Investigations on the Dynamical Characteristics of One Water Molecule Embedded in a Singlewalled Carbon Nanotube
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1 Ivesgaos o he Dyamcal Chaacescs of Oe Wae Molecule Embedded a Sglewalled Cabo Naoube Ja-Mg Lu * Tzu-Hua Wu 2 ad Su-Tog Cho 2 Naoal Cee fo Hgh-Pefomace Compug Naoal Appled Reseach Laboaoes 2 Depame of Aeoaucs ad Asoaucs Naoal Cheg Kug Uvesy * Coespodece: ockylu@chc.og.w
2 Oule INTRODUCTION MD SIMULATION METHODOLOGY RESULTS AND DISCUSSION CONCLUSIONS FUTURE DIRECTIONS ACKNOWLEDGMENTS
3 Ioduco I CNT Applcaos 24/4/ 3
4 Ioduco II - Applcaos Baees Bosesos fo hamful gases ad chemcal aalyses Capacos Cahodes fo mcowave ubes Chemcal facoy-o-a-chp applcaos Compues ad TVs wh ao ccus Coducg composes Coducos fo mco elecoc devces Coolled dug elease applcaos DNA chps Elecoc applcaos Elecoc ecfcao ballsc swchg ad logc fucos Elecoc aocompoes ad maeal poeco applcaos Feld effec assos Feld-emsso fla pael dsplays Fle applcaos Fuel cell membaes Hea ppe Hydoge soage LEDs Mcoscope pobes Molecula pumps Naomec es ubes Naoube efoced composes Nao-daa soage Quaum wes Sgle eleco assos Spog goods Wae desalaos Weless devces hp://
5 Movao Ieesg pheomea ad physcal popees may be foud he wae-aoube composes. Sce he dscovey of cabo aoubes eseaches vgoously vesgaed he faasc behavo of cabo aoubes wh o whou cluso aoms. povdg avalable fomao o esmae he effecve Youg s modulus of he wae-aoube compose.
6 Pape Suvey PublsheNaue Yea2 AuhoHumme G Rasaah JC Nowoya JP TleWae coduco hough he hydophobc chael of a cabo aoube Humme e al. ulzed he molecula dyamcs mehod ad foud ha wae aages oedmesoal ode sde a hydophobc cabo aoube by sog eaco of hydoge bods. He vesgaed wae a log cha ode ad s fludy a pulsed mode
7 Pape Suvey Publshe Nao Les Yea24 AuhoN. Nagub H. Ye Y. Gogos A. G. Yazcoglu C. M. Megads M. Yoshmua TleObsevao of wae cofed aomee chaels of closed cabo aoubes Nagub e al. suded wae passg o he defecs of a cabo aoube ad vesgaed he behavo of wae sde a cabo aoube. They foud ha he flow of wae s much less ha ha of macoscopc wae ageeme wh Lu s esuls. Also wae ca be soldfed by ceasg he pessue ad s foud ha hexagoal ad hepagoal cy colums chage o ecagula ad peagoal oes whe exeal pessue s ceased
8 Pape Suvey Publshe Phys. Rev. B Yea25 Auho Lu YC Wag Q TleTaspo behavo of wae cofed cabo aoubes Lu ad Wag foud ha wae sde a cabo aoube behaves as of asoopc aspoao by he molecula dyamcs mehod. They also vesgaed ha axal hea coduco ae dffusve ae ad vscosy ae much moe ha logude ha. The dffusve ae of wae deceases oceably wh he decease of a cabo aoube s damee. Howeve he axal hea coducve ae ad shea vscosy of wae ae much moe ha ha of macoscopc wae. Moeove he chal ode ad lama dsbuo of wae wee also vesgaed
9 Pape Suvey Publshe J. Phys.: Codes. Mae Yea 26 AuhoN R de Souza A I Koleskov C J Buham ad C-K Loog TleSucue ad dyamcs of wae cofed sgle-wall cabo aoubes Souza e al. used he euo dffaco ad he molecula dyamcs mehod o vesgae wae sde a cabo aoube ad foud ha wae s able o pass hough a SWNT a shell-cha sucue a lowe empeaue. They defed ha wae eaages ad chages o a cubc cy sucue whch coas cha-sucued wae molecules. The hydoge bods ae ceaed ad boke volely wh he empeaue ceasg. He foud ha he shell-cha sucue dsappeas whe he empeaue s beyod 2K
10 Pape Suvey Publshe Nao Les Yea27 AuhoWag Z. C L. Che L. Nayak S. Ajaya P.M. ad Koaka N. TlePolay-Depede Elecochemcally Coolled Taspo of Wae hough Cabo Naoube Membaes Wag e al. obseved wae egave chage by bgg posve volage o a waeembedded cabo aoube ad foud ha a cabo aoube s popees chage o hydophlc fom hydophobc. Moeove he flow ae ceases subsaally wh he elecc feld ceasg. They dcaed ha he echque ca be appled o pufy dkg wae ad gee eseach.
