European Polymer Journal 49 (2013) 184–193

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European Polymer Journal

journal homepage: www.elsevier .com/locate /europol j

Influence of molecular architecture on the isothermal time-dependentresponse of amorphous shape memory polyurethanes

Charly Azra, Yaobo Ding, Christopher J.G. Plummer ⇑, Jan-Anders E. MånsonLaboratoire de Technologie des Composites et Polymères (LTC), Ecole Polytechnique Fédérale de Lausanne (EPFL), Station 12, CH-1015 Lausanne, Switzerland

a r t i c l e i n f o a b s t r a c t

Article history:Received 6 June 2012Received in revised form 16 July 2012Accepted 15 October 2012Available online 24 October 2012

Keywords:Shape memory polymersGlass transitionDynamic mechanical analysisLoss tangentPolyurethanesTime dependence

0014-3057/$ - see front matter � 2012 Elsevier Ltdhttp://dx.doi.org/10.1016/j.eurpolymj.2012.10.012

⇑ Corresponding author. Tel.: +41 021 693 2856; faE-mail address: christopher.plummer@epfl.ch (C

The thermomechanical response of a series of thermally activated shape memory polyure-thanes (SMPUs), determined by dynamic mechanical analysis (DMA), has been adjusted bysystematic modification of the molecular architecture. It is argued that the free recoverybehavior of these SMPUs at temperatures in the vicinity of the calorimetric glass transitiontemperature is dependent not only on the recovery temperature, but also on the form ofthe corresponding peak in tan d in DMA temperature scans at constant frequency. Onthe basis of simple correlations between recovery rates and the width and shape of thetan d peak, it is suggested that DMA may provide a relatively simple and rapid means ofassessing the potential of the SMPUs with respect both to recovery and shape fixity at agiven storage temperature. This in turn allows establishment of a direct link betweenthe shape memory performance and molecular architecture.

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1. Introduction

Shape memory polymers (SMPs) are able to transformfrom a deformation-induced temporary shape to a ‘‘pri-mary’’ shape characteristic of the equilibrium conforma-tion of a molecular network defined by entanglementand physical and/or chemical cross-linking [1]. While sucha transformation may occur in response to various types ofstimulus, it is usually triggered by raising the temperature,T, above a softening temperature, e.g. a glass transitiontemperature, Tg, or a melting point, below which the tem-porary shape is effectively frozen-in, owing to the limitedmobility of the polymer molecules.

SMPs are typically designed to show well-definedrecovery temperatures [2], and a high level of reproducibil-ity of the recovered shape [3] within a relatively short time[4]. However, many potential applications, particularly inthe biomedical field, also require adequate control of theshape recovery kinetics, e.g. to avoid damaging body tissue[5] or to ensure well-defined flow rates in microfluidic de-

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x: +41 021 693 5880..J.G. Plummer).

vices [6]. Moreover, if a passive source of thermal energysuch as the human body is used to actuate the SMP, itmay be important to limit the sensitivity of the recoveryrate to fluctuations with respect to the targeted actuationtemperature.

At T well above Tg, i.e. in the rubbery state, the segmen-tal mobility of a glassy polymer is high, so that the molec-ular network is able to rearrange quasi-instantaneously toreach a new equilibrium configuration in response to anapplied stress, resulting in a quasi-instantaneous (macro-scopic) elastic strain [7]. Well below Tg, on the other hand,the polymer is in a non-equilibrium state, conformationalrearrangements are extremely slow, and brittle failuremay intervene prior to any significant stress relaxation. Ifintermediate recovery rates are required, the recoverytemperature should therefore be in the vicinity of Tg [8].However, the relaxation and retardation times associatedwith conformational rearrangements in this regime gener-ally show a strong temperature dependence [7], which im-plies the recovery rate also to be strongly dependent on T.

One strategy to reduce the temperature sensitivity ofthe free recovery rate might be to compensate the temper-ature dependence of individual retardation times by

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broadening the retardation time spectrum, bearing in mindthat too broad a transition may compromise shape fixity atlow T (indeed, for this reason the actuation temperature inmost commercial SMPs, which are designed for rapiddeployment, tends to be associated with a sharp transitionin the mechanical response). In the present work, wetherefore examine the effect of molecular architecture onthe free recovery behavior of a series of amorphous shapememory polyurethanes (PUR) based on a formulation de-scribed previously by Buckley et al. [9], for which the retar-dation time spectrum is relatively broad. The results arecompared with data from a commercial thermoset SMPUand discussed in the light of results from low strain dy-namic mechanical analysis (DMA) temperature sweeps atconstant frequency, which allow relatively rapid character-ization of the linear viscoelastic response in the transitionzone.

