Beer's Law‐Why Integrated Absorbance Depends Linearly on Concentration
As derived by Max Planck in 1903 from dispersion theory, Beer's law has a fundamental limitation. The concentration dependence of absorbance can deviate from linearity, even in the absence of any interactions or instrumental nonlinearities. Integrated absorbance, not peak absorbance, depends li...
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Veröffentlicht in: | Chemphyschem 2019-11, Vol.20 (21), p.2748-2753 |
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description | As derived by Max Planck in 1903 from dispersion theory, Beer's law has a fundamental limitation. The concentration dependence of absorbance can deviate from linearity, even in the absence of any interactions or instrumental nonlinearities. Integrated absorbance, not peak absorbance, depends linearly on concentration. The numerical integration of the absorbance leads to maximum deviations from linearity of less than 0.1 %. This deviation is a consequence of a sum rule that was derived from the Kramers‐Kronig relations at a time when the fundamental limitation of Beer's law was no longer mentioned in the literature. This sum rule also links concentration to (classical) oscillator strengths and thereby enables the use of dispersion analysis to determine the concentration directly from transmittance and reflectance measurements. Thus, concentration analysis of complex samples, such as layered and/or anisotropic materials, in which Beer's law cannot be applied, can be achieved using dispersion analysis.
Absorbance at a particular spectral point does not necessarily depend linearly on the concentration. Based on electromagnetic theory, it can be demonstrated, however, that for the integrated absorbance, Beer's law still holds. |
doi_str_mv | 10.1002/cphc.201900787 |
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Absorbance at a particular spectral point does not necessarily depend linearly on the concentration. Based on electromagnetic theory, it can be demonstrated, however, that for the integrated absorbance, Beer's law still holds.</description><identifier>ISSN: 1439-4235</identifier><identifier>EISSN: 1439-7641</identifier><identifier>DOI: 10.1002/cphc.201900787</identifier><identifier>PMID: 31544999</identifier><language>eng</language><publisher>Germany: Wiley Subscription Services, Inc</publisher><subject>Absorbance ; Beer's law ; Communication ; Communications ; concentration dependence ; Dependence ; Dispersion ; dispersion analysis ; isotropic media ; Linearity ; Numerical integration ; Oscillator strengths ; Reflectance ; Sum rules</subject><ispartof>Chemphyschem, 2019-11, Vol.20 (21), p.2748-2753</ispartof><rights>2019 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA.</rights><rights>2019 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c5057-6df64685f134416146aa33a92cbe04fbdd771c06b534a8396909a3e43279deb33</citedby><cites>FETCH-LOGICAL-c5057-6df64685f134416146aa33a92cbe04fbdd771c06b534a8396909a3e43279deb33</cites><orcidid>0000-0001-9396-7365</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fcphc.201900787$$EPDF$$P50$$Gwiley$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fcphc.201900787$$EHTML$$P50$$Gwiley$$Hfree_for_read</linktohtml><link.rule.ids>230,314,776,780,881,1411,27901,27902,45550,45551</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/31544999$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Mayerhöfer, Thomas G.</creatorcontrib><creatorcontrib>Pipa, Andrei V.</creatorcontrib><creatorcontrib>Popp, Jürgen</creatorcontrib><title>Beer's Law‐Why Integrated Absorbance Depends Linearly on Concentration</title><title>Chemphyschem</title><addtitle>Chemphyschem</addtitle><description>As derived by Max Planck in 1903 from dispersion theory, Beer's law has a fundamental limitation. The concentration dependence of absorbance can deviate from linearity, even in the absence of any interactions or instrumental nonlinearities. Integrated absorbance, not peak absorbance, depends linearly on concentration. The numerical integration of the absorbance leads to maximum deviations from linearity of less than 0.1 %. This deviation is a consequence of a sum rule that was derived from the Kramers‐Kronig relations at a time when the fundamental limitation of Beer's law was no longer mentioned in the literature. This sum rule also links concentration to (classical) oscillator strengths and thereby enables the use of dispersion analysis to determine the concentration directly from transmittance and reflectance measurements. Thus, concentration analysis of complex samples, such as layered and/or anisotropic materials, in which Beer's law cannot be applied, can be achieved using dispersion analysis.