11 Oule INTRODUCTION MD SIMULATION METHODOLOGY RESULTS AND DISCUSSION CONCLUSIONS FUTURE DIRECTIONS ACKNOWLEDGMENTS
12 Huma ha ~ -5 mm wde Red blood cells wh whe cell ~ 2-5 mm Thgs Naual Dus me 2 mm ~ m damee The Scale of Thgs -- Naomees ad Moe A ~ 5 mm Fly ash ~ -2 mm ATP syhase The Mcowold The Naowold -2 m -3 m -4 m -5 m -6 m -7 m -8 m aomees = mllmee mm Ulavole Vsble Ifaed Mcowave cm mm. mm mm. mm mm aomees = mcomee mm. mm m. mm m MD Thgs Mamade McoElecoMechacal devces - mm wde Red blood cells Polle ga Zoe plae x-ay les Ouemos g spacg ~35 m Naoube elecode Head of a p -2 mm Naoube asso 2s Ceuy Challege O O S O O O O O O O O O O O S O S O S Combe aoscale buldg blocks o make ovel fucoal devces e.g. a phoosyhec eaco cee wh egal semcoduco soage O S P O O O O S O O S O S -9 m aomee m DNA ~2-/2 m damee Aoms of slco spacg ~ehs of m - m Sof x-ay. m Quaum coal of 48 o aoms o coppe suface posoed oe a a me wh a STM p Coal damee 4 m Cabo aoube ~2 m damee Offce of Basc Eegy Sceces Offce of Scece U.S. DOE Veso 3-5-2
13 Legh ad Tme Scales Numecal Modelg Tme Scale msec Naoechology sec psec fsec QC QMD MD Sascs Mechacs Couum Mechacs m m mm Space Scale
14 Molecula Dyamcs A compue smulao echque ha allows oe o pedc he me evoluo of a sysem of eacg pacles aoms molecules.. ec.
15 Two Seps o pefom MD smulao I Seg al codos e.q. al poso ad veloces of all pacles he sysem Selecg accuae eaco poeal fo descbg he foces amog all he pacles.
16 II Solvg a se of classcal equaos of moo j : eaomc poeal
17 Schemac dagam of a basc MD code Defe al posos ad veloces ad V Pa A 2 3 N a Calculae foces a cue me F V... Pa B Solve equaos of moo fo all pacles he sysem Ove a sho mesep V V Pa C Calculae desed physcal quaes we daa o ajecoy fle Pa D s max We o he dsk fal aomc cofguao & fsh 7
18 Pa A Seg Ial Codo s Pa A HPC-NMR Pa B V... Defe al posos ad veloces ad Calculae foces a cue me F 2 3 N a Solve equaos of moo fo all pacles he sysem Ove a sho mesep V V Calculae desed physcal quaes we daa o ajecoy fle Pa D s max V Pa C We o he dsk fal aomc cofguao & fsh esablshg al posos ad veloces of all aoms befoe MD smulao Two sklls o acheve he elaxao pocess usg values afe elaxao pocess Udegog a elaxao pocess Relaxao cycles Re-zeo smulao sums Poduco cycles 8 Schemac fom lecue of D. A. Kofke
19 s Pa A HPC-NMR Pa B F V... Defe al posos ad veloces ad Calculae foces a cue me 2 3 N a Solve equaos of moo fo all pacles he sysem Ove a sho mesep Pa C V V V Geeag a Ial Cofguao Calculae desed physcal quaes we daa o ajecoy fle s max We o he dsk fal aomc cofguao & fsh Pa D The aageme of he Ial cofguao s maly based o he maeal aue we wa o smulae fo example b.c.c f.c.c h.c.p amophous. H.C.P F.C.C
20 s Pa A HPC-NMR Pa B V... Defe al posos ad veloces ad Calculae foces a cue me F 2 3 N a Solve equaos of moo fo all pacles he sysem Ove a sho mesep Pa C V V V Ial Veloces Calculae desed physcal quaes we daa o ajecoy fle s max We o he dsk fal aomc cofguao & fsh Pa D Geeag veloces of aoms x y z decos ove a ufom adom umbes ove -. Scalg he kec eegy of he sysem o he coespodg empeaue we desed. shfg he cee-of-mass momeum o be zeo
