Universality of block copolymer melts. Glaser, J., Medapuram, P., Beardsley, T. M., Matsen, M. W., & Morse, D. C. Physical Review Letters, 113(6):068302, August, 2014. arXiv: 1402.1118![Universality of block copolymer melts [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper doi abstract bibtex Simulations of five different coarse-grained models of symmetric diblock copolymers are compared to demonstrate a universal (i.e., model-independent) dependence of the free energy and order-disorder transition (ODT) on the invariant degree of polymerization ¯ N. The actual values of χN at the ODT approach predictions of the Fredrickson-Helfand (FH) theory for ¯ N ≳ 10 4 but significantly exceed FH predictions at lower values characteristic of most experiments. The FH theory fails for modest ¯ N because the competing phases become strongly segregated near the ODT, violating an underlying assumption of weak segregation. DOI: 10.1103/PhysRevLett.113.068302 PACS numbers: 82.35.Jk, 64.60.De, 64.70.km Universality is a powerful feature of polymer physics that allows the behavior of real systems to be predicted on the basis of simple generic models. The best example of this is the scaling theory of dilute and semidilute polymer solutions in good solvent [1–3]. This theory predicts a universal dependence on two thermodynamic state param-eters—an excluded volume parameter and an overlap parameter. Experimental verification of this scaling hypoth-esis [3–5] was a key step in the development of a very sophisticated understanding of polymer solutions. Here, we use computer simulations to verify an analogous scaling hypothesis regarding the thermodynamics of block copolymers and to study universal characteristics of the order-disorder transition (ODT). We consider a dense liquid of AB diblock copolymers, with N monomers per chain, and a fraction f A of A monomers. We focus on the symmetric case f A ¼ 1=2. Self-consistent field theory (SCFT) is the dominant theo-retical approach for block copolymers [6–8]. SCFT describes polymers as random walks with a monomer statistical segment length b, which we take to be equal for A and B monomers. The free energy cost of contact between A and B monomers is characterized by an effective Flory-Huggins interaction parameter χ e . Let g denote a dimen-sionless excess free energy per chain, normalized by the thermal energy k B T. SCFT predicts a free energy g for each phase that depends only upon f A and the product χ e N, or upon χ e N alone for f A ¼ 1=2. This yields a predicted phase diagram [6,7] that likewise depends only on f A and χ e N. For f A ¼ 1=2, SCFT predicts a transition between the disordered and lamellar phases at ðχ e NÞ ODT ¼ 10.495. SCFT has long been believed to be exact in the limit of infinitely long, strongly interpenetrating polymers [9,10]. The degree of interpenetration in a polymer liquid may be characterized by a dimensionless concentration ¯ C ≡ cR 3 =N, in which c is monomer concentration, c=N is molecule concentration, and R ¼ ffiffiffiffi N p b is coil size. Alternatively, we may use the invariant degree of polym-erization ¯ N ≡ ¯ C
@article{Glaser2014,
title = {Universality of block copolymer melts},
volume = {113},
issn = {10797114},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.113.068302},
doi = {10.1103/PhysRevLett.113.068302},
abstract = {Simulations of five different coarse-grained models of symmetric diblock copolymers are compared to demonstrate a universal (i.e., model-independent) dependence of the free energy and order-disorder transition (ODT) on the invariant degree of polymerization ¯ N. The actual values of χN at the ODT approach predictions of the Fredrickson-Helfand (FH) theory for ¯ N ≳ 10 4 but significantly exceed FH predictions at lower values characteristic of most experiments. The FH theory fails for modest ¯ N because the competing phases become strongly segregated near the ODT, violating an underlying assumption of weak segregation. DOI: 10.1103/PhysRevLett.113.068302 PACS numbers: 82.35.Jk, 64.60.De, 64.70.km Universality is a powerful feature of polymer physics that allows the behavior of real systems to be predicted on the basis of simple generic models. The best example of this is the scaling theory of dilute and semidilute polymer solutions in good solvent [1–3]. This theory predicts a universal dependence on two thermodynamic state param-eters—an excluded volume parameter and an overlap parameter. Experimental verification of this scaling hypoth-esis [3–5] was a key step in the development of a very sophisticated understanding of polymer solutions. Here, we use computer simulations to verify an analogous scaling hypothesis regarding the thermodynamics of block copolymers and to study universal characteristics of the order-disorder transition (ODT). We