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Kirchner KA, Cassar DR, Zanotto ED, Ono M, Kim SH, Doss K, Bødker ML, Smedskjaer MM, Kohara S, Tang L, Bauchy M, Wilkinson CJ, Yang Y, Welch RS, Mancini M, Mauro JC. Beyond the Average: Spatial and Temporal Fluctuations in Oxide Glass-Forming Systems. Chem Rev 2022; 123:1774-1840. [PMID: 35511603 DOI: 10.1021/acs.chemrev.1c00974] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Atomic structure dictates the performance of all materials systems; the characteristic of disordered materials is the significance of spatial and temporal fluctuations on composition-structure-property-performance relationships. Glass has a disordered atomic arrangement, which induces localized distributions in physical properties that are conventionally defined by average values. Quantifying these statistical distributions (including variances, fluctuations, and heterogeneities) is necessary to describe the complexity of glass-forming systems. Only recently have rigorous theories been developed to predict heterogeneities to manipulate and optimize glass properties. This article provides a comprehensive review of experimental, computational, and theoretical approaches to characterize and demonstrate the effects of short-, medium-, and long-range statistical fluctuations on physical properties (e.g., thermodynamic, kinetic, mechanical, and optical) and processes (e.g., relaxation, crystallization, and phase separation), focusing primarily on commercially relevant oxide glasses. Rigorous investigations of fluctuations enable researchers to improve the fundamental understanding of the chemistry and physics governing glass-forming systems and optimize structure-property-performance relationships for next-generation technological applications of glass, including damage-resistant electronic displays, safer pharmaceutical vials to store and transport vaccines, and lower-attenuation fiber optics. We invite the reader to join us in exploring what can be discovered by going beyond the average.
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Affiliation(s)
- Katelyn A Kirchner
- Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Daniel R Cassar
- Department of Materials Engineering, Federal University of São Carlos, São Carlos, Sao Paulo 13565-905, Brazil
- Ilum School of Science, Brazilian Center for Research in Energy and Materials, Campinas, Sao Paulo 13083-970, Brazil
| | - Edgar D Zanotto
- Department of Materials Engineering, Federal University of São Carlos, São Carlos, Sao Paulo 13565-905, Brazil
| | - Madoka Ono
- Research Institute for Electronic Science, Hokkaido University, Sapporo, Hokkaido 001-0021, Japan
- Materials Integration Laboratories, AGC Incorporated, Yokohama, Kanagawa 230-0045, Japan
| | - Seong H Kim
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Karan Doss
- Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Mikkel L Bødker
- Department of Chemistry and Bioscience, Aalborg University, Aalborg 9220, Denmark
| | - Morten M Smedskjaer
- Department of Chemistry and Bioscience, Aalborg University, Aalborg 9220, Denmark
| | - Shinji Kohara
- Research Center for Advanced Measurement and Characterization National Institute for Materials Science, 1-2-1, Sengen, Tsukuba, Ibaraki 305-0047, Japan
| | - Longwen Tang
- Department of Civil and Environmental Engineering, University of California, Los Angeles, California 90095, United States
| | - Mathieu Bauchy
- Department of Civil and Environmental Engineering, University of California, Los Angeles, California 90095, United States
| | - Collin J Wilkinson
- Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
- Department of Research and Development, GlassWRX, Beaufort, South Carolina 29906, United States
| | - Yongjian Yang
- Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Rebecca S Welch
- Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Matthew Mancini
- Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - John C Mauro
- Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
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Weigl P, Schadt D, Weißheit S, Thiele CM, Walther T, Blochowicz T. Triplet state solvation dynamics: extending the accessible timescale by using indole as local probe. Phys Chem Chem Phys 2021; 23:683-693. [PMID: 33336668 DOI: 10.1039/d0cp05240j] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Triplet state solvation dynamics (TSD) is a truly local measurement technique, where a dye molecule is dissolved as a probe at low concentration in a solvent. Depending on the dye molecule, local information on mechanical or dielectric solvation can be obtained. So far, this method has mainly been used to investigate topics such as fundamentals of glassy dynamics and confinement effects. Based on the procedure presented in [P. Weigl et al., Z. Phys. Chem., 2018, 232, 1017-1039] in the present contribution two new TSD probes, namely indole and its derivative cbz-tryptophan, are identified and characterized in detail. In particular, their longer phosphorescence lifetime allows for a significant extension of the timescale of local mechanical and dipolar solvation measurements. In combination with previously used dyes a measurement window of up to five orders of magnitude in time can be covered. Furthermore, we show that in cbz-tryptophan the indole unit is the phosphorescence center, while the rest of the molecule only slightly contributes to the solvation response function. The detailed understanding of these two new TSD probes presented in this work, will allow in depth investigations of solvation and the corresponding dynamics also for biologically relevant systems in the future.
