Temperature Memory Effect in Amorphous Shape Memory Polymers. Kai Yu 1, H. Jerry Qi 1, *
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1 Electroc Supplemetary Materal (ESI) for Soft Matter. h joural he Royal Socety of Chemtry 214 Supplemetary Materal for: emperature Memory Effect Amorphou Shape Memory Polymer Ka Yu 1, H. Jerry Q 1, * 1 he George Woodruff School of Mechacal Egeerg, Georga Ittute of echology, Atlata, GA 3332, USA. * Author to hom correpodece hould be addreed: qh@me.gatech.edu h fle clude: 1. Mult-brach Rheologcal Model ad the Materal Parameter Idetfcato
2 1. Mult-brach Rheologcal Model ad the Materal Parameter Idetfcato he thermomechacal properte of a thermo-rheologcally mple polymer decrbed by a mult-brach rheologcal model, a ho Fgure S1. A detaled decrpto of the mult-brach model for SMP applcato ca be foud Yu et al [1], ad t exteo for 3D olear model ca be foud Wetbrook et al [2]. A ho the fgure, the model cot of oe ulbrum brach ad everal thermovcoelatc oulbrum brache (umber of ) to repreet the multple relaxato procee (for example, Roue mode) of the polymer. Fgure. S1. 1D rheologcal repreetato of the ued 1D mult-brach model By applyg the Boltzma uperpoto prcple [3], the total tre ( t) of the model : e m 1 ( t) E e ( t) E e (S1a) t ( ) t e dem dt th e exp, (S1b) d dt, t to decrbe the elatc tra evoluto each oulbrum brache. I Eq. S1a ad S1b, e ( m t ) the total tra. E ad E the elatc modulu the ulbrum ad
3 oulbrum brache, repectvely. ( ) deote the temperature depedet relaxato tme the dahpot. Here, t aumed that the tme-temperature hft for each brach follo the ame rule. Accordg to the ell-etablhed thermorheologcal mplcty prcple [3] uder a o-othermal codto, the relaxato tme (or vcoty) of each oulbrum brach vary a the temperature chage: ( ), (S2) here ( ) a tme-temperature uperpoto (SP) hftg factor, ad the referece relaxato tme at the temperature he ( ) 1. Follog O Coell ad McKea [4], the method for calculatg the temperature fluece o the vcoelatc behavor deped o hether the materal temperature above or belo a hftg temperature. For temperature above ad ear, the (Wllam-Ladel-Ferry) WLF uato ued to calculate ( ) [5]: log C 1 r ( ) C2, (S3a) r here r the WLF referece temperature, ad C 1 ad C 2 are materal cotat that deped o the choce of r. I comparo, for temperature belo, ( ) follo the Arrheu-ype behavor [6]: AF c 1 1 l ( ), (S3b) k b g here A a materal cotat, F c the cofguratoal eergy ad k b Boltzma cotat. the crog pot of to curve repreetg Eq. S3a ad S3b o a ( ) v plot.
4 he model parameter ere determed by ug the ta δ ad torage modulu of the SMP obtaed the DMA tet. A detaled model parameter detfcato method of the mult-brach model ca be foud our prevou tudy [1, 7]. A ho Fgure 3, the acrylate SMP poee a torage modulu of 3.5 MPa he the temperature 95 o C. h modulu could be codered a the ulbrum modulu of the materal a the relaxato tme each oulbrum brach at th temperature mmal. Uder the temperature of 5 o C, the SMP compote ha a torage modulu of MPa. So e have E E MPa. 1 By ug the olear regreo (NLREG) method [8, 9], the parameter for SP, the umber of oulbrum brache, a ell a the modulu ad relaxato tme each dvdual brach, ca be determed by fttg the model predcto th the expermetal DMA reult ho Fgure 3 [7]. For the 1D mult-brach lear model, the temperature depedet torage modulu E ( ), lo modulu E ( ) ad ta ( ) are repectvely expreed a: E ( ) E 1 E 1 l, (S4a) E ( ) l 1 E 1, (S4b) ta ( ) El ( ), (S4c) E ( ) here the tetg fruecy. For the coveece of operato, e aume that the relaxato tme the rubbery brach creae a tefold uetal. Durg the NLREG aaly, oulbrum brache are gradually added to the model to
5 mprove the predcto, ad the brach umber fally determed he the NLREG etmato (ho a dah le Fgure 3) could capture the expermetal torage ad taδ curve th the etre tetg temperature rage (5 o C-95 o C). By ug the determed SP parameter, the hft factor ere calculated by ug Eq. S3 ad plotted Fgure 3b a a fucto of temperature. he fal et of model parameter are the lted able 1. Referece 1. Yu, K., G. Q, ad H.J. Q, Reduced tme a a ufed parameter determg fxty ad free recovery of hape memory polymer. Nature commucato, : p Wetbrook, K.K., et al., A 3D Fte Deformato Cottutve Model for Amorphou Shape Memory Polymer: A Mult-Brach Modelg Approach for Noulbrum Relaxato Procee,. Mechac of Materal, (12): p Rubte, M. ad R.H. Colby, Polymer phyc. 23, Ne York: Oxford Uverty Pre, Oxford. 4. O'Coell, P.A. ad G.B. McKea, Arrheu-type temperature depedece of the egmetal relaxato belo -g. Joural of Chemcal Phyc, (22): p Wllam, M.L., R.F. Ladel, ad J.D. Ferry, emperature Depedece of Relaxato Mecham Amorphou Polymer ad Other Gla-Formg Lqud. Phycal Reve, (5): p D Marzo, E.A. ad A.J.M. Yag, Cofguratoal etropy approach to the ketc of glae. Joural of Reearch of the Natoal Ittute of Stadard ad echology, (2): p Yu, K., et al., A thermomechacal cottutve model for a epoxy baed hape memory polymer ad t parameter detfcato. Mechac of me- Depedet Materal, (2): p Daa, J., et al., Predctg thermal hape memory of crolked polymer etork from lear vcoelatcty. Iteratoal Joural of Sold ad Structure, (4): p Sherrod, P.H., Nolear Regreo Aaly Program. NLREG Vero 5.. 2;, Avalable from:
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