1
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Yang Z, Xu X, Douglas JF, Xu WS. Confinement effect of inter-arm interactions on glass formation in star polymer melts. J Chem Phys 2024; 160:044503. [PMID: 38265089 DOI: 10.1063/5.0185412] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2023] [Accepted: 12/25/2023] [Indexed: 01/25/2024] Open
Abstract
We utilized molecular dynamic simulation to investigate the glass formation of star polymer melts in which the topological complexity is varied by altering the number of star arms (f). Emphasis was placed on how the "confinement effect" of repulsive inter-arm interactions within star polymers influences the thermodynamics and dynamics of star polymer melts. All the characteristic temperatures of glass formation were found to progressively increase with increasing f, but unexpectedly the fragility parameter KVFT was found to decrease with increasing f. As previously observed, stars having more than 5 or 6 arms adopt an average particle-like structure that is more contracted relative to the linear polymer size having the same mass and exhibit a strong tendency for intermolecular and intramolecular segregation. We systematically analyzed how varying f alters collective particle motion, dynamic heterogeneity, the decoupling exponent ζ phenomenologically linking the slow β- and α-relaxation times, and the thermodynamic scaling index γt. Consistent with our hypothesis that the segmental dynamics of many-arm star melts and thin supported polymer films should exhibit similar trends arising from the common feature of high local segmental confinement, we found that ζ increases considerably with increasing f, as found in supported polymer films with decreasing thickness. Furthermore, increasing f led to greatly enhanced elastic heterogeneity, and this phenomenon correlates strongly with changes in ζ and γt. Our observations should be helpful in building a more rational theoretical framework for understanding how molecular topology and geometrical confinement influence the dynamics of glass-forming materials more broadly.
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Affiliation(s)
- Zhenyue Yang
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People's Republic of China
- Academy for Advanced Interdisciplinary Studies, Northeast Normal University, Changchun 130024, People's Republic of China
| | - Xiaolei Xu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People's Republic of China
| | - Jack F Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Wen-Sheng Xu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People's Republic of China
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2
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Xu X, Xu WS. Melt Properties and String Model Description of Glass Formation in Graft Polymers of Different Side-Chain Lengths. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c00327] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
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
| | - 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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3
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Yang Z, Xu X, Xu WS. Influence of Ionic Interaction Strength on Glass Formation of an Ion-Containing Polymer Melt. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c01719] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Zhenyue Yang
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
| | - Xiaolei Xu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
| | - 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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4
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Zhang H, Wang X, Yu HB, Douglas JF. Dynamic heterogeneity, cooperative motion, and Johari-Goldstein [Formula: see text]-relaxation in a metallic glass-forming material exhibiting a fragile-to-strong transition. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:56. [PMID: 33871722 DOI: 10.1140/epje/s10189-021-00060-7] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2021] [Accepted: 03/21/2021] [Indexed: 06/12/2023]
Abstract
We investigate the Johari-Goldstein (JG) [Formula: see text]-relaxation process in a model metallic glass-forming (GF) material ([Formula: see text]), previously studied extensively by both frequency-dependent mechanical measurements and simulation studies devoted to equilibrium properties, by molecular dynamics simulations based on validated and optimized interatomic potentials with the primary aim of better understanding the nature of this universal relaxation process from a dynamic heterogeneity (DH) perspective. The present relatively low temperature and long-time simulations reveal a direct correspondence between the JG [Formula: see text]-relaxation time [Formula: see text] and the lifetime of the mobile particle clusters [Formula: see text], defined as in previous DH studies, a relationship dual to the corresponding previously observed relationship between the [Formula: see text]-relaxation time [Formula: see text] and the lifetime of immobile particle clusters [Formula: see text]. Moreover, we find that the average diffusion coefficient D nearly coincides with [Formula: see text] of the smaller atomic species (Al) and that the 'hopping time' associated with D coincides with [Formula: see text] to within numerical uncertainty, both trends being in accord with experimental studies. This indicates that the JG [Formula: see text]-relaxation is dominated by the smaller atomic species and the observation of a direct relation between this relaxation process and rate of molecular diffusion in GF materials at low temperatures where the JG [Formula: see text]-relaxation becomes the prevalent mode of structural relaxation. As an unanticipated aspect of our study, we find that [Formula: see text] exhibits fragile-to-strong (FS) glass formation, as found in many other metallic GF liquids, but this fact does not greatly alter the geometrical nature of DH in this material and the relation of DH to dynamical properties. On the other hand, the temperature dependence of the DH and dynamical properties, such as the structural relaxation time, can be significantly altered from 'ordinary' GF liquids.
