**4. Mechanism of shape memory behavior of SMPs**

It is well known that the segmental motions of the polymer chains ceased on cooling the polymer below *T*<sup>g</sup> , but the motions start dramatically above this *T*<sup>g</sup> . Basically, the polymers are transformed from a glassy state to a rubbery-elastic state during this transition. In this state, if uniaxial stress is applied for a short period of time, then the entanglement of polymer chains prevents a large-scale movement of chains, resulting in the storage of entropic energy. However, if the application of stress occurs over a longer period of time, the relaxation process can take place and that causes chain slippage and bulk flow of polymer chains. Thus, the reversible macromolecular deformation can be achieved by using network chains as a kind of molecular switch. At a certain dose of external applied energy (stimulus), the chains are flexible at a temperature above the *T*trans, whereas their flexibility below *T*trans is limited. Thus, the freezing of the molecular motion of the amorphous zone or the crystallization of the crystalline zone of the polymers prevents the molecular chains from immediately reforming the coil-like structures and instinctive recovery of the original shape, that is, programmed shape is fixed. Therefore, the stability of molecular orientation depends on the strength of interaction between the macromolecular segments and on the conformations of the chains constituting a polymer. The stretching of molecular chains leads to a drop in entropy, which can be compensated for by the cooling process, where the internal energy is decreased. Again, when the system is heated, the oriented polymer chains are softened from their glassy state or melted from the crystals, and thereby molecular chains relax the orientation to form more stable, coiled conformations. Such relaxation or shrinkage of the molecular chains caused shape recovery [23]. Therefore, the elastic strain energy produced during the deformation process is the driving force for shape recovery in SMPU. The molecular mechanism of shape memory behavior of SMPUs is shown in **Figure 3**.

At a high temperature, the rubber modulus of SMPU is lower, which makes the orientation of SMPU chains more feasible. So the deformation is much easier at high temperature. On the contrary, deformation at a lower temperature is tougher as glassy state modulus of the SMPU is high. However, the orientation of SMPU chain will withstand at a higher degree due to the slowdown of the relaxation process. Therefore, higher glassy state modulus (*E*<sup>g</sup> ) will offer higher shape fixity during concurrent cooling and unloading, where a higher rubber modulus (*E*r ) will offer higher elastic recovery at a higher temperature. Shape memory effect can thus be described by mathematical modeling as follows [24 ]:

unfavorable for a more sophisticated experiment of SMC. For example, if the testing sample is annealed under a constant stress at any stage of the experiment, the information about the annealing time and the strain reaches equilibrium or not during the annealing process would

the recovery portion of the SMC (**Figure 2a**), the time derivative of the strain as defined in Eq. (3)

It is well known that the segmental motions of the polymer chains ceased on cooling the

are transformed from a glassy state to a rubbery-elastic state during this transition. In this state, if uniaxial stress is applied for a short period of time, then the entanglement of polymer chains prevents a large-scale movement of chains, resulting in the storage of entropic energy. However, if the application of stress occurs over a longer period of time, the relaxation process can take place and that causes chain slippage and bulk flow of polymer chains. Thus, the reversible macromolecular deformation can be achieved by using network chains as a kind of molecular switch. At a certain dose of external applied energy (stimulus), the chains are flexible at a temperature above the *T*trans, whereas their flexibility below *T*trans is limited. Thus, the freezing of the molecular motion of the amorphous zone or the crystallization of the crystalline zone of the polymers prevents the molecular chains from immediately reforming the coil-like structures and instinctive recovery of the original shape, that is, programmed shape is fixed. Therefore, the stability of molecular orientation depends on the strength of interaction between the macromolecular segments and on the conformations of the chains constituting a polymer. The stretching of molecular chains leads to a drop in entropy, which can be compensated for by the cooling process, where the internal energy is decreased. Again, when the system is heated, the oriented polymer chains are softened from their glassy state or melted from the crystals, and thereby molecular chains relax the orientation to form more stable, coiled conformations. Such relaxation or shrinkage of the molecular chains caused shape recovery [23]. Therefore, the elastic strain energy produced during the deformation process is the driving force for shape recovery in SMPU. The molecular mechanism of shape memory behavior

At a high temperature, the rubber modulus of SMPU is lower, which makes the orientation of SMPU chains more feasible. So the deformation is much easier at high temperature. On the contrary, deformation at a lower temperature is tougher as glassy state modulus of the SMPU is high. However, the orientation of SMPU chain will withstand at a higher degree due to the

higher shape fixity during concurrent cooling and unloading, where a higher rubber modulus

) will offer higher elastic recovery at a higher temperature. Shape memory effect can thus

slowdown of the relaxation process. Therefore, higher glassy state modulus (*E*<sup>g</sup>

be described by mathematical modeling as follows [24 ]:

, but the motions start dramatically above this *T*<sup>g</sup>

can also be calculated from the strain curve in

*δt* × 100% (3)

. Basically, the polymers

) will offer

not be known. The rapid strain recovery rate *V*<sup>r</sup>

*Vr* <sup>=</sup> \_\_*δε*

polymer below *T*<sup>g</sup>

58 Aspects of Polyurethanes

of SMPUs is shown in **Figure 3**.

(*E*r

**4. Mechanism of shape memory behavior of SMPs**

**Figure 3.** The molecular mechanism of the shape memory effect under different stimuli. Black dots: net points; blue lines: SMPU chains below *T*trans (low mobility); red lines: SMPU chains above *T*trans (high mobility).

$$R\_{\rangle} = \left(1 - \frac{E\_s}{E\_g}\right) \tag{4}$$

$$R\_r = \frac{(1 - f\_k)}{\left[ \left( \frac{1 - E\_r}{E\_g} \right) f\_a \right]} \tag{5}$$

where *f* R is the viscous flow strain and *f* <sup>α</sup> is the strain when *T* >>> *T*<sup>s</sup> . A high elastic ratio (*E*<sup>g</sup> /*E*r ) offers easy shaping of SMPs at *T* > *T*<sup>s</sup> and provides a great resistance to deformation at *T* < *T*<sup>s</sup> . The polymer should have thus greater *E*<sup>g</sup> /*E*r . The fixation of the temporary shape is caused by strain-induced crystallization and strain-oriented reorganization. The processing conditions of SMPs have also an effect on the shape memory behavior, as there may be a variation in modulus under different processing conditions. A significant variation of rubbery modulus in SMPU was observed when cooled at different rates. Further, the recovery ratio increased with the increase of deformation speed with decreasing maximum strain. *T*<sup>s</sup> of SMPU could be tuned over a wide range of temperature from −30 to +100°C by using different structures and compositions of the components like diisocyanate, polyol (macroglycol), and chain extender. Further, the shape memory effect can be monitored by the proper choice of nature and the amount of reinforcing nanomaterials.
