Dynamics and Time Scales of Higher-Order Correlations in Supercooled Colloidal SystemsClick to copy article linkArticle link copied!
- Nele N. Striker*Nele N. Striker*[email protected]Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, GermanyMore by Nele N. Striker
- Irina LoktevaIrina LoktevaDeutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, GermanyThe Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, GermanyMore by Irina Lokteva
- Michael DartschMichael DartschDeutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, GermanyThe Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, GermanyMore by Michael Dartsch
- Francesco DallariFrancesco DallariDeutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, GermanyMore by Francesco Dallari
- Claudia GoyClaudia GoyDeutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, GermanyMore by Claudia Goy
- Fabian WestermeierFabian WestermeierDeutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, GermanyMore by Fabian Westermeier
- Verena MarkmannVerena MarkmannDeutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, GermanyMore by Verena Markmann
- Svenja C. HövelmannSvenja C. HövelmannDeutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, GermanyInstitut für Experimentelle und Angewandte Physik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 19, 24098 Kiel, GermanyMore by Svenja C. Hövelmann
- Gerhard GrübelGerhard GrübelDeutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, GermanyThe Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, GermanyMore by Gerhard Grübel
- Felix Lehmkühler*Felix Lehmkühler*[email protected]Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, GermanyThe Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, GermanyMore by Felix Lehmkühler
Abstract
The dynamics and time scales of higher-order correlations are studied in supercooled colloidal systems. A combination of X-ray photon correlation spectroscopy (XPCS) and X-ray cross-correlation analysis (XCCA) shows the typical slowing of the dynamics of a hard sphere system when approaching the glass transition. The time scales of higher-order correlations are probed using a novel time correlation function gC, tracking the time evolution of cross-correlation function C. With an increasing volume fraction, the ratio of relaxation times of gC to the standard individual particle relaxation time obtained by XPCS increases from ∼0.4 to ∼0.9. While a value of ∼0.5 is expected for free diffusion, the increasing values suggest that the local orders within the sample are becoming more long-lived for larger volume fractions. Furthermore, the dynamics of local order is more heterogeneous than the individual particle dynamics. These results indicate that not only the presence but also the lifetime of locally favored structures increases close to the glass transition.
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You are free to share(copy and redistribute) this article in any medium or format and to adapt(remix, transform, and build upon) the material for any purpose, even commercially within the parameters below:
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Figure 1
Figure 1. Structure and dynamics. (a) Structure factors S(q) for samples of HS1 (solid lines) and HS2 (dashed lines), shown as a function of qR for R of each sample. The corresponding volume fractions ϕ are shown in the legend. For the sake of visibility, not all structure factors are shown. (b) Relative diffusivity D0/D(qnn) as a function of volume fraction ϕ for HS1 (circles) and HS2 (triangles). The line represents a fit of the VFT law to the data with a ϕVFT of 0.65 ± 0.04.
Figure 2
Figure 2. Schematics of the XPCS and time scales of higher-order correlations. A sample is illuminated with coherent X-rays, and the resulting scattering patterns are recorded at time intervals Δtmin. Via calculation of intensity correlation function g2 and the time scales of higher-order correlation function gC, more details about the local order, its time scale, and the heterogenity of the system can be obtained.
Figure 3
Figure 3. Correlation functions. (a) Intermediate scattering functions and (b) gC functions at qnn for the various volume fractions ϕ of HS1 (circles) and HS2 (triangles). The respective fits are shown as solid lines.
Figure 4
Figure 4. Comparison of the correlation functions. (a) Quotient of the relaxation times, , obtained from the gC and g2 functions as a function of volume fraction ϕ. The dashed line signifies . The inset shows as a function of relaxation time . (b) Exponents and plotted against each other. The solid line signifies and is a guide to the eye, and the dashed line is a linear fit to the data with a = 0.73 and b = 0.17. The inset shows as a function of with the solid line representing .
Experimental Section
Supporting Information
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpclett.3c00631.
2D simulations for particles undergoing free diffusion and additional analysis of particle dynamics (PDF)
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Acknowledgments
The authors thank Walter Kob for the discussion, Andrew Schofield for providing the samples, and Wojciech Roseker for the proofreading. The research was carried out at light source PETRA III at DESY, a member of the Helmholtz Association (HGF). The authors also thank Michael Sprung for assistance in using beamline P10. This work is supported by the Cluster of Excellence Advanced Imaging of Matter of the Deutsche Forschungsgemeinschaft (DFG) (EXC 2056, Project 390715994). The authors also acknowledge the scientific exchange and support of the Centre for Molecular Water Science (CMWS).
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- 9Hocky, G. M.; Coslovich, D.; Ikeda, A.; Reichman, D. R. Correlation of local order with particle mobility in supercooled liquids is highly system dependent. Phys. Rev. Lett. 2014, 113, 157801, DOI: 10.1103/PhysRevLett.113.157801Google Scholar9https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhvFKqsL3O&md5=28129822a6f603392666f335bf54ad92Correlation of local order with particle mobility in supercooled liquids is highly system dependentHocky, Glen M.; Coslovich, Daniele; Ikeda, Atsushi; Reichman, David R.Physical Review Letters (2014), 113 (15), 157801/1-157801/5, 5 pp.CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)We investigate the connection between local structure and dynamical heterogeneity in supercooled liqs. Through the study of four different models, we show that the correlation between a particle's mobility and the degree of local order in nearby regions is highly system dependent. Our results suggest that the correlation between local structure and dynamics is weak or absent in systems that conform well to the mean-field picture of glassy dynamics and strong in those that deviate from this paradigm. Finally, we investigate the role of order-agnostic point-to-set correlations and reveal that they provide similar information content to local structure measures, at least in the system where local order is most pronounced.
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- 16Boattini, E.; Marín-Aguilar, S.; Mitra, S.; Foffi, G.; Smallenburg, F.; Filion, L. Autonomously revealing hidden local structures in supercooled liquids. Nat. Commun. 2020, 11, 5479, DOI: 10.1038/s41467-020-19286-8Google Scholar16https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXit1OjtLjJ&md5=31bbf257ad6f0d7690b126cdbfa072c0Autonomously revealing hidden local structures in supercooled liquidsBoattini, Emanuele; Marin-Aguilar, Susana; Mitra, Saheli; Foffi, Giuseppe; Smallenburg, Frank; Filion, LauraNature Communications (2020), 11 (1), 5479CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)Abstr.: Few questions in condensed matter science have proven as difficult to unravel as the interplay between structure and dynamics in supercooled liqs. To explore this link, much research has been devoted to pinpointing local structures and order parameters that correlate strongly with dynamics. Here we use an unsupervised machine learning algorithm to identify structural heterogeneities in three archetypical glass formers-without using any dynamical information. In each system, the unsupervised machine learning approach autonomously designs a purely structural order parameter within a single snapshot. Comparing the structural order parameter with the dynamics, we find strong correlations with the dynamical heterogeneities. Moreover, the structural characteristics linked to slow particles disappear further away from the glass transition. Our results demonstrate the power of machine learning techniques to detect structural patterns even in disordered systems, and provide a new way forward for unraveling the structural origins of the slow dynamics of glassy materials.
- 17Schoenholz, S. S.; Cubuk, E. D.; Kaxiras, E.; Liu, A. J. Relationship between local structure and relaxation in out-of-equilibrium glassy systems. Proc. Natl. Acad. Sci. U.S.A. 2017, 114, 263– 267, DOI: 10.1073/pnas.1610204114Google Scholar17https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XitFGntr3M&md5=af4e898ff0b8a444ff33ec8e2e941444Relationship between local structure and relaxation in out-of-equilibrium glassy systemsSchoenholz, Samuel S.; Cubuk, Ekin D.; Kaxiras, Efthimios; Liu, Andrea J.Proceedings of the National Academy of Sciences of the United States of America (2017), 114 (2), 263-267CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)The dynamical glass transition is typically taken to be the temp. at which a glassy liq. is no longer able to equilibrate on exptl. timescales. Consequently, the phys. properties of these systems just above or below the dynamical glass transition, such as viscosity, can change by many orders of magnitude over long periods of time following external perturbation. During this progress toward equil., glassy systems exhibit a history dependence that has complicated their study. In previous work, we bridged the gap between structure and dynamics in glassy liqs. above their dynamical glass transition temps. by introducing a scalar field called "softness," a quantity obtained using machine-learning methods. Softness is designed to capture the hidden patterns in relative particle positions that correlate strongly with dynamical rearrangements of particle positions. Here we show that the out-of-equil. behavior of a model glass-forming system can be understood in terms of softness. To do this we first demonstrate that the evolution of behavior following a temp. quench is a primarily structural phenomenon: The structure changes considerably, but the relationship between structure and dynamics remains invariant. We then show that the relaxation time can be robustly computed from structure as quantified by softness, with the same relation holding both in equil. and as the system ages. Together, these results show that the history dependence of the relaxation time in glasses requires knowledge only of the softness in addn. to the usual state variables.
