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Hanel R, Thurner S. Equivalence of information production and generalised entropies in complex processes. PLoS One 2023; 18:e0290695. [PMID: 37672525 PMCID: PMC10482297 DOI: 10.1371/journal.pone.0290695] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2023] [Accepted: 08/15/2023] [Indexed: 09/08/2023] Open
Abstract
Complex systems with strong correlations and fat-tailed distribution functions have been argued to be incompatible with the Boltzmann-Gibbs entropy framework and alternatives, so-called generalised entropies, were proposed and studied. Here we show, that this perceived incompatibility is actually a misconception. For a broad class of processes, Boltzmann entropy -the log multiplicity- remains the valid entropy concept. However, for non-i.i.d. processes, Boltzmann entropy is not of Shannon form, -k∑ipi log pi, but takes the shape of generalised entropies. We derive this result for all processes that can be asymptotically mapped to adjoint representations reversibly where processes are i.i.d. In these representations the information production is given by the Shannon entropy. Over the original sampling space this yields functionals identical to generalised entropies. The problem of constructing adequate context-sensitive entropy functionals therefore can be translated into the much simpler problem of finding adjoint representations. The method provides a comprehensive framework for a statistical physics of strongly correlated systems and complex processes.
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Affiliation(s)
- Rudolf Hanel
- Section for Science of Complex Systems, CeMDS, Medical University of Vienna, Vienna, Austria
- Complexity Science Hub Vienna, Vienna, Austria
| | - Stefan Thurner
- Section for Science of Complex Systems, CeMDS, Medical University of Vienna, Vienna, Austria
- Complexity Science Hub Vienna, Vienna, Austria
- Santa Fe Institute, NM, Santa Fe, NM, United States of America
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2
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McKenna GB, Chen D, Mangalara SCH, Kong D, Banik S. Some open challenges in polymer physics*. POLYM ENG SCI 2022. [DOI: 10.1002/pen.25938] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Gregory B. McKenna
- Department of Chemical Engineering Texas Tech University Lubbock Texas USA
- Department of Chemical and Biomolecular Engineering North Carolina State University Raleigh North Carolina USA
| | - Dongjie Chen
- Department of Chemical Engineering Texas Tech University Lubbock Texas USA
| | | | - Dejie Kong
- Department of Chemical Engineering Texas Tech University Lubbock Texas USA
| | - Sourya Banik
- Department of Chemical Engineering Texas Tech University Lubbock Texas USA
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3
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Jia XM, Lin WF, Zhao HY, Qian HJ, Lu ZY. Supercooled melt structure and dynamics of single-chain nanoparticles: A computer simulation study. J Chem Phys 2021; 155:054901. [PMID: 34364327 DOI: 10.1063/5.0056293] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
By using coarse-grained molecular dynamics simulations, we have investigated the structure and dynamics of supercooled single-chain cross-linked nanoparticle (SCNP) melts having a range of cross-linking degrees ϕ. We find a nearly linear increase in glass-transition temperature (Tg) with increasing ϕ. Correspondingly, we have also experimentally synthesized a series of polystyrene-based SCNPs and have found that the measured Tg estimated from differential scanning calorimetry is qualitatively consistent with the trend predicted by our simulation estimates. Experimentally, an increase in Tg as large as ΔTg = 61 K for ϕ = 0.36 is found compared with their linear chain counterparts, indicating that the changes in dynamics with cross-links are quite appreciable. We attribute the increase in Tg to the enlarged effective hard-core volume and the corresponding reduction in the free volume of the polymer segments. Topological constraints evidently frustrate the local packing. In addition, the introduction of intra-molecular cross-linking bonds slows down the structural relaxation and simultaneously enhances the local coupling motion on the length scales within SCNPs. Consequently, a more pronounced dynamical heterogeneity (DH) is observed for larger ϕ, as quantified by measuring the dynamical correlation length through the four-point susceptibility parameter, χ4. The increase in DH is directly related to the enhanced local cooperative motion derived from intra-molecular cross-linking bonds and structural heterogeneity derived from the cross-linking process. These results shed new light on the influence of intra-molecular topological constraints on the segmental dynamics of polymer melts.