21 Dmesos ad Us s Pa A HPC-NMR Pa B F V... Defe al posos ad veloces ad Calculae foces a cue me 2 3 N a Solve equaos of moo fo all pacles he sysem Ove a sho mesep Pa C V V Calculae desed physcal quaes we daa o ajecoy fle Pa D V s max We o he dsk fal aomc cofguao & fsh Scalg by model paamees sze s eegy e mass m Tables fom he lecue of D. A. Kofke
22 Themosas s Pa A HPC-NMR Pa B F V... Defe al posos ad veloces ad Calculae foces a cue me 2 3 N a Solve equaos of moo fo all pacles he sysem Ove a sho mesep Pa C V V Calculae desed physcal quaes we daa o ajecoy fle Pa D V s max We o he dsk fal aomc cofguao & fsh momeum empeaue s popooal o oal kec eegy kt N 2 2 p Nd m Nd K eegy flucuae bewee K ad U p N Q N
23 s Pa A HPC-NMR Pa B F V... Defe al posos ad veloces ad Calculae foces a cue me 2 3 N a Solve equaos of moo fo all pacles he sysem Ove a sho mesep Pa C V V V Calculae desed physcal quaes we daa o ajecoy fle Pa D s max Foce momeum empeaue o ema cosa. Isokec Themosag Themosag va Wall Collsos.Adese Themosa 2. Nosé Themosa 3. Nosé-Hoove Themosa We o he dsk fal aomc cofguao & fsh
24 Peodc Bouday Codo geomec bouday s Pa A HPC-NMR Pa B V... Defe al posos ad veloces ad Calculae foces a cue me F 2 3 N a Solve equaos of moo fo all pacles he sysem Ove a sho mesep Pa C V V Calculae desed physcal quaes we daa o ajecoy fle Pa D s max We o he dsk fal aomc cofguao & fsh V
25 Pa B Poeals used he MD smulao s Pa A HPC-NMR Pa B V... Defe al posos ad veloces ad Calculae foces a cue me F 2 3 N a Solve equaos of moo fo all pacles he sysem Ove a sho mesep Pa C V V Calculae desed physcal quaes we daa o ajecoy fle Pa D s max V Bodg Foce a bod segh V bod legh N b N b / 2 k b b b c bod oso We o he dsk fal aomc cofguao & fsh b bod bedg 2 V bedg N N We o he dsk fal aomc cofguao & fsh k 2 N V dhedal K -cos[ - ]
26 d Va de Wal V [ j j 2 2 j j 6 A ] vdw j SC j vdw j A S s Pa A HPC-NMR Pa B V... Defe al posos ad veloces ad Calculae foces a cue me F 2 3 N a Solve equaos of moo fo all pacles he sysem Ove a sho mesep Pa C V V Calculae desed physcal quaes we daa o ajecoy fle Pa D s max We o he dsk fal aomc cofguao & fsh V S A vdw j [ j j 2 j j 6 j j 2 j j 6 A SC j 2 j ] 2 c [ ASC j 2 j ] c No-bodg Foce e Coulomb foce V. j coul 332 [ q q j j ] q paal ch ag es j A S els j j c c q q 2 c f Hydoge foce q j S A els V HB M 2 N
27 Two ypes of eaomc poeal s Pa A HPC-NMR Pa B V... Defe al posos ad veloces ad Calculae foces a cue me F 2 3 N a Solve equaos of moo fo all pacles he sysem Ove a sho mesep Pa C V V Calculae desed physcal quaes we daa o ajecoy fle Pa D s max We o he dsk fal aomc cofguao & fsh V Pawse Poeal May body poeal
28 Lead-Joes poeal s Pa A HPC-NMR Pa B V... Defe al posos ad veloces ad Calculae foces a cue me F 2 3 N a Solve equaos of moo fo all pacles he sysem Ove a sho mesep Pa C V V V Two-body poeal U j 4 j j Mose poeal 2 6 exp 2 2*exp j D j o j o Calculae desed physcal quaes we daa o ajecoy fle s max We o he dsk fal aomc cofguao & fsh Pa D m
