1
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Diezemann G. Nonlinear response theory for Markov processes. IV. The asymmetric double-well potential model revisited. Phys Rev E 2022; 106:064122. [PMID: 36671146 DOI: 10.1103/physreve.106.064122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2022] [Accepted: 12/02/2022] [Indexed: 06/17/2023]
Abstract
The dielectric response of noninteracting dipoles is discussed in the framework of the classical model of stochastic reorientations in an asymmetric double-well potential (ADWP). In the nonlinear regime, this model exhibits some pecularities in the static response. We find that the saturation behavior of the symmetric double-well potential model does not follow the Langevin function and only in the linear regime are the standard results recovered. If a finite asymmetry is assumed, then the nonlinear susceptibilities are found to change the sign at a number of characteristic temperatures that depend on the magnitude of the asymmetry, as has been observed earlier for the third-order and fifth-order responses. If the kinetics of the barrier crossing in the ADWP model is described as a two-state model, then we can give analytical expressions for the values of the characteristic temperatures. The results for the response obtained from a (numerical) solution of the Fokker-Planck equation for the Brownian motion in a model ADWP behaves very similarly to the two-state model for high barriers. For small barriers no clear-cut timescale separation between the barrier crossing process and the intrawell relaxation exists and the model exhibits a number of timescales. In this case, the frequency-dependent linear susceptibility at low temperatures is dominated by the fast intrawell transitions and at higher temperatures by the barrier crossing kinetics. We find that for nonlinear susceptibilities the latter process appears to be more important and the intrawell transitions play only a role at the lowest temperatures.
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Affiliation(s)
- Gregor Diezemann
- Department Chemie, Johannes Gutenberg Universität Mainz, 55128 Mainz, Germany
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2
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Moch K, Münzner P, Böhmer R, Gainaru C. Molecular Cross-correlations Govern Structural Rearrangements in a Nonassociating Polar Glass Former. PHYSICAL REVIEW LETTERS 2022; 128:228001. [PMID: 35714246 DOI: 10.1103/physrevlett.128.228001] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2021] [Revised: 01/22/2022] [Accepted: 04/14/2022] [Indexed: 06/15/2023]
Abstract
Self- and cross-correlation dynamics of deeply supercooled liquids were recently identified using photon correlation spectroscopy on the one hand and dielectric investigations on the other. These results fueled a controversial discussion whether the "generic" response identified by photon correlation spectroscopy, or rather the nonuniversal dielectric response, reflect the liquid's structural relaxation. The present study employs physical aging and oscillatory shear rheology to directly access the structural relaxation of a nonassociating glass-forming liquid and reveals that collective equilibrium fluctuations of simple liquids and not single-particle dynamics govern their structural relaxation. The present results thus challenge recent views that the glassy response of polar supercooled liquids can generically be decomposed into a Debye-type, supramolecular response and a single-particle dynamics with the latter reflecting the "true" structural relaxation. Furthermore, the current findings underscore the pivotal role dielectric spectroscopy plays in glass science as one of the rare molecular-level reorientation techniques that senses dynamical cooperativity directly.
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Affiliation(s)
- K Moch
- Fakultät Physik, Technische Universität Dortmund, 44221 Dortmund, Germany
| | - P Münzner
- Fakultät Physik, Technische Universität Dortmund, 44221 Dortmund, Germany
| | - R Böhmer
- Fakultät Physik, Technische Universität Dortmund, 44221 Dortmund, Germany
| | - C Gainaru
- Fakultät Physik, Technische Universität Dortmund, 44221 Dortmund, Germany
- Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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3
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Riechers B, Roed LA, Mehri S, Ingebrigtsen TS, Hecksher T, Dyre JC, Niss K. Predicting nonlinear physical aging of glasses from equilibrium relaxation via the material time. SCIENCE ADVANCES 2022; 8:eabl9809. [PMID: 35294250 PMCID: PMC8926348 DOI: 10.1126/sciadv.abl9809] [Citation(s) in RCA: 16] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
The noncrystalline glassy state of matter plays a role in virtually all fields of materials science and offers complementary properties to those of the crystalline counterpart. The caveat of the glassy state is that it is out of equilibrium and therefore exhibits physical aging, i.e., material properties change over time. For half a century, the physical aging of glasses has been known to be described well by the material-time concept, although the existence of a material time has never been directly validated. We do this here by successfully predicting the aging of the molecular glass 4-vinyl-1,3-dioxolan-2-one from its linear relaxation behavior. This establishes the defining property of the material time. Via the fluctuation-dissipation theorem, our results imply that physical aging can be predicted from thermal-equilibrium fluctuation data, which is confirmed by computer simulations of a binary liquid mixture.
