High-Temperature Shape Memory Behavior of Semicrystalline Polyamide Thermosets
|
|
- Audra Eaton
- 5 years ago
- Views:
Transcription
1 This is n open ccess rticle pulished under Cretive Commons Non-Commercil No Derivtive Works (CC-BY-NC-ND) Attriution License, which permits copying nd redistriution of the rticle, nd cretion of dpttions, ll for non-commercil purposes. Cite This: Downloded vi on Decemer 31, 2018 t 13:44:33 (UTC). See for options on how to legitimtely shre pulished rticles. High-Temperture Shpe Memory Behvior of Semicrystlline Polymide Thermosets Ming Li,,, Qingo Gun, nd Theo J. Dingemns*,, Ntionl Engineering Reserch Center for Biotechnology, Nnjing Tech University, Nnjing , Chin Fculty of Aerospce Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlnds Dutch Polymer Institute (DPI), P.O. Box 902, 5600 AX Eindhoven, The Netherlnds Deprtment of Mteril Science nd Engineering, Soochow University, Suzhou , Chin Deprtment of Applied Physicl Sciences, University of North Crolin t Chpel Hill, 1113 Murry Hll, Chpel Hill, North Crolin , United Sttes *S Supporting Informtion ABSTRACT: We hve explored semicrystlline poly- (decmethylene terephthlmide) (PA 10T) sed thermosets s single-component high-temperture (>200 C) shpe memory polymers (SMPs). The PA 10T thermosets were prepred from rective thermoplstic precursors. Rective phenylethynyl (PE) functionlities were either ttched t the chin termini or plced s side groups long the polymer min chin. The shpe fixtion nd recovery performnce of the thermoset films were investigted using rheometer in torsion mode. By controlling the M n of the rective oligomers, or the PE concentrtion of the PE side-group functionlized copolymides, we were le to design dul-shpe memory PA 10T thermosets with rod recovery temperture rnge of C. The thermosets sed on the 1000 g mol 1 rective PE precursor nd the copolymide with 15 mol % PE side groups show the highest fixtion rte (99%) nd recovery rte ( 90%). High temperture triple-shpe memory ehvior cn e chieved s well when we use the melt trnsition (T m 200 C) nd the glss trnsition (T g = 125 C) s the two switches. The recovery rte of the two recovery steps re highly dependent on the crystllinity of the thermosets nd vry within wide rnge of 74% 139% nd 40 82% for the two steps, respectively. Reversile shpe memory events could lso e demonstrted when we perform forwrd nd ckwrd deformtion in triple shpe memory cycle. We lso studied the ngulr recovery velocity s function of temperture, which provides thermokinemtic picture of the shpe recovery process nd helps to progrm for desired shpe memory ehvior. KEYWORDS: semiromtic polymides, semicrystlline thermosets, high-temperture shpe memory, dul-shpe memory, triple-shpe memory, recovery velocity 1. INTRODUCTION Interest in shpe memory polymers (SMPs) hs grown rpidly since the 1980s. 1 5 Typicl pplictions re het-shrink tuing, temperture sensors nd ctutors, iomedicl nd surgicl mterils, nd erospce devices. 6,7 Thermoresponsive SMPs re the most investigted systems tht polymers re le to dopt temporry shpe upon deformtion nd to revert ck to the permnent shpe upon exposure to het. 7,8 They re generlly composed of polymer network to mintin the permnent shpe nd reversile switch responsile for the shpe fixtion nd recovery The glss trnsition temperture (T g ) nd melting temperture (T m ) re the two most importnt therml trnsitions for thermoresponsive SMPs. Polyurethnes, polyesters, nd (methyl)crylte-sed polymer networks hve een investigted s SMPs sed on the glss trnsition. Cross-linked semicrystlline networks or (multi)- lock copolymer systems hve een developed to design T m - sed SMPs, such s polyolefins, polyethers, nd polyesters. 6 However, most SMPs exhiit switching temperture lower thn 100 C, which my not meet the requirements for high temperture erospce, utomotive, or electronic pplictions. Recently, severl exmples of high-temperture (>200 C) SMPs hve een reported Vi nd co-workers synthesized n morphous fluorinted polyimide with shpe recovery temperture of 220 C. 20 This ws the first exmple of single-component high-temperture SMP. However, this fluorinted polyimide cn only e otined s thin films, which excludes the possiility to produce complex shpes using melt processing methods. Weiss et l. hve introduced ionic moieties into poly(ether ether ketone) (PEEK) leding to T g -sed SMP with switching temperture close to 200 C, where the exct switching temperture depends on the metl counterions Received: Mrch 4, 2018 Accepted: April 27, 2018 Pulished: My 9, Americn Chemicl Society 19106
2 Scheme 1. Structures of Precursors vi (A) Rective End-Group Approch nd (B) Rective Side-Group Approch used. 14 In lter puliction, this system ws further developed into T m -sed SMP y incorportion of sodium olete, which displys higher switching temperture of C due to the melting of sodium olete. 15 In contrst to the dul SMPs mentioned ove, triple SMPs feturing two independent temporry shpes were first reported y Lendlein s group. 22 They require two progrmming steps nd show two recovery steps. Triple-shpe memory effects cn e relized in polymer mteril possessing two distinct therml trnsitions 15,22 24 or one single rod trnsition such s rod glss trnsition. 16,25 High temperture triple SMPs sed on single-component thermotropic liquid crystlline poly(esterimide) thermosets hve recently een reported y Gun et l. The polymer shows two glss trnsition tempertures t 120 nd 200 C, oth of which cn e used s switches for triple SMPs. 21 In previous pulictions we reported on the synthesis nd (thermo)mechnicl properties of semiromtic polymide thermosets sed on poly(decmethylene terephthlmide) (PA 10T). 26,27 We showed tht this clss of polymers cn e processed into semicrystlline thermoset films where the degree of crystllinity cn e controlled. The melting/crystlliztion of the crystlline phse nd the covlent network cn e used s the high-temperture switch nd permnent scffold, respectively, for dul shpe memory effect (SME). More sophisticted triple nd one-wy reversile SME cn e designed with the glss trnsition s the second switch. To the est of our knowledge, this is the first demonstrtion of high-temperture SMP sed on single-component semicrystlline polymide thermoset. 2. EXPERIMENTAL SECTION 2.1. Mterils. The syntheses of phenylethynyl (PE) end-cpped PA 10T oligomers (Scheme 1A) nd PE side-group-functionlized copolymides (Scheme 1B) hve een descried in detil elsewhere. 26,27 In order to otin covlently cross-linked polymide network, the rective precursors were thermlly cured. A stndrd melt compression technique ws used to prepre the thermoset films ccording to the following procedure: The precursor polymers were ground into fine powder using mortr nd pestle. The powder ws plced etween two metl pltes lined with Kpton film, nd this stck ws consolidted in Joos hot-press using predetermined temperture progrm nd 5 kn force. The temperture progrm ws set to het to 350 C t5 C min 1, hold for 15 min, nd cooled to 50 C t20 C min 1. The otined cured films were used for further chrcteriztion. The film smples prepred from PA 10T rective oligomers (M n of 1000 nd 3000 g mol 1 ) re denoted s PE-1K nd PE-3K. TPE-5, TPE-10, nd TPE-15 represent the film smples prepred from rective TPE-copolymides with 5, 10, nd 15 mol % of rective TPE comonomer, respectively. A PA 10T thermoplstic smple (M n = 7500 g mol 1 ) ws used s the reference in this pper nd denoted s Ref. The 1 H NMR spectr of the synthesized precursors (Supporting Informtion, Figure S1) confirms tht the concentrtion of rective functionlities, either s end-cps or s side groups, is consistent with the feed rtio of the monomers Chrcteriztion. 1 H NMR spectr were recorded on 400 MHz Bruker WM-400 t 25 C using trifluorocetic cid-d s solvent. DSC ws conducted on PerkinElmer Spphire DSC under nitrogen tmosphere t heting/cooling rte of 20 C min 1. DMTA ws performed on PerkinElmer Dimond DMTA with film smples ( mm thick) t heting rte of 2 C min 1 under nitrogen tmosphere. Dt were collected t frequency of 1 Hz. The SME ws chrcterized in cyclic torsion mode s illustrted in Figure 1. Compred to the trditionl extension or ending tests, 28 torsion tests involve nonhomogeneous strins nd stresses in the cross section of rectngulr r nd enle the SMPs to rech lrge deformtions with moderte strins, which re elieved to e more representtive of prcticl pplictions of SMPs The shpe progrmming nd recovery cycles were performed using Thermofisher Hke MARS III rheometer equipped with solid clmp geometry under N 2 tmosphere. Rectngulr thin films with width of 2.5 mm nd thickness of 0.25 mm were loded into the setup with length of 15 mm etween the clmps. The smples were deformed in torsion mode t constnt strin rte of 0.1% s 1 equivlent to rottion speed of 3.4 s 1. The procedure of one cycle for dul SME test includes the following steps: (1) het the smple to the progrmming temperture 19107
