1
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Jiang C, Baggioli M, Douglas JF. Stringlet excitation model of the boson peak. J Chem Phys 2024; 160:214505. [PMID: 38832741 DOI: 10.1063/5.0210057] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2024] [Accepted: 05/20/2024] [Indexed: 06/05/2024] Open
Abstract
The boson peak (BP), a low-energy excess in the vibrational density of states over the Debye contribution, is often identified as a characteristic of amorphous solid materials. Despite decades of efforts, its microscopic origin still remains a mystery. Recently, it has been proposed, and corroborated with simulations, that the BP might stem from intrinsic localized modes involving one-dimensional (1D) string-like excitations ("stringlets"). We build on a theory originally proposed by Lund that describes the localized modes as 1D vibrating strings, but we specify the stringlet size distribution to be exponential, as observed in simulations. We provide an analytical prediction for the BP frequency ωBP in the temperature regime well below the observed glass transition temperature Tg. The prediction involves no free parameters and accords quantitatively with prior simulation observations in 2D and 3D model glasses based on inverse power law potentials. The comparison of the string model to observations is more uncertain when compared to simulations of an Al-Sm metallic glass material at temperatures well above Tg. Nonetheless, our stringlet model of the BP naturally reproduces the softening of the BP frequency upon heating and offers an analytical explanation for the experimentally observed scaling with the shear modulus in the glass state and changes in this scaling in simulations of glass-forming liquids. Finally, the theoretical analysis highlights the existence of a strong damping for the stringlet modes above Tg, which leads to a large low-frequency contribution to the 3D vibrational density of states, observed in both experiments and simulations.
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Affiliation(s)
- Cunyuan Jiang
- School of Physics and Astronomy, Shanghai Jiao Tong University, 200240 Shanghai, China
- Wilczek Quantum Center, Shanghai Jiao Tong University, 200240 Shanghai, China
- Shanghai Research Center for Quantum Sciences, 200240 Shanghai, China
| | - Matteo Baggioli
- School of Physics and Astronomy, Shanghai Jiao Tong University, 200240 Shanghai, China
- Wilczek Quantum Center, Shanghai Jiao Tong University, 200240 Shanghai, China
- Shanghai Research Center for Quantum Sciences, 200240 Shanghai, China
| | - Jack F Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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2
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Schirmacher W, Paoluzzi M, Mocanu FC, Khomenko D, Szamel G, Zamponi F, Ruocco G. The nature of non-phononic excitations in disordered systems. Nat Commun 2024; 15:3107. [PMID: 38600083 PMCID: PMC11258284 DOI: 10.1038/s41467-024-46981-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2023] [Accepted: 03/18/2024] [Indexed: 04/12/2024] Open
Abstract
The frequency scaling exponent of low-frequency excitations in microscopically small glasses, which do not allow for the existence of waves (phonons), has been in the focus of the recent literature. The density of states g(ω) of these modes obeys an ωs scaling, where the exponent s, ranging between 2 and 5, depends on the quenching protocol. The orgin of these findings remains controversal. Here we show, using heterogeneous-elasticity theory, that in a marginally-stable glass sample g(ω) follows a Debye-like scaling (s = 2), and the associated excitations (type-I) are of random-matrix type. Further, using a generalisation of the theory, we demonstrate that in more stable samples, other, (type-II) excitations prevail, which are non-irrotational oscillations, associated with local frozen-in stresses. The corresponding frequency scaling exponent s is governed by the statistics of small values of the stresses and, therefore, depends on the details of the interaction potential.
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Affiliation(s)
- Walter Schirmacher
- Institut für Physik, Staudinger Weg 7, Universität Mainz, D-55099, Mainz, Germany.
- Center for Life Nano Science @Sapienza, Istituto Italiano di Tecnologia, 291 Viale Regina Elena, I-00161, Roma, Italy.
| | - Matteo Paoluzzi
- Istituto per le Applicazioni del Calcolo del Consiglio Nazionale delle Ricerche, Via Pietro Castellino 111, 80131, Napoli, NA, Italy
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Carrer de Martí i Franquès 1, 08028, Barcelona, Spain
- Dipartimento di Fisica, Universita' di Roma "La Sapienza", P'le Aldo Moro 5, I-00185, Roma, Italy
| | - Felix Cosmin Mocanu
- Dept. of Materials, Univ. of Oxford, Parks Road, Oxford, OX13PH, UK
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, France
| | - Dmytro Khomenko
- Dipartimento di Fisica, Universita' di Roma "La Sapienza", P'le Aldo Moro 5, I-00185, Roma, Italy
| | - Grzegorz Szamel
- Dept. of Chemistry, Colorado State University, Fort Collins, CO, 80523, USA
| | - Francesco Zamponi
- Dipartimento di Fisica, Universita' di Roma "La Sapienza", P'le Aldo Moro 5, I-00185, Roma, Italy
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, France
| | - Giancarlo Ruocco
- Center for Life Nano Science @Sapienza, Istituto Italiano di Tecnologia, 291 Viale Regina Elena, I-00161, Roma, Italy.
- Dipartimento di Fisica, Universita' di Roma "La Sapienza", P'le Aldo Moro 5, I-00185, Roma, Italy.
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3
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Kölbel J, Anuschek ML, Stelzl I, Santitewagun S, Friess W, Zeitler JA. Dynamical Transition in Dehydrated Proteins. J Phys Chem Lett 2024; 15:3581-3590. [PMID: 38527099 PMCID: PMC11000241 DOI: 10.1021/acs.jpclett.3c03584] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2023] [Revised: 03/16/2024] [Accepted: 03/19/2024] [Indexed: 03/27/2024]
Abstract
Terahertz time-domain spectroscopy and differential scanning calorimetry were used to study the role of the dynamics of biomolecules decoupled from solvent effects. Lyophilized sucrose exhibited steadily increasing absorption with temperature as anharmonic excitations commenced as the system emerged from a deep minimum of the potential energy landscape where harmonic vibrations dominate. The polypeptide bacitracin and two globular proteins, lysozyme and human serum albumin, showed a more complex temperature dependence. Further analysis focused on the spectral signature below and above the boson peak. We found evidence of the onset of anharmonic motions that are characteristic for partial unfolding and molecular jamming in the dry biomolecules. The activation of modes of the protein molecules at temperatures comparable to the protein dynamical transition temperature was observed in the absence of hydration. No evidence of Fröhlich coherence, postulated to facilitate biological function, was found in our experiments.
