Table Of ContentThe air pressure effect on the homogeneous nucleation of carbon
dioxide by molecular simulation
M. Horscha, Z. Lina,1,T. Windmanna, H. Hasseb, J.Vrabeca,∗
aUniversitätPaderborn,LehrstuhlfürThermodynamikundEnergietechnik,WarburgerStr.100,33098Paderborn,
Germany
bTechnischeUniversitätKaiserslautern,LehrstuhlfürThermodynamik,Erwin-Schrödinger-Str.44,67663
0 Kaiserslautern,Germany
1
0
2
n
a
Abstract
J
2 Vapour-liquid equilibria (VLE) and the influence of an inert carrier gas on homogeneous vapour
1
to liquid nucleation are investigated by molecular simulation for quaternary mixtures of carbon
] dioxide, nitrogen, oxygen, and argon. Canonical ensemble molecular dynamics simulation using
h
p the Yasuoka-Matsumoto method is applied to nucleation in supersaturated vapours that contain
-
o morecarbon dioxidethan in thesaturated state at thedew line. Establishedmolecular modelsare
a employedthatareknowntoaccuratelyreproducetheVLEofthepurefluidsaswellastheirbinary
.
s andternarymixtures. Onthebasisofthesemodels,alsothequaternaryVLEpropertiesofthebulk
c
i fluidare determinedwiththeGrandEquilibriummethod.
s
y Simulation results for the carrier gas influence on the nucleation rate are compared with the
h
classical nucleation theory (CNT) considering the ‘pressure effect’ [Phys. Rev. Lett. 101: 125703
p
[ (2008)]. It is found that the presence of air as a carrier gas decreases the nucleation rate only
1 slightly and, in particular, to a significantly lower extent than predicted by CNT. The nucleation
v rateofcarbondioxideisgenerallyunderestimatedbyCNT,leadingtoadeviationbetweenoneand
7
twoordersofmagnitudeforpurecarbondioxideinthevicinityofthespinodallineanduptothree
5
8 orders of magnitudein presence of air as a carrier gas. Furthermore, CNT predicts a temperature
1
dependence of the nucleation rate in the spinodal limit, which cannot be confirmed by molecular
.
1
simulation.
0
0 Keywords: homogeneousnucleation,carrier gas,pressureeffect, moleculardynamics
1
: PACS:64.60.Ej,05.70.Np,36.40.-c
v
i
X
r
a
∗Author to whom correspondence should be addressed: Jadran Vrabec, Universität Paderborn, Institut für
Verfahrenstechnik, Lehrstuhl für Thermodynamik und Energietechnik, +49 5251 60 2421 (phone), +49 5251 60
3522(fax).
Emailaddress: [email protected](J.Vrabec)
URL:http://thet.upb.de/(J.Vrabec)
1蔺增勇(LinZengyong)
PreprintsubmittedtoAtmosphericResearch 12thJanuary2010
1. Introduction
If significant reductions in greenhouse gas emissionsare to be achieved, it is essential to min-
imize the energy required for separating carbon dioxide from air as a prerequisite for rendering
purification, recovery and sequestration processes economically and ecologically more efficient
(Kaule, 2002). This requires an accurate understanding of the phase behaviour of carbon dioxide
(CO )intheearth’satmosphereunderdiverseconditions,correspondingtotherespectivetechnical
2
applications.
Condensationprocesses, initiatedby nucleation,as well as vapour-liquidequilibria(VLE)are
particularlyrelevant in this context,since theycharacterize capture and storage ofCO , i.e. phase
2
separationandphaseequilibrium. Thepresentstudyconcentratesonunderstandinghomogeneous
nucleation and VLE properties for quaternary mixtures consisting of CO , nitrogen (N ), oxygen
2 2
(O ), and argon (Ar) by means of molecular simulation. Thereby, the properties of the investig-
2
ated fluid itself can be fully isolated from phenomena induced by impurities or boundary effects
in the vicinity of a solid wall, which would be much harder to accomplish in an experimental
arrangement.