consider a dense liquid of AB diblock copolymers, with N monomers per chain, and a fraction f A of A monomers. We focus on the symmetric case f A ¼ 1=2. Self-consistent field theory (SCFT) is the dominant theo-retical approach for block copolymers [6–8]. SCFT describes polymers as random walks with a monomer statistical segment length b, which we take to be equal for A and B monomers. The free energy cost of contact between A and B monomers is characterized by an effective Flory-Huggins interaction parameter χ e . Let g denote a dimen-sionless excess free energy per chain, normalized by the thermal energy k B T. SCFT predicts a free energy g for each phase that depends only upon f A and the product χ e N, or upon χ e N alone for f A ¼ 1=2. This yields a predicted phase diagram [6,7] that likewise depends only on f A and χ e N. For f A ¼ 1=2, SCFT predicts a transition between the disordered and lamellar phases at ðχ e NÞ ODT ¼ 10.495. SCFT has long been believed to be exact in the limit of infinitely long, strongly interpenetrating polymers [9,10]. The degree of interpenetration in a polymer liquid may be characterized by a dimensionless concentration ¯ C ≡ cR 3 =N, in which c is monomer concentration, c=N is molecule concentration, and R ¼ ffiffiffiffi N p b is coil size. Alternatively, we may use the invariant degree of polym-erization ¯ N ≡ ¯ C},
number = {6},
urldate = {2014-10-17},
journal = {Physical Review Letters},
author = {Glaser, Jens and Medapuram, Pavani and Beardsley, Thomas M. and Matsen, Mark W. and Morse, David C.},
month = aug,
year = {2014},
note = {arXiv: 1402.1118},
pages = {068302},
}
Downloads: 0
{"_id":"M6QdyXSvtcmupQt9t","bibbaseid":"glaser-medapuram-beardsley-matsen-morse-universalityofblockcopolymermelts-2014","downloads":0,"creationDate":"2018-11-12T00:32:22.002Z","title":"Universality of block copolymer melts","author_short":["Glaser, J.","Medapuram, P.","Beardsley, T. M.","Matsen, M. W.","Morse, D. C."],"year":2014,"bibtype":"article","biburl":"https://api.zotero.org/groups/5315842/items?key=aJYPXNdgkztwX5veTDCe51qx&format=bibtex&limit=100","bibdata":{"bibtype":"article","type":"article","title":"Universality of block copolymer melts","volume":"113","issn":"10797114","url":"http://link.aps.org/doi/10.1103/PhysRevLett.113.068302","doi":"10.1103/PhysRevLett.113.068302","abstract":"Simulations of five different coarse-grained models of symmetric diblock copolymers are compared to demonstrate a universal (i.e., model-independent) dependence of the free energy and order-disorder transition (ODT) on the invariant degree of polymerization ¯ N. The actual values of χN at the ODT approach predictions of the Fredrickson-Helfand (FH) theory for ¯ N ≳ 10 4 but significantly exceed FH predictions at lower values characteristic of most experiments. The FH theory fails for modest ¯ N because the competing phases become strongly segregated near the ODT, violating an underlying assumption of weak segregation. DOI: 10.1103/PhysRevLett.113.068302 PACS numbers: 82.35.Jk, 64.60.De, 64.70.km Universality is a powerful feature of polymer physics that allows the behavior of real systems to be predicted on the basis of simple generic models. The best example of this is the scaling theory of dilute and semidilute polymer solutions in good solvent [1–3]. This theory predicts a universal dependence on two thermodynamic state param-eters—an excluded volume parameter and an overlap parameter. Experimental verification of this scaling hypoth-esis [3–5] was a key step in the development of a very sophisticated understanding of polymer solutions. Here, we use computer simulations to verify an analogous scaling hypothesis regarding the thermodynamics of block copolymers and to study universal characteristics of the order-disorder transition (ODT). We consider a dense liquid of AB diblock copolymers, with N monomers per chain, and a fraction f A of A monomers. We focus on the symmetric case f A ¼ 1=2. Self-consistent field theory (SCFT) is the dominant theo-retical approach for block copolymers [6–8]. SCFT describes polymers as random walks with a monomer statistical segment length b, which we take to be equal for A and B monomers. The free energy cost of contact between A and B monomers is characterized by an effective Flory-Huggins interaction parameter χ e . Let g denote a dimen-sionless excess free energy per chain, normalized by the thermal energy k B T. SCFT predicts a free energy g for each phase that depends only upon f A and the product χ e N, or upon χ e N alone for f A ¼ 1=2. This yields a predicted phase diagram [6,7] that likewise depends only on f A and χ e N. For f A ¼ 1=2, SCFT predicts a transition between the disordered and lamellar phases at ðχ e NÞ ODT ¼ 10.495. SCFT has long been believed to be exact in the limit of infinitely