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Ehrburger-Dolle F, Morfin I, Bley F, Livet F, Heinrich G, Chushkin Y, Sutton M. Anisotropic and heterogeneous dynamics in stretched elastomer nanocomposites. SOFT MATTER 2019; 15:3796-3806. [PMID: 30990483 DOI: 10.1039/c8sm02289e] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We use X-ray photon correlation spectroscopy (XPCS) to investigate the dynamics of a stretched elastomer by means of probe particles. The particles dispersed in the elastomer were carbon black or silica aggregates classically used for elastomer reinforcement but their volume fraction is very low (φ < 10-2). We show that their dynamics is slower in the direction of the tensile strain than in the perpendicular one. For hydroxylated silica which is poorly wetted by the elastomer, there is no anisotropy. Two-time correlation functions confirm anisotropic dynamics and suggest dynamical heterogeneity already expected from the q-1 behavior of the relaxation times. The height χ* of the peak of the dynamical susceptibility, determined by the normalized variance of the instantaneous correlation function, is larger in the direction parallel to the strain than in the perpendicular one. It also appears that its q dependence changes with the morphology of the probe particle. Therefore, the heterogeneous dynamic probed by the particles is not related only to that of the strained elastomer matrix. In fact, it results from modification of the dynamics of the polymer chains near the surface of the particles and within the aggregate porosity (bound polymer). It is concluded that XPCS is a powerful method for investigating the dynamics, at a given strain, of the bound polymer-particle units which are responsible, at large volume fractions, for the reinforcement.
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Taamalli S, Belmabrouk H, Van Hoang V, Teboul V. How do packing defects modify the cooperative motions in supercooled liquids? Chem Phys 2017. [DOI: 10.1016/j.chemphys.2017.04.006] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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3
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Righetti MC, Tombari E, Johari GP. Aging kinetics of levoglucosan orientational glass as a rate dispersion process and consequences for the heterogeneous dynamics view. J Chem Phys 2016; 145:054501. [PMID: 27497559 DOI: 10.1063/1.4959806] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Maria Cristina Righetti
- Consiglio Nazionale delle Ricerche, Istituto per i Processi Chimico-Fisici (CNR-IPCF), Via Moruzzi 1, 56124 Pisa, Italy
| | - Elpidio Tombari
- Consiglio Nazionale delle Ricerche, Istituto per i Processi Chimico-Fisici (CNR-IPCF), Via Moruzzi 1, 56124 Pisa, Italy
| | - G. P. Johari
- Department of Materials Science and Engineering, McMaster University, Hamilton, Ontario L8S 4L7, Canada
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4
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Zhang R, Schweizer KS. Theory of activated penetrant diffusion in viscous fluids and colloidal suspensions. J Chem Phys 2015; 143:144906. [PMID: 26472397 DOI: 10.1063/1.4932679] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We heuristically formulate a microscopic, force level, self-consistent nonlinear Langevin equation theory for activated barrier hopping and non-hydrodynamic diffusion of a hard sphere penetrant in very dense hard sphere fluid matrices. Penetrant dynamics is controlled by a rich competition between force relaxation due to penetrant self-motion and collective matrix structural (alpha) relaxation. In the absence of penetrant-matrix attraction, three activated dynamical regimes are predicted as a function of penetrant-matrix size ratio which are physically distinguished by penetrant jump distance and the nature of matrix motion required to facilitate its hopping. The penetrant diffusion constant decreases the fastest with size ratio for relatively small penetrants where the matrix effectively acts as a vibrating amorphous solid. Increasing penetrant-matrix attraction strength reduces penetrant diffusivity due to physical bonding. For size ratios approaching unity, a distinct dynamical regime emerges associated with strong slaving of penetrant hopping to matrix structural relaxation. A crossover regime at intermediate penetrant-matrix size ratio connects the two limiting behaviors for hard penetrants, but essentially disappears if there are strong attractions with the matrix. Activated penetrant diffusivity decreases strongly with matrix volume fraction in a manner that intensifies as the size ratio increases. We propose and implement a quasi-universal approach for activated diffusion of a rigid atomic/molecular penetrant in a supercooled liquid based on a mapping between the hard sphere system and thermal liquids. Calculations for specific systems agree reasonably well with experiments over a wide range of temperature, covering more than 10 orders of magnitude of variation of the penetrant diffusion constant.
