Phase transformations in metastable liquids combined with polymerization
This paper is concerned with the theory of nucleation and growth of crystals in a metastable polymer melt with allowance for the polymerization of a monomer. A mathematical model consisting of the heat balance equation, equations governing the particle-radius distribution function and the polymeriza...
Saved in:
Published in | Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences Vol. 377; no. 2143; p. 20180215 |
---|---|
Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
England
The Royal Society Publishing
22.04.2019
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Abstract | This paper is concerned with the theory of nucleation and growth of crystals in a metastable polymer melt with allowance for the polymerization of a monomer. A mathematical model consisting of the heat balance equation, equations governing the particle-radius distribution function and the polymerization degree is formulated. The exact steady-state analytical solutions are found. In the case of unsteady-state crystallization with polymerization, the particle-size distribution function is determined analytically for different space-time regions by means of the Laplace transform. Two functional integro-differential equations governing the dimensionless temperature and polymerization degree are deduced. These equations are solved by means of the saddle-point technique for the evaluation of a Laplace-type integral. The time-dependent distribution function, temperature and polymerization degree at different polymerization rates and nucleation kinetics are derived with allowance for the main contribution to the Laplace-type integral. In addition, the general analytical solution by means of the saddle-point technique and an example showing how to construct the analytical solutions in particular cases are given in the appendices. The analytical method developed in the present paper can be used to describe the similar phase transition phenomena in the presence of chemical reactions. This article is part of the theme issue 'Heterogeneous materials: metastable and non-ergodic internal structures'. |
---|---|
AbstractList | Here, we report on the theory of nucleation and growth of crystals in a metastable polymer melt with allowance for the polymerization of a monomer. A mathematical model consisting of the heat balance equation, equations governing the particle-radius distribution function and the polymerization degree is formulated. The exact steady-state analytical solutions are found. In the case of unsteady-state crystallization with polymerization, the particle-size distribution function is determined analytically for different space–time regions by means of the Laplace transform. Two functional integro-differential equations governing the dimensionless temperature and polymerization degree are deduced. These equations are solved by means of the saddle-point technique for the evaluation of a Laplace-type integral. The time-dependent distribution function, temperature and polymerization degree at different polymerization rates and nucleation kinetics are derived with allowance for the main contribution to the Laplace-type integral. In addition, the general analytical solution by means of the