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

This study investigates the relationship between nucleation rates and the microscopic energy of small cluster formation within a model Lennard-Jones system. By calculating growth and decay rate constants at varying temperatures, we derive nucleation rates from kinetic formalism and analyze the scaling behavior through the comparison of logJ versus lnS. Using Monte Carlo simulations, we explore the dependence of nucleation on supersaturation ratios, revealing evidence of scaling emerging from the temperature-dependent free energy differences. Our findings contribute to the understanding of non-ideal gas behavior in cluster formation.

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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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