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Mean free path and Mean free time01:22

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Although gaseous molecules travel at tremendous speeds (hundreds of meters per second), they collide with other gaseous molecules and travel in many different directions before reaching the desired target. At room temperature, a gaseous molecule will experience billions of collisions per second. The mean free path is the average distance a molecule travels between collisions. The mean free path increases with decreasing pressure; in general, the mean free path for a gaseous molecule will be...
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The motion of molecules in a gas is random in magnitude and direction for individual molecules, but a gas of many molecules has a predictable distribution of molecular speeds. This predictable distribution of molecular speeds is known as the Maxwell-Boltzmann distribution. The distribution of molecular speeds in liquids is comparable to that of gases but not identical and can help to understand the phenomenon of the boiling and vapor pressure of a liquid. Consider that a molecule requires a...
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Ligand-Mediated Nucleation and Growth of Palladium Metal Nanoparticles
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Analysis of nucleation using mean first-passage time data from molecular dynamics simulation.

David A Nicholson1, Gregory C Rutledge1

  • 1Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

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|April 10, 2016
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Summary

We developed a new method to analyze nucleation dynamics using molecular dynamics simulations and mean first-passage time (MFPT) statistics. This approach accurately estimates nucleation kinetics, even when time scales are similar.

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Area of Science:

  • Physical Chemistry
  • Materials Science
  • Computational Chemistry

Background:

  • Nucleation is a critical process in phase transitions.
  • Analyzing nucleation dynamics is challenging, especially when nucleation and growth timescales are similar.
  • Existing methods may rely on assumptions not always met in simulations.

Purpose of the Study:

  • To introduce a novel method for analyzing nucleation dynamics using molecular dynamics simulations.
  • To rigorously account for system size dependence in first-passage statistics.
  • To provide accurate kinetic parameter estimation for nucleation processes.

Main Methods:

  • Utilizing mean first-passage time (MFPT) statistics from molecular dynamics simulations.
  • Applying the Becker-Döring model for nucleation dynamics.
  • Employing a cumulant expansion approximation for computational practicality.
  • Fitting MFPT data to estimate free energy barriers, critical nucleus size, and attachment pre-factors.

Main Results:

  • The developed method accurately describes first-passage time distributions, even when non-exponential at short times.
  • Demonstrated applicability on n-eicosane crystal nucleation from the melt.
  • Successfully estimated kinetic parameters and steady-state nucleation/growth rates.
  • Showcased incompatibility of observed data with assumptions of some other methods.

Conclusions:

  • The new MFPT-based method offers a robust approach for nucleation analysis.
  • It provides reliable estimates of key kinetic parameters and rates.
  • The method is suitable for systems with small free energy barriers or large system sizes.