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Shape Memory and Mechanical Properties of Cross-linked Polyethylene Clay Nanocomposites

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Macromolecular Nanotechnology Shape memory and mechanical properties of cross-linked polyethylene/clay nanocomposites Sayena Rezanejad, Mehrdad Kokabi * Polymer Engineering Group, Chemical Engineering Department, Faculty of Engineering, Tarbiat Modares University, P.O. Box 14115-143, Tehran, Islamic Republic of Iran Received 8 October 2006; received in revised form 7 April 2007; accepted 23 April 2007 Available online 5 May 2007 Abstract Shape memory polymer (SMP) such as cross-linked low-density polyethylene (XLDPE), can return from its temporary shape to the original (permanent) shape upon heating. SMP in comparison with shape memory alloy (SMA) and shape memory ceramic (SMC) has lower stiffness, so generates lower recovery force when it is being used as an actuator. Also, when SMP is reinforced with traditional micro-fillers, it often loses its shape memory effect due to the high weight fraction of filler (20–30%). To overcome these disadvantages, nanoclays can be used. The smart resultant nanocomposite, even in small clay loading level (0–10 wt.%), shows higher modulus, strength, and the other physical properties such as higher recovery force, required to act as an actuator. In this work, the effect of modified montmorillonite on mechanical and shape memory properties as well as the force generation of a shape memory cross-linked low density polyethylene were investigated. The results show that the modulus of elasticity, the recovery temperature, the recovery force and force recovery rate increase with increasing organoclay in nanocomposites, but final recovery strain decreases slightly. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Nanocomposite; Shape memory effect; Low density polyethylene; Organoclay; Actuator; Smart polymer 1. Introduction Smart/intelligent/adaptive systems are composed of three basic elements: sensors, actuators, and con- trol processors [1]. An intelligent material can respond adaptively to an environmental stimulus, such as a change in temperature and loading [2]. Smart materials have been the subject of much investigation in recent years. Shape memory materi- als are defined by their potential to store a deformed (temporary) shape and recover the original (perma- nent) shape [3]. The shape memory behaviour is typ- ically induced by a change in temperature and has been observed in metals, ceramics, and polymers [4]. Shape memory polymers have many advantages over shape memory counterparts in easy processing, low density, high shape recovery, high recoverable strain, and low manufacturing cost. Especially, their 0014-3057/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.eurpolymj.2007.04.031 * Corresponding author. Tel.: +98 21 8801 1001; fax: +98 21 8800 6544. E-mail address: [email protected] (M. Kokabi). European Polymer Journal 43 (2007) 2856–2865 www.elsevier.com/locate/europolj EUROPEAN POLYMER JOURNAL MACROMOLECULAR NANOTECHNOLOGY
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Page 1: Shape Memory and Mechanical Properties of Cross-linked Polyethylene Clay Nanocomposites

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European Polymer Journal 43 (2007) 2856–2865

www.elsevier.com/locate/europolj

POLYMERJOURNAL

Macromolecular Nanotechnology

Shape memory and mechanical propertiesof cross-linked polyethylene/clay nanocomposites

Sayena Rezanejad, Mehrdad Kokabi *

Polymer Engineering Group, Chemical Engineering Department, Faculty of Engineering, Tarbiat Modares University,

P.O. Box 14115-143, Tehran, Islamic Republic of Iran

Received 8 October 2006; received in revised form 7 April 2007; accepted 23 April 2007Available online 5 May 2007

Abstract

Shape memory polymer (SMP) such as cross-linked low-density polyethylene (XLDPE), can return from its temporaryshape to the original (permanent) shape upon heating. SMP in comparison with shape memory alloy (SMA) and shapememory ceramic (SMC) has lower stiffness, so generates lower recovery force when it is being used as an actuator. Also,when SMP is reinforced with traditional micro-fillers, it often loses its shape memory effect due to the high weight fractionof filler (20–30%). To overcome these disadvantages, nanoclays can be used. The smart resultant nanocomposite, even insmall clay loading level (0–10 wt.%), shows higher modulus, strength, and the other physical properties such as higherrecovery force, required to act as an actuator.

In this work, the effect of modified montmorillonite on mechanical and shape memory properties as well as the forcegeneration of a shape memory cross-linked low density polyethylene were investigated.