2. Materials and methods

2.1. Specimen preparation

A range of thermoset SMPUs was synthesized followingBuckley et al. [9], based on a polytetrahydrofuran (PTHF)macrodiol with two weight average molar masses,Mw = 650 and 1000 g/mol, 4,40-diphenylmethane diisocya-nate (MDI), and trimethylolpropane (TMP) as a cross-linker. The chain extender 1,4-butanediol (BDO) was alsoincluded in certain formulations. All chemicals were pur-chased from Sigma–Aldrich, Switzerland and were usedwithout further purification.

1 mm thick sheets of the SMPUs were prepared asfollows. First, the PTHF was vacuum-dried at 110 �C anda pressure of less than 50 mbar for one and a half hoursand then cooled under vacuum to 70 �C. At the same time,the TMP was vacuum-dried at 70 �C and a pressure of lessthan 50 mbar. Where BDO was included in the formula-tion, it was mixed with the TMP and the mixture vac-uum-dried as for the TMP. The MDI was introduced tothe PTHF at 70 �C, followed by vigorous hand mixing for30 s. The TMP or TMP/BDO was then added to the resultingpre-polymer and hand mixing continued for 30 s. A reac-tion temperature of 70 �C was preferred to that of 90 �Cused elsewhere [9], so as to increase the pot life of the reac-tion mixture and hence facilitate subsequent liquid injec-tion molding. The injection molding apparatus compriseda sealed steel chamber connected to a closed aluminummold, which was preheated to 90 �C for 1 h, a vacuumpump and a compressed air supply. This allowed rapidswitching from the very low pressure required for efficientdegassing (50 mbar for 45 s) to the pressure of 2 bar neces-sary to inject the reactive mixture into the mold within its3 min pot-life. Once the mold was filled, the oven temper-ature was increased to 110 �C and the specimen cured atthis temperature for 24 h at 2 bar, after which the moldwas left to cool to room temperature. All specimens werestored in a desiccator at ambient temperature prior totesting.

To study the effect of the cross-link density on the ther-momechanical properties of the SMPUs, two formulations

were considered: PTHF (650 g/mol):MDI:TMP = 2:5:2 and1:4:2, corresponding to TMP concentrations nc = 0.71mol/kg and 1.04 mol/kg, respectively, nc providing a mea-sure of the cross-link density [9]. These will be referredto as P650-lowCD and P650-highCD in what follows. Ablend of PTHF with weight average molar masses ofMw = 650 and 1000 g/mol was also used to produce anSMPU with an increased degree of polydispersity of themolar mass between cross-links, which will be referredto as P650 + 1000. Finally, the chain extender BDO wasused to modify the mobility at the junction between thePTHF and the TMP, and between 2 TMPs, in a formulationthat will be referred to as P650 + CE. These formulationsand the corresponding nc are summarized in Table 1. Aschematic representation of the morphology of the SMPUsis given in Fig. 2.

A two-part thermoset SMPU resin purchased from SMPTechnologies (Japan) with the trade name MP5510 and arelatively narrow glass transition in the cured state wasalso investigated for comparison. The two components ofthe resin were degassed at room temperature under vac-uum (50 mbar) for 1 h. They were then thoroughly hand-mixed for 30 s in the ratio 40:60 by mass, giving a reactivemixture with a pot life of about 5 min. The mixture was in-jected as described above, with a mold temperature of 70 �Cand a curing time of 4 h, following the manufacturer’s rec-ommendations. The final Tg, measured by differential scan-ning calorimetry (DSC) at a heating rate of 10 �C/min was65 �C. All the specimens were post-cured at 110 �C (70 �Cfor MP5510) and slowly cooled to room temperature imme-diately before testing in order to erase any effects of phys-ical aging during storage. This precaution was important forthe reproducibility of the experimental results owing to theproximity of the Tg to room temperature in certain of theSMPUs investigated here.