- 18Royall, C. P.; Williams, S. R. The role of local structure in dynamical arrest. Phys. Rep. 2015, 560, 1– 75, DOI: 10.1016/j.physrep.2014.11.004Google Scholar18https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXitV2mt73M&md5=ebae5a39f0ac2c20ef02169e9c7cc572The role of local structure in dynamical arrestRoyall, C. Patrick; Williams, Stephen R.Physics Reports (2015), 560 (), 1-75CODEN: PRPLCM; ISSN:0370-1573. (Elsevier B.V.)A review. Amorphous solids, or glasses, are distinguished from cryst. solids by their lack of long-range structural order. At the level of two-body structural correlations, glassformers show no qual. change upon vitrifying from a supercooled liq. Nonetheless the dynamical properties of a glass are so much slower that it appears to take on the properties of a solid. While many theories of the glass transition focus on dynamical quantities, a solid's resistance to flow is often viewed as a consequence of its structure. Here we address the viewpoint that this remains the case for a glass. Recent developments using higher-order measures show a clear emergence of structure upon dynamical arrest in a variety of glass formers and offer the tantalising hope of a structural mechanism for arrest. However a rigorous fundamental identification of such a causal link between structure and arrest remains elusive. We undertake a crit. survey of this work in expts., computer simulation and theory and discuss what might strengthen the link between structure and dynamical arrest. We move on to highlight the relationship between crystn. and glass-forming ability made possible by this deeper understanding of the structure of the liq. state, and emphasize the potential to design materials with optimal glassforming and crystn. ability, for applications such as phase-change memory. We then consider aspects of the phenomenol. of glassy systems where structural measures have yet to make a large impact, such as polyamorphism (the existence of multiple liq. states), ageing (the time-evolution of non-equil. materials below their glass transition) and the response of glassy materials to external fields such as shear.
- 19Gast, A. P.; Russel, W. B. Simple ordering in complex fluids. Phys. Today 1998, 51, 24– 30, DOI: 10.1063/1.882495Google Scholar19https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1MXhvF2qsw%253D%253D&md5=a1913b7f4fc955f651c02fe7257ece7aSimple ordering in complex fluids: colloidal particles suspended in solution provide intriguing models for studying phase transitionsGast, Alice P.; Russel, William B.Physics Today (1998), 51 (12), 24-30CODEN: PHTOAD; ISSN:0031-9228. (American Institute of Physics)A review with 17 refs. The topics include entropy and ordering of hard spheres, tunable repulsions of soft spheres, bcc→fcc transition, attraction and gas-liq. phase transition, and two-dimensional crystn.
- 20Marín-Aguilar, S.; Wensink, H. H.; Foffi, G.; Smallenburg, F. Tetrahedrality dictates dynamics in hard sphere mixtures. Phys. Rev. Lett. 2020, 124, 208005, DOI: 10.1103/PhysRevLett.124.208005Google Scholar20https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhsFCntrnJ&md5=e339ead5a2ca0330742cdb2bea2af487Tetrahedrality Dictates Dynamics in Hard Sphere MixturesMarin-Aguilar, Susana; Wensink, Henricus H.; Foffi, Giuseppe; Smallenburg, FrankPhysical Review Letters (2020), 124 (20), 208005CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)The link between local structure and dynamical slowdown in glassy fluids has been the focus of intense debate for the better part of a century. Nonetheless, a simple method to predict the dynamical behavior of a fluid purely from its local structural features is still missing. Here, we demonstrate that the diffusivity of perhaps the most fundamental family of glass formers-hard sphere mixts.-can be accurately predicted based on just the packing fraction and a simple order parameter measuring the tetrahedrality of the local structure. Essentially, we show that the no. of tetrahedral clusters in a hard sphere mixt. is directly linked to its global diffusivity. Moreover, the same order parameter is capable of locally pinpointing particles in the system with high and low mobility. We attribute the power of the local tetrahedrality for predicting local and global dynamics to the high stability of tetrahedral clusters, the most fundamental building and densest-packing building blocks for a disordered fluid.
- 21Zhang, Z.; Kob, W. Revealing the three-dimensional structure of liquids using four-point correlation functions. Proc. Natl. Acad. Sci. U.S.A. 2020, 117, 14032– 14037, DOI: 10.1073/pnas.2005638117Google Scholar21https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhsVCgsrfN&md5=cab7fc04743baeebe2728231e466c6e1Revealing the three-dimensional structure of liquids using four-point correlation functionsZhang, Zhen; Kob, WalterProceedings of the National Academy of Sciences of the United States of America (2020), 117 (25), 14032-14037CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)Disordered systems like liqs., gels, glasses, or granular materials are not only ubiquitous in daily life and in industrial applications, but they are also crucial for the mech. stability of cells or the transport of chem. and biol. agents in living organisms. Despite the importance of these systems, their microscopic structure is understood only on a rudimentary level, thus in Stark contrast to the case of gases and crystals. Since scattering expts. and anal. calcns. usually give only structural information that is spherically averaged, the three-dimensional (3D) structure of disordered systems is basically unknown. Here, we introduce a simple method that allows probing of the 3D structure of such systems. Using computer simulations, we find that hard sphere-like liqs. have on intermediate and large scales a simple structural order given by alternating layers with icosahedral and dodecahedral symmetries, while open network liqs. like silica have a structural order with tetrahedral symmetry. These results show that liqs. have a highly nontrivial 3D structure and that this structural information is encoded in nonstandard correlation functions.
- 22Schöpe, H. J.; Bryant, G.; van Megen, W. Two-step crystallization kinetics in colloidal hard-sphere systems. Phys. Rev. Lett. 2006, 96, 175701, DOI: 10.1103/PhysRevLett.96.175701Google Scholar22https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28Xkt12hsbY%253D&md5=c7475daf2ec0ea490e1372e6647a895bTwo-Step Crystallization Kinetics in Colloidal Hard-Sphere SystemsSchope, Hans Joachim; Bryant, Gary; van Megen, WilliamPhysical Review Letters (2006), 96 (17), 175701/1-175701/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)The crystn. kinetics of colloidal hard spheres was studied using a special Bragg spectrometer with high sensitivity. In contrast with the classical scenario we observe a two-step nucleation process: the no. of crystallites increases slowly at early times, followed by a dramatic redn. at intermediate times, prior to undergoing a rapid increase at late times. We explain these results in terms of a polydispersity limited growth of crystallites, where the crystn. at early times is governed by local fractionation processes, leading to a long delay prior to final crystn.
- 23Tan, P.; Xu, N.; Xu, L. Visualizing kinetic pathways of homogeneous nucleation in colloidal crystallization. Nat. Phys. 2014, 10, 73– 79, DOI: 10.1038/nphys2817Google Scholar23https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXhvFent7%252FP&md5=4411f12feb2f56fa1dfeeed0eca118efVisualizing kinetic pathways of homogeneous nucleation in colloidal crystallizationTan, Peng; Xu, Ning; Xu, LeiNature Physics (2014), 10 (1), 73-79CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)When a system undergoes a transition from a liq. to a solid phase, it passes through multiple intermediate structures before reaching the final state. However, our knowledge on the exact pathways of this process is limited, mainly owing to the difficulty of realizing direct observations. Here, we exptl. study the evolution of symmetry and d. for various colloidal systems during liq.-to-solid phase transitions, and visualize kinetic pathways with single-particle resoln. We observe the formation of relatively ordered precursor structures with different symmetries, which then convert into metastable solids. During this conversion, two major cross-symmetry pathways always occur, regardless of the final state and the interaction potential. In addn., we find a broad decoupling of d. variation and symmetry development, and discover that nucleation rarely starts from the densest regions. These findings hold for all of our samples, suggesting the possibility of finding a unified picture for the complex crystn. kinetics in colloidal systems.
