MODELLING SOLUBILITY IN POLYMERS

RESEARCH GROUP: Giovanni Cocchi, Matteo Minelli, Maria Grazia De Angelis, Marco Giacinti Baschet- ti, Giulio C. Sarti, Ferruccio Doghieri

KEYWORDS: solubility, glassy polymers, non equilibrium, thermodynamics, polymer solutions.

The solubility 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 specif- ically devoted to the prediction of solubility in glassy polymers named Non Equilibrium Ther- modynamics 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, respectively.

Such approach indeed adopts, to identify univo- cally the out-of- equilibrium state of the system, the density of the glassy phase, and allows to ex- tend to the non equilibrium domains the most accurate equation of state (EoS) models available for polymeric systems, such as the Lattice Fluid theory (LF), the Statistical Associating Fluid Theory (SAFT) and the related Perturbed Hard Sphere Chain theory (PHSC) model. The system parameters can be taken from the literature, from experimental data or molecular simulations. The approach has been applied to the prediction of pure and mixed gas, vapor and liquid solubility in glassy polymers in a wide range of tempera- tures and pressures. The approach can be applied to homopolymers, polymer blends and block copolymers, as well as to composite materials (mixed matrix membranes), and can span at tem- peratures above and below Tg.

The approach can account for the effects of his- tory and processing conditions on the sorption properties, and it has been recently implemented with molecular techniques to obtain the parame- ters of poorly characterized polymers. The model is downloadable from the group website and is interfaced to an user-friendly Excel spreadsheet, containing also a large database with the parame- ters of several fluids and polymers.

Fig. 1. below: CO₂ solubility in blends of Poly- styrene and Poly(phenylene oxide) (PS/PPO) at 35°C, lines are NELF model prediction based on binary mixture data only (PS- CO₂ and PPO-CO₂), reported in the figure above.

Fig. 2. Infinite dilution solubility coefficient of CO₂ in polycarbonate at infinite dilution as a function of reciprocal temperature. Dashed line: SAFT EoS; Solid line: NE-SAFT model.

MAIN PUBLICATIONS

M. Minelli, G. Cocchi, L. Ansaloni, M. Giacinti Baschetti, M.G. De Angelis, F. Doghieri (2013). Vapor and Liquid Sorption in Matrimid Polyim- ide: Experimental Characterization and Mode- ling. Ind. Eng Chem. Res., 52, pp. 8936-8945. Minelli M., De Angelis M.G., Hofmann D. (2012). A novel multiscale method for the pre- diction of the volumetric and gas solubility be- havior of high-Tg polyimides, Fluid Phase Equi-

libria, 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 poly- mers, 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: correlations and predictions based on the NELF model, Industrial & Engineering Chemistry Re- search, 47, pp. 5214-5226.

De Angelis M.G., Sarti G.C., Doghieri F. (2007). NELF model prediction of the infinite dilution gas solubility in glassy polymers, Journal of Mem- brane Science, 289, pp. 106-122.

Doghieri F., De Angelis M.G., Giacinti Baschet- ti M., Sarti G.C. (2006). Solubility of gases and vapors in glassy polymers modelled through non-equilibrium PHSC theory, Fluid Phase Equilibria, 241(1-2), pp. 300-307.

Giacinti Baschetti M., De Angelis M.G., Doghieri F., Sarti G.C. (2005). Solubility of gases in poly- meric membranes, in: M. A. Galan E. Martin Del Valle, Chemical Engineering - Trends And Develop- ments, Chichester, Wiley & Sons, pp. 41-62. Grassia F., Giacinti Baschetti M., Doghieri F., Sarti G.C. (2001). Solubility of gases and vapors

in glassy polymer blends, In: I. Pinnau; B. Free- man, Advanced Materials For Membrane Separa- tions, New York, Oxford Univ. Press, pp. 55-73. Giacinti Baschetti, M., Doghieri, F., Sarti, G.C. (2007). Solubility in glassy polymers: correla- tions through the non-equilibrium lattice fluid model, Industrial and Engineering Chemistry Re- search, Vol. 40, 3027-3037.

Sarti G.C., Doghieri F. (1998). Prediction of the solubility of gases in glassy polymers based on the NELF Model, Chemical Engineering Science, 53, 3435-3447.

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 solubil- ity in glassy polymers, Macromolecules, 29, 7885- 7896.

De Angelis M.G., Sarti G.C., Sanguineti A., Maccone P. (2004). Permeation, Diffusion, and Sorption of Dimethyl Ether in Fluoroelastomers, Journal of Polymer Science. Part B, Polymer Phys- ics, Vol. 42, pp. 1987-2006.

RESEARCH PROJECTS

PRIN 08: Characterization and macroscopic modeling of the thermodynamic behavior of bi- nary and ternary polymers/solvent mixtures for the fabrication of biomedical devices through thermally induced phase separation (TIPS). Vigoni 2009: Multiscale prediction of gas solu- bility in high performance polymers.

FP6 Project: Multimat Design 2005-2008: Computer aided molecular design of multifunc- tional materials with controlled permeability properties. CONTACTS [email protected] [email protected] [email protected] [email protected] [email protected]