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The experimental conditions in a gravimetric analysis should be optimized to maximize the particle size and purity of the obtained precipitate. Ideally, the concentration of the precipitating reagent should be low with effective stirring to maintain low relative supersaturation for the growth of large crystals. In homogeneous precipitation, the precipitant is slowly generated by a chemical reaction in the solution to avoid local reagent excesses. For example, urea decomposes gradually to...
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Finite-size effects in addition and chipping processes.

R R Dyachenko1,2, S A Matveev1,2, P L Krapivsky3,4

  • 1Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, 119991, Russia.

Physical Review. E
|November 18, 2023
PubMed
Summary
This summary is machine-generated.

This study explores cluster evolution through monomer collisions. Depending on whether monomers attach or chip away, systems jam, reach a quasistationary state, or form a unique non-extensive jammed state.

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Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Investigates cluster dynamics and phase transitions.
  • Focuses on systems with monomer-cluster collisions.

Purpose of the Study:

  • Analyze cluster evolution under competing addition and chipping processes.
  • Characterize system behavior and final states based on process probabilities.

Main Methods:

  • Analytical investigation of cluster systems.
  • Numerical simulations of evolving clusters.

Main Results:

  • Addition-dominant: Monomers disappear logarithmically with mass (N), leading to a jammed state.
  • Chipping-dominant: System exhibits exponential scaling in time before a giant fluctuation causes monomer disappearance.
  • Marginal case: Monomers disappear linearly with N, forming a non-extensive jammed supercluster.

Conclusions:

  • The balance between monomer addition and chipping dictates system evolution and final state.
  • Identifies distinct dynamical regimes and unique jammed states in cluster aggregation systems.