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Affiliation(s)
- Johanna Kölbel
- Department
of Chemical Engineering, University of Cambridge, Cambridge CB3 0AS, U.K.
| | - Moritz L. Anuschek
- Department
of Chemical Engineering, University of Cambridge, Cambridge CB3 0AS, U.K.
- Department
of Pharmacy - Center for Drug Research, Pharmaceutical Technology
and Biopharmaceutics, Ludwig-Maximilians
Universität, Butenandtstrasse
5, 81377 Munich, Germany
| | - Ivonne Stelzl
- Department
of Pharmacy - Center for Drug Research, Pharmaceutical Technology
and Biopharmaceutics, Ludwig-Maximilians
Universität, Butenandtstrasse
5, 81377 Munich, Germany
| | - Supawan Santitewagun
- Department
of Chemical Engineering, University of Cambridge, Cambridge CB3 0AS, U.K.
| | - Wolfgang Friess
- Department
of Pharmacy - Center for Drug Research, Pharmaceutical Technology
and Biopharmaceutics, Ludwig-Maximilians
Universität, Butenandtstrasse
5, 81377 Munich, Germany
| | - J. Axel Zeitler
- Department
of Chemical Engineering, University of Cambridge, Cambridge CB3 0AS, U.K.
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4
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Ahammed B, Ertekin E. Configurational Disorder, Strong Anharmonicity, and Coupled Host Dynamics Lead to Superionic Transport in Li 3YCl 6 (LYC). ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2024; 36:e2310537. [PMID: 38279784 DOI: 10.1002/adma.202310537] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2023] [Revised: 12/30/2023] [Indexed: 01/28/2024]
Abstract
In superionic crystals, liquid-like ionic diffusivities often come hand-in-hand with ultra-low thermal conductivity and soft vibrational dynamics. However, generalized relationships between ion transport and vibrational dynamics remain elusive due to the diversity of superionic materials and complex underlying mechanisms. Here, the links between vibrational dynamics and ion transport in close-packed lithium halide ion conductor Li3YCl6 (LYC) are examined using a suite of atomistic first-principles methods. It is shown that configurational disorder, lattice anharmonicity, and coupled host-mobile ion vibrational dynamics together induce a transition to the superionic state. Statistical correlations between ionic hops and activation of the distribution of vibrational modes are found. However, typical phenomena associated with superionic conductors such as selective breakdown of zone-boundary soft phonons, or long wavelength transverse acoustic modes as in the 'phonon-liquid-electron crystal' concept, are not present. Instead, anharmonic zone-boundary modes aiding Li diffusion are found to broaden and soften selectively but persist across the superionic transition. These anharmonic modes couple Li ion motion with the vibrations of the flexible close-packed anion framework, which remains stable and facilitates ionic hopping. The results provide insights into how configurational disorder and soft-yet-resilient vibrational modes enable ionic hopping, particularly in 3D close-packed crystals.
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Affiliation(s)
- Ballal Ahammed
- Department of Mechanical Science & Engineering, University of Illinois at Urbana-Champaign, Illinois, 61801, USA
| | - Elif Ertekin
- Department of Mechanical Science & Engineering, University of Illinois at Urbana-Champaign, Illinois, 61801, USA
- Materials Research Laboratory, University of Illinois at Urbana-Champaign, Illinois, 61801, USA
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5
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Abstract
An analytical derivation of the vibrational density of states (DOS) of liquids, and, in particular, of its characteristic linear in frequency low-energy regime, has always been elusive because of the presence of an infinite set of purely imaginary modes—the instantaneous normal modes (INMs). By combining an analytic continuation of the Plemelj identity to the complex plane with the overdamped dynamics of the INMs, we derive a closed-form analytic expression for the low-frequency DOS of liquids. The obtained result explains, from first principles, the widely observed linear in frequency term of the DOS in liquids, whose slope appears to increase with the average lifetime of the INMs. The analytic results are robustly confirmed by fitting simulations data for Lennard-Jones liquids, and they also recover the Arrhenius law for the average relaxation time of the INMs, as expected.
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6
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Cui B, Zaccone A. Vibrational density of states of amorphous solids with long-ranged power-law-correlated disorder in elasticity. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2020; 43:72. [PMID: 33242169 DOI: 10.1140/epje/i2020-11995-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2020] [Accepted: 11/02/2020] [Indexed: 06/11/2023]
Abstract
A theory of vibrational excitations based on power-law spatial correlations in the elastic constants (or equivalently in the internal stress) is derived, in order to determine the vibrational density of states D([Formula: see text]) of disordered solids. The results provide the first prediction of a boson peak in amorphous materials where spatial correlations in the internal stresses (or elastic constants) are of power-law form, as is often the case in experimental systems, leading to a logarithmic enhancement of (Rayleigh) phonon attenuation. A logarithmic correction of the form [Formula: see text] is predicted to occur in the plot of the reduced excess DOS for frequencies around the boson peak in 3D. Moreover, the theory provides scaling laws of the density of states in the low-frequency region, including a [Formula: see text] regime in 3D, and provides information about how the boson peak intensity depends on the strength of power-law decay of fluctuations in elastic constants or internal stress. Analytical expressions are also derived for the dynamic structure factor for longitudinal excitations, which include a logarithmic correction factor, and numerical calculations are presented supporting the assumptions used in the theory.
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Affiliation(s)
- Bingyu Cui
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, CB3 0HE, Cambridge, UK
| | - Alessio Zaccone
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, CB3 0HE, Cambridge, UK.
- Department of Physics "A. Pontremoli", University of Milan, via Celoria 16, 20133, Milano, Italy.
- Statistical Physics Group, Department of Chemical Engineering and Biotechnology, University of Cambridge, Philippa Fawcett Drive, CB3 0AS, Cambridge, UK.
