Relative Intermolecular Orientation Probed via Molecular Heat Transport

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1 pubs.acs.org/jpca Relave Inermolecular Orenaon Probed va Molecular Hea Transpor Halong Chen, Hongao Ban, Jebo L, Xewen Wen, and Junrong Zheng* Deparmen of Chemsry, Rce Unversy, Houson, Texas 7700, Uned Saes *S Supporng Informaon ABSTRACT: In hs work, hrough nvesgang a seres of lqud, glassy, and crysallne samples wh ulrafas mulplemode 2D IR and IR ransen absorpon mehods, we demonsraed ha he sgnal ansoropy of vbraonal relaxaon-nduced hea effecs s deermned by boh relave molecular orenaons and molecular roaons. If he relave molecular orenaons are randomzed or molecular roaons are fas compared o hea ransfer, he sgnal ansoropy of hea effecs s zero. If he relave molecular orenaons are ansoropc and he molecular roaons are slow, he sgnal ansoropy of hea effecs can be nonzero, whch s deermned by he relave orenaons of he energy source mode and he hea sensor mode whn he same molecule and n dfferen molecules. We also demonsraed ha he correlaon beween he ansoropy value of hea sgnal and he relave molecular orenaons can be quanavely calculaed. 1. INTRODUCTION Fas molecular conformaonal flucuaons n condensed phases play crcal roles n many mporan chemcal and bologcal acves. 1,2 Monorng real me hree-dmensonal molecular conformaons s of grea sgnfcance n undersandng hese acves, e.g., chemcal reacons, proen foldngs, and molecular recognons. Nuclear magnec resonance (NMR) mehods have been successfully developed for hs purpose. 3 However, her nrnsc low emporal resoluon (longer han 10 6 s) provdes only a longme average. The ulrafas mulple-dmensonal vbraonal specroscopy echnques developed n he pas decade have a suffcenly hgh emporal resoluon ( 100 fs) o reveal fas molecular nformaon ha NMR mehods have dffcules o oban However, because of echncal dffcules and complex heorecal nerpreaons of molecular vbraonal couplngs and ransfers, s generally beleved ha ulrafas nonlnear vbraonal specroscopc mehods are more suable for nvesgang some specfcally labeled molecular segmens raher han he enre molecular srucures. Recenly, combnng new echncal desgns and model sysem sudes, we demonsraed ha real me hree-dmensonal molecular conformaons of some relavely smple molecular sysems n condensed phases can be deermned by he mulple-mode mehod by whch vbraons coverng he enre molecular space are smulaneously measured To resolve he 3D srucure of a molecule, boh lenghs and relave orenaons of s chemcal bonds mus be deermned. Therefore, n order o acheve our ulmae goal of developng he ulrafas mulplemode mulple-dmensonal vbraonal specroscopy no a selfconssen molecular srucural ool, we have desgned expermens o explore s possbles of acqurng hese wo ypes of molecular nformaon. To explore s poenal for deermnng nerbond dsances, we have conduced a seres of expermens o nvesgae he correlaons beween mode-specfc vbraonal energy ransfer knecs and bond dsances To explore s poenal for deermnng relave bond orenaons, we have conduced expermens o nvesgae he correlaons beween vbraonal cross angles and correspondng chemcal bond angles. 14,16 In prncple, boh mode-specfc vbraonal energy ransfer and vbraonal cross angle mehods are suable for deermnng boh ner- and nramolecular srucures. In realy, he wo approaches are manly applcable o nramolecular srucures and some very srong nermolecular neracons, e.g., H-bonds and onc neracons. A he curren sage, hey have dffcules n probng mos relavely weak nermolecular neracons, because he vbraonal couplngs n hese nermolecular neracons are oo weak o provde sgnals wh a suffcenly hgh sgnal/nose rao. In many praccal suaons, e.g., crysals, gues/hos neracons, and caalyss of asymmerc synhess, he relave orenaons of adjacen molecules whch do no necessarly srongly nerac wh each oher are mporan. In hs work, we wll nroduce a new approach o probe he relave orenaons of some molecules of whch he nermolecular neracons are weak. The approach s based on he nermolecular vbraonal relaxaon-nduced hea effecs. Specal Issue: Prof. John C. Wrgh Fesschrf Receved: December 21, 2012 Revsed: February 2, 2013 Publshed: February 2, Amercan Chemcal Socey 602

2 In a ypcal nonlnear vbraonal specroscopc measuremen n condensed phases, he relaxaon of a vbraonal excaon no hermal moons resuls n a emperaure ncrease whn a shor perod of me n he sample whn he focus spo. 1,17,24,2 The emperaure ncrease can affec he sample n several ways, 1.e., alerng he absorpon coeffcens of he vbraonal modes, changng he populaons of molecules n dfferen subsaes, and/or shfng he local srucures and chemcal equlbrum followng he emperaure change; e.g., H- bonds become weaker a hgher emperaure. 26,27 As a resul, hese vbraonal relaxaon-nduced hea effecs produce new absorpons and bleachngs a varous emperaures n boh emperaure dfference FTIR specra and 2D IR specra. 18 In hs paper, we defne hea as hose hermal moons whch nclude low frequency molecular vbraons, roaons, and ranslaons nduced by he excaon relaxaon of a hgh frequency vbraonal mode (denoed as energy source mode ) and he hea effecs as he opcal responses of hgh frequency vbraonal modes (denoed as hea sensor modes ) o he hermal moons. Smlar o he nernal vbraonal relaxaon processes suded wh relaxaon-asssed wo-dmensonal nfrared (RA 2DIR) specroscopy, he heorecal bass of he nermolecular vbraonal relaxaon-nduced hea ransfer s no enrely clear. Generally speakng, he nermolecular vbraonal relaxaonnduced hea can be ransferred from he orgnal exed molecules o adjacen molecules a he me scales of fs (femosecond) o ns (nanosecond), dependen on he vbraonal lfemes of modes nvolved n he nramolecular relaxaon. 