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

Graphs of Polar Equations

Graphs of Polar Equations

The polar coordinate system represents points using a distance from a central point (the pole) and an angle from a reference direction (the polar axis). Unlike rectangular coordinates, polar coordinates are ideal for graphing curves with radial symmetry or periodic behavior.Some general forms of graphs in polar coordinates include the following:Equation of a Circle (Centered at the Pole):A graph where the radius remains constant for all angles traces a circle centered at the pole:Equation of a...

Polar Curves

Polar Curves

The spirograph is a versatile tool for visualizing the relationship between geometry and mathematical representation. In particular, it demonstrates how polar coordinates offer an alternative framework for describing curves in comparison to Cartesian coordinates. Instead of specifying a point by its horizontal and vertical displacements (x, y), polar coordinates use a radius r, the distance from the origin, and an angle θ, measured counterclockwise from the polar axis. This system is...

Group Polarization

Group Polarization

Group polarization is the strengthening of an original group attitude following the discussion of views within a group (Teger & Pruitt, 1967). That is, if a group initially favors a viewpoint, after discussion the group consensus is likely a stronger endorsement of the viewpoint. Conversely, if the group was initially opposed to a viewpoint, group discussion would likely lead to stronger opposition.

Molecular Shape and Polarity

Molecular Shape and Polarity

Dipole Moment of a Molecule

Polar Coordinates: Problem Solving

Polar Coordinates: Problem Solving

Directional radiation patterns are central to antenna analysis, as they illustrate how signal strength varies with direction. These patterns are often modeled using polar plots, where the radial distance from the origin represents signal intensity at a given angle. A commonly used idealized form is the four-lobed rose curve, which captures the concept of directional beams in a simplified mathematical form.The four-lobed rose curve, described by r = cos⁡(2θ), features four symmetric lobes, each...

Polar Equations of Conics

Polar Equations of Conics

A conic section can be defined in polar coordinates as the set of all points whose distance from a fixed point, known as the focus, bears a constant ratio to their distance from a fixed line, known as the directrix. This constant ratio is called the eccentricity. This definition unifies all types of conic sections—ellipses, parabolas, and hyperbolas—under a single framework. When the focus is positioned at the origin of the polar coordinate system, a single polar equation can describe any conic...

You might also read

Related Articles

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

Sort by

Same author

Structural alterations of branched <i>versus</i> linear mixed-surfactant micellar systems with the addition of a complex perfume mixture and dipropylene glycol as cosolvent.

RSC advances·2022

Same author

Effects of a Multicomponent Perfume Accord and Dilution on the Formation of ST2S/CAPB Mixed-Surfactant Microemulsions.

Langmuir : the ACS journal of surfaces and colloids·2022

Same author

Form Factors for Branched Polymers with Excluded Volume.

Journal of research of the National Institute of Standards and Technology·2021

Same author

Supramolecular Self-assembly of a Model Hydrogelator: Characterization of Fiber Formation and Morphology.

Gels (Basel, Switzerland)·2017

Same author

Are Bragg Peaks Gaussian?

Journal of research of the National Institute of Standards and Technology·2015

Same author

Temperature Effect on the Nanostructure of SDS Micelles in Water.

Journal of research of the National Institute of Standards and Technology·2015

Search research articles

Related Experiment Video

Updated: Jun 9, 2026

Spatial Separation of Molecular Conformers and Clusters

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

Clustering in polar media.

Boualem Hammouda¹

¹Center for Neutron Research, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899-6102, USA. hammouda@nist.gov

The Journal of Chemical Physics

|September 7, 2010

Summary

This summary is machine-generated.

Clustering in poly(ethylene oxide)/d-water solutions is driven by temperature-dependent interactions. Specifically, increasing repulsion between oxygen and ethylene groups at lower temperatures causes ethylene groups to attract and aggregate.

More Related Videos

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Polarization-Sensitive Two-Photon Microscopy for a Label-Free Amyloid Structural Characterization

Polarization-Sensitive Two-Photon Microscopy for a Label-Free Amyloid Structural Characterization

Published on: September 8, 2023

Related Experiment Videos

Last Updated: Jun 9, 2026

Spatial Separation of Molecular Conformers and Clusters

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Polarization-Sensitive Two-Photon Microscopy for a Label-Free Amyloid Structural Characterization

Polarization-Sensitive Two-Photon Microscopy for a Label-Free Amyloid Structural Characterization

Published on: September 8, 2023

Area of Science:

Polymer Science
Physical Chemistry
Materials Science

Background:

Clustering is a common phenomenon in water-soluble polymers and biological macromolecules.
Observed in polar solvent mixtures, the underlying causes of clustering require systematic investigation.

Purpose of the Study:

To systematically investigate clustering in poly(ethylene oxide)/d-water solutions.
To elucidate the driving forces behind polymer aggregation in aqueous environments.

Main Methods:

Utilized small-angle neutron scattering (SANS) to study poly(ethylene oxide)/d-water solutions.
Employed the random phase approximation (RPA) to derive partial Flory-Huggins interaction parameters.

Main Results:

Derived interaction parameters for oxygen/d-water, ethylene/d-water, and oxygen/ethylene pairs.
Identified lower critical solution temperature (LCST) behavior for oxygen/d-water and ethylene/d-water interactions.
Observed upper critical solution temperature (UCST) behavior for oxygen/ethylene interactions.

Conclusions:

Clustering is attributed to increasing repulsive interactions between oxygen and ethylene with decreasing temperature and increasing polymer concentration.
This repulsion promotes attractive interactions between ethylene groups, leading to aggregation.
Findings provide insights into polymer solution behavior and phase transitions.