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Affiliation(s)
- Xiang-Meng Jia
- State Key Laboratory of Supramolecular Structure and Materials, Institute of Theoretical Chemistry, Jilin University, Changchun 130021, China
| | - Wen-Feng Lin
- State Key Laboratory of Supramolecular Structure and Materials, Institute of Theoretical Chemistry, Jilin University, Changchun 130021, China
| | - Huan-Yu Zhao
- State Key Laboratory of Supramolecular Structure and Materials, Institute of Theoretical Chemistry, Jilin University, Changchun 130021, China
| | - Hu-Jun Qian
- State Key Laboratory of Supramolecular Structure and Materials, Institute of Theoretical Chemistry, Jilin University, Changchun 130021, China
| | - Zhong-Yuan Lu
- State Key Laboratory of Supramolecular Structure and Materials, Institute of Theoretical Chemistry, Jilin University, Changchun 130021, China
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Xu X, Douglas JF, Xu WS. Influence of Side-Chain Length and Relative Rigidities of Backbone and Side Chains on Glass Formation of Branched Polymers. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c00834] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Xiaolei Xu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
| | - Jack F. Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Wen-Sheng Xu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
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Xu WS, Douglas JF, Sun ZY. Polymer Glass Formation: Role of Activation Free Energy, Configurational Entropy, and Collective Motion. Macromolecules 2021. [DOI: 10.1021/acs.macromol.0c02740] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- Wen-Sheng Xu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
| | - Jack F. Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Zhao-Yan Sun
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
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Xu WS, Douglas JF, Xia W, Xu X. Understanding Activation Volume in Glass-Forming Polymer Melts via Generalized Entropy Theory. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c01269] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Affiliation(s)
- Wen-Sheng Xu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
| | - Jack F. Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Wenjie Xia
- Department of Civil and Environmental Engineering, North Dakota State University, Fargo, North Dakota 58108, United States
| | - Xiaolei Xu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
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7
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Xu WS, Douglas JF, Xu X. Molecular Dynamics Study of Glass Formation in Polymer Melts with Varying Chain Stiffness. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c00731] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Affiliation(s)
- Wen-Sheng Xu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
| | - Jack F. Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Xiaolei Xu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
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8
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Alesadi A, Xia W. Understanding the Role of Cohesive Interaction in Mechanical Behavior of a Glassy Polymer. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c00067] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Affiliation(s)
- Amirhadi Alesadi
- Department of Civil & Environmental Engineering, North Dakota State University, Fargo, North Dakota 58108, United States
| | - Wenjie Xia
- Department of Civil & Environmental Engineering, North Dakota State University, Fargo, North Dakota 58108, United States
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Ginzburg VV. A simple mean-field model of glassy dynamics and glass transition. SOFT MATTER 2020; 16:810-825. [PMID: 31840706 DOI: 10.1039/c9sm01575b] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We propose a phenomenological model to describe the equilibrium dynamic behavior of amorphous glassy materials. It is assumed that a material can be represented by a lattice of cooperatively re-arranging regions (CRRs), with each CRR having two states, the low-temperature "solid" and the high-temperature "liquid". At low temperatures, the material exhibits two characteristic relaxation times, corresponding to the slow large-scale motion between the "solid" CRRs (α-relaxation) and the faster local motion within individual CRRs (β-relaxation). At high temperatures, the α- and β-relaxation times merge, as observed experimentally and suggested by the "Coupling Model" framework. Our new approach is labeled "Two-state, two (time)scale model" or TS2. It is shown that the TS2 treatment can successfully describe the "two-Arrhenius" relaxation time behavior described in several recent experiments. We also apply TS2 to describe the pressure- and molecular-weight dependence of the glass transition temperature in bulk polymers, as well as its dependence on film thickness in thin films.
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Affiliation(s)
- Valeriy V Ginzburg
- Core Research and Development, The Dow Chemical Company, Midland, MI 48674, USA.
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Xu W, Xia W. Energy Renormalization for Coarse‐Graining Polymers with Different Fragilities: Predictions from the Generalized Entropy Theory. MACROMOL THEOR SIMUL 2020. [DOI: 10.1002/mats.201900051] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Wen‐Sheng Xu
- State Key Laboratory of Polymer Physics and Chemistry Changchun Institute of Applied Chemistry, Chinese Academy of Sciences Changchun 130022 P. R. China
| | - Wenjie Xia
- Department of Civil & Environmental Engineering North Dakota State University Fargo ND 58108 USA
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11
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Zou W, Moghadam S, Hoy RS, Larson RG. Multiscale Modeling of Sub-Entanglement-Scale Chain Stretching and Strain Hardening in Deformed Polymeric Glasses. Macromolecules 2019. [DOI: 10.1021/acs.macromol.9b00901] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Weizhong Zou
- Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Soroush Moghadam
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Robert S. Hoy
- Department of Physics, University of South Florida, Tampa, Florida 33620, United States
| | - Ronald G. Larson
- Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States
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12
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Qian Z, Cao Z, Galuska L, Zhang S, Xu J, Gu X. Glass Transition Phenomenon for Conjugated Polymers. MACROMOL CHEM PHYS 2019. [DOI: 10.1002/macp.201900062] [Citation(s) in RCA: 48] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Affiliation(s)
- Zhiyuan Qian
- School of Polymer Science and Engineering Center for Optoelectronic Materials and Device The University of Southern Mississippi Hattiesburg MS 39406 USA
| | - Zhiqiang Cao
- School of Polymer Science and Engineering Center for Optoelectronic Materials and Device The University of Southern Mississippi Hattiesburg MS 39406 USA
| | - Luke Galuska
- School of Polymer Science and Engineering Center for Optoelectronic Materials and Device The University of Southern Mississippi Hattiesburg MS 39406 USA
| | - Song Zhang
- School of Polymer Science and Engineering Center for Optoelectronic Materials and Device The University of Southern Mississippi Hattiesburg MS 39406 USA
| | - Jie Xu
- Argonne National Laboratory Lemont IL 60439 USA
| | - Xiaodan Gu
- School of Polymer Science and Engineering Center for Optoelectronic Materials and Device The University of Southern Mississippi Hattiesburg MS 39406 USA
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13
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Vural D, Smith JC, Petridis L. Dynamics of the lignin glass transition. Phys Chem Chem Phys 2018; 20:20504-20512. [DOI: 10.1039/c8cp03144d] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
Despite lignin being a heterogenous polyphenolic, its glass transition obeys well-established polymer theory concepts.