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Affiliation(s)
- Rui Zhang
- Department of Materials Science and Frederick Seitz Materials Research Laboratory, University of Illinois, 1304 West Green Street, Urbana, Illinois 61801, USA
| | - Kenneth S Schweizer
- Department of Materials Science and Frederick Seitz Materials Research Laboratory, University of Illinois, 1304 West Green Street, Urbana, Illinois 61801, USA
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Kim J, Sung BJ. Tracer Shape and Local Media Structure Determine the Trend of Translation-Rotation Decoupling in Two-Dimensional Colloids. PHYSICAL REVIEW LETTERS 2015; 115:158302. [PMID: 26550756 DOI: 10.1103/physrevlett.115.158302] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2015] [Indexed: 06/05/2023]
Abstract
The translational diffusion of tracers in glass-forming materials often violates the Stokes-Einstein relation while their rotation follows the Debye-Stokes-Einstein relation faithfully, thus decoupling translational and rotational diffusion. In this Letter, we show by performing molecular dynamics simulations for two-dimensional (2D) colloids that the tracer shape and the local media structure are critical such that rotational diffusion is either suppressed or enhanced depending on the tracer shape. For square tracers dissimilar in structure to the local media structure of 2D colloids, the translation-rotation decoupling occurs and the rotational diffusion is enhanced relative to the translation. For sufficiently large diamond tracers similar in structure to the local media structure, tracers undergo rotational hopping motions and their rotation is suppressed relative to the translation. For distorted-diamond tracers, the decoupling is marginal. Translational diffusion does not change significantly with the tracer shape and obeys the Stokes-Einstein relation.
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Affiliation(s)
- Jeongmin Kim
- Department of Chemistry and Research Institute for Basic Science, Sogang University, Seoul 121-742, Republic of Korea
| | - Bong June Sung
- Department of Chemistry and Research Institute for Basic Science, Sogang University, Seoul 121-742, Republic of Korea
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Teboul V, Barillé R, Tajalli P, Ahmadi-Kandjani S, Tajalli H, Zielinska S, Ortyl E. Light mediated emergence of surface patterns in azopolymers at low temperatures. SOFT MATTER 2015; 11:6444-6449. [PMID: 26179125 DOI: 10.1039/c5sm00846h] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Polymer thin films doped with azobenzene molecules do have the ability to organize themselves in spontaneous surface relief gratings (SRG) under irradiation using a single polarized beam. To shed some light on this still unexplained phenomenon, we use a new method that permits us to access experimentally the very first steps of the pattern formation process. By decreasing the temperature, we slow down the formation and organization of patterns, due to the large increase in the viscosity and relaxation time of the azopolymer. As a result, decreasing the temperature allows us to access and study much shorter time scales, in the physical mechanisms underlying the pattern formation, than those previously reported. We find that the patterns organize themselves in sub-structures which size increases with the temperature, following the diffusion coefficient evolution of the material. This result suggests that the pattern formation and organization are mainly governed by diffusive processes, in agreement with some theories of SRG formation. Upon decreasing the temperature further, we observe the emergence of small voids located at the junction of the sub-structures.
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Affiliation(s)
- V Teboul
- Laboratoire de Photonique d'Angers EA 4464, University of Angers, Physics Department, 2 Bd Lavoisier, 49045 Angers, France.
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7
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Mishra CK, Ganapathy R. Shape of dynamical heterogeneities and fractional Stokes-Einstein and Stokes-Einstein-Debye relations in quasi-two-dimensional suspensions of colloidal ellipsoids. PHYSICAL REVIEW LETTERS 2015; 114:198302. [PMID: 26024202 DOI: 10.1103/physrevlett.114.198302] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2014] [Indexed: 06/04/2023]
Abstract
We examine the influence of the shape of dynamical heterogeneities on the Stokes-Einstein (SE) and Stokes-Einstein-Debye (SED) relations in quasi-two-dimensional suspensions of colloidal ellipsoids. For ellipsoids with repulsive interactions, both SE and SED relations are violated at all area fractions. On approaching the glass transition, however, the extent to which this violation occurs changes beyond a crossover area fraction. Quite remarkably, we find that it is not just the presence of dynamical heterogeneities but their change in the shape from stringlike to compact that coincides with this crossover. On introducing a suitable short-range depletion attraction between the ellipsoids, associated with the lack of morphological evolution of dynamical heterogeneities, the extent to which the SE and SED relations are violated remains unchanged even for deep supercooling.