3 Figure 2. DSC heting scns (first het) of (A) reference polymer (Ref), PE-3K, nd PE-1K nd (B) reference polymer (Ref), TPE-5, TPE-10, nd TPE-15. The sterisk refers to melting peks (N 2 tmosphere nd heting rte of 20 C min 1 ). Tle 1. Therml Properties of the Thermoplstic Reference Polymer (Ref) nd the Cured Thermoset Smples Figure 1. Illustrtion of shpe deformtion, fixtion, nd recovery cycle of the dul SME in torsion mode. (T prog ); (2) rotte the smple to the predetermined ngle (ϕ d ); (3) keep the ngle constnt, cool to the fixtion temperture (T f )t10 C min 1 nd stilize for 10 min; (4) remove the stress; (5) het the smple to T prog t 10 C min 1 in stress-free condition followed y n isotherml hold t T prog for 10 min to stilize. This cycle ws repeted multiple times to chrcterize the reproduciility of the shpe memory performnce. The rottion ngle of the smple ws monitored nd recorded during the whole test. For triple SME mesurements, the smple ws consecutively deformed in two steps in one progrmming cycle. Two different T prog s were used, one eing ove T m nd the other etween T g nd T m. 3. RESULTS AND DISCUSSION 3.1. Melting nd Thermomechnicl Properties. In generl, either the T g or the T m trnsition of polymer cn e pplied to trigger dul-shpe memory event; however, to chieve high-temperture triple-shpe memory ehvior in single-component polymer is chllenging, s two high-temperture temporry networks with distinct ruery plteus re required. 15,22 24 One solution to relize this type of structure is to introduce moderte cross-links into high-t g semicrystlline polymer. In our previous work, we hve explored semiromtic polymide, PA 10T (T g = 125 C, T m = 315 C), s the se polymer to prepre semicrystlline polymide thermosets. Phenylethynyl (PE) shows high cure-temperture of C nd thus is le to provide proper processing window for the PA 10T-sed precursors. Therefore, we hve synthesized rective PE-sed end-cp nd rective PEsed comonomer, which were copolymerized with terephthlic cid nd 1,10-diminodecne to yield curle PE end-cpped oligomers nd PE side-group functionlized copolymers. The polymide thermosets were otined fter susequent therml cure t temperture of 350 C for 15 min. PE-1K nd PE-3K refer to the cured end-cpped oligomers with M n = 1000 nd 3000 g mol 1, respectively. TPE-5, TPE-10, nd TPE- 15 represent the cured side-group functionlized copolymides with 5, 10, nd 15 mol % PE side groups, respectively. The melting curves nd properties of thermoplstic PA 10T reference polymer (Ref) nd the resultnt polymide thermosets re shown in Figure 2 nd Tle 1. The thermoset smples fter cure re semicrystlline showing T m of smple T m ΔH m (J g 1 ) T g cross-linking density c (kmol m 3 ) Ref PE-3K PE-1K TPE TPE TPE T m refers to the mx of the melting pek s oserved in DSC experiments. T g refers to the mx of E s oserved in DMTA experiments. c Cross-linking density (υ) ws clculted using υ =, RT where E is the storge modulus of cured films t 350 C (T = 623 K) nd R the universl gs constnt (8.314 J K 1 mol 1 ). C nd ΔH m of 8 33 J g 1. These vlues re much lower thn the T m nd the ΔH m of the reference polymer (Ref) (318 C nd 82 J g 1 ), which mens the crystllizility of the polymer chins in the thermosets is strongly suppressed. Figure 3 shows the thermomechnicl ehvior of the reference polymer (Ref) nd the thermosets. The Ref film exhiits T g t 127 C, ut this film fils t 297 C ecuse it hs reched the melting point (T m ). In contrst to the reference polymer (Ref), the thermoset smples show two plteu regions (T g T m nd >T m ) in the DMTA profiles. The second plteu of the thermosets is stle up to 400 C, which confirms the presence of network structure. The T g s of oth thermoset smples remin virtully unchnged ( C) when compred to tht of the reference polymer (Ref). The moleculr structure of the resultnt semicrystlline thermosets is depicted in Figure 4. PE groups comine t the cure temperture resulting in cross-links with multiple ftercure chemicl structures depending on cure temperture, time, nd PE concentrtion. We ttempted to investigte the cure chemistry using Rmn nd FTIR spectroscopy. 33,34 However, Rmn spectroscopy filed due to strong fluorescence ckground, nd FTIR cnnot detect the cetylene ond of PE ecuse of IR insensitivity. Hence, direct evidence is not ville to confirm the chemicl chnge of the PE functionlities. The DMTA results of the cured smples show ruery plteu ove T m, nd this plteu is stle up to 400 C, which confirms tht cross-linking hs tken plce during cure. The two-plteu therml ehvior enles tripleshpe memory properties y tking oth T g nd T m trnsitions s the switches. The T m trnsition cn e solely used s switch 19108
4 Figure 3. DMTA of (A) reference polymer (Ref), PE-1K, nd PE-3K films nd (B) reference polymer (Ref), TPE-5, TPE-10, nd TPE-15 films. Heting rte 2 C min 1 under N 2 tmosphere nd frequency of 1 Hz. The insets show E t the glss trnsition temperture. Figure 4. Moleculr representtion of the semicrystlline PA 10T thermosets. Crystlline polymer (drk lue) is emedded in n morphous mtrix (light lue), nd the red dots represent covlent cross-link points. to design high-temperture (>200 C) dul-shpe memory polymer Dul-Shpe Memory Behvior. Becuse of the semicrystlline nture of the synthesized polymide thermosets, their melting nd crystlliztion processes cn e used s the thermoresponsive switch for dul-shpe memory ehvior. Three consecutive deformtion, fixtion, nd recovery cycles in torsion mode were conducted for ech smple to test the shpe memory performnce over multiple cycles. Shpe fixtion rte ( ) nd shpe recovery rte ( ) re the most importnt prmeters to chrcterize the shpe memory performnce. 35 descries how ccurtely the temporry shpe cn e fixed, nd quntifies the ility of the polymer to memorize its permnent shpe. When performing the mesurements in torsion mode, nd cn e clculted using eqs 1 nd 2. φf = 100% φd (1) φ φ d r = 100% φd (2) where φ d, φ f, nd φ r denote the rottionl ngle fter deformtion, t the fixed temporry shpe t T f, nd fter Figure 5. Three consecutive dul-shpe memory cycles for (A) reference polymer (Ref), (B) PE-3K, nd (C) PE-1K. Shpe recovery velocity s function of temperture in the second cycle for (D) reference polymer (Ref), (E) PE-3K, nd (F) PE-1K. Cooling/heting rte 10 C min 1 nd N 2 tmosphere
5 recovery, respectively. The instntneous recovery velocity V r cn e clculted s the time derivtive of the ngle s shown in eq 3. = φ Vr t Plotting V r ginst temperture revels the temperture rnge corresponding to the shpe recovery process. 21 This provides cler thermokinemtic view of the shpe recovery nd helps to progrm for desired SME. The thermoplstic reference film (ref) cnnot e deformed ove the melting temperture ecuse of the sence of ruery plteu, thus the glss trnsition ws used s the switch for the SME. As shown in Figure 5A, the smple ws deformed t 220 C, which lies etween T g (127 C) nd T m (318 C), nd the shpe ws fixed t 100 C where the smple is in glssy stte. Therefore, the crystlline domins ct s the scffold, nd the deformtion of the polymer tkes plce in the morphous stte. In contrst to the reference polymer (Ref), PE-3K nd PE- 1K thermoset films re stle up to 400 C in DMTA experiments nd exhiit two plteu regions (T g T m nd >T m ), s shown in Figure 3. This llows for deforming the film smples in the second plteu region (>T m ). Figures 5B nd 5C show tht PE-3K nd PE-1K were deformed t 315 nd 275 C, respectively, which is out 30 C higher thn their T m s (283 nd 244 C). At this temperture the covlent network cts s the scffold, nd the temporry shpe is fixed y crystlliztion nd vitrifiction t the fixtion step. At the recovery step, the ngle shows slight decrese when the smple psses through the glss trnsition, which is ssocited with the relese of the stress trpped in the moile morphous region. A susequent slow increse in the ngle is oserved, which cn e explined y therml expnsion. 