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7
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Zhang W, Douglas JF, Starr FW. What does the instantaneous normal mode spectrum tell us about dynamical heterogeneity in glass-forming fluids? J Chem Phys 2019; 151:184904. [PMID: 31731864 DOI: 10.1063/1.5127821] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Abstract
We examine the instantaneous normal mode spectrum of model metallic and polymeric glass-forming liquids. We focus on the localized modes in the unstable part of the spectrum [unstable localized (UL) modes] and find that the particles making the dominant contribution to the participation ratio form clusters that grow upon cooling in a fashion similar to the dynamical heterogeneity in glass-forming fluids, i.e., highly mobile (or immobile) particles form clusters that grow upon cooling; however, a comparison of the UL mode clusters to the mobile and immobile particle clusters indicates that they are distinct entities. We also show that the cluster size provides an alternate method to distinguish localized and delocalized modes, offering a significant practical advantage over the finite-size scaling approach. We examine the trajectories of particles contributing most to the UL modes and find that they have a slightly enhanced mobility compared to the average, and we determine a characteristic time quantifying the persistence time of this excess mobility. This time scale is proportional to the structural relaxation time τα of the fluid, consistent with a prediction by Zwanzig [Phys. Rev. 156, 190 (1967)] for the lifetime of collective excitations in cooled liquids. Evidently, these collective excitations serve to facilitate relaxation but do not actually participate in the motion associated with barrier crossing events governing activated transport. They also serve as a possible concrete realization of the "facilitation" clusters postulated in previous modeling of glass-forming liquids.
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Affiliation(s)
- Wengang Zhang
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Jack F Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Francis W Starr
- Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA
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8
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9
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Shen H, Tan P, Xu L. Probing the Role of Mobility in the Collective Motion of Nonequilibrium Systems. PHYSICAL REVIEW LETTERS 2016; 116:048302. [PMID: 26871359 DOI: 10.1103/physrevlett.116.048302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2015] [Indexed: 06/05/2023]
Abstract
By systematically varying the mobility of self-propelled particles in a 2D lattice, we experimentally study the influence of particle mobility on system's collective motion. Our system is intrinsically nonequilibrium due to the lack of energy equipartition. By constructing the covariance matrix of spatial fluctuations and solving for its eigenmodes, we obtain the collective motions of the system with various magnitudes. Interestingly, our structurally ordered nonequilibrium system exhibits properties almost identical to disordered glassy systems under thermal equilibrium: the modes with large overall motions are spatially correlated and quasilocalized while the modes with small collective motions are highly localized, resembling the low- and high-frequency modes in glass. More surprisingly, a peak similar to the boson peak forms in our nonequilibrium system as the number of mobile particles increases, revealing the possible origin of the boson peak from a dynamic aspect. We further illustrate that the spatially correlated large-movement modes can be produced by the cooperation of highly active particles above a threshold fraction, while the localized small-movement modes can be created by adding individual inactive particles. Our study clarifies the role of mobility in collective motions, and further suggests a promising possibility of extending the powerful mode analysis approach to nonequilibrium systems.
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Affiliation(s)
- Hongchuan Shen
- Department of Physics, The Chinese University of Hong Kong, Hong Kong, China
| | - Peng Tan
- Department of Physics, The Chinese University of Hong Kong, Hong Kong, China
- Department of Physics, State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China
| | - Lei Xu
- Department of Physics, The Chinese University of Hong Kong, Hong Kong, China
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10
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Wang Z, Liu KH, Le P, Li M, Chiang WS, Leão JB, Copley JRD, Tyagi M, Podlesnyak A, Kolesnikov AI, Mou CY, Chen SH. Wang et al. Reply. PHYSICAL REVIEW LETTERS 2015; 115:149802. [PMID: 26551830 DOI: 10.1103/physrevlett.115.149802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2015] [Indexed: 06/05/2023]
Affiliation(s)
- Zhe Wang
- Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Kao-Hsiang Liu
- Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan, Republic of China
| | - Peisi Le
- Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Mingda Li
- Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Wei-Shan Chiang
- Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Juscelino B Leão
- NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - John R D Copley
- NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Madhusudan Tyagi
- NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
- Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742, USA
| | - Andrey Podlesnyak
- Spallation Neutron Source, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Alexander I Kolesnikov
- Spallation Neutron Source, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Chung-Yuan Mou
- Department of Chemistry, National Taiwan University, Taipei 106, Taiwan, Republic of China
| | - Sow-Hsin Chen
- Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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11
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Chakraborty S, Reed J, Sage JT, Branagan NC, Petrik ID, Miner KD, Hu MY, Zhao J, Alp EE, Lu Y. Recent advances in biosynthetic modeling of nitric oxide reductases and insights gained from nuclear resonance vibrational and other spectroscopic studies. Inorg Chem 2015; 54:9317-29. [PMID: 26274098 PMCID: PMC4677664 DOI: 10.1021/acs.inorgchem.5b01105] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
This Forum Article focuses on recent
advances in structural and spectroscopic studies of biosynthetic models
of nitric oxide reductases (NORs). NORs are complex metalloenzymes
found in the denitrification pathway of Earth’s nitrogen cycle
where they catalyze the proton-dependent two-electron reduction of
nitric oxide (NO) to nitrous oxide (N2O). While much progress
has been made in biochemical and biophysical studies of native NORs
and their variants, a clear mechanistic understanding of this important
metalloenzyme related to its function is still elusive. We report
herein UV–vis and nuclear resonance vibrational spectroscopy
(NRVS) studies of mononitrosylated intermediates of the NOR reaction
of a biosynthetic model. The ability to selectively substitute metals
at either heme or nonheme metal sites allows the introduction of independent 57Fe probe atoms at either site, as well as allowing the preparation
of analogues of stable reaction intermediates by replacing either
metal with a redox inactive metal. Together with previous structural
and spectroscopic results, we summarize insights gained from studying
these biosynthetic models toward understanding structural features
responsible for the NOR activity and its mechanism. The outlook on
NOR modeling is also discussed, with an emphasis on the design of
models capable of catalytic turnovers designed based on close mimics
of the secondary coordination sphere of native NORs. New insights into nitric oxide reductases (NORs) are obtained. Using
nuclear resonance vibrational spectroscopy, we probe both iron atoms
in mononitrosylated intermediates of the NOR reaction in a biosynthetic
protein model that reveal new insights into the structural and electronic
features responsible for the NOR activity and its likely mechanism.