The results show that the modulus of elasticity, the recovery temperature, the recovery force and force recovery rateincrease with increasing organoclay in nanocomposites, but final recovery strain decreases slightly.� 2007 Elsevier Ltd. All rights reserved.

Keywords: Nanocomposite; Shape memory effect; Low density polyethylene; Organoclay; Actuator; Smart polymer

1. Introduction

Smart/intelligent/adaptive systems are composedof three basic elements: sensors, actuators, and con-trol processors [1]. An intelligent material canrespond adaptively to an environmental stimulus,such as a change in temperature and loading [2].

0014-3057/$ - see front matter � 2007 Elsevier Ltd. All rights reserved

doi:10.1016/j.eurpolymj.2007.04.031

* Corresponding author. Tel.: +98 21 8801 1001; fax: +98 218800 6544.

E-mail address: [email protected] (M. Kokabi).

Smart materials have been the subject of muchinvestigation in recent years. Shape memory materi-als are defined by their potential to store a deformed(temporary) shape and recover the original (perma-nent) shape [3]. The shape memory behaviour is typ-ically induced by a change in temperature and hasbeen observed in metals, ceramics, and polymers[4].

Shape memory polymers have many advantagesover shape memory counterparts in easy processing,low density, high shape recovery, high recoverablestrain, and low manufacturing cost. Especially, their

.

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Fig. 1. 3DS stress–strain–temperature relations in the typicalthermomechanical cycles [8].

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recoverable strain is of an order of 100%, whileshape memory metals or ceramics can recover onlyabout 10% or 1%, respectively [5].

All shape memory polymers have a two phasestructure [3]:

1. Hard phase (segment) which retains the perma-nent shape of the shape memory article doesnot melt or soften in the transition temperatureof soft segments. These segments could becross-linked rigid local structures or entangle-ments which will not disentangle in the recoverytemperature.

2. Soft phase (segment) which upon heatingbecomes soft and acts as a switch to rememberthe original (permanent) shape of the article.

The ability of shape memory polymers to spon-taneously recover large strains in restricted environ-ments has been exploited in numerous applications,such as heat-shrink tubing, deployable aerospacestructures, microsystems, and biomedical devices.Deformation (i.e., strain energy) is stored by areversible morphological change or a suppres-sion of molecular relaxation [6]. Theoretically, thestored energy can also be used to exert force, butto achieve this, the performance of such materialshas to be increased by enhancing the rubbery mod-ulus (elastic modulus above glass transition temper-ature) [7].

Typically, micro-scale fillers such as chopped car-bon, glass or Kevlar fibres are used to enhance therubbery modulus [2]. Ni et al. found that the tensilestrength besides thermo-mechanical stress of PU/fibre glass composites became higher by incrementalincrease of fibre weight fraction, but final recoverystrain decreased [7].

Recently, some interesting results have beenreported using nanocomposites such as polymericnanocomposites [5]. Studies have shown that con-strained bending recovery force of shape memorypolymer could be increased by 50% with the addi-tion of 20 wt.% of SiC [8,9]. Zheng found that shaperecovery time was shorter for poly (D,L-lactide)/hydroxyapatite composites in comparison with neatpolymers [10]. Also the work done by Koerner et al.shows uniform dispersion of 1–5 vol.% of carbonnanotubes in a thermoplastic elastomer yields nano-composites that can store and subsequently release,through remote means, up to 50% or more recoverystress than the pristine resin. The anisotropic nano-tubes increase the rubbery modulus by a factor of

2–5 and improve shape fixity by enhancing straininduced crystallization [11].

A typical pre-deformation and recovery cycle forshape memory polymers was described by Gall inthree steps (Fig. 1) [8]. First the SMP material hasto be heated to an elevated temperature. In the firststep of the cycle (step 1) sample is deformed to adesired strain (em). In the second step (step 2)SMP is cooled to fix the temporary shape. At thelower temperature, the SMP molecular chain seg-ments are frozen in a temporary position and uponremoving the constraint the induced shape isretained. In the final step, the SMP structure isheated up to transition temperature. In this stepthe two limiting cases of constraint are applied:unconstrained recovery (free recovery of strainupon heating in the absence of external limit as instep 3a) and constrained recovery (generation ofrecovery stress upon heating in SMP fixed at thepre-deformation strain (step 3b)).