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Affiliation(s)
- Hao Zhang
- Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, T6G 1H9, Canada.
| | - Xinyi Wang
- Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, T6G 1H9, Canada
| | - Hai-Bin Yu
- Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, China
| | - Jack F Douglas
- Material Measurement Laboratory, Materials Science and Engineering Division, National Institute of Standards and Technology(NIST), Gaithersburg, MD, 20899, USA.
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5
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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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6
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Xu WS, Douglas JF, Xu X. Role of Cohesive Energy in Glass Formation of Polymers with and without Bending Constraints. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c01876] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
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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7
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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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8
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Xu WS, Douglas JF, Xia W, Xu X. Investigation of the Temperature Dependence of Activation Volume in Glass-Forming Polymer Melts under Variable Pressure Conditions. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c01268] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
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
- Material Measurement Laboratory, 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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9
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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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11
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Zhang H, Wang X, Chremos A, Douglas JF. Superionic UO2: A model anharmonic crystalline material. J Chem Phys 2019; 150:174506. [DOI: 10.1063/1.5091042] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Affiliation(s)
- Hao Zhang
- Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta T6G 1H9, Canada
| | - Xinyi Wang
- Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta T6G 1H9, Canada
| | - Alexandros Chremos
- Material Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Jack F. Douglas
- Material Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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12
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Pan D, Sun ZY. Influence of chain stiffness on the dynamical heterogeneity and fragility of polymer melts. J Chem Phys 2018; 149:234904. [DOI: 10.1063/1.5052153] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Deng Pan
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China and University of Chinese Academy of Sciences, Beijing 100039, China
| | - Zhao-Yan Sun
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China and University of Chinese Academy of Sciences, Beijing 100039, China
- Xinjiang Laboratory of Phase Transitions and Microstructures in Condensed Matters, College of Physical Science and Technology, Yili Normal University, Yining 835000, China
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13
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Parmar ADS, Sengupta S, Sastry S. Power law relationship between diffusion coefficients in multi-component glass forming liquids. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2018; 41:90. [PMID: 30078172 DOI: 10.1140/epje/i2018-11702-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2018] [Accepted: 07/13/2018] [Indexed: 06/08/2023]
Abstract
The slow down of dynamics in glass forming liquids as the glass transition is approached has been characterised through the Adam-Gibbs relation, which relates relaxation time scales to the configurational entropy. The Adam-Gibbs relation cannot apply simultaneously to all relaxation times scales unless they are coupled, and exhibit closely related temperature dependences. The breakdown of the Stokes-Einstein relation presents an interesting situation to the contrary, and in analysing it, it has recently been shown that the Adam-Gibbs relation applies to diffusion coefficients rather than to viscosity or structural relaxation times related to the decay of density fluctuations. However, for multi-component liquids --the typical cases considered in computer simulations, metallic glass formers, etc.-- such a statement raises the question of which diffusion coefficient is described by the Adam-Gibbs relation. All diffusion coefficients can be consistently described by the Adam-Gibbs relation if they bear a power law relationship with each other. Remarkably, we find that for a wide range of glass formers, and for a wide range of temperatures spanning the normal and the slow relaxation regimes, such a relationship holds. We briefly discuss possible rationalisations of the observed behaviour.
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Affiliation(s)
- Anshul D S Parmar
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur Campus, 560064, Bengaluru, India
- Tata Institute of Fundamental Research, 500107, Hyderabad, Ranga Reddy District, India
| | - Shiladitya Sengupta
- Department of Fundamental Engineering, Institute of Industrial Science, The University of Tokyo, Komaba 4-6-1, 153-8505, Meguro-ku, Tokyo, Japan
| | - Srikanth Sastry
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur Campus, 560064, Bengaluru, India.