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Affiliation(s)
| | | | - J Timothy Sage
- Department of Physics, Northeastern University , Boston, Massachusetts 02115, United States
| | - Nicole C Branagan
- Department of Physics, Northeastern University , Boston, Massachusetts 02115, United States
| | | | | | - Michael Y Hu
- Advanced Photon Source, Argonne National Laboratory , Argonne, Illinois 60439, United States
| | - Jiyong Zhao
- Advanced Photon Source, Argonne National Laboratory , Argonne, Illinois 60439, United States
| | - E Ercan Alp
- Advanced Photon Source, Argonne National Laboratory , Argonne, Illinois 60439, United States
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12
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Venuti V, Rossi B, D'Amico F, Mele A, Castiglione F, Punta C, Melone L, Crupi V, Majolino D, Trotta F, Gessini A, Masciovecchio C. Combining Raman and infrared spectroscopy as a powerful tool for the structural elucidation of cyclodextrin-based polymeric hydrogels. Phys Chem Chem Phys 2015; 17:10274-82. [DOI: 10.1039/c5cp00607d] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
UV Raman spectroscopy and infrared spectroscopy have been efficiently implemented for the structural and dynamic elucidation of cyclodextrin-based polymeric hydrogels.
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13
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Liu K, Rykov AI, Wang J, Zhang T. Recent Advances in the Application of Mößbauer Spectroscopy in Heterogeneous Catalysis. ADVANCES IN CATALYSIS 2015. [DOI: 10.1016/bs.acat.2015.09.001] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
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14
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DeGiuli E, Laversanne-Finot A, Düring G, Lerner E, Wyart M. Effects of coordination and pressure on sound attenuation, boson peak and elasticity in amorphous solids. SOFT MATTER 2014; 10:5628-5644. [PMID: 24981002 DOI: 10.1039/c4sm00561a] [Citation(s) in RCA: 105] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Connectedness and applied stress strongly affect elasticity in solids. In various amorphous materials, mechanical stability can be lost either by reducing connectedness or by increasing pressure. We present an effective medium theory of elasticity that extends previous approaches by incorporating the effect of compression, of amplitude e, allowing one to describe quantitative features of sound propagation, transport, the boson peak, and elastic moduli near the elastic instability occurring at a compression ec. The theory disentangles several frequencies characterizing the vibrational spectrum: the onset frequency where strongly-scattered modes appear in the vibrational spectrum, the pressure-independent frequency ω* where the density of states displays a plateau, the boson peak frequency ωBP found to scale as , and the Ioffe-Regel frequency ωIR where scattering length and wavelength become equal. We predict that sound attenuation crosses over from ω(4) to ω(2) behaviour at ω0, consistent with observations in glasses. We predict that a frequency-dependent length scale ls(ω) and speed of sound ν(ω) characterize vibrational modes, and could be extracted from scattering data. One key result is the prediction of a flat diffusivity above ω0, in agreement with previously unexplained observations. We find that the shear modulus does not vanish at the elastic instability, but drops by a factor of 2. We check our predictions in packings of soft particles and study the case of covalent networks and silica, for which we predict ωIR ≈ ωBP. Overall, our approach unifies sound attenuation, transport and length scales entering elasticity in a single framework where disorder is not the main parameter controlling the boson peak, in agreement with observations. This framework leads to a phase diagram where various glasses can be placed, connecting microscopic structure to vibrational properties.
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Affiliation(s)
- Eric DeGiuli
- Center for Soft Matter Research, New York University, 4 Washington Place, New York, NY 10003, USA.
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15
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Lerner E, DeGiuli E, Düring G, Wyart M. Breakdown of continuum elasticity in amorphous solids. SOFT MATTER 2014; 10:5085-5092. [PMID: 24905568 DOI: 10.1039/c4sm00311j] [Citation(s) in RCA: 67] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We show numerically that the response of simple amorphous solids (elastic networks and particle packings) to a local force dipole is characterized by a lengthscale lc that diverges as unjamming is approached as lc ∼ (z - 2d)(-1/2), where z ≥ 2d is the mean coordination, and d is the spatial dimension, at odds with previous numerical claims. We also show how the magnitude of the lengthscale lc is amplified by the presence of internal stresses in the disordered solid. Our data suggests a divergence of lc ∼ (pc - p)(-1/4) with proximity to a critical internal stress pc at which soft elastic modes become unstable.
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Affiliation(s)
- Edan Lerner
- New York University, Center for Soft Matter Research, 4 Washington Place, New York, NY 10003, USA.