18,31 Once he molecules receve he hea energy, he absorpon coeffcens and frequences of her vbraonal modes and her chemcal saes wll shf o new values because of he emperaure change. The changes of molecular properes wll resul n new absorpons and bleachngs n IR specra whch can be monored n real me. In he relaxaonnduced heang process, he hea source s from one vbraonal mode of one molecule, and he sensor of he hea effecs can be anoher vbraonal mode of anoher molecule. In prncple, he relave orenaon and dsance beween he energy source mode and he hea sensor mode are correlaed o he hea ransfer knecs. Such a correlaon can be ulzed o deermne he relave orenaon and dsance of he wo molecules o whch he wo vbraonal modes belong. In hs work, we frs smply nroduce he generaon mechansm of relaxaon-nduced hea and equaons o calculae he ansoropy of he hea sgnal. Then, examples of a lqud and a crysal are used o demonsrae ha a nonzero ansoropc value of relaxaon-nduced hea sgnal can exs n a sample where molecular orenaons are ansoropc and molecular roaons are slow. In he las par of he work, we use hree polysyrene samples wh dfferen molecular orenaons: soropc (amorphous glass) and ansoropc (crysal) o demonsrae ha he correlaon beween he relave nermolecular orenaon and he nonzero ansoropy value of he molecular hea ranspor sgnal can be quanavely calculaed. 2. EXPERIMENTS The opcal seup s smlar bu wh a dfferen probe pulse generaon mehod o ha descrbed prevously. 1,17 Brefly, a ps amplfer and a fs amplfer are synchronzed wh he same seed pulse. The ps amplfer pumps an OPA o produce 0.8 ps (vary from 0.7 o 0.9 ps n dfferen frequences) md-ir pulses 603 wh a bandwdh of 10 3 cm 1 n a unable frequency range from 400 o 4000 cm 1 wh energy 1 40 μj/pulse (1 10 μj/ pulse for cm 1 and >10 μj/pulse for hgher frequences) a 1 khz. Lgh from he fs amplfer s used o generae a hgh-nensy md-ir and eraherz superconnuum pulse wh a duraon of <100 fs n he frequency range from <400 o >3000 cm 1 a 1 khz, wh a modfed eraherz generaon mehod whch s smlar o hose used n oher groups Specfcally, he collmaed 800 nm beam from he fs amplfer s frequency doubled by passng hrough a ype-i 10-μm-hck BBO crysal cu a 29.2 o generae 400 nm lgh. A dual wave plae s used o une he relave polarzaons of he 800 and 400 nm pulses, whch operaes as a full-wave plae a 400 nm and a half-wave plae a 800 nm. Temporal walkoff beween wo beams s compensaed by nserng a 2- mm-hck BBO (cu a ) beween he doublng crysal and he wave plae, where he 800 and 400 nm pulses propagae a orhogonal polarzaons wh dfferen veloces n he delay plae. 36,37 The superconnuum pulse s generaed by focusng he wo copropagang beams on ar. In nonlnear IR expermens, he ps IR pulse s he excaon beam (he excaon power s adjused on he bass of need, and he neracon spo vares from 100 o 00 μm). The superconnuum pulse s he probe beam whch s frequency resolved by a specrograph (resoluon s 1 3 cm 1 dependen on he frequency), yeldng he deecon axs of a 2D IR specrum. Scannng he excaon frequency yelds he oher axs of he specrum. Two polarzers are added no he deecon beam pah o selecvely measure he parallel or perpendcular polarzed sgnal relave o he excaon beam. The whole seup ncluded frequency unng s compuer conrolled. KSeCN, D 2 O, aacc polysyrene, and L-cysene were purchased from Aldrch and used as receved. The raw maeral of syndoacc polysyrene (sps) was produced and kndly suppled by Idemsu Kosan Co. Ld., Japan. Amorphous sps flms were prepared by rapdly quenchng mel flms n an ce waer bah. The crysallne sps flms were prepared by slowly coolng mel flms down o room emperaure accordng o he leraure. 38 All samples for 2D IR measuremens were conaned n sample cells composed of wo CaF 2 wndows separaed by a Teflon spacer. All he measuremens were carred ou a room emperaure (21 C). Densy funconal heory (DFT) calculaons were used o conver aomc coordnaes (relave aomc orenaons) no vbraonal coordnaes (relave vbraonal orenaons). The DFT calculaons were carred ou usng Gaussan 09. The level and bass se used were Becke s hree-parameer hybrd funconal combned wh he Lee Yang Parr correcon funconal, abbrevaed as B3LYP, and 6-311G(d,p). 3. SIGNAL GENERATION MECHANISM AND ANISOTROPY 3.1. Generaon Mechansm of Vbraonal Relaxaon- Induced Hea. The vbraonal relaxaon-nduced hea effecs descrbed n hs work refer o he opcal absorpons and bleachngs caused by he hermal moons due o he relaxaon of vbraonal excaon of hgh frequency modes (>200 cm 1 ) no low frequency modes and he dsspaons of he resulng low frequency excaons. The phenomenon can be monored n real me wh ulrafas nonlnear vbraonal specroscopc mehods. 17,18,24,27,39,40 The average resuls of vbraonal relaxaon-nduced hea effecs are dencal o he dfferences of FTIR specra a varous emperaures. 17,18,27,40 Fgure 1

3 Fgure 1. Specra of a sauraed KSeCN/D 2 O soluon (molar rao 1/2.): (A) FTIR specrum a room emperaure showng he CN 0 1 ranson peak of SeCN a 2070 cm 1, he OD 0 1 ranson peak of D 2 O from 2400 o 2800 cm 1, and a combnaon band (possbly C N plus Se C sreches) of SeCN a 263 cm 1 ; (B) 2D IR specra (each conour represens 10% nensy change) showng he me evoluons of new absorpons (blue) and bleachngs (red) n he OD frequency range (ω 3 = cm 1 ) nduced by he vbraonal relaxaon of CN excaon a 2070 cm 1 (ω 1 = 2070 cm 1 ); (C) he emperaure dfference FTIR specrum (specrum a 68 C specrum a 22 C, red) and a slce cu (black) of panel 1000 ps n par B along he ω 3 axs a ω 1 = 2070 cm 1, showng ha he specral changes caused by hea effecs n 2D IR can be deeced by emperaure dfference FTIR. dsplays a ypcal example of vbraonal relaxaon-nduced hea effecs monored wh 2D IR and emperaure dfference FTIR. Fgure 1A s he FTIR specrum of a sauraed KSeCN/D 2 O soluon (molar rao 1/2.) a room emperaure. The CN srech 0 1 ranson frequency of SeCN s a 2070 cm 1. The OD srech 0 1 ranson of D 2 O has a very broad peak from 2400 o 2800 cm 1. The peak a 263 cm 1 whch can also be clearly seen n a KSeCN/H 2 O soluon s assgned o a combnaon band (possbly he CN srech plus he Se C srech) of SeCN. Fgure 1B dsplays he wang me dependen 2D IR specra of he same sample by excng he CN srech of SeCN and deecng responses n he frequency range cm 1. A a shor wang me, e.g., 0 ps, a peak par shows up n he specrum. These wo peaks are from he vbraonal couplng beween he CN srech and he combnaon band a 263 cm 1, smlar o hose nramolecular vbraonal couplngs prevously observed. 