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14
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Pazmiño Betancourt BA, Starr FW, Douglas JF. String-like collective motion in the α- and β-relaxation of a coarse-grained polymer melt. J Chem Phys 2018; 148:104508. [DOI: 10.1063/1.5009442] [Citation(s) in RCA: 37] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Beatriz A. Pazmiño Betancourt
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
- Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA
| | - Francis W. Starr
- Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA
| | - Jack F. Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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15
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Parmar ADS, Sengupta S, Sastry S. Length-Scale Dependence of the Stokes-Einstein and Adam-Gibbs Relations in Model Glass Formers. PHYSICAL REVIEW LETTERS 2017; 119:056001. [PMID: 28949755 DOI: 10.1103/physrevlett.119.056001] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2016] [Indexed: 05/23/2023]
Abstract
The Adam-Gibbs (AG) relation connects the dynamics of a glass-forming liquid to its thermodynamics via the configurational entropy and is of fundamental importance in descriptions of glassy behavior. The breakdown of the Stokes-Einstein relation (SEB) between the diffusion coefficient and the viscosity (or structural relaxation times) in glass formers raises the question as to which dynamical quantity the AG relation describes. By performing molecular dynamics simulations, we show that the AG relation is valid over the widest temperature range for the diffusion coefficient and not for the viscosity or relaxation times. Studying relaxation times defined at a given wavelength, we find that SEB and the deviation from the AG relation occur below a temperature at which the correlation length of dynamical heterogeneity equals the wavelength probed.
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Affiliation(s)
- Anshul D S Parmar
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bengaluru 560064, India
- TIFR Center for Interdisciplinary Sciences, 21 Brundavan Colony, Narsingi, Hyderabad 500075, India
| | - Shiladitya Sengupta
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bengaluru 560064, India
- Department of Fundamental Engineering, Institute of Industrial Science, The University of Tokyo, Komaba 4-6-1, Meguro-ku, Tokyo 153-8505, Japan
| | - Srikanth Sastry
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bengaluru 560064, India
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16
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Xu WS, Douglas JF, Freed KF. Influence of Pressure on Glass Formation in a Simulated Polymer Melt. Macromolecules 2017. [DOI: 10.1021/acs.macromol.7b00080] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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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17
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Cho HW, Sung BJ. The glass transition and interfacial dynamics of single strand fibers of polymers. SOFT MATTER 2017; 13:1190-1199. [PMID: 28098313 DOI: 10.1039/c6sm02468h] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We investigate the glass transition and interfacial dynamics of single strand fibers of flexible polymers by employing molecular dynamics (MD) simulations along with a coarse grained model. While the polymer fiber has drawn significant attention due to its applicability in tissue engineering and stretchable electronics, its dynamic properties, especially the glass transition temperature (Tg), are yet to be understood at the molecular level. For example, there has been a controversy on the effect of the polymer fiber radius (R) on Tg: Tg decreased with a decrease in R for some polymer fibers, whereas Tg of other polymer fibers was not sensitive to R. In this article, we estimate the bond relaxation time of polymers and evaluate both Tg and fragility (m) as a function of R. We illustrate that Tg of the polymer fiber decreased with a decrease in R monotonically and also that the values of Tg follow faithfully the empirical equation proposed by Keddie et al. as a function of R, which was successfully employed to fit the values of Tg of both polyvinyl alcohol (PVA) fibers and polyethylene (PE) fibers. We also find that the dynamics of polymers at the interface between a polymer fiber and air is faster than that of polymers at the center. By employing Adam-Gibbs theory, we show that the fast interface dynamics of polymer fibers should influence the cooperative motion of monomers, which should be responsible for the decrease in Tg for smaller values of R. Near the interface there are more mobile monomers that participate in the cooperative motions of polymers. Interesting is that due to the curved surface (unlike flat polymer films) the cooperative motion of monomers is anisotropic in polymer fibers.
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Affiliation(s)
- Hyun Woo Cho
- Department of Chemistry and Research Institute for Basic Science, Sogang University, Seoul 121-742, Republic of Korea.
| | - Bong June Sung
- Department of Chemistry and Research Institute for Basic Science, Sogang University, Seoul 121-742, Republic of Korea.
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18
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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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19
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Xu WS, Douglas JF, Freed KF. Stringlike Cooperative Motion Explains the Influence of Pressure on Relaxation in a Model Glass-Forming Polymer Melt. ACS Macro Lett 2016; 5:1375-1380. [PMID: 35651209 DOI: 10.1021/acsmacrolett.6b00795] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Numerous experiments reveal that the dynamics of glass-forming polymer melts are profoundly influenced by the application of pressure, but a fundamental microscopic understanding of these observations remains incomplete. We explore the structural relaxation of a model glass-forming polymer melt over a wide range of pressures (P) by molecular dynamics simulation. In accord with experiments for nonassociating polymer melts and the generalized entropy theory, we find that the P dependence of the structural relaxation time (τα) can be described by a pressure analog of the Vogel-Fulcher-Tammann equation and that the characteristic temperatures of glass formation increase with P, while the fragility decreases with P. Further, we demonstrate that τα for various P can quantitatively be described by the string model of glass formation, where the enthalpy and entropy of activation are found to be proportional, an effect that is expected to apply to polymeric materials under various applied fields.
