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Gadige P, Albert S, Michl M, Bauer T, Lunkenheimer P, Loidl A, Tourbot R, Wiertel-Gasquet C, Biroli G, Bouchaud JP, Ladieu F. Unifying different interpretations of the nonlinear response in glass-forming liquids. Phys Rev E 2018; 96:032611. [PMID: 29346923 DOI: 10.1103/physreve.96.032611] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2017] [Indexed: 11/07/2022]
Abstract
This work aims at reconsidering several interpretations coexisting in the recent literature concerning nonlinear susceptibilities in supercooled liquids. We present experimental results on glycerol and propylene carbonate, showing that the three independent cubic susceptibilities have very similar frequency and temperature dependences, for both their amplitudes and phases. This strongly suggests a unique physical mechanism responsible for the growth of these nonlinear susceptibilities. We show that the framework proposed by two of us [J.-P. Bouchaud and G. Biroli, Phys. Rev. B 72, 064204 (2005)PRBMDO1098-012110.1103/PhysRevB.72.064204], where the growth of nonlinear susceptibilities is intimately related to the growth of glassy domains, accounts for all the salient experimental features. We then review several complementary and/or alternative models and show that the notion of cooperatively rearranging glassy domains is a key (implicit or explicit) ingredient to all of them. This paves the way for future experiments, which should deepen our understanding of glasses.
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Affiliation(s)
- P Gadige
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, Bâtiment 772, 91191 Gif-sur-Yvette Cedex, France
| | - S Albert
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, Bâtiment 772, 91191 Gif-sur-Yvette Cedex, France
| | - M Michl
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany
| | - Th Bauer
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany
| | - P Lunkenheimer
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany
| | - A Loidl
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany
| | - R Tourbot
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, Bâtiment 772, 91191 Gif-sur-Yvette Cedex, France
| | - C Wiertel-Gasquet
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, Bâtiment 772, 91191 Gif-sur-Yvette Cedex, France
| | - G Biroli
- IPhT, CEA, CNRS, Université Paris-Saclay, CEA Saclay, Bâtiment 774, 91191 Gif-sur-Yvette Cedex, France.,LPS, Ecole Normale Supérieure, 24 Rue Lhomond, 75231 Paris Cedex 05, France
| | - J-P Bouchaud
- Capital Fund Management, 23 Rue de l'Université, 75007 Paris, France
| | - F Ladieu
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, Bâtiment 772, 91191 Gif-sur-Yvette Cedex, France
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2
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Richert R. Nonlinear dielectric effects in liquids: a guided tour. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:363001. [PMID: 28665294 DOI: 10.1088/1361-648x/aa7cc4] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Dielectric relaxation measurements probe how the polarization of a material responds to the application of an external electric field, providing information on structure and dynamics of the sample. In the limit of small fields and thus linear response, such experiments reveal the properties of the material in the same thermodynamic state it would have in the absence of the external field. At sufficiently high fields, reversible changes in enthalpy and entropy of the system occur even at constant temperature, and these will in turn alter the polarization responses. The resulting nonlinear dielectric effects feature field induced suppressions (saturation) and enhancements (chemical effect) of the amplitudes, as well as time constant shifts towards faster (energy absorption) and slower (entropy reduction) dynamics. This review focuses on the effects of high electric fields that are reversible and observed at constant temperature for single component glass-forming liquids. The experimental challenges involved in nonlinear dielectric experiments, the approaches to separating and identifying the different sources of nonlinear behavior, and the current understanding of how high electric fields affect dielectric materials will be discussed. Covering studies from Debye's initial approach to the present state-of-the-art, it will be emphasized what insight can be gained from the nonlinear responses that are not available from dielectric relaxation results obtained in the linear regime.