- 24Russo, J.; Tanaka, H. Crystal nucleation as the ordering of multiple order parameters. J. Chem. Phys. 2016, 145, 211801, DOI: 10.1063/1.4962166Google Scholar24https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhsFWnurfI&md5=49091a43a50415d8fa29531a5831bf57Crystal nucleation as the ordering of multiple order parametersRusso, John; Tanaka, HajimeJournal of Chemical Physics (2016), 145 (21), 211801/1-211801/17CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Nucleation is an activated process in which the system has to overcome a free energy barrier in order for a first-order phase transition between the metastable and the stable phases to take place. In the liq.-to-solid transition, the process occurs between phases of different symmetry, and it is thus inherently a multi-dimensional process, in which all symmetries are broken at the transition. In this Focus Article, we consider some recent studies which highlight the multi-dimensional nature of the nucleation process. Even for a single-component system, the formation of solid crystals from the metastable melt involves fluctuations of two (or more) order parameters, often assocd. with the decoupling of positional and orientational symmetry breaking. The authors needed at least two order parameters to describe the free-energy of a system including its liq. and cryst. states. This decoupling occurs naturally for asym. particles or directional interactions, focusing here on the case of water, but we will show that it also affects spherically sym. interacting particles, such as the hard-sphere system. They will show how the treatment of nucleation as a multi-dimensional process has shed new light on the process of polymorph selection, on the effect of external fields on the nucleation process and on glass-forming ability. (c) 2016 American Institute of Physics.
- 25Lehmkühler, F.; Roseker, W.; Grübel, G. From femtoseconds to hours─measuring dynamics over 18 orders of magnitude with coherent X-rays. Appl. Sci. 2021, 11, 6179, DOI: 10.3390/app11136179Google Scholar25https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXit1Gqsb%252FO&md5=ea1f8411e8cec370531ef0c27c5b4531From Femtoseconds to Hours-Measuring Dynamics over 18 Orders of Magnitude with Coherent X-raysLehmkuehler, Felix; Roseker, Wojciech; Gruebel, GerhardApplied Sciences (2021), 11 (13), 6179CODEN: ASPCC7; ISSN:2076-3417. (MDPI AG)X-ray photon correlation spectroscopy (XPCS) enables the study of sample dynamics between micrometer and at. length scales. As a coherent scattering technique, it benefits from the increased brilliance of the next-generation synchrotron radiation and Free-Electron Laser (FEL) sources. In this article, we will introduce the XPCS concepts and review the latest developments of XPCS with special attention on the extension of accessible time scales to sub-μs and the application of XPCS at FELs. Furthermore, we will discuss future opportunities of XPCS and the related technique X-ray speckle visibility spectroscopy (XSVS) at new X-ray sources. Due to its particular signal-to-noise ratio, the time scales accessible by XPCS scale with the square of the coherent flux, allowing to dramatically extend its applications. This will soon enable studies over more than 18 orders of magnitude in time by XPCS and XSVS.
- 26Grübel, G.; Madsen, A.; Robert, A. Soft matter characterization; Springer Netherlands: Dordrecht, The Netherlands, 2008; pp 953– 995.Google ScholarThere is no corresponding record for this reference.
- 27Sandy, A. R.; Zhang, Q.; Lurio, L. B. Hard X-ray photon correlation spectroscopy methods for materials studies. Annu. Rev. Mater. Res. 2018, 48, 167– 190, DOI: 10.1146/annurev-matsci-070317-124334Google Scholar27https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXmsVensro%253D&md5=cb131e737010cd09e572d44ace789f94Hard X-Ray Photon Correlation Spectroscopy Methods for Materials StudiesSandy, Alec R.; Zhang, Qingteng; Lurio, Laurence B.Annual Review of Materials Research (2018), 48 (), 167-190CODEN: ARMRCU; ISSN:1531-7331. (Annual Reviews)Understanding and designing sophisticated new materials require measurements of not only their av. structural properties but also their dynamic behavior. X-ray photon correlation spectroscopy (XPCS) provides this information by characterizing fluctuations in condensed matter across a broad range of length scales and timescales. Over the past two decades, XPCS has provided a wide variety of results in the study of materials properties. In this review, we provide an overview of coherence, photon correlation spectroscopy, and the dynamic structure factor as well as information on the mechanics of XPCS expts. We highlight the impact that this infrastructure has had on materials research and the bright future that is forthcoming with the anticipated upgrade of many third-generation synchrotron sources to fourth-generation multibend achromat sources.
- 28Madsen, A.; Fluerasu, A.; Ruta, B. In Synchrotron light sources and free-electron lasers: accelerator physics, instrumentation and science applications; Jaeschke, E. J., Khan, S., Schneider, J. R., Hastings, J. B., Eds.; Springer International Publishing: Cham, Switzerland, 2016; pp 1617– 1641.Google ScholarThere is no corresponding record for this reference.
- 29Kurta, R. P.; Altarelli, M.; Vartanyants, I. A. Advances in Chemical Physics; John Wiley and Sons, Ltd.: Hoboken, NJ, 2016; pp 1– 39.Google ScholarThere is no corresponding record for this reference.
- 30Wochner, P.; Gutt, C.; Autenrieth, T.; Demmer, T.; Bugaev, V.; Ortiz, A. D.; Duri, A.; Zontone, F.; Grübel, G.; Dosch, H. X-ray cross correlation analysis uncovers hidden local symmetries in disordered matter. Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 11511– 11514, DOI: 10.1073/pnas.0905337106Google Scholar30https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXptVKjsLg%253D&md5=5bb7ee07cdc5a5505ac0d1c3669680a1X-ray cross correlation analysis uncovers hidden local symmetries in disordered matterWochner, Peter; Gutt, Christian; Autenrieth, Tina; Demmer, Thomas; Bugaev, Volodymyr; Ortiz, Alejandro Diaz; Duri, Agnes; Zontone, Federico; Gruebel, Gerhard; Dosch, HelmutProceedings of the National Academy of Sciences of the United States of America (2009), 106 (28), 11511-11514, S11511/1-S11511/5CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)The authors explore the different local symmetries in colloidal glasses beyond the std. pair correlation anal. Using the newly developed x-ray cross correlation anal. (XCCA) concept together with brilliant coherent X-ray sources, the authors were able to access and classify the otherwise hidden local order within disorder. The emerging local symmetries are coupled to distinct momentum transfer (Q) values, which do not coincide with the maxima of the amorphous structure factor. Four-, 6-, 10- and, most prevalently, 5-fold symmetries are obsd. The observation of dynamical evolution of these symmetries forms a connection to dynamical heterogeneities in glasses, which is far beyond conventional diffraction anal. The XCCA concept opens up a fascinating view into the world of disorder and will definitely allow, with the advent of free electron x-ray lasers, an accurate and systematic exptl. characterization of the structure of the liq. and glass states.
- 31Zaluzhnyy, I. A.; Kurta, R. P.; Scheele, M.; Schreiber, F.; Ostrovskii, B. I.; Vartanyants, I. A. Angular X-ray cross-correlation analysis (AXCCA): basic concepts and recent applications to soft Matter and nanomaterials. Materials 2019, 12, 3464, DOI: 10.3390/ma12213464Google Scholar31https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXotFGksLY%253D&md5=7802ba1bbbef7307ccf5c43878c52a73Angular X-ray cross-correlation analysis (AXCCA): basic concepts and recent applications to soft matter and nanomaterialsZaluzhnyy, Ivan A.; Kurta, Ruslan P.; Scheele, Marcus; Schreiber, Frank; Ostrovskii, Boris I.; Vartanyants, Ivan A.Materials (2019), 12 (21), 3464CODEN: MATEG9; ISSN:1996-1944. (MDPI AG)Angular X-ray cross-correlation anal. (AXCCA) is a technique which allows quant. measurement of the angular anisotropy of X-ray diffraction patterns and provides insights into the orientational order in the system under investigation. This method is based on the evaluation of the angular cross-correlation function of the scattered intensity distribution on a two-dimensional (2D) detector and further averaging over many diffraction patterns for enhancement of the anisotropic signal. Over the last decade, AXCCA was successfully used to study the anisotropy in various soft matter systems, such as solns. of anisotropic particles, liq. crystals, colloidal crystals, superlattices composed by nanoparticles, etc. This review provides an introduction to the technique and gives a survey of the recent exptl. work in which AXCCA in combination with micro- or nanofocused X-ray microscopy was used to study the orientational order in various soft matter systems.