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Affiliation(s)
- Peter Weigl
- Institute for Condensed Matter Physics, Technical University of Darmstadt, 64289 Darmstadt, Germany.
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Xie SJ, Schweizer KS. Microscopic Theory of Dynamically Heterogeneous Activated Relaxation as the Origin of Decoupling of Segmental and Chain Relaxation in Supercooled Polymer Melts. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c00849] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Shi-Jie Xie
- Departments of Materials Science, University of Illinois, Urbana, Illinois 61801, United States
- Material Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States
- Center for Membrane Separation and Water Science & Technology, Ocean College, Zhejiang University of Technology, Hangzhou 310014, PR China
| | - Kenneth S. Schweizer
- Departments of Materials Science, University of Illinois, Urbana, Illinois 61801, United States
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, United States
- Material Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States
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Xie SJ, Schweizer KS. A collective elastic fluctuation mechanism for decoupling and stretched relaxation in glassy colloidal and molecular liquids. J Chem Phys 2020; 152:034502. [DOI: 10.1063/1.5129550] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Shi-Jie Xie
- Department of Materials Science, University of Illinois, Urbana, Illinois 61801, USA
- Material Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
- Center for Membrane Separation and Water Science and Technology, Ocean College, Zhejiang University of Technology, Hangzhou 310014, People’s Republic of China
| | - Kenneth S. Schweizer
- Department of Materials Science, University of Illinois, Urbana, Illinois 61801, USA
- Material Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, USA
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5
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Richert R. Supercooled Liquids and Glasses by Dielectric Relaxation Spectroscopy. ADVANCES IN CHEMICAL PHYSICS 2014. [DOI: 10.1002/9781118949702.ch4] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/03/2022]
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6
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Samanta S, Richert R. Limitations of heterogeneous models of liquid dynamics: Very slow rate exchange in the excess wing. J Chem Phys 2014; 140:054503. [DOI: 10.1063/1.4863347] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Medvedev GA, Starry AB, Ramkrishna D, Caruthers JM. Stochastic Model for Volume Relaxation in Glass Forming Materials: Local Specific Volume Model. Macromolecules 2012. [DOI: 10.1021/ma300441a] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Grigori A. Medvedev
- School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907, United States
| | - Adam B. Starry
- School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907, United States
| | - Doraiswamy Ramkrishna
- School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907, United States
| | - James M. Caruthers
- School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907, United States
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9
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Grebenkin SY. Dynamical Heterogeneity in Glassy o-Terphenyl. 2. Measurement of Environment Structure Lifetime Using Reversible Reactions. J Phys Chem B 2008; 112:15369-75. [DOI: 10.1021/jp806159b] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- S. Yu. Grebenkin
- Institute of Chemical Kinetics and Combustion, Novosibirsk 630090, Russian Federation
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Rajian JR, Quitevis EL. Translational diffusion in sucrose benzoate near the glass transition: Probe size dependence in the breakdown of the Stokes-Einstein equation. J Chem Phys 2007; 126:224506. [PMID: 17581062 DOI: 10.1063/1.2738474] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The translational diffusion coefficient D(trans) for rubrene, 9,10-bis(phenylethynyl)anthracene (BPEA), and tetracene in the fragile molecular glass-former sucrose benzoate (SB) (Tg=337 K) was studied as a function of temperature from Tg+3 K to Tg+71 K by use of the holographic fluorescence recovery after photobleaching technique. The values of D(trans) vary by five to six orders of magnitude in this temperature