Boltzmann equation for the modelling of formation of silver nanoparticles using trisodium citrate as the reducing agent
The kinetics of formation of silver nanoparticles using trisodium citrate as the reducing agent was studied in order to evaluate the rate constants and the rate expression. The inability to measure the concentration of the reactant (precursor silver salt) at millimolar concentrations using conventio...
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| Veröffentlicht in: | Bulletin of materials science 2021-12, Vol.44 (4), p.249, Article 249 |
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| creator | Nagnath, Jadhav Pankaj Davis, Delphy Ovia, P Swaminathan, SamDavid Deepa, Kannan |
| description | The kinetics of formation of silver nanoparticles using trisodium citrate as the reducing agent was studied in order to evaluate the rate constants and the rate expression. The inability to measure the concentration of the reactant (precursor silver salt) at millimolar concentrations using conventional spectrophotometric techniques renders the studies of kinetics cumbersome. An attempt was made to study the kinetics of this reaction by measuring the concentration of silver nanoparticles instead of the silver ions as a function of time. The initial concentration of the reducing agent (trisodium citrate) was taken to be nearly 20 times that of the initial concentration of the silver ions. Hence, the reaction could be modelled as pseudo-first-order kinetics, considering the bimolecular nature of the reaction. The final second-order rate constant was evaluated using integral method of analysis as 0.254 l (g min)
–1
. The key steps in the formation of silver nanoparticles (i.e., reduction, nucleation, growth and saturation) were modelled as a sigmoidal plot using Boltzmann equation. A very good fit of experimental data (
R
2
≈ 0.99) was observed with the model. |
| doi_str_mv | 10.1007/s12034-021-02542-y |
| format | Article |
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–1
. The key steps in the formation of silver nanoparticles (i.e., reduction, nucleation, growth and saturation) were modelled as a sigmoidal plot using Boltzmann equation. A very good fit of experimental data (
R
2
≈ 0.99) was observed with the model.</description><identifier>ISSN: 0250-4707</identifier><identifier>EISSN: 0973-7669</identifier><identifier>DOI: 10.1007/s12034-021-02542-y</identifier><language>eng</language><publisher>Bangalore: Indian Academy of Sciences</publisher><subject>Boltzmann transport equation ; Chemical reactions ; Chemistry and Materials Science ; Electrons ; Engineering ; Kinetics ; Materials Science ; Mathematical analysis ; Nanoparticles ; Nitrates ; Nucleation ; Rate constants ; Reducing agents ; Silver ; Sodium citrate ; Spectrophotometry</subject><ispartof>Bulletin of materials science, 2021-12, Vol.44 (4), p.249, Article 249</ispartof><rights>Indian Academy of Sciences 2021</rights><rights>Indian Academy of Sciences 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c200t-263706eb7a4eb32b643bb1a9bdea3c3e6acc4629d9d364815cea907566042e7a3</cites><orcidid>0000-0001-9605-9696</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.proquest.com/docview/2919484736/fulltextPDF?pq-origsite=primo$$EPDF$$P50$$Gproquest$$H</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2919484736?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,780,784,21387,27923,27924,33743,41487,42556,43804,51318,64384,64388,72340,74173</link.rule.ids></links><search><creatorcontrib>Nagnath, Jadhav Pankaj</creatorcontrib><creatorcontrib>Davis, Delphy</creatorcontrib><creatorcontrib>Ovia, P</creatorcontrib><creatorcontrib>Swaminathan, SamDavid</creatorcontrib><creatorcontrib>Deepa, Kannan</creatorcontrib><title>Boltzmann equation for the modelling of formation of silver nanoparticles using trisodium citrate as the reducing agent</title><title>Bulletin of materials science</title><addtitle>Bull Mater Sci</addtitle><description>The kinetics of formation of silver nanoparticles using trisodium citrate as the reducing agent was studied in order to evaluate the rate constants and the rate expression. The inability to measure the concentration of the reactant (precursor silver salt) at millimolar concentrations using conventional spectrophotometric techniques renders the studies of kinetics cumbersome. An attempt was made to study the kinetics of this reaction by measuring the concentration of silver nanoparticles instead of the silver ions as a function of time. The initial concentration of the reducing agent (trisodium citrate) was taken to be nearly 20 times that of the initial concentration of the silver ions. Hence, the reaction could be modelled as pseudo-first-order kinetics, considering the bimolecular nature of the reaction. The final second-order rate constant was evaluated using integral method of analysis as 0.254 l (g min)
–1
. The key steps in the formation of silver nanoparticles (i.e., reduction, nucleation, growth and saturation) were modelled as a sigmoidal plot using Boltzmann equation. A very good fit of experimental data (
R
2
