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Related Concept Videos

Diffusion01:21

Diffusion

Diffusion is a type of passive transport. In passive transport, a substance tends to move from an area of high concentration to an area of low concentration until the concentration is equal across the space. For example, take the diffusion of substances through the air. When someone opens a perfume bottle in a room filled with people, the perfume is at its highest concentration in the bottle and is at its lowest at the edges of the room. The perfume vapor will diffuse, or spread away, from the...
Diffusion01:12

Diffusion

Diffusion is the passive movement of substances down their concentration gradients—requiring no expenditure of cellular energy. Substances, such as molecules or ions, diffuse from an area of high concentration to an area of low concentration in the cytosol or across membranes. Eventually, the concentration will even out, with the substance moving randomly but causing no net change in concentration. Such a state is called dynamic equilibrium, which is essential for maintaining overall...
Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion03:48

Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion

Although gaseous molecules travel at tremendous speeds (hundreds of meters per second), they collide with other gaseous molecules and travel in many different directions before reaching the desired target. At room temperature, a gaseous molecule will experience billions of collisions per second. The mean free path is the average distance a molecule travels between collisions. The mean free path increases with decreasing pressure; in general, the mean free path for a gaseous molecule will be...
¹H NMR: Complex Splitting01:13

¹H NMR: Complex Splitting

A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied first.
Passive Diffusion: Overview and Kinetics01:17

Passive Diffusion: Overview and Kinetics

Passive diffusion is a critical process that allows small lipophilic drugs to cross the cell membrane along a concentration gradient. This mechanism's efficiency depends on four primary factors: the membrane's surface area, the drug's lipid-water partition coefficient, the concentration gradient, and the membrane's thickness.
When administered orally, drugs establish a substantial concentration gradient between the gastrointestinal (GI) lumen and the bloodstream, expediting their diffusion into...
Radical Reactivity: Overview01:11

Radical Reactivity: Overview

Radicals, the highly reactive species, gain stability by undergoing three different reactions. The first reaction involves a radical-radical coupling, in which a radical combines with another radical, forming a spin‐paired molecule. The second reaction is between a radical and a spin‐paired molecule, generating a new radical and a new spin‐paired molecule. The third reaction is radical decomposition in a unimolecular reaction, forming a new radical and a spin‐paired molecule. These three...

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Related Experiment Video

Updated: May 10, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Diffusion along the splitting/commitment probability reaction coordinate.

Alexander M Berezhkovskii1, Attila Szabo

  • 1Mathematical and Statistical Computing Laboratory, Division of Computational Bioscience, Center for Information Technology, National Institutes of Health , Bethesda, Maryland 20892, United States.

The Journal of Physical Chemistry. B
|June 20, 2013
PubMed
Summary
This summary is machine-generated.

This study simplifies complex chemical reaction dynamics by projecting multidimensional diffusion onto a single splitting probability coordinate. This method accurately predicts equilibrium reaction rates, even when time scale assumptions are not strictly met.

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Area of Science:

  • Chemical Dynamics
  • Statistical Mechanics
  • Physical Chemistry

Background:

  • The theory of chemical reactions relies on understanding state commitment probabilities.
  • These probabilities are crucial in the configuration space separating reactants and products.

Purpose of the Study:

  • To develop a simplified model for predicting chemical reaction rates.
  • To investigate the accuracy of a reduced-dimensional diffusion model.

Main Methods:

  • Projecting multidimensional diffusive dynamics onto the splitting probability coordinate.
  • Assuming a slow change in splitting probability compared to other coordinates.
  • Deriving a one-dimensional diffusion equation.

Main Results:

  • The derived one-dimensional diffusion equation, while not always exact, accurately predicts equilibrium reaction rates.
  • The model successfully calculates the number of transitions between reactants and products per unit time at equilibrium.
  • In specific cases (two deep basins, harmonic saddle), the model aligns with diffusion perpendicular to the transition state.

Conclusions:

  • A simplified diffusion model based on splitting probability can accurately determine chemical reaction rates.
  • The approach offers a valuable tool for analyzing complex reaction dynamics.
  • The model's accuracy in predicting equilibrium rates highlights the importance of the splitting probability coordinate.