range. Contrary to the predictions of the Stokes-Einstein equation, the temperature dependence of probe diffusion in SB over the temperature range of the measurements is weaker than that of T/eta, where eta is the shear viscosity. In going from the crossover temperature Tx approximately 1.2Tg to Tg, D(trans)eta/T increases by factors of 2.4+/-0.2 decades for rubrene, 3.4+/-0.2 decades for BPEA, and 3.8+/-0.4 decades for tetracene. The decoupling between probe diffusion in SB and viscosity is characterized by the scaling law D(trans) approximately T/eta(xi), with xi=0.621 for tetracene, 0.654 for BPEA, and 0.722 for rubrene. Data for probe diffusion in SB are combined with data from the literature for probe diffusion in ortho-terphenyl and alphaalphabeta-tris(naphthyl)benzene in a plot of enhancement versus the relative probe size parameter rho(m)=(m(p)m(h))(1/3), where m(p) and m(h) are, respectively, the molecular weights of the probe and host solvent. The plot clearly shows a sharp increase in enhancement of translational diffusion at rho(m) approximately 1. By applying temperature shifts, D(trans) for probe diffusion in SB and the dielectric relaxation time tau(D) can be superimposed on a single master curve based on the Williams-Landel-Ferry equation. This suggests that the dynamics of probe diffusion in SB is described by the scaling relationship D(trans) approximately 1/tau(D)(T+DeltaT), where tau(D)(T+DeltaT) is the temperature-shifted dielectric relaxation time. The results from this study are discussed within the context of dynamic heterogeneity in glass-forming liquids.
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Affiliation(s)
- Justin Rajesh Rajian
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409, USA
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Ellegaard NL, Christensen T, Christiansen PV, Olsen NB, Pedersen UR, Schrøder TB, Dyre JC. Single-order-parameter description of glass-forming liquids: A one-frequency test. J Chem Phys 2007; 126:074502. [PMID: 17328615 DOI: 10.1063/1.2434963] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Thermoviscoelastic linear-response functions are calculated from the master equation describing viscous liquid inherent dynamics. From the imaginary parts of the frequency-dependent isobaric specific heat, isothermal compressibility, and isobaric thermal expansion coefficient, we define a "linear dynamic Prigogine-Defay ratio" LambdaTp(omega) with the property that if LambdaTp(omega)=1 at one frequency, then LambdaTp(omega) is unity at all frequencies. This happens if and only if there is a single-order-parameter description of the thermoviscoelastic linear responses via an order parameter (which may be nonexponential in time). Generalizations to other cases of thermodynamic control parameters than temperature and pressure are also presented.
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Affiliation(s)
- Niels L Ellegaard
- DNRF Centre Glass and Time, IMFUFA (27), Department of Sciences, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark
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Szabat B, Weron K, Hetman P. Wait-and-switch relaxation model: relationship between nonexponential relaxation patterns and random local properties of a complex system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:021114. [PMID: 17358320 DOI: 10.1103/physreve.75.021114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2006] [Indexed: 05/14/2023]
Abstract
The wait-and-switch stochastic model of relaxation is presented. Using the "random-variable" formalism of limit theorems of probability theory we explain the universality of the short- and long-time fractional-power laws in relaxation responses of complex systems. We show that the time evolution of the nonequilibrium state of a macroscopic system depends on two stochastic mechanisms: one, which determines the local statistical properties of the relaxing entities, and the other one, which determines the number (random or deterministic) of the microscopic and mesoscopic relaxation contributions. Within the proposed framework we derive the Havriliak-Negami and Kohlrausch-Williams-Watts functions. We also discuss the influence of the random-walk characteristics of migrating defects on the homogeneous and heterogeneous relaxation scenarios and show the origins of the stretched-exponential integral kernel in the integral representation of the ensemble-averaged relaxation function.