4,14 The couplng beween CN and OD s oo weak o be observed. A longer wang mes, he excaon of CN srech of whch he lfeme has a fas componen of 4 ps (22%) and a slow componen of 100 ps (78%) begns o relax no hea and rase he local emperaure. As he emperaure ncreases, he ranson dpole momens of OD sreches change, and some hydrogen bonds n he soluon break and some new bonds form, resulng n new absorpons (blue) and bleachngs (red) n 2D IR specra. In Fgure 1B, a ps, some of he hea effecs (red peaks a 200 cm 1 ) are already vsble. A 20 ps, he hea effecs (he blue peak a 2680 cm 1, red peaks a 280 and 2480 cm 1 ) are remarkable. A 0 ps, when he relaxaon of CN excaon has no compleed, he hea effec s already much larger han he vbraonal couplng peaks so ha only he hea effec s clearly vsble. The specral paern of he hea effecs n 2D IR remans essenally consan o he longes wang me, 1000 ps, n our expermens. Because he specral changes observed from 2D IR measuremens are n naure caused by he emperaure ncrease, such changes should also be observed by comparng FTIR specra of he same sample a room emperaure and a a hgher emperaure. Fgure 1C dsplays he emperaure dfference FTIR specrum (specrum a 68 C specrum a 22 C, red) and a slce cu (black) of panel 1000 ps of par B along he ω 3 axs a ω 1 = 2070 cm 1. The wo curves are essenally dencal, verfyng ha he specral changes n 2D IR specra n Fgure 1B are from he emperaure ncrease because of he relaxaon of CN excaon. The vbraonal relaxaon-nduced hea effecs can be explaned wh Feynman dagrams shown n Fgure 2, followng Fgure 2. Feynman dagrams conrbung o he vbraonal relaxaonnduced hea effecs: bleachng (R 1 and R 1 ) and absorpon (R 2 and R 2 ). 0 and 1 represen he ground sae and he frs exced sae of he energy source mode he nally vbraonally exced mode by laser, e.g., he CN srech n Fgure 1, respecvely. 0 and 1 represen he ground sae and he frs exced sae of he hea sensor mode he mode whch has opcal responses o he hea, e.g., he OD srech n Fgure 1, respecvely. L represens he exced saes of low frequency modes (modes of hea) whch accep energy from he relaxaon of he energy source mode. he hrd order opcal sgnal generaon mechansm. 1,24 The 2D IR sgnals n our expermens are from he pump/probe scheme where he frs wo excaon beams k 1 and k 2 are collnear, and he hrd excaon beam k 3 and he local oscllaor are also collnear. Therefore, boh rephasng (k e = k 1 k 2 k 3, k s he wave vecor of lgh pulse ) and nonrephasng (k n = k 1 k 2 k 3 ) phase mach condons conrbue he sgnals expermenally observed. In he dagrams n Fgure 2, 0 and 1 respecvely represen he ground sae and he frs exced sae of he energy source mode he nally vbraonally exced mode by laser, e.g., he CN srech n Fgure 1. 0 and 1 respecvely represen he ground sae and he frs exced sae of he hea sensor mode he mode whch has opcal responses o he hea, e.g., he OD srech n Fgure 1. L represens he exced sae(s) of low frequency 604

4 modes (modes of hea) whch accep energy from he relaxaon of he energy source mode. Dagrams R 1 (rephasng) and R 1 (nonrephasng) descrbe he process of hea-nduced bleachng. They can be qualavely undersood n he followng way. The frs beam creaes a coherence (superposon) beween he ground sae and he frs exced sae of he energy source mode whch s oscllang durng he 1 perod beween he frs wo neracons. The coherence provdes nformaon for he excaon frequency ω 1. The second neracon exces some of he molecules o he frs exced sae, resulng n a populaon hole n he ground sae. Durng he T w perod, he vbraonal excaon begns o relax, and he exced molecules gradually go back o he ground sae (hole recovered) as he relaxaon hea dsspaes o oher molecules. A he same me, oher molecules receve he hea and are exced so ha ground sae holes are generaed n hem. The process herefore looks lke he exchange of ground sae hole beween wo speces. Afer he process, here are ground sae holes n anoher speces (hea sensor). The hrd pulse can hen produce coherence beween he ground sae and he frs exced sae of he sensor mode o provde he deecon frequency ω 3. Ths explans he generaon of red peaks a cm 1 a longer wang mes n Fgure 1. ω 1 of hese peaks s 2070 cm 1 whch s he 0 1 ranson frequency of he CN srech, ndcang ha he energy source s he CN excaon. The relaxaon of CN excaon heas up adjacen waer molecules and generaes ground sae holes of he OD srech, resulng n bleachng sgnals n he frequency range of he OD 0 1 ranson deeced as ω 3. If dela pulses are assumed, 41 2D IR or pump/probe sgnals from dagrams R 1 and R 1 can be expressed as S cos θ cos θ cos θ cos θ μ μ and S R1 E1/ μ01 E2/ μ01 E3/ μ01 Es/ μ01 01 ω ω e e Γ R ( 1, Tw, 3) exp[ g (, T, )] 1 R 1 w 3 1 (1) 2 R cos θ μ cos θ μ cos θ μ cos θ μ μ 1 E1/ 01 E2/ 01 E3/ 01 Es/ ω ω μ01 R1 1 w 3 R 1 w e e Γ (, T, ) exp[ g (, T, )] (2) where Γ( 1, T w, 3 ) s a me-dampng facor whose deals depend on he knec models. g() s a lne-broadenng funcon, μ 01 s he ranson dpole momen of he 0 1 ranson of he energy source mode, and μ 01 s he ranson dpole momen of he 0 1 ranson of he hea sensor mode. ω 1 = ω 01 s he 0 1 ranson frequency of he energy source mode. ω 3 = ω 01 s he 0 1 ranson frequency of he hea sensor mode. θ E /μ kl s he cross angle beween he polarzaon drecon of he h elecrc feld (ncludng sgnal) and he drecon of he ranson dpole momen of μ kl. In our expermens, cos θ E1 /μ = cosθ 01 E2 /μ and cos θ 01 E / μ cos θe s / μ 01. A smlar suaon holds for R 2 and R 2. Dagrams R 2 and R = descrbe he process of relaxaonnduced absorpon. Smlar o dagrams R 1 and R 1,nR 2 and R 2, he frs pulse creaes a superposon beween he ground sae and he frs exced sae of he energy source mode whch provde he frequency nformaon for ω 1. The second pulse creaes a populaon on he frs exced sae of he energy source mode. Durng he T w perod, he frs exced sae populaon begns o relax no low frequency modes (hea) and dsspaes o oher molecules. The process produces excaons on hese low frequency modes. Whle hese low frequency modes are exced, he hrd pulse creaes a superposon beween he ground sae and he frs exced sae of he hea sensor mode whch provdes he frequency nformaon for ω 3. Sgnals from dagrams R 2 and R 2 can be expressed as and S cos θ cos θ cos θ R2 E1/ μ01 E2/ μ01 E3/ μl 0 L ω011 ωl 0 L 1 3 cos θe / μ μ μ e e s L 0 L 1 01 L 0 L 1 S Γ R (, T, ) exp[ g (, T, )] 2 1 w 3 R 1 w 3 2 (3) cos θ cos θ cos θ R2 E1/ μ01 E2/ μ01 E3/ μl 0 L ω011 ωl 0 L 1 3 cos θe / μ μ μ e e s L 0 L 1 01 L 0 L 1 Γ R (, T, ) exp[ g (, T, )] 2 1 w 3 R 1 w 3 2 (4) where μ 01 s he ranson dpole momen of he 0 1 ranson of he energy source mode and μ L 0 L 1 s he ranson dpole momen of he 0 1 ranson of he hea sensor mode under he condon ha he low frequency mode(s) L s (are) smulaneously exced. ω 1 = ω 01 s he 0 1 ranson