185.

Minelli M., Friess K., Vopička O., De Angelis M.G. (2013). Modeling gas and vapor sorption in a polymer of intrinsic microporosity (PIM-1), Fluid Phase Equilibria, 347, pp. 35–44.

Minelli M., Cocchi G., Ansaloni L., Giacinti Bas-chetti M., De Angelis M.G., Doghieri F. (2013), Vapor and liquid sorption in Matrimid polyimide: experimental characterization and modelling, In-dustrial & Engineering Chemistry Research, 52, pp 8936–8945

Minelli M., Doghieri F. (2012), A Predictive Model for Vapor Solubility and Volume Dilation in Glassy Polymers, Industrial & Engineering Chemistry Research, 51, pp 16505–16516.

Minelli M., De Angelis M.G., Hofmann D. (2012). A novel multiscale method for the predic-tion of the volumetric and gas solubility behavior of high-Tg polyimides, Fluid Phase Equilibria, 333, pp. 87 – 96.

Sarti G.C., De Angelis M.G. (2012). Calculation of the solubility of liquid solutes in glassy poly-mers, AIChE Journal, 58, pp. 292–301.

Minelli M., Campagnoli S., De Angelis M.G., Doghieri F., Sarti G.C. (2011). Predictive model for the solubility of fluid mixtures in glassy pol-ymers, Macromolecules, 44, pp. 4852 – 4862.

De Angelis M.G., Sarti G.C. (2011). Solubility of gases and liquids in glassy polymers, Annual Re-view of Chemical and Biomolecular Engineering, 2, pp. 97–120.

De Angelis M.G., Sarti G.C. (2008). Solubility and diffusivity of gases in Mixed Matrix Mem-branes containing hydrophobic fumed silica: cor-relations and predictions based on the NELF model, Industrial & Engineering Chemistry Re-search, 47, pp. 5214–5226.

Doghieri F., De Angelis M.G., Giacinti Baschetti M., Sarti G.C. (2006). Solubility of gases and va-pors in glassy polymers modelled through non-equilibrium PHSC theory, Fluid Phase Equilibria, 241, pp. 300–307.

Giacinti Baschetti, M., Doghieri, F., Sarti, G.C. (2001). Solubility in glassy polymers: correlations through the non-equilibrium lattice fluid model, Industrial and Engineering Chemistry Research, Vol. 40, 3027-3037.

Doghieri F., Sarti G.C. (1998). Predicting the Low-pressure solubility of gases and vapors in glassy polymers by the NELF model, Journal of Membrane Science, 147(1), 73-86.

Doghieri F., Sarti G.C. (1996). Non-equilibrium lattice fluids - A predictive model for the solubility in glassy polymers, Macromolecules, 29, 7885-7896.

Research projects

H2020 project: NanoMEMC2 2016-2019: Nano-material based membranes and processes for im-proved pre/post combustion Carbon Capture.

Vigoni 2009: Multiscale prediction of gas solubil-ity in high performance polymers.

PRIN 08: Characterization and macroscopic modeling of the thermodynamic behavior of binary and ternary polymers/solvent mixtures for the fabrication of biomedical devices through ther-mally induced phase separation (TIPS).

FP6 Project: Multimat Design 2005-2008: Com-puter aided molecular design of multifunctional materials with controlled permeability properties.