2.2. Dynamic mechanical analysis (DMA)

DMA measurements were made using a TA InstrumentQ800 DMA calibrated with steel standards. 1 � 5 �10 mm3 rectangular specimens cut from the molded sheetswere tested in tensile mode in dry air at a heating rate of2 �C/min, a frequency of 1 Hz and a dynamic strain of0.01%, after equilibration at �50 �C. 1 Hz was chosen tobe the measurement frequency in order to provide dataconsistent with the timescale of the shape memory testsdescribed in the next section, i.e. so that processes occur-ring at fixed T in the time domain between 1 and100 min corresponded to processes occurring immediatelyabove this temperature in the DMA sweeps.

2.3. Tensile shape memory tests

Rectangular SMPU strips of 1 � 10 � 100 mm3 (ASTMstandard D 882) were tested using a Universal Testing Sys-tem (UTS, Walter + Bai AG, Switzerland) equipped with a1 kN load cell and an environmental chamber (Noske-Kae-ser, Germany), capable of raising and lowering T undercontrolled conditions. A K-type thermocouple placed on adummy specimen close to the test specimen was used toprovide a precise indication of the specimen temperature.

Table 1Molar composition corresponding to the different formulations, along with the molar concentration of TMP in the SMPUs, nc, and the glass transitiontemperature measured by differential scanning calorimetry (DSC) at a heating rate of 10 �C/min.

Designation PTHF 650 PTHF 1000 MDI TMP BDO nc (mol/kg) Tg (�C)

P650-lowCD 2 5 2 0.71 45P650-highCD 1 4 2 1.04 91P650 + 1000 0.5 0.5 4 2 0.95 71P650 + CE 1 4 1.2 1.2 0.63 –

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The strain was determined from the cross-head displace-ment. The test temperature was adjusted using heatingand cooling ramps of 10 �C/min. Under these conditions,fine tuning of the heating and cooling system allowedthe temperature set-point to be reached with a smooth,over-damped response, i.e. without overshoot. The timethe system took to reach a stable temperature within0.5 K of the set-point was between 6 and 10 min for therange of set-points investigated. There was generally asmall offset between the specimen temperature atequilibrium as measured by the thermocouple and thechamber temperature. The measured specimen tempera-ture rather than the set-point is therefore referred to inSection 3. The complete programming sequence was asfollows:

� Isotherm at the deformation temperature, Td, for15 min.� Deformation at Td to a strain em at a strain rate of

25%/min (step 1).� Cooling to the storage temperature, Ts, (25 �C in all

cases) immediately after deformation while maintain-ing em (step 2).� Unloading at a rate of 1 N/s to zero stress at Ts (step 3).� Storage at Ts for 10 min at zero stress, resulting in a final

fixed strain ef (step 4).

Fig. 1. Schematic of the programming and free recovery sequences, along withposition during periods of deformation and force control respectively. The spinterrupted during the 1 min interval between the programming sequence and

These steps are shown in Fig. 1 along with a qualitativeindication of the evolution of the force and the cross-headposition during periods of deformation and force controlrespectively. The duration of step 2 was fixed at 15 minregardless of Td, because this was the time required for sta-bilization of the temperature at Ts. For all the experiments,em was set to 25% because higher values resulted in thefailure of certain specimens. After unloading (step 3), itwas found that significant stress build-up took place ifthe cross-head position (as opposed to the stress) wasmaintained fixed during storage at Ts over relatively longtimes. While the subsequent free recovery behavior ofMP5510, for example, has been shown to be insensitiveto increases in the duration of step 4 to up to 2 h [8], inview of the potential influence of accompanying structuralchanges [10], as a precaution the storage time at Ts in theunloaded state was strictly limited to 10 min throughout.Moreover, the time interval between each programmingand recovery sequence during which it was necessary tointerrupt stress control was exactly 1 min in each case,which was sufficiently short for stress build-up in theclamped specimens to be negligible in all cases. The defor-mation temperature Td was chosen to be the temperaturecorresponding to the peak of tan d in the DMA scans, sothat at all the materials were deformed in the same visco-elastic regime.

a qualitative indication of the evolution of the force and the cross-headecimens remained in the clamps throughout but the force control wasthe recovery sequence.