29 May body poeal Tgh-bdg poeal Co Cu T s Pa A HPC-NMR Pa B F V... Defe al posos ad veloces ad Calculae foces a cue me 2 3 N a Solve equaos of moo fo all pacles he sysem Ove a sho mesep Pa C V V Calculae desed physcal quaes we daa o ajecoy fle Pa D s max We o he dsk fal aomc cofguao & fsh V May-body Poeal exp 2 exp 2 j j E q A p j j May-body em-log age foce aacve foce Whee s a effecve hoppg egal j o /2 s he dsace bewee aom ad j s he fs-eghbo dsace Bo-Maye ype pawse em-sho age epulsve foce
30 May-body PoealNo-bodg Foce May body poeal V Tesoff poeal C S Ge A complcaed poeal o descbe he covale bodg bewee aoms V R V j f c E j Aj exp jj A j Bj exp jj f j R j Rj f c j cos f 2 2 Sj Rj f j Sj V j j [ V b V j R j j A j ] Pawse em-sho age epulsve foce Thee-body em-log age aacve foce bodg agle s also cosdeed j R j j S j s Pa A HPC-NMR Pa B F V... Defe al posos ad veloces ad Calculae foces a cue me 2 3 N a Solve equaos of moo fo all pacles he sysem Ove a sho mesep V V Calculae desed physcal quaes we daa o ajecoy fle Cuoff Fuco whch s used o smooh he eegy fuco o be zeo a he cuoff dsace bewee aoms. s max We o he dsk fal aomc cofguao & fsh V Pa D Pa C
31 Cuoff Mehod s Pa A HPC-NMR Pa B F V... Defe al posos ad veloces ad Calculae foces a cue me 2 3 N a Solve equaos of moo fo all pacles he sysem Ove a sho mesep Pa C V V Calculae desed physcal quaes we daa o ajecoy fle Pa D V s max We o he dsk fal aomc cofguao & fsh Vele ls Cell ls Vele combe cell ls
32 Vele combe Cell Ls s Pa A HPC-NMR Pa B V... Defe al posos ad veloces ad Calculae foces a cue me F 2 3 N a Solve equaos of moo fo all pacles he sysem Ove a sho mesep Pa C V V Calculae desed physcal quaes we daa o ajecoy fle Pa D V s max We o he dsk fal aomc cofguao & fsh 2 3 L L L
33 s Pa A HPC-NMR Pa B V... Defe al posos ad veloces ad Calculae foces a cue me F 2 3 N a Solve equaos of moo fo all pacles he sysem Ove a sho mesep Pa C V V V Calculae desed physcal quaes we daa o ajecoy fle Pa D s max We o he dsk fal aomc cofguao & fsh Algohm Compue Tme Sec./Tme sep Effce% Noe Vele Ls Cell lk Vele + Cell lk.66
34 Pa C Iegao Algohms s Pa A HPC-NMR Pa B V... Defe al posos ad veloces ad Calculae foces a cue me F 2 3 N a Solve equaos of moo fo all pacles he sysem Ove a sho mesep Pa C V V Calculae desed physcal quaes we daa o ajecoy fle Pa D V s max We o he dsk fal aomc cofguao & fsh. Vele Algohm 2. Leapfog Algohm 3. Velocy Vele Algohm 4. Gea Pedco-Coeco Algohm 34
35 Pa D Daa samplg Pa A Pa B F V... Defe al posos ad veloces ad Calculae foces a cue me 2 3 N a Solve equaos of moo fo all pacles he sysem Ove a sho mesep Pa C V V Calculae desed physcal quaes we daa o ajecoy fle Pa D V Pogess of smulao s max We o he dsk fal aomc cofguao & fsh MD me sep o MC cycle popey value m m m 3 m 5m6 m 7 m 9 m 2 m 4 m 8 Smulao block block aveage m. b m b m b- m b m3 m4 m5 Complee smulao smulao aveage m m k k. m 35 Schemac fom lecue of D. A. Kofke
36 Oule INTRODUCTION MD SIMULATION METHODOLOGY RESULTS AND DISCUSSION CONCLUSIONS FUTURE DIRECTIONS ACKNOWLEDGMENTS
37 MD SIMULATION The al codos: The boom ed of he cabo aoube s fxed. The me sep s chose o be =. fs fo he case of a cabo aoube whou wae; =.5 fs fo cabo aoubes wh wae. The empeaue s se o be 3 ad 2K. The NTV esemble s chose ad he cu-off dsace s 2 Å. Fo he wae-aoube compose o he cabo aoube hee ae execued fo al elaxao ad addoal 5 me seps fo eachg he lowes eegy cofguao.