≈ 0.99) was observed with the model.</description><subject>Boltzmann transport equation</subject><subject>Chemical reactions</subject><subject>Chemistry and Materials Science</subject><subject>Electrons</subject><subject>Engineering</subject><subject>Kinetics</subject><subject>Materials Science</subject><subject>Mathematical analysis</subject><subject>Nanoparticles</subject><subject>Nitrates</subject><subject>Nucleation</subject><subject>Rate constants</subject><subject>Reducing agents</subject><subject>Silver</subject><subject>Sodium citrate</subject><subject>Spectrophotometry</subject><issn>0250-4707</issn><issn>0973-7669</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNp9kM1PwyAchhujiXP6D3gi8Vzlq7AedfErMfGiZ0Lpr5OlhQ2oZv71stXEmwcCP3jel-QpikuCrwnG8iYSihkvMSV5VZyWu6NihmvJSilEfZzPtMIll1ieFmcxrjEmNedkVnzd-T59D9o5BNtRJ-sd6nxA6QPQ4Fvoe-tWyHf7y2F6zkO0_ScE5LTzGx2SNT1ENMY9moKNvrXjgIxNQSdAOh7aArSj2RN6BS6dFyed7iNc_O7z4v3h_m35VL68Pj4vb19KQzFOJRVMYgGN1BwaRhvBWdMQXTctaGYYCG0MF7Ru65YJviCVAV1jWQmBOQWp2by4mno3wW9HiEmt_Rhc_lLROjtYcMlEpuhEmeBjDNCpTbCDDjtFsNoLVpNglQWrg2C1yyE2hWKG3QrCX_U_qR91j4Es</recordid><startdate>20211201</startdate><enddate>20211201</enddate><creator>Nagnath, Jadhav Pankaj</creator><creator>Davis, Delphy</creator><creator>Ovia, P</creator><creator>Swaminathan, SamDavid</creator><creator>Deepa, Kannan</creator><general>Indian Academy of Sciences</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SR</scope><scope>8BQ</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>AFKRA</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>D1I</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>JG9</scope><scope>KB.</scope><scope>PDBOC</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><orcidid>https://orcid.org/0000-0001-9605-9696</orcidid></search><sort><creationdate>20211201</creationdate><title>Boltzmann equation for the modelling of formation of silver nanoparticles using trisodium citrate as the reducing agent</title><author>Nagnath, Jadhav Pankaj ; Davis, Delphy ; Ovia, P ; Swaminathan, SamDavid ; Deepa, Kannan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c200t-263706eb7a4eb32b643bb1a9bdea3c3e6acc4629d9d364815cea907566042e7a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Boltzmann transport equation</topic><topic>Chemical reactions</topic><topic>Chemistry and Materials Science</topic><topic>Electrons</topic><topic>Engineering</topic><topic>Kinetics</topic><topic>Materials Science</topic><topic>Mathematical analysis</topic><topic>Nanoparticles</topic><topic>Nitrates</topic><topic>Nucleation</topic><topic>Rate constants</topic><topic>Reducing agents</topic><topic>Silver</topic><topic>Sodium citrate</topic><topic>Spectrophotometry</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Nagnath, Jadhav Pankaj</creatorcontrib><creatorcontrib>Davis, Delphy</creatorcontrib><creatorcontrib>Ovia, P</creatorcontrib><creatorcontrib>Swaminathan, SamDavid</creatorcontrib><creatorcontrib>Deepa, Kannan</creatorcontrib><collection>CrossRef</collection><collection>Engineered Materials Abstracts</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Materials Science Collection</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>Materials Research Database</collection><collection>Materials Science Database</collection><collection>Materials Science Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><jtitle>Bulletin of materials science</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Nagnath, Jadhav Pankaj</au><au>Davis, Delphy</au><au>Ovia, P</au><au>Swaminathan, SamDavid</au><au>Deepa, Kannan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Boltzmann equation for the modelling of formation of silver nanoparticles using trisodium citrate as the reducing agent</atitle><jtitle>Bulletin of materials science</jtitle><stitle>Bull Mater Sci</stitle><date>2021-12-01</date><risdate>2021</risdate><volume>44</volume><issue>4</issue><spage>249</spage><pages>249-</pages><artnum>249</artnum><issn>0250-4707</issn><eissn>0973-7669</eissn><abstract>The kinetics of formation of silver nanoparticles using trisodium citrate as the reducing agent was studied in order to evaluate the rate constants and the rate expression. The inability to measure the concentration of the reactant (precursor silver salt) at millimolar concentrations using conventional spectrophotometric techniques renders the studies of kinetics cumbersome. An attempt was made to study the kinetics of this reaction by measuring the concentration of silver nanoparticles instead of the silver ions as a function of time. The initial concentration of the reducing agent (trisodium citrate) was taken to be nearly 20 times that of the initial concentration of the silver ions. Hence, the reaction could be modelled as pseudo-first-order kinetics, considering the bimolecular nature of the reaction. The final second-order rate constant was evaluated using integral method of analysis as 0.254 l (g min)
–1
. The key steps in the formation of silver nanoparticles (i.e., reduction, nucleation, growth and saturation) were modelled as a sigmoidal plot using Boltzmann equation. A very good fit of experimental data (
R
2
≈ 0.99) was observed with the model.</abstract><cop>Bangalore</cop><pub>Indian Academy of Sciences</pub><doi>10.1007/s12034-021-02542-y</doi><orcidid>https://orcid.org/0000-0001-9605-9696</orcidid></addata></record> |
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| source | Indian Academy of Sciences; EZB-FREE-00999 freely available EZB journals; ProQuest Central UK/Ireland; Free Full-Text Journals in Chemistry; SpringerLink Journals - AutoHoldings; ProQuest Central |
| subjects | Boltzmann transport equation Chemical reactions Chemistry and Materials Science Electrons Engineering Kinetics Materials Science Mathematical analysis Nanoparticles Nitrates Nucleation Rate constants Reducing agents Silver Sodium citrate Spectrophotometry |
| title | Boltzmann equation for the modelling of formation of silver nanoparticles using trisodium citrate as the reducing agent |
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