frequency of he energy source mode. ω 3 = ω L 0 L 1 s he 0 1 ranson frequency of he hea sensor mode under he condon ha he low frequency mode(s) L s (are) smulaneously exced. In general, he excaons of hese low frequency modes can change he vbraonal frequences and ranson dpole momens of hose hgh frequency modes, or change he chemcal equlbrum of he sysem, e.g., formng a weaker H- bond n Fgure 1. Therefore, he 0 1 ranson frequences of hose hgh frequency modes deeced wh low frequency modes a exced saes are dfferen from hose deeced wh low frequency modes a he ground sae; e.g., ω L 0 L 1 s dfferen from ω 01. Ths explans he generaon of he blue peak a 2680 cm 1 a longer wang mes n Fgure 1. ω 1 of he peaks s 2070 cm 1 whch s he 0 1 ranson frequency of he CN srech, ndcang ha he energy source s he CN excaon. The relaxaon of CN excaon heas up adjacen waer molecules and breaks some of he hydrogen bonds, shfng he OD 0 1 ranson frequency from 200 o 2680 cm 1 as deeced n ω 3. The hea effecs descrbed n hs work are caused by he excaon relaxaon of he energy source mode and he dsspaon of hermal moons from he relaxaon, dfferen from he mode-specfc vbraonal energy ransfer beween he energy source mode and he probe mode whch occurs before he relaxaon of he source mode. 20,21 A wang mes much longer han he vbraonal lfemes of eher mode, sgnals n 2D IR or pump/probe daa are manly from he hea effecs. The dealed dfference beween hese wo processes has been descrbed n our prevous publcaons. 1, Ansoropy of Vbraonal Relaxaon-Induced Hea Sgnal. From eqs 1 4, we can see ha he sgnals of relaxaon-nduced hea effecs depend on he hea ransfer knecs whch s ncluded n Γ( 1, T w, 3 ). The hea ransfer knecs s correlaed o he dsance beween he energy source and he hea sensor. In prncple, he correlaon can be ulzed o deermne he relave dsance beween he wo molecules 60

5 from he growh knecs of hea effecs. Ths s an neresng opc for fuure sudes. In hs work, we wll focus on anoher aspec ansoropy of he expermenal sgnals from he hea effecs. Equaons 1 4 show ha he hea sgnal s also dependen on he cross angles beween he polarzaon drecons of he excaon (E 1 and E 2 ) and deecon (E 3 ) lghs and he ranson dpole momen drecons of he energy source mode and he hea sensor mode. The sgnal wll be maxmzed f boh excaon and deecon polarzaons are respecvely parallel o hose of he wo modes (θ E /μ kl = 0). In oher words, he sgnal nensy of hea effecs s correlaed o he relave orenaon of he energy source mode and he sensor mode, whch can be expermenally deermned by unng he polarzaon angle beween he excaon and deecon pulses. Smlar o he polarzaon selecve fluorescence measuremens, 42 f he hea ransfer s soropc and he molecular dsrbuon whn he laser focus spo s soropc, he ranson dpole momen cross angle θ() beween he energy source mode and he hea sensor mode can be expressed as 3cos θ() 1 R() = 2 where R() s he ansoropy of he hea sgnal, defned as R() = () P () P () P () 2 P () (6) where P () and P () are he sgnal nenses from expermens wh he deecon pulse parallel and perpendcular o he excaon pulse, respecvely, and s he wang me (T w n Fgure 2) beween he wo pulses. In general, he hea ransfer s no necessarly soropc. In addon, whn he lgh/maer neracon volume (laser focus spo), he energy source mode and he hea sensor mode do no necessarly have only one relave orenaon because molecules o whch hese modes belong can have varous orenaons relave o each oher. For hese cases, eq canno be mmedaely appled. Le us consder a smple case: he vbraonal cross angle beween he wo modes has a random value because he molecules are orenaed randomly relave o each oher. As a resul, he hea sgnal s no longer dependen on he polarzaons of laser beams. An dencal resul from P () and P () wll be obaned, leadng o a zero ansoropc value whch gves θ = 4.7 based on eq. The value ceranly does no mean ha he cross angle beween he wo modes s 4.7. In a more general case, a sysem conans dfferen ses of molecules. In each molecular se, he vbraonal cross angle beween he energy source mode and he hea sensor mode s a fxed value so ha he ansoropy of hea sgnal from hs se of molecules s a sngle value R () whch conrbues o he oal sgnal nensy wh a fracon f. The oal ansoropy s he weghed sum of he ndvdual ansoropes accordng o he addvy law of ansoropy: 43 R() = f R() Equaon 7 can be derved n he followng way. When a sysem conans dfferen ses of molecules, each wh a fxed ansoropy R () and conrbung o he oal sgnal nensy wh a fracon f,defned as f = P ()/P(), we have (7) R () = P () P () = P() 2 P () P () P () P () (8) where P () and P () are he sgnal nenses for he h se of molecules wh he deecon beam parallel and perpendcular o he excaon beam, respecvely, a wang me (T w ). P () = P () 2P () represens he oal sgnal nensy of he h se of molecules. Thus, we have he oal sgnal nensy P() = P () 2P () = P (), and P () = P (), P () = P (). Accordng o eqs 6 and 8, we oban P () P () R() = P () 2 P () = P() P () P () P () P () P() = P() P () = fr() From he above dervaon, we know ha f s dfferen from he molar fracon of he h se of molecules n he sample. The wo quanes can be consdered o be he same only when he hree condons are fulflled: (1) he dsrbuon of each se of molecules whn he lgh/maeral neracon s soropc, (2) her response o he same amoun of hea s dencal, and (3) he hea ransfer rae s soropc nsde each molecular se. The frs condon can be easly fulflled, snce expermenally he dameer of neracon cross secon s 100 μm and praccally s no dffcul o creae a sample wh he szes of randomly dsrbued mcrodomans a he order of ens o hundreds of nanomeers. The second condon can be problemac for some cases; e.g., n some ses, molecules nerac wh each oher hrough H-bonds whch are hghly sensve o hea effecs, and n some ses, because of geomerc consrans, he same molecules can only nerac wh each oher hrough weak nermolecular neracons whch are less sensve o hea effecs. The dfferen responses o hea need o be calbraed and normalzed for each se of molecules n order o conver he molar fracon no he sgnal fracon. The hrd condon s probably fulflled n mos expermens because he number of he low frequency modes (hea) whch accep vbraonal energy from he energy source mode s large and her ranson dpole momen vecors are probably ponng o all drecons, resulng n smlar hea ransfer raes n dfferen drecons. To use eq 7, we assume he sgnal fracon f o be a wang me ndependen parameer so ha s nal value a me zero can be used. Ths assumpon should hold, snce we expec ha he lfemes of he hea modes n dfferen ses of molecules should be very smlar whn he wang me perod of measuremens (ens of ps o several ns) unless here are some molecular ransformaons occurng durng he hea ransfer process. Durng he wang me perod (T w n Fgure 2), molecules can roae. If he molecular roaon s fas and he randomzaon of molecular orenaon s compleed before hea ransfer reaches equlbrum, he ansoropy of hea effecs deeced wll be zero. Therefore, n order o use he hea (9) 606

