Energy Storage Capacity of Shape-Memory Polymers

Note pubs.acs.org/Macromolecules

Energy Storage Capacity of Shape-Memory Polymers Mitchell Anthamatten,* Supacharee Roddecha, and Jiahui Li

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Department of Chemical Engineering, 206 Gavett Hall, University of Rochester, Rochester, New York 14627-1066, United States

INTRODUCTION Shape-memory polymers (SMPs) form an exciting class of materials that can store and recover elastic deformation energy upon application of an external stimulus such as heat or light.1−3 SMPs are differentiated from shape-memory alloys because they can be triggered to recover from extremely large strainsup to several hundred percentimposed upon mechanical loading. Over the past decade, research has focused on developing SMPs with stagewise programming and recovery. New stimuli, including light and magnetic fields, have been developed to trigger shape recovery. Research has also emphasized tuning the stiffness and responsiveness of SMPs to meet specific application needs. SMPs are particularly recognized for their potential to serve in biomedical devices such as vascular stents, clot-removal devices, catheters, programmable sutures, and implants.4 Applications increasingly demand that shape-memory materials perform mechanical work against external loads. The ability of SMPs to stabilize deformed shapes and perform mechanical work upon shape recovery is limited by the strength and density of bonds created during shape stabilization. SMPs usually contain a permanent network that can be elastically deformed and mechanically stabilized by a temporary network. The temporary network typically forms upon cooling beneath a well-defined shape-memory transition temperature TSM that is associated with crystallization or vitrification of an amorphous phase. Elastically deformed shapes may also be quenched by dynamic noncovalent bonds such as hydrogen bonds.5,6 In a typical shape-memory cycle (Figure 1), the material is heated above TSM and is elastically deformed to strain εm. While maintaining the applied stress, the sample is cooled beneath TSM. In the cooled state, after stress is removed, the material maintains a significant amount of fixed strain, εf. Upon subsequent heating above TSM, most of the elastic strain energy is recovered, and the specimen returns to a strain εp, nearly that of its original shape. The shape fixity ratio (Rf = εf/ εm) quantifies the material’s ability to stabilize its temporary shape, and the shape recovery ratio (Rr = εm/(εm − εp)) describes the ability to regain its original shape. While Rf and Rr may be useful in establishing shape-memory behavior, these figures of merit fail to quantify the amount of stored elastic energy because they are based on stress-free shape recovery. In this Note, we examine a collection of existing experimental data to estimate the capacity of several different materials to volumetrically store elastic energy, and we examine how material stiffness and type of temporary network affect energy storage capacity.

Figure 1. Schematic showing typical stress−strain behavior during a shape-memory cycle. The second and higher cycles (dashed line) can differ from the first.

material above TSM. This quantity can be directly calculated from a material’s stress−strain (σ, ε) relationship. We will assume that SMPs behave as incompressible, isotropic, and perfectly elastic neo-Hookean solids.7,8 The neo-Hookean relationship between true stress and strain for uniaxial deformation is ⎡ 1 ⎤ σ = G⎢(1 + ε)2 − ⎥ ⎣ 1 + ε⎦

where G, the material’s shear modulus, is the model’s only parameter and can be obtained from a single stress−strain point from a shape-memory cycle. The neo-Hookean relationship is identical to that obtained from the classical theory of rubbery elasticity involving affine deformation of an ideal network, and G corresponds to the product of strand density n, Boltzmann’s constant kB, and temperature T. The elastic work density required to deform a sample to an elongation ε is ⎡ (1 + ε)2 1 3⎤ W = G⎢ + − ⎥ 2 1+ε 2⎦ V ⎣

(2)

where V is the sample volume. This work energy density represents an upper bound of elastic energy that can be stored in a shape-memory material upon elastic deformation. The use of the neo-Hookean model is appropriate here because it requires only a single point on a material’s the stress−strain curve to estimate work energy density, permitting otherwise

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ENERGY STORAGE The amount of recoverable elastic energy of an SMP is limited by the amount of reversible (elastic) work input into the © XXXX American Chemical Society

