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

The Principle of Superposition and the Gravitational Field

The Principle of Superposition and the Gravitational Field

The principle of superposition applies to gravitational forces of objects that are sufficiently far apart. It states that the net gravitational force on a point object is the vector sum of the gravitational forces on it due to various objects. The principle helps calculate the force by listing the individual forces and then vectorially summing them up. However, it should be noted that the principle of superposition is not always apparent. In the presence of a second force, the first force could...

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 has a uniform...

Electric Field of a Non Uniformly Charged Sphere

Electric Field of a Non Uniformly Charged Sphere

Gauss's law states that the electric flux through any closed surface equals the net charge enclosed within the surface. This law is beneficial for determining the expressions for the electric field for a particular charge distribution if the electric flux is known.
Consider a non-uniformly charged sphere, for which the density of charge depends only on the distance from a point in space and not on the direction. Such a sphere has a spherically symmetrical charge distribution. Here, the electric...

Gravitation Between Spherically Symmetric Masses

Gravitation Between Spherically Symmetric Masses

The gravitational potential energy between two spherically symmetric bodies can be calculated from the masses and the distance between the bodies, assuming that the center of mass is concentrated at the respective centers of the bodies.

Dimensional Analysis

Dimensional Analysis

Dimensional analysis is a powerful tool that is used in physics and engineering to understand and predict the behavior of physical systems. The basic idea behind dimensional analysis is to express physical quantities in terms of fundamental dimensions such as the mass, length, and time. Derived dimensions like the velocity, acceleration, and force are derived from the combinations of these fundamental dimensions.
Dimensional analysis allows us to analyze and compare physical quantities on a...

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...

You might also read

Related Articles

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

Sort by

Same author

Microstructure of supercritical CO2-in-water microemulsions: a systematic contrast variation study.

Physical chemistry chemical physics : PCCP·2011

Same author

Giant biocompatible and biodegradable PEG-PMCL vesicles and microcapsules by solvent evaporation from double emulsion droplets.

Journal of colloid and interface science·2010

Same author

Rapid ejection of giant Pluronic L121 vesicles from spreading double emulsion droplets.

Langmuir : the ACS journal of surfaces and colloids·2010

Same author

Small-angle-neutron-scattering from giant water-in-oil microemulsion droplets. II. Polymer-decorated droplets in a quaternary system.

The Journal of chemical physics·2008

Same author

Small-angle neutron scattering from giant water-in-oil microemulsion droplets. I. Ternary system.

The Journal of chemical physics·2008

Same journal

Donor-Acceptor Separation Augments Temperature Dependence of Kinetic Isotope Effects in NADH Model Hydride Transfer Reactions: Mimicking Enzyme versus Mutant Dynamics.

The journal of physical chemistry. B·2026

Same journal

Disordered Worm-Like Clusters in a Hexagonal Mesophase Former: Simulation and Thermodynamic Description.

The journal of physical chemistry. B·2026

Same journal

Comparative Biophysical Analysis of Healthy and Inflamed Intestinal Membrane Models Using Langmuir Monolayers.

The journal of physical chemistry. B·2026

Same journal

Phosphoserine Charge State Drives Ion Condensation and Spatial Polyamine Presentation in Multirepeat Silaffin.

The journal of physical chemistry. B·2026

Same journal

pH-Dependent Conformational Transition of the Glutamate-GABA Antiporter GadC Revealed by <sup>19</sup>F NMR.

The journal of physical chemistry. B·2026

Same journal

Hydrogen-Bond Network in Equimolar <i>N</i>-Methylacetamide-Water: Integrated Neutron Scattering, Molecular Dynamics, DFT-NBO-AIM, and Machine Learning Analysis.

The journal of physical chemistry. B·2026

See all related articles

Search research articles

Related Experiment Video

Updated: May 31, 2026

Assembly and Characterization of Polyelectrolyte Complex Micelles

Assembly and Characterization of Polyelectrolyte Complex Micelles

Published on: March 2, 2020

Universal analytical scattering form factor for shell-, core-shell, or homogeneous particles with continuously

Tobias Foster¹

¹University of Cologne, Institute for Physical Chemistry, Luxemburger Str. 16, 50939 Cologne, Germany. tobias.foster@uni-koeln.de

The Journal of Physical Chemistry. B

|July 5, 2011

Summary

This summary is machine-generated.

A new continuous density distribution function and its analytical scattering form factor are introduced. This universally describes scattering from various particle types, enabling precise analysis of small-angle scattering data.

More Related Videos

Measurement of Particle Size Distribution in Turbid Solutions by Dynamic Light Scattering Microscopy

Measurement of Particle Size Distribution in Turbid Solutions by Dynamic Light Scattering Microscopy

Published on: January 9, 2017

Related Experiment Videos

Last Updated: May 31, 2026

Assembly and Characterization of Polyelectrolyte Complex Micelles

Assembly and Characterization of Polyelectrolyte Complex Micelles

Published on: March 2, 2020

Measurement of Particle Size Distribution in Turbid Solutions by Dynamic Light Scattering Microscopy

Measurement of Particle Size Distribution in Turbid Solutions by Dynamic Light Scattering Microscopy

Published on: January 9, 2017

Area of Science:

Materials Science
Physics
Chemistry

Background:

Scattering data analysis often relies on models for particle density profiles.
Existing models may lack flexibility in describing diverse radial density distributions.
Accurate modeling is crucial for interpreting scattering experiments.

Purpose of the Study:

To develop a novel, continuous, and analytical density distribution function.
To derive an analytical scattering form factor applicable to various particle structures.
To provide a versatile tool for analyzing small-angle scattering data.

Main Methods:

A continuous density distribution function is constructed using a sum of two Fermi-Dirac functions.
A single shape parameter ('d') allows continuous alteration of the density profile.
An analytical scattering form factor is derived via an approximation of the density function.

Main Results:

The derived function can continuously model profiles from step-like to hyperbolic.
The analytical form factor is accurate for rescaled shape parameters (d/R) up to approximately 0.1.
The form factor universally describes scattering from homogeneous spheres, shells, and core-shell particles.

Conclusions:

The novel analytical form factor offers a universal description for particle scattering.
This tool is particularly valuable for model-dependent analysis of small-angle scattering data.
Direct comparison with model-free extracted profiles is facilitated, enhancing data interpretation.