Fig. 2. (a) Schematic of the morphology of the SMPUs in Table 1;structure of the cross-links (b) without and (c) with BDO.

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After programming, the subsequent behavior was stud-ied under free recovery conditions, i.e. at zero stress. Freerecovery was initiated by maintaining the stress at zerowhile heating to the recovery temperature, Tr, as shownin Fig. 1. The total recovery time, including temperatureequilibration at Tr, was 60 min for all the specimens. Threevalues of Tr were investigated in each case, correspondingto values of tan d of 0.05, 0.1 and 0.15 from the low tem-perature side of the tan d peak, i.e. the onset of the glasstransition, where slow shape recovery is expected [8].

In what follows, the time-dependent shape memory ef-fect will be described in terms of two normalized quanti-

Fig. 3. (a) Storage modulus, E0 , (b) loss modulus, E00 , and (c) loss factor, tan d, asscans at 1 Hz.

ties, the shape fixity ratio Rf(t) and the shape recoveryratio Rr(t) defined by

RfðtÞ ¼eðtÞem� 100 and RrðtÞ ¼

ef � eðtÞef

� 100

where e(t) is the measured strain at time t, em is the pro-gramming strain (25%) and ef is the as-programmed strain,i.e. the strain fixed at Ts after completion of the program-ming procedure. Given that the effective strain evolved lit-tle during the subsequent 1 min interval, the straincorresponding to the beginning of the recovery step wastaken to be ef. This definition of Rr differs slightly fromthe usual definition [1], and is preferred here because ittakes into account the slight decrease in strain that wasconsistently observed on unloading the specimens afterthe cooling step.

3. Results and discussion

3.1. Dynamic mechanical analysis

The storage modulus E0, loss modulus E00 and loss factortan d are shown as a function of T in Fig. 3. Each of theSMPUs showed a well-defined a transition in the temper-ature range investigated, characterized by a steep decrease

a function of temperature for the different SMPUs from DMA temperature

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in E0 with increasing T, and peaks in E00 and tan d. MP5510also showed a further decrease in E0 at temperatures above100 �C corresponding to the melting of a dispersed phaseassociated with physical cross-linking (in addition to thechemical cross-links also present in this formulation, asdiscussed elsewhere [8]).

Results derived from the DMA scans are summarized inTable 2. The crosslink densities, mx, were derived from E0 inthe rubbery plateau regime using E0 = 3kTmx. The mx in Table2 correlated well with nc (Table 1). One may therefore inferthe effective crosslink density of MP5510 to be similar tothat of P650 + CE. A systematic measure of the transitionwidth is given by the half height width (HHW) of the tand peak, i.e. the interval between the two temperatures atwhich tan d = tan dmax/2, where tan dmax is the maximumvalue of tan d. According to this criterion, the transitionwas much broader in the SMPUs based on P650 than inMP5510, consistent with previous reports, based on creepexperiments, of relatively broad retardation spectra in sim-ilar formulations to those in Table 1 [9]. As also shown inTable 2, the product of HHW and tan dmax was in the range18–20 K for all the SMPUs, indicating inverse proportional-ity between the height and width of the peak, as observedin the frequency domain for a variety of polymers, includ-ing polyurethanes [11]. It follows that one can gain a rapidappreciation of the relative widths of a series of peakssimply by comparing their heights.

In interpreting the widths of the tan d peaks in terms ofthe widths of the corresponding retardation time spectra,it is necessary to assume a thermorheologically simple re-sponse and that the time–temperature shift factors for thedifferent SMPUs show the same temperature dependencein the regime of interest. In the present case, this is to someextent justified in the temperature range down to about30 �C below the temperature of the tan d peak measuredat 1 Hz, in which shift factors derived from DMA frequencysweeps for certain of the SMPUs discussed here show asimilar WLF-type dependence [12]. However, significantdiscrepancies are seen at lower T, where there is overlapwith the calorimetric glass transition (cf. Tables 1 and 2)and possibly also lower temperature secondary transitions,depending on the chemical structure, so that the low tem-perature tail of the DMA temperature scans should be trea-ted with particular caution. This may be demonstrated byvarying the measurement frequency or the temperatureramp rate in the DMA scans, reduction of the ramp rate(and hence the effective Tg) at fixed measurement fre-quency leading to significant changes in the form of thetan d peak at T well below the temperature of the peakmaximum, for example. As discussed further in Section

Table 2Selected results from the DMA scans.