38 MD SIMULATION The coolled paamees: The eval of me sep ad he cu-off dsace ae pe-chose. Tempeaue 3 ad 2K. The umbe of wae molecules ad 25. The ug me of a case 5 me seps. The vesgaed paamees: The vbao dsplacemes he amplude ad he vaace ad he mea value of he ampludes of he cabo aoube ae suded. Summay: The fee-vbao dsplaceme of he cabo aoube s p s vesgaed ad he dyamcal behavo of wae sde he cabo aoube s also ecoded. The elaoshp bewee he vaace ad mea value of vbag ampludes of he cabo aoube ad empeaue ae dscussed.
39 Mehodology TesoffCabo j j k E j V V f [ V bv ] j c j R j j A j V A exp R j j j j V B exp A j j j j j jk k f j Rj j R j f cos f R S 2 2 Sj R j f j Sj c j j j j b j j j 2
40 Mehodology Tesoff Cabo whee E s he oal eegy of all he covalely boded cabo aoms E he eegy fo aom V j he eaco eegy bewee aoms ad j j he dsace bewee hem jk s he bod agle bewee aoms j ad k ad f c s a cuoff fuco o esc he age of he poeal. I he pese wok he oal eegy calculaed fom he Tesoff poeal s assumed o be he oal sa eegy of he sysem. E j V V f [ V bv ] j c j R j j A j V A exp R j j j j V B exp A j j j j f j Rj j R j f cos f R S 2 2 Sj R j f j Sj c j j j j j b j j j 2
41 Mehodology Tesoff Cabo Paamees used he Tesoff poeal fo cabo-cabo bdg. Paamee A ev B ev Å - Å - c d H R Å S Å Value
42 Mehodology TIP3P wae Wae E whee ad ae cosa. They ae us of g-å 2 /fs 2 ad Å especvely.
43 Mehodology ME3Ogac Bodg Tems Wae-Cabo a Bod Sechg Poeal E 2 K R b Bod Agle Poeal 2 Hee K s a cosa us of kcal/mol/å 2. Å s he dsace bewee aom ad aom j. R Å s he equlbum bod sechg dsace. E C 2 2s C cos cos cos 2 8 Hee C s a cosa us of kcal/mol. deg s he equlbum bod agle.
44 Mehodology ME3Ogac Bodg Tems Wae-Cabo c Tosoal Agle Poeal V E [ cos{ }] 2 d Ou-of of-plae Poeal K cos cos 2 E 2s C cos Hee V s a cosa us of kcal/mol. deg s he equlbum osoal agle ad s a peodc paamee. Hee K s a cosa us of kcal/mol. deg s he equlbum ou-of of-plae agle. 2
45 Mehodology ME3Ogac No-bodg Tems Wae-Cabo e LJ oly UFF Poeal E D R R The above equao s he o-bodg em. D s a cosa whose u s kcal/mol. R Å s also a cosa.