- 32Lehmkühler, F.; Hankiewicz, B.; Schroer, M. A.; Müller, L.; Ruta, B.; Sheyfer, D.; Sprung, M.; Tono, K.; Katayama, T.; Yabashi, M. Slowing down of dynamics and orientational order preceding crystallization in hard-sphere systems. Sci. Adv. 2020, 6, eabc5916 DOI: 10.1126/sciadv.abc5916Google ScholarThere is no corresponding record for this reference.
- 33Hu, Z.; Donatelli, J. J.; Sethian, J. A. Cross-correlation analysis of X-ray photon correlation spectroscopy to extract rotational diffusion coefficients. Proc. Natl. Acad. Sci. U. S. A. 2021, 118, e2105826118 DOI: 10.1073/pnas.2105826118Google Scholar33https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhvVOqu73F&md5=1e42858badc92c4e7a62d926ea8332fbCross-correlation analysis of X-ray photon correlation spectroscopy to extract rotational diffusion coefficientsHu, Zixi; Donatelli, Jeffrey J.; Sethian, James A.Proceedings of the National Academy of Sciences of the United States of America (2021), 118 (34), e2105826118CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)Coeffs. for translational and rotational diffusion characterize the Brownian motion of particles. Emerging X-ray photon correlation spectroscopy (XPCS) expts. probe a broad range of length scales and time scales and are well-suited for investigation of Brownian motion. While methods for estg. the translational diffusion coeffs. from XPCS are well-developed, there are no algorithms for measuring the rotational diffusion coeffs. based on XPCS, even though the required raw data are accessible from such expts. In this paper, we propose angular-temporal cross-correlation anal. of XPCS data and show that this information can be used to design a numerical algorithm (Multi-Tiered Estn. for Correlation Spectroscopy [MTECS]) for predicting the rotational diffusion coeff. utilizing the cross-correlation: This approach is applicable to other wavelengths beyond this regime. We verify the accuracy of this algorithmic approach across a range of simulated data.
- 34Hallett, J. E.; Turci, F.; Royall, C. P. Local structure in deeply supercooled liquids exhibits growing lengthscales and dynamical correlations. Nat. Commun. 2018, 9, 3272, DOI: 10.1038/s41467-018-05371-6Google Scholar34https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BB3c7ovFWluw%253D%253D&md5=1ed02edf2d5394e0ddc48342179d7517Local structure in deeply supercooled liquids exhibits growing lengthscales and dynamical correlationsHallett James E; Turci Francesco; Royall C Patrick; Hallett James E; Turci Francesco; Royall C Patrick; Royall C PatrickNature communications (2018), 9 (1), 3272 ISSN:.Glasses are among the most widely used of everyday materials, yet the process by which a liquid's viscosity increases by 14 decades to become a glass remains unclear, as often contradictory theories provide equally good descriptions of the available data. Knowledge of emergent lengthscales and higher-order structure could help resolve this, but this requires time-resolved measurements of dense particle coordinates-previously only obtained over a limited time interval. Here we present an experimental study of a model colloidal system over a dynamic window significantly larger than previous measurements, revealing structural ordering more strongly linked to dynamics than previously found. Furthermore we find that immobile regions and domains of local structure grow concurrently with density, and that these regions have low configurational entropy. We thus show that local structure plays an important role at deep supercooling, consistent with a thermodynamic interpretation of the glass transition rather than a principally dynamic description.
- 35Di Cola, E.; Moussaïd, A.; Sztucki, M.; Narayanan, T.; Zaccarelli, E. Correlation between structure and rheology of a model colloidal glass. J. Chem. Phys. 2009, 131, 144903, DOI: 10.1063/1.3240345Google Scholar35https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXht1yjsrrK&md5=7e3b57394d8cbca38e2d707ad1c4d3f6Correlation between structure and rheology of a model colloidal glassDi Cola, E.; Moussaid, A.; Sztucki, M.; Narayanan, T.; Zaccarelli, E.Journal of Chemical Physics (2009), 131 (14), 144903/1-144903/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)The microstructure and rheol. properties of a model colloidal system was probed in the vicinity of the glass transition by small-angle and ultra small-angle x-ray scattering, dynamic light scattering (DLS) and bulk rheol. The vol. fraction of the particles was deduced by modeling the structure factor and the abs. scattered intensity in a self-consistent way. The glass transition (φG) was identified from the frequency dependence of the shear moduli in the linear regime. The exptl. obsd. behavior was then compared with the viscoelastic properties derived from mode-coupling theory (MCT) using the exptl. structure factor as input to the theory. The ensemble-averaged intermediate scattering functions from DLS measurements were also compared with those calcd. from the MCT and reasonable agreement was obtained. (c) 2009 American Institute of Physics.
- 36Frenzel, L.; Dartsch, M.; Balaguer, G. M.; Westermeier, F.; Grübel, G.; Lehmkühler, F. Glass-liquid and glass-gel transitions of soft-shell particles. Phys. Rev. E 2021, 104, L012602, DOI: 10.1103/PhysRevE.104.L012602Google Scholar36https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhvValt7bK&md5=c88dee4a530c6d691bf64d6712db86d7Glass-liquid and glass-gel transitions of soft-shell particlesFrenzel, Lara; Dartsch, Michael; Balaguer, Gerard Marti; Westermeier, Fabian; Gruebel, Gerhard; Lehmkuehler, FelixPhysical Review E (2021), 104 (1), L012602CODEN: PREHBM; ISSN:2470-0053. (American Physical Society)We study the structure and dynamics of colloidal particles with a spherical hard core and a thermo-responsive soft shell over the whole phase diagram by means of small-angle x-ray scattering and x-ray photon correlation spectroscopy. By changing the effective vol. fraction by temp. and particle concn., liq., repulsive glass. and attractive gel phases are obsd. The dynamics slow down with increasing vol. fraction in the liq. phase and reflect a Vogel-Fulcher-Tamann behavior known for fragile glass formers. We find a liq.-glass transition above 50 vol.% that is independent of the particles' concn. and temp. In an overpacked state at effective vol. fractions above 1, the dispersion does not show a liq. phase but undergoes a gel-glass transition at an effective vol. fraction of 34 vol.%. At the same concn., extrema of subdiffusive dynamics are found in the liq. phase at lower wt. fractions. We interpret this as dynamic precursors of the glass-gel transition.
- 37Philippe, A.-M.; Truzzolillo, D.; Galvan-Myoshi, J.; Dieudonné-George, P.; Trappe, V.; Berthier, L.; Cipelletti, L. Glass transition of soft colloids. Phys. Rev. E 2018, 97, 040601, DOI: 10.1103/PhysRevE.97.040601Google Scholar37https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXkvFOkt7s%253D&md5=fa9c59371bf5e847f1ee2e22acb65e55Glass transition of soft colloidsPhilippe, Adrian-Marie; Truzzolillo, Domenico; Galvan-Myoshi, Julian; Dieudonne-George, Philippe; Trappe, Veronique; Berthier, Ludovic; Cipelletti, LucaPhysical Review E (2018), 97 (4), 040601CODEN: PREHBM; ISSN:2470-0053. (American Physical Society)We explore the glassy dynamics of soft colloids using microgels and charged particles interacting by steric and screened Coulomb interactions, resp. In the supercooled regime, the structural relaxation time ταof both systems grows steeply with vol. fraction, reminiscent of the behavior of colloidal hard spheres. Computer simulations confirm that the growth of τα on approaching the glass transition is independent of particle softness. By contrast, softness becomes relevant at very large packing fractions when the system falls out of equil. In this nonequil. regime, τα depends surprisingly weakly on packing fraction, and time correlation functions exhibit a compressed exponential decay consistent with stress-driven relaxation. The transition to this novel regime coincides with the onset of an anomalous decrease in local order with increasing d. typical of ultrasoft systems. We propose that these peculiar dynamics results from the combination of the nonequil. aging dynamics expected in the glassy state and the tendency of colloids interacting through soft potentials to refluidize at high packing fractions.