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Affiliation(s)
- Derya Vural
- UT/ORNL Center for Molecular Biophysics
- Oak Ridge National Laboratory
- Tennessee 37831
- USA
- Department of Physics, Giresun University
| | - Jeremy C. Smith
- UT/ORNL Center for Molecular Biophysics
- Oak Ridge National Laboratory
- Tennessee 37831
- USA
- Department of Biochemistry and Cellular and Molecular Biology, University of Tennessee
| | - Loukas Petridis
- UT/ORNL Center for Molecular Biophysics
- Oak Ridge National Laboratory
- Tennessee 37831
- USA
- Department of Biochemistry and Cellular and Molecular Biology, University of Tennessee
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14
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Xu WS, Douglas JF, Freed KF. Generalized entropy theory of glass-formation in fully flexible polymer melts. J Chem Phys 2016; 145:234509. [DOI: 10.1063/1.4972412] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Affiliation(s)
- Wen-Sheng Xu
- James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| | - Jack F. Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Karl F. Freed
- James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
- Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA
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15
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Xu WS, Douglas JF, Freed KF. Influence of Cohesive Energy on Relaxation in a Model Glass-Forming Polymer Melt. Macromolecules 2016. [DOI: 10.1021/acs.macromol.6b01504] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
| | - Jack F. Douglas
- Materials
Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
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16
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Xu WS, Douglas JF, Freed KF. Influence of Cohesive Energy on the Thermodynamic Properties of a Model Glass-Forming Polymer Melt. Macromolecules 2016. [DOI: 10.1021/acs.macromol.6b01503] [Citation(s) in RCA: 51] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
| | - Jack F. Douglas
- Materials
Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
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Xu WS, Douglas JF, Freed KF. ENTROPY THEORY OF POLYMER GLASS-FORMATION IN VARIABLE SPATIAL DIMENSION. ADVANCES IN CHEMICAL PHYSICS 2016. [DOI: 10.1002/9781119290971.ch6] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Affiliation(s)
- Wen-Sheng Xu
- James Franck Institute; The University of Chicago; Chicago IL USA
| | - Jack F. Douglas
- Materials Science and Engineering Division; National Institute of Standards and Technology; Gaithersburg MD USA
| | - Karl F. Freed
- James Franck Institute; The University of Chicago; Chicago IL USA
- Department of Chemistry; The University of Chicago; Chicago IL USA
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Xu WS, Freed KF. Self-assembly and glass-formation in a lattice model of telechelic polymer melts: Influence of stiffness of the sticky bonds. J Chem Phys 2016; 144:214903. [PMID: 27276966 DOI: 10.1063/1.4952979] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Telechelic polymers are chain macromolecules that may self-assemble through the association of their two mono-functional end groups (called "stickers"). A deep understanding of the relation between microscopic molecular details and the macroscopic physical properties of telechelic polymers is important in guiding the rational design of telechelic polymer materials with desired properties. The lattice cluster theory (LCT) for strongly interacting, self-assembling telechelic polymers provides a theoretical tool that enables establishing the connections between important microscopic molecular details of self-assembling polymers and their bulk thermodynamics. The original LCT for self-assembly of telechelic polymers considers a model of fully flexible linear chains [J. Dudowicz and K. F. Freed, J. Chem. Phys. 136, 064902 (2012)], while our recent work introduces a significant improvement to the LCT by including a description of chain semiflexibility for the bonds within each individual telechelic chain [W.-S. Xu and K. F. Freed, J. Chem. Phys. 143, 024901 (2015)], but the physically associative (or called "sticky") bonds between the ends of the telechelics are left as fully flexible. Motivated by the ubiquitous presence of steric constraints on the association of real telechelic polymers that impart an additional degree of bond stiffness (or rigidity), the present paper further extends the LCT to permit the sticky bonds to be semiflexible but to have a stiffness differing from that within each telechelic chain. An analytical expression for the Helmholtz free energy is provided for this model of linear telechelic polymer melts, and illustrative calculations demonstrate the significant influence of the stiffness of the sticky bonds on the self-assembly and thermodynamics of telechelic polymers. A brief discussion is also provided for the impact of self-assembly on glass-formation by combining the LCT description for this extended model of telechelic polymers with the Adam-Gibbs relation between the structural relaxation time and the configurational entropy.
