Pressure-Temperature Diagram. Heterogeneous Liquid Droplet Nucleation on Solid Surface Mirror. 5. Nucleation Dynamics
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1 . Nuclato Dyamcs A. Homogous Nuclato o Lqud Droplt ad Vapor ubbl. Htrogous Nuclato o Lqud Droplt ad Vapor ubbl. Grato o Spcal Structurs Prssur Stabl Lqud rtcal Pot D Ustabl go E Lqud Saturato F Stabl Vapor Vapor Saturato G A, FG: stabl, EF: mtastabl P < v D, DE: ustabl P > v Lqud Spodal Vapor Spodal Volum hrmodyamc lmt o suprhat Htrogous Lqud Droplt Nuclato o Sold Surac rror Argo Vapor L-J Yasuoka & atsumoto (998).Å.Å K S K ρ ρ Homogous Nuclato.Å O-Layr Sold Harmoc +Phatom Prssur [Pa] Numbr o olcul Argo mpratur Prssur Wall mpratur 8 Numbr o oomr axmum lustr Sz m [ps] mpratur [K] K lustr: r.σ A Prssur, tmpratur, umbr o o moomr ad maxmum clustr sz varatos (E) K ps K Prssur (Pa) Saturato Spodal E E 8 mpratur (K) Prssur-mpratur Dagram E
2 wall: lu () moo: Wht () -: d () -9: Orag () -9: Yllow () : Gr () Sapshots o clustr largr tha atoms (E) orag yllow gr lustr Sz Dstrbuto ps ps ps ps ps lustr Sz lustr Sz Dstrbuto τ. ps S.8 Homogous by Yasuoka & atsumoto Numbr o lustrs 8 Paralll Ls Stady Growth * * th. J sm. cm - s - m [ps] Numbr o lustrs Largr tha hrshold r * rtcal adus & Fr Ergy Fr Ergy o lustr Numbr o molculs γ ρ k l S l Ara A πr Volum V π r Surac tso γ ρ V l G γa + gv Fr rgy drc ρ I sold ad vapor or ut volum g ρlk l( ) Assumpto o dal gas ρ * ρ l Suprsaturato ρ ato S ρ πγ * πγ G ( k l S ) ( k l S) ρ l Htrogous uclato rom pla sold surac + cosθ σ ( ) πσ θ J N xp ( ) πm θ k ( ηp ( ) P) SA P v( P P ( )), η xp, ( θ ) ( + cosθ cos θ ) SA η ( ) PSA Nuclato at J (/m s) Prssur p (Pa) Nuclato at J [/m s] 8 Lqud Sold surac Vapor bubbl otact Agl cosθ θ G [ J] E E E 8 K K K lustr Sz Symbols: Estmato rom clustr dstrbuto c() Vald utl rtcal Sz G ( ) ρ xp k Gbb s Fr Ergy c lu: Homogous d: Htrogous Ls: lasscal hory G πr γ πr ρlk l S πr ρ l
3 [ ] alculato odtos ad Nuclato ats G [J] Labl ε IN [ - J] θ [dg] av [K] J sm [cm - s - ] J th [cm - s - ] E E..8.. lustr Sz E: lss wttabl Homogous Yasuoka & atsumoto (998) E Smulatd lasscal hory omparso o Fr Ergy Yasuoka & atsumoto: Homogous D: J sm was ordrs largr tha J th... p A. crtcal pot D E p.. D Q. -. v Isothrm o va dr Waals spodal l A sapshot o lqud argo btw paralll sold suracs Nuclato o Vapor o Sold Surac (a) ps (b) ps (c) ps Slc Vw pv Vod Vw (d) ps () ps () 8 ps Sapshots o vod pattrs or P
4 Prssur (Pa) ubbl Sz P P P P mpratur(p) Wall Prssur(P) a a a a m (ps) Prssur, tmpratur ad bubbl sz varatos 8 mpratur (K) Prssur (Pa) E E E E Saturato l P P P P Spodal l Homogous Kjo&atsumoto (99) 8 mpratur (K) wttabl surac d hghr suprhat to uclat Prssur ad tmpratur varatos ad spodal l Prssur [Pa] mpratur Prssur Expaso 9 mpratur [K] ~ ps 等温体積弾性率 -V( p/ V) Pa Prssur [Pa] mpratur Prssur (a). Å (b). Å (c). Å 9 mpratur [K] 気泡核成長の待ち時間 τ ps 核生成速度 J D. cm - s - Vod adus [Å] 8 otuous (a). Å (b). Å m [ps] 気泡半径. Å 圧力上昇 p- ( V/V). Pa Vod adus [Å] 8 a m [ps] 最大ボイド半径 8 Å 臨界気泡核半径 - Å Nuclato procss by by stoppg xpaso at at crta pot Nuclato procss by by stoppg xpaso at at crta pot Htrogous uclato rom pla sold surac Lqud + cosθ σ ( ) πσ θ J N xp ( ) πm θ k ( ηp ( ) ) sat p v( p psat ( )), η xp, ( θ ) ( + cosθ cos θ ) Nuclato at J [cm s ] Sold surac ηpsat ( ) p r σ Vapor bubbl K p -.8 Pa J H. cm - s -, r.9 Å θ 8 J D. cm - s - θ m hstory o vod pattr (h.å) Prssur p [Pa]