- 38Tong, H.; Tanaka, H. Structural order as a genuine control parameter of dynamics in simple glass formers. Nat. Commun. 2019, 10, 5596, DOI: 10.1038/s41467-019-13606-3Google Scholar38https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXitlyntrbE&md5=81bc411fbedc82d670dae09c32a9e4ccStructural order as a genuine control parameter of dynamics in simple glass formersTong, Hua; Tanaka, HajimeNature Communications (2019), 10 (1), 5596CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)Glass transition is characterised by drastic dynamical slowing down upon cooling, accompanied by growing spatial heterogeneity. Its rationalisation by subtle changes in the liq. structure has been long debated but remains elusive, due to intrinsic difficulty in detecting the underlying complex structural ordering. Here we report that structural order parameter characterizing local packing capability can well describe the glassy dynamics not only macroscopically but also microscopically, no matter whether it is driven by temp. or d. A Vogel-Fulcher-Tammann (VFT)-like relation is universally identified between the structural relaxation time and the order parameter for supercooled liqs. with isotropic interactions. More importantly, we find such an intriguing VFT-like relation to be statistically valid even at a particle level, between spatially coarse-grained structural order and microscopic particle-level dynamics. Such a unified description of glassy dynamics based solely on structural order is expected to contribute to the ultimate understanding of the long-standing glass-transition problem.
- 39Laurati, M.; Maßhoff, P.; Mutch, K. J.; Egelhaaf, S. U.; Zaccone, A. Long-lived neighbors determine the rheological response of glasses. Phys. Rev. Lett. 2017, 118, 018002, DOI: 10.1103/PhysRevLett.118.018002Google Scholar39https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXpt1Gntb4%253D&md5=bc9ba6c5497a3088a9bcb5fee2cff24bLong-lived neighbors determine the rheological response of glassesLaurati, M.; Masshoff, P.; Mutch, K. J.; Egelhaaf, S. U.; Zaccone, A.Physical Review Letters (2017), 118 (1), 018002/1-018002/6CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)Glasses exhibit a liquidlike structure but a solidlike rheol. response with plastic deformations only occurring beyond yielding. Thus, predicting the rheol. behavior from the microscopic structure is difficult, but important for materials science. Here, we consider colloidal suspensions and propose to supplement the static structural information with the local dynamics, namely, the rearrangement and breaking of the cage of neighbors. This is quantified by the mean squared nonaffine displacement and the no. of particles that remain nearest neighbors for a long time, i.e., long-lived neighbors, resp. Both quantities are followed under shear using confocal microscopy and are the basis to calc. the affine and nonaffine contributions to the elastic stress, which is complemented by the viscoelastic stress to give the total stress. During start-up of shear, the model predicts three transient regimes that result from the interplay of affine, nonaffine, and viscoelastic contributions. Our prediction quant. agrees with rheol. data and their dependencies on vol. fraction and shear rate.
- 40Higler, R.; Krausser, J.; van der Gucht, J.; Zaccone, A.; Sprakel, J. Linking slow dynamics and microscopic connectivity in dense suspensions of charged colloids. Soft Matter 2018, 14, 780– 788, DOI: 10.1039/C7SM01781BGoogle Scholar40https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXitVWnsbvN&md5=7c7a325f307f81abe8f827925b674d69Linking slow dynamics and microscopic connectivity in dense suspensions of charged colloidsHigler, Ruben; Krausser, Johannes; van der Gucht, Jasper; Zaccone, Alessio; Sprakel, JorisSoft Matter (2018), 14 (5), 780-788CODEN: SMOABF; ISSN:1744-6848. (Royal Society of Chemistry)The quest to unravel the nature of the glass transition, where the viscosity of a liq. increases by many orders of magnitude, while its static structure remains largely unaffected, remains unresolved. While various structural and dynamical precursors to vitrification have been identified, a predictive and quant. description of how subtle changes at the microscopic scale give rise to the steep growth in macroscopic viscosity is missing. It was recently proposed that the presence of long-lived bonded structures within the liq. may provide the long-sought connection between local structure and global dynamics. Here we directly observe and quantify the connectivity dynamics in liqs. of charged colloids en route to vitrification using three-dimensional confocal microscopy. We det. the dynamic structure from the real-space van Hove correlation function and from the particle trajectories, providing upper and lower bounds on connectivity dynamics. Based on these data, we extend Dyre's model for the glass transition to account for particle-level structural dynamics; this results in a microscopic expression for the slowing down of relaxations in the liq. that is in quant. agreement with our expts. These results indicate how vitrification may be understood as a dynamical connectivity transition with features that are strongly reminiscent of rigidity percolation scenarios.
- 41Schaertl, W.; Sillescu, H. Brownian dynamics of polydisperse colloidal hard spheres: Equilibrium structures and random close packings. J. Stat. Phys. 1994, 77, 1007– 1025, DOI: 10.1007/BF02183148Google ScholarThere is no corresponding record for this reference.
- 42Kwaśniewski, P.; Fluerasu, A.; Madsen, A. Anomalous dynamics at the hard-sphere glass transition. Soft Matter 2014, 10, 8698– 8704, DOI: 10.1039/C4SM01671HGoogle Scholar42https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhsVGjtL3P&md5=22f50226221cfb94a29ce20ec4649157Anomalous dynamics at the hard-sphere glass transitionKwasniewski, Pawel; Fluerasu, Andrei; Madsen, AndersSoft Matter (2014), 10 (43), 8698-8704CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)We use X-ray photon correlation spectroscopy to study the dynamics of hard sphere suspensions and report the emergence of ergodicity restoring anomalous intermittent relaxation modes in the highest concn. suspension that is estd. to be above the glass transition concn. We assoc. these phenomena with non-thermal stress induced relaxations and support our interpretation by a direct comparison of the results with predictions of the mode coupling theory.
- 43Zaccone, A. Explicit analytical solution for random close packing in d = 2 and d = 3. Phys. Rev. Lett. 2022, 128, 028002, DOI: 10.1103/PhysRevLett.128.028002Google Scholar43https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XitFCktr0%253D&md5=f5a3016d8ebf479a10309b1714c320a3Explicit Analytical Solution for Random Close Packing in d=2 and d=3Zaccone, AlessioPhysical Review Letters (2022), 128 (2), 028002CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)We present an anal. derivation of the vol. fractions for random close packing (RCP) in both d=3 and d=2, based on the same methodol. Using suitably modified nearest neighbor statistics for hard spheres, we obtain .vphi.RCP=0.658 96 in d=3 and .vphi.RCP=0.886 48 in d=2. These values are well within the interval of values reported in the literature using different methods (expts. and numerical simulations) and protocols. This statistical derivation suggests some considerations related to the nature of RCP: (i) RCP corresponds to the onset of mech. rigidity where the finite shear modulus emerges, (ii) the onset of mech. rigidity marks the maximally random jammed state and dictates .vphi.RCP via the coordination no. z, (iii) disordered packings with .vphi.>.vphi.RCP are possible at the expense of creating some order, and z=12 at the fcc limit acts as a boundary condition.
- 44Anzivino, C.; Casiulis, M.; Zhang, T.; Moussa, A. S.; Martiniani, S.; Zaccone, A. Estimating random close packing in polydisperse and bidisperse hard spheres via an equilibrium model of crowding. J. Chem. Phys. 2023, 158, 044901, DOI: 10.1063/5.0137111Google Scholar44https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3sXhs1Orsro%253D&md5=73328a3deddb83a0cb6ea47bc88830b6Estimating random close packing in polydisperse and bidisperse hard spheres via an equilibrium model of crowdingAnzivino, Carmine; Casiulis, Mathias; Zhang, Tom; Moussa, Amgad Salah; Martiniani, Stefano; Zaccone, AlessioJournal of Chemical Physics (2023), 158 (4), 044901CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)It is shown that an analogy between crowding in fluid and jammed phases of hard spheres captures the d. dependence of the kissing no. for a family of numerically generated jammed states. This analogy is extended to jams of mixts. of hard spheres in d = 3 dimensions and, thus, obtain an est. of the random close packing vol. fraction, ΦRCP, as a function of size polydispersity. First mixts. of particle sizes with discrete distributions are considered. For binary systems, agreement between the predictions and simulations is shown using both our own results and results reported in previous studies, as well as agreement with recent expts. from the literature. The approach is applied to systems with continuous polydispersity using three different particle size distributions, namely, the log-normal, Gamma, and truncated power-law distributions. In all cases, the agreement is obsd. between the theor. findings and numerical results up to rather large polydispersities for all particle size distributions when using as ref. the simulations and results from the literature. In particular, it was found that ΦRCP to increase monotonically with the relative std. deviation, sσ, of the distribution and to sat. at a value that always remains < 1. A perturbative expansion yields a closed-form expression for ΦRCP that quant. captures a distribution-independent regime for sσ < 0.5. Beyond that regime, it is shown that the gradual loss in agreement is tied to the growth of the skewness of size distributions. (c) 2023 American Institute of Physics.