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Moch K, Bierwirth SP, Gainaru C, Böhmer R. First- and third-order shear nonlinearities across the structural relaxation peak of the deeply supercooled pharmaceutical liquid indomethacin. J Chem Phys 2021; 155:134901. [PMID: 34624979 DOI: 10.1063/5.0065572] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
Nonlinear rheological properties of viscous indomethacin are studied in the frequency range of its structural relaxation, that is, in a range so far inaccessible to standard techniques involving medium-amplitude oscillatory shear amplitudes. The first- and third-order nonlinearity parameters thus recorded using a sequence of small and large shear excitations in a time efficient manner are compared with predictions from rheological models. By properly phase cycling the shear amplitudes, build-up and decay transients are recorded. Analogous to electrical-field experiments, these transients yield direct access to the structural relaxation times under linear and nonlinear shearing conditions. To demonstrate the broader applicability of the present approach, transient analyses are also carried out for the glass formers glycerol, ortho-terphenyl, and acetaminophen.
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Affiliation(s)
- Kevin Moch
- Fakultät Physik, Technische Universität Dortmund, D-44221 Dortmund, Germany
| | - S Peter Bierwirth
- Fakultät Physik, Technische Universität Dortmund, D-44221 Dortmund, Germany
| | - Catalin Gainaru
- Fakultät Physik, Technische Universität Dortmund, D-44221 Dortmund, Germany
| | - Roland Böhmer
- Fakultät Physik, Technische Universität Dortmund, D-44221 Dortmund, Germany
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5
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Thoms E, Richert R. New experimental approach to nonlinear dielectric effects in the static limit. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2021.117107] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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6
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Richert R, Matyushov DV. Quantifying dielectric permittivities in the nonlinear regime. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:385101. [PMID: 34198283 DOI: 10.1088/1361-648x/ac108f] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2021] [Accepted: 07/01/2021] [Indexed: 06/13/2023]
Abstract
In contrast to the static dielectric permittivity,ε, associated with linear response, its high-field counterpart,εE, is not a material specific quantity, but rather depends on the experimental method used to determine the nonlinear dielectric effect (NDE). Here, we defineεEin a manner consistent with how high field permittivities are typically derived from a capacitance measurement using high voltages. Based upon characterizing the materials nonlinear behavior via its third order susceptibility,χ3, the relations between a givenχ3and the observableεEis calculated for six different experimental or theoretical approaches to NDEs in the static limit. It is argued that the quantityχ3is superior overεEor the Piekara factor, (εE-ε)/E2, because it facilitates an unambiguous comparison among different experimental techniques and it provides a more robust connection between experiment and theory.
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Affiliation(s)
- Ranko Richert
- School of Molecular Sciences, Arizona State University, Tempe, AZ 85287, United States of America
| | - Dmitry V Matyushov
- Department of Physics and School of Molecular Sciences, Arizona State University, Tempe, AZ 85287, United States of America
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7
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Speck T. Modeling non-linear dielectric susceptibilities of supercooled molecular liquids. J Chem Phys 2021; 155:014506. [PMID: 34241396 DOI: 10.1063/5.0056657] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Advances in high-precision dielectric spectroscopy have enabled access to non-linear susceptibilities of polar molecular liquids. The observed non-monotonic behavior has been claimed to provide strong support for theories of dynamic arrest based on the thermodynamic amorphous order. Here, we approach this question from the perspective of dynamic facilitation, an alternative view focusing on emergent kinetic constraints underlying the dynamic arrest of a liquid approaching its glass transition. We derive explicit expressions for the frequency-dependent higher-order dielectric susceptibilities exhibiting a non-monotonic shape, the height of which increases as temperature is lowered. We demonstrate excellent agreement with the experimental data for glycerol, challenging the idea that non-linear response functions reveal correlated relaxation in supercooled liquids.
