Equilibrium Swelling of Polystyrene by Alkanes and Carboxylic Acids: A Simple Quantitative Correlation Model Gabriel Bernardo, 1,2 Drahosh Vesely 3 1 Institute for Polymers and Composites, University of Minho-Campus de Azurem, Guimara ˜es 4800-058, Portugal 2 Institute for Nanostructures, Nanomodeling, and Nanofabrication (I3N), University of Minho-Campus de Azurem, Guimara ˜es 4800-058, Portugal 3 Department of Materials, Oxford University, Parks Road, Oxford OX1 3PH, United Kingdom Received 29 June 2009; accepted 11 October 2009 DOI 10.1002/app.31582 Published online 23 December 2009 in Wiley InterScience (www.interscience.wiley.com). ABSTRACT: In this study, we show that the equilib- rium saturation swelling of polystyrene by linear alkanes and linear carboxylic acids, as reported earlier (Bernardo and Vesely, Eur Polym J 2007, 43, 4983, Bernardo and Vesely, J Appl Polym Sci 2008, 110, 2393) can be corre- lated quantitatively using a model where only the alkyl- chain lengths and the saturated vapor pressures of the organic liquids are considered. According to this model, at very low vapor pressures, the number of polystyrene monomer units per solvent molecule is directly propor- tional to the alkyl chain length of the solvent molecule under consideration. At higher vapor pressures, the number of polystyrene monomer units per solvent mole- cule tends to become independent of its alkyl chain length. V C 2009 Wiley Periodicals, Inc. J Appl Polym Sci 116: 1348–1356, 2010 Key words: miscibility; modeling; polystyrene; swelling INTRODUCTION It is known that when a solvent, in the liquid state, miscible with a polymer diffuses into a matrix of that polymer sorption occurs until an equilibrium saturation plateau is attained. 1–7 Saturation is reached when the osmotic pressure of the solvent is counter-balanced by the elastic energy penalty upon stretching of the entangled polymer chains. This con- stant saturated swelling is, for the same polymer-sol- vent system and temperature (at atmospheric pres- sure), a highly reproducible and measurable physical quantity. Several different techniques have been used so far to detect this constant saturation plateau including gravimetry, 1–3,5 FTIR, 6 and neu- tron and x-ray analysis. 7 The authors have recently measured the equilib- rium swelling of polystyrene along the homologous series of carboxylic acids 1 and alkanes, 2 at different temperatures. Our results show that in all the stud- ied systems, solubility diagrams of the upper critical solubility temperature type have been obtained. The measurement, usually at 25  C, of the sorption of homologous series of organic compounds into polymer matrices has long been a standard method used to determine polymer solubility parameters. 8 The solubility parameter of a polymer is usually considered as equal to the solubility parameter of the strongest solvent, producing the largest swel- ling. 8 The solubility parameter approaches either in the form of total solubility parameter, as originally developed by Hildebrand and Scott 9 or in the form of partial solubility parameters, as later developed by Hansen, 10 have played during the last 60 years a central role in the interpretation and qualitative pre- diction of polymer solubility. However, despite their irrefutable qualitative value, the solubility parameter approaches have sev- eral problems associated with them, as it was recently emphasized by several different authors. 11–20 The cor- relation between polymer swelling and solubility pa- rameters are often not precise enough to allow the quantitative prediction of the swelling of a polymer in a given liquid. 11,12,17 The determination of polymer solubility parameter depends on the class of solvents used 20 and quite often severe deviations are observed and some data do not correlate even qualitatively. Furthermore, in certain cases, the criterion for differ- entiating ‘‘good’’ from ‘‘bad’’ solvents has a strong influence on the values obtained for the polymer Han- sen solubility parameters (HSP). 12 In addition, the ab- sence of a theoretically justified and experimentally Correspondence to: G. Bernardo (gabriel.bernardo@dep. uminho.pt). Contract grant sponsor: Fundac ¸a ˜o para a Cie ˆncia e a Tecnologia (Portugal); contract grant number: SFRH/BD/ 4908/2001. Journal of Applied Polymer Science, Vol. 116, 1348–1356 (2010) V C 2009 Wiley Periodicals, Inc.