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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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20
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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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21
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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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22
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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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Karmakar S, Dasgupta C, Sastry S. Length scales in glass-forming liquids and related systems: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2016; 79:016601. [PMID: 26684508 DOI: 10.1088/0034-4885/79/1/016601] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The central problem in the study of glass-forming liquids and other glassy systems is the understanding of the complex structural relaxation and rapid growth of relaxation times seen on approaching the glass transition. A central conceptual question is whether one can identify one or more growing length scale(s) associated with this behavior. Given the diversity of molecular glass-formers and a vast body of experimental, computational and theoretical work addressing glassy behavior, a number of ideas and observations pertaining to growing length scales have been presented over the past few decades, but there is as yet no consensus view on this question. In this review, we will summarize the salient results and the state of our understanding of length scales associated with dynamical slow down. After a review of slow dynamics and the glass transition, pertinent theories of the glass transition will be summarized and a survey of ideas relating to length scales in glassy systems will be presented. A number of studies have focused on the emergence of preferred packing arrangements and discussed their role in glassy dynamics. More recently, a central object of attention has been the study of spatially correlated, heterogeneous dynamics and the associated length scale, studied in computer simulations and theoretical analysis such as inhomogeneous mode coupling theory. A number of static length scales have been proposed and studied recently, such as the mosaic length scale discussed in the random first-order transition theory and the related point-to-set correlation length. We will discuss these, elaborating on key results, along with a critical appraisal of the state of the art. Finally we will discuss length scales in driven soft matter, granular fluids and amorphous solids, and give a brief description of length scales in aging systems. Possible relations of these length scales with those in glass-forming liquids will be discussed.
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Affiliation(s)
- Smarajit Karmakar
- TIFR Centre for Interdisciplinary Sciences, 21 Brundavan Colony, Narsingi, Hyderabad 500075, India
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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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25
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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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27
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Xu WS, Freed KF. Lattice model of linear telechelic polymer melts. I. Inclusion of chain semiflexibility in the lattice cluster theory. J Chem Phys 2015; 143:024901. [PMID: 26178121 DOI: 10.1063/1.4926358] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
Abstract
The lattice cluster theory (LCT) for the thermodynamics of polymer systems has recently been reformulated to treat strongly interacting self-assembling polymers composed of fully flexible linear telechelic chains [J. Dudowicz and K. F. Freed, J. Chem. Phys. 136, 064902 (2012)]. Here, we further extend the LCT for linear telechelic polymer melts to include a description of chain semiflexibility, which is treated by introducing a bending energy penalty whenever a pair of consecutive bonds from a single chain lies along orthogonal directions. An analytical expression for the Helmholtz free energy is derived for the model of semiflexible linear telechelic polymer melts. The extension provides a theoretical tool for investigating the influence of chain stiffness on the thermodynamics of self-assembling telechelic polymers, and for further exploring the influence of self-assembly on glass formation in such systems.
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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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28
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Correlation between fragility and cooperativity in segmental dynamics of glass-forming para-substituted polystyrenes. Polym J 2015. [DOI: 10.1038/pj.2015.50] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
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Hanakata PZ, Pazmiño Betancourt BA, Douglas JF, Starr FW. A unifying framework to quantify the effects of substrate interactions, stiffness, and roughness on the dynamics of thin supported polymer films. J Chem Phys 2015; 142:234907. [DOI: 10.1063/1.4922481] [Citation(s) in RCA: 102] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Zhang H, Zhong C, Douglas JF, Wang X, Cao Q, Zhang D, Jiang JZ. Role of string-like collective atomic motion on diffusion and structural relaxation in glass forming Cu-Zr alloys. J Chem Phys 2015; 142:164506. [DOI: 10.1063/1.4918807] [Citation(s) in RCA: 74] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Hao Zhang
- International Center for New-Structured Materials (ICNSM), Zhejiang University and Laboratory of New-Structured Materials, School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, People’s Republic of China
- Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta T6G 2V4, Canada
| | - Cheng Zhong
- International Center for New-Structured Materials (ICNSM), Zhejiang University and Laboratory of New-Structured Materials, School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, People’s Republic of China