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Affiliation(s)
- Bozena Szabat
- Institute of Physics, Wroclaw University of Technology, 50-370 Wroclaw, Poland.
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Richert R, Weinstein S. Nonlinear dielectric response and thermodynamic heterogeneity in liquids. PHYSICAL REVIEW LETTERS 2006; 97:095703. [PMID: 17026377 DOI: 10.1103/physrevlett.97.095703] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2006] [Indexed: 05/12/2023]
Abstract
If large amplitude time-dependent fields (e.g., dielectric, magnetic, mechanical) are applied to a sample that displays relaxational modes, some energy of the external field is absorbed by the slow degrees of freedom. The weak coupling of these modes to the phonon bath leads to long persistence times of the resulting higher fictive temperature. Assuming heterogeneities regarding dielectric and thermal relaxation times, extremely strong nonlinear dielectric effects are predicted and experimentally verified. For glycerol at T = 213 K, the dielectric loss measured at 280 kV/cm increases by more than 6% over its low-field value. This nonlinearity shows a characteristic frequency dependence and implies that dielectric and thermal time constants are locally correlated in viscous liquids.
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Affiliation(s)
- Ranko Richert
- Department of Chemistry and Biochemistry, Arizona State University, Tempe, Arizona 85287-1604, USA
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Blochowicz T, Rössler EA. Nonresonant dielectric hole burning in neat and binary organic glass formers. J Chem Phys 2005; 122:224511. [PMID: 15974695 DOI: 10.1063/1.1931647] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Binary mixtures of the molecular glass former 2-picoline in oligostyrene, in which the dielectric response of 2-picoline exhibits a particularly broad distribution of correlation times, are investigated by nonresonant dielectric hole-burning (NDHB) spectroscopy and the results are compared with NDHB in neat systems, in particular, glycerol. It turns out that in both substance classes spectral selectivity is achieved, which indicates that dynamics is heterogeneous, i.e., slow and fast responses coexist in the material. However, in binary systems the position of the spectral modifications is completely determined by the spectral density of the pump field, and thus shifts linearly with burn frequency as expected, also at pump frequencies around the alpha-relaxation maximum. It is shown that in binary systems the lifetime tau(rec) of the spectral modifications is determined by the burn frequency omega(p) and exceeds its inverse by about one order of magnitude, indicating long-lived dynamic heterogeneity. The data are described in terms of a previously suggested model of dynamically selective heating, which was extended to include intrinsic nonexponential relaxation. It turns out that the spectral broadening in binary mixtures is not only due to pronounced dynamic heterogeneity, but partially also due to intrinsic broadening of the relaxation function.
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Affiliation(s)
- T Blochowicz
- Technischen Universität-Darmstadt, 64289 Darmstadt, Germany.
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15
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Sakurai M, Yoshimori A. Bandwidth analysis of solvation dynamics in a simple liquid mixture. J Chem Phys 2005; 122:104509. [PMID: 15836334 DOI: 10.1063/1.1857480] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
The time-dependent energy distribution of solvation dynamics is studied by molecular dynamics simulations of a Lennard-Jones mixture. We calculate the response functions of the average and the variance which correspond to the spectral peak shift and bandwidth. Our calculation shows that the variance relaxation is slower than that of the average. The result agrees qualitatively with the experimental results. Dividing the obtained response functions into subcomponents caused by each solvent, we find that the relaxation is dominated by that solvent which strongly interacts with the solute. Extracting the redistribution component from the response functions, we find that it causes the slower relaxation of the response function. Thus, we conclude that the difference of the slower relaxations between the average and variance is caused by the redistribution process.
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Affiliation(s)
- M Sakurai
- Department of Physics, Kyushu University, Fukuoka 812-8581, Japan.