Although a systematic discussion of CO nucleation was, surprisingly enough, published for
2
the ambient conditions prevailing on Mars (Määtänen et al., 2005), to the authors’ knowledge
no analogous study is available for the ecologically and technically more relevant atmosphere
compositionofourownplanet. Thepresentworkclosesthisgapandcharacterizestheairpressure
effectonthecondensationprocessinavapourcontainingmoreCO thanatsaturationonthebasis
2
ofmolecularmodelsthatareknowntoaccurately reproduceVLE properties.
Direct MD simulation of nucleation in the canonical ensemble with the Yasuoka-Matsumoto
(YM)methodisanestablishedapproach(Yasuokaand Matsumoto,1998,Matsubaraet al.,2007).
Itcanbesuccessfullyappliedtotheregimewherethesupersaturationissufficientlyhightopermit
significant droplet formation in a nanoscopic volume within a few nanoseconds, but not as high
that the nucleation rate j is affected by depletion of the vapour due to droplet formation within
the same time interval (Horsch et al., 2008a,b, Chkoniaet al., 2009). Lower nucleation rates can
bedetermined by forward flux samplingor methodsbased on umbrellasampling(Valerianiet al.,
2005), whereas in the immediate vicinity of the spinodal line, where the metastable state would
otherwisebreakdown,astationaryvalueforthenucleationratecanbeobtainedbygrandcanonical
MDsimulationwithMcDonald’sdaemon(Horsch and Vrabec,2009).
The present work focuses on the intermediate regime, where the YM method is viable, and
comparessimulationresultswiththeoreticalpredictionsonthebasisoftwovariantsoftheclassical
nucleationtheory(CNT).
2. The pressure effect
If the pressure effect (PE) is taken into account, the free energy G of formation according to
CNT isgivenby (Wedekind etal., 2008)
P − p
dG = µ −µ− s dN +γdF, (1)
PE s ρ′ !
2
foradropletcontainingN molecules,whereasthemorecommonlyused–butthermodynamically
inconsistent–simplifiedclassical(SC) variantofCNT implies
dG = (µ −µ)dN +γdF. (2)
SC s
Therein,µ andP aswellasµand prepresentthesaturatedandsupersaturatedvaluesofchemical
s s
potential and pressure, respectively. While P refers to the pure substance vapour pressure of the
s
nucleatingcomponent, pisthetotalpressureincludingthepressurecontributionofaninertcarrier
gas,ifpresent. Thedropletsurfacetensionisgivenbyγ,theareaofthesurfaceoftensionisF,and
ρ′ representsthedensityoftheliquidwhichisassumedtobeincompressible. Wherethechemical
potentialdifference∆µ = µ−µ appears in theSC expression,PE appliesan ‘effective’difference
s
(Wedekindet al., 2008)
P − p
∆µ = ∆µ+ s , (3)
e ρ′
whichisalways smallerthan ∆µ. Assumingaspherical shapefortheemerging droplets,i.e.
1/3
32π
dF = dN, (4)
3ρ′2N!
and neglecting the curvature dependence of the surface tension, the free energy barrier of the
nucleationprocessaccording tothePE variantofCNT
16πγ3 6 2/3
∆G⋆ = 0 +∆µ −π1/3 γ , (5)
PE 3(ρ′∆µ )2 e ρ′! 0
e
isreached forthecritical dropletsize
3
32π γ
N⋆ = 0 . (6)
PE 3ρ′2 ∆µ !
e
Theseexpressionsusethesurfacetensionγ oftheplanarvapour-liquidinterfaceaswellasthe‘in-
0
ternally consistent’ approach of Blanderand Katz (1972) which equates single-moleculedroplets
with vapour monomers and assigns them a free energy of formation ∆G = 0. The same results
followfortheSC variant,with∆µinsteadof∆µ inEqs.(5)and (6).
e
Thelong-termgrowthprobabilityQ(M) ofadropletcontaining M moleculescan begivenby
M 2∆G(N) ∞ 2∆G(N) −1
Q(M) = exp dN exp dN , (7)
Z kT ! "Z kT ! #
1 1
under the approximation that the reaction coordinate of the nucleation process only depends on
thedroplet size order parameter N (Horsch et al., 2009). The transition rate of vapourmonomers
ofthenucleatingcomponentthroughan interface, normalizedby thesurface areaoftheinterface,
is
β = P(2πm kT)−1/2, (8)
0
3
according to kinetic gas theory, where k is the Boltzmann constant, m is the molecular mass and
0
P the pressure of the nucleating component in its pure gaseous state at the same partial density.