- 45Dallari, F.; Martinelli, A.; Caporaletti, F.; Sprung, M.; Grübel, G.; Monaco, G. Microscopic pathways for stress relaxation in repulsive colloidal glasses. Sci. Adv. 2020, 6, eaaz2982 DOI: 10.1126/sciadv.aaz2982Google ScholarThere is no corresponding record for this reference.
- 46Jain, A.; Schulz, F.; Dallari, F.; Markmann, V.; Westermeier, F.; Zhang, Y.; Grübel, G.; Lehmkühler, F. Three-step colloidal gelation revealed by time-resolved x-ray photon correlation spectroscopy. J. Chem. Phys. 2022, 157, 184901, DOI: 10.1063/5.0123118Google Scholar46https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XivVKntL3J&md5=1c560b81febbabad9dacfff0fb3d840fThree-step colloidal gelation revealed by time-resolved x-ray photon correlation spectroscopyJain, Avni; Schulz, Florian; Dallari, Francesco; Markmann, Verena; Westermeier, Fabian; Zhang, Yugang; Gruebel, Gerhard; Lehmkuehler, FelixJournal of Chemical Physics (2022), 157 (18), 184901CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)The gelation of PEGylated gold nanoparticles dispersed in a glycerol-water mixt. is probed in situ by x-ray photon correlation spectroscopy. Following the evolution of structure and dynamics over 104 s, a three-step gelation process is found. First, a simultaneous increase of the Ornstein-Zernike length ξ and slowdown of dynamics is characterized by an anomalous q-dependence of the relaxation times of τ ∞ q-6 and strongly stretched intermediate scattering functions. After the structure of the gel network has been established, evidenced by a const. ξ, the dynamics show aging during the second gelation step accompanied by a change toward ballistic dynamics with τ ∞ q-1 and compressed correlation functions. In the third step, aging continues after the arrest of particle motion. Our observations further suggest that gelation is characterized by stress release as evidenced by anisotropic dynamics once gelation sets in. (c) 2022 American Institute of Physics.
- 47Ruta, B.; Chushkin, Y.; Monaco, G.; Cipelletti, L.; Pineda, E.; Bruna, P.; Giordano, V. M.; Gonzalez-Silveira, M. Atomic-scale relaxation dynamics and aging in a metallic glass probed by X-ray photon correlation spectroscopy. Phys. Rev. Lett. 2012, 109, 165701, DOI: 10.1103/PhysRevLett.109.165701Google Scholar47https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38Xhs1CisLnN&md5=e46954e866df320b2c1443d50d09b074Atomic-scale relaxation dynamics and aging in a metallic glass probed by X-ray photon correlation spectroscopyRuta, B.; Chushkin, Y.; Monaco, G.; Cipelletti, L.; Pineda, E.; Bruna, P.; Giordano, V. M.; Gonzalez-Silveira, M.Physical Review Letters (2012), 109 (16), 165701/1-165701/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)We use x-ray photon correlation spectroscopy to investigate the structural relaxation process in a metallic glass on the at. length scale. We report evidence for a dynamical crossover between the supercooled liq. phase and the metastable glassy state, suggesting different origins of the relaxation process across the transition. Furthermore, using different cooling rates, we observe a complex hierarchy of dynamic processes characterized by distinct aging regimes. Strong analogies with the aging dynamics of soft glassy materials, such as gels and concd. colloidal suspensions, point at stress relaxation as a universal mechanism driving the relaxation dynamics of out-of-equil. systems.
- 48Wu, Z.; Kob, W.; Wang, W.; Xu, L. Stretched and compressed exponentials in the relaxation dynamics of a metallic glass-forming melt. Nat. Commun. 2018, 9, 5334, DOI: 10.1038/s41467-018-07759-wGoogle Scholar48https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXisFersLrE&md5=ed4faf497b081c816507000bd7c63a88Stretched and compressed exponentials in the relaxation dynamics of a metallic glass-forming meltWu, Zhen Wei; Kob, Walter; Wang, Wei-Hua; Xu, LimeiNature Communications (2018), 9 (1), 5334CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)The dynamics of glass-forming systems shows a multitude of features that are absent in normal liqs., such as non-exponential relaxation and a strong temp.-dependence of the relaxation time. Connecting these dynamic properties to the microscopic structure of the system is challenging because of the presence of the structural disorder. Here we use computer simulations of a metallic glass-former to establish such a connection. By probing the temp. and wave-vector dependence of the intermediate scattering function we find that the relaxation dynamics of the glassy melt is directly related to the local arrangement of icosahedral structures: Isolated icosahedra give rise to a liq.-like stretched exponential relaxation whereas clusters of icosahedra lead to a compressed exponential relaxation that is reminiscent to the one found in a solid. Our results show that in metallic glass-formers these two types of relaxation processes can coexist and give rise to a dynamics that is surprisingly complex.
- 49Trachenko, K.; Zaccone, A. Slow stretched-exponential and fast compressed-exponential relaxation from local event dynamics. J.Phys. Condens. 2021, 33, 315101, DOI: 10.1088/1361-648X/ac04cdGoogle Scholar49https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhvF2gsrbO&md5=4fd231901e9fe00e2aabfe920c29faf8Slow stretched-exponential and fast compressed-exponential relaxation from local event dynamicsTrachenko, K.; Zaccone, A.Journal of Physics: Condensed Matter (2021), 33 (31), 315101CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)We propose an atomistic model for correlated particle dynamics in liqs. and glasses predicting both slow stretched-exponential relaxation (SER) and fast compressed-exponential relaxation (CER). The model is based on the key concept of elastically interacting local relaxation events. SER is related to slowing down of dynamics of local relaxation events as a result of this interaction, whereas CER is related to the avalanche-like dynamics in the low-temp. glass state. The model predicts temp. dependence of SER and CER seen exptl. and recovers the simple, Debye, exponential decay at high temp. Finally, we reproduce SER to CER crossover across the glass transition recently obsd. in metallic glasses.
- 50Liu, A. C. Y.; Tabor, R. F.; de Jonge, M. D.; Mudie, S. T.; Petersen, T. C. Favored local structures in amorphous colloidal packings measured by microbeam X-ray diffraction. Proc. Natl. Acad. Sci. U.S.A. 2017, 114, 10344– 10349, DOI: 10.1073/pnas.1707198114Google Scholar50https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXhsV2jtLrE&md5=cece575aee26b10d41b4ea05b6cc51d6Favored local structures in amorphous colloidal packings measured by microbeam X-ray diffractionLiu, Amelia C. Y.; Tabor, Rico F.; de Jonge, Martin D.; Mudie, Stephen T.; Petersen, Timothy C.Proceedings of the National Academy of Sciences of the United States of America (2017), 114 (39), 10344-10349CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)Local structure and symmetry are keys to understanding how a material is formed and the properties it subsequently exhibits. This applies to both crystals and amorphous and glassy materials. In the case of amorphous materials, strong links between processing and history, structure and properties have yet to be made because measuring amorphous structure remains a significant challenge. The authors demonstrate a method to quantify proportions of the bond-orientational order of nearest neighbor clusters [Steinhardt, et al. (1983) Phys Rev B 28:784-805] in colloidal packings by statistically analyzing the angular correlations in an ensemble of scanning transmission microbeam small-angle X-ray scattering (μSAXS) patterns. Local order can be modulated by tuning the potential between monodisperse, spherical colloidal silica particles using salt and surfactant additives and that more pronounced order is obtained by centrifugation than sedimentation. The order in the centrifuged glasses reflects the ground state order in the dispersion at lower packing fractions. This diffraction-based method can be applied to amorphous systems across decades in length scale to connect structure to behavior in disordered systems with a range of particle interactions.
- 51Ackerson, B. J.; Taylor, T. W.; Clark, N. A. Characterization of the local structure of fluids by apertured cross-correlation functions. Phys. Rev. A 1985, 31, 3183– 3193, DOI: 10.1103/PhysRevA.31.3183Google Scholar51https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaL2MXktFWlsr8%253D&md5=f719da6ee0e5c992706f6f14958358f1Characterization of the local structure of fluids by apertured cross-correlation functionsAckerson, Bruce J.; Taylor, Thomas W.; Clark, Noel A.Physical Review A: Atomic, Molecular, and Optical Physics (1985), 31 (5), 3183-93CODEN: PLRAAN; ISSN:0556-2791.The described apertured cross-correlation functions (ACCF's) can be used to study local structure in disordered systems. A formal expression for the apertured intensity cross-correlation function was obtained in terms of multiparticle ACCF's. This expression is related to a variety of correlation functions, which can be studied via scattered-light-intensity cross-correlation expts. (C., et al., 1983). ACCF's were obtained for a two-dimensional hard-disk system by computer simulation. Three- and four-body correlations must, in general, be included to give accurate representation of the apertured intensity cross-correlation function.