36 When the smple strts melting, the ngle recovers rpidly due to the fst relese of the trpped stress. The shpe-memory performnce of the first few cycles is usully not representtive, s cn e seen in Figure 5B,C. This is generlly ttriuted to residul strin from the processing history of the smple. 13,35 Tle 2 shows the fixtion nd Tle 2. Dul-Shpe Fixtion nd Recovery Results of the Reference Thermoplstic Polymer (Ref), PE-3K, nd PE-1K Thermoset Films cycle 1 cycle 2 cycle 3 smple T prog T r Ref PE-3K PE-1K , T prog refers to the progrmming temperture. T r refers to the temperture t the mximum recovery velocity. recovery results of the first three cycles of the reference thermoplstic polymer (Ref), the PE-3K, nd PE-1K thermoset films. The PE-3K film shows very low of 36% in the first cycle compred to the following cycles ( = 72% nd 76%), wheres the of the PE-1K film shows medium chnge over cycles ( = 81%, 90%, nd 88%). Such significnt difference cn originte from the different cross-linking densities of these two smples. PE-3K hs lower cross-linking density nd (3) therefore longer polymer chins etween cross-links, which is more likely to store residul strin. The recovery of oth smples cnnot rech 100% ecuse the irreversile chinsegment orienttion nd the relxtion effect in the polymer network prtly dissipte the stored entropy. 20 The shpe recovery velocity of the second cycle is plotted s function of temperture s shown in Figure 5D F. The reference polymer (Ref) shows low velocity (<20 min 1 ) through the recovery process ecuse the shpe recovery is triggered y the ctivtion of the morphous chin segments, which re strongly restricted y the crystlline domins. A low recovery velocity is generlly oserved in T g -sed shpememory polymers. 8 In contrst, PE-3K shows quick recovery in the temperture rnge of C nd reches mximum V r of 60 min 1 t 285 C, which is close to its T m (283 C). The shpe recovery is triggered y melting of the crystlline domins, which is reltively fst process. It is worthy to note tht the PE-1K film ws deformed t 275 C in one step; however, this polymer shows two distinct recovery steps with mximum recovery velocity of min 1 t round 144 nd 240 C, respectively. The first recovery tkes plce when the smple psses through the glss trnsition nd reches n of 42% t 200 C. The second recovery is triggered y the melting of the crystlline domins. These two recovery steps indicte tht the crystlline domins in PE-1K re not le to form penetrting scffold throughout the smple nd thus cnnot completely lock the morphous chins. This llows the smple to prtilly recover t the T g T m rnge. These results demonstrte tht the degree of crystllinity, which is reflected in the ΔH m vlues in Tle 1, strongly ffects the shpe memory ehvior of our semicrystlline PAs. The dul-shpe memory ehvior of the TPE-sed thermosets were investigted using the sme method. Tle 3 Tle 3. Dul-Shpe Fixtion nd Recovery Results of the TPE Thermoset Films cycle 1 cycle 2 cycle 3 smple T prog T r TPE TPE TPE , T prog refers to the progrmming temperture. T r refers to the temperture t the mximum recovery velocity. shows the shpe fixtion nd recovery results for these smples. All smples revel good shpe fixtion with vlues of 93 99%. The TPE-15 smples with the highest cross-linking density shown in Tle 1 exhiit excellent recovery efficiency ( > 90%), wheres the other smples show vlues of 62 66% in the first cycle nd 78 82% in the second nd third cycles. Figure 6 shows the dul-shpe memory cycles nd the recovery velocity of the TPE thermoset films. Similr to the PE- 3K smple, TPE-5 nd TPE-10 exhiit one recovery step in the temperture rnges of nd C, respectively. Interestingly, the TPE-15 film lso displys two recovery steps, which is similr to tht of the PE-1K film. The two recovery steps originte from the low degree of crystllinity in TPE-15 nd PE-1K, where the morphous chin segments cnnot e 19110
6 Figure 6. Three consecutive dul-shpe memory cycles for the TPE series (A) TPE-5, (B) TPE-10, nd (C) TPE-15. Shpe recovery velocity s function of temperture in the second cycle for the TPE series (D) TPE-5, (E) TPE-10, nd (F) TPE-15. Cooling nd heting rte 10 C min 1 nd N 2 tmosphere. Figure 7. Three consecutive triple-shpe memory cycles for the PE series (A) PE-3K nd (B) PE-1K. Shpe recovery velocity s function of temperture in the second cycle for the PE series (C) PE-3K nd (D) PE-1K. Cooling nd heting rte 10 C min 1 nd N 2 tmosphere. completely fixed when the temperture is ove T g. TPE-5, TPE-10, nd PE-3K, on the other hnd, show higher degrees of crystllinity, nd this prevents the T g -induced shpe recovery. The difference etween these smples clerly indictes tht the shpe memory ehvior strongly depends on the degree of crystllinity of the semicrystlline thermosets. By chnging the concentrtion of the PE side groups in the rective copolymides, the cross-linking density of the thermosets cn e controlled, consequently leding to djustle crystllinity nd shpe memory ehvior Triple-Shpe Memory Behvior. Bsed on our study ove, two reversile processes, the glss trnsition nd the melting process, cn oth ct s the switches to trigger shpe recovery. Unlike the trditionl high-temperture triple-smp composed of multiple components, we were le to design single-component triple-smp using oth switches to chieve two distinct recovery processes. Figure 7A shows the three consecutive triple-shpe memory cycles for PE-3K. The film smple ws first heted up to 315 C, which is ove the T m (283 C) nd rotted y 90 from the originl shpe A (φ A ) to temporry shpe B (φ B ). The smple ws cooled to 200 C, temperture etween T m nd T g,tofix the shpe B. A second rottion of 90 ws then pplied to rech the temporry shpe C (φ C ). The smple ws susequently cooled to 60 C, which is elow the T g of 127 C, to fix the shpe C. The externl stress ws then removed, 19111
7 Tle 4. Triple-Shpe Fixtion nd Recovery Results of the PE- nd TPE-Series Thermoset Films smple T prog1 T prog2 T r1 T r2 cycle 1 cycle 2 cycle 3 (C B) PE-3K PE-1K TPE TPE TPE T prog1 nd T prog2 refer to the first nd second progrmming temperture, respectively. T r1 nd T r2 refer to the temperture t the first nd second mximum recovery velocity, respectively. (B A) (C B) (B A) (C B) (B A) Figure 8. Three consecutive triple-shpe memory cycles for (A) TPE-5, (B) TPE-10, nd (C) TPE-15. Angulr velocity of shpe recovery s function of temperture in the second cycle for (D) TPE-5, (E) TPE-10, nd (F) TPE-15. Cooling nd heting rte 10 C min 1 nd N 2 tmosphere. leding to the finl fixed temporry shpe (φ f ). A shpe fixtion rte ( )of 90% ws clculted using eq 4. φf = 100% φc (4) In the susequent recovery step, the smple ws heted up to 315 C in stress-free stte to monitor the recovery of the rottionl ngle. The shpe recovery ws ccomplished in two distinct steps, s shown in Figure 7A. This mens the thermoset cn memorize two temporry shpes in one single shpe memory cycle. The shpe recovery rte (C B) nd (B A) were clculted sed on eqs 5 nd 6, respectively. 21 φ φ f B/rec (C B) = 100% φ φ C B (5) φ φ B/rec A/rec (B A) = 100% φ φ B A (6) where φ A, φ B, nd φ C denote the rottionl ngle of shpe A (φ A =0 ), shpe B (φ B =90 ), nd shpe C (φ C = 180 ); φ B/rec nd φ A/rec re the rottionl ngles of the first nd second recovered shpes, respectively. Figure 7B shows the triple-shpe memory cycles of PE-1K. This polymer exhiits lower T m (244 C) compred to PE-3K (283 C); therefore, lower progrmming tempertures (275 nd 150 C) were used. PE-3K shows moderte (C B) vlues of 67 80% in the first recovery step nd (B A) vlues of 60 73% in the second recovery step, s listed in Tle 4. Compred to PE-3K, PE-1K shows much higher (C B) vlues of % nd lower (B A) vlues of 40 49%. The first recovery is triggered y the glss trnsition nd is due to the relese of stress in the morphous phse. The mjor recovery tkes plce in the first step, indicting tht the crystlline phse cnnot completely lock the stress in the morphous phse. The stress, which is supposed to relese in the second recovery step, is ctully prtilly relesed in the first recovery step. This, together with the stress induced y the second deformtion, drives the smple to rech high recovery rte (>100%) in the first step. This result is consistent with the result we otined from the dulshpe memory experiments nd origintes from the low degree of crystllinity of the PE-1K thermoset. Figures 7C nd 7D show the shpe recovery velocity of PE- 3K nd PE-1K smples s function of temperture. The first recovery step of PE-3K shows lower V r (13 min 1 ) thn the second step (28 min 1 ) ecuse of the limited moility of the morphous chin segments restricted y the crystlline domins. In contrst, the PE-1K smple shows much higher V r (54 min 1 ) in the first step, which is due to its low degree of crystllinity. The triple-shpe memory cycles nd recovery velocity of the TPE thermosets re shown in Figure 8. The TPE-5 nd TPE