saddle-point technique and an example showing how to construct the analytical solutions in particular cases are given in the appendices. The analytical method developed in this paper can be used to describe the similar phase transition phenomena in the presence of chemical reactions. This paper is concerned with the theory of nucleation and growth of crystals in a metastable polymer melt with allowance for the polymerization of a monomer. A mathematical model consisting of the heat balance equation, equations governing the particle-radius distribution function and the polymerization degree is formulated. The exact steady-state analytical solutions are found. In the case of unsteady-state crystallization with polymerization, the particle-size distribution function is determined analytically for different space–time regions by means of the Laplace transform. Two functional integro-differential equations governing the dimensionless temperature and polymerization degree are deduced. These equations are solved by means of the saddle-point technique for the evaluation of a Laplace-type integral. The time-dependent distribution function, temperature and polymerization degree at different polymerization rates and nucleation kinetics are derived with allowance for the main contribution to the Laplace-type integral. In addition, the general analytical solution by means of the saddle-point technique and an example showing how to construct the analytical solutions in particular cases are given in the appendices. The analytical method developed in the present paper can be used to describe the similar phase transition phenomena in the presence of chemical reactions. This article is part of the theme issue ‘Heterogeneous materials: metastable and non-ergodic internal structures’. This paper is concerned with the theory of nucleation and growth of crystals in a metastable polymer melt with allowance for the polymerization of a monomer. A mathematical model consisting of the heat balance equation, equations governing the particle-radius distribution function and the polymerization degree is formulated. The exact steady-state analytical solutions are found. In the case of unsteady-state crystallization with polymerization, the particle-size distribution function is determined analytically for different space-time regions by means of the Laplace transform. Two functional integro-differential equations governing the dimensionless temperature and polymerization degree are deduced. These equations are solved by means of the saddle-point technique for the evaluation of a Laplace-type integral. The time-dependent distribution function, temperature and polymerization degree at different polymerization rates and nucleation kinetics are derived with allowance for the main contribution to the Laplace-type integral. In addition, the general analytical solution by means of the saddle-point technique and an example showing how to construct the analytical solutions in particular cases are given in the appendices. The analytical method developed in the present paper can be used to describe the similar phase transition phenomena in the presence of chemical reactions. This article is part of the theme issue 'Heterogeneous materials: metastable and non-ergodic internal structures'. |
