Polycondensation Kinetics: 4. Growth of Acyclic Randomly Branched Chains
Master equations for concentrations of nb -mers ( n is the number of units, b is the number of branch points randomly located among the units) in the polycondensation of trifunctional monomers (PC-3) take into account the set of irreversible consecutive–parallel reactions between functional groups (...
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| Veröffentlicht in: | High energy chemistry 2021-05, Vol.55 (3), p.169-178 |
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| container_title | High energy chemistry |
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| creator | Kim, I. P. Kotkin, A. S. Benderskii, V. A. |
| description | Master equations for concentrations of
nb
-mers (
n
is the number of units,
b
is the number of branch points randomly located among the units) in the polycondensation of trifunctional monomers (PC-3) take into account the set of irreversible consecutive–parallel reactions between functional groups (
n
,
b
) and (
n
′,
b
′)-mers with rate constants χ(
b
,
b
′). Stoichiometric coefficients are equal to the number of permutations of bond-forming groups at ∆(
b
+
b
′) = 0, 1, 2. Reaction coordinates are combined into a network of an inhomogeneous Markov process. It is shown that the Flory hypothesis (all χ(
b
,
b
′) values are identical) leads to an explicitly time-independent Gaussian distribution
W
n
(
b
) with a maximum
b
max
that grows linearly with the chain length
n
. |
| doi_str_mv | 10.1134/S0018143921030061 |
| format | Article |
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nb
-mers (
n
is the number of units,
b
is the number of branch points randomly located among the units) in the polycondensation of trifunctional monomers (PC-3) take into account the set of irreversible consecutive–parallel reactions between functional groups (
n
,
b
) and (
n
′,
b
′)-mers with rate constants χ(
b
,
b
′). Stoichiometric coefficients are equal to the number of permutations of bond-forming groups at ∆(
b
+
b
′) = 0, 1, 2. Reaction coordinates are combined into a network of an inhomogeneous Markov process. It is shown that the Flory hypothesis (all χ(
b
,
b
′) values are identical) leads to an explicitly time-independent Gaussian distribution
W
n
(
b
) with a maximum
b
max
that grows linearly with the chain length
n
.</description><identifier>ISSN: 0018-1439</identifier><identifier>EISSN: 1608-3148</identifier><identifier>DOI: 10.1134/S0018143921030061</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Chain branching ; Chains ; Chemistry ; Chemistry and Materials Science ; Functional groups ; General Aspects ; Markov processes ; Normal distribution ; Permutations ; Physical Chemistry ; Rate constants</subject><ispartof>High energy chemistry, 2021-05, Vol.55 (3), p.169-178</ispartof><rights>Pleiades Publishing, Ltd. 2021. ISSN 0018-1439, High Energy Chemistry, 2021, Vol. 55, No. 3, pp. 169–178. © Pleiades Publishing, Ltd., 2021. Russian Text © The Author(s), 2021, published in Khimiya Vysokikh Energii, 2021, Vol. 55, No. 3, pp. 171–180.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-7d051c8c08eb4120b94566102529a34d462ea7275170e471a3d76fa78595dd603</citedby><cites>FETCH-LOGICAL-c316t-7d051c8c08eb4120b94566102529a34d462ea7275170e471a3d76fa78595dd603</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S0018143921030061$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S0018143921030061$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,777,781,27905,27906,41469,42538,51300</link.rule.ids></links><search><creatorcontrib>Kim, I. P.</creatorcontrib><creatorcontrib>Kotkin, A. S.</creatorcontrib><creatorcontrib>Benderskii, V. A.</creatorcontrib><title>Polycondensation Kinetics: 4. Growth of Acyclic Randomly Branched Chains</title><title>High energy chemistry</title><addtitle>High Energy Chem</addtitle><description>Master equations for concentrations of
nb
-mers (
n
is the number of units,
b
is the number of branch points randomly located among the units) in the polycondensation of trifunctional monomers (PC-3) take into account the set of irreversible consecutive–parallel reactions between functional groups (
n
,
b
) and (
n
′,
b
′)-mers with rate constants χ(
b
,
b
′). Stoichiometric coefficients are equal to the number of permutations of bond-forming groups at ∆(
