Diffusion of reacting epoxy and amine monomers in polysulfone: a diffusivity model G. Rajagopalan a , J.W. Gillespie Jr. a,b, * , S.H. McKnight c a Center for Composite Materials and Department of Materials Science and Engineering, University of Delaware, Newark, DE 19716, USA b Department of Civil and Environmental Engineering, University of Delaware, Newark, DE 19716, USA c Army Research Laboratory, Materials Directorate, Aberdeen Proving Grounds, Aberdeen, MD, USA Received 31 August 1999; received in revised form 28 January 2000; accepted 28 January 2000 Abstract In this work, a diffusivity model based on free volume theory is presented for the simultaneous diffusion of diglycidyl ether of bisphenol A (DGEBA) epoxy and bis(p-aminocyclohexyl) methane (PACM 20) amine monomers into amorphous polysulfone (PSU). This model is expected to predict and explain the diffusion behavior of the epoxy and amine monomers into PSU during the initial time periods. The overall free volume of the polymer system is estimated using a Kelley–Bueche approximation for free volume in a binary mixture consisting of a non-reacting thermoplastic and the reacting thermoset. The fractional free volume of the thermoset is estimated by the DiBenedetto equation. The model is valid only for low epoxy–amine concentrations and degrees of cure. The diffusivity model developed here suggests that reaction reduces the species diffusivity with increasing cure from a loss of the overall fractional free volume for diffusion. Further, a model for increased epoxy diffusivity from amine-induced PSU swelling is presented and validated using data from previous studies on the single- component diffusion of epoxy into amine-swollen PSU. By combining the reaction and swelling terms with the Arrhenius epoxy diffusivity, the epoxy diffusivity expression during the simultaneous diffusion and reaction of epoxy and amine into PSU for small times, is determined. Parametric studies on the nature of diffusivity are performed to determine the influence of the various free volume parameters on thermoset diffusion, and these studies show that the thermoset diffusivity, in general, decreases with time from reaction.  2000 Elsevier Science Ltd. All rights reserved. Keywords: Epoxy–amine/polysulfone; Cure-dependent diffusivity model; Free volume theory 1. Introduction The study of the transport of thermosets into thermoplas- tics is important from both a technological and scientific point of view. As thermosetting monomers concurrently diffuse and react into fully polymerized thermoplastics, an interphase is formed during processing. Within the inter- phase chain entanglements and a network structure are established. This network structure represents one mechan- ism for adhesion at dissimilar polymeric material interfaces. Previous work [1–3] has shown that the size of the inter- phase is largely controlled by the processing conditions of time and temperature and the diffusivity of the thermoset- ting monomers into the thermoplastic. Cure kinetics, and the available free volume within the system govern the thermoset diffusivity. This overall free volume is deter- mined by the thermoplastic and the volume fraction and degree of cure of the diffusing thermoset. As seen previously [4], there are few empirical studies on the diffusion of thermosetting monomers into thermoplas- tics and these studies have not produced a unified, compre- hensive theoretical framework to understand the interdiffusion of reacting thermosets into thermoplastics. Further, the interphase plays a critical role in the load trans- fer across dissimilar material interfaces [1–3]. Thus, in order to design and produce controllable diffuse interphase regions the diffusion process must be evaluated and modeled. One main component essential for such a mathe- matical study is a model for the diffusivity of the thermoset into the thermoplastic. For the present study, a model is developed that incorporates swelling and reaction effects, identified in previous experimental studies performed using the Attenuated Total Reflectance-Fourier Transform Infrared Spectroscopy (ATR-FTIR) technique [1,2,4]. During the initial stages, small molecular amine was Polymer 41 (2000) 7723–7733 0032-3861/00/$ - see front matter  2000 Elsevier Science Ltd. All rights reserved. PII: S0032-3861(00)00131-2 * Corresponding author. Center for Composite Materials, University of Delaware, Newark, DE 19716, USA. Tel.: +1-302-831-8702; fax: +1-302- 831-8525. E-mail address: gillepie@ccm.udel.edu (J.W. Gillespie Jr.).