Author | Ivanov, Alexander A Alexandrov, Dmitri V Alexandrova, Irina V |
AuthorAffiliation | Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling , Ural Federal University , Ekaterinburg 620000 , Russian Federation |
AuthorAffiliation_xml | – name: Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling , Ural Federal University , Ekaterinburg 620000 , Russian Federation |
Author_xml | – sequence: 1 givenname: Alexander A surname: Ivanov fullname: Ivanov, Alexander A organization: Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling , Ural Federal University , Ekaterinburg 620000 , Russian Federation – sequence: 2 givenname: Irina V surname: Alexandrova fullname: Alexandrova, Irina V organization: Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling , Ural Federal University , Ekaterinburg 620000 , Russian Federation – sequence: 3 givenname: Dmitri V surname: Alexandrov fullname: Alexandrov, Dmitri V organization: Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling , Ural Federal University , Ekaterinburg 620000 , Russian Federation |
BackLink | https://www.ncbi.nlm.nih.gov/pubmed/30827217$$D View this record in MEDLINE/PubMed https://www.osti.gov/servlets/purl/1547036$$D View this record in Osti.gov |
BookMark | eNpVkc1L7TAQxYMofm9dSnHlptdkmqTtRpCL7ykIulBwF6Zp6o20yTXJVfSvt33XJ7qagTlz5gy_PbLpvDOEHDE6Y7SuzkJMOAPKqhkFJjbILuMly6GWsDn2heS5oMXjDtmL8ZlSxqSAbbJT0ApKYOUuubpbYDRZCuhi58OAyXoXM-uywSQczZveZL19Wdk2ZtoPjXWmzd5sWmRL378PJtiPfzsHZKvDPprDr7pPHv5c3s-v8pvbv9fzi5tcc8lSXghdaWg7pF0pgLUS6gY5M9gC1BR5AWNo2XFRUtli2QFHQCnrqtHYQSOLfXK-9l2umsG02rgxe6-WwQ4Y3pVHq35PnF2oJ_-qJJeUisngZG3gY7IqapuMXmjvnNFJMcFLWkyi068rwb-sTExqsFGbvkdn_CoqYFVZC8kpG6WztVQHH2Mw3XcWRtXESE2M1MRITYzGheOfH3zL_0MpPgG8O5EW |
CitedBy_id | crossref_primary_10_1140_epjs_s11734_022_00513_w crossref_primary_10_1098_rsta_2018_0210 crossref_primary_10_1098_rsta_2018_0353 crossref_primary_10_1002_mma_9191 crossref_primary_10_1002_mma_7991 crossref_primary_10_1140_epjs_s11734_022_00514_9 crossref_primary_10_1140_epjs_s11734_022_00517_6 crossref_primary_10_1140_epjs_s11734_022_00519_4 crossref_primary_10_1098_rsta_2019_0247 crossref_primary_10_1002_mma_6970 crossref_primary_10_1098_rsta_2019_0246 crossref_primary_10_3390_cryst12111634 crossref_primary_10_1098_rsta_2019_0245 crossref_primary_10_1098_rsta_2020_0325 crossref_primary_10_1098_rsta_2020_0306 crossref_primary_10_1002_mma_7864 crossref_primary_10_1098_rsta_2020_0308 crossref_primary_10_1098_rsta_2020_0307 crossref_primary_10_1098_rsta_2020_0309 crossref_primary_10_1140_epjst_e2020_000037_9 crossref_primary_10_1002_mma_7927 crossref_primary_10_1088_1742_6596_2114_1_012003 crossref_primary_10_1140_epjst_e2019_800201_3 crossref_primary_10_3390_cryst12070949 crossref_primary_10_1140_epjst_e2020_000032_3 crossref_primary_10_1140_epjs_s11734_022_00522_9 crossref_primary_10_1140_epjs_s11734_022_00525_6 crossref_primary_10_1140_epjs_s11734_022_00521_w crossref_primary_10_1140_epjst_e2019_900049_4 crossref_primary_10_1140_epjst_e2020_000113_3 crossref_primary_10_1002_mma_7560 crossref_primary_10_1140_epjst_e2019_900174_5 crossref_primary_10_1002_mma_8112 crossref_primary_10_1098_rsta_2020_0002 crossref_primary_10_1002_mma_6485 crossref_primary_10_1002_mma_6987 crossref_primary_10_1140_epjst_e2019_900081_0 crossref_primary_10_1002_mma_6749 crossref_primary_10_1140_epjst_e2020_000048_8 crossref_primary_10_1140_epjs_s11734_023_00857_x crossref_primary_10_1140_epjst_e2019_900080_6 |