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16
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Crupi V, Fontana A, Giarola M, Longeville S, Majolino D, Mariotto G, Mele A, Paciaroni A, Rossi B, Trotta F, Venuti V. Vibrational Density of States and Elastic Properties of Cross-Linked Polymers: Combining Inelastic Light and Neutron Scattering. J Phys Chem B 2014; 118:624-33. [DOI: 10.1021/jp410448y] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Affiliation(s)
- Vincenza Crupi
- Department
of Physics and Earth Sciences, University of Messina, CNISM UdR Messina, Viale Ferdinando Stagno D’Alcontres 31, 98166 Messina, Italy
| | - Aldo Fontana
- Department
of Physics, University of Trento, Via Sommarive 14, 38123 Povo, Trento, Italy
| | - Marco Giarola
- Department
of Computer Science, University of Verona, Strada le Grazie 15, 37134 Verona, Italy
| | - Stéphane Longeville
- Laboratoire Léon
Brillouin (CEA/CNRS), CEA Saclay, 91191 Gif-sur-Yvette Cedex, France
| | - Domenico Majolino
- Department
of Physics and Earth Sciences, University of Messina, CNISM UdR Messina, Viale Ferdinando Stagno D’Alcontres 31, 98166 Messina, Italy
| | - Gino Mariotto
- Department
of Computer Science, University of Verona, Strada le Grazie 15, 37134 Verona, Italy
| | - Andrea Mele
- Department
of Chemistry, Materials and Chemical Engineering “G. Natta”, Politecnico di Milano, Piazza L. da Vinci 32, 20133 Milano, Italy
| | - Alessandro Paciaroni
- Department
of Physics, University of Perugia, Via A. Pascoli, 06123 Perugia, Italy
| | - Barbara Rossi
- Department
of Physics, University of Trento, Via Sommarive 14, 38123 Povo, Trento, Italy
| | - Francesco Trotta
- Dipartimento
di Chimica, Università di Torino, Via Pietro Giuria 7, 10125 Torino, Italy
| | - Valentina Venuti
- Department
of Physics and Earth Sciences, University of Messina, CNISM UdR Messina, Viale Ferdinando Stagno D’Alcontres 31, 98166 Messina, Italy
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17
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Tomaras C, Schirmacher W. High-frequency vibrational density of states of a disordered solid. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:495402. [PMID: 24214818 DOI: 10.1088/0953-8984/25/49/495402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We investigate the high-frequency behavior of the density of vibrational states in three-dimensional elasticity theory with spatially fluctuating elastic moduli. At frequencies well above the mobility edge, instanton solutions yield an exponentially decaying density of states. The instanton solutions describe excitations, which become localized due to the disorder-induced fluctuations, which lower the sound velocity in a finite region compared to its average value. The exponentially decaying density of states (known in electronic systems as the Lifshitz tail) is governed by the statistics of a fluctuating-elasticity landscape, capable of trapping the vibrational excitations.
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Affiliation(s)
- C Tomaras
- Institut für Physik, Universität Mainz, Staudinger Weg 7, D-55099 Mainz, Germany. Inst. f. funktionelle Materialien, Physik Department E13, TU München, D-85747 Garching, Germany
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Alkhalil A, Babu Nanubolu J, Burley JC. Analysis of phase transitions in molecular solids: quantitative assessment of phonon-mode vs intra-molecular spectral data. RSC Adv 2012. [DOI: 10.1039/c1ra00422k] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
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Pavlik JW, Barabanschikov A, Oliver AG, Alp EE, Sturhahn W, Zhao J, Sage JT, Scheidt WR. Probing vibrational anisotropy with nuclear resonance vibrational spectroscopy. Angew Chem Int Ed Engl 2010; 49:4400-4. [PMID: 20422668 DOI: 10.1002/anie.201000928] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Jeffrey W Pavlik
- Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, IN 46556, USA
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21
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Density of states and vibrational modes of PDMS studied by terahertz time-domain spectroscopy. Chem Phys Lett 2010. [DOI: 10.1016/j.cplett.2010.06.050] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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Pavlik J, Barabanschikov A, Oliver A, Alp E, Sturhahn W, Zhao J, Sage J, Scheidt W. Probing Vibrational Anisotropy with Nuclear Resonance Vibrational Spectroscopy. Angew Chem Int Ed Engl 2010. [DOI: 10.1002/ange.201000928] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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23
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Wyart M. Correlations between vibrational entropy and dynamics in liquids. PHYSICAL REVIEW LETTERS 2010; 104:095901. [PMID: 20366995 DOI: 10.1103/physrevlett.104.095901] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2009] [Indexed: 05/29/2023]
Abstract
An approximate relation between the vibrational entropy and the mean square displacement of the particles is derived. Using observations of the short-time dynamics in liquids of various fragility, it is argued that (i) if the crystal entropy is significantly smaller than the liquid entropy at T{g}, the extrapolation of the vibrational entropy leads to the correlation T{K} approximately T{0}, where T{K} is the Kauzmann temperature and T0 is the temperature extracted from the Vogel-Fulcher fit of the viscosity, and (ii) the jump in specific heat associated with vibrational entropy is very small for strong liquids, and increases with fragility. The analysis suggests that these correlations stem from the stiffening of the Boson peak under cooling, underlying the importance of this phenomenon on the dynamical arrest.
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Affiliation(s)
- Matthieu Wyart
- Lewis-Sigler Institute, Princeton University, Princeton, New Jersey 08544, USA
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Abraham SE, Bagchi B. Vibrational dynamics and boson peak in a supercooled polydisperse liquid. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:031506. [PMID: 20365739 DOI: 10.1103/physreve.81.031506] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2009] [Revised: 01/21/2010] [Indexed: 05/29/2023]
Abstract
Vibrational density of states (VDOS) in a supercooled polydisperse liquid is computed by diagonalizing the Hessian matrix evaluated at the potential energy minima for systems with different values of polydispersity. An increase in polydispersity leads to an increase in the relative population of localized high-frequency modes. At low frequencies, the density of states shows an excess compared to the Debye squared-frequency law, which has been identified with the boson peak. The height of the boson peak increases with polydispersity and shows a rather narrow sensitivity to changes in temperature. While the modes comprising the boson peak appear to be largely delocalized, there is a sharp drop in the participation ratio of the modes that exist just below the boson peak indicative of the quasilocalized nature of the low-frequency vibrations. Study of the difference spectrum at two different polydispersity reveals that the increase in the height of boson peak is due to a population shift from modes with frequencies above the maximum in the VDOS to that below the maximum, indicating an increase in the fraction of the unstable modes in the system. The latter is further supported by the facilitation of the observed dynamics by polydispersity. Since the strength of the liquid increases with polydispersity, the present result provides an evidence that the intensity of boson peak correlates positively with the strength of the liquid, as observed earlier in many experimental systems.
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Affiliation(s)
- Sneha Elizabeth Abraham
- Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560 012, India.