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Affiliation(s)
- Ranko Richert
- School of Molecular Sciences, Arizona State University, Tempe, AZ 85287-1604, United States of America
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3
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Diezemann G. Nonlinear response theory for Markov processes. II. Fifth-order response functions. Phys Rev E 2017; 96:022150. [PMID: 28950644 DOI: 10.1103/physreve.96.022150] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2017] [Indexed: 06/07/2023]
Abstract
The nonlinear response of stochastic models obeying a master equation is calculated up to fifth order in the external field, thus extending the third-order results obtained earlier [G. Diezemann, Phys. Rev. E 85, 051502 (2012)PLEEE81539-375510.1103/PhysRevE.85.051502]. For sinusoidal fields the 5ω component of the susceptibility is computed for the model of dipole reorientations in an asymmetric double well potential and for a trap model with a Gaussian density of states. For most realizations of the models a hump is found in the higher-order susceptibilities. In particular, for the asymmetric double well potential model there are two characteristic temperature regimes showing the occurrence of such a hump as compared to a single characteristic regime in the case of the third-order response. In the case of the trap model the results strongly depend on the variable coupled to the field. As for the third-order response, the low-frequency limit of the susceptibility plays a crucial role with respect to the occurrence of a hump. The findings are discussed in light of recent experimental results obtained for supercooled liquids. The differences found for the third-order and the fifth-order response indicate that nonlinear response functions might serve as a powerful tool to discriminate among the large number of existing models for glassy relaxation.
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Affiliation(s)
- Gregor Diezemann
- Institut für Physikalische Chemie, Universität Mainz, Duesbergweg 10-14, 55128 Mainz, Germany
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4
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Buchenau U. Modeling the nonlinear dielectric response of glass formers. J Chem Phys 2017; 146:214503. [DOI: 10.1063/1.4984929] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
Affiliation(s)
- U. Buchenau
- Jülich Center for Neutron Science, Forschungszentrum Jülich, Postfach 1913, D–52425 Jülich, Germany
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5
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Kim P, Young-Gonzales AR, Richert R. Dynamics of glass-forming liquids. XX. Third harmonic experiments of non-linear dielectric effects versus a phenomenological model. J Chem Phys 2016. [DOI: 10.1063/1.4960620] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
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6
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Albert S, Bauer T, Michl M, Biroli G, Bouchaud JP, Loidl A, Lunkenheimer P, Tourbot R, Wiertel-Gasquet C, Ladieu F. Fifth-order susceptibility unveils growth of thermodynamic amorphous order in glass-formers. Science 2016; 352:1308-11. [DOI: 10.1126/science.aaf3182] [Citation(s) in RCA: 140] [Impact Index Per Article: 17.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2016] [Accepted: 05/09/2016] [Indexed: 11/02/2022]
Affiliation(s)
- S. Albert
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay Bat 772, 91191 Gif-sur-Yvette Cedex, France
| | - Th. Bauer
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany
| | - M. Michl
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany
| | - G. Biroli
- IPhT, CEA, CNRS, Université Paris-Saclay, CEA Saclay Bat 774, 91191 Gif-sur-Yvette Cedex, France
- LPS, Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France
| | - J.-P. Bouchaud
- Capital Fund Management, 23 rue de l’Université, 75007 Paris, France
| | - A. Loidl
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany
| | - P. Lunkenheimer
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany
| | - R. Tourbot
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay Bat 772, 91191 Gif-sur-Yvette Cedex, France
| | - C. Wiertel-Gasquet
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay Bat 772, 91191 Gif-sur-Yvette Cedex, France
| | - F. Ladieu
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay Bat 772, 91191 Gif-sur-Yvette Cedex, France
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7
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Michl M, Bauer T, Lunkenheimer P, Loidl A. Nonlinear dielectric spectroscopy in a fragile plastic crystal. J Chem Phys 2016; 144:114506. [DOI: 10.1063/1.4944394] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Affiliation(s)
- M. Michl
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86135 Augsburg, Germany
| | - Th. Bauer
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86135 Augsburg, Germany
| | - P. Lunkenheimer
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86135 Augsburg, Germany
| | - A. Loidl
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86135 Augsburg, Germany
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8
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Richert R. Non-linear dielectric signatures of entropy changes in liquids subject to time dependent electric fields. J Chem Phys 2016; 144:114501. [DOI: 10.1063/1.4943885] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
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9
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Ngai KL. Interpreting the nonlinear dielectric response of glass-formers in terms of the coupling model. J Chem Phys 2015; 142:114502. [DOI: 10.1063/1.4913980] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
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10
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Pick RM. Third order dielectric time dependent susceptibilities and the "box model". J Chem Phys 2015; 142:064511. [PMID: 25681927 DOI: 10.1063/1.4906807] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present here the calculation of the "time dependent" moduli of the third order, dielectric, susceptibilities measured at the frequency ω of the applied electric field and at the frequency 3ω. The calculation is performed within the frame work of the "box model," both in the ideal case of a pure third order polarization and in the practical case studied by Samanta and Richert [J. Chem. Phys. 140, 247101 (2014)] where a first order polarization contribution is also detected. We show that, in the two cases, those two modules have a largely different dynamics and that the results can be easily compared with experiments thanks to the data gathered by Samanta and Richert [J. Chem. Phys. 140, 247101 (2014)]. This should provide a new test on the validity of the "box model."