8 Figure 9. Three consecutive triple-shpe memory cycles for TPE-10 nd shpe recovery velocity s function of temperture in the second cycle. (A) nd (B) deformtion of 180 nd 180 in two steps, respectively; (C) nd (D) deformtion of 180 nd 360 in two steps, respectively. films show moderte (C B) nd (B A) (64 91%) nd higher V r vlues in the second recovery step, which is similr to the ehvior of PE-3K, wheres the TPE-15 smple, similr to PE- 1K, exhiits high (C B) (97 136%) nd V r vlues (38 min 1 ) in the first recovery step, ecuse this polymer hs the lowest degree of crystllinity. The tempertures t the first mximum recovery velocity (T r1 ) of ll smples re within nrrow rnge of C ecuse the T g of ll smples is round 125 C. However, the tempertures of the second mximum recovery velocity (T r2 ), which depend on the T m of the smples, disply rod vrition etween 236 nd 289 C. Therefore, the triple-shpe memory ehvior of the thermosets is highly tunle over wide temperture regime. Besides deforming the smple in one direction only, more interestingly, we cn involve oth forwrd nd ckwrd deformtions in triple-shpe memory cycle; therefore, the corresponding temporry shpes would recover in reverse direction. To demonstrte this, the TPE-10 thermoset smple, which shows high (>90%), (C B) ( 90%), nd (B A) ( 80%), ws selected s representtive exmple. The results of test I re shown in Figure 9A,B. The smple ws progrmmed forwrd nd ckwrd y 180 in two steps nd reched finl temporry shpe, which is identicl to the originl shpe. The susequent heting resulted in n increse in ngle in the first recovery step chieving mximum recovery velocity t 142 C nd n (C B) of 79 91% t 213 C. By incresing the temperture further, the smple recovered in the reverse direction reching mximum recovery velocity t 243 C nd n (B A) of 81 87% (Tle 5). These results demonstrte tht our semicrystlline PA thermosets show onewy reversile shpe memory ehvior. The reversile shpe chnges in this experiment occurred without ppliction of ny Tle 5. Triple-Shpe Fixtion nd Recovery Results of TPE-10 Deformed in Two Opposite Directions test cycle no. Δφ d1 (deg) Δφ d2 (deg) (C B) (B A) T mx I II Δφ d1 nd Δφ d2 refer to the deformtion ngles in the first nd second deformtion steps. T mx refers to the temperture t the mximum ngle. externl force. The shpe chnges were driven y internl stress of the oppositely strined networks formed in the first nd second progrmming steps. We cn djust the second progrmming step from Δφ d2 = 180 to Δφ d2 = 360 in test II, which results in two opposite temporry shpes, s shown in Figure 9C,D. The smple shows of 89 91%, (C B) of 82 86%, nd (B A) of 54 61% (Tle 5). The mximum recovery velocity occurs t 142 nd 244 C in the first nd second recovery steps, respectively, which is consistent with the results of Test I. Our results clerly demonstrte tht high-temperture SME with tunle recovery directions nd mplitudes cn e designed sed on our single-component semicrystlline polymide thermosets. 4. CONCLUSIONS We hve investigted two novel series semicrystlline PA thermosets nd demonstrted tht they cn e s singlecomponent high-temperture (>200 C) shpe memory 19113
9 polymers (SMPs). Two moleculr design pproches sed on rective phenylethynyl (PE) functionlities hve een explored: cross-linked semicrystlline PA films were prepred y curing rective thermoplstic PA 10T oligomers, nd films were prepred y curing rective thermoplstic side-group functionlized copolymides. Compred to the thermoplstic PA 10T reference polymer, the PE-3K, TPE-5, nd TPE-10 thermoset films show high-temperture dul-shpe memory ehvior (>200 C) when T m is used s the switching temperture. The densely cross-linked PE-1K nd TPE-15 films show the highest fixtion rte (99%) nd recovery rte ( 90%) nd two distinct recovery steps ecuse the degree of crystllinity is too low nd cnnot provide scffold tht locks the shpe t tempertures etween T g nd T m. Triple-shpe memory ehvior cn e demonstrted when the T g ( 125 C) is used s the second switching temperture. The recovery rte of the two recovery steps is highly dependent on the degree of crystllinity of the thermosets nd vry within rod rnge of 74% 139% nd 40 82% for the first nd second step, respectively. One-wy reversile shpe memory events cn lso e designed when we perform forwrd nd ckwrd deformtion in triple shpe memory cycle. We lso studied the recovery velocity s function of temperture to elorte the thermokinemtics of the shpe recovery process. The use of phenylethynyl rective functionlities llows us to control the degree of crystllinity in the finl polymide thermosets nd in turn tune their shpe memory ehvior in terms of recovery temperture, velocity, nd efficiency. We elieve tht the design rules presented herein will help in designing new shpe memory polymers sed on well-known semicrystlline polymide chemistries. ASSOCIATED CONTENT *S Supporting Informtion The Supporting Informtion is ville free of chrge on the ACS Pulictions wesite t. Figure S1 (PDF) AUTHOR INFORMATION Corresponding Author *E-mil: tjd@unc.edu (T.J.D.). ORCID Qingo Gun: Theo J. Dingemns: Present Address T.J.D.: Deprtment of Applied Physicl Sciences, University of North Crolin t Chpel Hill, 1113 Murry Hll, 121 South Rod, Chpel Hill, NC Notes The uthors declre no competing finncil interest. ACKNOWLEDGMENTS This reserch forms prt of the reserch progrm of the Dutch Polymer Institute (DPI), Project #743. The uthors thnk the DPI for finncil support. The uthors thnk Prof. S. Sheiko, Dr. J. Bijleveld, Dr. R. Bose, nd Dr. R. Rulkens for fruitful discussions. REFERENCES (1) Xie, T. Recent dvnces in polymer shpe memory. Polymer 2011, 52 (22), (2) Hu, J.; Zhu, Y.; Hung, H.; Lu, J. Recent dvnces in shpe memory polymers: Structure, mechnism, functionlity, modeling nd pplictions. Prog. Polym. Sci. 2012, 37 (12), (3) Rousseu, I. A. Chllenges of shpe memory polymers: A review of the progress towrd overcoming SMP s limittions. Polym. Eng. Sci. 2008, 48 (11), (4) Behl, M.; Rzzq, M. Y.; Lendlein, A. Multifunctionl Shpe- Memory Polymers. Adv. Mter. 2010, 22 (31), (5) Pilte, F.; Tonchev, A.; Duois, P.; Rquez, J.-M. Shpe-memory polymers for multiple pplictions in the mterils world. Eur. Polym. J. 2016, 80, (6) Hger, M. D.; Bode, S.; Weer, C.; Schuert, U. S. Shpe memory polymers: Pst, present nd future developments. Prog. Polym. Sci. 2015, 49-50, (7) Leng, J.; Ln, X.; Liu, Y.; Du, S. Shpe-memory polymers nd their composites: stimulus methods nd pplictions. Prog. Mter. Sci. 2011, 56 (7), (8) Zho, Q.; Qi, H. J.; Xie, T. Recent progress in shpe memory polymer: New ehvior, enling mterils, nd mechnistic understnding. Prog. Polym. Sci. 2015, 49-50, (9) Wu, X.; Hung, W. M.; Zho, Y.; Ding, Z.; Tng, C.; Zhng, J. Mechnisms of the shpe memory effect in polymeric mterils. Polymers 2013, 5 (4), (10) Meng, H.; Li, G. A review of stimuli-responsive shpe memory polymer composites. Polymer 2013, 54 (9), (11) Lewis, C. L.; Dell, E. M. A review of shpe memory polymers ering reversile inding groups. J. Polym. Sci., Prt B: Polym. Phys. 2016, 54 (14), (12) Xio, X.; Kong, D.; Qiu, X.; Zhng, W.; Liu, Y.; Zhng, S.; Zhng, F.; Hu, Y.; Leng, J. Shpe memory polymers with high nd low temperture resistnt properties. Sci. Rep. 2015, 5, (13) Xio, X.; Kong, D.; Qiu, X.; Zhng, W.; Zhng, F.; Liu, L.; Liu, Y.; Zhng, S.; Hu, Y.; Leng, J. Shpe-memory polymers with djustle high glss trnsition tempertures. Mcromolecules 2015, 48 (11), (14) Shi, Y.; Weiss, R. Sulfonted Poly (ether ether ketone) Ionomers nd Their High Temperture Shpe Memory Behvior. Mcromolecules 2014, 47 (5), (15) Shi, Y.; Yoonessi, M.; Weiss, R. High temperture shpe memory polymers. Mcromolecules 2013, 46 (10), (16) Yng, Z.; Chen, Y.; Wng, Q.; Wng, T. High performnce multiple-shpe memory ehviors of Poly (enzoxzole-co-imide) s. Polymer 2016, 88, (17) Xio, X.; Qiu, X.; Kong, D.; Zhng, W.; Liu, Y.; Leng, J. Opticlly trnsprent high temperture shpe memory polymers. Soft Mtter 2016, 12 (11), (18) Bi, Y.; Mo, L.; Liu, Y. High temperture shpe memory polyimide ionomer. J. Appl. Polym. Sci. 2016, 133 (30), (19) Wng, Q.; Bi, Y.; Chen, Y.; Ju, J.; Zheng, F.; Wng, T. High performnce shpe memory polyimides sed on π π interctions. J. Mter. Chem. A 2015, 3 (1), (20) Koerner, H.; Strong, R. J.; Smith, M. L.; Wng, D. H.; Tn, L.