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Silbert LE, Silbert M. Long-wavelength structural anomalies in jammed systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:041304. [PMID: 19905305 DOI: 10.1103/physreve.80.041304] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2008] [Revised: 09/18/2009] [Indexed: 05/28/2023]
Abstract
The structural properties of static, jammed packings of monodisperse spheres in the vicinity of the jamming transition are investigated using large-scale computer simulations. At small wave number k , we argue that the anomalous behavior in the static structure factor, S(k) approximately k , is consequential of an excess of low-frequency, collective excitations seen in the vibrational spectrum. This anomalous feature becomes more pronounced closest to the jamming transition, such that S(0)-->0 at the transition point. We introduce an appropriate dispersion relation that accounts for these phenomena that leads us to relate these structural features to characteristic length scales associated with the low-frequency vibrational modes of these systems. When the particles are frictional, this anomalous behavior is suppressed providing yet more evidence that the jamming transitions for frictional spheres lie at lower packing fractions than for frictionless spheres. These results suggest that the mechanical properties of jammed and glassy media may therefore be inferred from measurements of both the static and dynamical structure factors.
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Affiliation(s)
- Leonardo E Silbert
- Department of Physics, Southern Illinois University, Carbondale, Illinois 62901, USA
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Yu. Eremchev I, Naumov A, Gorshelev A, Vainer YG, Kador L, Köhler J. Do impurity chromophores affect the tunneling dynamics of an amorphous polymer? Investigation by single-molecule spectroscopy. Mol Phys 2009. [DOI: 10.1080/00268970802672676] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Leu BM, Ching TH, Zhao J, Sturhahn W, Alp EE, Sage JT. Vibrational dynamics of iron in cytochrome C. J Phys Chem B 2009; 113:2193-200. [PMID: 19173569 DOI: 10.1021/jp806574t] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Nuclear resonance vibrational spectroscopy (NRVS) and Raman spectroscopy on (54)Fe- and (57)Fe-enriched cytochrome c (cyt c) identify multiple bands involving vibrations of the heme Fe. Comparison with predictions from Fe isotope shifts reveals that 70% of the NRVS signal in the 300-450 cm(-1) frequency range corresponds to vibrations resolved in Soret-enhanced Raman spectra. This frequency range dominates the "stiffness", an effective force constant determined by the Fe vibrational density of states (VDOS), which measures the strength of nearest-neighbor interactions with Fe. The stiffness of the low-spin Fe environment in both oxidation states of cyt c significantly exceeds that for the high-spin Fe in deoxymyoglobin, where the 200-300 cm(-1) frequency range dominates the VDOS. This situation is reflected in the shorter Fe-ligand bond lengths in the former with respect to the latter. The longer Fe-S(Met80) in oxidized cyt c with respect to reduced cyt c leads to a decrease in the stiffness of the iron environment upon oxidation. Comparison with NRVS measurements allows us to assess assignments for vibrational modes resolved in this region of the heme Raman spectrum. We consider the possibility that the 372 cm(-1) band in reduced cyt c involves the Fe-S(Met80) bond.
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Affiliation(s)
- Bogdan M Leu
- Department of Physics and Center for Interdisciplinary Research on Complex Systems, Northeastern University, Boston, Massachusetts 02115, USA
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Eremchev IY, Naumov AV, Vainer YG, Kador L. Effect of impurity molecules on the low-temperature vibrational dynamics of polyisobutylene: Investigation by single-molecule spectroscopy. J Chem Phys 2009; 130:184507. [DOI: 10.1063/1.3130677] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Fabiani E, Fontana A, Buchenau U. Neutron scattering study of the vibrations in vitreous silica and germania. J Chem Phys 2008; 128:244507. [DOI: 10.1063/1.2937731] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Riggleman RA, Lee HN, Ediger MD, de Pablo JJ. Free volume and finite-size effects in a polymer glass under stress. PHYSICAL REVIEW LETTERS 2007; 99:215501. [PMID: 18233224 DOI: 10.1103/physrevlett.99.215501] [Citation(s) in RCA: 54] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2007] [Indexed: 05/07/2023]
Abstract
Molecular dynamics simulations of the nonlinear creep response of a polymer glass under tension and compression have been performed at the glass transition temperature. The dynamics were measured as the deformation proceeds using the bond autocorrelation function, and the relaxation times measured as the system is compressed or elongated exhibit a universal response. In tension, the volume increases with strain rate and the relaxation times decrease. In compression, however, the volume decreases by approximately the same amount for all of the applied stresses. Thus, decreases in free volume take place alongside a decrease of the relaxation times by over a factor of 100. We find direct evidence that a characteristic length scale exists below which the deformation of the system exhibits distinct anomalies.
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Affiliation(s)
- Robert A Riggleman
- Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
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Zeitler JA, Taday PF, Pepper M, Rades T. Relaxation and Crystallization of Amorphous Carbamazepine Studied by Terahertz Pulsed Spectroscopy. J Pharm Sci 2007; 96:2703-9. [PMID: 17696163 DOI: 10.1002/jps.20908] [Citation(s) in RCA: 51] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
At the example of carbamazepine the crystallization of a small organic molecule from its amorphous phase was studied using in situ variable temperature terahertz pulsed spectroscopy (TPS). Even though terahertz spectra of disordered materials in the glassy state exhibit no distinct spectral features we demonstrate subtle changes in the spectra with increasing temperature and discuss the findings in respect to the density of vibrational states. The crystallization leads to distinct spectral features allowing the crystallization and subsequent polymorphic phase transition at higher temperatures to be studied in detail. It is possible to study both relaxation and crystallization processes by variable temperature TPS.
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Affiliation(s)
- J Axel Zeitler
- School of Pharmacy, University of Otago, P.O. Box 913, Dunedin, New Zealand
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Bordallo HN, Argyriou DN, Barthès M, Kalceff W, Rols S, Herwig KW, Fehr C, Juranyi F, Seydel T. Hydrogen in N-Methylacetamide: Positions and Dynamics of the Hydrogen Atoms Using Neutron Scattering. J Phys Chem B 2007; 111:7725-34. [PMID: 17571870 DOI: 10.1021/jp068528z] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
This work reports neutron diffraction and incoherent neutron scattering experiments on N-methylacetamide (NMA), which can be considered the model building block for the peptide linkage of polypeptides and proteins. Using the neutron data, we have been able to associate the onset of a striking negative thermal expansion (NTE) along the a-axis with a dynamical transition around 230 K, consistent with our calorimetric experiments. Observation of the NTE raises the question of possible proton transfer in NMA, which, from our data alone, still cannot be settled. We can only speculate that intermolecular repulsive forces increase as the O...H distance decreases upon cooling, and that around 230 K the lattice relaxes without observation of an actual proton transfer. However, the existence of a nonharmonic potential, reflected by the behavior of the phonon vibrations together with the observation of NTE, could be justified by the "vibrational" polaron theory in which a dynamic localization of the vibrational energy is created by coupling an internal molecular mode to a lattice phonon. More generally, this work shows that neutron powder diffraction techniques can be very powerful for investigating structural deformations in small peptide systems.