Theisothermalnucleationrateaccording toCNT is (Feder et al., 1966)
−∆G⋆
j = ZF⋆βρ˜exp , (9)
T
kT !
whichdependson thesurfacearea F⋆ ofthecritical droplet,theZeˇl’dovicˇ (1942)factor
−d2G/dN2 1/2
Z = , (10)
2πm kT !
0 N=N⋆
as well as the density of vapour monomers belonging to the nucleating component ρ˜. Droplet
overheating due to rapid growth, however, is neglected in the expression for j . The monomer
T
densityin themetastablestatecan beobtainedfrom
N⋆
−∆G(N)
ρY = ρ˜ N exp , (11)
0
kT !
NX=1
aseriesthatusuallyconvergesveryfast,whereinρisthetotaldensityofthesupersaturatedvapour
andY isthemolefractionofthenucleatingcomponentinthesupersaturatedvapour. Thepresence
0
ofacarriergasalsoinfluencesthethermalizationofgrowingdroplets,facilitatingtheheattransfer
fromtheliquidtothesurroundingvapourandtherebydecreasingtheamountofoverheating. This
effect iscoveredby thethermal non-accomodationprefactor ofFederet al. (1966)
b2
j = j , (12)
b2 +q2 T
consistingof
kT dF
q = h′′ −h′ − −γ , (13)
2 dN!
N=N⋆
aswellasthemeansquarefluctuationofthekineticenergy forthevapourmolecules(Federet al.,
1966, Wedekindet al., 2008)
k K Ym1/2(c +k/2)
b2 = kT2 c + i 0 v,i , (14)
v,0 2! Y m1/2(c +k/2)
Xi=0 0 i v,0
where h′ and h′′ are saturated liquid and vapour enthalpy, respectively, c is the isochoric heat
v,i
capacity of component i, where i = 0 indicates the nucleating component and 1 ≤ i ≤ K the
components of the inert carrier gas. Within the scope of the present study, the heat capacity of
thepure saturated vapouris used for c whereas for theother c the valuein the limitof infinite
v,0 v,i
dilution is used, since CNT assumes the carrier gas to have ideal properties (Wedekindet al.,
2008).
4
Withintheframework ofCNT,it followsthattheprefactor
2 γ 1/2
ZF⋆ = 0 , (15)
ρ′ kT
(cid:18) (cid:19)
does not depend on the pressure contribution of the carrier gas, and neither does β, while the
influenceofthecarriergaspressureonρ˜,whichisusuallysimilarinmagnitudetoρY ,isofminor
0
significance. This eliminates all contributions to the pressure effect except for those discussed by
Wedekindet al. (2008)as
j b2 j
PE = PE T,PE. (16)
j b2 +q2 j
T,SC PE PE T,SC
Normalized to unity for the pure fluid (Y = 1) with the PE variant of CNT, the Wedekindet al.
0
(2008)pressureeffect can beexpressedas
b2 (Y ) b2 (Y = 1)+q2 (Y = 1) ∆G⋆ (Y = 1)−∆G⋆ (Y )
W(Y ) = PE 0 PE 0 PE 0 exp PE 0 PE 0 , (17)
0 h i
b2 (Y )+q2 (Y ) b2 (Y = 1) kT !
PE 0 PE 0 PE 0
h i
giventhat j , thedenominatorofEq.(16), does notdepend onY .
T,SC 0
Undercertainconditions,thepressureeffectdoesnotexceedtheexperimentaluncertaintyand
can thus be neglected (Iland et al., 2004). In other cases, however, the influence can be experi-
mentally detected, with apparently contradictory results: sometimes j increases with the amount
ofcarriergas,inothercasestheoppositetendencyisobserved(Hyvärinen et al.,2006,Brus et al.,
2008). The W factor explains this in principle, since it combines the thermal non-accomodation
factor, which increases with Y → 0, and the free energy effect that leads to an effective chem-
0
ical potential difference ∆µ < ∆µ. Depending on the thermodynamic conditions, each of these
e
contributionscan bepredominant(Wedekind etal., 2008).
