A study of scaled nucleation in a model lennard jones system
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A Study of Scaled Nucleation in a Model Lennard-Jones System. Barbara Hale and Tom Mahler Physics Department University of Missouri – Rolla Jerry Kiefer Physics Department St. Bonaventure University. Motivation.

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A study of scaled nucleation in a model lennard jones system

A Study of Scaled Nucleationin a Model Lennard-Jones System

Barbara Hale and Tom Mahler

Physics Department University of Missouri – RollaJerry Kiefer

Physics Department

St. Bonaventure University


Motivation
Motivation

To understand how scaling of the nucleation rate is related to the microscopic energy of formation of small clusters.


Scaling w lk and strey water data c o t c 240 1 3 2 t c 647 3 k
Scaling:Wölk and Strey Water DataCo = [Tc/240-1]3/2 ; Tc = 647.3 K

B. Hale, J. Chem. Phys. 122, 204509 (2005)


Schmitt et al toluene c 7 h 8 data c o t c 240 1 3 2 t c 591 8k
Schmitt et al Toluene (C7H8) data Co = [Tc /240-1]3/2 ; Tc = 591.8K


Study of scaling in lj system
Study of Scaling in LJ System

  • calculate rate constants for growth and decay of model Lennard-Jones clusters at three temperatures;

  • determine model nucleation rates from kinetic nucleation rate formalism;

  • compare logJ vs lnS and

    logJ vs lnS/[Tc/T-1]3/2


Model lennard jones system law of mass action
Model Lennard-Jones System Law of mass action

dilute vapor system with volume, V;

non-interacting mixture of ideal gases;

each n-cluster size is ideal gas of Nn particles;

full atom-atom LJ interaction potential;

separable classical Hamiltonian


Law of mass action
Law of Mass Action

Nn/[Nn-1N1] = Q(n)/[Q(n-1)Q(1)n]

Q(n) = n-cluster canonical configurational

partition function


Relation to growth decay
Relation to Growth & Decay

(n-1)Nn-1N1= (n)Nn

we calculate:

Q(n)/[Q(n-1)Q(1)n]= Nn/[Nn-1N1]

= (n-1)/(n)


Kinetic nucleation rate formalism
Kinetic Nucleation Rate Formalism

1/J = n=1,M 1/Jn ; M large

Jn = (n)(N1S)2j=2,n [N1S(j-1)/(j)]

S = N1exp/N1


Free energy differences
Free Energy Differences

- f(n) = ln [Q(n)/(Q(n-1)Q(1))]calculated

= ln [ (ρoliq/ρovap)(j-1)/(j) ]

Use Monte Carlo Bennett technique.


Monte carlo simulations
Monte Carlo Simulations

Ensemble A:

(n -1) cluster plus monomer

probe interactions turned off

Ensemble B:

n cluster with normal

probe interactions

Calculate f(n) =[F(n)-F(n-1)]/kT


The nucleation rate can be calculated for a range of supersaturation ratios s
The nucleation rate can be calculated for a range of supersaturation ratios, S.

1/J = n=1,M 1/Jn ; M large

Jn = (n)(N1S)2j=2,n [N1S(j-1)/(j)]

S = N1exp/N1


Comments conclusions
Comments & Conclusions

  • Experimental data indicate that Jexp is a function of lnS/[Tc/T-1]3/2.

  • No “first principles” derivation of scaling exists.

  • Monte Carlo LJ cluster simulations show evidence of scaling.

  • Scaling appears to emerge from [Tc/T-1] dependence of the f(n).