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Area of Science:

  • Computational chemistry and physics
  • Materials science
  • Statistical mechanics

Background:

  • Classical nucleation theory requires robust methods to validate its predictions at the microscopic level.
  • Accurate simulation of phase separation and crystallization necessitates well-defined reaction coordinates.
  • Identifying suitable order parameters is crucial for understanding nucleation mechanisms and rates.

Purpose of the Study:

  • To apply the variational approach to Markov processes for evaluating reaction coordinate suitability in crystallization.
  • To identify optimal collective variables (CVs) for describing crystallization from supersaturated colloid suspensions.
  • To construct and analyze Markov State Models (MSMs) for elucidating nucleation pathways and rates.

Main Methods:

  • Utilized the variational approach to Markov processes to quantify reaction coordinate effectiveness.
  • Employed collective variables (CVs) including particle count, potential energy, and configurational entropy.
  • Applied time-lagged independent component analysis to reduce dimensionality and build Markov State Models (MSMs).

Main Results:

  • CVs correlating with condensed phase particle number, system energy, and configurational entropy are identified as optimal order parameters.
  • MSMs reveal a two-barrier energy landscape separating the supersaturated fluid from the crystalline phase.
  • Consistent nucleation rates are obtained across different order parameter dimensionalities, with the two-step mechanism clearer in higher dimensions.

Conclusions:

  • The variational approach provides a general and transferable framework for studying crystal nucleation.
  • Collective variables related to particle aggregation, energy, and entropy are key to describing crystallization.
  • The identified two-step nucleation mechanism highlights the complexity of phase transitions in colloidal systems.