Rui Xiao
Institute of Soft Matter Mechanics, College of Mechanics and Materials, Hohai University, Nanjing, Jiangsu 210098, China. E-mail: rxiao@hhu.edu.cn
First published on 22nd December 2015
For amorphous polymers, the thermally-activated and solvent-activated shape-memory effect share the same physical mechanism. The programmed shape can be recovered either by increasing the environment temperature above the activation temperature (thermally-activated mechanism) or decreasing the activation temperature below the ambient temperature (solvent-activated mechanism). An equivalent role exists for solvent and heat in activating shape recovery. Based on this assumption, we presented a method to simulate solvent-activated shape-memory behaviors through the widely available models developed for the thermally-activated mechanism. The recovery in the solvent was treated as increasing the temperature of the specimen, while the diffusion of the solvent into the polymer matrix was analogous to heat conduction. The model was employed to simulate the solvent-activated temperature memory effect of Nafion in acetone and ethanol. The model predictions showed good agreement with the experimental results.
Early experimental characterization of solvent-activated shape-memory behaviors focused on water-polymer systems.16,18–22 Huang and coworkers found that the Tg of polyurethane SMPs decreased with increasing immersion time in water.18 Chen and coworkers19 synthesized novel polyurethane SMPs, which showed the good absorption of moisture. The corresponding moisture-activated shape recovery depended on the relative humidity and ambient temperature.19 Xiao and Nguyen20 demonstrated that programmed acrylate copolymers can achieve shape recovery in water. The equilibrium concentration of water or moisture is typically small (less than 10%) in the above polymer systems. In contrast, large amounts of organic solvent can diffuse into the polymer matrix and activate shape recovery.23–26 The recovery ratio and recovery rate depends on the solvent types24,25 as well as the deformation temperature.25
Compared with the continuously growing work on experimental characterization, the efforts to model solvent-activated shape-memory behaviors have lagged. Lu et al.27 developed a phenomenological model on the basis of a permeation transition model. The model did not incorporate the kinetics of the diffusion process. Xiao and Nguyen20 developed a coupled chemical–mechanical model and implemented the model into finite element software including the diffusion process. However, the model can only be applied to low concentration solvent–polymer systems. There still lacks a model that can describe the time-dependent recovery of polymers in organic solvents. In contrast, the amount of work modeling thermally-activated shape-memory behaviors has greatly expanded.28–33 Numerous three-dimensional finite deformation constitutive models have been developed30–33 and can be implemented into finite element software. These models are capable of simulating complex three dimensional shape recovery performance under various thermo-mechanical programming and recovery conditions.
In this paper, we demonstrated that the model developed for thermally-activated SMPs can also be applied to describe the solvent-activated shape-memory behaviors. We made the following assumptions: increasing the solvent concentration in polymers has the same effect on viscosity as increasing the temperature; the diffusion process can be approximated as the heat conduction process. To validate this method, we adopted the constitutive model reported by Xiao et al.34 which was previously developed for studying the temperature memory and multiple shape-memory effect of Nafion, to simulate the shape recovery performance of Nafion in solvent. Experimentally we measured the influence of the programmed temperature on the shape recovery of Nafion films in acetone and ethanol. We further performed a parameter study to investigate the effect of the diffusion coefficient, equivalent temperature of solvent and specimen thickness on the shape recovery performance.
(1) |
Stress σ is represented by an equilibrium distortional component, N nonequilibrium distortional components, and a time-independent volumetric component,
(2) |
The following nonlinear evolution equation is adopted for Dvi,35
(3) |
According to time–temperature superposition, υi(T) can be represented as υi(T) = υrefia(T), where υrefi is the characteristic viscosity at the reference temperature and a(T) is the shift factor. We further define the characteristic stress relaxation time as τrefi = υrefi/Gneqi.
(4) |
We employed the model to study the shape-memory behaviors of Nafion films as shown in Fig. 2. Due to symmetry, we only simulated one eighth of the whole specimen. The shape was discretized using hexahedral elements. The displacement boundary conditions for the film was set as ux(x = 0, y, z) = 0, uy(x, y = 0, z) = 0, uz(x, y, z = 0) and uz(x, y, z = 5) = u(t). The boundary conditions for displacement and temperature for the programming step were the same as in the experiment setup described in Section 2. At the beginning of the recovery process, the temperature at the surfaces ABCD, BB′C′C and CC′D′D was ramped from room temperature (25 °C) to the equivalent temperature Te in 2 seconds and during the recovery process all the surfaces were set as traction free. At each time step, both the mechanical part and heat conduction part were solved. An iterative staggered scheme was employed to couple the mechanical process and heat conduction process to guarantee that the solution for both processes got converged.
log(a(T)) = 2.76 × 10−6T3 − 4.78 × 10−4T2 − 0.171T + 28.2. | (5) |
Parameter | Values | Physical significance |
---|---|---|
Geq (MPa) | 0.087 | Equilibrium shear modulus |
κ (MPa) | 744.4 | Bulk modulus |
Te1 (°C) | 125 | Equivalent temperature of acetone |
Te2 (°C) | 135 | Equivalent temperature of ethanol |
D01 (mm2 s−1) | 6 × 10−4 | Thermal diffusivity to represent diffusion coefficient of acetone |
D02 (mm2 s−1) | 2 × 10−4 | Thermal diffusivity to represent diffusion coefficient of ethanol |
The equivalent temperature Te and the diffusion coefficient (thermal diffusivity) D0 are obtained by fitting to the experimentally measured shape recovery of specimens programmed at 140 °C.
