Radial Distribution Function. Long-Range Corrections (1) Temperature. 3. Calculation of Equilibrium Properties. Thermodynamics Properties
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1 . Calculato o qulbrum Prorts. hrmodamc Prorts mratur, Itral rg ad Prssur Fr rg ad tro. Calculato o Damc Prorts Duso Coct hrmal Coductvt Shar scost Irard Absorto Coct k k k mratur m v Rmmbr hrmodamcs or mooatomcmolculs 5 or datomc molculs For Moatomc Molcul Ktc rg or ach rdom hrmodamcs Prorts Itral rg or otal rg U k + k + φ( rj j Rmmbr hrmodamcs or Idal Gas U k Ak R r mol U R u R r mass m' m' k : oltzma Costat,.66 - J/K A : Avogadro umbr, 6.5 /mol R : Uvrsal Gas Costat,. J/(mol K m : Molcular Wght (kg/mol Prssur b vral thorm P k j φ rj r hrmodamcs or Idal Gas P k P k R A j For mol A P k ρk ρ: umbr dst Radal Dstrbuto Fucto Radal Dstrbuto Fucto (Par Corrlato Fucto ρ δ[ r r j ] j ( r, ρ ( r, Rato o a local dst ρ( to th sstm dst ρ Log-Rag Corrctos ( πρ φ( rc πρ φ + πρ φ ( ( r rc ~ + LR πρ φ( LR r c dr LR πρ πρ 6 ( rc ( rc For Lard-Jos ( rc
2 Log-Rag Corrctos ( For Prssur mrcal Rlatos( mratur Dst ~ + LR LR LR πρ 6πρ ( r c r c dφ( r dr 6πρ 6 ( rc ( r c For Lard-Jos Prssur Hlmholtz Fr rg Gbbs Fr rg Pottal rg Itral rg tro R corrlato ad colas t al. corrlato mrcal Rlatos( P ρ + P ρ + ( ρ, A ρ P dρ ρ ρ ( / A ρ ρ P U P d ρ ρ ρ S µ st Partcl Mthod( k l Ω µ µ µ / U t g k l ( k x / k k k µ k l /( g /( k [ ρλ ] Istataous mratur Chmcal Pottal or Idal Gas P S U + µ ρ Λ U U t h /(πmk t, MD 6π ρ rc hrmal D rogl Wavlgth wc log-rag corrcto xcss chmcal ottal µ.5 st Partcl Mthod ( 56 5 colas t al. xcss chmcal ottal µ.6.. st Partcl Mthod ( t 96 t 6 mratur R colas mratur.5 6 m (s 6. m (s
3 st Partcl Mthod ( st Partcl Mthod (5 xcss chmcal ottal umbr o tst artcls xcss chmcal ottal µ ρ. ρ mratur ρ.6 R colas t al. Damc Prorts Damc Prorts (Sl Dusvt, Fck s Law D hrmal Coductvt, Fourr s Law q λ scost, wto Fluds u F µ ts o mthod: qulbrum Molcular Damcs :Corrlato uctos oqulbrum Molcular Damcs :Fctous Fld Drct Molcular Damcs :oudar Codto qulbrum Molcular Damcs (Sl Dusvt D < v( t v( dt < vx vx ( + v v ( + vz vz ( dt st s quato: γ < A A ( dt tγ < ( A( t A( t D < r r ( 6t For larg t Duso Coct <(r (t r ( [A ] 6 D. A /s.x 9 m /s Grad.5 A /s m τ [s]
4 qulbrum Molcular Damcs hrmal Coductvt D k < j j ( dt λ < ( δ( t δ ( k t δ δx δ r ( < r ( < x r ( < / m + j v( r j hrmal Coductvt [ 5 ] <(δ (t δ ( /(k [J/Km] 5 λ.5 mw/km Grad.99x 6 J/(Km / s 5 m τ [s] qulbrum Molcular Damcs Shar scost < ( ( dt µ Pβ t Pβ k < ( Dβ Dβ ( k t D β r β Prort Dto Statstcal Mchacal Gr-Kubo Formula Duso D coct v v ( dt hrmal q λ coductvt q ~ q~ ( dt k Shar U F µ t dt vscost k ~ ( ~ β ( Wth st Rlato For larg t 6t r r ( ( δ ( t k t ( δ ~ ~ k t ( Dβ ( β D β q~ dδ, δ ( dt r, mv + φ( rj, x,, z j ol. ~ mv v + rj j, D ~ m β β β r v, β x, z, β β j zx Damc Prorts.57 A 55. A A sold } lars Lqud aor Lqud sold } lars Coolg Hatg mratur [K] Dst [/Å ] loct [m/s]... 5 s 5 s s 5 s mratur jum: 6. K 5. K <v z Posto [Å] hrmal oudar Rsstac ovr Lqud-Sold Itrac: m K/W hrm. hrm. Sc. Sc. gg., 999, 999, vol. vol. 7, 7, o. o.,, mratur [K] Dst [/Å ] loct [m/s]... 5 s 5 s s 5 s mratur jum: 6. K 5. K <v z Posto [Å] hrmal Coductvt λ L q W /( / z. W/m K Hadbook valu.97 W/m K at th saturatd tmratur o K hrmal Rsstac ovr Lqud-Sold Itrac
5 Absorto Cross Scto (ω ( ω πω{ x( ω / k } c rasto Rat I(ω I( ω, I ( ω µ t π x( ωtdt µ ( ( Classcal Lmt πω ω / k ( ω I( ω k c Quatum Mchacs Prturbato hor Powr Sctrum o Dol Momt Irard Absorto Sctrum Radom umbr Cogurato o Molculs Wghtd Avrag or Statstcal Prort Radom Chag o Cogurato Slct or ot b th Probablt Dstrbuto ad Radom umbr costat (umbr, volum ad rg: mcrocaocal costat (umbr, volum ad tmratur: caocal costat P (umbr, rssur ad tmratur costat µ (chmcal ottal, volum ad tmratur: grad-caocal Mot Carlo Smulato (Mtrools Mthod 5
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