Radial distribution function of rod-like polyelectrolytes

R Zandi1, J Rudnick, R Golestanian

  • 1Department of Chemistry and Biochemistry, UCLA, Box 951569, Los Angeles, CA 90095-1569, USA.

Related Concept Videos

Determination of Molar Masses of Polymers I01:24

Determination of Molar Masses of Polymers I

Polymerization produces macromolecules with a range of chain lengths due to the random nature of molecular growth processes. As chains form and terminate at different stages, a single polymer sample contains molecules of varying sizes rather than a uniform structure. This variability is described using average molar masses and distribution-related parameters, which together provide a comprehensive understanding of polymer characteristics.The distribution of molar masses plays a critical role in...
Atomic Orbitals02:44

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.
Polymers: Molecular Weight Distribution01:10

Polymers: Molecular Weight Distribution

For any given polymer, the weight average molecular weight (Mw) is higher than, if not equal to, the number average molecular weight (Mn). The only situation in which the weight average molecular weight and the number average molecular weight are equal is when a polymer consists only of chains with equal molecular weight. However, this never happens in a synthetic polymer, since it is difficult to control the polymerization process up to a molecular level with accuracy to a hundred percent.
Determination of Molar Masses of Polymers II01:27

Determination of Molar Masses of Polymers II

Polymer samples typically consist of macromolecular chains with a distribution of lengths, resulting in a range of molar masses rather than a single discrete value. Conventional descriptors such as the number-average molar mass and weight-average molar mass quantify this distribution but do not fully capture polymer behavior in solution..The viscosity-average molar mass provides a more realistic description of polymer behavior in solution because it accounts for the enhanced contribution of...
Potential Due to a Polarized Object01:29

Potential Due to a Polarized Object

A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water,...
Polar Coordinates: Problem Solving01:27

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...