Low density polyethylene (LDPE) by volume hasthe highest production in world plastics industry. Itsrather poor properties can be improved by cross-linking [12]. Cross-linked polyethylene deforms eas-ily above its crystalline melting point and this defor-mation can be fixed by cooling. On heating, it mayrestore to its original shape. Therefore, cross-linkedLDPE can be put into the class of shape memorypolymers particularly used in the heat-shrinkableproducts, packaging, and electrical industries [13].

Previous works on polyolefin nanocompositesshow that the addition of clay to polyolefin matrixwill effect physical properties such as crystallinity[14–16], and increase the mechanical properties such

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as modulus [17,18] and dynamic mechanical proper-ties (E 0/E00) [19]. These will enhance shape memoryeffect in the nanocomposites.

In this work, the dependency of mechanical andshape memory properties of cross-linked LDPE/clay nanocomposite on the weight fraction of claywas investigated.

2. Experimental

2.1. Materials

Organically modified clay (Org-MMT) Cloisite15A with 31.5 A intergallary spacing, ion exchangedby dimethyl dehydrogenated tallow ammoniumbromide were provided by Southern Clay Products.

Low density polyethylene (LDPE) grade LF0200with MFI of 1.6 g/10 min and density of 0.923 g/ml,was obtained from Bandar Imam PetrochemicalCompany, Iran.

Irganox 1010 antioxidant with density of 1.45g/ml was purchased from Ciba Geigy Co.

Dicumyl peroxide (DCP) with purity of 98% anddensity of 1.02 g/ml was obtained from HerculesCo.

2.2. Preparation of LDPE/Org-MMT compound

LDPE and 3, 5, 8 and 10 wt.% Cloisite 15A weremelt blended in a Brabender Plasticorder with achamber of 50 cm3 and roller blades at 170 �C.The screw speed was kept at a low speed of30 rpm for the first 5 min, and then increased to60 rpm for 25 min to obtain a well mixed system.Then the compound was removed from the chamberand cooled to room temperature.

2.3. Preparation of cross-linked LDPE/Org-MMT

Nanocomposites compound obtained from pre-vious section were mixed with 0.5 wt.% DCP and0.1 wt.% antioxidant at 130 �C and a screw speedof 50 rpm for 8 min. Original shape of the articlewas obtained by curing under a hot press at180 �C and 80 ton pressure.

2.4. Instrumentation

X-ray diffraction (XRD) patterns were per-formed using a Philips X-Pert apparatus withk = 1.5404 A. Transmission electron microscopy(TEM) image was obtained at 200 kV with a Philips

CM200 electron microscope. The sample wasembedded in an epoxy matrix and ultra-microtomedwith a diamond knife on a Coreichart OMUSmicrotome at room temperature to give 60–100 nmthick section. The section was transferred fromwater to Cu grades of 400 meshes.

To measure the gel content, samples in the formof fine granules were weighed and extracted withboiling xylene for 16 h at 140 �C according toASTM D2765.

Differential thermal analysis (DTA) was per-formed on a PL-STA 1500. Samples were heatedfrom 25 �C to 200 �C at a heating rate of 10 �C/min, and then cooled to room temperature at thesame rate. A Netzch 242C dynamic mechanical ana-lyzer (DMA) was used in tension mode with 1 Hzfrequency and dynamic force of 4 mN. Sampleswere heated from �100 �C to +100 �C with a heat-ing rate of 2 �C/min.

To measure the tensile properties of nanocom-posites, a tensile device with HBM load-cell andScott 55 amplifier which had a heating chamberwas used at four different temperatures (25, 60,108 and 150 �C) and cross-head speed of1.063 mm/s. To measure the thermo-mechanicalproperties of the products mentioned before, thesamples with 15 mm width, 1.3 mm thickness and50 mm length were heated up to 150 �C andstretched up to different pre-deformation strains(em) and then cooled instantaneously. Then, thedeformed samples were examined at the differentconditions.

2.4.1. Non-isothermal constant strain

The samples were heated from 25 �C to 150 �C atthe constant strain equal to em and generation ofstress in the sample was recorded by the load cell.

2.4.2. Isothermal constant strain

The samples were left at 108 �C instantaneouslyand the generation of stress with time was recorded.