- 52Lehmkühler, F.; Fischer, B.; Müller, L.; Ruta, B.; Grübel, G. Structure beyond pair correlations: X-ray cross-correlation from colloidal crystals. J. Appl. Crystallogr. 2016, 49, 2046– 2052, DOI: 10.1107/S1600576716017313Google Scholar52https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XitVSqsr3L&md5=766d7f3a4c97abf0ce29a168073540e2Structure beyond pair correlations: X-ray cross-correlation from colloidal crystalsLehmkuehler, Felix; Fischer, Birgit; Mueller, Leonard; Ruta, Beatrice; Gruebel, GerhardJournal of Applied Crystallography (2016), 49 (6), 2046-2052CODEN: JACGAR; ISSN:1600-5767. (International Union of Crystallography)The results of an X-ray cross-correlation anal. (XCCA) study on hard-sphere colloidal crystals and glasses are presented. The article shows that cross-correlation functions can be used to ext. structural information beyond the static structure factor in such systems. In particular, the powder av. can be overcome by accessing the crystals' unit-cell structure. In this case, the results suggest that the crystal is of face-centered cubic type. It is demonstrated that XCCA is a valuable tool for X-ray crystallog., in particular for studies on colloidal systems. These are typically characterized by a rather poor cryst. quality due to size polydispersity and limitations in exptl. resoln. because of the small q values probed. Furthermore, nontrivial correlations are obsd. that allow a more detailed insight into crystal structures beyond conventional crystallog., esp. to extend knowledge in structure formation processes and phase transitions.
- 53Lokteva, I.; Koof, M.; Walther, M.; Grübel, G.; Lehmkühler, F. Monitoring nanocrystal self-assembly in real time using in situ small-angle X-ray scattering. Small 2019, 15, 1900438, DOI: 10.1002/smll.201900438Google ScholarThere is no corresponding record for this reference.
- 54Lokteva, I.; Dartsch, M.; Dallari, F.; Westermeier, F.; Walther, M.; Grübel, G.; Lehmkühler, F. Real-time X-ray scattering discovers rich phase behavior in PbS nanocrystal superlattices during in situ assembly. Chem. Mater. 2021, 33, 6553– 6563, DOI: 10.1021/acs.chemmater.1c02159Google Scholar54https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhs12ms7rI&md5=70c1c51463bb68b7af73b6214890cabaReal-Time X-ray Scattering Discovers Rich Phase Behavior in PbS Nanocrystal Superlattices during In Situ AssemblyLokteva, Irina; Dartsch, Michael; Dallari, Francesco; Westermeier, Fabian; Walther, Michael; Gruebel, Gerhard; Lehmkuehler, FelixChemistry of Materials (2021), 33 (16), 6553-6563CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)During the self-organization of colloidal semiconductor nanoparticles by solvent evapn., nanoparticle interactions are substantially detd. by the org. ligands covering the inorg. core. However, the influence of the ligand grafting d. on the assembly pathway is often not considered in expts. Here, we carry out an in situ synchrotron small-angle X-ray scattering and X-ray cross-correlation anal. study of the real-time assembly of oleic acid-capped PbS nanocrystals at a low ligand coverage of 2.7 mols./nm2. With high temporal and spatial resoln., we monitor the transitions from the colloidal suspension through the solvated superlattice states into the final dried superstructure. In a single in situ expt., we observe a two-dimensional hexagonal, hcp., body-centered cubic, body-centered tetragonal (with different degrees of tetragonal distortion), and face-centered cubic superlattice phases. Our results are compared to the self-organization of PbS nanocrystals with a higher ligand coverage up to 4.5 mols./nm2, revealing different assembly pathways. This highlights the importance of detg. the ligand coverage in assembly expts. to approach a complete understanding of the assembly mechanism as well as to be able to predict and produce the targeted superstructures.
- 55Schulz, F.; Lokteva, I.; Parak, W. J.; Lehmkühler, F. Recent notable approaches to study self-assembly of nanoparticles with X-Ray scattering and electron microscopy. Part. Part. Sys. Charact. 2021, 38, 2100087, DOI: 10.1002/ppsc.202100087Google ScholarThere is no corresponding record for this reference.
- 56Duri, A.; Bissig, H.; Trappe, V.; Cipelletti, L. Time-resolved-correlation measurements of temporally heterogeneous dynamics. Phys. Rev. E 2005, 72, 051401, DOI: 10.1103/PhysRevE.72.051401Google Scholar56https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXhtlSgtbzJ&md5=b82962c69b4dbbaa456b59579ade1df7Time-resolved-correlation measurements of temporally heterogeneous dynamicsDuri, Agnes; Bissig, Hugo; Trappe, Veronique; Cipelletti, LucaPhysical Review E: Statistical, Nonlinear, and Soft Matter Physics (2005), 72 (5-1), 051401/1-051401/17CODEN: PRESCM; ISSN:1539-3755. (American Physical Society)Time resolved correlation (TRC) is a recently introduced light scattering technique that allows one to detect and quantify dynamic heterogeneities. The technique is based on the anal. of the temporal evolution of the speckle pattern generated by the light scattered by a sample, which is quantified by cI(t,τ), the degree of correlation between speckle images recorded at time t and t+τ. Heterogeneous dynamics results in significant fluctuations of cI(t,τ) with time t. We describe how to optimize TRC measurements and how to detect and avoid possible artifacts. The statistical properties of the fluctuations of cI are analyzed by studying their variance, probability distribution function, and time autocorrelation function. We show that these quantities are affected by a noise contribution due to the finite no. N of detected speckles. We propose and demonstrate a method to correct for the noise contribution, based on a N→∞ extrapolation scheme. Examples from both homogeneous and heterogeneous dynamics are provided. Connections with recent numerical and anal. works on heterogeneous glassy dynamics are briefly discussed.
- 57Dallari, F.; Martinelli, A.; Caporaletti, F.; Sprung, M.; Baldi, G.; Monaco, G. Stochastic atomic acceleration during the X-ray-induced fluidization of a silica glass. Proc. Natl. Acad. Sci. U. S. A. 2023, 120, e2213182120 DOI: 10.1073/pnas.2213182120Google ScholarThere is no corresponding record for this reference.
- 58Schroer, C. G.; Agapov, I.; Brefeld, W.; Brinkmann, R.; Chae, Y.-C.; Chao, H.-C.; Eriksson, M.; Keil, J.; Nuel Gavaldà, X.; Röhlsberger, R. PETRA IV: the ultralow-emittance source project at DESY. J. Synchrotron Rad. 2018, 25, 1277– 1290, DOI: 10.1107/S1600577518008858Google Scholar58https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhs1GktbzE&md5=f00f665ddd2c274f03839d9043d5de0cPETRA IV: the ultralow-emittance source project at DESYSchroer, Christian G.; Agapov, Ilya; Brefeld, Werner; Brinkmann, Reinhard; Chae, Yong-Chul; Chao, Hung-Chun; Eriksson, Mikael; Keil, Joachim; Nuel Gavalda, Xavier; Roehlsberger, Ralf; Seeck, Oliver H.; Sprung, Michael; Tischer, Markus; Wanzenberg, Rainer; Weckert, EdgarJournal of Synchrotron Radiation (2018), 25 (5), 1277-1290CODEN: JSYRES; ISSN:1600-5775. (International Union of Crystallography)The PETRA IV project aims at upgrading the present synchrotron radiation source PETRA III at DESY into an ultralow-emittance source. Being diffraction limited up to X-rays of about 10 keV, PETRA IV will be ideal for three-dimensional X-ray microscopy of biol., chem. and phys. processes under realistic conditions at length scales from at. dimensions to millimetres and time scales down to the sub-nanosecond regime. In this way, it will enable groundbreaking studies in many fields of science and industry, such as health, energy, earth and environment, mobility and information technol. The science case is reviewed and the current state of the conceptual design is summarized, discussing a ref. lattice, a hybrid multi-bend achromat with an interleaved sextupole configuration based on the ESRF-EBS design, in more detail as well as alternative lattice concepts.