- S.; Lee, K. M.; White, T. J.; Vi, R. A. Polymer design for high temperture shpe memory: Low crosslink density polyimides. Polymer 2013, 54 (1), (21) Gun, Q.; Picken, S. J.; Sheiko, S. S.; Dingemns, T. J. High- Temperture Shpe Memory Behvior of Novel All-Aromtic (AB)n- Multilock Copoly(ester imide)s. Mcromolecules 2017, 50 (10), (22) Bellin, I.; Kelch, S.; Lnger, R.; Lendlein, A. Polymeric tripleshpe mterils. Proc. Ntl. Acd. Sci. U. S. A. 2006, 103 (48), (23) Behl, M.; Lendlein, A. Triple-shpe polymers. J. Mter. Chem. 2010, 20 (17), (24) Xie, T.; Xio, X.; Cheng, Y. T. Reveling triple-shpe memory effect y polymer ilyers. Mcromol. Rpid Commun. 2009, 30 (21), (25) Xie, T. Tunle polymer multi-shpe memory effect. Nture 2010, 464 (7286),
10 (26) Li, M.; Dingemns, T. J. Synthesis nd chrcteriztion of semicrystlline poly (decmethylene terephthlmide) thermosets. Polymer 2017, 108, (27) Li, M.; Bijleveld, J.; Dingemns, T. J. Synthesis nd Properties of Semi-crystlline Poly(decmethylene terephthlmide) Thermosets from Rective Side-group Copolymides. Eur. Polym. J. 2018, 98, (28) Wgermier, W.; Krtz, K.; Heuchel, M.; Lendlein, A. Chrcteriztion methods for shpe-memory polymers. In Shpe- Memory Polymers; Springer: 2009; pp (29) Dini, J.; Fredy, C.; Gilormini, P.; Merckel, Y.; Reǵnier, G.; Rousseu, I. A torsion test for the study of the lrge deformtion recovery of shpe memory polymers. Polym. Test. 2011, 30 (3), (30) Bghni, M. Anlyticl study on torsion of shpe-memorypolymer prismtic rs with rectngulr cross-sections. Int. J. Eng. Sci. 2014, 76, (31) Bghni, M.; Nghddi, R.; Arghvni, J.; Sohrpour, S. A constitutive model for shpe memory polymers with ppliction to torsion of prismtic rs. J. Intell. Mter. Syst. Struct. 2012, 23 (2), (32) Dini, J.; Gilormini, P.; Fre dy, C.; Rousseu, I. Predicting therml shpe memory of crosslinked polymer networks from liner viscoelsticity. Int. J. Solids Struct. 2012, 49 (5), (33) Roerts, C. C.; Apple, T. M.; Wnek, G. E. Curing chemistry of phenylethynyl-terminted imide oligomers: Synthesis of 13C-leled oligomers nd solid-stte NMR studies. J. Polym. Sci., Prt A: Polym. Chem. 2000, 38 (19), (34) Iql, M.; Norder, B.; Mendes, E.; Dingemns, T. J. All-romtic liquid crystlline thermosets with high glss trnsition tempertures. J. Polym. Sci., Prt A: Polym. Chem. 2009, 47 (5), (35) Lendlein, A.; Kelch, S. Shpe-memory polymers. Angew. Chem., Int. Ed. 2002, 41 (12), (36) Većhmre, C.; Buleón, A.; Chunier, L.; Guthier, C.; Lourdin, D. Understnding the mechnisms involved in shpe memory strch: mcromoleculr orienttion, stress recovery nd moleculr moility. Mcromolecules 2011, 44 (23),
Effects of peripheral drilling moment on delamination using special drill bits
journl of mterils processing technology 01 (008 471 476 journl homepge: www.elsevier.com/locte/jmtprotec Effects of peripherl illing moment on delmintion using specil ill bits C.C. Tso,, H. Hocheng b Deprtment
More informationp-adic Egyptian Fractions
p-adic Egyptin Frctions Contents 1 Introduction 1 2 Trditionl Egyptin Frctions nd Greedy Algorithm 2 3 Set-up 3 4 p-greedy Algorithm 5 5 p-egyptin Trditionl 10 6 Conclusion 1 Introduction An Egyptin frction
More informationDetermination of the activation energy of silicone rubbers using different kinetic analysis methods
Determintion of the ctivtion energy of silicone rubbers using different kinetic nlysis methods OU Huibin SAHLI ohmed BAIEE Thierry nd GELIN Jen-Clude FETO-ST Institute / Applied echnics Deprtment, 2 rue
More informationCHAPTER 20: Second Law of Thermodynamics
CHAER 0: Second Lw of hermodynmics Responses to Questions 3. kg of liquid iron will hve greter entropy, since it is less ordered thn solid iron nd its molecules hve more therml motion. In ddition, het
More informationThermal Stability of Ti-C-Ni-Cr and Ti-C-Ni-Cr-Al-Si Nanocomposite Coatings
Journl of Physics: Conference Series PAPER OPEN ACCESS Therml Stility of Ti-C-Ni-Cr nd Ti-C-Ni-Cr-Al-Si Nnocomposite Cotings To cite this rticle: A V Andreev et l 2015 J. Phys.: Conf. Ser. 652 012057 View
More informationI1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3
2 The Prllel Circuit Electric Circuits: Figure 2- elow show ttery nd multiple resistors rrnged in prllel. Ech resistor receives portion of the current from the ttery sed on its resistnce. The split is
More informationEnergy (kcal mol -1 ) Force (kcal mol -1 Å -1 ) Pore axis (Å) Mixed Mo-only S-only Graphene
Force (kcl mol -1 Å -1 ) Energy (kcl mol -1 ) 3 1-1 - -3 Mixed Mo-only S-only Grphene 6 5 3 1 Mixed Mo-only S-only Grphene - -1-1 1 Pore xis (Å) -1 1 Pore xis (Å) Supplementry Figure 1 Energy Brriers.
More informationNew Expansion and Infinite Series
Interntionl Mthemticl Forum, Vol. 9, 204, no. 22, 06-073 HIKARI Ltd, www.m-hikri.com http://dx.doi.org/0.2988/imf.204.4502 New Expnsion nd Infinite Series Diyun Zhng College of Computer Nnjing University
More informationDETERMINATION OF MECHANICAL PROPERTIES OF NANOSTRUCTURES WITH COMPLEX CRYSTAL LATTICE USING MOMENT INTERACTION AT MICROSCALE
Determintion RevAdvMterSci of mechnicl 0(009) -7 properties of nnostructures with complex crystl lttice using DETERMINATION OF MECHANICAL PROPERTIES OF NANOSTRUCTURES WITH COMPLEX CRYSTAL LATTICE USING
More informationThermal Diffusivity. Paul Hughes. Department of Physics and Astronomy The University of Manchester Manchester M13 9PL. Second Year Laboratory Report
Therml iffusivity Pul Hughes eprtment of Physics nd Astronomy The University of nchester nchester 3 9PL Second Yer Lbortory Report Nov 4 Abstrct We investigted the therml diffusivity of cylindricl block
More informationa * a (2,1) 1,1 0,1 1,1 2,1 hkl 1,0 1,0 2,0 O 2,1 0,1 1,1 0,2 1,2 2,2
18 34.3 The Reciprocl Lttice The inverse of the intersections of plne with the unit cell xes is used to find the Miller indices of the plne. The inverse of the d-spcing etween plnes ppers in expressions
More informationLesson 8. Thermomechanical Measurements for Energy Systems (MENR) Measurements for Mechanical Systems and Production (MMER)
Lesson 8 Thermomechnicl Mesurements for Energy Systems (MEN) Mesurements for Mechnicl Systems nd Production (MME) A.Y. 205-6 Zccri (ino ) Del Prete Mesurement of Mechnicl STAIN Strin mesurements re perhps
More informationThe development of nanoscale morphology in polymer:fullerene. photovoltaic blends during solvent casting
Supplementry informtion Supplementry Mteril (ES) for Soft Mtter The development of nnoscle morphology in polymer:fullerene photovoltic lends during solvent csting To Wng, * Aln D. F. Dunr, Pul A. Stniec,
More informationSTRUCTURAL AND MAGNETIC PROPERTIES OF Fe/Si x Fe 1! x MULTILAYERS
MOLECULAR PHYSICS REPORTS 0 (00) 8-86 STRUCTURAL AND MAGNETIC PROPERTIES OF Fe/ x Fe! x MULTILAYERS P. WANDZIUK, M. KOPCEWICZ, B. SZYMAŃSKI, AND T. LUCIŃSKI Institute of Moleculr Physics, Polish Acdemy
More informationFully Kinetic Simulations of Ion Beam Neutralization
Fully Kinetic Simultions of Ion Bem Neutrliztion Joseph Wng University of Southern Cliforni Hideyuki Usui Kyoto University E-mil: josephjw@usc.edu; usui@rish.kyoto-u.c.jp 1. Introduction Ion em emission/neutrliztion
More informationHomework Solution - Set 5 Due: Friday 10/03/08
CE 96 Introduction to the Theory of Computtion ll 2008 Homework olution - et 5 Due: ridy 10/0/08 1. Textook, Pge 86, Exercise 1.21. () 1 2 Add new strt stte nd finl stte. Mke originl finl stte non-finl.