long, strongly interpenetrating polymers [9,10]. The degree of interpenetration in a polymer liquid may be characterized by a dimensionless concentration ¯ C ≡ cR 3 =N, in which c is monomer concentration, c=N is molecule concentration, and R ¼ ffiffiffiffi N p b is coil size. Alternatively, we may use the invariant degree of polym-erization ¯ N ≡ ¯ C","number":"6","urldate":"2014-10-17","journal":"Physical Review Letters","author":[{"propositions":[],"lastnames":["Glaser"],"firstnames":["Jens"],"suffixes":[]},{"propositions":[],"lastnames":["Medapuram"],"firstnames":["Pavani"],"suffixes":[]},{"propositions":[],"lastnames":["Beardsley"],"firstnames":["Thomas","M."],"suffixes":[]},{"propositions":[],"lastnames":["Matsen"],"firstnames":["Mark","W."],"suffixes":[]},{"propositions":[],"lastnames":["Morse"],"firstnames":["David","C."],"suffixes":[]}],"month":"August","year":"2014","note":"arXiv: 1402.1118","pages":"068302","bibtex":"@article{Glaser2014,\n\ttitle = {Universality of block copolymer melts},\n\tvolume = {113},\n\tissn = {10797114},\n\turl = {http://link.aps.org/doi/10.1103/PhysRevLett.113.068302},\n\tdoi = {10.1103/PhysRevLett.113.068302},\n\tabstract = {Simulations of five different coarse-grained models of symmetric diblock copolymers are compared to demonstrate a universal (i.e., model-independent) dependence of the free energy and order-disorder transition (ODT) on the invariant degree of polymerization ¯ N. The actual values of χN at the ODT approach predictions of the Fredrickson-Helfand (FH) theory for ¯ N ≳ 10 4 but significantly exceed FH predictions at lower values characteristic of most experiments. The FH theory fails for modest ¯ N because the competing phases become strongly segregated near the ODT, violating an underlying assumption of weak segregation. DOI: 10.1103/PhysRevLett.113.068302 PACS numbers: 82.35.Jk, 64.60.De, 64.70.km Universality is a powerful feature of polymer physics that allows the behavior of real systems to be predicted on the basis of simple generic models. The best example of this is the scaling theory of dilute and semidilute polymer solutions in good solvent [1–3]. This theory predicts a universal dependence on two thermodynamic state param-eters—an excluded volume parameter and an overlap parameter. Experimental verification of this scaling hypoth-esis [3–5] was a key step in the development of a very sophisticated understanding of polymer solutions. Here, we use computer simulations to verify an analogous scaling hypothesis regarding the thermodynamics of block copolymers and to study universal characteristics of the order-disorder transition (ODT). We consider a dense liquid of AB diblock copolymers, with N monomers per chain, and a fraction f A of A monomers. We focus on the symmetric case f A ¼ 1=2. Self-consistent field theory (SCFT) is the dominant theo-retical approach for block copolymers [6–8]. SCFT describes polymers as random walks with a monomer statistical segment length b, which we take to be equal for A and B monomers. The free energy cost of contact between A and B monomers is characterized by an effective Flory-Huggins interaction parameter χ e . Let g denote a dimen-sionless excess free energy per chain, normalized by the thermal energy k B T. SCFT predicts a free energy g for each phase that depends only upon f A and the product χ e N, or upon χ e N alone for f A ¼ 1=2. This yields a predicted phase diagram [6,7] that likewise depends only on f A and χ e N. For f A ¼ 1=2, SCFT predicts a transition between the disordered and lamellar phases at ðχ e NÞ ODT ¼ 10.495. SCFT has long been believed to be exact in the limit of infinitely long, strongly interpenetrating polymers [9,10]. The degree of interpenetration in a polymer liquid may be characterized by a dimensionless concentration ¯ C ≡ cR 3 =N, in which c is monomer concentration, c=N is molecule concentration, and R ¼ ffiffiffiffi N p b is coil size. Alternatively, we may use the invariant degree of polym-erization ¯ N ≡ ¯ C},\n\tnumber = {6},\n\turldate = {2014-10-17},\n\tjournal = {Physical Review Letters},\n\tauthor = {Glaser, Jens and Medapuram, Pavani and Beardsley, Thomas M. and Matsen, Mark W. and Morse, David C.},\n\tmonth = aug,\n\tyear = {2014},\n\tnote = {arXiv: 1402.1118},\n\tpages = {068302},\n}\n\n","author_short":["Glaser, J.","Medapuram, P.","Beardsley, T. M.","Matsen, M. W.","Morse, D. C."],"key":"Glaser2014","id":"Glaser2014","bibbaseid":"glaser-medapuram-beardsley-matsen-morse-universalityofblockcopolymermelts-2014","role":"author","urls":{"Paper":"http://link.aps.org/doi/10.1103/PhysRevLett.113.068302"},"metadata":{"authorlinks":{}}},"search_terms":["universality","block","copolymer","melts","glaser","medapuram","beardsley","matsen","morse"],"keywords":[],"authorIDs":[],"dataSources":["eJ9d2SWWJDCrSLaKb"]}