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Affiliation(s)
- Wen-Sheng Xu
- James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| | - Karl F Freed
- James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
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Jeong C, Douglas JF. Mass dependence of the activation enthalpy and entropy of unentangled linear alkane chains. J Chem Phys 2015; 143:144905. [DOI: 10.1063/1.4932601] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
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20
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Freed KF. Communication: The simplified generalized entropy theory of glass-formation in polymer melts. J Chem Phys 2015; 143:051102. [DOI: 10.1063/1.4927766] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Karl F. Freed
- James Franck Institute and Department of Chemistry, University of Chicago, Chicago, Illinois 60615, USA
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Dudowicz J, Douglas JF, Freed KF. The meaning of the "universal" WLF parameters of glass-forming polymer liquids. J Chem Phys 2015; 142:014905. [PMID: 25573581 DOI: 10.1063/1.4905216] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Abstract
Although the Williams-Landell-Ferry (WLF) equation for the segmental relaxation time τ(T) of glass-forming materials is one of the most commonly encountered relations in polymer physics, its molecular basis is not well understood. The WLF equation is often claimed to be equivalent to the Vogel-Fulcher-Tammann (VFT) equation, even though the WLF expression for τ(T) contains no explicit dependence on the fragility parameter D of the VFT equation, while the VFT equation lacks any explicit reference to the glass transition temperature Tg, the traditionally chosen reference temperature in the WLF equation. The observed approximate universality of the WLF parameters C1((g)) and C2((g)) implies that τ(T) depends only on T-Tg, a conclusion that seems difficult to reconcile with the VFT equation where the fragility parameter D largely governs the magnitude of τ(T). The current paper addresses these apparent inconsistencies by first evaluating the macroscopic WLF parameters C1((g)) and C2((g)) from the generalized entropy theory of glass-formation and then by determining the dependence of C1((g)) and C2((g)) on the microscopic molecular parameters (including the strength of the cohesive molecular interactions and the degree of chain stiffness) and on the molar mass of the polymer. Attention in these calculations is restricted to the temperature range (Tg < T < Tg + 100 K), where both the WLF and VFT equations apply.
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Affiliation(s)
- Jacek Dudowicz
- The James Franck Institute and the Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA
| | - Jack F Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Karl F Freed
- The James Franck Institute and the Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA
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Xu WS, Freed KF. Lattice model of linear telechelic polymer melts. II. Influence of chain stiffness on basic thermodynamic properties. J Chem Phys 2015; 143:024902. [PMID: 26178122 DOI: 10.1063/1.4926359] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
The lattice cluster theory (LCT) for semiflexible linear telechelic melts, developed in Paper I, is applied to examine the influence of chain stiffness on the average degree of self-assembly and the basic thermodynamic properties of linear telechelic polymer melts. Our calculations imply that chain stiffness promotes self-assembly of linear telechelic polymer melts that assemble on cooling when either polymer volume fraction ϕ or temperature T is high, but opposes self-assembly when both ϕ and T are sufficiently low. This allows us to identify a boundary line in the ϕ-T plane that separates two regions of qualitatively different influence of chain stiffness on self-assembly. The enthalpy and entropy of self-assembly are usually treated as adjustable parameters in classical Flory-Huggins type theories for the equilibrium self-assembly of polymers, but they are demonstrated here to strongly depend on chain stiffness. Moreover, illustrative calculations for the dependence of the entropy density of linear telechelic polymer melts on chain stiffness demonstrate the importance of including semiflexibility within the LCT when exploring the nature of glass formation in models of linear telechelic polymer melts.
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Affiliation(s)
- Wen-Sheng Xu
- James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| | - Karl F Freed
- James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
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23
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Affiliation(s)
- Karl F. Freed
- James Franck Institute and Department of Chemistry, University of Chicago, Chicago, Illinois 60637, USA
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24
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Xu WS, Freed KF. Generalized Entropy Theory of Glass Formation in Polymer Melts with Specific Interactions. Macromolecules 2015. [DOI: 10.1021/acs.macromol.5b00144] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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