Cites_doi | 10.1016/j.ijheatmasstransfer.2003.08.009 10.1007/BF00851592 10.1021/ma047622f 10.1016/S0017-9310(05)80154-1 10.1016/0022-0248(90)90112-X 10.1021/ma990891z 10.1088/1751-8113/47/12/125102 10.1016/j.physleta.2014.03.051 10.1016/S0967-0661(01)00048-X 10.1016/0009-2509(91)80050-9 10.1016/S0378-4371(97)00561-X 10.1016/j.ijheatmasstransfer.2018.08.119 10.1088/1751-8113/46/45/455101 10.1098/rspa.2013.0647 10.1098/rsta.2017.0327 10.1016/S0022-0248(99)00763-0 10.1021/ma00047a021 10.1002/vnl.730060403 10.1088/0965-0393/22/1/015003 10.1098/rsta.2018.0209 10.1021/ma00030a022 10.1002/app.1979.070230210 10.1016/S0017-9310(05)80153-X 10.1088/1751-8121/aaa5b7 |
ContentType | Journal Article |
Copyright | 2019 The Author(s) 2019 |
Copyright_xml | – notice: 2019 The Author(s) 2019 |
CorporateAuthor | SLAC National Accelerator Lab., Menlo Park, CA (United States) |
CorporateAuthor_xml | – name: SLAC National Accelerator Lab., Menlo Park, CA (United States) |
DBID | NPM AAYXX CITATION 7X8 OIOZB OTOTI 5PM |
DOI | 10.1098/rsta.2018.0215 |
DatabaseName | PubMed CrossRef MEDLINE - Academic OSTI.GOV - Hybrid OSTI.GOV PubMed Central (Full Participant titles) |
DatabaseTitle | PubMed CrossRef MEDLINE - Academic |
DatabaseTitleList | CrossRef PubMed |
Database_xml | – sequence: 1 dbid: NPM name: PubMed url: https://proxy.k.utb.cz/login?url=http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed sourceTypes: Index Database |
DeliveryMethod | fulltext_linktorsrc |
Discipline | Engineering Mathematics Sciences (General) Physics |
DocumentTitleAlternate | Phase transitions with polymerization |
EISSN | 1471-2962 |
EndPage | 20180215 |
ExternalDocumentID | 1547036 10_1098_rsta_2018_0215 30827217 |
Genre | Journal Article |
GrantInformation_xml | – fundername: ; grantid: 18-19-00008 |
GroupedDBID | --- -~X 0R~ 18M 2WC 4.4 5VS AACGO AANCE ABBHK ABFAN ABPLY ABTLG ABXSQ ABYWD ACGFO ACIWK ACMTB ACNCT ACQIA ACTMH ADACV ADBBV ADODI AEUPB AEXZC AFVYC ALMA_UNASSIGNED_HOLDINGS ALMYZ AQVQM BTFSW DCCCD DIK DOOOF DQDLB DSRWC EBS ECEWR EJD F5P H13 HH5 HQ6 HZ~ IPSME JAAYA JBMMH JENOY JHFFW JKQEH JLS JLXEF JMS JPM JSG JST KQ8 MRS MV1 NPM NSAHA O9- OK1 OP1 P2P RHF RRY SA0 TN5 TR2 V1E W8F XSW YNT ~02 AAYXX CITATION 7X8 79B ABPTK ABXXB ADZLD AFXKK DNJUQ DWIUU EFSUC ICLEN JSODD OIOZB OTOTI 5PM |
ID | FETCH-LOGICAL-c461t-35c8c2dfa0f7521d629ba41ead2290a4321366f45706da7f24a2a6698bcaf2b63 |
ISSN | 1364-503X |
IngestDate | Tue Sep 17 21:12:06 EDT 2024 Thu May 18 22:32:29 EDT 2023 Sat Aug 17 00:19:18 EDT 2024 Thu Sep 26 19:33:15 EDT 2024 Sat Sep 28 08:28:07 EDT 2024 |
IsDoiOpenAccess | true |
IsOpenAccess | true |
IsPeerReviewed | true |
IsScholarly | true |
Issue | 2143 |
Keywords | crystallization nucleation polymerization metastable liquid |
Language | English |
License | Published by the Royal Society. All rights reserved. |
LinkModel | OpenURL |
MergedId | FETCHMERGED-LOGICAL-c461t-35c8c2dfa0f7521d629ba41ead2290a4321366f45706da7f24a2a6698bcaf2b63 |
Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 USDOE AC02-76SF00515 One contribution of 17 to a theme issue ‘Heterogeneous materials: metastable and non-ergodic internal structures’. |