Crosslink density, mx (m�3) E00 peak temperature (�C) tan

MP5510 6.3 � 1026 68 81P650-lowCD 7.2 � 1026 38 67P650-highCD 1 � 1027 84 107P650 + 1000 9.5 � 1026 61 92P650 + CE 6.4 � 1026 65 84

3.2.1, the behavior in this temperature regime is also ex-pected to be sensitive to physical aging.

In the absence of the chain extender, the tan d peak gen-erally shifted to higher T as the crosslink density increasedin the PTHF-based polymers. The sensitivity of tan d tocrosslink density is thought to indicate a certain degreeof miscibility between the hard (MDI/TMP) and soft (PTHF)segments in these formulations, providing a convenientmeans of fine-tuning the effective actuation temperature.Comparison of the results for P650-lowCD and P650-highCD also suggests the tan d peak to broaden withincreasing crosslink density and to become increasinglyasymmetric, with an apparent cut-off in the longest retar-dation times (corresponding to the highest T). Thus, whilethe increased concentration of hard segments is assumedto reduce the mobility of the soft segments, and thecross-links apparently limit long-range cooperative mo-tion, the mobility associated with soft segments remotefrom the cross-links remains high. The presence of theserelatively mobile segments may also explain the highvalues of tan d and reduced glassy moduli observed at Twell below Tg compared with the corresponding valuesfor MP5510. This is reflected by the values of tan d at Ts

(25 �C throughout) given in Table 2, which provide an indi-cation of the capacity of an SMP to fix a secondary shape, aswill be discussed further in Section 3.2.1. The broadest tand peak was obtained for P650 + 1000, as expected given therelatively broad distribution of molar masses betweencross-links in this case, which implies a broad distributionof retardation times.

The effect of adding the chain extender (BDO) to thepolymer network is seen from comparison of P650 + CEwith P650-lowCD and P650-highCD. The crosslink densityfor P650-CE was close to that for P650-lowCD, resultingin a similar plateau modulus. However, the PTHF to MDIratio was the same as for P650-highCD. The peak temper-ature of tan d was consequently intermediate betweenthose of P650-lowCD and P650-highCD. However, the tand peak was significantly narrower than for these latter,suggesting a correspondingly narrower retardation timespectrum. To explain this effect, it is necessary to considerthe synthetic procedure used for P650 + CE in more detail.The BDO may be incorporated into the network in a varietyof ways; it may link two or more pre-polymer molecules,thus increasing the effective molar mass between adjacentcross-links, or form the junction between the pre-polymerand the hard MDI/TMP segments, or act as a spacer withinthe hard segments. These latter two possibilities (Fig. 2(c))were clearly favored by the present mixing procedure, inwhich the BDO was added to the reaction mixture at the

d peak temperature (�C) HHW (�C) HHW.tan dmax (�C) tan d(Ts)

21 19.5 0.02132 19.2 0.08834 17.9 0.03538 19.3 0.05328 19.6 0.042

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same time as the crosslinker. Incorporation of the chain ex-tender is therefore expected to increase the mobility of thehard segments. Moreover, given that BDO is chemicallysimilar to the PTHF repeat unit, its presence is also ex-pected to result in improved miscibility between the hardand soft segments. The resulting homogenization of themolecular mobility implies a reduction in the width ofthe retardation time spectrum and is hence consistent withthe relatively narrow tan d peak and intermediate tan dpeak temperature observed for P650-CE, in spite of itslow crosslink density.

Fig. 5. Shape loss on unloading, 100 � Rfu, as a function of the differencebetween Td and Ts.

