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

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 ofmaterials that can store and recover elastic deformation energyupon application of an external stimulus such as heat orlight.1−3 SMPs are differentiated from shape-memory alloysbecause they can be triggered to recover from extremely largestrainsup to several hundred percentimposed uponmechanical loading. Over the past decade, research has focusedon developing SMPs with stagewise programming andrecovery. New stimuli, including light and magnetic fields,have been developed to trigger shape recovery. Research hasalso emphasized tuning the stiffness and responsiveness ofSMPs to meet specific application needs. SMPs are particularlyrecognized for their potential to serve in biomedical devicessuch as vascular stents, clot-removal devices, catheters,programmable sutures, and implants.4 Applications increasinglydemand that shape-memory materials perform mechanicalwork against external loads. The ability of SMPs to stabilizedeformed shapes and perform mechanical work upon shaperecovery is limited by the strength and density of bonds createdduring shape stabilization.SMPs usually contain a permanent network that can be

elastically deformed and mechanically stabilized by a temporarynetwork. The temporary network typically forms upon coolingbeneath a well-defined shape-memory transition temperatureTSM that is associated with crystallization or vitrification of anamorphous phase. Elastically deformed shapes may also bequenched by dynamic noncovalent bonds such as hydrogenbonds.5,6 In a typical shape-memory cycle (Figure 1), thematerial is heated above TSM and is elastically deformed tostrain εm. While maintaining the applied stress, the sample iscooled 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 strainenergy 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 temporaryshape, 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 ofstored elastic energy because they are based on stress-free shaperecovery. In this Note, we examine a collection of existingexperimental data to estimate the capacity of several differentmaterials to volumetrically store elastic energy, and we examinehow material stiffness and type of temporary network affectenergy storage capacity.

■ ENERGY STORAGE

The amount of recoverable elastic energy of an SMP is limitedby the amount of reversible (elastic) work input into the

material above TSM. This quantity can be directly calculatedfrom a material’s stress−strain (σ, ε) relationship. We willassume that SMPs behave as incompressible, isotropic, andperfectly elastic neo-Hookean solids.7,8 The neo-Hookeanrelationship between true stress and strain for uniaxialdeformation is

σ εε

= + −+

⎡⎣⎢

⎤⎦⎥G (1 )

11

2

(1)

where G, the material’s shear modulus, is the model’s onlyparameter and can be obtained from a single stress−strain pointfrom a shape-memory cycle. The neo-Hookean relationship isidentical to that obtained from the classical theory of rubberyelasticity involving affine deformation of an ideal network, andG corresponds to the product of strand density n, Boltzmann’sconstant kB, and temperature T. The elastic work densityrequired to deform a sample to an elongation ε is

εε

= + ++

−⎡⎣⎢

⎤⎦⎥

WV

G(1 )

21

132

2

(2)

where V is the sample volume. This work energy densityrepresents an upper bound of elastic energy that can be storedin a shape-memory material upon elastic deformation. The useof the neo-Hookean model is appropriate here because itrequires only a single point on a material’s the stress−straincurve to estimate work energy density, permitting otherwise

Received: April 9, 2013

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

Note

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incongruent shape-memory reports to be compared. Moreover,since the neo-Hookean model overestimates stress at highelongation (∼100%), then fitting a single experimental datapoint to the neo-Hookean curve will typically result in anunderestimation 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 triggerrecovery. In an unconstrained shape-recovery (free recovery)experiment, the ends are free, and the sample’s strain isrecorded. In a constrained recovery experiment, the ends arefixed, and sample stress is recorded. The first shape-memorycycle is markedly different from the others because a significantresidual 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

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

ε ε ε ε′ = − +( )/(1 )m m p p (3)

and

ε ε ε ε′ = − +( )/(1 )f f p p (4)

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

Figure 2. Stored elastic energy density for representative shape-memory polymers from unconstrained cyclical tensile testing. Filled circles indicatethe elastic energy input upon sample deformation, asterisks indicate the amount of elastic energy upon cooling under fixed stress, and hollowtriangles indicate the stored elastic energy following load removal. All estimates are based on the neo-Hookean stress−strain relationship discussed inthe 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 crystallizableSMPs, and blue labels indicate glass-forming SMPs.