ORCID | 0000-0002-2490-160X 0000-0002-6628-745X 000000026628745X 000000022490160X |
OpenAccessLink | https://www.osti.gov/servlets/purl/1547036 |
PMID | 30827217 |
PQID | 2187956401 |
PQPubID | 23479 |
PageCount | 1 |
ParticipantIDs | pubmedcentral_primary_oai_pubmedcentral_nih_gov_6460056 osti_scitechconnect_1547036 proquest_miscellaneous_2187956401 crossref_primary_10_1098_rsta_2018_0215 pubmed_primary_30827217 |
PublicationCentury | 2000 |
PublicationDate | 2019-04-22 |
PublicationDateYYYYMMDD | 2019-04-22 |
PublicationDate_xml | – month: 04 year: 2019 text: 2019-04-22 day: 22 |
PublicationDecade | 2010 |
PublicationPlace | England |
PublicationPlace_xml | – name: England – name: United States |
PublicationTitle | Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences |
PublicationTitleAlternate | Philos Trans A Math Phys Eng Sci |
PublicationYear | 2019 |
Publisher | The Royal Society Publishing |
Publisher_xml | – name: The Royal Society Publishing |
References | Barrett KEJ (e_1_3_6_7_2) 1975 Heiskanen T (e_1_3_6_9_2) 1985; 165 e_1_3_6_30_2 e_1_3_6_31_2 Sharplez A (e_1_3_6_10_2) 1966 Fedoruk MV (e_1_3_6_27_2) 1977 e_1_3_6_19_2 e_1_3_6_14_2 e_1_3_6_13_2 e_1_3_6_12_2 e_1_3_6_11_2 e_1_3_6_18_2 e_1_3_6_17_2 e_1_3_6_16_2 e_1_3_6_15_2 e_1_3_6_21_2 e_1_3_6_5_2 e_1_3_6_4_2 Nývlt J (e_1_3_6_20_2) 1985 e_1_3_6_3_2 e_1_3_6_2_2 e_1_3_6_6_2 e_1_3_6_26_2 e_1_3_6_28_2 e_1_3_6_29_2 Ballard MJ (e_1_3_6_8_2) 1984; 22 e_1_3_6_22_2 e_1_3_6_23_2 e_1_3_6_24_2 e_1_3_6_25_2 |
References_xml | – ident: e_1_3_6_31_2 doi: 10.1016/j.ijheatmasstransfer.2003.08.009 – volume-title: Saddle-point method year: 1977 ident: e_1_3_6_27_2 contributor: fullname: Fedoruk MV – ident: e_1_3_6_17_2 doi: 10.1007/BF00851592 – ident: e_1_3_6_13_2 doi: 10.1021/ma047622f – volume-title: Dispersion polymerization in organic media year: 1975 ident: e_1_3_6_7_2 contributor: fullname: Barrett KEJ – ident: e_1_3_6_29_2 doi: 10.1016/S0017-9310(05)80154-1 – volume-title: Crystallization of polymers year: 1966 ident: e_1_3_6_10_2 contributor: fullname: Sharplez A – ident: e_1_3_6_2_2 doi: 10.1016/0022-0248(90)90112-X – ident: e_1_3_6_12_2 doi: 10.1021/ma990891z – ident: e_1_3_6_23_2 doi: 10.1088/1751-8113/47/12/125102 – ident: e_1_3_6_5_2 doi: 10.1016/j.physleta.2014.03.051 – volume: 22 start-page: 3225 year: 1984 ident: e_1_3_6_8_2 article-title: Kinetics of emulsion polymerization of methyl methacrylate publication-title: J. Polymer Sci. contributor: fullname: Ballard MJ – ident: e_1_3_6_18_2 doi: 10.1016/S0967-0661(01)00048-X – volume: 165 start-page: 1 year: 1985 ident: e_1_3_6_9_2 article-title: Mathematical model for continuous emulsion polymerization of vinyl chloride and its steady-state solution publication-title: Acta Polytech. Scand. contributor: fullname: Heiskanen T – ident: e_1_3_6_21_2 doi: 10.1016/0009-2509(91)80050-9 – ident: e_1_3_6_19_2 doi: 10.1016/S0378-4371(97)00561-X – ident: e_1_3_6_25_2 doi: 10.1016/j.ijheatmasstransfer.2018.08.119 – ident: e_1_3_6_3_2 doi: 10.1088/1751-8113/46/45/455101 – ident: e_1_3_6_4_2 doi: 10.1098/rspa.2013.0647 – ident: e_1_3_6_6_2 doi: 10.1098/rsta.2017.0327 – ident: e_1_3_6_30_2 doi: 10.1016/S0022-0248(99)00763-0 – ident: e_1_3_6_11_2 doi: 10.1021/ma00047a021 – ident: e_1_3_6_15_2 doi: 10.1002/vnl.730060403 – ident: e_1_3_6_22_2 doi: 10.1088/0965-0393/22/1/015003 – ident: e_1_3_6_26_2 doi: 10.1098/rsta.2018.0209 – ident: e_1_3_6_16_2 doi: 10.1021/ma00030a022 – ident: e_1_3_6_14_2 doi: 10.1002/app.1979.070230210 – volume-title: The kinetics of industrial crystallization year: 1985 ident: e_1_3_6_20_2 contributor: fullname: Nývlt J – ident: e_1_3_6_28_2 doi: 10.1016/S0017-9310(05)80153-X – ident: e_1_3_6_24_2 doi: 10.1088/1751-8121/aaa5b7 |