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Leu BM, Silvernail NJ, Zgierski MZ, Wyllie GRA, Ellison MK, Scheidt WR, Zhao J, Sturhahn W, Alp EE, Sage JT. Quantitative vibrational dynamics of iron in carbonyl porphyrins. Biophys J 2007; 92:3764-83. [PMID: 17350996 PMCID: PMC1868970 DOI: 10.1529/biophysj.106.093773] [Citation(s) in RCA: 45] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We use nuclear resonance vibrational spectroscopy and computational predictions based on density functional theory (DFT) to explore the vibrational dynamics of (57)Fe in porphyrins that mimic the active sites of histidine-ligated heme proteins complexed with carbon monoxide. Nuclear resonance vibrational spectroscopy yields the complete vibrational spectrum of a Mössbauer isotope, and provides a valuable probe that is not only selective for protein active sites but quantifies the mean-squared amplitude and direction of the motion of the probe nucleus, in addition to vibrational frequencies. Quantitative comparison of the experimental results with DFT calculations provides a detailed, rigorous test of the vibrational predictions, which in turn provide a reliable description of the observed vibrational features. In addition to the well-studied stretching vibration of the Fe-CO bond, vibrations involving the Fe-imidazole bond, and the Fe-N(pyr) bonds to the pyrrole nitrogens of the porphyrin contribute prominently to the observed experimental signal. All of these frequencies show structural sensitivity to the corresponding bond lengths, but previous studies have failed to identify the latter vibrations, presumably because the coupling to the electronic excitation is too small in resonance Raman measurements. We also observe the FeCO bending vibrations, which are not Raman active for these unhindered model compounds. The observed Fe amplitude is strongly inconsistent with three-body oscillator descriptions of the FeCO fragment, but agrees quantitatively with DFT predictions. Over the past decade, quantum chemical calculations have suggested revised estimates of the importance of steric distortion of the bound CO in preventing poisoning of heme proteins by carbon monoxide. Quantitative agreement with the predicted frequency, amplitude, and direction of Fe motion for the FeCO bending vibrations provides direct experimental support for the quantum chemical description of the energetics of the FeCO unit.
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Affiliation(s)
- Bogdan M Leu
- Department of Physics and Center for Interdisciplinary Research on Complex Systems, Northeastern University, Boston, Massachusetts, USA
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Papakonstantopoulos GJ, Doxastakis M, Nealey PF, Barrat JL, de Pablo JJ. Calculation of local mechanical properties of filled polymers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:031803. [PMID: 17500718 DOI: 10.1103/physreve.75.031803] [Citation(s) in RCA: 47] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/11/2006] [Indexed: 05/15/2023]
Abstract
A study is presented on the effects of smooth nanoparticles on the structure and elastic moduli of a polymer matrix. Structural changes between the unfilled polymer matrix and the nanocomposite give rise to the formation of a glassy layer that surrounds the nanoparticles. Results for the effects of particle size and concentration on the local and overall mechanical properties of the polymer are consistent with experimental macroscopic observations. At the molecular level, it is found that dispersed, attractive nanoparticles alter the nonaffine displacement fields that arise in the polymer glass upon deformation, thereby rendering the nanocomposite glass less fragile.
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Schirmacher W, Ruocco G, Scopigno T. Acoustic attenuation in glasses and its relation with the boson peak. PHYSICAL REVIEW LETTERS 2007; 98:025501. [PMID: 17358618 DOI: 10.1103/physrevlett.98.025501] [Citation(s) in RCA: 122] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2006] [Indexed: 05/14/2023]
Abstract
A theory for the vibrational dynamics in disordered solids [W. Schirmacher, Europhys. Lett. 73, 892 (2006), based on the random spatial variation of the shear modulus, has been applied to determine the wave vector (k) dependence of the Brillouin peak position (Omega(k)) and width (Gamma(k)), as well as the density of vibrational states [g(omega)], in disordered systems. As a result, we give a firm theoretical ground to the ubiquitous k2 dependence of Gamma(k) observed in glasses. Moreover, we derive a quantitative relation between the excess of the density of states (the boson peak) and Gamma(k), two quantities that were not considered related before. The successful comparison of this relation with the outcome of experiments and numerical simulations gives further support to the theory.
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Affiliation(s)
- W Schirmacher
- Physik-Department E13, Technische Universität München, Garching, Germany
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Maczka M, Hanuza J, Baran J, Hushur A, Kojima S. Heat capacity, Raman, and Brillouin scattering studies of M2O–MgO–WO3–P2O5 glasses (M=K,Rb). J Chem Phys 2006; 125:244503. [PMID: 17199351 DOI: 10.1063/1.2403127] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The authors report the results of temperature-dependent Brillouin scattering from both transverse and longitudinal acoustic waves, heat capacity studies as well as room temperature Raman scattering studies on M2O-MgO-WO3-P2O5 glasses (M=K,Rb). These results were used to obtain information about structure and various properties of the studied glasses such as fragility, elastic moduli, ratio of photoelastic constants, and elastic anharmonicity. They have found that both glasses have similar properties but replacement of K+ ions by Rb+ ions in the glass network leads to decrease of elastic parameters and P44 photoelastic constant due to increase of fragility. Based on Brillouin spectroscopy they show that a linear correlation between longitudinal and shear elastic moduli holds over a large temperature range. This result supports the literature data that the Cauchy-type relation represents a general rule for amorphous solids. An analysis of the Boson peak revealed that the form of the frequency distribution of the excess density of states is in agreement with the Euclidean random matrix theory. The reason of the observed shift of the maximum frequency of the Boson peak when K+ ions are substituted for Rb+ ions is also briefly discussed.