3.2. Tensile shape memory tests

3.2.1. Shape fixity3.2.1.1. Instantaneous elastic recoil. The overall shape fixityratios, Rf, during the unloading and storage steps (steps 3and 4) of the programming sequence are shown in Fig. 4.For all the materials, Rf showed an initial linear decreasecorresponding to the unloading step, during which the loadwas reduced at a constant rate of 1 N/s. This instantaneouselastic recoil, as expressed by the value of the fixity ratioimmediately after unloading, Rfu, is attributed to reversiblethermal stresses developed below the glass transition tem-perature, and is hence assumed to be roughly proportionalto Td � Ts for a given coefficient of thermal expansion. Theassociated losses in shape fixity are shown in Fig. 5. Thelargest instantaneous elastic recoil of about 3.2%, corre-sponding to a change in absolute strain of 0.8%, was indeedobserved for P650-highCD, which had the highest tan dpeak temperature, and hence the highest Td (see Table 2).One might therefore expect P650-lowCD to show the low-est elastic recoil, but the extensive time-dependent shapeloss subsequent to unloading in this case (see the followingparagraph) suggests shape loss may also have been signif-icant during the unloading period, so that this material didnot follow the overall trend suggested by Fig. 5.

3.2.1.2. Time-dependent shape loss. Subsequent to the linearelastic recoil during unloading, Rf showed a further non-linear decrease during storage at Ts, as shown in Fig. 4.The shape loss, Rfu � Rf, and average rate of shape loss overthe 10 min storage period are given in Fig. 6. The rate of

Fig. 4. Overall shape fixity ratio, Rf, as a function of time, t, duringunloading and storage at Ts.

shape loss was between about 0.04% and 0.06%/min forall the SMPUs with the exception of P650-lowCD, for whichit reached about 0.16%/min. Even so, the overall shape lossafter unloading and 10 min storage at Ts did not exceed 5%in any of the SMPUs, as seen from Fig. 4, so that the shapefixity ratios were more than 95% in each case (98% forMP5510 and P650 + CE).

The time-dependent loss in shape fixity that followedunloading may be attributed to either viscoelastic recoveryof the polymer in the glassy state in response to the stored(internal) stresses or structural relaxation (physical aging)[7,10]. Volume contraction owing to physical aging occursover extended times and the total reduction in volume istypically less than 0.5% in amorphous polymers [13], corre-sponding to a linear strain of 0.17%, so that it is not thoughtto be a dominant contribution to the loss in shape fixity.Certainly the 2.5% time-dependent loss in shape fixity ob-served in P650-lowCD, which corresponds to an absolutestrain of about 0.6%, developed over around 10 min, cannotbe ascribed to physical aging alone, and hence necessarilyinvolves significant viscoelastic recovery. The chain mobil-ity at Ts (25 �C) is therefore too high in this case to ensurelong-term stability of the secondary shape. From the DMAcurves in Fig. 3, it is seen that Ts also overlapped stronglywith the tan d peak in in P650-lowCD, resulting in a rela-tively elevated value of tan d(Ts) compared with the otherSMPUs (Table 2). While long-term shape fixity studies arestill required, it is inferred from Fig. 6 that values of tand < 0.02 at Ts, for which Rf exceeds 98%, should result insatisfactory stability on the timescale of the presentexperiments.

It would also be of interest in future work to investigatethe effect of coupling between physical aging and visco-elastic recovery rates on shape fixity, because it is knownthat small amounts of volume contraction can dramaticallyreduce creep, for example [14]. Physical aging has alsobeen shown to reduce tan d in the temperature range cor-responding to the onset of the glass transition [15]. Thisimplies that subjecting glassy SMPs to physical aging priorto unloading, for example by reducing the cooling rate orintroducing a suitable isothermal heat treatment step priorto unloading, could be used to improve shape fixity. Phys-ical aging prior to unloading would presumably also

Fig. 6. (a) Overall shape loss, Rfu � Rf, during the 10 min period of storage at Ts and (b) average rate of shape loss during this period.

Fig. 7. Shape recovery ratio, Rr, versus time, t, for different Tr: (a) MP5510, (b) P650-lowCD, (c) P650-highCD, (d) P650 + 1000 and (e) P650 + CE.

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reduce subsequent aging effects, and hence reduce uncer-tainty in the recovery rates after long-term storage.

3.2.2. Shape recoveryRr is given as a function of recovery time in Fig. 7 for Tr

corresponding to tan d of 0.05, 0.1 and 0.15. As described inthe experimental section, T was ramped from Ts to Tr at arate of about 10 �C/min (the duration of this step dependedon Tr, but was generally between 6 and 10 min) and iso-thermal recovery then took place at Tr for the remainderof the cycle, which lasted a total of 60 min. Data corre-sponding to isothermal recovery were therefore obtainedafter at most 10 min in all the SMPUs.

