A dynamic hysteresis model for customized glass transition in amorphous polymer towards multiple shape memory effects

Abstract

Coexistence of multiple and discrete segments as well as their distinctive hysteresis relaxations enables amorphous shape memory polymers (SMPs) exhibiting complex disordered dynamics, which is critical for the glass transition behavior to determine the shape memory effect (SME), but remained largely unexplored. In this study, a dynamic hysteresis model is proposed to explore the working principle and collective dynamics in discrete segments of amorphous SMPs, towards a dynamic connection between complex relaxation hysteresis and glass transition behavior, which can be applied for design and realization of multiple SMEs in the amorphous SMPs. In combination of free volume theory and Adam-Gibbs domain size model, a phase transition model is formulated to identify the working principle of dynamic relaxation hysteresis in the glass transition of amorphous SMP. Furthermore, constitutive relationships among relaxation time, strain, storage modulus, loss angle and temperature have been established to describe the dynamic connection between complex relaxation hysteresis and customized glass transition, which is then utilized to achieve multiple SMEs based on the extended Maxwell model. Finally, effectiveness of the proposed models is verified using experimental results of SMPs with multiple SMEs reported in literature.

An extended shoving model for dynamic fluctuation of glass transition in amorphous polymer towards cooperative shape-memory effect

“…To verify the effectiveness of equation (2.10), analytical results of strain-temperature curves were obtained with the different size ratios ( r 2 / r 1 ) and thermal expansion coefficients ( α s ) of the CRRs, and are shown in figure 3. The values of parameters used in equation (2.10) for the calculations are ε 0 = 0%, ε pre = 10% [34], A = 1, r 1 = 1 × 10 −9 m, T ref = 270 K, T * = 750 K, T 0 = 275 K, G = 3 GPa, α = 0.031 K −1 [32,40]. As shown in figure 3 a , with an increase in the size ratio ( r 2 / r 1 ) of the CRR from 0.2, 0.4, 0.6, 0.8 to 1.0, the shape recovery temperature is decreased from 395 K, 392 K, 389 K, 386 K to 384 K, at the given recovery strain of ε = 1% and thermal expansion coefficient of α s = 3 × 10 −12 m K −1 .…”

“…Effects of size ratio ( r 2 / r 1 ) of CRR and the thermal expansion coefficient ( α s ) on the storage modulus-temperature of the CRRs were further investigated based on equation (2.12), and the obtained results are plotted in figure 4. The values of parameters used in equation (2.12) for the calculations are E eq = 5 MPa, E neq = 2000 MPa [35], τ 0 = 0.01 s, r 1 = 1 × 10 −9 m, T ref = 290 K, T * = 750K, T 0 = 265 K, G = 3 GPa, α = 0.04 K −1 and ω = 8 s −1 [32,40].

Figure 4The storage modulus-temperature curves calculated using the proposed model (12).

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“…As shown in figure 4 b , the shape recovery temperature is increased from 375 K, 386 K, 396 K, 402 K to 407 K, with an increase in the thermal expansion coefficient ( α s ) from 1 × 10 −12 m K −1 , 3 × 10 −12 m K −1 , 5 × 10 −12 m K −1 , 7 × 10 −12 m K −1 to 9 × 10 −12 m K −1 , at the same storage modulus of E ′ = 40 MPa and size ratio of r 2 / r 1 = 0.4. These analytical results indicate that the size ratio ( r 2 / r 1 ) and thermal expansion coefficient ( α s ) play essential roles in determining the thermomechanical modulus of the CRR [22,40].…”

“…To verify the effectiveness of the proposed model based on equation (2.10), the experimental data of strain-temperature behaviours of epoxy SMP [33] were used, and the corresponding analytical results obtained using equation (2.10) are plotted in figure 6 a . All the parameters used in the calculation based on equation (2.10) are listed in table 1, where A = 1, r 1 = 1 × 10 −9 m, T ref = 300 K, T * = 750 K, T 0 = 375 K and G = 3 GPa [32,40].

Figure 6Comparisons of analytical results using equation (2.10) and experimental data [33] of the stored strain as a function of temperature for epoxy SMP.

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“…Stimulus-responsive polymers, which have the capabilities of responding to the environmental stimulations [1][2][3][4][5][6][7], have attracted great attention in the scientific community. Due to their numerous advantages, including designable properties [8][9][10], excellent biodegradability and biocompatibility [11], these stimulus-responsive polymers have shown great potential applications in biomedical devices [12][13][14], flexible electronics [15,16], smart robotics [17] and space deployable structures [18,19].…”