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Affiliation(s)
- M Maczka
- Institute of Low Temperature and Structure Research, Polish Academy of Sciences, P.O. Box 1410, 50-950 Wroclaw 2, Poland
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Vainer YG, Naumov AV, Bauer M, Kador L. Experimental evidence of the local character of vibrations constituting the Boson peak in amorphous solids. PHYSICAL REVIEW LETTERS 2006; 97:185501. [PMID: 17155551 DOI: 10.1103/physrevlett.97.185501] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2006] [Indexed: 05/12/2023]
Abstract
We report the first measurement of the density of states of low-energy vibrational excitations in a disordered solid via single-molecule (SM) spectroscopy. Optical spectra of many single tetra-tert-butylterrylene (TBT) molecules embedded to amorphous polyisobutylene (PIB) as spectral probes were recorded at low temperatures. The T dependences of SM spectral linewidths showed the broad distribution of local frequencies of vibrations under study. The obtained distribution was compared with the "Boson peak" in pure PIB measured in [R. Inoue, J. Chem. Phys. 95, 5332 (1991)] by neutron scattering. We found that embedding of a small amount of TBT into PIB does not influence markedly on the observed vibrational dynamics. These results prove the local character of low-energy vibrational excitations in glasses and the existence of relationship between these excitations and the Boson peak.
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Affiliation(s)
- Yu G Vainer
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow Region, 142190, Russia
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Taraskin SN, Simdyankin SI, Elliott SR, Neilson JR, Lo T. Universal features of terahertz absorption in disordered materials. PHYSICAL REVIEW LETTERS 2006; 97:055504. [PMID: 17026113 DOI: 10.1103/physrevlett.97.055504] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2006] [Indexed: 05/12/2023]
Abstract
Using an analytical theory, experimental terahertz time-domain spectroscopy data, and numerical evidence, we demonstrate that the frequency dependence of the absorption coupling coefficient between far-infrared photons and atomic vibrations in disordered materials has the universal functional form, C(omega)=A+Bomega(2), where the material-specific constants A and B are related to the distributions of fluctuating charges obeying global and local charge neutrality, respectively.
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Affiliation(s)
- S N Taraskin
- St. Catharine's College, Trumpington Street, Cambridge CB2 1RL, United Kingdom.
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Monaco A, Chumakov AI, Yue YZ, Monaco G, Comez L, Fioretto D, Crichton WA, Rüffer R. Density of vibrational states of a hyperquenched glass. PHYSICAL REVIEW LETTERS 2006; 96:205502. [PMID: 16803182 DOI: 10.1103/physrevlett.96.205502] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2006] [Indexed: 05/10/2023]
Abstract
The vibrational density of states of a hyperquenched and an annealed glass has been measured using nuclear inelastic scattering. The hyperquenched sample shows a higher number of vibrational states in the low-energy region with respect to the annealed glass. It reveals, however, lower density and sound velocity and, therefore, smaller Debye energy. After rescaling the energy axes in Debye energy units and area renormalization, the density of states of both samples becomes identical. Thus, the effect of quenching is described by the transformation of the continuous medium.
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Affiliation(s)
- A Monaco
- European Synchrotron Radiation Facility, B.P. 220, F-38043 Grenoble, France
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Ciliberti S, De Los Rios P, Piazza F. Glasslike structure of globular proteins and the boson peak. PHYSICAL REVIEW LETTERS 2006; 96:198103. [PMID: 16803144 DOI: 10.1103/physrevlett.96.198103] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2005] [Indexed: 05/10/2023]
Abstract
Vibrational spectra of proteins and topologically disordered solids display a common anomaly at low frequencies, known as boson peak. We show that such feature in globular proteins can be deciphered in terms of an energy landscape picture, as it is for glassy systems. Exploiting the tools of Euclidean random matrix theory, we clarify the physical origin of such anomaly in terms of a mechanical instability of the system. As a natural explanation, we argue that such instability is relevant for proteins in order for their molecular functions to be optimally rooted in their structures.
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Affiliation(s)
- Stefano Ciliberti
- Laboratoire de Physique Théorique et Modèles Statistiques, Université de Paris-Sud, Orsay, France
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Mamedov S, Stachel D, Soltwisch M, Quitmann D. Local environment and dynamics of PO4 tetrahedra in Na–Al–PO3 glasses and melts. J Chem Phys 2005; 123:124515. [PMID: 16392505 DOI: 10.1063/1.2038707] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Glasses and melts in the system (NaPO3)(1-x)(Al(PO3)3)x were studied with the aim of obtaining information about the structure on the next larger scale beyond the PO4 group. Magic angle spinning NMR was applied to the pure NaPO3 glass and Raman scattering to systems with x = 0.00, 0.03, 0.06, 0.15, and 0.60 in the temperature range T = 300-1100 K. Comparison of the 31P chemical shift between glass and crystalline forms revealed that polymerization of the metaphosphate into tricyclophosphatelike (PO3)3(3-) rings is the dominant structure, ca. 80%, formed by the twofold vertex-joined PO4 groups in the glass. In the Raman study we focused on the prominent polarized band at ca. 1170 cm(-1) which is due to the symmetric breathing mode of the tetrahedral PO4 group. This band was decomposed into a few Gaussian lines. These component lines could be identified using the NMR results: two narrow components are due to PO4 groups in the tricyclophosphatelike rings, which have either a Na or an Al counterion and a third broad component is due to chain-polymerized (PO3(-))n. The variations of the component lines (peak positions, widths, and intensities) with respect to x and T are presented. We derive the shifts of the symmetric breathing mode frequency which are caused by Na or Al counterions, by ring closure, by x > 0, etc. The relative intensities of the narrow and broad components in the 1170-cm(-1) band of the Raman spectra are discussed. The amount of ring-to-chain transformation on addition of Al3+, and as functions of T and x, is derived. Indications for ordering on a next larger scale, derivable from Raman, NMR, and thermodynamics, are compared.
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Affiliation(s)
- S Mamedov
- Horiba Jobin Yvon Inc., Edison, New Jersey 08820-3012, USA
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