The shape recovery rates for MP5510 were signifi-cantly higher than for the other SMPUs at any giventan d. The relatively narrow tan d peak observed forMP5510 in the DMA scans and the associated sensitivityof E0 to T were clearly important factors in this case, sug-gesting that there might be a simple correlation betweenHHW of the tan d peak and the shape recovery rate atfixed tan d. As shown in Fig. 8(a), Rr after the 60 minrecovery cycle generally increased with decreasingHHW at fixed tan d, although there were departuresfrom the overall trend and the correlation was weak atlarge HHW. For example, P650 + CE showed a similar Rr

to P650-highCD for tan d = 0.15 in spite of its signifi-cantly narrower tan d peak. However, it is seen fromFig. 8(b) that the average shape recovery rate over thelast 10 mins of the test, <Vr>, was higher for P650 + CE,implying it would show substantially greater recoverythan P650-highCD after longer times. This apparentcross-over may be explained by the somewhat bettershape fixity of P650 + CE. More generally, <Vr> showedimproved correlation with HHW for the SMPUs in Table1. However, the limitations of this approach are also evi-dent from the results for MP5510, which showed anapparent maximum in <Vr> at intermediate tan d. In thiscase, relatively large values of Rr were measured towardsthe end of the recovery step, particularly for tan d = 0.15,from which it may be inferred that the number of relax-ation processes activated per unit time was falling offrapidly. This follows from the assumption that time–

Fig. 8. (a) Shape recovery ratio after 60 min and (b) average shape recovery rate dheight width (HHW) of the tan d peak.

temperature shift factors may be used to transform vis-coelastic functions from the T domain to the frequencydomain, and that the approximate form of the retarda-tion time spectrum, L(s), at fixed T may be inferred di-rectly from the form of tan dx [12]. Thus, recovery asa function of time is effectively equivalent to the effectof increasing T at fixed x, in which case, large valuesof Rr presumably correspond to the high T side of thetan d peak and hence regimes where L(s) is decreasingrapidly with increasing s.

Fig. 9(a) and (b) show Rr after 60 min and <Vr> as a func-tion of the local slope of tan d at Tr. The local slope of tand(Tr) provides an alternative measure of the effective widthof the tan d peak, and has the advantage of being specific tothe shape of the tan d peak close to the measurement tem-perature. (In the case of a highly asymmetric peak, forexample, HHW may be strongly influenced by high T re-gions of the curve that are not directly relevant to shortterm processes characteristic of much lower Tr). Moreover,the slope of tan d(Tr) gives a rough indication of the num-ber of relaxation processes activated during a relativelyshort time interval (assuming the slope to remain roughlyconstant in the equivalent temperature range) and henceshould reflect the initial isothermal recovery rate, regard-less of the absolute value of Tr (provided one remains inthe temperature range corresponding to the low T side ofthe tan d peak).

As seen from Fig. 9, there was some correlation betweenthe recovery data and slope of tan d(Tr), as well as somedeviations. In this case, the deviations may be attributedat least in part to the simplifications implicit in theassumption of a direct link between tan d(T) at fixed xand H(s), as discussed in Section 3.1 [12]. Moreover, thedifferences in the time taken by the different specimensto reach Tr, depending on Tr � Ts, may influence the effec-tive timescale of the isothermal recovery and the extentof physical aging. Finally, as discussed previously in thecontext of Fig. 8, the large values of Rr measured towardsthe end of the recovery step for MP5510 imply that a largeproportion of the retardation time spectrum has beenswept out during the measurement, so that the final stagesof recovery correspond to temperature regimes in which

uring the last 10 min of the recovery period, <Vr>, as a function of the half

Fig. 9. (a) Shape recovery ratio, Rr, after 60 min and (b) average shape recovery rate during the last 10 min of the recovery period, <Vr>, as a function of thelocal slope of tan d for the different Tr.

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the slope in tan d may have changed significantly from itsvalue at Tr (its becoming negative on the high T side of thetan d peak). It follows that there should no longer be adirect correlation between <Vr> and tan d(Tr), under theseconditions, as borne out by Fig. 9(b).