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Received: April 9, 2013

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Figure 2. Stored elastic energy density for representative shape-memory polymers from unconstrained cyclical tensile testing. Filled circles indicate the elastic energy input upon sample deformation, asterisks indicate the amount of elastic energy upon cooling under fixed stress, and hollow triangles indicate the stored elastic energy following load removal. All estimates are based on the neo-Hookean stress−strain relationship discussed in the text. Dashed lines are reference lines that show the elastic behavior of ideal neo-Hookean solids. Selected studies are PU-1,19 PU-2,12 PU-3,11 PU-4,20 PU-5,21 PMCP,12 PCL,22 PCL-EC,23 SMEX-1,24 SMEX-2,25 PS,26 CPN,27 HS-A,28 and PET−PEG.29 Red labels indicate crystallizable SMPs, and blue labels indicate glass-forming SMPs.

that of the previous cycle. To eliminate shape-training effects from our analysis, data from higher cycle numbers were used for material comparison. However, since data are reported on the same strain scale for all cycles, relative strains were corrected by reducing by a factor of (1 + εp). Corrected values of maximum and fixed strain were calculated by

incongruent shape-memory reports to be compared. Moreover, since the neo-Hookean model overestimates stress at high elongation (∼100%), then fitting a single experimental data point to the neo-Hookean curve will typically result in an underestimation of work energy density. Experiments to study shape-memory behavior typically involve uniaxial tensile deformation at a high temperature, followed by cooling, load removal, and reheating to trigger recovery. In an unconstrained shape-recovery (free recovery) experiment, the ends are free, and the sample’s strain is recorded. In a constrained recovery experiment, the ends are fixed, and sample stress is recorded. The first shape-memory cycle is markedly different from the others because a significant residual strain εp remains. This cycle is referred to as shape “training”. The stress−strain curves for higher cycles (N = 2−5) are much more reproducible, and the strain nearly returns to

εm′ = (εm − εp)/(1 + εp)

(3)

and εf ′ = (εf − εp)/(1 + εp)

(4)

Substituting εm′ and the cycle’s maximum stress σm into eq 1, the parameter G to the neo-Hookean model was obtained, and subsequently the volumetric elastic energy input into the material was determined by eq 2. When the load is removed, only part of the input energy is stored, and this can be B

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Table 1. Representative Shape-Memory Polymers from the Literature study PU-1

19

PU-212

PU-311

PU-420 PU-521 PMCP35

HS-A28 SMEX-124 SMEX-225 PCL22 ZOE36 PCL-EC23 PPS37

PET−PEG29 CPN27 PS26 PMMA−PEG32 a

sample/test

TSM (°C)

εm′

εf′

G = nRT/3 [MPa]

(W/V)max [MJ/m3]

(W/V)stored [MJ/m3]

N (NT)a

IIc-100% IIc-200% 55%SS-PCL-8K-200% 70%SS-PCL-8K-200% 80%SS-PCL-8K-200% 70%SS-PCL-4K-600% 70%SS-PCL-4K-200% 70%SS-PCL-4K-100% 55%SS-PCL-2K-200% 70%SS-PCL-2K-200% 80%SS-PCL-2K-200% L-0 C1−5 C1−10 C1−15 C2−5 C2−10 C2−15 PU5 PDC35 PMCP PMCP−PE1 PMCP−PE2 HSP I-28 SM epoxies thermoset epoxy DP7AR PCL-4FUR/PCL-4MAL Zn-SEPDM; Zn oleate, Sylgard/PCL Elastomer Comp. D0 D50 D100 G-25; PET-co-20%PEG w/glycerine crosslinker N−P-LG(16)-8000 polystyrene A-38 wt %; PMMA−PEG composite

45−55 45−55 45−50 45−50 45−50 45−50 45−50 45−50 45−50 45−50 45−50 10−20 10−20 10−20 10−20 10−20 10−20 10−20 70 40 50−70 50−70 50−70 28−55 55 118 54 70 60 67 35 57 ∼25

