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Using Rotational Averaging To Calculate the Bulk Response of Isotropic and Anisotropic Samples from Molecular Parameters

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Steven S. Andrews

Department of Chemistry, Stanford University, Stanford, CA 94305

J. Chem. Educ., 2004, 81 (6), p 877

DOI: 10.1021/ed081p877

Publication Date (Web): June 1, 2004

Section:

History, Education, and Documentation

Abstract

Most physical chemistry experiments analyze bulk samples, rather than single molecules, with the result that each measurement yields an average response from many molecules. In particular, investigation of vector or matrix molecular properties, such as dipole moments or polarizabilities, leads to results that are averaged over a range of molecular orientations. This article presents mathematical methods for calculating these averages for isotropic and partially oriented samples, where the latter might arise from external electric or magnetic fields, flow gradients, or photoselection. Rotational averaging is demonstrated with several examples, including calculations for the potential energy of fixed and mobile molecules in an electric field and quantitative absorption and fluorescence spectroscopy. In the process, the fluorescence anisotropy and the Langevin function are derived. A table of direction cosine averages allows the method to be used for new experiments.

Keywords (Audience):

Second-Year Undergraduate

Keywords (Domain):

Physical Chemistry

Keywords (Feature):

Research: Science and Education

Keywords (Subject):

Fluorescence Spectroscopy

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This article has been cited by 2 ACS Journal articles (2 most recent appear below).

Fluorescence Anisotropy Spectra Disclose the Role of Disorder in Optical Spectra of Branched Intramolecular-Charge-Transfer Molecules
Cristina Sissa, Anna Painelli, Mireille Blanchard-Desce, and Francesca Terenziani
The Journal of Physical Chemistry B2011 Article ASAP
- Fluorescence Anisotropy Spectra Disclose the Role of Disorder in Optical Spectra of Branched Intramolecular-Charge-Transfer Molecules
  Cristina Sissa, Anna Painelli, Mireille Blanchard-Desce, and Francesca Terenziani
  The Journal of Physical Chemistry B2011 Article ASAP
  Fluorescence excitation and emission spectra and corresponding anisotropies of branched intramolecular charge-transfer (ICT) chromophores are reported. To unravel the role of disorder related to polar solvation, we collected spectra of molecules with ...
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Stark Realities
Steven G. Boxer
The Journal of Physical Chemistry B2009 113 (10), 2972-2983
- Stark Realities
  Steven G. Boxer
  The Journal of Physical Chemistry B2009 113 (10), 2972-2983
  Electric fields affect any process or transition that involves the movement of charge. Stark spectroscopy is a general term describing the study of spectral changes in the presence of electric fields, and it has proven to be a broadly useful approach for ...
  Abstract | Full Text HTML | Hi-Res PDF | PDF w/ Links