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Affiliation(s)
- Chandan K Mishra
- Chemistry and Physics of Materials Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India
| | - Rajesh Ganapathy
- International Centre for Materials Science, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India
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Kaufman LJ. Heterogeneity in Single-Molecule Observables in the Study of Supercooled Liquids. Annu Rev Phys Chem 2013; 64:177-200. [DOI: 10.1146/annurev-physchem-040412-110033] [Citation(s) in RCA: 50] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Bulk approaches to studying heterogeneous systems obscure important details, as they report average behavior rather than the distribution of behaviors in such environments. Small-molecule and polymeric supercooled liquids, which display heterogeneity in their dynamics without an underlying structural heterogeneity that sets those dynamics, are important constituents of this category of condensed matter systems. A variety of approaches have been devised to unravel ensemble averaging in supercooled liquids. This review focuses on the ultimate subensemble approach, single-molecule measurements, as they have been applied to the study of supercooled liquids. We detail how three key experimental observables (single-molecule probe rotation, translation, and fluorescence lifetime) have been employed to provide detail on dynamic heterogeneity in supercooled liquids. Special attention is given to the potential for, but also the challenges in, discriminating spatial and temporal heterogeneity and detailing the length scales and timescales of heterogeneity in these systems.
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Affiliation(s)
- Laura J. Kaufman
- Department of Chemistry, Columbia University, New York, NY 10027
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9
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Johari GP, Khouri J. Effects of 2 nm size added heterogeneity on non-exponential dielectric response, and the dynamic heterogeneity view of molecular liquids. J Chem Phys 2013; 137:104502. [PMID: 22979869 DOI: 10.1063/1.4748355] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
To investigate how non-exponential response could vary under different conditions, we studied the effects of adding 2 nm size polyhedral oligomeric silsesquioxane (POSS) to diglycidyl ether of bisphenol-A, whose molecules have the same terminal (epoxide) dipoles as the tentacle-like side chains attached to the silsesquioxane core of the POSS molecule. Dielectric relaxation spectra show that, on initial addition, the POSS nano-heterogeneity decreases the non-exponential response parameter β, which is consistent with the dynamic heterogeneity view, but it also decreases the relaxation time τ(m), which is inconsistent with that view. The variations in β and τ(m) with the composition have a thermal equivalence. Despite the lack of translational diffusion required for dynamic heterogeneity, plastic crystals show non-exponential response and non-Arrhenius dynamics. Measurements of β and τ(m) seem more appropriate than using probe molecules or modeling nonlinear response data as a sum of linear responses for testing the dynamic heterogeneity view. Data on molecular liquid mixtures is not generally consistent with this view, and adding a solute does not always decrease β. Studies of mixtures of different size rigid molecules with identical dipolar groups, including polymers, may be useful for comparing the relative effects of temperature and molecular size on β and τ(m).
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Affiliation(s)
- G P Johari
- Department of Materials Science and Engineering, McMaster University, Hamilton, Ontario L8S 4L7, Canada.
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10
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Decoupling of rotational and translational diffusion in supercooled colloidal fluids. Proc Natl Acad Sci U S A 2012; 109:17891-6. [PMID: 23071311 DOI: 10.1073/pnas.1203328109] [Citation(s) in RCA: 104] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We use confocal microscopy to directly observe 3D translational and rotational diffusion of tetrahedral clusters, which serve as tracers in colloidal supercooled fluids. We find that as the colloidal glass transition is approached, translational and rotational diffusion decouple from each other: Rotational diffusion remains inversely proportional to the growing viscosity whereas translational diffusion does not, decreasing by a much lesser extent. We quantify the rotational motion with two distinct methods, finding agreement between these methods, in contrast with recent simulation results. The decoupling coincides with the emergence of non-Gaussian displacement distributions for translation whereas rotational displacement distributions remain Gaussian. Ultimately, our work demonstrates that as the glass transition is approached, the sample can no longer be approximated as a continuum fluid when considering diffusion.
