Applying Gradient theory Applying Gradient theory to calculate nucleation to calculate nucleation rates and compare with rates and compare with data.data.

Nora Al-ZubiNora Al-Zubi

Dr. Abdalla ObeidatDr. Abdalla Obeidat

Department of PhysicsDepartment of Physics

JUSTJUST

OutlineOutline

Metastability and nucleationMetastability and nucleation Temperature dependence of Temperature dependence of

classical theoriesclassical theories DFT and the road to GT (why GT?)DFT and the road to GT (why GT?) Applications to GTApplications to GT ConclusionsConclusions

• The binodal curve (solid dome)separates one-phase and two-phase states

• TC = critical temperature

• The spinodal curve (dashed dome) separates metastable and unstable states

• One true horizontal isotherm is shown

• Adapted from Davis (1996)

gas

liquid

fluid

critical point

binodal spinodal

Metastable and unstable Metastable and unstable regions for the van der regions for the van der Waals fluidWaals fluid

Classical nucleation rates Classical nucleation rates are too low at low are too low at low TT; too ; too high at high high at high TT..

Chain of Rotators Equation Chain of Rotators Equation of state for Ethanol and of state for Ethanol and MethanolMethanol

DFT and the road to GTDFT and the road to GTAUH

N eQQN

AH UFF

rrddrrunnrdrnfrnF h333 )()r((r)

2

1))(())((

rdrnrnFrn B3)())(())((

0n

rdrrurnrn Bh3)()())((

Density Gradient Density Gradient theorytheory

)()(2

1)()()( 322 nOnrrnrrrnrn

rdrnfF 3))((

20 )(

2)()( n

cnfnf

ncnB2

0 )(

The ingredients for GTThe ingredients for GT

dvnc

W GT

2

2

)()( Bnn Bnnfn )()( 0

l

g

n

n

B dnnnc ))()((2

)()( lg nPnP )()( lg nn

GT Why?GT Why?

DFTDFT Adv.Adv.

– Statistical Statistical Mechanical Mechanical approachapproach

disAdv.disAdv.– Depends on Depends on

intermolecular intermolecular potentialpotential

GTGT disAdv.disAdv.

– Approximation to Approximation to DFTDFT

Adv.Adv.– Semi form of DFTSemi form of DFT– Depends on EOSDepends on EOS

Applications to GT Applications to GT using JA and CPHBusing JA and CPHB Density profilesDensity profiles ThicknessesThicknesses Number of moleculesNumber of molecules Radius of dropletsRadius of droplets Work formationWork formation Nucleation ratesNucleation rates

Density ProfilesDensity Profiles

Nucleation rates of Nucleation rates of H2O based on CPHBH2O based on CPHB

ConclusionsConclusions

Gradient theory is promising Gradient theory is promising theory to improve the theory to improve the temperature dependence of temperature dependence of nucleation rates.nucleation rates.

Thank YouThank You