ORIGINAL Prediction of carbon dioxide diffusivity in biodegradable polymers using diffusion neural network Mahmood Reza Rahimi • Hajir Karimi • Fakhri Yousefi Received: 9 March 2011 / Accepted: 23 January 2012 / Published online: 5 February 2012 Ó Springer-Verlag 2012 Abstract An accurate and efficient artifcial neural net- work based on mega-trend diffusion algorithm (MD) is developed for predicting CO 2 diffusivity in biodegradable polymers. This mega-trend diffusion neural network (MD- NN) model could predict diffusivities close to experimental data. Furthermore, the comparison of MD-NN model with free-volume model and conventional back-propagation model demonstrates that proposed model is a powerful method and has better precision. Abbreviations MAE Mean absolute error MD-NN Mega-trend diffusion neural network MSE Mean square error P Input vector of network P Pressure PNN Conventional neural network RE Relative error W j Weight vector of unit (neuron) j 1 Introduction The use of vast amount of non-recyclable polymers throughout the last and current centuries has become a worldwide pollution problem. Therefore, the development of biodegradable materials is in the core of interest and is known to be a way of overcoming this problem. Therefore, biodegradable polymers have increasing attention over the past two decades in the fundamental research as well as in the chemical industry [1]. Nowadays, the synthesis and processing of polymers have received considerable atten- tion. The use of supercritical fluids as a processing solvent has already been looked on as a potential alternative to noxious organic solvents and chlorofluorocarbon [2]. One of the supercritical fluids is carbon dioxide, a clean and versatile solvent, which has an inert nature and a low cost and has been paid particular attention in the synthesis and processing of polymers [2–5]. So the knowledge of gas solubility and diffusivity in polymers is crucial for the commercial success of supercritical-polymer processes. The solubility provides a quantitative answer to the amount of carbon dioxide that is absorbed. This is useful for determining the swelling of polymer foam or the amount of carbon dioxide needed to arrive at a reduction in viscosity. The diffusivity can prove useful in determining the time needed to obtain the expected result. This is an important consideration since many companies have adopted con- tinuous processing equipment, such as extruders, to improve processing time and efficiency [5]. The diffusivity measurements were reported for volatiles in polypropylene, ethylene vinyl acetate copolymer (EVA) and ethylene acrylate copolymer (EDA) granules [6] and solvents in polymer by magnetic suspension balance for binary sys- tems poly(vinyl acetate)–methanol and poly(vinyl ace- tate)–toluene systems [7]. Diffusivity data of CO 2 in M. R. Rahimi (&) Process Intensification Lab., Chemical Engineering Department, School of Engineering, Yasouj University, 75918-74831 Yasouj, Iran e-mail: mrrahimi@mail.yu.ac.ir H. Karimi Chemical Engineering Department, School of Engineering, Yasouj University, 75918 Yasouj, Iran F. Yousefi Chemistry Department, School of Science, Yasouj University, 75918 Yasouj, Iran 123 Heat Mass Transfer (2012) 48:1357–1365 DOI 10.1007/s00231-012-0982-1