46 Oule INTRODUCTION MD SIMULATION METHODOLOGY RESULTS AND DISCUSSION CONCLUSIONS FUTURE DIRECTIONS ACKNOWLEDGMENTS
47 RESULTS AND DISCUSSION Mea-SDA TempeaueK I shows ha loge ug me blue le 5 me seps pedcs less vaao ha shoe ug me whe le me seps bu o sgfcaly dcag ou esuls have eached umecal equlbum. Also by hs slgh dffeece ca be see ha he ase sae of a cabo aoube s vbao s moe vole ha he seady-sae oe. The vaace of he amplude of a capped cabo aoube s p deceases wh he execug me ceasg. The elaoshp bewee he mea value ad he vaace of a capped SWCNT ad empeaue whou wae 47
48 RESULTS AND DISCUSSION Mea-SDA TempeaueK I shows ha he amplude of a SWCNT s p ceases wh empeaue. Is ceasg ae s ealy lealy. Also s foud ha he vaace of a cabo aoube s he lages ea 3K. We obseve ha he sysem coag oe wae molecule dsubs he ube s vbao mos whe empeaue s ea he bolg po. I s suspeced ha wae s bolg s esposble fo hs obsevao. Whe he empeaue of wae s above he bolg po he volume of he wae vapo expads moe ha ha of he wae. Hece he collso bewee wae molecules ad he wall of a cabo aoube ceases ad esuls he vaace of he amplude of a cabo aoube. The elaoshp bewee he mea value ad he vaace of a capped SWCNT ad empeaue wh oly oe wae molecule 48
49 RESULTS AND DISCUSSION 4 Mea-SDA I shows ha he amplude of a SWCNT s p ceases wh empeaue. Is ceasg ae s ealy lealy whe he case has 25 wae molecules sde a SWNT TempeaueK The elaoshp bewee he mea value ad he vaace of a capped SWCNT ad empeaue wh 25 wae molecules. 49
50 RESULTS AND DISCUSSION a b c d The spaal poso of oe wae molecule he axal deco of a capped SWCNT whch s execued me seps a dffee empeaue a K; b 3K; c K; d 2K. The ed of dyamcal behavo of oe wae molecules lke walkg adomly a oe-dmesoal space as show Fg. Oe wae molecule behaves adomwalk fasho moe oceable wh empeaue ceasg. The kec eegy of wae ceases wh he cease of empeaue ad esuls he moveme of wae molecule. Howeve he ceasg he umbe of wae molecules deceases he adom-walk ed. The dffuso pahways ae dve by he mechasm of adom-walk ad he coceao of wae. Wh empeaue ad execug me ceasg wae molecules dsbue ufomly gadually alog he axal deco of he SWCNT. The beahg ad sechg-shoeg modes of he SWCNT ae cuely ude vesgao by ou goup 5
51 RESULTS AND DISCUSSION
52 RESULTS AND DISCUSSION a b 552 Å298Ka5Kb 52
53 RESULTS AND DISCUSSION a b a 9b 55 53
54 RESULTS AND DISCUSSION 55 54
55 Resuls Å Å Å
56 Oule INTRODUCTION MD SIMULATION METHODOLOGY RESULTS AND DISCUSSION CONCLUSIONS FUTURE DIRECTIONS ACKNOWLEDGMENTS
57 Coclusos The moe empeaue s he moe he vbag amplude of he SWNT ad he dyamcal behavo of wae moome sde s. 2 The opmal geomecal dsace s almos lealy elaed wh he damee of a SWNT o wh he chal veco of ha. 3 The wae moome emas he opmal geomecal dsace ad says close o he wall of a SWNT sead of o keep ealy he z-axal cee of a SWNT afe achevg he seady sae.
58 Oule INTRODUCTION MD SIMULATION METHODOLOGY RESULTS AND DISCUSSION CONCLUSIONS FUTURE DIRECTIONS ACKNOWLEDGMENTS
59 Ackowledgemes A ga fom he compuaoal suppos of Naoal Cee fo Hgh-Pefomace Compug Tawa. 2 A ga fom he Tawa Naoal Scece Coucl ude he coac NSC E MY3 s gaefully appecaed. 3 We ae also hakful he asssace of he Chu-Y Wu Q. Y. Kuo Cheg-Shu Hug ad S. S. Tu.
60
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