Absorbance at a particular spectral point does not necessarily depend linearly on the concentration. Based on electromagnetic theory, it can be demonstrated, however, that for the integrated absorbance, Beer's law still holds.</description><subject>Absorbance</subject><subject>Beer's law</subject><subject>Communication</subject><subject>Communications</subject><subject>concentration dependence</subject><subject>Dependence</subject><subject>Dispersion</subject><subject>dispersion analysis</subject><subject>isotropic media</subject><subject>Linearity</subject><subject>Numerical integration</subject><subject>Oscillator strengths</subject><subject>Reflectance</subject><subject>Sum rules</subject><issn>1439-4235</issn><issn>1439-7641</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>24P</sourceid><recordid>eNqFkT1PwzAQhi0EglJYGVEkBlha_BUnXpBK-ChSJRhAjJaTXGiq1C52S9WNn8Bv5Jdg1FI-FqY76Z57dKcXoQOCuwRjelpMhkWXYiIxTtJkA7UIZ7KTCE42Vz2nLN5Bu96PMMYpTsg22mEk5lxK2UL9cwB37KOBnr-_vj0OF9GNmcKT01Moo17urcu1KSC6gAmYMnC1Ae2aRWRNlNkwMdPA1tbsoa1KNx72V7WNHq4u77N-Z3B7fZP1Bp0ixnHSEWUluEjjijDOiSBcaM2YlrTIAfMqL8skIQUWecy4TpkUEkvNgDOayBJyxtrobOmdzPIxlMsDGjVx9Vi7hbK6Vr8nph6qJ_uiRColF3EQnKwEzj7PwE_VuPYFNI02YGdeUSoFoTGlJKBHf9CRnTkT3lOUEUoFTyUOVHdJFc5676BaH0Ow-gxJfYak1iGFhcOfL6zxr1QCIJfAvG5g8Y9OZXf97Fv-ASehnoE</recordid><startdate>20191105</startdate><enddate>20191105</enddate><creator>Mayerhöfer, Thomas G.</creator><creator>Pipa, Andrei V.</creator><creator>Popp, Jürgen</creator><general>Wiley Subscription Services, Inc</general><general>John Wiley and Sons Inc</general><scope>24P</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>K9.</scope><scope>7X8</scope><scope>5PM</scope><orcidid>https://orcid.org/0000-0001-9396-7365</orcidid></search><sort><creationdate>20191105</creationdate><title>Beer's Law‐Why Integrated Absorbance Depends Linearly on Concentration</title><author>Mayerhöfer, Thomas G. ; Pipa, Andrei V. ; Popp, Jürgen</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c5057-6df64685f134416146aa33a92cbe04fbdd771c06b534a8396909a3e43279deb33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Absorbance</topic><topic>Beer's law</topic><topic>Communication</topic><topic>Communications</topic><topic>concentration dependence</topic><topic>Dependence</topic><topic>Dispersion</topic><topic>dispersion analysis</topic><topic>isotropic media</topic><topic>Linearity</topic><topic>Numerical integration</topic><topic>Oscillator strengths</topic><topic>Reflectance</topic><topic>Sum rules</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Mayerhöfer, Thomas G.</creatorcontrib><creatorcontrib>Pipa, Andrei V.</creatorcontrib><creatorcontrib>Popp, Jürgen</creatorcontrib><collection>Wiley-Blackwell Open Access Titles</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>ProQuest Health & Medical Complete (Alumni)</collection><collection>MEDLINE - Academic</collection><collection>PubMed Central (Full Participant titles)</collection><jtitle>Chemphyschem</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Mayerhöfer, Thomas G.</au><au>Pipa, Andrei V.</au><au>Popp, Jürgen</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Beer's Law‐Why Integrated Absorbance Depends Linearly on Concentration</atitle><jtitle>Chemphyschem</jtitle><addtitle>Chemphyschem</addtitle><date>2019-11-05</date><risdate>2019</risdate><volume>20</volume><issue>21</issue><spage>2748</spage><epage>2753</epage><pages>2748-2753</pages><issn>1439-4235</issn><eissn>1439-7641</eissn><abstract>As derived by Max Planck in 1903 from dispersion theory, Beer's law has a fundamental limitation. The concentration dependence of absorbance can deviate from linearity, even in the absence of any interactions or instrumental nonlinearities. Integrated absorbance, not peak absorbance, depends linearly on concentration. The numerical integration of the absorbance leads to maximum deviations from linearity of less than 0.1 %. This deviation is a consequence of a sum rule that was derived from the Kramers‐Kronig relations at a time when the fundamental limitation of Beer's law was no longer mentioned in the literature. This sum rule also links concentration to (classical) oscillator strengths and thereby enables the use of dispersion analysis to determine the concentration directly from transmittance and reflectance measurements. Thus, concentration analysis of complex samples, such as layered and/or anisotropic materials, in which Beer's law cannot be applied, can be achieved using dispersion analysis.
Absorbance at a particular spectral point does not necessarily depend linearly on the concentration. Based on electromagnetic theory, it can be demonstrated, however, that for the integrated absorbance, Beer's law still holds.</abstract><cop>Germany</cop><pub>Wiley Subscription Services, Inc</pub><pmid>31544999</pmid><doi>10.1002/cphc.201900787</doi><tpages>6</tpages><orcidid>https://orcid.org/0000-0001-9396-7365</orcidid><oa>free_for_read</oa></addata></record> |
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subjects | Absorbance Beer's law Communication Communications concentration dependence Dependence Dispersion dispersion analysis isotropic media Linearity Numerical integration Oscillator strengths Reflectance Sum rules |
title | Beer's Law‐Why Integrated Absorbance Depends Linearly on Concentration |
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