A Thermodynamic Approach to the Interfacial Flux during Ice Nucleation

Donifan Barahona Global Modeling and Assimilation Office

NASA Goddard Space Flight Center

Greenbelt, MD, USA

Atmospheric Ice Nucleation Conference

Leeds, UK, January 2017

Homogeneous Ice Nucleation

•  A significant fraction (30%-70%) of cirrus form by HOM nucleation.

•  Can alter significantly the evolution and radiative properties of cirrus.

•  Nucleation rates are still uncertain, particularly at low temperature.

Jensenetal.PNAS,2013.

Classical Nucleation Theory, CNT Gibbsdividingsurface

InterfacialTension Ac@va@onEnergy

σwandΔGactareambiguousquan55esandingeneralcan’tbeobtainedbyindependentmeasurements.

Cri@calnucleiconcentra@on

Zeldovichfactor

Interfacialdiffusivity

Bulkliquid

Bulkice

Assumptions: •  Spherical ice germ,

capillarity, infinite liquid phase, ideal gas–like behavior, denser condense phase, independency of germ size.

•  Bulk liquid extends up to the dividing surface. MD shows that a finite interface is more likely.

NNF •  Neg-entropic Nucleation Framework:

–  Emphasizes entropic changes across the interface. Liquid molecules “trapped” by the ice phase.

–  Core-shell structure: Finite interface.

–  Change in the composition of the liquid phase upon nucleation.

–  No need for an spherical germ, although a defined lattice is required.

–  Obviates the explicit parameterization of the interfacial energy.

Barahona,ACP,2014

Icegermμs,ns

Bulkliquid

interface

Δhf: Enthalpy of fusion aw: Water activity Γw: Interface thickess (1.46) s: Lattice geometry (1.05)

CNT-NNF

•  NNF reproduces observed constant shift in water activity. •  Underestimation in Jhom at low T: role of kinetic prefactor.

Barahona,ACP,2014

NNF… but CNT kinetics

Bulkice

Bulkliquid

DNNF?BulkliquidBulkIce

Random-jumpbasedinterfacialdiffusion.

Howcanwemodeltheincorpora5onofwatermoleculestotheicegermusingamorerealis5cpictureoftheinterface?

The environment within the interface differs from the bulk.

•  Path (1)è(2) implies spontaneous organization.

•  Spontaneous however does not mean “free”.

•  Transient “violations of the second law” (not really).

Intermediate State (2)Bulkliquid(1) BulkIce(3)(2)

Theincorpora,onofeachmoleculetothela2cerequirestherearrangementofneighboringmolecules.

ΔGeq

Spontaneous Reorganization

Workdistribu@onsassociatedwiththefolding/unfoldingofRNA.Collinsetal.Nature,2005.

ΔGeq

Spontaneous Reorganization

•  Crooks Fluctuation Theorem (CFT)

P(forwardprocess)

P(backwardprocess)

Totalwork

EquilibriumWork

Workdissipated

Wdiss=

Workdistribu@onsassociatedwiththefolding/unfoldingofRNA.Collinsetal.Nature,2005.

Interfacial Diffusion

Bulkliquid BulkIce

nt=Numberoftrajectoriesintheforma@onoftheintermediatestate~16.

Bulkdiffusion

Dissipa5on(non-equilibrium)

Barahona,ACP,2015

:ProbabilityoftheforwardprocessP(1->3)

Forwardprocess

Activation Energy

Barahona,ACP,2015

Bulk-based

NNFAc@va@on

Dissipa@on

•  For pure water nucleation temperatures, much lower than the nucleation work; “constant activation energy”.

–  Differences likely significant at low T, for solution droplets and for heterogeneous ice nucleation.

•  Preexponential factor decreases much faster for bulk-based activation energy.

•  Slight dependency on water activity: implicit dependency on germ size.

Nucleation Rate

•  Much higher nucleation rates for T<200 K. •  CNT constrained by NNF-derived activation energies also in good

agreement with observations.

Barahona,ACP,2015

, Ickes et al. 2015

No need for an explicitly defined activation energy

2 - Work dissipation can also be understood as part of the nucleation process:

Non-equilibrium Equilibrium

3 - Dissipation as part of a two-step nucleation process (Pan et al. 2005).

Pre-nuclea@on Nuclea@on

1- Bulk diffusion and dissipated work determine interfacial flux. Both have a clear meaning and can in principle be measured.

Conclusions

•  The neg-entropic nucleation framework (NNF) explicitly accounts for the finite nature of the interface and the difference between the bulk and the interface environment.

•  Interface transfer was shown to be a function of bulk diffusion and of the irreversible work dissipated within the interface. Both quantities have a more specific meaning that the activation energy and may be amenable to direct measurement.

•  The approach presented here leads to a better prediction of Jhom, particularly at low T , and may improve the simulation of cold cirrus in atmospheric models.

•  MD and other detailed methods may help in elucidating the structure of the intermediate configurations during transfer and the structure of ice during the first stages of nucleation.

Interfacial Diffusion

(Microscopicreversibility)

Bulkliquid BulkIce

nt=Numberoftrajectoriesintheforma@onoftheintermediatestate.For4-coordinatedwater,nt=16.

Bulkdiffusion

Dissipa5on(non-equilibrium)

Barahona,ACP,2015

Probabilityofrearrangementofntmoleculeswithintheinterfacei.e.,P(1->3)

Spontaneous Reorganization

Workdistribu@onsassociatedwiththefolding/unfoldingofRNA.Collinsetal.Nature,2005.

ΔGeq