Dynamic equilibria with glass transition heterogeneity and tailorable mechanics in amorphous shape memory polymers

Abstract

Modelling dynamic heterogeneity in amorphous shape memory polymers (SMPs) is a huge challenge due to the complex statistics of strain energy distributions during their thermodynamic relaxations. In this study, based on the dynamic heterogeneity of strain energy distribution, we have considered, for the first time, the influences of different temperature rates and strain rates on strain energy evolution as a dynamic equilibria, rather than a quasi-static problem. We propose a phase transition model incorporated with Gaussian distribution statistics to investigate the dynamic equilibria with glass transition heterogeneity and tailorable mechanics for the amorphous SMPs. The Gaussian distribution statistics is firstly applied to characterize the heterogeneity of strain energy distributions in the amorphous polymers. Phase transition theory is then developed to describe working principles of strain energy evolution, glass transition heterogeneity, thermodynamic relaxation and tailorable mechanics. Finally, the dynamic equilibria of heterogeneity about the statistics of strain energy distribution are formulated based on the one dimensional Maxwell multi-branch model. The analytical results are compared with the experimental data of epoxy, polyamide and vinylester SMPs reported in literature, and good agreements between them are demonstrated. This study provides a new insight into the dynamic heterogeneity in the mechanics of amorphous SMPs.

A bridging model of a water-triggered shape-memory effect in an amorphous polymer undergoing multiple glass transitions

“…Thus, the shape memory behavior occurs during the heating stage and is largely completely recovered during the constant temperature stage. All the parameters used in the calculation using equation ( 12) are listed in table 2, where T = 403 K, A 0 = 0.01, m = 0.1, α = 0.01 K −1 [15,50], γ = 0.8 [47], R = 8.314 J (mol K) −1 [51] and F a = 8000 J mol −1 [51]. With a decrease in the recovery temperatures from 433 K, 413 K, 393 K, 373 K to 353 K, the strain (ε) of Nafion SMP is gradually decreased from 0.24, 0.08, 0.007, 0.002 to 0 at the relaxation time of 2000 s. The temporary shape is achieved at a lower temperature, resulting in a shorter relaxation time for shape recovery.…”

“…All the experimental and analytical results are plotted in figure 7. The parameters used in the calculation based on equations ( 15) and ( 16) are φ b = 0.05, C = 99.5% [49], D = 5 × 10 −8 cm 2 s −1 [40,53], A 0 = 0.025, m = 1, α = 0.01 K −1 [15,50], γ = 0.8 [47], N l = 100 [40], χ P-S = 0.45 [40], χ b-n = 0.5 [40] and x = 0.001 cm [53] and all the variables are listed in table 3. Figure 7(a) shows that with the decrease in temperature from 433 K, 413 K, 393 K, 373 K to 353 K, the recovery strain (ε) gradually decreases from 0.2, 0.05, 0, 0 to 0.…”

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

“…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].…”

“…For the SMPs, the stored strain energy has been identified as the driving force to determine the dynamic glass transition and SME in amorphous SMPs with various and tailorable relaxation behaviours [22,23]. To understand the working principles of glass transition in amorphous SMPs, considerable effort has been made to develop various constitutive models in the past three decades.…”

Thermo-mechanical modeling of semicrystalline triple shape memory polymers

“…For the amorphous SMPs, the modeling efforts can be traced back to the 1990s. Since then, much fundamental research has been done (Dai and Xiao, 2021;Fan et al, 2020;Li et al, 2017Li et al, , 2018Liu et al, 2022;Wang et al, 2021;Xiao et al, 2022;Xue et al, 2022). Therefore, the modeling approaches are relatively mature.…”