In spite of the above reservations, and bearing in mindthe restricted range of experimental conditions so farinvestigated, the ensemble of the SMPUs investigated hereshowed generally consistent trends, suggesting that DMAtemperature scans may provide a rapid, semi-quantitativeindication of the capacity of a given formulation to meet agiven set of performance criteria. This is perhaps surprisingin view of the somewhat different chemical structure ofMP5510 from that of the other SMPUs, resulting in distinctrigid domains and hence ‘‘hybrid’’ chemical and physicalcrosslinking. However, given that programming was car-ried out at temperatures corresponding to the peak in tand for the soft phase, the physical crosslinking was unlikelyto have been disrupted by the deformation step [8], so thatunder the present conditions MP5510 may be consideredto behave as an ideal thermoset, whose effective crosslinkdensity may be estimated from the onset of the rubberyplateau (cf. Table 2).

It follows from these overall trends and the underlyingassumptions in the above discussion, that the sensitivity ofthe shape recovery rate to fluctuations in T will be reducedin systems in which the slope of tan d measured at 1 Hzvaries slowly in the temperature regime corresponding tothe target shape recovery rate (assumed to be situated onthe low T side of the tan d peak), or, equivalently, systemswith a broad retardation time spectrum. It also follows thatthe maximum achievable recovery rates should decreaseas the retardation time spectrum broadens.

The width of the retardation time spectrum is expectedto be influenced by factors such as the chemistry of theindividual components (polyol, isocyanate and cross-linker), the crosslink density and polydispersity of themolar mass between crosslinks and the homogeneity ofthe network. The chemistry determines the strength ofthe intermolecular and intramolecular interactions andhence the range of available molecular motions [7]. Forexample, Buckley et al. [9] observed broader retardationspectra with PTHF diol than with polycaprolactone diol,

or when using MDI rather than TDI as a co-reagent.Increasing the crosslink density may also affect the widthof the retardation time spectrum by limiting the molarmass between crosslinks, for example, and hence truncat-ing the long retardation time end of the spectrum, as seenhere for P650-highCD (Section 3.1) and suppressing thefastest retardation processes corresponding to segmentsremote from the crosslinks. In the present case, however,as seen from Table 2, there was little overall correlationbetween the crosslink density and the width of the tan dpeak. At the same time, the tan d peak temperature in-creased systematically with crosslink density in the seriesP650-lowCD, P650-highCD and P650 + 1000, suggestingthis chemistry to provide considerable scope for varyingthe actuation temperature and the temperature sensitivityof the rate of deployment of an SMPU component indepen-dently, which is one of the overall goals of the presentwork. It follows that chemical homogeneity is of primaryimportance in the present systems, as borne out by theresults for P650 + CE, on which basis it may be argued thatimproving the miscibility of hard and soft segmentsresults in a reduction of the width of the retardation timespectrum. In the case of MP5510, on the other hand, it iscomplete phase separation between the hard and soft seg-ments that leads to a relatively homogeneous ‘‘soft’’ phase,the hard segments being assimilated with the crosslinksand therefore not participating in the main a transition.Thus, not only is the a transition relatively sharp, but thetemperature of the tan d peak is also lower than thatof most of the other formulations investigated here (seeTable 2).

4. Conclusions

This work has shown that by modifying the moleculararchitecture of a series of chemically similar amorphousSMPUs it is possible to manipulate the width and positionof the tan d peak corresponding to the a transition in con-stant frequency DMA temperature scans. These changesare argued to reflect changes in the retardation time spec-trum, which may in turn be accounted for in terms inchanges in the crosslink density and chemical homogene-

C. Azra et al. / European Polymer Journal 49 (2013) 184–193 193

ity of the SMPUs. It follows that the shape memoryresponse may also be correlated with the form of the tand peak, allowing one to establish a direct link with changesin chemical structure. Based on the consistent trendsobserved in the SMPUs investigated so far, it is suggestedthat this may provide a convenient means of rapidlyscreening trial formulations. Work is currently in progressaimed at establishing a method for the quantitative predic-tion of shape recovery rates from DMA temperature scans,which should allow more detailed assessment of the valid-ity and the limitations of the various assumptions implicitin the present approach [12].

Acknowledgements

The authors gratefully acknowledge the financial sup-port of the Swiss Innovation Promotion Association, KTI/CTI and Debiotech SA, Lausanne.

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