# A Systematic Experimental and Computational Analysis of Commercially Available Aliphatic Polyesters
## 1 Introduction  
Aliphatic polyesters, in particular homo- and copolymers made of lactic and glycolic acid, have attracted significant interest in the biomedical field [1; 2; 3; 4; 5]. Indeed, polymers like polylactic acid (PLA), polyglycolic acid (PGA), and polylactic-co-glycolic acid (PLGA) have unique and peculiar properties, which combine to form a natural in situ degradation through hydrolysis (that allows avoiding additional surgery for device removal) and an intrinsic biocompatibility, since degradation products are recognized and metabolized by the body itself [2]. In addition, they can be processed with standard and established technologies (such as extrusion and injection molding) [6; 7] and their physical and mechanical properties, as well as degradation rate, can be properly tuned by changing, e.g., molecular weight or polymer composition. Notably, material properties can be also modified through blending with other bioresorbable or non-bioresorbable polymers, or by realizing composite materials, e.g., through the addition of hydroxyapatite nanoparticles or fibers [8]. Such versatility ledto a wide range of applications and uses in currently marketed medical devices, such as suture threads, bone fixation screws, but also for the manufacturing of drug-loaded micro and nanoparticles for local drug delivery and stents, just to name a few [1; 9; 10; 11]. Degradation occurs through acid-catalyzed hydrolysis. Water molecules diffuse into the polymer matrix and break that ester bonds that constitute chains backbone. Thanks to comprehensive experimental and modeling activities, the main phenomena behind degradation and the most important factors that influence its kinetics are well-established in the scientific literature. First, it is possible to discriminate two degradation regimes, according to the ratio between the water diffusion rate and water consumption rate. If the degradation rate is faster than the water penetration rate, surface or heterogeneous degradation occurs; only a thin layer at the polymer/water interface is subjected to degradation and erosion (i.e., mass loss), while the bulk remains unaffected. Device shape does not change over time, but its volume decreases. When the water diffusion rate is faster than the water consumption rate, homogeneous or bulk degradation takes place. Water concentration is (almost) constant over time and space, and the entire volume (that does not change in time) is uniformly subjected to degradation. Mass loss does not immediately occur after degradation onset but only when chain scission has created small fragments, which have enough mobility to diffuse out of the polymer matrix. The degradation of aliphatic polyesters is also characterized by autocatalysis. Indeed, hydrolysis creates oligomers that lower the microenvironmental pH (upH) by virtue of their dissociated carboxyl end groups, thereby accelerating the chain scission [12]. In other words, pH decreases as the acid-catalyzed hydrolysis proceeds and thus leads to an autocatalytic behavior. This phenomenon is relevant, because it can determine a transition between homogeneous and heterogeneous degradation. If intraphase mass transport resistances play a key role, oligomers can accumulate in the core of the matrix and locally reduce upH. Consequently, degradation is faster in the bulk than close to the surface. In order to evaluate a priori the expected degradation regime, [PERSON], et al. [13] introduced the concept of critical thickness \(L_{crit}\). If the characteristic size of the device is higher than \(L_{crit}\) surface degradation occurs, otherwise bulk degradation takes place. The value of the critical thickness depends on the interplay between diffusion and hydrolysis, as well as on the specific material. The \(L_{crit}\) for aliphatic polyesters is about 7.4 cm [13], which means that, for common applications, homogeneous degradation is expected.