- State Key Laboratory of Silicon Materials, Zhejiang University, Hangzhou 310027, People’s Republic of China
| | - Jack F. Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Xiaodong Wang
- International Center for New-Structured Materials (ICNSM), Zhejiang University and Laboratory of New-Structured Materials, School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, People’s Republic of China
- State Key Laboratory of Silicon Materials, Zhejiang University, Hangzhou 310027, People’s Republic of China
| | - Qingping Cao
- International Center for New-Structured Materials (ICNSM), Zhejiang University and Laboratory of New-Structured Materials, School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, People’s Republic of China
- State Key Laboratory of Silicon Materials, Zhejiang University, Hangzhou 310027, People’s Republic of China
| | - Dongxian Zhang
- State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027, People’s Republic of China
| | - Jian-Zhong Jiang
- International Center for New-Structured Materials (ICNSM), Zhejiang University and Laboratory of New-Structured Materials, School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, People’s Republic of China
- State Key Laboratory of Silicon Materials, Zhejiang University, Hangzhou 310027, People’s Republic of China
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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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Pazmiño Betancourt BA, Hanakata PZ, Starr FW, Douglas JF. Quantitative relations between cooperative motion, emergent elasticity, and free volume in model glass-forming polymer materials. Proc Natl Acad Sci U S A 2015; 112:2966-71. [PMID: 25713371 PMCID: PMC4364219 DOI: 10.1073/pnas.1418654112] [Citation(s) in RCA: 139] [Impact Index Per Article: 15.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The study of glass formation is largely framed by semiempirical models that emphasize the importance of progressively growing cooperative motion accompanying the drop in fluid configurational entropy, emergent elasticity, or the vanishing of accessible free volume available for molecular motion in cooled liquids. We investigate the extent to which these descriptions are related through computations on a model coarse-grained polymer melt, with and without nanoparticle additives, and for supported polymer films with smooth or rough surfaces, allowing for substantial variation of the glass transition temperature and the fragility of glass formation. We find quantitative relations between emergent elasticity, the average local volume accessible for particle motion, and the growth of collective motion in cooled liquids. Surprisingly, we find that each of these models of glass formation can equally well describe the relaxation data for all of the systems that we simulate. In this way, we uncover some unity in our understanding of glass-forming materials from perspectives formerly considered as distinct.
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Affiliation(s)
- Beatriz A Pazmiño Betancourt
- Materials Science and Engineering, National Institute of Standards and Technology, Gaithersburg, MD 20899; and Department of Physics, Wesleyan University, Middletown, CT 06459
| | - Paul Z Hanakata
- Department of Physics, Wesleyan University, Middletown, CT 06459
| | - Francis W Starr
- Department of Physics, Wesleyan University, Middletown, CT 06459
| | - Jack F Douglas
- Materials Science and Engineering, National Institute of Standards and Technology, Gaithersburg, MD 20899; and
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Zhang H, Yang Y, Douglas JF. Influence of string-like cooperative atomic motion on surface diffusion in the (110) interfacial region of crystalline Ni. J Chem Phys 2015; 142:084704. [PMID: 25725748 DOI: 10.1063/1.4908136] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Although we often think about crystalline materials in terms of highly organized arrays of atoms, molecules, or even colloidal particles, many of the important properties of this diverse class of materials relating to their catalytic behavior, thermodynamic stability, and mechanical properties derive from the dynamics and thermodynamics of their interfacial regions, which we find they have a dynamics more like glass-forming (GF) liquids than crystals at elevated temperatures. This is a general problem arising in any attempt to model the properties of naturally occurring crystalline materials since many aspects of the dynamics of glass-forming liquids remain mysterious. We examine the nature of this phenomenon in the "simple" case of the (110) interface of crystalline Ni, based on a standard embedded-atom model potential, and we then quantify the collective dynamics in this interfacial region using newly developed methods for characterizing the cooperative dynamics of glass-forming liquids. As in our former studies of the interfacial dynamics of grain-boundaries and the interfacial dynamics of crystalline Ni nanoparticles (NPs), we find that the interface of bulk crystalline Ni exhibits all the characteristics of glass-forming materials, even at temperatures well below the equilibrium crystal melting temperature, Tm. This perspective offers a new approach to modeling and engineering the properties of crystalline materials.
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Affiliation(s)
- Hao Zhang
- Department of Chemical and Materials Engineering, University of Alberta, Alberta T6G 2V4, Canada
| | - Ying Yang
- Department of Chemical and Materials Engineering, University of Alberta, Alberta T6G 2V4, Canada
| | - Jack F Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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Dudowicz J, Douglas JF, Freed KF. Advances in the generalized entropy theory of glass-formation in polymer melts. J Chem Phys 2014; 141:234903. [DOI: 10.1063/1.4903842] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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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