## 1 Introduction  
Starting from the synthesis in the 1960s [1], poly-lactide or polylactic acid (PLA) began to gain successful attention from researchers and industry for the first interesting applications in the biomedical field [2; 3], because PLA is a biocompatible and a biodegradable polymer. In the last two decades, the attention for PLA-based materials has been further increased due to the recent problems of waste management, especially for packaging materials. Many papers and studies have been published on biodegradable polyesters and mainly on poly(lactide), as summarized and reviewed in selected literature [4; 5; 6; 7]. PLA represents the denomination of a family of polymers derived from lactic-acid or from various lactides; it could be a homopolymer or a copolymer of L-lactic acid and/or D-lactic acid monomers at different degrees of enantiomeric purity, derived both from oil and from renewable resources [8]. For instance, P-L-LA, poly(L-lactic acid), and P-D-LA, poly(D-lactic acid), or poly-L-lactide and poly-D-lactide, are enantiomerically pure semicrystalline polymers, with melting temperatures of about \(180\)\({}^{\circ}\)C and a high crystallinity degree [9]. On the other hand, P-D,L-LA, poly(D,L-lactic acid) or poly-D,L-lactide is a statistical copolymer, completely amorphous with a glass transition temperature of about \(50\)-\(60\)\({}^{\circ}\)C, which is obtained from a equimolar mixture of L-lactic acid and D-lactic acid enantiomers. PLA possesses a good balance of performances and degradation kinetics in dependence on the enantiomeric composition, showing particularly higher thermal, mechanical,and optical properties with respect to other biodegradable polyesters [4; 10]. From a mechanical point of view, PLA-based polymers have a relatively brittle behavior with properties dependent on the molecular weight, the enantiomeric purity, the crystallinity content and the processing conditions [5; 6]. Usually a tensile modulus of 2-4 GPa, tensile strength of 30-50 MPa, and deformation at break in the range of 1% and 7% are obtained [10; 11]. For the packaging industry, relatively low enantiomeric purity PLAs found a wide diffusion, and those polymers are typically processed by injection molding, extrusion, and thermoforming [6; 12]. These materials are characterized by excellent transparency and good mechanical properties, but they evidence a certain brittleness and a low creep and thermal stability with respect to the traditional polymers for packaging applications [13]. The addition of cellulose or inorganic micro- and nanofillers represents an interesting way to increase its stiffness and thermal stability. For instance, natural fibers [14], micro- and nanocellulose [15], micrometric fillers such as talc, hydroxy apatite calcium phosphate, barium sulphate, calcium carbonate, and calcium sulfate at concentrations between 5 and 40 wt% were considered and properly added to various PLAs with some positive results in a wide range of physical properties [16]. On the one hand, various inorganic nanoparticles have been more efficiently dispersed in different PLA matrices to improve their toughness and strength, to increase their thermal stability and to enhance their barrier properties [17], and/or to reduce their electrical resistivity by using carbonaceous fillers [16]. In particular, lamellar silicates (clays) [18; 19; 20] and hydroxy apatite have been the most utilized nanofillers [21; 22]. On the other hand, in the last years some more attention has been devoted to the introduction of iso-dimensional nanofillers, such as fumed silica nanoparticles, for the production of PLA-nanocomposites. Fumed silica (FS) nanoparticles are available in a wide range of specific surface area (ranging from 50 to 400 m\({}^{2}\).g\({}^{-1}\)) and with a variety of surface treatments. Due to its morphological properties, this nanofiller is able to self-aggregate when dispersed in polymer matrices, forming an interconnected network of interacting particles.