Progress in Organic Coatings 97 (2016) 301–306 Contents lists available at ScienceDirect Progress in Organic Coatings j o ur na l ho me pa ge: www.elsevier.com/locate/porgcoat On the diffusion phenomenon of solvent within polymeric coatings: Development of a new model Sajjad Ghojavand, Reza Arefinia ∗ , Hamidreza Sahrayi Chemical Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran a r t i c l e i n f o Article history: Received 2 August 2015 Received in revised form 16 February 2016 Accepted 15 April 2016 Keywords: Diffusion Polymeric coating Modeling Diffusion coefficient a b s t r a c t Diffusion phenomenon of solvent molecules within the polymeric coatings has a great influence on their properties. To study this phenomenon, a new semi-empirical model was developed using the combination of a theoretical model proposed based on the Fick’s second law of diffusion with the empirical technique of coating capacitance measurement. The proposed model has both a simple form and high ability to deal with the diffusion behavior over the whole of immersion time. Additionally, the parameters of the diffusion coefficient and the type (Fickian or non-Fickian) were precisely calculated by fitting of the proposed model to the literature experimental data. According to this modeling approach, the diffusion coefficient has no constant value and reduces over the immersion time. © 2016 Elsevier B.V. All rights reserved. 1. Introduction Once a polymeric coating is exposed by a solution environment, the solvent molecules penetrate within the coating structure. This phenomenon can affect on the physical properties of coating such as electrical [1,2] and its anticorrosion behavior [2]. So far, investi- gating the water uptake of polymeric coatings has been attracted a great deal of interest in many studies [1,3–6] in them, the water uptake of coatings has been commonly determined by measure- ment of the electrical properties such as the dielectric constant. In this regard, the earliest work was made by Hartshorn [7] who proposed a mixing rule equation relating the water content to the dielectric constant of a coating as the following: ε t = ε Vc c ε Va a ε Vw w (1) in this equation, the parameters of ε and V are the dielectric con- stant and volume fraction, respectively and subtitles denote as c: dry coating, a: air, w: water as a representative of solution compo- nents and t: instant of immersion time. Frequently, researchers have utilized the parameter of coating capacitance instead of the dielectric constant in Eq. (1) due to read- ily measurement of the capacitance property during immersion ∗ Corresponding author. E-mail address: arefinia@um.ac.ir (R. Arefinia). time. However, these two parameters are related to each other by the following well-known equation: [2,8] C t = ε t ε 0 A s L (2) where C t is the coating capacitance at an instant of immersion time, ε 0 the dielectric constant of vacuum (8.854 × 10 −12 Fm −2 ), A s the coating surface area and L the thickness of coating. In this con- text, an applied coating is simulated as an electrical element of capacitance [9]. Furthermore, it has been generally accepted that the change of coating capacitance value during the immersion time is arisen from the variation of the dielectric constant under pene- tration of solution molecules within a coating [1]. Based on this approach, several correlations have been proposed for relating the solution content of coating to its capacitance. Early, Brasher and Kingsbury (in 1954) [6], suggested the following cor- relation to estimate the water content of coating: V w = log ( C t /C 0 ) log ε w (3) where C 0 is the coating capacitance at the initial time of immersion. Later, Castela et al. [1] introduced a relation for a binary system consists of coating and water as: V w = C t − C 0 C w − C 0 (4) However the estimation of water content is convenient by using the capacitance technique, it is actually time consuming for all over the immersion time. Moreover, it provides no information about the diffusion parameters. Therefore, some of researchers http://dx.doi.org/10.1016/j.porgcoat.2016.04.011 0300-9440/© 2016 Elsevier B.V. All rights reserved.