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

■ RESULTS AND DISCUSSION

The analysis described above was repeated on data obtainedfrom 17 representative peer reviewed reports. Selected resultsare shown in Figure 2, and data with references are tabulated inTable 1. Each sample is represented by two or three points inthe figure that correspond to different stages of the shape-memory cycle: initial deformation, cooling under constantstrain (or constant load), and load removal. For a given shape-memory cycle, points roughly lie on contours corresponding todeformation of a neo-Hookean elastomer. Estimated elasticenergy densities fall between 0.01 and 2 MJ/m3 for strains up tonearly 200%.Segmented polyurethanes (PUs) are among the earliest and

most developed shape-memory polymers.9−13 Urethane harddomain crystallization defines the permanent network, and softsegment crystallization enables elastic deformation to bequenched and recovered upon melting. PU shape-memory

properties can be tuned by changing the network structure andby choosing different soft and hard domain compositions. Astudy by Kim et al. on PUs containing poly(caprolactone) softsegments clarifies two trends in calculated energy density. Onesample, a polyurethane containing 70% soft segment, wasstudied at different elongations. As indicated in Figure 3, theelastic energy density increases with elongation, nearlyfollowing a constant shear modulus curve of about 4 MPa.The second notable trend is that increasing the hard segmentcontent or, equivalently, the permanent network cross-linkdensity, offers a way to move from one constant-moduluscontour to another. However, a trade-off is that highly cross-linked materials may break at lower strain. An ideal elasticenergy-storage material is stiff yet can be elongated to highlevels of strain and can effectively fix and maintain imposedstrain upon cooling.Four samples in Figure 2 (e.g., PU-4, PPS, PCL, and PCL-

EC) accumulate additional elastic energy when cooled under anexternal load, enabling two-way shape memory.14,15 Duringcooling, soft domains undergo reversible, stress-inducedcrystallization, leading to additional elongation. When sub-

Table 1. Representative Shape-Memory Polymers from the Literature

study sample/test TSM (°C) εm′ εf′G = nRT/3[MPa]

(W/V)max[MJ/m3]

(W/V)stored[MJ/m3] N (NT)

a

PU-119 IIc-100% 45−55 0.75 0.65 0.6 0.36 0.28 2.3 (2)IIc-200% 45−55 1.46 1.38 0.3 0.58 0.53 2.3 (2)

PU-212 55%SS-PCL-8K-200% 45−50 0.62 0.51 2.58 1.11 0.79 5 (4)70%SS-PCL-8K-200% 45−50 0.76 0.74 0.90 0.56 0.53 5 (5)80%SS-PCL-8K-200% 45−50 1.18 1.16 0.44 0.58 0.57 5 (3)70%SS-PCL-4K-600% 45−50 1.19 0.91 1.02 1.37 0.86 5 (5)70%SS-PCL-4K-200% 45−50 0.94 0.86 0.87 0.77 0.66 5 (5)70%SS-PCL-4K-100% 45−50 0.56 0.50 1.05 0.38 0.31 5 (4)55%SS-PCL-2K-200% 45−50 1.07 0.54 1.24 1.39 0.41 5 (3)70%SS-PCL-2K-200% 45−50 0.15 0.13 1.72 0.06 0.04 5 (5)80%SS-PCL-2K-200% 45−50 0.09 0.08 0.91 0.01 0.01 5 (3)

PU-311 L-0 10−20 0.85 0.69 0.76 0.57 0.40 4 (4)C1−5 10−20 0.69 0.63 1.27 0.67 0.56 4 (4)C1−10 10−20 0.74 0.67 0.82 0.48 0.40 4 (4)C1−15 10−20 0.67 0.60 0.73 0.36 0.30 4 (4)C2−5 10−20 0.83 0.67 1.13 0.83 0.56 4 (4)C2−10 10−20 0.89 0.70 1.06 0.86 0.56 4 (4)C2−15 10−20 0.82 0.65 1.02 0.71 0.48 4 (4)

PU-420 PU5 70 0.35 0.60 1.11 0.17 0.45 1 (−)PU-521 PDC35 40 1.00 0.99 0.80 0.80 0.79 1 (−)PMCP35 PMCP 50−70 0.74 0.55 0.14 0.08 0.05 4 (4)

PMCP−PE1 50−70 0.85 0.59 0.17 0.13 0.07 4 (4)PMCP−PE2 50−70 0.96 0.72 0.18 0.17 0.10 4 (4)