Themain inaccuracies of CNT concern thesurface tensionas well as thedropletsurface area.
For the surface tension, deviations from the capillarity approximation γ ≈ γ are known to oc-
0
cur for nanoscopically curved interfaces (MoodyandAttard, 2003, Szybiszand Urrutia, 2003,
Horschet al., 2008b). The Tolman (1949) approach implies huge deviations from γ for droplets
0
on the molecular length scale corresponding to the Tolman length δ. In particular, for R > δ the
γ
dependenceofγ on thesurfaceoftensionradiusR can beexpressed as
γ
2 3
δ δ 2 δ 4
γ = γ exp −2 + − +O δ/R , (18)
whereas γ ∼ R becomes0validfor RRγ!≪ δ .RγF!rom9th eRLγa!place e(cid:18)hquatiγoin(cid:19)along with the Tolman
γ γ
(1949)approach itcan bededucedthat thearea ofthesurfaceoftensionisgivenby
2dN
dF = , (19)
R ρ′
γ
foran incompressiblefluid,where therelation
3N 1/3
R = −δ, (20)
γ 4πρ′!
followsfor thedependence of thesurface oftension radius on N. Overall, thisleads to asignific-
antlyincreased surfacearea fordropletson themolecularlengthscale.
5
3. Simulationmethods andmodels
Theevaluationofthetheoretical predictionsrelies on knowledgeabout thechemical potential
difference between the saturated and the supersaturated state. This was obtained for pure CO by
2
Gibbs-Duhemintegration
p dp
∆µ(T,p) = , (21)
Z ρ(T,p)
ps(T)
usingMDsimulationresultsofsmallsystems(N ≈ 10000)in themetastablevapourregime. The
carrier gas influence according to the presented variants ofCNT was evaluatedby assumingideal
gaspropertiesforairas well asideal mixingbehaviour, i.e.
p = (1−Y )ρkT +P. (22)
0
For the homogeneous nucleation simulations, the YM method was applied to relatively large,
but still nanoscopic systems with N(CO ) = 300 000. The total number of molecules was up
2
to N = 900 000 such that the carrier gas with N(N ) : N(O ) : N(Ar) = 7812 : 2095 : 93
2 2
corresponded to the earth’s atmosphere composition. The condensation process is thereby re-
garded as a succession of three characteristic stages: relaxation, nucleation, and droplet growth
(ChesnokovandKrasnoperov, 2007). During the nucleation stage, the droplet formation rate
I(M), i.e. the number of droplets containing at least M molecules formed over time, is approx-
imately constant (Yasuokaand Matsumoto, 1998). The droplet formation rate depends on the
thresholdsize M and isrelated to thenucleationrateby
I(M) j
= , (23)
V Q(M)
since Q(M) indicates the probability for a droplet containing M molecules to reach macroscopic
size. Liquid and vapour were distinguished according to a Stillinger (1963) criterion such that
molecules separated by distances of their centres of mass below 5.08 Å were considered as part
of the liquid. Biconnected components, where any single connection can be eliminated without
disruptingtheinternal connectivity,weredefined tobeliquiddroplets.
Molecular models for Ar, which can be represented by one Lennard-Jones (LJ) site, and for
CO ,N aswellasO ,whichcanberepresentedbytwoLJsitesseparatedbytheelongationℓwith
2 2 2
asuperimposedquadrupolemomentQinthemolecule’scentreofmass(2CLJQ),wereadjustedto
purefluidVLEdatabyVrabecet al.(2001),cf.Tab.1. Ifadequatevaluesfortheunlikedispersive
interaction energy are used, so that binary VLE are reproduced correctly (Vrabec et al., 2009a),
cf. Fig. 1, ternary mixturesare accurately described without any further adjustment(Huanget al.,
2009). In Tab. 1, the unlike energy parameters are indicated in terms of the binary interaction
parameterξ ofthemodifiedBerthelot (1898)combiningrule(Schnabel et al., 2007b)
ε = ξ(ε ε )1/2, (24)
AB A B
while the unlike LJ size parameter is determined as an arithmetic mean according to the Lorentz
(1881)combiningrule. ThisapproachhasalsobeenvalidatedwithanemphasisonCO inparticu-
2
lar,confirmingitsviabilityformixtureswithN andO (Vrabec etal.,2009b)aswellashydrogen
2 2
bondingfluids(Schnabel et al., 2007a).
