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A Study of Scaled Nucleation in a Model Lennard-Jones System

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

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  1. 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

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

  3. Scaling:Wölk and Strey Water DataCo = [Tc/240-1]3/2 ; Tc = 647.3 K B. Hale, J. Chem. Phys. 122, 204509 (2005)

  4. Schmitt et al Toluene (C7H8) data Co = [Tc /240-1]3/2 ; Tc = 591.8K

  5. 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

  6. 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

  7. Law of Mass Action Nn/[Nn-1N1] = Q(n)/[Q(n-1)Q(1)n] Q(n) = n-cluster canonical configurational partition function

  8. 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)

  9. 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

  10. 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.

  11. 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

  12. 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

  13. 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).

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