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11
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Hunter GL, Weeks ER. The physics of the colloidal glass transition. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2012; 75:066501. [PMID: 22790649 DOI: 10.1088/0034-4885/75/6/066501] [Citation(s) in RCA: 329] [Impact Index Per Article: 27.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
As one increases the concentration of a colloidal suspension, the system exhibits a dramatic increase in viscosity. Beyond a certain concentration, the system is said to be a colloidal glass; structurally, the system resembles a liquid, yet motions within the suspension are slow enough that it can be considered essentially frozen. For several decades, colloids have served as a valuable model system for understanding the glass transition in molecular systems. The spatial and temporal scales involved allow these systems to be studied by a wide variety of experimental techniques. The focus of this review is the current state of understanding of the colloidal glass transition, with an emphasis on experimental observations. A brief introduction is given to important experimental techniques used to study the glass transition in colloids. We describe features of colloidal systems near and in glassy states, including increases in viscosity and relaxation times, dynamical heterogeneity and ageing, among others. We also compare and contrast the glass transition in colloids to that in molecular liquids. Other glassy systems are briefly discussed, as well as recently developed synthesis techniques that will keep these systems rich with interesting physics for years to come.
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Affiliation(s)
- Gary L Hunter
- Department of Physics, Emory University, Math and Science Center 400 Dowman Dr., N201 Atlanta, GA 30322, USA
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12
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Mackowiak SA, Noble JM, Kaufman LJ. Manifestations of probe presence on probe dynamics in supercooled liquids. J Chem Phys 2011; 135:214503. [PMID: 22149798 DOI: 10.1063/1.3664125] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Experimental studies that follow behavior of single probes embedded in heterogeneous systems are increasingly common. The presence of probes may perturb the system, and such perturbations may or may not affect interpretation of host behavior from the probe observables typically measured. In this study, the manifestations of potential probe-induced changes to host dynamics in supercooled liquids are investigated via molecular dynamics simulations. It is found that probe dynamics do not necessarily mirror host dynamics as they exist either in the probe-free or probe-bearing systems. In particular, for a binary supercooled liquid, we find that smooth probes larger than the host particles induce increased translational diffusion in the host system; however, the diffusion is anisotropic and enhances caging of the probe, suppressing probe translational diffusion. This in turn may lead experiments that follow probe diffusion to suggest Stokes-Einstein behavior of the system even while both the probe-free and probe-bearing systems exhibit deviations from that behavior.
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13
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Deres A, Floudas GA, Müllen K, Van der Auweraer M, De Schryver F, Enderlein J, Uji-i H, Hofkens J. The Origin of Heterogeneity of Polymer Dynamics near the Glass Temperature As Probed by Defocused Imaging. Macromolecules 2011. [DOI: 10.1021/ma201449p] [Citation(s) in RCA: 50] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Ania Deres
- Department of Chemistry, Katholieke Universiteit Leuven, Celestijnenlaan 200 F, 3001 Heverlee, Belgium
| | - George A. Floudas
- Department of Physics, University of Ioannina, 45110 Ioannina, Greece, and Foundation for Research and Technology-Hellas, Biomedical Research Institute
| | - Klaus Müllen
- Max-Planck-Institut für Polymerforschung, Ackermannweg 10, D-55128 Mainz, Germany
| | - Mark Van der Auweraer
- Department of Chemistry, Katholieke Universiteit Leuven, Celestijnenlaan 200 F, 3001 Heverlee, Belgium
| | - Frans De Schryver
- Department of Chemistry, Katholieke Universiteit Leuven, Celestijnenlaan 200 F, 3001 Heverlee, Belgium
| | - Jörg Enderlein
- Drittes Physikalisches Institut, Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany
| | - Hiroshi Uji-i
- Department of Chemistry, Katholieke Universiteit Leuven, Celestijnenlaan 200 F, 3001 Heverlee, Belgium
| | - Johan Hofkens
- Department of Chemistry, Katholieke Universiteit Leuven, Celestijnenlaan 200 F, 3001 Heverlee, Belgium
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Wang LM, Tian Y, Liu R, Richert R. Structural Relaxation Dynamics in Binary Glass-Forming Molecular Liquids with Ideal and Complex Mixing Behavior. J Phys Chem B 2010; 114:3618-22. [DOI: 10.1021/jp912223j] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Li-Min Wang
- State Key Lab of Metastable Materials Science and Technology, and College of Materials Science and Engineering, Yanshan University, Qinhuangdao, Hebei, 066004 China and Department of Chemistry and Biochemistry, Arizona State University, Tempe, Arizona 85287