2.4.3. Non-isothermal free strain recovery

The deformed samples were heated from 25 �C to150 �C in an oven and the free recovery of the sam-ples was determined as follows:

Freerecoverystrain ¼ ðLt � LrÞ=ðLt � LiÞ; ð1Þwhere Lt = temporary length: length of deformedsample, Lr = recovery length: length of sample dur-ing recovery that changes upon heating, Li = initiallength: original length of undeformed sample, and

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Scheme 1. Setup used to measure recovering length.

Fig. 2. XRD patterns of PE/Org-MMT nanocomposites andOrg-MMT (Cloisite 15A).

Table 1XRD data for PE/Org-MMT nanocomposites

Sample code 2h d-Spacing (nm)

Org-MMT (cloisite 15A) 2.75 3.1PE3 2.6 3.3PE5 2.49 3.7PE8 2.73 3.2PE10 2.79 3.1

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to measure Lr a setup similar to that shown inScheme 1 was employed.

By increasing the temperature, the sample beginsto shrink, thus pulls the wire and needle. Displace-ment of the needle is equal to the length change ofthe sample.

3. Results and discussion

3.1. Structure of nanocomposites

In the formation process of nanocomposite,polymer chains are inserted in the interlayer spaceof layered silicates to force them take distance fromeach other. XRD is a suitable means to evaluate thisprocess. According to the Bragg’s equation2d sinh = nk, every peak in XRD pattern is relatedto a distance (d), so the first peak observed in the2h below 5� is attributed to d001 or interlayer spac-ing. The XRD patterns of PE/Org-MMT nanocom-posites are shown in Fig. 2 and XRD datacalculated from the (001) peaks are summarizedin Table 1.

As is observed in Fig. 2 and Table 1, there is astrong peak at the position of 2.75� for Org-MMT, which corresponds to a d-spacing of3.15 nm. After melt blending with PE the positionof the (00 1) peak shifts to lower angles (higherd001) for each sample.

The viscosity of the matrix of nanocompositeswill increase with increasing of clay content, thusthe exerted shear stress to the layers will increaseand clay layers will separate easier up to the samplewith 5 wt.% of clay which has 3.7 nm d-spacing.But, after this point, the increasing clay contentprobably results in stacking layers and separation

of these layers may become more difficult. For thisreason, basal spacing will decrease. Finally noincrease could be observed in a 10 wt.% specimenin which nanocomposite would not be actuallyformed.

In most cases, TEM is combined with XRD totestify the microstructure of nanocomposites. It isconvenient to observe the dispersion of Org-MMTin the PE matrix by TEM. Fig. 3 is the TEM micro-graph of PE5, in which the dark lines are the layersof Org-MMT. According to the result obtainedfrom XRD, most of Org-MMT in PE5 system stillis parallel to each other and intercalation of PEchains only increases the interlayer space. Fromthe low magnification images one can see that theclay is well distributed in PE matrix and from thehigh magnification images the intercalated clay withPE chains can be observed. These results furthershow the intercalation effect of PE is limited. It isdue to its non-polar character even for an Org-MMT being modified with C-16.

Page 5: Shape Memory and Mechanical Properties of Cross-linked Polyethylene Clay Nanocomposites

Scheme 2. Schematic diagram of clay layers and macro-radicals.

Fig. 3. TEM micrograph of PE/Org-MMT nanocomposite PE5:(a) low magnification, (b) high magnification.

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3.2. Physical properties of nanocomposites

3.2.1. Cross-link density

Cross-link density of the samples was measuredand the results were listed in Table 2. It clearlyshows a decrease in cross-link density with increas-ing clay content.

To explain this trend, the mechanism of cross-linking by DCP must be realized. By applying heat,first DCP decomposes to free radicals and thenattacks the polymeric chains and converts them tomacro-radicals. These macro-radicals react witheach other and cross-link [20]. If a polymeric chainis caught between clay layers, it cannot find anotherchain to react with it. On the other hand, clay layers

Table 2Gel content of PE/Org-MMT nanocomposites

Sample code Gel content

PE 48PE3 46.44PE5 44.67PE8 30.79

behave like rigid obstacles that prevent cross-linkingreaction, and so the cross-link density decreases.This phenomenon is depicted as in Scheme 2.

According to the fact that cross-links are thehard segments that guarantee the shape memoryeffect, decreasing the cross-link density due to thepresence of clay will cause a drop in shape memoryeffect in the specimen and it prevents the sample toreturn completely back to its original shape, Fig. 4.