0.75 1.46 0.62 0.76 1.18 1.19 0.94 0.56 1.07 0.15 0.09 0.85 0.69 0.74 0.67 0.83 0.89 0.82 0.35 1.00 0.74 0.85 0.96 1.86 0.59 0.1 0.62 0.33 0.48 0.49 0.17 0.42 0.77

0.65 1.38 0.51 0.74 1.16 0.91 0.86 0.50 0.54 0.13 0.08 0.69 0.63 0.67 0.60 0.67 0.70 0.65 0.60 0.99 0.55 0.59 0.72 1.86 0.58 0.1 1.08 0.62 0.54 0.65 0.24 0.42 0.76

0.6 0.3 2.58 0.90 0.44 1.02 0.87 1.05 1.24 1.72 0.91 0.76 1.27 0.82 0.73 1.13 1.06 1.02 1.11 0.80 0.14 0.17 0.18 0.26 1.59 2.76 0.30 0.01 0.13 0.20 0.33 0.12 0.33

0.36 0.58 1.11 0.56 0.58 1.37 0.77 0.38 1.39 0.06 0.01 0.57 0.67 0.48 0.36 0.83 0.86 0.71 0.17 0.80 0.08 0.13 0.17 0.75 0.62 0.04 0.13 0.01 0.03 0.05 0.01 0.04 0.21

0.28 0.53 0.79 0.53 0.57 0.86 0.66 0.31 0.41 0.04 0.01 0.40 0.56 0.40 0.30 0.56 0.56 0.48 0.45 0.79 0.05 0.07 0.10 0.75 0.60 0.04 0.34 0.01 0.04 0.09 0.02 0.04 0.20

2.3 (2) 2.3 (2) 5 (4) 5 (5) 5 (3) 5 (5) 5 (5) 5 (4) 5 (3) 5 (5) 5 (3) 4 (4) 4 (4) 4 (4) 4 (4) 4 (4) 4 (4) 4 (4) 1 (−) 1 (−) 4 (4) 4 (4) 4 (4) 1 (5) 4 (4) 1 (−) 4 (4) 1 (−) 2 (2) 2 (2) 2 (2) 2 (2) 3 (3)

70 60 76

0.95 0.87 0.60

0.92 0.80 0.54

0.27 0.41 0.93

0.25 0.32 0.38

0.24 0.27 0.31

2 (2) 3 (3) 1 (−)

NT: estimated number of required training cycles.

estimated again from eq 2, using the corrected value of fixed strain, εf′.

properties can be tuned by changing the network structure and by choosing different soft and hard domain compositions. A study by Kim et al. on PUs containing poly(caprolactone) soft segments clarifies two trends in calculated energy density. One sample, a polyurethane containing 70% soft segment, was studied at different elongations. As indicated in Figure 3, the elastic energy density increases with elongation, nearly following a constant shear modulus curve of about 4 MPa. The second notable trend is that increasing the hard segment content or, equivalently, the permanent network cross-link density, offers a way to move from one constant-modulus contour to another. However, a trade-off is that highly crosslinked materials may break at lower strain. An ideal elastic energy-storage material is stiff yet can be elongated to high levels of strain and can effectively fix and maintain imposed strain upon cooling. Four samples in Figure 2 (e.g., PU-4, PPS, PCL, and PCLEC) accumulate additional elastic energy when cooled under an external load, enabling two-way shape memory.14,15 During cooling, soft domains undergo reversible, stress-induced crystallization, leading to additional elongation. When sub-

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RESULTS AND DISCUSSION The analysis described above was repeated on data obtained from 17 representative peer reviewed reports. Selected results are shown in Figure 2, and data with references are tabulated in Table 1. Each sample is represented by two or three points in the figure that correspond to different stages of the shapememory cycle: initial deformation, cooling under constant strain (or constant load), and load removal. For a given shapememory cycle, points roughly lie on contours corresponding to deformation of a neo-Hookean elastomer. Estimated elastic energy densities fall between 0.01 and 2 MJ/m3 for strains up to nearly 200%. Segmented polyurethanes (PUs) are among the earliest and most developed shape-memory polymers.9−13 Urethane hard domain crystallization defines the permanent network, and soft segment crystallization enables elastic deformation to be quenched and recovered upon melting. PU shape-memory C

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Figure 3. Elastic energy density estimates for polyurethane SMPs reported by Kim et al.:12 (a) variation of programmed strain and (b) variation of hard segment content. Filled circles indicate the elastic energy input upon sample deformation, and hollow triangles indicate the stored elastic energy following load removal.

