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Hodge SR, Berg MA. Nonlinear measurements of kinetics and generalized dynamical modes. I. Extracting the one-dimensional Green's function from a time series. J Chem Phys 2021; 155:024122. [PMID: 34266246 DOI: 10.1063/5.0053422] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
Often, a single correlation function is used to measure the kinetics of a complex system. In contrast, a large set of k-vector modes and their correlation functions are commonly defined for motion in free space. This set can be transformed to the van Hove correlation function, which is the Green's function for molecular diffusion. Here, these ideas are generalized to other observables. A set of correlation functions of nonlinear functions of an observable is used to extract the corresponding Green's function. Although this paper focuses on nonlinear correlation functions of an equilibrium time series, the results are directly connected to other types of nonlinear kinetics, including perturbation-response experiments with strong fields. Generalized modes are defined as the orthogonal polynomials associated with the equilibrium distribution. A matrix of mode-correlation functions can be transformed to the complete, single-time-interval (1D) Green's function. Diagonalizing this matrix finds the eigendecays. To understand the advantages and limitation of this approach, Green's functions are calculated for a number of models of complex dynamics within a Gaussian probability distribution. Examples of non-diffusive motion, rate heterogeneity, and range heterogeneity are examined. General arguments are made that a full set of nonlinear 1D measurements is necessary to extract all the information available in a time series. However, when a process is neither dynamically Gaussian nor Markovian, they are not sufficient. In those cases, additional multidimensional measurements are needed.
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Affiliation(s)
- Stuart R Hodge
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA
| | - Mark A Berg
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA
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2
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De Francesco A, Scaccia L, Formisano F, Guarini E, Bafile U, Maccarini M, Alatas A, Cai YQ, Nykypanchuk D, Cunsolo A. Onset of interfacial waves in the terahertz spectrum of a nanoparticle suspension. Phys Rev E 2020; 102:022601. [PMID: 32942392 DOI: 10.1103/physreve.102.022601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2020] [Accepted: 07/13/2020] [Indexed: 11/06/2022]
Abstract
We used inelastic x-ray scattering to gain insight into the complex terahertz dynamics of a diluted Au-nanoparticle suspension in glycerol. We observe that, albeit sparse, Au nanoparticles leave clear signatures on the dynamic response of the system, the main one being an additional mode propagating at the nanoparticle-glycerol interface. A Bayesian inferential analysis of the line shape reveals that such a mode, at variance with conventional acoustic modes, keeps a hydrodynamiclike behavior well beyond the continuous limit and down to subnanometer distances.
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Affiliation(s)
- Alessio De Francesco
- Consiglio Nazionale delle Ricerche, Istituto Officina dei Materiali, Operative Group in Grenoble (OGG) F-38042 Grenoble, France.,Institut Laue-Langevin (ILL), F-38042 Grenoble, France
| | - Luisa Scaccia
- Dipartimento di Economia e Diritto, Università di Macerata, Via Crescimbeni 20, 62100 Macerata, Italy
| | - Ferdinando Formisano
- Consiglio Nazionale delle Ricerche, Istituto Officina dei Materiali, Operative Group in Grenoble (OGG) F-38042 Grenoble, France.,Institut Laue-Langevin (ILL), F-38042 Grenoble, France
| | - Eleonora Guarini
- Dipartimento di Fisica e Astronomia, Università di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
| | - Ubaldo Bafile
- Consiglio Nazionale delle Ricerche, Istituto di Fisica Applicata "Nello Carrara," via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
| | - Marco Maccarini
- Université Grenoble-Alpes, CNRS, Grenoble INP, TIMC-IMAG, 38000 Grenoble, France
| | - Ahmet Alatas
- Argonne National Laboratory, Advanced Photon Source, P.O. Box 5000, Upton, New York 11973, USA
| | - Yong Q Cai
- Brookhaven National Laboratory, National Synchrotron Light Source, NSLS II, P.O. Box 5000, Upton, New York 11973, USA
| | - Dmytro Nykypanchuk
- Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - Alessandro Cunsolo
- Brookhaven National Laboratory, National Synchrotron Light Source, NSLS II, P.O. Box 5000, Upton, New York 11973, USA
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Vispa A, Monserrat D, Cuello GJ, Fernandez-Alonso F, Mukhopadhyay S, Demmel F, Tamarit JL, Pardo LC. On the microscopic mechanism behind the purely orientational disorder–disorder transition in the plastic phase of 1-chloroadamantane. Phys Chem Chem Phys 2017; 19:20259-20266. [PMID: 28726892 DOI: 10.1039/c7cp03630b] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
The microscopic mechanism behind the disorder–disorder phase transition in 1-chloroadamantane is related to changes both in structure and dynamics, as revealed by QENS and neutron diffraction experiments.