b
+
b
′) = 0, 1, 2. Reaction coordinates are combined into a network of an inhomogeneous Markov process. It is shown that the Flory hypothesis (all χ(
b
,
b
′) values are identical) leads to an explicitly time-independent Gaussian distribution
W
n
(
b
) with a maximum
b
max
that grows linearly with the chain length
n
.</description><subject>Chain branching</subject><subject>Chains</subject><subject>Chemistry</subject><subject>Chemistry and Materials Science</subject><subject>Functional groups</subject><subject>General Aspects</subject><subject>Markov processes</subject><subject>Normal distribution</subject><subject>Permutations</subject><subject>Physical Chemistry</subject><subject>Rate constants</subject><issn>0018-1439</issn><issn>1608-3148</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp1kEtLAzEUhYMoWKs_wF3A9dR785qpu1q0FQuKj_WQJhk7ZZrUZIrMv3dKBRfi6i7O950Lh5BLhBEiF9evAFig4GOGwAEUHpEBKigyjqI4JoN9nO3zU3KW0hoAZM8NyPw5NJ0J3jqfdFsHTx9r79rapBsqRnQWw1e7oqGiE9OZpjb0RXsbNk1Hb6P2ZuUsna507dM5Oal0k9zFzx2S9_u7t-k8WzzNHqaTRWY4qjbLLUg0hYHCLQUyWI6FVAqBSTbWXFihmNM5yyXm4ESOmttcVTov5Fhaq4APydWhdxvD586ltlyHXfT9y5JJriRnoh9kSPBAmRhSiq4qt7He6NiVCOV-sPLPYL3DDk7qWf_h4m_z_9I3gZZpmw</recordid><startdate>20210501</startdate><enddate>20210501</enddate><creator>Kim, I. P.</creator><creator>Kotkin, A. S.</creator><creator>Benderskii, V. A.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20210501</creationdate><title>Polycondensation Kinetics: 4. Growth of Acyclic Randomly Branched Chains</title><author>Kim, I. P. ; Kotkin, A. S. ; Benderskii, V. A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-7d051c8c08eb4120b94566102529a34d462ea7275170e471a3d76fa78595dd603</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Chain branching</topic><topic>Chains</topic><topic>Chemistry</topic><topic>Chemistry and Materials Science</topic><topic>Functional groups</topic><topic>General Aspects</topic><topic>Markov processes</topic><topic>Normal distribution</topic><topic>Permutations</topic><topic>Physical Chemistry</topic><topic>Rate constants</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kim, I. P.</creatorcontrib><creatorcontrib>Kotkin, A. S.</creatorcontrib><creatorcontrib>Benderskii, V. A.</creatorcontrib><collection>CrossRef</collection><jtitle>High energy chemistry</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kim, I. P.</au><au>Kotkin, A. S.</au><au>Benderskii, V. A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Polycondensation Kinetics: 4. Growth of Acyclic Randomly Branched Chains</atitle><jtitle>High energy chemistry</jtitle><stitle>High Energy Chem</stitle><date>2021-05-01</date><risdate>2021</risdate><volume>55</volume><issue>3</issue><spage>169</spage><epage>178</epage><pages>169-178</pages><issn>0018-1439</issn><eissn>1608-3148</eissn><abstract>Master equations for concentrations of
nb
-mers (
n
is the number of units,
b
is the number of branch points randomly located among the units) in the polycondensation of trifunctional monomers (PC-3) take into account the set of irreversible consecutive–parallel reactions between functional groups (
n
,
b
) and (
n
′,
b
′)-mers with rate constants χ(
b
,
b
′). Stoichiometric coefficients are equal to the number of permutations of bond-forming groups at ∆(
b
+
b
′) = 0, 1, 2. Reaction coordinates are combined into a network of an inhomogeneous Markov process. It is shown that the Flory hypothesis (all χ(
b
,
b
′) values are identical) leads to an explicitly time-independent Gaussian distribution
W
n
(
b
) with a maximum
b
max
that grows linearly with the chain length
n
.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S0018143921030061</doi><tpages>10</tpages></addata></record> |
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| identifier | ISSN: 0018-1439 |
| ispartof | High energy chemistry, 2021-05, Vol.55 (3), p.169-178 |
| issn | 0018-1439 1608-3148 |
| language | eng |
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| source | SpringerLink Journals |
| subjects | Chain branching Chains Chemistry Chemistry and Materials Science Functional groups General Aspects Markov processes Normal distribution Permutations Physical Chemistry Rate constants |
| title | Polycondensation Kinetics: 4. Growth of Acyclic Randomly Branched Chains |
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