3.2.2. Thermal properties

Fig. 5 shows the DTA curve of PE/Org-MMTnanocomposites. To avoid overlap between curves,they are shifted in the vertical direction. Accordingto the cooling curves, addition of clay would notextremely change the Tc of the nanocomposites,

Fig. 4. Gel content of nanocomposites.

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Fig. 5. DTA curves of the PE/Org-MMT nanocomposites: (a)cooling curves, (b) heating curves.

Fig. 6. DMA results of the PE/Org-MMT nanocomposites (a)E 0, (b) E00, (c) tand.

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thus subjecting the samples to pre-deformation atthe same temperature is a right method. From theheating curve it is evident that Tm of the nanocom-posites would not change extremely, but in order tocompare the degree of crystallinity of the nanocom-posites, this curve could be used. The area above thecurve in the vicinity of Tm is proportional to thecrystallinity. To make the comparison easier,the plots are shifted in the vertical direction. Crys-tallinity of the samples increases up to nanocompos-ite PE3 and then begins to decrease. However, thedegree of crystallinity of the nanocomposites ishigher than neat polymers.

Clay layers in the PE matrix will exhibit behav-iour somewhat like nucleating agents and thus causeincrease in crystallinity. But increasing clay contentmore than 3 wt.% will increase viscosity of thematrix, and so the propagation of these spheruliteswill be inhibited and finally the amount of crystal-linity will be diminished.

3.2.3. Dynamic mechanical properties

Fig. 6 shows the E 0, E00 and tand curves of nano-composites. Curves are in the logarithmic scale.

From these curves, increase in E 0 and E00 is evi-dent (about 300% increase in both of E 0 and E00)which means that the incorporation of clay layersin PE matrix increases both the elasticity and plas-ticity characteristics of the nanocomposites.

Increase in elasticity character of the chains ismore dramatic which causes increase in stress gener-ation rate in the samples at the recovery process. Theamount of tand of the nanocomposites decreaseswhich means that the damping character of thechains will decrease upon addition of clay layers.

As mentioned previously, nanocomposite matrixcontains crystal regions, cross-link regions andregions beside clay layers which cause restrictionin the mobility of the polymer chains. Chainsactivation in these regions takes place at different

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temperatures. Because of this variety of transitions(mobilities), the tand curves of these samples arevery broad and no sharp transition could beobserved.

Fig. 8. Elasticity modulus of PE/Org-MMT nanocomposites atfour different temperatures.

3.2.4. Tensile properties

Tensile test was carried out on the samples atfour different temperatures, as mentioned in theexperimental section. The results are shown inFig. 7. It is observed that by increasing clay contentan increase in elastic modulus (slope of the diagramsin the linear section) besides a decrease in elonga-tion-at-break are observed. The presence of clay lay-ers in the PE matrix will prevent PE chains from freemotions thus decreasing the toughness and increas-ing the brittleness.

The modulus of elasticity of the samples at vari-ous temperatures was plotted in Fig. 8. Extremeincrease in elasticity modulus due to increasing claycontent could be observable (143% increase for 8wt.% clay loading, in comparison with the neatpolymer at ambient temperature). Increasing in

Fig. 7. Tensile results of PE/Org-MMT nanoc

Young’s modulus will cause increase in generatedstress in the nanocomposite samples according toHook’s law (r = Ee).

3.3. Shape memory properties of nanocomposites

3.3.1. Free recovery strain

Fig. 9 shows the recovery strain obtained fromnanocomposites with different clay loading levels

omposites at four different temperatures.

Page 8: Shape Memory and Mechanical Properties of Cross-linked Polyethylene Clay Nanocomposites

Fig. 9. Recovery strain curve of nanocomposites with (a) 50%,(b) 100% pre-deformation strain.

Fig. 10. Recovery stress results of nanocomposites with (a) 50%,(b) 100% pre-deformation strain.

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at various pre-deformation strains. According tothese curves, increasing clay content shifts therecovery temperature (incline point of S-type recov-ery curve) to higher point and the final recoverablestrain to decrease.

DTA results show that increasing clay contentincreases crystallinity in nanocomposites whichcauses the recovery temperature to increase. Recov-ery temperature is the temperature in which poly-ethylene crystals melt and amorphous chains canreturn back to their initial random state. Thus,increasing crystallinity will increase the recoverytemperature.

