New approach for consideration of adsorption/desorption data Mihaela-Cristina Ba ˘leanu a,b , Raoul R. Nigmatullin c,⇑ , Salih Okur d , Kasim Ocakoglu e a Faculty of Physics, University of Bucharest, P.O. Box MG-7, Ma ˘gurele 077125, Romania b Mihail Sadoveanu Theoretical High School, District 2, Bucharest 021586, Romania c Kazan (Volga Region) Federal University, Kazan 420008, Tatarstan, Russia d Izmir Institute of Technology, Faculty of Science, Izmir TR-35430, Turkey e Advanced Technologies Research & Application Center, Mersin University, TR-33343 Yenisehir, Mersin, Turkey article info Article history: Available online 17 March 2011 Keywords: QCM Langmuir model Eigen-Coordinates Adsorption Desorption Ruthenium polypridyl complex abstract In this paper we proposed a new approach to modify the Langmuir model by considering nonlinear effects such as diffusion of water molecules in/out of an adsorbing film for humidity adsorption and desorption kinetics. The model was tested on the humidity adsorption and desorption data of a spin coated 50 nm thick Ruthenium polypridyl com- plex (Ru-PC K314) film, measured under relative humidity between 11% and 97% using by Quartz Crystal Microbalance (QCM) technique. Ó 2011 Elsevier B.V. All rights reserved. 1. Introduction Quartz Crystal Microbalance (QCM) has been frequently used investigate the kinetics of adsorption/desorption of adsor- bate molecules [1,2] for monolayer films. It is a powerful technique to determine humidity sensing properties of materials before designing a sensor device during development stages. It is well known that the Langmuir model has been used suc- cessfully for monolayer films to analyze adsorption kinetics. A novel ceramic nanowires of TiO2 and poly (2-acrylamido-2- methylpropane sulfonate) composite material films coated QCM was prepared as a low humidity sensor [3]. In the literature, the swelling behaviour of a series of hydrophilic random copolymer coatings in controlled humidity environments and in water has been investigated using QCM and spectroscopic ellipsometry by Chen et al. [4]. Thin films of polyaniline base, emeraldine base (EB), coating on the quartz crystal microbalance (QCM) electrode have been used as a sensitive layer for the detection of a number of primary aliphatic alcohols such as ethanol, methanol, 2-propanol and 1-propanol vapours [5]. A QCM coated with Nafion Ò film recast from Nafion Ò (Ag) complex solution has been used to inves- tigate the interaction between methanol, water and Nafion Ò (Ag) and to determine simultaneously the concentration of methanol and water (relative humidity) [6]. In this work, we suggest a generalized Langmuir model to include nonlinear effect such as diffusion and condensation during humidity adsorption/desorption process. The suggested model was used to analyze the humidity adsorption and desorption QCM data of spin coated 50 nm Ruthenium polypridyl complex (Ru-PC K314) obtained under relative humidity between 11 % and 97 %. 1007-5704/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cnsns.2011.02.030 ⇑ Corresponding author. E-mail addresses: cris_balance@yahoo.com (M.-C. Ba ˘leanu), nigmat@knet.ru (R.R. Nigmatullin), salihokuru@iyte.edu.tr (S. Okur), kasim.ocakoglu@ mersin.edu.tr (K. Ocakoglu). Commun Nonlinear Sci Numer Simulat 16 (2011) 4643–4648 Contents lists available at ScienceDirect Commun Nonlinear Sci Numer Simulat journal homepage: www.elsevier.com/locate/cnsns