Semicrystalline polymers have to be described by a three phase model consisting of a mobile amorphous (MAF), a crystalline (CF), and a rigid amorphous fraction (RAF). For nanocomposites based on a semi crystalline polymer the RAF is due to both the crystallites (RAF(crystal)) and the filler (RAF(filer)). Polymer nanocomposite based on poly(L-lactide) and MgAl layered double hydroxide nanofiller were prepared. Due to the low crystallization rate of PLA its crystallization can be suppressed by a high enough cooling rate, and the RAF is due only to the nanofiller. The MAF, CF, and RAF were estimated by Temperature Modulated DSC. For the first time CF, MAF, RAF(crystal), and RAF(filler) could be estimated. It was found, that RAF(filier) increases linearly with the concentration of the nanofiller for this system. Furthermore, RAF(crystal) is only slightly influenced by the presence of the nanofiller. (C) 2016 Elsevier Ltd. All rights reserved.