Determination of solvent/polymer interaction parameters of moderately concentrated polymer solutions by vapor pressure osmometry M. Karimi a, * , W. Albrecht b , M. Heuchel b , Th. Weigel b , A. Lendlein b a Amirkabir University of Technology, Department of Textile Engineering, Hafez Avenue,15914 Tehran, Iran b GKSS Research Center Geesthacht GmbH, Institute of Polymer Research, Kantstr. 55, D-14513 Teltow, Germany article info Article history: Received 27 November 2007 Received in revised form 21 February 2008 Accepted 26 March 2008 Available online 28 March 2008 Keywords: Immersion precipitation Thermodynamics Solvent/polymer interaction abstract The paper describes the application of vapor pressure osmometry (VPO) to determine solvent/polymer interaction parameters for various polymer solutions containing high-molecular weight polymers in the semi-diluted concentration range. The theoretical basis for the data evaluation is the Flory–Huggins (FH) model and a virial expansion up to the third virial term. For validation already well characterized polymer/solvent systems poly(vinylpyrrolidone)/water, polysulfone/N,N-dimethylformamide (DMF), and poly(ether sulfone)/DMF were investigated. In the second part interaction parameters of poly(ether imide) (PEI) in solvents with technical relevance for membrane formation (DMF, N-methylpyrrolidone (NMP), N,N-dimethylacetamide (DMAc)) were examined at different concentrations and temperatures. The results document that VPO is a fast and promising method for characterization of semi-diluted polymer solutions containing polymers with higher molecular weight. Results confirm the decrease of solvent power for PEI in the series: NMP > DMAc > DMF. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction The immersion precipitation process, in which a homogeneous polymer solution is separated by the addition of a nonsolvent through solvent/nonsolvent exchange into two phases (a polymer- rich and a polymer-lean phases), is the most commonly used one to fabricate polymeric membranes with various morphologies for different applications. The diffusive exchange between both liquid phases through the interface leads to changes in the composition resulting in a phase demixing. Besides the kinetics of the phase separation process, the thermodynamic state of the ternary non- solvent (1)/solvent (2)/polymer (3) system plays a crucial role in the creation of a specific morphology. The classical Flory–Huggins (FH) model [1] is commonly used for the thermodynamic analysis of the phase behavior during membrane formation. The model results in an expression for the Gibbs free energy of mixing of the system per mole of segments. For a ternary system, the Gibbs free energy of mixing DG M can be presented in form of Tompa’s extension [2] as DG M RT ¼ n 1 ln f 1 þ n 2 ln f 2 þ n 3 ln f 3 þ c 12 ðu 2 Þn 1 f 2 þc 23 ðf 3 Þn 2 f 3 þ c 13 n 1 f 3 ð1Þ where R is the gas constant, T is the absolute temperature, n i and f i are the number of moles and the volume fraction of components i, respectively, and c ij are the i/j interaction functions. u 2 is the volume fraction of solvent in a pseudo-binary nonsolvent/solvent mixture defined as: u 2 ¼ f 2 /(f 1 þ f 2 ). The application of Eq. (1) requires three precisely and independently determined (binary) interaction parameters or interaction parameter functions. Know- ing the interaction parameters between the three components, it is possible to calculate binodal, spinodal, tie lines, and critical points for the ternary system. More information about the mathematical/ numerical treatment may be found, e.g., in Ref. [3]. The solvent/polymer interaction parameter c 23 is one of these three essential parameters. It is often assumed as concentration dependent. The physical basis of its experimental determination is the measurement of the reduced solvent vapor pressure above a binary polymer mixture with respect to the state of pure solvent. Experimental data can be found either for the diluted concentration range (c 3  2.0 wt.%) of the polymer, measured with osmometry, light scattering, or viscosimetry [4], or for a very high concentration range (50 wt.%), derived, e.g., from sorption experiments [5,6]. However, for the typical concentration range of membrane for- mation (polymer concentration between about 10 and 30 wt.%) only very few suitable c 23 data (not to mention their concentration dependencies) can be found. Recently, Barth and Wolf [7] in- troduced headspace gas chromatography as a method to measure partial pressures of volatile components (solvents) in different homogeneous binary systems. However, precise measurements * Corresponding author. Tel.: þ98 21 6454 2658; fax: þ98 21 6640 0245. E-mail address: mkarimi@aut.ac.ir (M. Karimi). Contents lists available at ScienceDirect Polymer journal homepage: www.elsevier.com/locate/polymer Polymer 49 (2008) 2587–2594 Contents lists available at ScienceDirect Polymer journal homepage: www.elsevier.com/locate/polymer 0032-3861/$ – see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymer.2008.03.036