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Related Concept Videos

Crystal Density01:19

Crystal Density

The crystal lattice structure of a material allows us to determine how many molecules exist in its unit cell. With this information, alongside the unit-cell parameters - three distance parameters (a, b, c) and three angular parameters (α, β, γ).Density (ρ) = (Z × M) / (a × b × c × NA)where:Z is the number of formula units per unit cellM is the molar mass of the substancea, b, and c are the edge lengths of the unit cellNA is Avogadro’s numberFor a simple cubic lattice, atoms are located only at...
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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.
Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

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,...
Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
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Updated: Jun 18, 2026

Preparation and In Vitro Characterization of Dendrimer-based Contrast Agents for Magnetic Resonance Imaging
11:27

Preparation and In Vitro Characterization of Dendrimer-based Contrast Agents for Magnetic Resonance Imaging

Published on: December 4, 2016

Microscopic density functional theory for dendrimers.

Alexandr Malijevský1

  • 1Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom. a.malijevsky@imperial.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2009
PubMed
Summary
This summary is machine-generated.

A new density functional theory is proposed for modeling dendrimers, accounting for segment repulsion and connectivity correlations. This approach simplifies calculations for dendrimer properties, including dispersion forces.

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Synthesis, Cellular Delivery and In vivo Application of Dendrimer-based pH Sensors
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Synthesis, Cellular Delivery and In vivo Application of Dendrimer-based pH Sensors

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Synthesis, Cellular Delivery and In vivo Application of Dendrimer-based pH Sensors
16:19

Synthesis, Cellular Delivery and In vivo Application of Dendrimer-based pH Sensors

Published on: September 10, 2013

Area of Science:

  • Computational chemistry
  • Polymer physics

Background:

  • Dendrimers are complex branched macromolecules.
  • Accurate theoretical models are needed to understand their properties.

Purpose of the Study:

  • To develop a density functional theory for a simplified dendrimer model.
  • To provide a framework for calculating dendrimer properties.

Main Methods:

  • Utilizing fundamental measure theory for hard-sphere repulsion.
  • Applying Wertheim's first-order perturbation theory for connectivity correlations.
  • Deriving recurrence formulas for ideal chain contributions.

Main Results:

  • A theoretical framework for modeling dendrimers is established.
  • The method accounts for key physical interactions like repulsion and connectivity.
  • Dispersion forces can be incorporated using perturbation theory.

Conclusions:

  • The proposed density functional theory offers a simplified yet effective model for dendrimers.
  • This theory facilitates the calculation of dendrimer properties.
  • The framework is extensible to include additional physical interactions.