## 2 Fundamentals of Shape-Memory Polymers (SMPs) and Shape-Memory Polymer Nanocomposites (SMPNCs)
### Mechanisms and Shape-Memory Effects (SMEs)  
[PERSON] first introduced the concept of the SME in polymers in a US patent published in 1941 [34]. The mechanism underlying the SME in SMPs is intricately linked to their molecular architecture and the interaction between the temporary shape and the original  
Figure 1: Schematic representation of SMPNCs, including types of nanofillers, activation methods, and applications. (permanent) shape. When exposed to a suitable stimulus, SMPs can revert from their temporary shape to their permanent, memorized shape. In general, entropy variation can be used to describe this working cycle for thermally generated one-way SME (1W-SME) (Figure 2). In the first step, initiating the temporary shape of SMPs is crucial during programming by heating the polymer to T \(>\) T\({}_{\text{trans}}\) (glass transition temperature T\({}_{\text{g}}\) or melting temperature T\({}_{\text{m}}\)). Elevated temperatures increase the entropy of the polymer, lower the energy barrier, and facilitate increased mobility of the molecular chains, making the polymer easier to manipulate [35]. Once the polymer is deformed into the desired temporary shape with an external load, it is cooled to a temperature below T\({}_{\text{trans}}\) (T \(<\) T\({}_{\text{trans}}\)) while maintaining the external stress to freeze the chains. At the molecular level, in the shape-fixing step, the chain segments in the polymer matrix align in an oriented manner, resulting in decreased entropy. This alignment stores entropic energy, or strain energy, placing the SMPs in a thermodynamically unstable state. The permanent shape of the polymer is recovered by heating it again to T \(>\) T\({}_{\text{trans}}\), allowing for chain relaxation and the release of stored entropic energy [36; 37]. This entropic elasticity serves as the driving force for SMPs to transition from the low entropy-high energy state to the high entropy-low energy state, manifesting as a macroscopic shape [38]. To exhibit the SME, the polymer network structure must be composed of netpoints and switching domains [3; 35; 39]. The netpoints typically determine the permanent shape of the SMPs, arising from the crystalline phase, covalent (chemically cross-linked) or physical bonds (intermolecular interactions), molecular entanglement, or an interpenetrated network. Netpoints play a crucial role in preventing the movement of polymer chain segments during high-temperature programming, maintaining the stability of the entire system by generating a secure polymer network [19]. On the other hand, the switching segments establish the temporary shape of the SMPs, representing the flexible components responsible for reversible thermal phase transitions via thermal stimuli within the polymer network [29]. Switching domains are usually  
Figure 2: Schematic presentation of shape-memory cycle. involved in various mechanisms such as the crystallization/melting transition in the crystalline phase of polymers, vitrification/glass transition in the amorphous phase, liquid crystal anisotropic/isotropic transition in liquid crystalline polymers, reversible molecular cross-linking reactions like photodimerization, oxidation/redox reactions of mercaptan groups, Diels-Alder reactions, and supramolecular association/disassociation transitions such as hydrogen bonding, self-assembly of metal-ligand coordination, or \(\beta\)-CD self-assembly [3]. Macroscopic deformation in SMPs primarily results from the recoverable entropy change, preventing the dislocation of polymer chain segments. In terms of mechanical properties, SMPs demonstrate programmable mobility as the elasticity modulus drops dramatically at a temperature above their \(\mathrm{T_{trans}}\). The generation of a rubbery plateau signifies that netpoints can effectively hinder the slippage of chain segments within a defined range of force or temperature. Figure 3 depicts a schematic illustration of the entire architecture of SMPs, based on the evolution of molecular mechanisms.