Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Gauss's Law: Spherical Symmetry

Gauss's Law: Spherical Symmetry

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half...

Crystal Field Theory - Tetrahedral and Square Planar Complexes

Crystal Field Theory - Tetrahedral and Square Planar Complexes

Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...

Atomic Orbitals

Atomic Orbitals

An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.

Numerical Calculations

Numerical Calculations

In engineering applications, the representation of the numerical value is critical. Presenting or reporting the answer is one of the essential parts of engineering practices. Numerical calculations are performed using handheld calculators or computers since numerically accurate answers are always preferred.
The solution to a problem is obtained using different methods. While manually solving algebraic symbols is one of the most common methods, the graphical method is often preferred. Computers...

Quantum Numbers

Quantum Numbers

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.

Atomic Nuclei: Nuclear Relaxation Processes

Atomic Nuclei: Nuclear Relaxation Processes

In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis, the precessing magnetic moments are randomly oriented around the z-axis.

You might also read

Related Articles

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

Sort by

Same author

Reaction Medium as an Architect of Nanocrystal Superlattices.

Journal of the American Chemical Society·2026

Same author

Particle Size-Driven Transition from Multilayer Aggregates to Ordered Monolayers at Gas Marble Interfaces.

Langmuir : the ACS journal of surfaces and colloids·2026

Same author

3D electron diffraction-the missing slice completing nanoscale analysis of organic solar cells in TEM.

Nature communications·2026

Same author

Supraparticles with Enhanced Mechanical and Signal Stability for Identification of Objects.

ACS applied nano materials·2026

Same author

Laying the Foundation for Digital Material Design of Porous Transport Electrodes for PEM Water Electrolysis With Multiscale Tomography.

Small (Weinheim an der Bergstrasse, Germany)·2026

Same author

Quantifying Polydopamine Shell Hydration in Core-Shell Colloids by Analytical Ultracentrifugation: Implications for Self-Assembly and Structural Color of Photonic Crystals.

Langmuir : the ACS journal of surfaces and colloids·2026

Search research articles

Related Experiment Video

Updated: May 24, 2025

Confocal Imaging of Confined Quiescent and Flowing Colloid-polymer Mixtures

Confocal Imaging of Confined Quiescent and Flowing Colloid-polymer Mixtures

Published on: May 20, 2014

Breakdown of Magic Numbers in Spherical Confinement.

Junwei Wang^1,2, Jonathan Martín-González¹, Lukas J Römling¹

¹Institute of Particle Technology, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany.

|March 6, 2025

Summary

Magic numbers, crucial for understanding particle systems, disappear in larger colloidal clusters. Beyond a critical size, closed shells vanish, replaced by

Keywords:

clusters colloids confinement self-assembly thermodynamics

More Related Videos

Setting Limits on Supersymmetry Using Simplified Models

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Spatial Separation of Molecular Conformers and Clusters

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

Related Experiment Videos

Last Updated: May 24, 2025

Confocal Imaging of Confined Quiescent and Flowing Colloid-polymer Mixtures

Confocal Imaging of Confined Quiescent and Flowing Colloid-polymer Mixtures

Published on: May 20, 2014

Setting Limits on Supersymmetry Using Simplified Models

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Spatial Separation of Molecular Conformers and Clusters

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

Area of Science:

Condensed Matter Physics
Materials Science
Colloidal Science

Background:

Magic numbers define stable configurations in finite particle systems, crucial for nuclear physics and atomic clusters.
These stable states often feature closed surface shells, maximizing nearest-neighbor interactions and minimizing free energy.
The diminishing significance of magic numbers with increasing system size necessitates understanding their breakdown.

Purpose of the Study:

To investigate the behavior of magic numbers in confined colloidal clusters as system size increases.
To identify the critical system size at which magic number phenomena cease to be significant.
To characterize the structural and energetic properties of larger colloidal clusters.

Main Methods:

Experimental investigation of colloidal clusters formed via confined self-assembly.
Analysis of cluster symmetry, surface shell closure, and free energy minima.
Development of a sphere packing model to elucidate structural constraints.

Main Results:

Small magic number colloidal clusters exhibit icosahedral symmetry and closed surface shells with pronounced free energy minima.
Beyond a critical size, closed surface shells disappear, and free energy minima become less pronounced.
A new cluster type, 'football clusters,' with icosahedral symmetry but open facets, emerges in larger systems.

Conclusions:

Magic number phenomena break down in large confined colloidal systems due to the geometric impossibility of forming closed surface shells.
The emergence of football clusters signifies a transition to new stable configurations beyond the magic number regime.
This study clarifies the limits of magic number applicability in mesoscopic particle systems.