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Affiliation(s)
- R M Pick
- IMPMC, Université P. et M. Curie et CNRS-UMR 7590, Paris, France
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11
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Casalini R, Fragiadakis D, Roland CM. Dynamic correlation length scales under isochronal conditions. J Chem Phys 2015; 142:064504. [DOI: 10.1063/1.4907371] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- R. Casalini
- Naval Research Laboratory, Chemistry Division, Code 6120, Washington DC 20375-5342, USA
| | - D. Fragiadakis
- Naval Research Laboratory, Chemistry Division, Code 6120, Washington DC 20375-5342, USA
| | - C. M. Roland
- Naval Research Laboratory, Chemistry Division, Code 6120, Washington DC 20375-5342, USA
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12
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Michl M, Bauer T, Lunkenheimer P, Loidl A. Cooperativity and heterogeneity in plastic crystals studied by nonlinear dielectric spectroscopy. PHYSICAL REVIEW LETTERS 2015; 114:067601. [PMID: 25723245 DOI: 10.1103/physrevlett.114.067601] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/10/2014] [Indexed: 06/04/2023]
Abstract
The glassy dynamics of plastic-crystalline cyclo-octanol and ortho-carborane, where only the molecular reorientational degrees of freedom freeze without long-range order, is investigated by nonlinear dielectric spectroscopy. Marked differences to canonical glass formers show up: While molecular cooperativity governs the glassy freezing, it leads to a much weaker slowing down of molecular dynamics than in supercooled liquids. Moreover, the observed nonlinear effects cannot be explained with the same heterogeneity scenario recently applied to canonical glass formers. This supports ideas that molecular relaxation in plastic crystals may be intrinsically nonexponential. Finally, no nonlinear effects were detected for the secondary processes in cyclo-octanol.
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Affiliation(s)
- M Michl
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany
| | - Th Bauer
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany
| | - P Lunkenheimer
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany
| | - A Loidl
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany
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13
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Samanta S, Richert R. Dynamics of glass-forming liquids. XVIII. Does entropy control structural relaxation times? J Chem Phys 2015; 142:044504. [DOI: 10.1063/1.4906191] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Subarna Samanta
- Department of Chemistry and Biochemistry, Arizona State University, Tempe, Arizona 85287-1604, USA
| | - Ranko Richert
- Department of Chemistry and Biochemistry, Arizona State University, Tempe, Arizona 85287-1604, USA
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14
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Pick RM. Third order susceptibilities in supercooled liquids and the “box model” theory versus experiments. J Chem Phys 2014; 140:054508. [DOI: 10.1063/1.4861757] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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15
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Richert R. Frequency dependence of dielectric saturation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062313. [PMID: 24483450 DOI: 10.1103/physreve.88.062313] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2013] [Indexed: 06/03/2023]
Abstract
Dielectric saturation originates from the upper bound to dipole orientation, reached when all dipoles are aligned "perfectly" with respect to the electric field. For Debye-type dynamics, it is well established that the saturation effect is diminished at high frequencies relative to its steady-state value. Here, it is argued that a similar frequency dependence of this nonlinear dielectric effect is expected also for dispersive dynamics, provided that the system is dynamically homogeneous. By contrast, more realistic relaxation time dispersions based upon heterogeneous dynamics display a strongly reduced frequency dependence of dielectric saturation. Calculations demonstrate this effect in terms of both the fundamental and the third harmonic frequency susceptibilities. The relations of signatures of nonlinearity in different Fourier components of the response are briefly discussed.
