Thermomechanical properties of biodegradable films based on blends of gelatin and poly(vinyl alcohol)

The aim of this work was to study the effect of the poly(vinyl alcohol) (PVA) concentration on the thermal and viscoelastic properties of films based on blends of gelatin and PVA using differential scanning calorimetry (DSC) and dynamic-mechanical analysis (DMA). One glass transition was observed between 43 and 49 degrees C on the DSC curves obtained in the first scanning of the blended films, followed by fusion of the crystalline portion between 116 and 134 degrees C. However, the DMA results showed that only the films with 10% PVA had a single peak in the tan 5 spectrum. However, when the PVA concentration was increased the dynamic mechanical spectra showed two peaks on the tan 6 curves, indicating two T(g)s. Despite this phase separation behavior the Gordon and Taylor model was successfully applied to correlate T, as a function of film composition, thus determining k = 7.47. In the DMA frequency tests, the DMA spectra showed that the storage modulus values decreased with increasing temperature. The master curves for the PVA-gelatin films were obtained applying the TTS principle (T(r) = 100 degrees C). The WLF model was thus applied allowing for the determination of the constants C(1) and C(2). The values of these constants increased with increasing PVA concentrations in the blend: C(1) = 49-66 and C(2) = 463-480. These values were used to calculate the fractional free volume of the films at the T(g) and the thermal expansion coefficient of the films above the T(g). (c) 2007 Elsevier Ltd. All rights reserved.

Exact Search Directions for Optimization of Linear and Nonlinear Models Based on Generalized Orthonormal Functions

A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. It is well-known that the usual large number of parameters required to describe the Volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions. Such a representation results in the so-called OBF Volterra model, which has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the Volterra polynomial series. Aiming at optimizing the poles that fully parameterize the orthonormal bases, the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back-propagation-through-time technique. The expressions relative to the Kautz basis and to generalized orthonormal bases of functions (GOBF) are addressed; the ones related to the Laguerre basis follow straightforwardly as a particular case. The main innovation here is that the dynamic nature of the OBF filters is fully considered in the gradient computations. These gradients provide exact search directions for optimizing the poles of a given orthonormal basis. Such search directions can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into account the error of estimation of the system output. The Levenberg-Marquardt algorithm is adopted here as the optimization procedure. Unlike previous related work, the proposed approach relies solely on input-output data measured from the system to be modeled, i.e., no information about the Volterra kernels is required. Examples are presented to illustrate the application of this approach to the modeling of dynamic systems, including a real magnetic levitation system with nonlinear oscillatory behavior.