5 PVW omparso wth lasscal hory lasscal hory: J. cm - s -, r.9 Å (a) (b) (c) La@ 8 (d) 8 Watg m τ ps J /(A τ ). cm - s -? Vod adus 8 Å, Lmt o apd Growth c. 均質核生成 (. Kjo &. atsumoto, 998) J D. 9 cm - s - J H. cm - s - () SWN ypcal Structurs o Fullr () WN otal Ergy E b : E b * { V ( rj ) jva( rj )} j( < ) D V r) ( r) xp β S Pottal paramtrs D. V S 9. β. A. A δ. 89 a. c 9 d.. A. A { S ( r )} ( * j + j j, + j k (, j) G c c ( θ ) a + d d { } δ G ( θ ) ( r ) From D. W. rr: Phys. v.,, 98(99) c jk c + ( + cosθ ) DS VA( r) ( r) xp β ( r ) S S k k θ jk j ut-o ucto - Pottal Fucto r V V r v r, v, K k K k KV V k r ' r r v ' v v V total total total V K m v mr ' v' K mr ' KV m v' K K Nk K c k VV KV V k V mpratur otrol adomly dstrbutd carbo atoms wth radom vlocts PVW Å otrol tmpratur c K lustr Sz 8 alculatg odtos m (ps) Growth Procss carbo atoms Å cubc box c K
6 Prct (I h symmtry) K K K K K K 8 K lat cagd chaotc small pcs carbo atoms 8 Å box (about tms hghr dsty) Ital sampl Structurs o lustrs at Varous mpraturs Schlgl Dagram s 8 PVW (A) Sto-Wals rasormato A.8 s.8 s. s. s pottal rgy E p (V)...8. tal E p. s.8 s 8.9 s. s. s (I h ) N D I h 9 tm (s) # o damglg bods N D Aalg Procss to prct.9 s.9 s.9 s.98 s () Gralzd Sto-Wals rasormato Sto Wals rasormatos. s. s. s acto at (ps - ) mpratur (K) s at K bod swtchg.9 V µs at K ptago mgrato. V / (K - ). s at K Arrhus Plot or ypcal actos PVW Flat Avragd radus (A ) # o ods E P (V/atom) F F ajor F F 8 m (s) Local Aalg Procss o at c K agld Polycyclc
7 F F O O Flat PVW Avragd radus (A ) # o ods.... omparabl F F haotc -dmsoal (cag-lk) losd cag PVW Avragd radus (A ) # o ods.... omparabl O O Op cag E P (V/atom) m (s) Local Aalg Procss o at c K E P (V/atom) m (s) Local Aalg Procss o 8 at c K ha g Flat agld poly-cyclc haotc -dmsoal structur oo hgh tmpratur adom cag Prst Fullr Formato odl losd cag oo low tmpratur Op cag Fullr (stabl) Sto-Wals trasormatos Graphtc sht Hghr ullr Group Prod H H L N O F N Na g Al S P S l Ar K a Sc V r F o N u Z Ga G As S r Kr b Sr Y Zr Nb o c u h Pd Ag d I S Sb I X s a * H a W Os Ir Pt Au Hg l Pb Po At Fr a ** Uq Up Uh Us Uo U Uu Uuu Uub * Lathads La Pr Nd Pm Sm Eu Gd b Dy Ho Er m Yb Lu ** Actds Ac h Pa U Np Pu Am m k Es Fm d No Lr Studd tal Atoms E V + V + V j A V : pulsv trm D V rj ) xp S V : oulomb trm cc V ( rj ) πε r * : ormalzd bod ordr N : carbo coordat umbr N + ( ) c, c : charg o (+) ad (-) (r j ) : cut-o ucto V A : Attractv trm * DS VA ( rj ) xp β / S ( rj ) S ( { β S ( rj )} { } { + b( ) } δ * N carbo k ( j) r k c xp( k N + k ) - j c c / N N + ( r k mtal k ( j) - ad - Pottal Fucto Exprsso ) { ( N ) } { ( N ) } ( N ) xp D ( N ) D + D xp j j - j D j N : mtal coordat umbr ccj V ( rj ) πε r j N N j + N j pottal rgy (V) V (N ) E b (N ) E b (N ) V (N ) La dstac r (Å) (a) La- pottal rgy (V) V (N ) V (N ) E b (N ) E b (N ) Sc dstac r (Å) (b) Sc- pottal rgy (V) tal-arbo Pottal uctos E b (N ) E N b (N ) dstac r (Å) (c) N- abl. Pottal paramtrs or mtal-carbo tractos. D (V) S β (/Å) (Å) (Å) (Å) b δ k k La Sc N abl. Pottal paramtrs or mtal-mtal tractos. S β (/Å) D (V) D (V) D (Å) (Å) (Å) (Å) La-La Sc-Sc N-N
8 Å Ital codtos: carbo atoms & mtal atoms lustrg Procss adomly dstrbutd wth radom vlocts otrol tmpratur c K (a) Growth procss o a La@ La La 9 La La (b) Growth procss o a La PVW La8 La La@ clustr sz La La La La La9 8 La La tm (ps) ps ps ps & La ( Å) cubc box Growth Procss o La lustrs otrol tmpratur c K Fa-typ Grapht-lk tal outsd Op cag tal sd losd cag PVW N N 9 N N N N:, :.m box PVW Sc Sc 8 Sc Sc 9 Sc Sc 9 Sc@ Sc@ 8 tal sd & outsd clustr sz ha or g Grapht-lk Op cag N 8 N N N 9 N N clustr sz tm (ps) Sc:, :.m box Growth Procss o a Sc otag lustr tm (ps) Growth Procss o N Attachd lustrs N 8 N La La 8 (La@ ) La La tm (ps) ollso Procss o La Attachd lustrs clustr sz # o postv r products 8 tm (ps) sd outsd 8 Aalg o N 8 ad N lustr c K 8
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