More information- 5 - TEST 2. This test is on the final sections of this session's syllabus and. should be attempted by all students.
- 5 - TEST 2 This test is on the finl sections of this session's syllbus nd should be ttempted by ll students. Anything written here will not be mrked. - 6 - QUESTION 1 [Mrks 22] A thin non-conducting
More informationQUADRATURE is an old-fashioned word that refers to
World Acdemy of Science Engineering nd Technology Interntionl Journl of Mthemticl nd Computtionl Sciences Vol:5 No:7 011 A New Qudrture Rule Derived from Spline Interpoltion with Error Anlysis Hdi Tghvfrd
More informationMechanism of Roughness-induced CO 2 Microbubble Nucleation in Polypropylene Foaming
Electronic Supplementry Mteril (ESI) for Physicl Chemistry Chemicl Physics. This journl is the Owner Societies 2017 Supporting Informtion Mechnism of Roughness-induced CO 2 Microbubble Nucletion in Polypropylene
More informationShear Degradation and Possible viscoelastic properties of High Molecular Weight Oil Drag Reducer Polymers
ANNUAL TRANSACTIONS OF THE NORDIC RHEOLOGY SOCIETY, VOL. 3, 2005 Sher Degrdtion nd Possible viscoelstic properties of High Moleculr Weight Oil Drg Reducer Polymers A.A. Hmoud, C. Elissen, C. Idsøe nd T.
More informationMeasuring Enthalpy Changes and Gas Laws
Mesuring Enthlpy Chnges nd Gs Lws PURPOSE To oserve chnges in enthlpy in chemicl processes. To determine the reltionship etween the pressure nd volume of gs. GOALS 1 To identify exothermic nd endothermic
More informationStudies on Nuclear Fuel Rod Thermal Performance
Avilble online t www.sciencedirect.com Energy Procedi 1 (1) 1 17 Studies on Nucler Fuel od herml Performnce Eskndri, M.1; Bvndi, A ; Mihndoost, A3* 1 Deprtment of Physics, Islmic Azd University, Shirz
More informationEntropy ISSN
Entropy 006, 8[], 50-6 50 Entropy ISSN 099-4300 www.mdpi.org/entropy/ ENTROPY GENERATION IN PRESSURE GRADIENT ASSISTED COUETTE FLOW WITH DIFFERENT THERMAL BOUNDARY CONDITIONS Abdul Aziz Deprtment of Mechnicl
More informationDesigning Information Devices and Systems I Discussion 8B
Lst Updted: 2018-10-17 19:40 1 EECS 16A Fll 2018 Designing Informtion Devices nd Systems I Discussion 8B 1. Why Bother With Thévenin Anywy? () Find Thévenin eqiuvlent for the circuit shown elow. 2kΩ 5V
More informationThe practical version
Roerto s Notes on Integrl Clculus Chpter 4: Definite integrls nd the FTC Section 7 The Fundmentl Theorem of Clculus: The prcticl version Wht you need to know lredy: The theoreticl version of the FTC. Wht
More informationLecture Solution of a System of Linear Equation
ChE Lecture Notes, Dept. of Chemicl Engineering, Univ. of TN, Knoville - D. Keffer, 5/9/98 (updted /) Lecture 8- - Solution of System of Liner Eqution 8. Why is it importnt to e le to solve system of liner
More informationFig. 1. Open-Loop and Closed-Loop Systems with Plant Variations
ME 3600 Control ystems Chrcteristics of Open-Loop nd Closed-Loop ystems Importnt Control ystem Chrcteristics o ensitivity of system response to prmetric vritions cn be reduced o rnsient nd stedy-stte responses
More informationFlexible Beam. Objectives
Flexile Bem Ojectives The ojective of this l is to lern out the chllenges posed y resonnces in feedck systems. An intuitive understnding will e gined through the mnul control of flexile em resemling lrge
More informationEmission of K -, L - and M - Auger Electrons from Cu Atoms. Abstract
Emission of K -, L - nd M - uger Electrons from Cu toms Mohmed ssd bdel-rouf Physics Deprtment, Science College, UEU, l in 17551, United rb Emirtes ssd@ueu.c.e bstrct The emission of uger electrons from
More informationLecture 08: Feb. 08, 2019
4CS4-6:Theory of Computtion(Closure on Reg. Lngs., regex to NDFA, DFA to regex) Prof. K.R. Chowdhry Lecture 08: Fe. 08, 2019 : Professor of CS Disclimer: These notes hve not een sujected to the usul scrutiny
More informationInterpreting Integrals and the Fundamental Theorem
Interpreting Integrls nd the Fundmentl Theorem Tody, we go further in interpreting the mening of the definite integrl. Using Units to Aid Interprettion We lredy know tht if f(t) is the rte of chnge of
More informationPeriod #2 Notes: Electronic Structure of Atoms
Period # Notes: Electronic Structure of Atoms The logicl plce (for civil engineers) to begin in describing mterils is t the tomic scle. The bsic elements of the tom re the proton, the neutron, nd the electron:
More information1 Bending of a beam with a rectangular section
1 Bending of bem with rectngulr section x3 Episseur b M x 2 x x 1 2h M Figure 1 : Geometry of the bem nd pplied lod The bem in figure 1 hs rectngur section (thickness 2h, width b. The pplied lod is pure
More informationA Critical Path Problem Using Intuitionistic. Trapezoidal Fuzzy Number
pplied Mthemticl Sciences, Vol. 8, 0, no. 5, 555-56 HIKRI Ltd, www.m-hikri.com http://dx.doi.org/0.988/ms.0.9 Criticl Pth Prolem Using Intuitionistic Trpezoidl Fuzzy Numer P. Jygowri Deprtment of Mthemtics
More informationDesigning Information Devices and Systems I Spring 2018 Homework 7
EECS 16A Designing Informtion Devices nd Systems I Spring 2018 omework 7 This homework is due Mrch 12, 2018, t 23:59. Self-grdes re due Mrch 15, 2018, t 23:59. Sumission Formt Your homework sumission should
More informationChapter 4: Techniques of Circuit Analysis. Chapter 4: Techniques of Circuit Analysis
Chpter 4: Techniques of Circuit Anlysis Terminology Node-Voltge Method Introduction Dependent Sources Specil Cses Mesh-Current Method Introduction Dependent Sources Specil Cses Comprison of Methods Source
More informationAcceptance Sampling by Attributes
Introduction Acceptnce Smpling by Attributes Acceptnce smpling is concerned with inspection nd decision mking regrding products. Three spects of smpling re importnt: o Involves rndom smpling of n entire
More informationDesigning finite automata II
Designing finite utomt II Prolem: Design DFA A such tht L(A) consists of ll strings of nd which re of length 3n, for n = 0, 1, 2, (1) Determine wht to rememer out the input string Assign stte to ech of
More informationBasic model for traffic interweave
Journl of Physics: Conference Series PAPER OPEN ACCESS Bsic model for trffic interweve To cite this rticle: Ding-wei Hung 25 J. Phys.: Conf. Ser. 633 227 Relted content - Bsic sciences gonize in Turkey!
