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Optimizing the Growth of Endothiapepsin Crystals for Serial Crystallography Experiments
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Transient nucleation with a monotonically changing barrier.

Vitaly A Shneidman1

  • 1Department of Physics, New Jersey Institute of Technology, Newark, New Jersey 07102, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
PubMed
Summary
This summary is machine-generated.

Transient nucleation dynamics are crucial when the nucleation barrier changes over time. This study refines non-steady-state flux calculations and nucleus distributions, revealing distinct behaviors for increasing versus decaying barriers.

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Area of Science:

  • Physical Chemistry
  • Materials Science
  • Chemical Engineering

Background:

  • Standard nucleation theory often assumes an instantaneous establishment of quasi-steady-state (QSS) nucleation flux.
  • This adiabatic approximation is valid only for vanishingly small rates of change in the nucleation barrier (nonstationary index N→0).
  • Transient nucleation phenomena and deviations from QSS are significant for nonzero rates of change (N≠0).

Purpose of the Study:

  • To refine and generalize non-QSS transient nucleation flux calculations for arbitrary barrier and critical size change rates.
  • To investigate the impact of a variable nonstationary index N(t) on nucleation dynamics.
  • To obtain N-dependent transient distributions of growing nuclei and their numbers.

Main Methods:

  • Matched asymptotic (singular perturbation) analysis of the Becker-Döring equation (BDE).
  • Comparison with exact numerical simulations.
  • Application of the continuous Zeldovich-Frenkel approximation for specific barrier behaviors (increasing or decaying).

Main Results:

  • Transient nucleation flux and nucleus distributions are dependent on the nonstationary index N(t).
  • For decaying barriers (N>0), nucleus distributions are monotonic, and total particle numbers diverge over time.
  • For increasing barriers (N<0), distributions become asymmetric bell shapes with exponentially small total particle numbers compared to QSS.

Conclusions:

  • The standard QSS approximation is insufficient for non-zero rates of change in the nucleation barrier.
  • Transient effects and N-dependent distributions are essential for accurately describing nucleation dynamics under non-stationary conditions.
  • The study provides a generalized framework for nucleation under time-varying conditions, applicable to various physical and chemical systems.