6 Fgure 3. Polarzaon selecve pump/probe daa. (A) Pump/probe daa of a dlue HOD aqueous soluon (1 w % D 2 OnH 2 O) wh boh excaon and deecon frequency a 207 cm 1 (OD srech 0 1 ranson frequency). (B) Pump/probe daa of a L-cysene polycrysallne sample wh he excaon frequency a 243 cm 1 (SH and NH srech 0 1 ranson frequency) and he deecon frequency a 120 cm 1 (NH bendng 0 1 ranson frequency). (C) Pump/probe daa of par B a shor wang mes. Fgure 4. Ansoropes of pump/probe daa presened n Fgure 3. (A) Wang me dependen ansoropy daa of he HOD aqueous soluon; (B and C) wang me dependen ansoropy daa of he L-cysene crysallne sample. ransfer mehod o deermne relave nermolecular orenaons, s requred ha he molecular roaonal dynamcs be ndependenly measured or he molecular roaons are much slower han he hea ransfers. Anoher requremen s ha he sze of each molecular se or he separaons among hem should be larger han a ceran value. Ths s because he assumpon eq 9 s based on s ha he relaxaon of he energy source mode can only affec he hea sensor mode whn he same molecular se. Modes on oher ses wll no respond o he relaxaon hea of excaon on hs molecular se. Each molecular se or her separaon needs o be suffcenly large so ha mos of he relaxaon-nduced hea only ransfers whn he same molecular se. We can roughly esmae he crcal sze whch fulflls hs requremen. The vbraonal lfeme of a hgh frequency mode n organc molecules s ypcally a few ps n condensed phases. I akes ens o hundreds of ps for o conver no hea, whch means ha afer a few hundred ps mos sgnals observed n 2D IR or pump/probe expermens are from hea effecs. Now we wan o see how bg a volume he relaxaon-nduced hea from a hgh frequency mode, e.g., 2000 cm 1, can ravel a room emperaure whn a few hundred ps. If he sample densy s 1 g/cm 3 wh molecular wegh 100 g/ mol, here are molecules nsde a volume of (100 nm) 3. If he hea ransfer rae s assumed o be close o he speed of sound n ar, e.g., 300 m/s, and he molecular dsance s 0.3 nm, akes abou 602 ns for he relaxaon-nduced hea o ravel he volume, (100 nm) 3. Here we assume ha he excaon a 2000 cm 1 can relax no 10 phonons a room emperaure (RT = 200 cm 1 ). The resul ndcaes ha akes abou 600 ps for he phonons o ravel a volume of (10 nm) 3.If we wan fewer han 1% of he molecules whn nm of he surface, he dameer of he volume should be abou 200 nm. The esmaon gven here s very approxmae because he acual hea ransfer rae can be a few mes faser han he value used for he esmaon, bu ells us ha he crcal sze s probably a he order of ens o hundreds of nm, dependen on dealed molecular properes. Noneheless, n he nerfacal regons among dfferen molecular ses, he hea sgnal s randomzed, resulng n he measured ansoropy value beng smaller han he calculaed value from eq 9 whou consderng he sgnal randomzaon n he nerfacal regon. Anoher ssue abou usng eq o deermne relave molecular orenaons s ha he angle deermned from eq s he vbraonal cross angle whch s dfferen from he bond angle needed o deermne molecular orenaons. As demonsraed before, he vbraonal cross angles can be convered no bond angles hrough quanum molecular calculaons wh very hgh precson, whch s no heavly dependen on he bass ses of he calculaons. 14,16,44 4. RESULTS AND DISCUSSION 4.1. Ansoropes of Hea Effecs n Waer and n L- Cysene Crysal. The above nroducon abou he mechansm and sgnal ansoropy of vbraonal relaxaonnduced hea effecs predcs he followng: (1) In a lqud where molecular roaons are faser han he growh of hea effecs or molecular orenaons are randomzed, he sgnal ansoropy of hea effecs s zero. In oher words, he pump/ probe daa of hea effecs from boh parallel and perpendcular excaon/deecon confguraons are dencal. (2) In a sample where molecular roaons are slow and molecular orenaons are ansoropc, he sgnal ansoropy of hea effecs can be nonzero f he energy source mode and he hea sensor mode have a vbraonal cross angle oher han 4.7. We used wo samples o es hs predcon: (1) a 1 w % D 2 OnH 2 O lqud sample a room emperaure where waer molecules roae wh a me consan of 2.6 ps and (2) a L-cysene polycrysallne sample where molecular roaons are almos frozen and molecules are orenaed n an ordered ansoropc 607

7 way of whch he crysallne srucure has been deermned wh XRD. 4,46 Fgure 3A dsplays he polarzaon selecve pump/probe daa of he HOD soluon wh boh excaon and deecon frequences a 207 cm 1, he OD 0 1 ranson frequency. A shor wang mes, he sgnal n Fgure 3A s from he ground sae bleachng of OD srech because some OD srech modes have been exced o he frs exced sae of whch he lfeme s 1.3 ps as measured. The bleachng sgnal begns o decay as he exced modes relax back o he ground sae. If here s no hea effec, a a long wang me (compared o he vbraonal lfeme 1.3 ps), e.g., 10 ps, he sgnal wll go o zero. However, as shown, he sgnal n Fgure 1A does no go o zero bu remans a an almos consan value a long wang mes. Ths nonzero sgnal a long wang mes s caused by he hea effec of whch he generaon mechansm s exacly he same as ha elaboraed n he prevous secon o descrbe he hea-nduced bleachng sgnal n Fgure 1 n he frequency range cm 1. In Fgure 3A, a a long wang me, e.g., 20 ps, s obvous ha he hea sgnals from boh parallel confguraons are dencal whn expermenal uncerany. The ansoropy of he hea sgnal remans zero a long wang mes, as shown n Fgure 4A. Ths resul s conssen wh he frs predcon, because he molecular roaonal me 2.6 ps s much shorer han he wang me so ha he relave molecular orenaons have been randomzed. Very dfferen from he waer sample, hea sgnals n he L- cysene polycrysallne sample from he wo dfferen polarzaon confguraons are no he same. The hea sgnal from he