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Affiliation(s)
- Ranko Richert
- I. Physikalisches Institut, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany
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16
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Bauer T, Lunkenheimer P, Loidl A. Cooperativity and the freezing of molecular motion at the glass transition. PHYSICAL REVIEW LETTERS 2013; 111:225702. [PMID: 24329455 DOI: 10.1103/physrevlett.111.225702] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2013] [Indexed: 06/03/2023]
Abstract
The slowing down of molecular dynamics when approaching the glass transition generally proceeds much stronger than expected for thermally activated motions. This strange phenomenon can be formally ascribed to a temperature-dependent activation energy E(T). In the present work, via measurements of the third-order nonlinear dielectric susceptibility, we deduce the increase of the number of correlated molecules N(corr) when approaching the glass transition and find a surprisingly simple correlation of E(T) and N(corr)(T). This provides strong evidence that the noncanonical temperature development of glassy dynamics is caused by a temperature-dependent energy barrier arising from the cooperative motion of ever larger numbers of molecules at low temperatures.
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Affiliation(s)
- Th Bauer
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany
| | - P Lunkenheimer
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany
| | - A Loidl
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany
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17
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Bauer T, Lunkenheimer P, Kastner S, Loidl A. Nonlinear dielectric response at the excess wing of glass-forming liquids. PHYSICAL REVIEW LETTERS 2013; 110:107603. [PMID: 23521298 DOI: 10.1103/physrevlett.110.107603] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2012] [Indexed: 06/01/2023]
Abstract
We present nonlinear dielectric measurements of glass-forming glycerol and propylene carbonate applying electrical fields up to 671 kV/cm. The measurements extend to sufficiently high frequencies to allow for the investigation of the nonlinear behavior in the regime of the so-far mysterious excess wing, showing up in the loss spectra of many glass formers as a second power law at high frequencies. Surprisingly, we find a complete lack of nonlinear behavior in the excess wing, in marked contrast to the α relaxation where, in agreement with previous reports, a strong increase of dielectric constant and loss is found.
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Affiliation(s)
- Th Bauer
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86135 Augsburg, Germany
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18
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Mazinani SKS, Richert R. Enthalpy recovery in glassy materials: Heterogeneous versus homogenous models. J Chem Phys 2012; 136:174515. [DOI: 10.1063/1.4712032] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
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19
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Diezemann G. Nonlinear response theory for Markov processes: simple models for glassy relaxation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:051502. [PMID: 23004762 DOI: 10.1103/physreve.85.051502] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2012] [Indexed: 06/01/2023]
Abstract
The theory of nonlinear response for Markov processes obeying a master equation is formulated in terms of time-dependent perturbation theory for the Green's functions and general expressions for the response functions up to third order in the external field are given. The nonlinear response is calculated for a model of dipole reorientations in an asymmetric double well potential, a standard model in the field of dielectric spectroscopy. The static nonlinear response is finite with the exception of a certain temperature T_{0} determined by the value of the asymmetry. In a narrow temperature range around T_{0}, the modulus of the frequency-dependent cubic response shows a peak at a frequency on the order of the relaxation rate and it vanishes for both low frequencies and high frequencies. At temperatures at which the static response is finite (lower and higher than T_{0}), the modulus is found to decay monotonously from the static limit to zero at high frequencies. In addition, results of calculations for a trap model with a Gaussian density of states are presented. In this case, the cubic response depends on the specific dynamical variable considered and also on the way the external field is coupled to the kinetics of the model. In particular, a set of different dynamical variables that gives rise to identical shapes of the linear susceptibility and only to different temperature dependencies of the relaxation times is considered. It is found that the frequency dependence of the nonlinear response functions, however, strongly depends on the particular choice of the variables. The results are discussed in the context of recent theoretical and experimental findings regarding the nonlinear response of supercooled liquids and glasses.
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Affiliation(s)
- Gregor Diezemann
- Institut für Physikalische Chemie, Universität Mainz, Jakob-Welder-Weg 11, 55128 Mainz, Germany
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