Fig. 5 Comparison of the experimental results and model predictions of the recovery response of Nafion in (a) acetone and (b) ethanol (black: 160 °C, mauve: 140 °C, blue: 120 °C, red: 80 °C.). |
As shown in Fig. 5, the deformation temperature had a strong effect on the recovery behaviors. The specimens programmed at lower temperatures exhibited a larger recovery ratio. For example, the specimens programmed at 80 °C and 100 °C can achieve full recovery in both acetone and ethanol, while the specimens programmed at 140 °C and 160 °C can only achieve partial recovery. This temperature memory effect originated from the broad distribution of the relaxation time. For specimens programmed at lower temperatures, the temporary shape was fixed by the relaxation processes with a smaller relaxation time. Thus, the specimens programmed at lower temperatures can achieve a larger ratio of shape recovery. In addition to the programming temperature, the solvent type also had a strong influence on recovery behaviors. Compared with acetone, ethanol is a more efficient solvent to activate the shape recovery of the programmed Nafion films, represented as a larger recovery ratio. It can also be seen from the swelling results that Nafion can absorb more ethanol than acetone.
The recovery performance of the specimens programmed with two temporary shapes at both 160 °C and 80 °C is shown in Fig. 6. Both experimental results and model predictions showed that the recovery ratio first decreased to the minimum value, and then gradually increased to the steady state value. The decrease of the recovery ratio represented the recovery of the shape programmed at 80 °C. The recovery of the shape programmed at 160 °C dominated in the late recovery stages since the shape programmed at 80 °C had achieved full recovery. The simulation predicted a higher initial aspect ratio than the experimental data. One possible reason is the inhomogeneous deformation of the specimen during the second loading. We found that the surface of the specimen is not perfectly smooth when remounting onto the machine to program the second temporary shape.
Fig. 6 Comparison of the experimental results and simulation of the recovery of Nafion programmed with two temporary shapes in (a) acetone and (b) ethanol. |
As shown in Fig. 5 and 6, the solvent type has an effect on the recovery performance. Meanwhile, the diffusion coefficient of the solvent in polymers directly determines the initial recovery time and recovery rate. Thus we performed a parameter study to investigate these effects on the recovery performance. We adopted the test of the Nafion specimen programmed at 160 °C and recovered in acetone as the base experiment. Fig. 7a plots the influence of the diffusion coefficient on the recovery performance. A larger diffusion coefficient resulted in a smaller activation time and a larger initial recovery rate. We then investigated the influence of the specimen thickness on the recovery behaviors. As shown in Fig. 7b, increasing the specimen thickness has a similar effect as decreasing the diffusion coefficient. For the solvent-activated mechanism, two key factors determine the recovery behaviors: viscosity and solvent diffusion. The parameter study on specimen thickness provides a method to separate the effect of viscosity and diffusion on the recovery behaviors. As demonstrated in Fig. 7b, the shape recovery behaviors of the thin specimens are dominated by the influence of viscosity, while the recovery of the thick specimens is mainly controlled by the diffusion process. We then studied the effect of different solvents on viscosity by adjusting the Te as shown in Fig. 7c. The recovery ratio is determined by the equivalent recovery temperature Te, with only a small fraction of recovery at Te = 95 °C and nearly full recovery at Te = 155 °C.
Fig. 7 Parameter influence on the recovery behaviors: (a) diffusion constant, (b) specimen thickness and (c) recovery temperature. |
From the above results, we can see this method is able to simulate the solvent-activated shape-memory behaviors. However, there are still some limitations of the method which can be improved in the future. First, the current model does not consider the deformation caused by swelling. Thus it can not be adopted to simulate the force response during the constrained recovery. This can be improved by adopting thermal deformation to represent the deformation caused by swelling. Second, a constant diffusion coefficient is adopted for the diffusion process. As discussed in ref. 36, the diffusion coefficient may depend on the solvent concentration. This can also be improved by employing temperature-dependent thermal diffusivity. Third, we performed the shape recovery experiments only at room temperature. The experimental results in ref. 19 and 20 show that the recovery ratio and recovery rate increases with the recovery temperature. Thus the equivalent temperature Te may also be dependent on the recovery temperature. In this work, the specimens did not exhibit mechanical instability such as buckling or wrinkling, which has been observed in previous work.37 In order to apply our method to describe the mechanical instability in the solvent-activated shape recovery processes, the initial perturbation has to be incorporated in the simulation such as geometry imperfection.34,38
This journal is © The Royal Society of Chemistry 2016 |