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Affiliation(s)
- A. Vispa
- Grup de Caracterització de Materials
- Departament de Física
- EEBE
- Universitat Politècnica de Catalunya
- E-08019 Barcelona
| | - D. Monserrat
- Grup de Caracterització de Materials
- Departament de Física
- EEBE
- Universitat Politècnica de Catalunya
- E-08019 Barcelona
| | | | - F. Fernandez-Alonso
- ISIS Facility
- Rutherford Appleton Laboratory
- Oxfordshire OX11 0QX
- UK
- Department of Physics and Astronomy
| | - S. Mukhopadhyay
- ISIS Facility
- Rutherford Appleton Laboratory
- Oxfordshire OX11 0QX
- UK
- Department of Materials
| | - F. Demmel
- ISIS Facility
- Rutherford Appleton Laboratory
- Oxfordshire OX11 0QX
- UK
| | - J. Ll. Tamarit
- Grup de Caracterització de Materials
- Departament de Física
- EEBE
- Universitat Politècnica de Catalunya
- E-08019 Barcelona
| | - L. C. Pardo
- Grup de Caracterització de Materials
- Departament de Física
- EEBE
- Universitat Politècnica de Catalunya
- E-08019 Barcelona
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Gupta S, Fischer JKH, Lunkenheimer P, Loidl A, Novak E, Jalarvo N, Ohl M. Effect of adding nanometre-sized heterogeneities on the structural dynamics and the excess wing of a molecular glass former. Sci Rep 2016; 6:35034. [PMID: 27725747 PMCID: PMC5057163 DOI: 10.1038/srep35034] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2016] [Accepted: 09/21/2016] [Indexed: 11/17/2022] Open
Abstract
We present the relaxation dynamics of glass-forming glycerol mixed with 1.1 nm sized polyhedral oligomeric silsesquioxane (POSS) molecules using dielectric spectroscopy (DS) and two different neutron scattering (NS) techniques. Both, the reorientational dynamics as measured by DS and the density fluctuations detected by NS reveal a broadening of the α relaxation when POSS molecules are added. Moreover, we find a significant slowing down of the α-relaxation time. These effects are in accord with the heterogeneity scenario considered for the dynamics of glasses and supercooled liquids. The addition of POSS also affects the excess wing in glycerol arising from a secondary relaxation process, which seems to exhibit a dramatic increase in relative strength compared to the α relaxation.
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Affiliation(s)
- S Gupta
- Juelich Centre for Neutron science (JCNS) outstation at SNS, POB 2008, 1 Bethel Valley Road, TN 37831, Oak Ridge, USA.,Biology and Soft Matter Division, Neutron Sciences Directorate, Oak Ridge National Laboratory (ORNL), POB 2008, 1 Bethel Valley Road, TN 37831, Oak Ridge, USA.,Department of Chemistry and Macromolecular Studies Group, Louisiana State University, Baton Rouge, LA 70803, USA
| | - J K H Fischer
- 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
| | - E Novak
- Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37996, USA
| | - N Jalarvo
- Juelich Centre for Neutron science (JCNS) outstation at SNS, POB 2008, 1 Bethel Valley Road, TN 37831, Oak Ridge, USA.,Chemical and Engineering Materials Division, Oak Ridge National Laboratory (ORNL), PO BOX 2008 MS6473, TN 37831, Oak Ridge, USA
| | - M Ohl
- Juelich Centre for Neutron science (JCNS) outstation at SNS, POB 2008, 1 Bethel Valley Road, TN 37831, Oak Ridge, USA.,Biology and Soft Matter Division, Neutron Sciences Directorate, Oak Ridge National Laboratory (ORNL), POB 2008, 1 Bethel Valley Road, TN 37831, Oak Ridge, USA
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