perpendcular confguraon remans consanly larger han ha from he parallel confguraon a long wang mes, as shown n Fgure 3B and C. Fgure 3B and C are he polarzaon selecve pump/probe daa of he L-cysene polycrysallne sample by excng he SH srech mode a 243 cm 1 (he SH srech 0 1 ranson frequency) whch slghly overlaps wh he al of he NH srech n frequency, and deecng he NH bendng mode a 120 cm 1 (he NH bendng 0 1 ranson frequency). A shor wang mes, e.g., 0 ps, he pump/probe sgnal comes from he ground sae bleachng of he vbraonal couplng beween he SH (NH srech because of he frequency overlap) srech and he NH bendng. The sgnal nensy s dependen on he vbraonal cross angle of he wo modes, and decays wh he lfeme of he SH (NH) sreches whch s measured o be 1.4 ps, as we can see from Fgure 3C ha a fas decay occurs whn a few ps. A longer mes, smlar o ha dscussed above, he vbraonal relaxaon of he frs exced saes of SH (NH) sreches produces hea whch creaes a bleachng sgnal a he NH bendng 0 1 ranson frequency as deeced. The hea sgnal s long-lved. Up o 1000 ps, no clear decay s observed (Fgure 3B). In addon, he dfference beween hea sgnals from he wo polarzaon confguraons s remarkable, ndcang a nonzero ansoropy value, as shown n Fgure 4B and C. The resul verfes he above second predcon ha he hea sgnal can be ansoropc f he molecular orenaons are ansoropc and molecular roaons are slow Ansoropes of Hea Effecs n Glassy and Polycrysallne Polysyrene Samples Molecular Conformaons and Srucures. To furher confrm ha he nonzero ansoropy of hea sgnal observed n he crysallne L- cysene s caused by he ansoropc nermolecular orenaons n he sold raher han purely by beng a sold, and o demonsrae ha he nonzero ansoropy of hea sgnal can be quanavely derved from he relave nermolecular orenaons, we furher desgned expermens o nvesgae he relaxaon-nduced hea effecs n hree sold samples from he same knd of molecules wh dfferen nermolecular orenaons. Molecules used for hs purpose are aacc and syndoacc polysyrenes. Molecular srucures of hese wo polysyrenes are shown n Fgure. Polysyrene s a vnyl Fgure. Molecular srucures of syndoacc and aacc polysyrenes. polymer, whch has a long hydrocarbon backbone chan wh a phenyl group aached o every oher carbon aom. In he syndoacc polysyrene, he phenyl groups on he polymer chan are aached o alernang sdes of he polymer backbone. In he aacc polysyrene, he sdes of backbone o whch he phenyl groups are aached are dsordered. Because of he nrnsc dfference n molecular srucures, he wo polysyrenes adop dfferen packng paerns when hey form solds from mels or soluons. A room emperaure, he aacc polysyrene forms amorphous glass because s rregular molecular srucure prevens from formng ordered nermolecular paerns. The molecular chans nsde he glass are soropcally dsrbued. 47 A dfferen suaon occurs for he syndoacc polysyrene. Is regular molecular srucure allows o adop ordered molecular packng paerns o form crysals a room emperaure. Dependen on expermenal condons, syndoacc polysyrene can form a pure glass or semcrysallne solds wh varous crysallne srucures. 38,48 1 For our expermens, we prepared hree samples wh dfferen nermolecular packng paerns: (A) sample 1 s an amorphous glass from he aacc polysyrene, (B) sample 2 s also an amorphous glass from he syndoacc polysyrene, and (C) sample 3 s a semcrysallne sold conanng 2% of β crysals and 48% amorphous glass from he syndoacc polysyrene. XRD daa of he hree samples are shown n Fgure 6A. There are no clear dffracon peaks (black and red curves n Fgure 6A) n samples 1 and 2, ndcang ha molecular dsrbuons nsde he samples are random. Sample 3 has clear dffracon peaks (he blue curve n Fgure 6A), ndcang ha 608

8 Fgure 6. (A) XRD daa of he hree polysyrene samples. Only sample 3 shows clearly dffracon peaks. Samples 1 and 2 only have wo very broad bumps, ndcang hey are mosly amorphous. (B) FTIR daa of samples 2 and 3 a room emperaure. Peaks a around 90 and 841 cm 1 are characersc for he amorphous domans of he syndoacc polysyrene, and he wo peaks a 911 and 88 cm 1 belong o he β crysal of he syndoacc polysyrene. 3,4 (C) FTIR specrum of sample 3 and he peak fng resul wh wo Gaussans. Fgure 7. FTIR specra of (A) sample 1, (B) sample 2, and (C) sample 3. Inse: molecular formula of polysyrene. The assgnmens for peaks nvolved n he relaxaon hea-nduced measuremens are rng CC srech (1600 cm 1 ), backbone CH 2 srech (2924 cm 1 ), and rng CH srech (3026 cm 1, 3060 cm 1 ). Fgure 8. (A) 2D IR specra of sample 3 a dfferen wang mes. Each conour represens 10% nensy change. (B) Temperaure dfference FTIR specra of sample 3 obaned by subracng he FTIR specrum a a hgher emperaure from he specrum a room emperaure (21 C); e.g., lne 3 C represens he subracon resul from 21 o 24 C. perodcal ordered molecular paerns exs n he sample. By comparng he XRD daa n Fgure 6A o he leraure, we found ha he crysallne srucure of sample 3 s he so-called β crysal. 0,2 Typcally, s very dffcul for a polymer sample o 100% form crysallne srucures because durng he crysallzaon process here are always some polymer chans whch are enangled and form amorphous domans. The crysallne conen (crysallny) of a polymer sample vares wh crysallzaon condons. To deermne he crysallny of sample 3, we use FTIR daa (Fgure 6B) nsead of XRD daa (Fgure 6A) because he XRD mehod s no sensve o he amorphous domans. Accordng o he leraure, 3,4 peaks a around 90 and 841 cm 1 are characersc for he amorphous domans of he syndoacc polysyrene, and he wo peaks a 911 and 88 cm 1 belong o s β crysal. In he FTIR specrum of sample 3 n Fgure 6B (he red curve), all four peaks exs, ndcang ha boh amorphous domans and β crysallne domans coexs n he sample. The molar rao of hese wo domans can be deermned by he normalzed area rao of he wo peaks a 841 cm 1 (amorphous) and 88 cm 1 (β ). Accordng o he leraure, 3,4 he exncon coeffcen rao α of peak 88 cm 1 over peak 841 cm 1 s Therefore, he crysallny of β crysallne domans n sample 3 s = A88 A88 c / α α A 841 (10) where A 88 and A 841 are he areas of he peaks a 88 and 841 cm 1, respecvely. Expermenally, he wo areas were deermned o be 0.31 and 1.0, respecvely, by fng he peaks wh wo Gaussans (Fgure 6C). On he bass of hese values and eq 10, he crysallny n sample 3 s deermned o be 2%. The value s slghly hgher han 38.3% deermned on he bass of he same mehod on a crysal prepared under a smlar condon. 3,4 A very possble reason for hs dfference s ha he polymer we used s from a dfferen company. Is molecular wegh and qualy of srucural regulary whch can affec crysallzaon can be dfferen from he one used n he leraure D and 2D IR Daa. The major FTIR specral feaures of he hree samples n Fgure 7 (A, sample 1; B, sample 2; C, 609