HS-A28 HSP I-28 28−55 1.86 1.86 0.26 0.75 0.75 1 (5)SMEX-124 SM epoxies 55 0.59 0.58 1.59 0.62 0.60 4 (4)SMEX-225 thermoset epoxy DP7AR 118 0.1 0.1 2.76 0.04 0.04 1 (−)PCL22 PCL-4FUR/PCL-4MAL 54 0.62 1.08 0.30 0.13 0.34 4 (4)ZOE36 Zn-SEPDM; Zn oleate, 70 0.33 0.62 0.01 0.01 0.01 1 (−)PCL-EC23 Sylgard/PCL Elastomer Comp. 60 0.48 0.54 0.13 0.03 0.04 2 (2)PPS37 D0 67 0.49 0.65 0.20 0.05 0.09 2 (2)

D50 35 0.17 0.24 0.33 0.01 0.02 2 (2)D100 57 0.42 0.42 0.12 0.04 0.04 2 (2)

PET−PEG29 G-25; PET-co-20%PEG w/glycerine cross-linker

∼25 0.77 0.76 0.33 0.21 0.20 3 (3)

CPN27 N−P-LG(16)-8000 70 0.95 0.92 0.27 0.25 0.24 2 (2)PS26 polystyrene 60 0.87 0.80 0.41 0.32 0.27 3 (3)PMMA−PEG32 A-38 wt %; PMMA−PEG composite 76 0.60 0.54 0.93 0.38 0.31 1 (−)

aNT: estimated number of required training cycles.

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sequently heated, crystallites melt, causing elastic retraction.Two-way shape-memory requires an external load to directcrystallization along a specified axis. In principle, all semi-crystalline elastomers should exhibit two-way shape memory,but the common experimental protocol does not examine thispossibility because sample strain is fixed during cooling. Relatedcold-programmable elastomers, such as poly(ester ure-thanes)16,17 and cross-linked natural rubber,18 can also undergostress-induced crystallization which stabilizes elastically de-formed 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 areseldom reported. Nevertheless, for those that are, thecrystallization enthalpy (10−30 J/g) exceeds our estimates ofstored elastic energy by a factor of 10−30.11,12,19,30 Theeffectiveness of crystallites to stabilize strain likely depends ontheir size, distribution, and orientation and how well they arecoupled to the elastic network.Elastically deformed states can also be stabilized in

noncrystalline elastomers by cooling beneath a glass transitiontemperature, Tg. Shape recovery occurs when the material isheated above its Tg in the absence of stress. As evident fromFigure 2, glass-forming SMPs exhibit high shape fixity due totheir high modulus below Tg, and they are capable of storing acomparable amount of elastic energy as crystallizable SMPs.Glass transitions can stabilize recoverable strains exceedingseveral hundred percent; however, extensive shape-memorycharacterization at such high strains has not yet beenreported.28 Like crystalline-based SMPs, too many permanentcross-links can limit the achievable elastic strain and too few canresult in creep or can limit energy storage. Reports of glassySMPs include epoxy thermosets,25 copolyester networks,27

polystyrene-derived nanostructured materials,26,31 and poly-acrylates.28,32

Thermal annealing can increase the shape recovery temper-ature and improve the sharpness of shape recovery.33,34 Theseobservations suggest that the ability to quench elasticallydeformed shapes and to store elastic energy is linked to thethermodynamic stability of a polymer glass, i.e., its position onthe thermodynamic landscape. However, the influence ofapplied stress on viscous and structural relaxation near thepolymer glass transition is rarely studied.

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

ρ εε

=+

++

−⎛⎝⎜

⎞⎠⎟

WV

RTNM

(1 )2

11

32l

max2

max (5)

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

■ CONCLUDING REMARKSElastic work energy density is an increasingly important metricof shape-memory behavior. Existing shape-memory polymersare capable of storing elastic energy exceeding one MJ/m3 atstrains greater than 100%. Understanding and improving thecoupling between crystallization or glass formation and elasticstrain will be critical to achieve higher energy densities and tofurther develop shape-memory polymers.

■ AUTHOR INFORMATIONCorresponding Author*E-mail anthamatten@che.rochester.edu; tel (585) 273-5526;fax (585) 273-1348 (M.A.).NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThe authors acknowledge support from funding provided bythe National Science Foundation under Grant DMR-0906627.

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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 ofhard segment content. Filled circles indicate the elastic energy input upon sample deformation, and hollow triangles indicate the stored elastic energyfollowing load removal.

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