| | - Yongjun Tian
- State Key Lab of Metastable Materials Science and Technology, and College of Materials Science and Engineering, Yanshan University, Qinhuangdao, Hebei, 066004 China and Department of Chemistry and Biochemistry, Arizona State University, Tempe, Arizona 85287
| | - Riping Liu
- State Key Lab of Metastable Materials Science and Technology, and College of Materials Science and Engineering, Yanshan University, Qinhuangdao, Hebei, 066004 China and Department of Chemistry and Biochemistry, Arizona State University, Tempe, Arizona 85287
| | - Ranko Richert
- State Key Lab of Metastable Materials Science and Technology, and College of Materials Science and Engineering, Yanshan University, Qinhuangdao, Hebei, 066004 China and Department of Chemistry and Biochemistry, Arizona State University, Tempe, Arizona 85287
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Mackowiak SA, Herman TK, Kaufman LJ. Spatial and temporal heterogeneity in supercooled glycerol: Evidence from wide field single molecule imaging. J Chem Phys 2009; 131:244513. [DOI: 10.1063/1.3277141] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Caronna C, Chushkin Y, Madsen A, Cupane A. Dynamics of nanoparticles in a supercooled liquid. PHYSICAL REVIEW LETTERS 2008; 100:055702. [PMID: 18352390 DOI: 10.1103/physrevlett.100.055702] [Citation(s) in RCA: 85] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2007] [Revised: 12/19/2007] [Indexed: 05/20/2023]
Abstract
The dynamic properties of nanoparticles suspended in a supercooled glass forming liquid are studied by x-ray photon correlation spectroscopy. While at high temperatures the particles undergo Brownian motion the measurements closer to the glass transition indicate hyperdiffusive behavior. In this state the dynamics is independent of the local structural arrangement of nanoparticles, suggesting a cooperative behavior governed by the near-vitreous solvent.
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Affiliation(s)
- Chiara Caronna
- European Synchrotron Radiation Facility, B.P. 220, F-38043 Grenoble, France
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Adhikari AN, Capurso NA, Bingemann D. Heterogeneous dynamics and dynamic heterogeneities at the glass transition probed with single molecule spectroscopy. J Chem Phys 2007; 127:114508. [PMID: 17887858 DOI: 10.1063/1.2768955] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
Abstract
We studied the temperature dependence of the structural relaxation in poly(vinyl acetate) near the glass transition temperature with single molecule spectroscopy from Tg-1 K to Tg+12 K. The temperature dependence of the observed relaxation times matches results from bulk experiments; the observed relaxation times are, however, 80-fold slower than those from bulk experiments at the same temperature. We attribute this factor to the size of the probe molecule. The individual relaxation times of the single molecule environments are distributed normally on a logarithmic time scale, confirming that the dynamics in poly(vinyl acetate) is heterogeneous. The width of the distribution of individual relaxation times is essentially independent of temperature. The observed full width at half maximum (FWHM) on a logarithmic time axis is approximately 0.7, corresponding to a factor of about 5-fold, significantly narrower than the dielectric spectrum of the same material with a FWHM of about 2.0 on a logarithmic time axis, corresponding to a factor of about 100-fold. We explain this narrow width as the effect of temporal averaging of single molecule fluorescence signals over numerous environments due to a limited lifetime of the probed heterogeneities, indicating that heterogeneities are dynamic. We determine a loose upper limit for the ratio of the structural relaxation time to the lifetime of the heterogeneities (the rate memory parameter) of Q<80 for the range of investigated temperatures.
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Affiliation(s)
- Aashish N Adhikari
- Department of Chemistry, Williams College, 47 Lab Campus Drive, Williamstown, Massachusetts 01267, USA
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Zangi R, Kaufman LJ. Frequency-dependent Stokes-Einstein relation in supercooled liquids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:051501. [PMID: 17677067 DOI: 10.1103/physreve.75.051501] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2006] [Indexed: 05/16/2023]
Abstract
We investigate by molecular dynamics simulations the validity of the frequency-dependent Stokes-Einstein (SE) relation in supercooled liquids at different temperatures. The results indicate that the SE relation holds at intermediate frequencies that correspond to the beta -relaxation and the onset of the alpha -relaxation regimes. Large deviations, which increase as the temperature decreases, are observed at frequencies well below the frequency at which the non-Gaussian parameter alpha2 is maximum. We argue that the breakdown of the SE relation in supercooled liquids arises from underestimation of the diffusion coefficient due to neglect of correlated motions.
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Affiliation(s)
- Ronen Zangi
- Department of Chemistry, Columbia University, New York, NY 10027, USA
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