9 Fgure 9. Tme dependen polarzaon selecve nenses of peaks a ω 1 = 3060 cm 1 and ω 3 = 1600 cm 1 of (A) sample 1, (B) sample 2, and (C) sample 3, respecvely, and polarzaon selecve me dependen nenses of peaks a ω 1 = 2924 cm 1 and ω 3 = 1600 cm 1 of (D) sample 1, (E) sample 2, and (F) sample 3, respecvely. Each se of he daa was normalzed accordng o he nal maxmum of he oal nensy P(). Fgure 10. (A) The me dependen ansoropy of sample 3 calculaed from Fgure 9C. The nal value 0.3 ndcaes ha he drecons of he excaonal mode and he deecon mode are nearly parallel o each oher. (B) The ranson dpole momen drecons of he rng CH srech (3060 cm 1 ) and he rng CC srech (1600 cm 1 ) modes whn a benzene rng. In he fgure, he backbone of polysyrene s ponng along he paper normal. sample 3) are very smlar. All of hem conan he followng peaks nvesgaed n he vbraonal relaxaon nduced-hea measuremens: he rng CC srech (1600 cm 1 ), he rng CH srech (3026 cm 1, 3060 cm 1 ), and he backbone CH 2 srech (2924 cm 1 ). The frs hree modes are delocalzed whn he benzene rng. In 2D IR measuremens, he absorpon changes of he rng CC srech peak (1600 cm 1 ) were recorded as a funcon of wang me afer he respecve excaon of he oher hree modes. Fgure 8A shows wang me dependen 2D IR specra of sample 3. A earler wang mes, e.g., 0 and 0. ps, smlar o hose n Fgure 1, he peaks n Fgure 8A are manly conrbued by vbraonal couplngs beween chan CH 2 srech mode (2924 cm 1 ) or rng CH srech mode (3026 cm 1, 3060 cm 1 ) and rng CC srech mode (1600 cm 1 ). A a relavely long wang me, e.g., 100 ps, he peaks n he 2D IR specra are manly from he vbraonal relaxaon nduced hea effecs, as he vbraonal lfemes of he CH sreches are only 2 ps. The hea sgnal s no sgnfcanly dfferen from he couplng sgnal n Fgure 8A. Only he lneshapes slghly change. The opcal absorbance changes caused by relaxaon-nduced hea are conssen wh he emperaure dfference FTIR specra shown n Fgure 8B. The me dependen polarzaon selecve nenses of peaks a ω 1 = 3060 cm 1, ω 1 = 2924 cm 1, and ω 3 = 1600 cm 1 of he hree samples are shown n Fgure 9. In samples 1 (Fgure 9A and D) and 2 (Fgure 9B and E), sgnals from boh parallel and perpendcular polarzaon confguraons become equal regardless of wheher he nal vbraonal couplng sgnals a me 0 are he same or no. As dscussed above, he resuls are expeced, snce hese wo samples are amorphous glass. Insde he wo samples, he relave nermolecular orenaons are random, resulng n soropc vbraonal relaxaon-nduced hea sgnals a long wang mes. For sample 3 nsde whch a good poron of molecules form crysals, he hea sgnals from he wo polarzaon confguraons are no equal anymore, as shown n Fgure 9C and F. The sgnals from he parallel polarzaon confguraon reman consanly larger han hose from he perpendcular confguraon afer 100 ps. There s one pon we need o emphasze here. The hea effecs observed n he samples are manly from he nermolecular raher han nramolecular hea ransfer accompanyng he vbraonal relaxaon of he nally exced 6060

10 Fgure 11. Tme dependen polarzaon selecve nenses of peaks wh ω 1 = 3060 cm 1 and ω 3 = 1600 cm 1 of sample 3 a hree dfferen sample orenaons. A smlar nensy rao beween he wo polarzaon confguraons a all hree sample orenaons ndcaes ha he molecular dsrbuon whn he laser focus spo s soropc. mode. Ths concluson s suppored by a conrol expermen: he hea effec by excng/deecng he same par of modes n a 2 w % polysyrene/chloroform soluon s sgnfcanly smaller han ha n he bulk polysyrene sold sample because mos of he hea ( 8% as measured) s ransferred o he solven chloroform molecules. Daa are shown n he Supporng Informaon Ansoropy of Hea Effecs and Molecular Orenaons of Sample 3. The me dependen ansoropy of pump/probe sgnal of sample 3 n Fgure 9C was calculaed on he bass of eq 6 and shown n Fgure 10A. The nal ansoropc value can be used o deermne he nramolecular vbraonal cross angle beween he nally exced vbraonal mode, he rng CH srech (3060 cm 1 ), and he deecon mode, he rng CC srech (1600 cm 1 ), provded ha he molecular dsrbuon whn he maer/lgh neracon volume s soropc. 1 To es wheher he molecular orenaon n sample 3 s random whn he laser focus spo, we roaed he sample 4 and 90 n addon o 0 o acqure daa. There s a smlar nensy rao beween he wo polarzaon confguraons a all hree sample orenaons (0, 4, and 90, relave o he opcal able plane), ndcang a macroscopc random molecular dsrbuon whn he laser focus spo. Resuls are dsplayed n Fgure 11 (A, 0 ; B,4 ; C, 90 ). The nal ansoropc value n Fgure 10A s 0.3, whch ndcaes ha he vbraonal cross angle beween he excaon and deecon modes (he rng CH srech (3060 cm 1 ) and he rng CC srech (1600 cm 1 )) s 17 accordng o eq. Ths s conssen wh our densy funconal heory (DFT) calculaons. The calculaed drecons of hese wo vbraonal modes are nearly parallel ( 8.6 ) o each oher whn a benzene rng, boh of whch are along he C(1) C(4) axs whn he benzene rng, as shown n Fgure 10B. In hs sample, he vbraonal couplng beween hese wo modes on dfferen rngs s oo weak o be deeced because of he large dsance beween wo rngs. Therefore, he calculaed cross angle beween hese wo modes on dfferen rngs s no aken no consderaon. The DFT calculaon deals are provded n he Supporng Informaon. Fgure 10A shows ha he ansoropy decays rapdly afer he nal vbraonal excaon. Whn abou 10 ps, he ansoropy value drops from 0.3 o 0.1, and a longer mes, essenally remans consan a 0.0 ± In sample 3, he polymer molecules are n eher he glassy sae or he crysallne sae. Ther roaons are expeced o be hndered and exremely slow. Therefore, he nal fas ansoropy observed should no be caused by he molecular roaons. The resonan vbraonal energy ransfer among he nal excaonal modes (he rng CH srech a 3060 cm 1 )ondfferen benzene rngs s no a lkely reason eher, because her ranson dpole momen s oo small and her relave dsances are oo large o effecvely ransfer energy o each oher whn a few ps, compared o he KSCN sysems we suded prevously. 