Additionally, increasing clay content will preventpolymer chains to move freely and hinders theirmotion, thus prevents them to be recovered com-pletely to their original shape. The other reason ininterpreting this observation could be the presenceof clay layers without shape memory potentialwhich will properly decrease the total shape mem-ory effect of the nanocomposite so decreasing the

final recovery strain (12% decrease for PE8 in com-parison with neat polymer).

3.3.2. Recovery stress (force generation)3.3.2.1. Non-isothermal condition. Fig. 10 shows theforce generation in nanocomposites kept at constantstrain, while increasing the temperature. This phe-nomenon is very similar to increasing pressure ofgasses with increasing temperature at constant vol-ume PV ¼ nRT .

Increasing temperature will cause crystallineregions to melt and amorphous chains tend toreturn back to their original random shape withhigher entropy. In this stage, preventing the chainmotion (kept at constant strain) generates the forcein the samples. Increasing clay content will increasethe amount of the generated force in samples duringtemperature rise.

Tensile test results show that increasing claycontent enhances elastic modulus and accordingto Hook’s law, i.e., r = Ee, this will cause risein the generated stress. Thus, increase in modu-lus may cause an increase in recovery stress of

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Fig. 11. Recovery stress at 108 �C for nanocomposites with (a)50%, (b) 100% pre-deformation strain.

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nanocomposites which makes the polymeric chainsto generate higher forces during recovery.

Another interesting feature in these curves isincreasing the slope of curves by increasing claycontent. According to the rubber elasticity theory,the slope of stress curve versus temperature is pro-portional to the number of cross-links existing inthe polymeric matrix ðr ¼ n

V RT ða� 1aÞ, where n

Vand a are the number of cross-links per unit volumeand stretching ratio, respectively).

Recently, Mark [21] has found that n is not onlythe number of cross-links, but relates to every hardsegment that exists in the matrix, for instance in thisstudy, the crystalline regions as well as the clay lay-ers. Thus, increasing clay content and accordinglyincreasing crystalline regions may cause the slopeof these curves to increase.

Finally, in these curves a decrease in generatedstress after reaching its maximum value could beobserved. Trznadel relates this phenomenon to slip-page of polymeric chains above each other and theirdisentanglement [22]. By increasing clay content thisdecrease will become less and less and completelydisappears at 8 wt.% of clay. A schematic presenta-tion of molecules in neat polymer and nanocompos-ite is given in Scheme 3 (a: neat polymer, b:nanocomposite).

Cross-links could not be formed in the surface ofthe clays, thus the presence of clay layers causes thecross-links to distribute more efficiently in thematrix. In a good distributed system, the likelihoodof entanglements between two cross-links is higher,thus by stretching, disentanglement is less probableand only configurationally changes would occur inthe nanocomposites.

Scheme 3. Schematic design of (a) neat poly

3.3.2.2. Isothermal condition. To compare the rate ofstress generation in nanocomposites, a stress recov-ery test was performed in isothermal condition (at108 �C which is the maximum temperature thatnanocomposite with 8 wt.% clay reaches to its max-imum recovery stress). The results of the test areshown in Fig. 11.

mer chains, (b) nanocomposite chains.

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As it is evident, increasing clay content causes theslope of the curves (rate of stress generation innanocomposites) to increase. This increase is dueto the increased elastic character of the polymericchains (according to DMA results) which can gener-ate higher stresses in shorter time intervals.

4. Conclusions

Produced nanocomposites have intercalatedstructure as characterized by XRD and TEM. Pres-ence of clay layers in the matrix causes cross-linkdensity to decrease and crystallinity to increase.These layers extremely improve mechanical proper-ties such as storage, loss, and Young’s modulus.

Besides these changes, clay layers have strongeffect on shape memory properties. The final recov-ery strain decreases slightly (about 12%) but due totheir improved mechanical properties, recoverystress (force generation) increases extremely (about200%) in nanocomposites.

Increased recovery stress in shape memory cross-linked polyethylene nanocomposite is an advantageto produce high performance light weight actuatorwith reasonable recovery strains.

Acknowledgement

The authors thank the Ministry of Science,Research and Technology of Islamic Republic ofIran for the financial support.

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