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Schweizer KS, Saltzman EJ. Activated Hopping, Barrier Fluctuations, and Heterogeneity in Glassy Suspensions and Liquids. J Phys Chem B 2004. [DOI: 10.1021/jp047763j] [Citation(s) in RCA: 114] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Kenneth S. Schweizer
- Departments of Materials Science and Chemistry and Frederick Seitz Materials Research Laboratory, University of Illinois, 1304 West Green Street, Urbana, Illinois 61801
| | - Erica J. Saltzman
- Departments of Materials Science and Chemistry and Frederick Seitz Materials Research Laboratory, University of Illinois, 1304 West Green Street, Urbana, Illinois 61801
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Abstract
Using time resolved optical depolarization, we have studied the rotational behavior of molecular probes in supercooled liquids near the glass transition temperature T(g). Simultaneously, the dynamics of the liquid immediately surrounding these rigid probes is measured by triplet state solvation experiments. This direct comparison of solute and solvent dynamics is particularly suited for assessing the origin of exponential orientational correlation functions of probe molecules embedded in liquids which exhibit highly nonexponential structural relaxation. Polarization angle dependent Stokes shift correlation functions demonstrate that probe rotation time and solvent response time are locally correlated quantities in the case of smaller probe molecules. Varying the size of both guest and host molecules shows that the size ratio determines the rotational behavior of the probes. The results are indicative of time averaging being at the origin of exponential rotation of probes whose rotational time constant is slower than solvent relaxation by a factor of 20 or more.
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Affiliation(s)
- Li-Min Wang
- Department of Chemistry and Biochemistry, Arizona State University, Tempe, Arizona 85287-1604, USA
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Qi F, El Goresy T, Böhmer R, Döß A, Diezemann G, Hinze G, Sillescu H, Blochowicz T, Gainaru C, Rössler E, Zimmermann H. Nuclear magnetic resonance and dielectric spectroscopy of a simple supercooled liquid: 2-methyl tetrahydrofuran. J Chem Phys 2003. [DOI: 10.1063/1.1563599] [Citation(s) in RCA: 47] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
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Diezemann G. Time-dependent optical linewidth in fluctuating environments: Stochastic models. J Chem Phys 2002. [DOI: 10.1063/1.1429241] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Yang M, Richert R. Observation of heterogeneity in the nanosecond dynamics of a liquid. J Chem Phys 2001. [DOI: 10.1063/1.1380206] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Richert R. Spectral diffusion in liquids with fluctuating solvent responses: Dynamical heterogeneity and rate exchange. J Chem Phys 2001. [DOI: 10.1063/1.1380209] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Ilan B, Loring RF. Polymer motions from localization to Rouse dynamics in supercooled melts. J Chem Phys 2001. [DOI: 10.1063/1.1370071] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Deschenes LA, Vanden Bout DA. Single-molecule studies of heterogeneous dynamics in polymer melts near the glass transition. Science 2001; 292:255-8. [PMID: 11303094 DOI: 10.1126/science.1056430] [Citation(s) in RCA: 193] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Single-molecule spectroscopy was used to follow the orientation of a single probe molecule in a polymer film in real time. Broad spatially heterogeneous dynamics were observed on long time scales, which result from simple diffusive rotational motions on short time scales. This diffusive behavior persists for many rotations before the molecule's local environment changes to one characterized by a new time scale. This environmental exchange occurs instantaneously on the time scale of the experiment and may arise from large-scale collective motions. The distribution of exchange times for these environments was measured for several temperatures near the glass transition.
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Affiliation(s)
- L A Deschenes
- Department of Chemistry and Biochemistry, Center for Nano and Molecular Materials Science and Technology; and Texas Materials Institute, University of Texas, Austin, TX 78712-1167, USA
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Wang CY, Ediger MD. Lifetime of spatially heterogeneous dynamic domains in polystyrene melts. J Chem Phys 2000. [DOI: 10.1063/1.481319] [Citation(s) in RCA: 60] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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