Experimentally achievable energy densities can be compared to the maximum possible elastic energy storage based on complete entropic loss of strands. If N is the number of statistical steps per strand and l is the statistical step length, then, according to Gaussian statistics, a strand’s average end-toend distance increases from N1/2l to Nl. The strand’s maximum elongation is then given by εmax = √N − 1, and its corresponding elastic energy density can be shown to be

sequently heated, crystallites melt, causing elastic retraction. Two-way shape-memory requires an external load to direct crystallization along a specified axis. In principle, all semicrystalline elastomers should exhibit two-way shape memory, but the common experimental protocol does not examine this possibility because sample strain is fixed during cooling. Related cold-programmable elastomers, such as poly(ester urethanes)16,17 and cross-linked natural rubber,18 can also undergo stress-induced crystallization which stabilizes elastically deformed shapes without heating and cooling. For crystallizable shape-memory polymers, a large enthalpy of crystallization is needed to overcome elastic strain energy. Crystallization enthalpies of shape-memory polymers are seldom reported. Nevertheless, for those that are, the crystallization enthalpy (10−30 J/g) exceeds our estimates of stored elastic energy by a factor of 10−30.11,12,19,30 The effectiveness of crystallites to stabilize strain likely depends on their size, distribution, and orientation and how well they are coupled to the elastic network. Elastically deformed states can also be stabilized in noncrystalline elastomers by cooling beneath a glass transition temperature, Tg. Shape recovery occurs when the material is heated above its Tg in the absence of stress. As evident from Figure 2, glass-forming SMPs exhibit high shape fixity due to their high modulus below Tg, and they are capable of storing a comparable amount of elastic energy as crystallizable SMPs. Glass transitions can stabilize recoverable strains exceeding several hundred percent; however, extensive shape-memory characterization at such high strains has not yet been reported.28 Like crystalline-based SMPs, too many permanent cross-links can limit the achievable elastic strain and too few can result in creep or can limit energy storage. Reports of glassy SMPs include epoxy thermosets,25 copolyester networks,27 polystyrene-derived nanostructured materials,26,31 and polyacrylates.28,32 Thermal annealing can increase the shape recovery temperature and improve the sharpness of shape recovery.33,34 These observations suggest that the ability to quench elastically deformed shapes and to store elastic energy is linked to the thermodynamic stability of a polymer glass, i.e., its position on the thermodynamic landscape. However, the influence of applied stress on viscous and structural relaxation near the polymer glass transition is rarely studied.

2 ρRT ⎛ (1 + εmax ) W 1 3⎞ ⎜ = + − ⎟ V NMl ⎝ 2 1 + εmax 2⎠

(5)

where Ml is the molecular weight of a statistical step and ρ is the sample density. The maximum work energy density in the limit εmax → ∞ is ρRT/2Ml. Taking a statistical step to have a molecular mass of 30 g/mol and the density to be 1 g/cm3, then the maximum achievable work energy density is about 30 MJ/m3.

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CONCLUDING REMARKS Elastic work energy density is an increasingly important metric of shape-memory behavior. Existing shape-memory polymers are capable of storing elastic energy exceeding one MJ/m3 at strains greater than 100%. Understanding and improving the coupling between crystallization or glass formation and elastic strain will be critical to achieve higher energy densities and to further develop shape-memory polymers.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; tel (585) 273-5526; fax (585) 273-1348 (M.A.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge support from funding provided by the National Science Foundation under Grant DMR-0906627. REFERENCES

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