Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Structures of Solids02:22

Structures of Solids

17.2K
Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
17.2K
Trends in Lattice Energy: Ion Size and Charge02:54

Trends in Lattice Energy: Ion Size and Charge

26.3K
An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
26.3K
First Law: Particles in Two-dimensional Equilibrium01:18

First Law: Particles in Two-dimensional Equilibrium

13.8K
Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about...
13.8K
Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

11.1K
The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...
11.1K
Metallic Solids02:37

Metallic Solids

20.3K
Metallic solids such as crystals of copper, aluminum, and iron are formed by metal atoms. The structure of metallic crystals is often described as a uniform distribution of atomic nuclei within a “sea” of delocalized electrons. The atoms within such a metallic solid are held together by a unique force known as metallic bonding that gives rise to many useful and varied bulk properties.
All metallic solids exhibit high thermal and electrical conductivity, metallic luster, and malleability....
20.3K
Ionic Crystal Structures02:42

Ionic Crystal Structures

16.6K
Ionic crystals consist of two or more different kinds of ions that usually have different sizes. The packing of these ions into a crystal structure is more complex than the packing of metal atoms that are the same size.
Most monatomic ions behave as charged spheres, and their attraction for ions of opposite charge is the same in every direction. Consequently, stable structures for ionic compounds result (1) when ions of one charge are surrounded by as many ions as possible of the opposite...
16.6K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Effect of specific interactions on the double layer capacitance of concentrated ionic systems.

Physical chemistry chemical physics : PCCP·2026
Same author

Patterns with long and short-range order in monoloyers of binary mixtures with competing interactions.

Soft matter·2025
Same author

Mesoscopic theory for a double layer capacitance in concentrated ionic systems.

Physical chemistry chemical physics : PCCP·2025
Same author

Statistical Thermodynamic Description of Self-Assembly of Large Inclusions in Biological Membranes.

Current issues in molecular biology·2024
Same author

Adsorption on a Spherical Colloidal Particle from a Mixture of Nanoparticles with Competing Interactions.

Molecules (Basel, Switzerland)·2024
Same author

Lattice Model Results for Pattern Formation in a Mixture with Competing Interactions.

Molecules (Basel, Switzerland)·2024

Related Experiment Video

Updated: Dec 19, 2025

Origami Inspired Self-assembly of Patterned and Reconfigurable Particles
12:33

Origami Inspired Self-assembly of Patterned and Reconfigurable Particles

Published on: February 4, 2013

22.1K

Triangular lattice models for pattern formation by core-shell particles with different shell thicknesses.

V S Grishina1, V S Vikhrenko1, A Ciach2

  • 1Belarusian State Technological University, 13a Sverdlova str., 220006 Minsk, Belarus.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|June 5, 2020
PubMed
Summary
This summary is machine-generated.

We studied pattern formation in hard-core soft-shell particles using lattice models. Model II, with an additional soft shell, shows significantly more stable patterns and interfaces than Model I.

Keywords:
chemical potential-concentration isothermshard-core soft-shell particlesheat capacityline tensionordered structures

More Related Videos

Three-Dimensional Particle Shape Analysis Using X-ray Computed Tomography: Experimental Procedure and Analysis Algorithms for Metal Powders
10:10

Three-Dimensional Particle Shape Analysis Using X-ray Computed Tomography: Experimental Procedure and Analysis Algorithms for Metal Powders

Published on: December 4, 2020

2.1K
Liquid-cell Transmission Electron Microscopy for Tracking Self-assembly of Nanoparticles
08:39

Liquid-cell Transmission Electron Microscopy for Tracking Self-assembly of Nanoparticles

Published on: October 16, 2017

13.0K

Related Experiment Videos

Last Updated: Dec 19, 2025

Origami Inspired Self-assembly of Patterned and Reconfigurable Particles
12:33

Origami Inspired Self-assembly of Patterned and Reconfigurable Particles

Published on: February 4, 2013

22.1K
Three-Dimensional Particle Shape Analysis Using X-ray Computed Tomography: Experimental Procedure and Analysis Algorithms for Metal Powders
10:10

Three-Dimensional Particle Shape Analysis Using X-ray Computed Tomography: Experimental Procedure and Analysis Algorithms for Metal Powders

Published on: December 4, 2020

2.1K
Liquid-cell Transmission Electron Microscopy for Tracking Self-assembly of Nanoparticles
08:39

Liquid-cell Transmission Electron Microscopy for Tracking Self-assembly of Nanoparticles

Published on: October 16, 2017

13.0K

Area of Science:

  • Statistical Mechanics
  • Materials Science
  • Computational Physics

Background:

  • Understanding pattern formation in condensed matter systems is crucial for designing novel materials.
  • Particle models with complex interactions, like hard cores and soft shells, are essential for simulating interfacial phenomena.
  • Lattice models provide a simplified yet powerful framework for studying phase transitions and emergent structures.

Purpose of the Study:

  • To investigate the impact of shell thickness and structure on pattern formation in hard-core soft-shell particles at interfaces.
  • To compare pattern formation in two distinct models: Model I (hard core + cross-linked shell) and Model II (additional soft outer shell).
  • To analyze the phase diagrams, thermodynamic properties, and interfacial behavior of these particle systems.

Main Methods:

  • Development and analysis of triangular lattice models for hard-core soft-shell particles.
  • Simulation of ground states under fixed chemical potential or fixed site fraction.
  • Monte Carlo simulations to calculate isotherms, compressibility, and specific heat at finite temperatures.
  • Calculation of line tensions for interfaces between different phases.

Main Results:

  • Model I exhibits 4 distinct phases, while Model II, with an added soft outer shell, reveals 6 additional ordered periodic patterns.
  • The additional phases in Model II are primarily stable at phase coexistence lines in the (chemical potential, temperature) diagram.
  • In the canonical ensemble, Model II displays a greater variety of stable patterns and interfaces over larger intervals of occupied sites.
  • Favorable interface orientation in both models correlates with the smoothest interface shape, as indicated by line tension calculations.

Conclusions:

  • The addition of a soft outer shell (Model II) significantly enhances the complexity and diversity of observable patterns compared to Model I.
  • Interfacial properties, such as line tension and orientation, play a critical role in stabilizing emergent structures.
  • These lattice models provide valuable insights into the fundamental mechanisms governing pattern formation in soft matter systems.