6
type σ[Å] ε[meV] ℓ [Å] Q [eÅ2] ξ(Ar) ξ(O ) ξ(N )
2 2
CO 2CLJQ 2.9847 11.394 2.418 0.78985 0.999 0.979 1.041
2
N 2CLJQ 3.3211 3.0072 1.046 0.29974 1.008 1.007
2
O 2CLJQ 3.1062 3.7212 0.9699 0.16824 0.988
2
Ar LJ 3.3967 10.087
Table1: MolecularmodelparametersofVrabecetal.(2001)andbinaryinteractionparametersξadjustedtobinary
VLEdata(Vrabecetal.,2009a).
Onthatbasis,quaternaryphaseequilibriaweredeterminedusingtheGrandEquilibriummethod
(Vrabecand Hasse, 2002), introducing Ar into the the system studied by Vrabec et al. (2009b).
TheGrandEquilibriummethodcalculatesthevapourpressure p aswellasalldewlinemolefrac-
s
tions y by simulation for a specified temperature T and a specified bubble line mole fraction x
i i
forallcomponentsofthemixture. Althoughnoexperimentaldataareavailableforthequaternary
mixture, the simulation results can be trusted due to the extensive validation of the models with
respect to the VLE behaviour for all of the six binary (Vrabec et al., 2009a) and two of the four
ternary subsystems(Huang et al., 2009), i.e. N +O +Ar as wellas CO +N +O .
2 2 2 2 2
Figure1: (Colouron the web, b/w in print.) Experimentaldata (⋆) of Dodge (1927) and simulation results(◦) of
Vrabecetal. (2009a), using the Grand Equilibriummethodwith the molecular modelsgivenin Tab. 1, for VLE of
binarymixturescontainingnitrogenandoxygenattemperaturesofT =−193,−168,and−153◦C.
4. Simulationresults
GrandEquilibriumsimulationsofthequaternarymixtureCO +N +O +Arwereconducted
2 2 2
forVLEcoveringabroadtemperaturerangewithCO bubblelinemolefractions x(CO )of0.910,
2 2
0.941,and0.969,cf.Tab.2. Exceptforthehighesttemperature,whichcorrespondsto93%ofthe
criticaltemperatureT forpureCO ,themolefractionsy(N ),y(O ),andy(Ar)onthedewlineare
c 2 2 2
one order of magnitude higher than the corresponding bubble line mole fractions. This confirms
that for temperatures sufficiently below T (CO ), air only accumulates to a limited extent in the
c 2
7
liquidphase. Asafirstapproximation,itcanthereforebetreatedasacarriergasforCO nucleation
2
so that the PE variant of CNT with a single nucleating component can be applied, as opposed
to more complex mixtures such as ethanol + hexanol (Strey and Viisanen, 1993), water-alcohol
mixtures (Viisanen etal., 1994, Strey et al., 1995), or water + nonane + butanol (Nellaset al.,
2007), wheremulti-componentnucleationoccurs.
FromMDsimulationofsmallmetastablesystems,thespinodalvalueS∇ofthesupersaturation
withrespect todensity,which isdefined as
ρY
S = 0 , (25)
ρ′′(T)
wherein ρ′′(T) is the saturated vapour density of pure CO , was determined to be in the range
2
4.3 ≤ S∇ ≤ 5.1 at −44.8◦C, 3.6 ≤ S∇ ≤ 4.3 at −34.8◦C, and3.0 ≤ S∇ ≤ 3.6 at−23 ◦C forY = 1.
0
At these temperatures, canonical ensemble MD simulations for CO nucleation were conducted
2
using the YM method with CO mole fractions of 1/3, 1/2, and 1 at supersaturations below the
2
spinodalvalueS∇, but stillhigh enough to obtain statisticallyreliabledroplet formation rates in a
nanoscopicvolumeonthetimescaleofafew nanoseconds.