More informationConvert the NFA into DFA
Convert the NF into F For ech NF we cn find F ccepting the sme lnguge. The numer of sttes of the F could e exponentil in the numer of sttes of the NF, ut in prctice this worst cse occurs rrely. lgorithm:
More informationThermodynamics of Cu 47 Ti 34 Zr 11 Ni 8,Zr 52.5 Cu 17.9 Ni 14.6 Al 10 Ti 5 and Zr 57 Cu 15.4 Ni 12.6 Al 10 Nb 5 bulk metallic glass forming alloys
JOURNAL OF APPLIED PHYSICS VOLUME 87, NUMBER 10 15 MAY 2000 Thermodynmics of Cu 47 Ti 34 Zr 11 Ni 8,Zr 52.5 Cu 17.9 Ni 14.6 Al 10 Ti 5 nd Zr 57 Cu 15.4 Ni 12.6 Al 10 N 5 ulk metllic glss forming lloys
More informationPhysics 1402: Lecture 7 Today s Agenda
1 Physics 1402: Lecture 7 Tody s gend nnouncements: Lectures posted on: www.phys.uconn.edu/~rcote/ HW ssignments, solutions etc. Homework #2: On Msterphysics tody: due Fridy Go to msteringphysics.com Ls:
More informationPartial Derivatives. Limits. For a single variable function f (x), the limit lim
Limits Prtil Derivtives For single vrible function f (x), the limit lim x f (x) exists only if the right-hnd side limit equls to the left-hnd side limit, i.e., lim f (x) = lim f (x). x x + For two vribles
More informationSupplementary Figure 1 Supplementary Figure 2
Supplementry Figure 1 Comprtive illustrtion of the steps required to decorte n oxide support AO with ctlyst prticles M through chemicl infiltrtion or in situ redox exsolution. () chemicl infiltrtion usully
More informationKINEMATICS OF RIGID BODIES
KINEMTICS OF RIGID ODIES Introduction In rigid body kinemtics, e use the reltionships governing the displcement, velocity nd ccelertion, but must lso ccount for the rottionl motion of the body. Description
More informationRugby High School Physical Science I Can & Evidence Statements
Rugy High School Physicl Science I Cn & Evidence Sttements RHS-PS1-1 Students who demonstrte understnding cn: RHS-PS1-1. Use the periodic tle s model to predict the reltive properties of elements sed on
More informationMatching patterns of line segments by eigenvector decomposition
Title Mtching ptterns of line segments y eigenvector decomposition Author(s) Chn, BHB; Hung, YS Cittion The 5th IEEE Southwest Symposium on Imge Anlysis nd Interprettion Proceedings, Snte Fe, NM., 7-9
More informationMath 1B, lecture 4: Error bounds for numerical methods
Mth B, lecture 4: Error bounds for numericl methods Nthn Pflueger 4 September 0 Introduction The five numericl methods descried in the previous lecture ll operte by the sme principle: they pproximte the
More information7. Indefinite Integrals
7. Indefinite Integrls These lecture notes present my interprettion of Ruth Lwrence s lecture notes (in Herew) 7. Prolem sttement By the fundmentl theorem of clculus, to clculte n integrl we need to find
More informationVibrational Relaxation of HF (v=3) + CO
Journl of the Koren Chemicl Society 26, Vol. 6, No. 6 Printed in the Republic of Kore http://dx.doi.org/.52/jkcs.26.6.6.462 Notes Vibrtionl Relxtion of HF (v3) + CO Chng Soon Lee Deprtment of Chemistry,
More information13: Diffusion in 2 Energy Groups
3: Diffusion in Energy Groups B. Rouben McMster University Course EP 4D3/6D3 Nucler Rector Anlysis (Rector Physics) 5 Sept.-Dec. 5 September Contents We study the diffusion eqution in two energy groups
More informationA Brief Note on Quasi Static Thermal Stresses In A Thin Rectangular Plate With Internal Heat Generation
Americn Journl of Engineering Reserch (AJER) 13 Americn Journl of Engineering Reserch (AJER) e-issn : 3-847 p-issn : 3-936 Volume-, Issue-1, pp-388-393 www.jer.org Reserch Pper Open Access A Brief Note
More informationThis chapter will show you. What you should already know. 1 Write down the value of each of the following. a 5 2
1 Direct vrition 2 Inverse vrition This chpter will show you how to solve prolems where two vriles re connected y reltionship tht vries in direct or inverse proportion Direct proportion Inverse proportion
More informationLinear Systems with Constant Coefficients
Liner Systems with Constnt Coefficients 4-3-05 Here is system of n differentil equtions in n unknowns: x x + + n x n, x x + + n x n, x n n x + + nn x n This is constnt coefficient liner homogeneous system
More informationDirect indirect character of the band gap in methylammonium lead iodide perovskite
Direct indirect chrcter of the nd gp in methylmmonium led iodide perovskite Eline M. Hutter 1, Mrí C. Gélvez-Rued 1, Ann Osherov 2, Vldimir Bulović 2, Ferdinnd C. Grozem 1, Smuel D. Strnks 2,3*, nd Tom
More informationAQA Chemistry Paper 2
AQA hemistry Pper 2 1.1 A student is plnning n investigtion into how the concentrtion of hydrochloric cid ffects the rte of the rection with mrle chips. Wht is the independent vrile? Tick one ox. (1 mrk)
More informationTHERMAL EXPANSION COEFFICIENT OF WATER FOR VOLUMETRIC CALIBRATION
XX IMEKO World Congress Metrology for Green Growth September 9,, Busn, Republic of Kore THERMAL EXPANSION COEFFICIENT OF WATER FOR OLUMETRIC CALIBRATION Nieves Medin Hed of Mss Division, CEM, Spin, mnmedin@mityc.es
More informationCS103B Handout 18 Winter 2007 February 28, 2007 Finite Automata
CS103B ndout 18 Winter 2007 Ferury 28, 2007 Finite Automt Initil text y Mggie Johnson. Introduction Severl childrens gmes fit the following description: Pieces re set up on plying ord; dice re thrown or
More informationSUPPLEMENTARY INFORMATION
SUPPLEMENTARY INFORMATION Synthesis of metl oxide with roomtemperture photoreversile phse trnsition Shin-ichi Ohkoshi 1 *, Yoshihide Tsunouchi, 1 Tomoyuki Mtsud, 1 Kzuhito Hshimoto, 2 Asuk Nmi, 1 Fumiyoshi
More informationPoly(vinylamine) Microgels: ph-responsive Particles with High Primary Amine Contents
SUPPLEMENTARY INFORMATION Poly(vinylmine) Microgels: ph-responsive Prticles with High Primry Amine Contents Sineent Thioonro, Cory Berkln, Amir H. Milni, Rein Ulijn c n Brin R. Suners, * Polymer Science
More informationSome circular summation formulas for theta functions
Ci et l. Boundr Vlue Prolems 013, 013:59 R E S E A R C H Open Access Some circulr summtion formuls for thet functions Yi Ci, Si Chen nd Qiu-Ming Luo * * Correspondence: luomth007@163.com Deprtment of Mthemtics,
More informationRel Gses 1. Gses (N, CO ) which don t obey gs lws or gs eqution P=RT t ll pressure nd tempertures re clled rel gses.. Rel gses obey gs lws t extremely low pressure nd high temperture. Rel gses devited
More informationRadiation Measurements
Rdition Mesurements xxx (2012) 1e7 Contents lists ville t SciVerse ScienceDirect Rdition Mesurements journl homepge: www.elsevier.com/locte/rdmes Modeling of the shpe of infrred stimulted luminescence
More informationCBE 291b - Computation And Optimization For Engineers
The University of Western Ontrio Fculty of Engineering Science Deprtment of Chemicl nd Biochemicl Engineering CBE 9b - Computtion And Optimiztion For Engineers Mtlb Project Introduction Prof. A. Jutn Jn
More informationUNIVERSITY OF MALTA DEPARTMENT OF CHEMISTRY. CH237 - Chemical Thermodynamics and Kinetics. Tutorial Sheet VIII
UNIVERSITY OF MALTA DEPARTMENT OF CHEMISTRY CH237 - Chemicl Thermodynmics nd Kinetics Tutoril Sheet VIII 1 () (i) The rte of the rection A + 2B 3C + D ws reported s 1.0 mol L -1 s -1. Stte the rtes of
More informationAnalytically, vectors will be represented by lowercase bold-face Latin letters, e.g. a, r, q.
1.1 Vector Alger 1.1.1 Sclrs A physicl quntity which is completely descried y single rel numer is clled sclr. Physiclly, it is something which hs mgnitude, nd is completely descried y this mgnitude. Exmples
More informationAn Overview of Integration
An Overview of Integrtion S. F. Ellermeyer July 26, 2 The Definite Integrl of Function f Over n Intervl, Suppose tht f is continuous function defined on n intervl,. The definite integrl of f from to is
More informationCS 275 Automata and Formal Language Theory
CS 275 utomt nd Forml Lnguge Theory Course Notes Prt II: The Recognition Prolem (II) Chpter II.5.: Properties of Context Free Grmmrs (14) nton Setzer (Bsed on ook drft y J. V. Tucker nd K. Stephenson)
More information4.6 Numerical Integration
.6 Numericl Integrtion 5.6 Numericl Integrtion Approimte definite integrl using the Trpezoidl Rule. Approimte definite integrl using Simpson s Rule. Anlze the pproimte errors in the Trpezoidl Rule nd Simpson
More informationCHEMICAL KINETICS
CHEMICAL KINETICS Long Answer Questions: 1. Explin the following terms with suitble exmples ) Averge rte of Rection b) Slow nd Fst Rections c) Order of Rection d) Moleculrity of Rection e) Activtion Energy
More informationCompiler Design. Fall Lexical Analysis. Sample Exercises and Solutions. Prof. Pedro C. Diniz
University of Southern Cliforni Computer Science Deprtment Compiler Design Fll Lexicl Anlysis Smple Exercises nd Solutions Prof. Pedro C. Diniz USC / Informtion Sciences Institute 4676 Admirlty Wy, Suite
More informationu( t) + K 2 ( ) = 1 t > 0 Analyzing Damped Oscillations Problem (Meador, example 2-18, pp 44-48): Determine the equation of the following graph.