SSID | ssj0011652 |
Score | 2.5431478 |
Snippet | This paper is concerned with the theory of nucleation and growth of crystals in a metastable polymer melt with allowance for the polymerization of a monomer. A... Here, we report on the theory of nucleation and growth of crystals in a metastable polymer melt with allowance for the polymerization of a monomer. A... |
SourceID | pubmedcentral osti proquest crossref pubmed |
SourceType | Open Access Repository Aggregation Database Index Database |
StartPage | 20180215 |
SubjectTerms | CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY crystallization metastable liquid nucleation polymerization |
Title | Phase transformations in metastable liquids combined with polymerization |
URI | https://www.ncbi.nlm.nih.gov/pubmed/30827217 https://search.proquest.com/docview/2187956401 https://www.osti.gov/servlets/purl/1547036 https://pubmed.ncbi.nlm.nih.gov/PMC6460056 |
Volume | 377 |
hasFullText | 1 |
inHoldings | 1 |
isFullTextHit | |
isPrint | |
link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3fb5RAEN6cZ0z0wdj6C6sGExM1F66wLAs8NkZz1dRo0pq-kd0FUkwL9eCa2H_Sf8mZZYHjvIfqC-EWFjjmY2Z2d-YbQl5HsWTMd4UD5k45THrKiXMuHVfEvgQASVfhPOTRF744YZ9Og9PJ5Pda1NKqkXN1vTWv5H-kCm0gV8yS_QfJ9heFBtgH-cIWJAzbG8n46xnYIKzy0PueJi78ImsEuH2YFXVe_FwVaY2x4zAI7oLNL6vzX7hWcz0I5kd3TVPbQEuvGcqJ1104QTvj0IV74hqDLgkyR70D4-6ZnrI_6ulgdUUBM4PS7uNcfTbwIM6MFe69-0Pw7qurUfrN7GDeQ7NtW1ZX2u89hEuI2fcth7U6vSiaZdEdNrMbnl6ooWsTnp7PmRO4umYw2Ku2DQyqQ-OxFvdNNZgWrtRj_rpaRpoy2uaN_mUz3BjzIDCPCCP9onl34pice8No9qGM7SJ-lGD_BPsn2P8WuU3DOMAY08_fhmUtj-sSUP2f6llEo_3x_Ude0rQCbb9tBLQZyLvmGR0_IPfNkMY-aPG5QyZZuUvurRFdwq8BDvUuuaPDjnFvx5iW2n5r-M_fPSQLDWt7A9Z2UdoDrG0Da7uDtY2wtsewfkROPn44fr9wTMEPRzHuNY4fqEjRNBduHoJbmXIaS8E8UHZYlUAwn8Kb4zkLQpenIswpE1RwHkdSiZxK7j8m07Iqs6fE5mnAFPQB_zpgvq8kbLmgmB8IQwAZWeRN94KTy5bXJdkuSovs4ftP4FtAWmWF8WeqSWDogdx1FnnViSUBxYyrbaLMqlWdgO8MCODM9SzypBVTfyfkiAqpF1okHAmwPwFJ38dHyuJMk79zxpG-99mNn3-P3B0-rOdk2ixX2QtwpBv5UoPzDydJzLA |
link.rule.ids | 230,315,786,790,891,27955,27956 |
linkProvider | Colorado Alliance of Research Libraries |
openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Phase+transformations+in+metastable+liquids+combined+with+polymerization&rft.jtitle=Philosophical+transactions+of+the+Royal+Society+of+London.+Series+A%3A+Mathematical%2C+physical%2C+and+engineering+sciences&rft.au=Ivanov%2C+Alexander+A.&rft.au=Alexandrova%2C+Irina+V.&rft.au=Alexandrov%2C+Dmitri+V.&rft.date=2019-04-22&rft.issn=1364-503X&rft.eissn=1471-2962&rft.volume=377&rft.issue=2143&rft.spage=20180215&rft_id=info:doi/10.1098%2Frsta.2018.0215&rft.externalDBID=n%2Fa&rft.externalDocID=10_1098_rsta_2018_0215 |
thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1364-503X&client=summon |
thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1364-503X&client=summon |
thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1364-503X&client=summon |