YMdropletformationrates I fromthepresentworkas wellasapreviousstudy(Horschet al.,
2008a) are shown in Fig. 2 for Y = 1, i.e. pure CO . The dependence of I on the threshold size
0 2
M reproduces the typical picture: for low threshold sizes (probably smaller than N⋆) the droplet
formation rate can be elevated by several orders of magnitude, and it converges for M ≫ N⋆
under the condition that the depletion of the vapour can be neglected (Yasuokaand Matsumoto,
1998). For very large values of M – not shown in Fig. 2 – the droplet formation rate decreases
again,becausethepresenceofmanylargedropletsimpliesthatasubstantialamountofthevapour
monomershavealready been consumedbytheemergingliquidphase.
The most striking observation is that while both variants of CNT predict the value of j in the
spinodal limit to increase with temperature – mainly because T occurs in the denominator of the
exponentialintheArrheniusterm ofEq. (9)– thesimulationresultsdonotexhibitanysignificant
temperature dependence for the attainable value of j. In the spinodal limit, the nucleation rate
appears to be about j(T,S∇) ≈ 1027 cm−3s−1 over the whole temperature range. The pressure
effectinthepurefluid,expressedby j /j ,ismostsignificantathightemperatures,becausethis
SC PE
T [◦C] x(CO ) p [MPa] y/x(N ) y/x(O ) y/x(Ar) ρ′ [mol/l] ρ′′ [mol/l] h′′ −h′ [kJ/mol]
2 s 2 2
−90.3 0.969 2.53(8) 40(2) 24.5(9) 24.7(9) 29.24(1) 1.854(2) 17.092(9)
0.941 3.9(1) 21.5(8) 13.9(5) 13.7(5) 29.13(1) 3.031(5) 16.27(1)
0.910 6.0(2) 13.7(4) 9.1(3) 9.0(3) 29.01(2) 5.29(2) 15.12(1)
−40.3 0.941 4.38(5) 14.0(2) 10.8(1) 10.3(1) 24.94(3) 2.663(5) 13.30(1)
0.910 5.30(4) 9.7(1) 7.72(8) 7.34(8) 24.47(2) 3.247(7) 12.64(1)
9.7 0.969 5.97(4) 5.6(1) 4.88(8) 4.72(7) 19.3(2) 3.90(1) 8.55(5)
0.941 6.98(3) 4.31(5) 3.82(5) 3.67(4) 18.55(9) 4.63(2) 7.79(4)
Table2: VLEdataforthequaternarysystemCO +N +O +Ar. Theliquidcompositionisequimolarinnitrogen,
2 2 2
oxygen,andargon,i.e.x(N )= x(O )= x(Ar)=[1−x(CO )]/3,andvaluesinparenthesesindicatetheuncertainty
2 2 2
intermsofthelastgivendigit.
8
correspondstoalowerdensityoftheliquidandbecause∆µissmallersothattherelativedeviation
between∆µ and ∆µis increased.
e
Figure 2: (Colour on the web and in print.) Pure CO nucleation rate j according to the PE (—) and SC (– –)
2
variantsofCNTincomparisontoI/VforthresholdsizesofM=(∆)50,(◦)75,and250(•)moleculesfromcanonical
ensembleMDsimulationoversupersaturationS = ρ/ρ′′(T)attemperaturesofT =−44.8,−34.8,−23,and−4.2◦C.
The simulation results for T = −4.2 ◦C are taken from previous work and were obtained using a different cluster
criterion(Horschetal.,2008a).
Table 3 indicates the results for the carrier gas effect on CO nucleation at T = −44.8 ◦C. As
2
usual, I decreases when larger values of thethreshold size M are regarded, but it can also be seen
that this effect is clearly stronger when more air is present in the system. This leads to values for
theoverallcarrier gaseffect Gon thedropletformationrate
I(S,Y ,M)
G = 0 , (26)
I(S,Y = 1,M)
0
that are greater than unity for relatively small values of M, but converge to values significantly
below unity as M is increased. This result can be understood if the carrier gas effect on N⋆ ac-
cordingtoEqs.(3)and(6)isconsidered: withahighertotalpressure,∆µ decreases whichaffects
e
thecritical droplet sizeto thethird power, leadingto significantlylarger values ofN⋆ , cf. Tab. 3.