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Affiliation(s)
- Thomas Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
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8
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Honorio G, Bierwirth SP, Gainaru C, Böhmer R. Nonlinear electrical and rheological spectroscopies identify structural and supramolecular relaxations in a model peptide. SOFT MATTER 2019; 15:4334-4345. [PMID: 31073564 DOI: 10.1039/c9sm00434c] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Supercooled liquid secondary amides display an electrical absorption peak characterized by an almost Debye-like shape, indicative of a close-to-exponential polarization response. This response, believed to be supramolecular in nature, is so enormously intense that the amide's structural process, contributing only a few percent to the total relaxation strength, is hard to resolve reliably using standard dielectric spectroscopy. To overcome this issue, nonlinear dielectric spectroscopy involving field-induced structural recovery and temperature-induced physical aging, was applied near the calorimetric glass transition of a mixture of N-methylformamide and N-ethylacetamide. Without the need to rely on cumbersome deconvolution procedures, it is thus demonstrated that the supramolecular response is by a factor of 6 slower than the structural relaxation. Conversely, in linear rheological experiments only the structural relaxation could be resolved, but not the supramolecular one. However, medium-amplitude oscillatory shear experiments carried out at 160 K do reveal the supramolecular process. Hence, the combination of linear and nonlinear mechanical measurements corroborates the dielectrically uncovered spectral separation of the two processes.
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Affiliation(s)
- Gabriel Honorio
- Fakultät Physik, Technische Universität Dortmund, 44221 Dortmund, Germany
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9
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Richert R. Perspective: Nonlinear approaches to structure and dynamics of soft materials. J Chem Phys 2018; 149:240901. [DOI: 10.1063/1.5065412] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
Affiliation(s)
- Ranko Richert
- School of Molecular Sciences, Arizona State University, Tempe, Arizona 85287, USA and I. Physikalisches Institut, Universität Göttingen, D-37077 Göttingen, Germany
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10
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Wieland F, Sokolov AP, Böhmer R, Gainaru C. Transient Nonlinear Response of Dynamically Decoupled Ionic Conductors. PHYSICAL REVIEW LETTERS 2018; 121:064503. [PMID: 30141682 DOI: 10.1103/physrevlett.121.064503] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2018] [Indexed: 06/08/2023]
Abstract
The present study demonstrates that large electric fields progressively enhance the conductivity of ionic systems up to timescales corresponding to those on which their structural rearrangements take place. Yet, in many ionic materials, some regarded as candidates for electrical energy storage applications, the structural relaxation process can be tremendously slower than (or highly decoupled from) the charge fluctuations. Consequently, nonlinear dielectric spectroscopy may be employed to access rheological information in dynamically decoupled ionic conductors, whereas the combination of large electric power density and good mechanical stability, both technologically highly desired, imposes specific experimental constraints to reliably determine the steady-state conductivity of such materials.
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Affiliation(s)
- Felix Wieland
- Fakultät Physik, Technische Universität Dortmund, 44221 Dortmund, Germany
| | - Alexei P Sokolov
- Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, USA
| | - Roland Böhmer
- Fakultät Physik, Technische Universität Dortmund, 44221 Dortmund, Germany
| | - Catalin Gainaru
- Fakultät Physik, Technische Universität Dortmund, 44221 Dortmund, Germany
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11
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Casalini R, Roland CM. Nonlinear dielectric spectroscopy of propylene carbonate derivatives. J Chem Phys 2018; 148:134506. [DOI: 10.1063/1.5024379] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Affiliation(s)
- R. Casalini
- Naval Research Laboratory, Chemistry Division, Washington, DC 20375-5342, USA
| | - C. M. Roland
- Naval Research Laboratory, Chemistry Division, Washington, DC 20375-5342, USA
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12
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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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13
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Young-Gonzales AR, Adrjanowicz K, Paluch M, Richert R. Nonlinear dielectric features of highly polar glass formers: Derivatives of propylene carbonate. J Chem Phys 2017; 147:224501. [DOI: 10.1063/1.5003813] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023] Open
Affiliation(s)
- A. R. Young-Gonzales
- School of Molecular Sciences, Arizona State University, Tempe, Arizona 85287-1604, USA
| | - K. Adrjanowicz
- Institute of Physics, University of Silesia, Ulica Uniwersytecka 4, 40-007 Katowice, Poland
- SMCEBI, Ulica 75 Pulku Piechoty 1a, 41-500 Chorzow, Poland
| | - M. Paluch
- Institute of Physics, University of Silesia, Ulica Uniwersytecka 4, 40-007 Katowice, Poland
- SMCEBI, Ulica 75 Pulku Piechoty 1a, 41-500 Chorzow, Poland
| | - R. Richert
- School of Molecular Sciences, Arizona State University, Tempe, Arizona 85287-1604, USA
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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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15
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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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16
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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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17
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Richert R. Relaxation time and excess entropy in viscous liquids: Electric field versus temperature as control parameter. J Chem Phys 2017; 146:064501. [DOI: 10.1063/1.4975389] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ranko Richert
- School of Molecular Sciences, Arizona State University, Tempe, Arizona 85287-1604, USA
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