20,21 The mos lkely reason for he nal fas ansoropy decay s he vbraonal relaxaon-nduced hea effecs. As measured, he vbraonal lfeme of he CH srech s only 2.1 ps. Is relaxaon whn he nal few ps produces a sgnfcan amoun of hea whch dsspaes nramolecularly no oher segmens of he same polymer chan and nermolecularly no oher molecules. A early wang mes when he amoun of vbraonal relaxaon s small, he ansoropy of he sgnal n Fgure 10A s deermned by he cross angle beween he rng CH srech mode and he rng CC srech mode whch s purely deermned by he nrarng aomc posons, snce boh modes are on he same rng. A longer wang mes when relaxaon-nduced hea effecs become sgnfcan, he deecon mode, he rng CC srech, s no necessarly on he same rng as he nal exced mode, he rng CH srech, because he same mode on dfferen rngs experences he same hea and opcally responds smlarly o he hea as dsspaes away from he nally exced rng. Therefore, he ansoropy value under hs crcumsance s deermned by he average angle beween he wo modes on boh he same and dfferen rngs. As dscussed above, sample 3 has 48% amorphous domans whch gve an ansoropy value of 0. In he res of he 2% crysallne domans, he relave orenaons of benzene rngs are no parallel, whch can also reduce he ansoropy from he nal value 0.3, snce 0.3 s close o he possble maxmum ansoropy value 0.4 from a par of parallel modes. Therefore, because of he nermolecular and ner-rng relave orenaons, no maer n he glass domans or he crysallne domans, he hea effecs reduce he ansoropy value. However, before he majory of he nal excaon of he rng CH srech has relaxed, he ansoropy value of he sgnal n Fgure 10A conans conrbuons from vbraonal couplngs, possble mode specfc vbraonal energy ransfers, and he hea effecs. I would be very complcaed o exrac he relave nermolecular orenaons n sample 3 from he mxed sgnals whch come from a leas hree dfferen mechansms. A longer wang mes, e.g., afer 100 ps, mos of he nal excaon of he rng CH srech has relaxed no hea, as ndcaed by he me ndependen hea sgnals n Fgure 9C. The pump/probe sgnals observed n Fgure 9C are manly from he hea effecs. Now s possble o analyze he nermolecular orenaons n sample 3 based on he ansoropy 6061

11 Fgure 12. Sackng of macromolecular blayers n he β crysal, wh A and B ndcang wo knds of macromolecular blayers. 2 The upper rgh represens he chans of four dfferen orenaons, wh red and blue arrows ndcang he ranson dpole momen drecons of he rng CH srech (3060 cm 1 ) and he rng CC srech (1600 cm 1 ) modes, respecvely. The boom rgh shows he molecular conformaon of a polymer chan. value a long wang mes n Fgure 10A, accordng o he equaons gven n secon 3. Accordng o eq 9, he oal ansoropy of hea sgnal s he weghed sum of subcomponens ansoropes. In sample 3, here are wo componens: (1) he amorphous glass of whch he ansoropy s 0 and (2) he ordered crysals of whch he ansoropy s dependen on he molecular orenaons and ner-rng orenaons whn a polymer chan. The molar fracons of hese wo domans are 48% (glass) and 2% (crysal), respecvely. However, as dscussed n secon 3, he molecular fracon can be used as he weghng facor n eq 9 only when he hree condons are smulaneously fulflled. For sample 3, we found ha f he crera: (1) The molecular dsrbuon whn he lgh/maeral neracon s soropc, as suppored by he observed same ansoropc behavors obaned by roang he sample. (2) The molecular responses n dfferen domans are approxmaely dencal (±10%), as we can see from he normalzed nenses of hea sgnals n Fgure 9C compared o hose n Fgure 9A or B. (3) The resuls n (2) also ndcae he hea ransfer nsde he crysal s probably soropc, snce he hea ransfers are very smlar n boh amorphous and crysallne saes. As dscussed n secon 3, he dmensons of he crysallne and amorphous domans mus be larger han ens of nm n order for mos of he relaxaonnduced hea o ravel whn he same domans. We do no have drec evdence o show how large he domans are, bu from he opaque naure of sample 3, we esmae ha a leas one dmenson of he crysals mus be larger han 100 nm (1/4 of 400 nm). The phoographs of samples 1 and 3 are provded n he Supporng Informaon, where he glassy sample 1 s ransparen bu he semcrysallne sample 3 s opaque. To calculae he ansoropy of hea sgnal from he β crysallne domans of sample 3, we need nformaon abou s molecular conformaons and crysallne srucures. Accordng o he leraure, 38,2, nsde he β crysallne domans, a polysyrene molecule akes he all-rans-planar-zgzag (T4) chan conformaon, as shown n he boom rgh of Fgure 12. The molecular orenaons nsde he crysal are also dsplayed n he lef sde of Fgure 12. When vewed along he chan axs, he crysal can be descrbed n erms of a slghly dsordered sackng of wo knds of macromolecular blayers characerzed by dfferen orenaons of lnes connecng wo adjacen benzene rngs nsde each chan, ndcaed as A and B n Fgure 12. As a resul of crysallne symmery, he benzene rngs can be dvded no four groups accordng o he dfferen orenaons o calculae he ansoropy value, wh he molar fracon of 1:1:1:1. As shown n he upper rgh of Fgure 12, he dfferen ranson dpole momen drecons of he energy source mode, he rng CH srech (3060 cm 1 ) and he hea sensor mode, he rng CC srech (1600 cm 1 ) are denoed as drecon 1 4 and 1 4, respecvely. φ s he vbraonal cross angle beween he wo modes whn he same rng, whch s 8.6 from DFT calculaon. θ s he cross angle beween he energy source modes n wo dfferen drecons whn a sngle chan. As shown n Fgure 10B, he calculaed drecons of he energy source mode are along he C(1) C(4) axs. Therefore, accordng o he crysal srucure, 2 he cross angle θ can be obaned as 111. Here we ake boh he CH and CC srech ranson dpole momen vecors o be whn he rng plane o smplfy calculaons. Ths can cause abou 1 % uncerany n he fnal resul, snce he calculaed CC srech has a cross angle of 2 3 ou of he benzene plane. The energy source modes n four dfferen drecons 1 4 has an equal probably o be exced, and hence conrbue equally o he oal ansoropy of he crysallne regon from each drecon. For he energy source modes a drecon 1, he hea sensor modes can be dvded no four speces accordng o dfferen drecons 1 4, wh he cross angle beween he energy source mode and he hea sensor modes as φ, φ, θ φ, and θ φ, successvely. Then, he correspondng ansoropy can be calculaed from 6062