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Related Concept Videos

Types of Coprecipitation01:10

Types of Coprecipitation

Coprecipitation is the contamination of a precipitate by otherwise soluble species and occurs via different processes. In colloidal precipitates, coprecipitation occurs via surface adsorption. For instance, barium sulfate has a primary layer of adsorbed barium ions and a secondary layer of nitrate counterions. This results in contamination of the precipitate by barium nitrate.
Sometimes, ions in a crystal lattice can undergo isomorphous replacement by inclusions of similar charge and size. For...
Colloidal precipitates01:09

Colloidal precipitates

The high insolubility of some precipitates can result in an unfavorable relative supersaturation. This can lead to colloidal particles with a large surface-to-mass ratio, where adsorption is promoted. For instance, in the precipitation of silver chloride, silver ions are adsorbed on the surface of the colloidal particles, forming a primary layer. This layer attracts ions of opposite charge (such as nitrate ions), forming a diffuse secondary layer of adsorbed ions. This electric double layer...
Precipitate Formation and Particle Size Control01:16

Precipitate Formation and Particle Size Control

In precipitation gravimetry, the precipitating agent should react specifically or selectively with the analyte. While a specific reagent reacts with the analyte alone, a selective reagent can react with a limited number of chemical species.
The obtained precipitate should be either a pure substance of known composition or easily converted to one by a simple process, such as ignition or drying. In addition, the precipitate should be insoluble and easily filterable. In general, filterability...
The Colloidal State01:29

The Colloidal State

The formation of a colloidal system is exemplified by an aqueous solution containing Cl− ions is introduced to another containing Ag+ ions, resulting in the precipitation of solid AgCl as extremely tiny crystals. Instead of settling out as a filterable precipitate, these crystals remain suspended in the liquid, showcasing a colloidal system.A colloidal system involves colloidal particles within the approximate range of 1 to 1000 nm in at least one dimension, dispersed in a medium called the...
Phase Transitions: Vaporization and Condensation02:39

Phase Transitions: Vaporization and Condensation

The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize (convert into vapor). The process is called vaporization—a surface phenomenon. Vaporization occurs when the thermal motion of the molecules overcome the intermolecular forces, and the molecules (at the surface) escape into the gaseous state. When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase molecules...
Phase Transitions: Melting and Freezing02:39

Phase Transitions: Melting and Freezing

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Related Experiment Video

Updated: May 24, 2026

Measuring Sub-23 Nanometer Real Driving Particle Number Emissions Using the Portable DownToTen Sampling System
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Published on: May 22, 2020

Contact percolation transition in athermal particulate systems.

Tianqi Shen1, Corey S O'Hern, M D Shattuck

  • 1Department of Physics, Yale University, New Haven, Connecticut 06520-8120, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 10, 2012
PubMed
Summary
This summary is machine-generated.

Researchers discovered that particle systems exhibit cooperative motion below the jamming transition. This contact percolation transition signals a significant mechanical response even in unjammed states, challenging previous assumptions about rigidity.

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Last Updated: May 24, 2026

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Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Jammed packings of repulsive, frictionless particles are typically generated via quasistatic compression from dilute states.
  • Isotropic compression leads to a jamming transition (φ(J)) from an unjammed state (zero pressure, no force-bearing contacts) to a jammed state (non-zero pressure, percolating force-bearing contacts, coordination number z=2d).
  • A contact percolation transition (φ(P)) precedes jamming (φ(P)<φ(J)), indicating the formation of a system-spanning cluster of non-force-bearing contacts.

Purpose of the Study:

  • To investigate the second-order-like contact percolation transition in two-dimensional systems.
  • To determine if the contact percolation transition signals the onset of a nontrivial mechanical response.
  • To explore the nature of cooperative particle motion in relation to jamming and percolation transitions.

Main Methods:

  • Computer simulations of two-dimensional systems with monodisperse and bidisperse particle size distributions.
  • Analysis of the number of nonfloppy modes of the dynamical matrix.
  • Measurement of displacement fields and overlap of the adjacency matrix representing contacting grains.

Main Results:

  • The contact percolation transition (φ(P)) precedes the jamming transition (φ(J)).
  • The contact percolation transition signals the onset of a nontrivial mechanical response to applied stress.
  • Cooperative particle motion is observed in unjammed systems for packing fractions between φ(P) and φ(J), not just in jammed systems (φ>φ(J)).

Conclusions:

  • The formation of a connected network of contacts, even non-force-bearing ones, is crucial for initiating mechanical response.
  • Cooperative particle motion is a hallmark of systems approaching rigidity, occurring earlier than previously thought.
  • This study reveals a more nuanced understanding of the mechanical behavior of granular materials near the jamming transition.