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Related Concept Videos

Phase Diagrams of Ternary Systems01:28

Phase Diagrams of Ternary Systems

96
Consider a ternary system, which is composed of three components: water (W), ethanoic acid (E), and trichloromethane (T). Here, Ethanoic acid (E) is fully miscible with both water (W) and trichloromethane (T), meaning it can mix entirely with either of them. However, water and trichloromethane have partial miscibility, meaning they can only mix to a certain extent, beyond which two separate phases will form.The phase diagram of a ternary system is represented as an equilateral triangle, where...
96
Types of Coprecipitation01:10

Types of Coprecipitation

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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...
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Precipitation and Co-precipitation01:17

Precipitation and Co-precipitation

5.6K
Precipitation and coprecipitation methods can be used to separate a mixture of ions in a solution. In qualitative inorganic analysis, ions that form sparingly soluble precipitates with the same reagent are separated based on the differences in solubility products. For example, consider the separation of Cu(II) and Fe(II) ions by precipitation as insoluble sulfides. First, copper(II) sulfide is precipitated by the addition of acidic H2S, where the dissociation of H2S is suppressed. Adding H2S...
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Critical Region, Critical Values and Significance Level01:16

Critical Region, Critical Values and Significance Level

13.8K
The critical region, critical value, and significance level are interdependent concepts crucial in hypothesis testing.
In hypothesis testing, a sample statistic is converted to a test statistic using z, t, or chi-square distribution. A critical region is an area under the curve in  probability distributions demarcated by the critical value. When the test statistic falls in this region, it suggests that the null hypothesis must be rejected. As this region contains all those values of the...
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Woodward–Hoffmann Selection Rules and Microscopic Reversibility01:34

Woodward–Hoffmann Selection Rules and Microscopic Reversibility

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Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
4.2K
Colloidal precipitates01:09

Colloidal precipitates

6.8K
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...
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Related Experiment Video

Updated: Apr 1, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
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Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

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Correlated percolation and tricriticality.

L Cao1, J M Schwarz

  • 1Physics Department, Syracuse University, Syracuse, New York 13244, USA. lcao01@syr.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 2, 2013
PubMed
Summary

Discontinuous percolation transitions were sought in correlated models. Two models, k ≥ 3-core and counter-balance, exhibit discontinuous transitions, offering insights into glassy and jamming systems.

Area of Science:

  • Statistical Physics
  • Complex Networks
  • Phase Transitions

Background:

  • Correlated percolation models aim to explain discontinuous transitions, but explosive percolation models have been shown not to exhibit them.
  • Previous research disproved discontinuous transitions in many explosive percolation models.
  • Understanding correlated percolation is crucial for modeling complex systems.

Purpose of the Study:

  • Investigate two lesser-known correlated percolation models: the k ≥ 3-core model and the counter-balance model.
  • Explore the potential for tricriticality by mixing these models with standard percolation models.
  • Identify conditions favoring discontinuous transitions in low-dimensional systems.

Main Methods:

  • Analysis of k ≥ 3-core and counter-balance percolation models.

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Reservoir Condition Pore-scale Imaging of Multiple Fluid Phases Using X-ray Microtomography
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Last Updated: Apr 1, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
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1,3,5-Triphenylbenzene and Corannulene as Electron Receptors for Lithium Solvated Electron Solutions
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  • Construction of model mixtures to search for tricritical points.
  • Application of a rate equation approach for theoretical analysis.
  • Numerical simulations and heuristic arguments for two-dimensional systems.

    • Main Results:

    • The k = 2-core and k = 3-core mixture on random graphs exhibits a tricritical point.
    • A mixture of k-core and counter-balance models in 2D suggests a line of continuous transitions ending in a discontinuous one.
    • Heuristic arguments provide potential criteria for discontinuous transitions in low dimensions.

    Conclusions:

    • Discontinuous transitions are achievable in specific correlated percolation models.
    • Tricriticality is observed in mixtures of k-core models on random graphs.
    • The study offers insights into the mechanisms driving discontinuous transitions and their relevance to glassy and jamming phenomena.