PE
Thus,forrelativelysmallthresholdsizes,thelong-termgrowthprobabilityissignificantlysmaller,
cf.Eq.(7),whichinturnincreasesthedropletformationrateaccordingtoEq.(23). Hence,theap-
parentlycontradictoryvaluesofGareactuallyconsistentandcorrespondtoanegativedependence
ofthenucleationrateon thecarriergas density.
While this qualitatively confirms CNT with the pressure effect, which leads to W factors
on the order of 0.1 for Y = 1/2 and 0.01 for Y = 1/3, the actual decrease of I approaches
0 0
the range 0.3 to 0.4 in the limit of large threshold sizes for both values of Y . This impression
0
consolidatesitselfiftheresults forT =−34.8 and −23 ◦C are alsoregarded, cf. Fig. 3 and Tab. 4.
ThenormalizedWedekindet al.(2008)pressureeffectW,correspondingtothedeviationbetween
j (Y ) and j (Y = 1), decreases even faster with Y → 0 at high temperatures. Qualitatively,
PE 0 PE 0 0
thisisconfirmedbysimulationresults,e.g.nonucleationatallwasdetectedatthesetemperatures
9
S Y M I/V [cm−3s−1] G N⋆ W j [cm−3s−1] j/Q [cm−3s−1]
0 PE PE PE
3.42 1/3 50 2.7×1027 3.6 61 8.5×10−3 5.2×1023 3.0×1024
75 5.2×1026 0.79 6.1×1023
85 3.8×1026 0.63 5.4×1023
1/2 50 1.1×1027 1.5 44 0.17 9.8×1024 1.4×1025
75 3.1×1026 0.47 9.8×1024
85 2.4×1026 0.39 9.8×1024
1 50 7.3×1026 1 33 1 5.0×1025 5.2×1025
75 6.5×1026 1 5.0×1025
85 6.1×1026 1 5.0×1025
3.72 1/3 50 1.4×1028 8.7 61 5.8×10−3 5.9×1023 3.4×1024
85 5.0×1027 2.9 6.1×1023
150 7.0×1026 0.63 5.9×1023
1/2 50 2.3×1027 1.4 43 0.15 1.3×1025 1.8×1025
85 1.2×1027 0.71 1.3×1025
150 4.4×1026 0.38 1.3×1025
1 50 1.6×1027 1 32 1 7.9×1025 8.1×1025
85 1.7×1027 1 7.9×1025
150 1.1×1027 1 7.9×1025
4.02 1/3 85 7.7×1027 2.5 61 3.8×10−3 5.4×1023 5.6×1023
150 3.4×1027 1.6 5.4×1023
300 6.3×1026 0.47 5.4×1023
1/2 85 2.4×1027 0.77 42 0.13 1.7×1025 1.7×1025
150 1.1×1027 0.49 1.7×1025
300 6.1×1026 0.46 1.7×1025
1 85 3.2×1027 1 31 1 1.1×1026 1.1×1026
150 2.1×1027 1 1.1×1026
300 1.3×1027 1 1.1×1026
Table3: DropletformationrateandcarriergaseffectfromYMcanonicalensembleMDsimulationaswellascritical
dropletsize(inmolecules),normalizedWedekindetal.(2008)pressureeffect,nucleationrateanddropletformation
rateaccordingtothePEvariantofCNT,independenceofsupersaturationandmolefractionofCO inthevapouras
2
wellastheYMthresholdsize(inmolecules)atatemperatureofT =−44.8◦C.
forY = 1/3, whichimplies j < 1025 cm−3s−1. However,from theavailableresults forY = 1/2 it
0 0
isevidentthatthepressureeffect isoverestimatedbyCNT, inparticularat T = −23 ◦C.
5. Conclusion
Vapour-liquidcoexistenceinequilibriumandnon-equilibriumwasstudiedbymolecularsimu-
lationforsystemsconsistingofCO ,N ,O ,andAr. ForthenucleationofpureCO ,itwasfound
2 2 2 2
thatboth theSC and thePE variant ofCNT underestimatethenucleationrate by up toa factor20
forSCand between oneand threeorders ofmagnitudeforPE.
It should be noted that this result for pure CO nucleation is both qualitatively and quantitat-
2
ivelysimilartothedeviationofCNTforhomogeneousnucleationofthetruncated-shiftedLJfluid
10