nlyzing Dmped Oscilltions Prolem (Medor, exmple 2-18, pp 44-48): Determine the eqution of the following grph. The eqution is ssumed to e of the following form f ( t) = K 1 u( t) + K 2 e!"t sin (#t + $
More informationRates of chemical reactions
Rtes of chemicl rections Mesuring rtes of chemicl rections Experimentl mesuring progress of the rection Monitoring pressure in the rection involving gses 2 NO( g) 4 NO ( g) + O ( g) 2 5 2 2 n(1 α) 2αn
More informationResources. Introduction: Binding. Resource Types. Resource Sharing. The type of a resource denotes its ability to perform different operations
Introduction: Binding Prt of 4-lecture introduction Scheduling Resource inding Are nd performnce estimtion Control unit synthesis This lecture covers Resources nd resource types Resource shring nd inding
More informationMinimum Energy State of Plasmas with an Internal Transport Barrier
Minimum Energy Stte of Plsms with n Internl Trnsport Brrier T. Tmno ), I. Ktnum ), Y. Skmoto ) ) Formerly, Plsm Reserch Center, University of Tsukub, Tsukub, Ibrki, Jpn ) Plsm Reserch Center, University
More informationDriving Cycle Construction of City Road for Hybrid Bus Based on Markov Process Deng Pan1, a, Fengchun Sun1,b*, Hongwen He1, c, Jiankun Peng1, d
Interntionl Industril Informtics nd Computer Engineering Conference (IIICEC 15) Driving Cycle Construction of City Rod for Hybrid Bus Bsed on Mrkov Process Deng Pn1,, Fengchun Sun1,b*, Hongwen He1, c,
More informationMeasuring Electron Work Function in Metal
n experiment of the Electron topic Mesuring Electron Work Function in Metl Instructor: 梁生 Office: 7-318 Emil: shling@bjtu.edu.cn Purposes 1. To understnd the concept of electron work function in metl nd
More informationSUPPLEMENTARY INFORMATION
DOI: 1.138/NMAT3984 Supplementry Informtion for Improved performnce nd stility in quntum dot solr cells through nd lignment engineering Chi- Ho M. Chung 1, Ptrick R. Brown 2, Vldimir Bulović 3 & Moungi
More informationSupplementary Information
Supplementry Informtion Spontneously mplified homochirl orgnic-inorgnic nno-helix complex vi self-prolifertion Hlei Zhi, Yn Qun, Li Li, Xing-Yng Liu, Xurong Xu c nd Ruikng Tng*,c Centre for Biomterils
More informationDesigning Information Devices and Systems I Spring 2018 Homework 8
EECS 16A Designing Informtion Devices nd Systems I Spring 2018 Homework 8 This homework is due Mrch 19, 2018, t 23:59. Self-grdes re due Mrch 22, 2018, t 23:59. Sumission Formt Your homework sumission
More informationThermal Performance of Electrocaloric Refrigeration using Thermal Switches of Fluid Motion and Changing Contact Conductance
Americn Journl of Physics nd Applictions 2016; 4(5): 134-139 http://www.sciencepublishinggroup.com/j/jp doi:.11648/j.jp.20160405.12 ISSN: 2330-4286 (Print); ISSN: 2330-4308 (Online) Therml Performnce of
More informationCS 311 Homework 3 due 16:30, Thursday, 14 th October 2010
CS 311 Homework 3 due 16:30, Thursdy, 14 th Octoer 2010 Homework must e sumitted on pper, in clss. Question 1. [15 pts.; 5 pts. ech] Drw stte digrms for NFAs recognizing the following lnguges:. L = {w
More informationNew data structures to reduce data size and search time
New dt structures to reduce dt size nd serch time Tsuneo Kuwbr Deprtment of Informtion Sciences, Fculty of Science, Kngw University, Hirtsuk-shi, Jpn FIT2018 1D-1, No2, pp1-4 Copyright (c)2018 by The Institute
More informationSet up Invariable Axiom of Force Equilibrium and Solve Problems about Transformation of Force and Gravitational Mass
Applied Physics Reserch; Vol. 5, No. 1; 013 ISSN 1916-9639 E-ISSN 1916-9647 Published by Cndin Center of Science nd Eduction Set up Invrible Axiom of orce Equilibrium nd Solve Problems bout Trnsformtion
More informationBME 207 Introduction to Biomechanics Spring 2018
April 6, 28 UNIVERSITY O RHODE ISAND Deprtment of Electricl, Computer nd Biomedicl Engineering BME 27 Introduction to Biomechnics Spring 28 Homework 8 Prolem 14.6 in the textook. In ddition to prts -e,
More informationFiras J. Kadhim, Abbas J. Al-Watttar, Baha T. Chiad, Asmaa N. Ahmed Department of Physics, College of Science, University of Baghdad, Baghdad, Iraq
ISSN: 2277-3754 Influence of Solvent Environment on the Shpol'skii Spectr of Anthrcene nd Benzonthrcene Molecules Firs J. Kdhim, As J. Al-Wtttr, Bh T. Chid, Asm N. Ahmed Deprtment of Physics, College of
More informationTorsion in Groups of Integral Triangles
Advnces in Pure Mthemtics, 01,, 116-10 http://dxdoiorg/1046/pm011015 Pulished Online Jnury 01 (http://wwwscirporg/journl/pm) Torsion in Groups of Integrl Tringles Will Murry Deprtment of Mthemtics nd Sttistics,
More informationGenetic Programming. Outline. Evolutionary Strategies. Evolutionary strategies Genetic programming Summary
Outline Genetic Progrmming Evolutionry strtegies Genetic progrmming Summry Bsed on the mteril provided y Professor Michel Negnevitsky Evolutionry Strtegies An pproch simulting nturl evolution ws proposed
More information9.4. The Vector Product. Introduction. Prerequisites. Learning Outcomes
The Vector Product 9.4 Introduction In this section we descrie how to find the vector product of two vectors. Like the sclr product its definition my seem strnge when first met ut the definition is chosen
More informationFinite Automata-cont d
Automt Theory nd Forml Lnguges Professor Leslie Lnder Lecture # 6 Finite Automt-cont d The Pumping Lemm WEB SITE: http://ingwe.inghmton.edu/ ~lnder/cs573.html Septemer 18, 2000 Exmple 1 Consider L = {ww
More informationMAC-solutions of the nonexistent solutions of mathematical physics
Proceedings of the 4th WSEAS Interntionl Conference on Finite Differences - Finite Elements - Finite Volumes - Boundry Elements MAC-solutions of the nonexistent solutions of mthemticl physics IGO NEYGEBAUE
More informationset is not closed under matrix [ multiplication, ] and does not form a group.
Prolem 2.3: Which of the following collections of 2 2 mtrices with rel entries form groups under [ mtrix ] multipliction? i) Those of the form for which c d 2 Answer: The set of such mtrices is not closed
More informationSection 6: Area, Volume, and Average Value
Chpter The Integrl Applied Clculus Section 6: Are, Volume, nd Averge Vlue Are We hve lredy used integrls to find the re etween the grph of function nd the horizontl xis. Integrls cn lso e used to find
More informationUSA Mathematical Talent Search Round 1 Solutions Year 21 Academic Year
1/1/21. Fill in the circles in the picture t right with the digits 1-8, one digit in ech circle with no digit repeted, so tht no two circles tht re connected by line segment contin consecutive digits.
More informationModule 2: Rate Law & Stoichiomtery (Chapter 3, Fogler)
CHE 309: Chemicl Rection Engineering Lecture-8 Module 2: Rte Lw & Stoichiomtery (Chpter 3, Fogler) Topics to be covered in tody s lecture Thermodynmics nd Kinetics Rection rtes for reversible rections
More informationDIRECT CURRENT CIRCUITS
DRECT CURRENT CUTS ELECTRC POWER Consider the circuit shown in the Figure where bttery is connected to resistor R. A positive chrge dq will gin potentil energy s it moves from point to point b through
More informationLINEAR ALGEBRA APPLIED
5.5 Applictions of Inner Product Spces 5.5 Applictions of Inner Product Spces 7 Find the cross product of two vectors in R. Find the liner or qudrtic lest squres pproimtion of function. Find the nth-order
More informationSupporting Information
Supporting Informtion Ultrfst nd Stble CO Cpture Using Alkli Metl Slt-Promoted MgO-CCO 3 Sorbents Hongjie Cui, Qiming Zhng, Yunwu Hu, Chong Peng, Xingchen Fng, Zhenmin Cheng, Vldimir V. Glvit nd Zhiming
More informationThe Trapezoidal Rule
_.qd // : PM Pge 9 SECTION. Numericl Integrtion 9 f Section. The re of the region cn e pproimted using four trpezoids. Figure. = f( ) f( ) n The re of the first trpezoid is f f n. Figure. = Numericl Integrtion
More informationChapter 6 Techniques of Integration
MA Techniques of Integrtion Asst.Prof.Dr.Suprnee Liswdi Chpter 6 Techniques of Integrtion Recll: Some importnt integrls tht we hve lernt so fr. Tle of Integrls n+ n d = + C n + e d = e + C ( n ) d = ln
More information