- 59Revol, J.-L. ESRF-EBS: implementation, performance and restart of user operation. Proc. IPAC’21 2021, 3929– 3932, DOI: 10.18429/JACoW-IPAC2021-THPAB074Google ScholarThere is no corresponding record for this reference.
- 60White, S. Commissioning and restart of ESRF-EBS. Proc. IPAC’21 2021, 1– 6, DOI: 10.18429/JACoW-IPAC2021-MOXA01Google ScholarThere is no corresponding record for this reference.
- 61Borland, M.; The upgrade of the advanced photon source. Proceedings of the 9th International Particle Accelerator Conference (IPAC’18), Vancouver, BC, Canada, April 29 to May 4, 2018; Geneva, 2018; pp 2872– 2877.Google ScholarThere is no corresponding record for this reference.
- 62Royall, C. P.; Poon, W. C. K.; Weeks, E. R. In search of colloidal hard spheres. Soft Matter 2013, 9, 17– 27, DOI: 10.1039/C2SM26245BGoogle Scholar62https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhslKktb7K&md5=33717dd66c6a8a156ca1ae20d2af549fIn search of colloidal hard spheresRoyall, C. Patrick; Poon, Wilson C. K.; Weeks, Eric R.Soft Matter (2013), 9 (1), 17-27CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)A review. We recently reviewed the exptl. detn. of the vol. fraction, [phis], of hard-sphere colloids, and concluded that the abs. value of [phis] was unlikely to be known to better than ±3-6%. Here, in a second part to that review, we survey effects due to softness in the interparticle potential, which necessitates the use of an effective vol. fraction. We review current exptl. systems, and conclude that the one that most closely approximates hard spheres remains polymethylmethacrylate spheres sterically stabilized by polyhydroxystearic acid hairs'. For these particles their effective hard sphere diam. is around 1-10% larger than the core diam., depending on the particle size. We argue that for larger colloids suitable for confocal microscopy, the effect of electrostatic charge cannot be neglected, so that mapping to hard spheres must be treated with caution.
- 63Wertheim, M. S. Exact solution of the Percus-Yevick integral equation for hard spheres. Phys. Rev. Lett. 1963, 10, 321– 323, DOI: 10.1103/PhysRevLett.10.321Google ScholarThere is no corresponding record for this reference.
- 64Westermeier, F.; Fischer, B.; Roseker, W.; Grübel, G.; Nägele, G.; Heinen, M. Structure and short-time dynamics in concentrated suspensions of charged colloids. J. Chem. Phys. 2012, 137, 114504, DOI: 10.1063/1.4751544Google Scholar64https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhtlKisrbJ&md5=c06e02b6c3618f63d80d120f4389be65Structure and short-time dynamics in concentrated suspensions of charged colloidsWestermeier, Fabian; Fischer, Birgit; Roseker, Wojciech; Gruebel, Gerhard; Naegele, Gerhard; Heinen, MarcoJournal of Chemical Physics (2012), 137 (11), 114504/1-114504/17CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)The authors report a comprehensive joint exptl.-theor. study of the equil. pair-structure and short-time diffusion in aq. suspensions of highly charged poly-acrylate (PA) spheres in the colloidal fluid phase. Low-polydispersity PA sphere systems with 2 different hard-core radii, R0 = 542 and 1117 Å, are explored over a wide range of concns. and salinities using static and dynamic light scattering (DLS), small angle x-ray scattering, and x-ray photon correlation spectroscopy (XPCS). The measured static and dynamic scattering functions are analyzed using state-of-the-art theor. methods. For all samples, the measured static structure factor, S(Q), is in good agreement with results by an anal. integral equation method for particles interacting by a repulsive screened Coulomb plus hard-core pair potential. In DLS and XPCS measurements, the authors detd. the short-time diffusion function D(Q) = D0 H(Q)/S(Q), comprising the free diffusion coeff. D0 and the hydrodynamic function H(Q). The latter is calcd. anal. using a self-part cor. version of the δγ-scheme by Beenakker and Mazur which accounts approx. for many-body hydrodynamic interactions (HIs). Except for low-salinity systems at the highest studied vol. fraction φ ≈ 0.32, the theor. predictions for H(Q) are in excellent agreement with the exptl. data. In particular, the increase in the collective diffusion coeff. Dc = D(Q → 0), and the decrease of the self-diffusion coeff., Ds = D(Q → ∞), with increasing φ is well described. In accord with the theor. prediction, the peak value, H(Qm), of H(Q) relates to the nearest neighbor cage size ∼2π/Qm, for which concn. scaling relations are discussed. The peak values H(Qm) are globally bound from below by the corresponding neutral hard-spheres peak values, and from above by the limiting peak values for low-salinity charge-stabilized systems. HIs usually slow short-time diffusion on colloidal length scales, except for the cage diffusion coeff., Dcge = D(Qm), in dil. low-salinity systems where a speed up of the system dynamics and corresponding peak values of H(Qm) > 1 are obsd. exptl. and theor. (c) 2012 American Institute of Physics.
- 65Poon, W. C. K.; Weeks, E. R.; Royall, C. P. On measuring colloidal volume fractions. Soft Matter 2012, 8, 21– 30, DOI: 10.1039/C1SM06083JGoogle Scholar65https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXhsFCmsLvL&md5=89ca418624e7a0f32b9e9c98f44a0467On measuring colloidal volume fractionsPoon, Wilson C. K.; Weeks, Eric R.; Royall, C. PatrickSoft Matter (2012), 8 (1), 21-30CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)Hard-sphere colloids are popular as models for testing fundamental theories in condensed matter and statistical physics, from crystal nucleation to the glass transition. A single parameter, the vol. fraction ([phis]), characterizes an ideal, monodisperse hard-sphere suspension. In comparing expts. with theories and simulation, researchers to date have paid little attention to likely uncertainties in exptl.-quoted [phis] values. We critically review the exptl. measurement of [phis] in hard-sphere colloids, and show that while statistical uncertainties in comparing relative values of [phis] can be as low as 10-4, systematic errors of ⪆3% are probably unavoidable. The consequences of this are illustrated by way of a case study comparing literature data sets on hard-sphere viscosity and diffusion.
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- C. Patrick Royall, Patrick Charbonneau, Marjolein Dijkstra, John Russo, Frank Smallenburg, Thomas Speck, Chantal Valeriani. Colloidal hard spheres: Triumphs, challenges, and mysteries. Reviews of Modern Physics 2024, 96
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Abstract
Figure 1
Figure 1. Structure and dynamics. (a) Structure factors S(q) for samples of HS1 (solid lines) and HS2 (dashed lines), shown as a function of qR for R of each sample. The corresponding volume fractions ϕ are shown in the legend. For the sake of visibility, not all structure factors are shown. (b) Relative diffusivity D0/D(qnn) as a function of volume fraction ϕ for HS1 (circles) and HS2 (triangles). The line represents a fit of the VFT law to the data with a ϕVFT of 0.65 ± 0.04.
Figure 2
Figure 2. Schematics of the XPCS and time scales of higher-order correlations. A sample is illuminated with coherent X-rays, and the resulting scattering patterns are recorded at time intervals Δtmin. Via calculation of intensity correlation function g2 and the time scales of higher-order correlation function gC, more details about the local order, its time scale, and the heterogenity of the system can be obtained.
Figure 3
Figure 3. Correlation functions. (a) Intermediate scattering functions and (b) gC functions at qnn for the various volume fractions ϕ of HS1 (circles) and HS2 (triangles). The respective fits are shown as solid lines.
Figure 4
Figure 4. Comparison of the correlation functions. (a) Quotient of the relaxation times, , obtained from the gC and g2 functions as a function of volume fraction ϕ. The dashed line signifies . The inset shows as a function of relaxation time . (b) Exponents and plotted against each other. The solid line signifies and is a guide to the eye, and the dashed line is a linear fit to the data with a = 0.73 and b = 0.17. The inset shows as a function of with the solid line representing .
References
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- 2Hunter, G. L.; Weeks, E. R. The physics of the colloidal glass transition. Rep. Prog. Phys. 2012, 75, 066501, DOI: 10.1088/0034-4885/75/6/0665012https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhtFCmsrzO&md5=2584f510811bd5b8f9f9c8662b54982cThe physics of the colloidal glass transitionHunter, Gary L.; Weeks, Eric R.Reports on Progress in Physics (2012), 75 (6), 066501/1-066501/30CODEN: RPPHAG; ISSN:0034-4885. (Institute of Physics Publishing)A review. As one increases the concn. of a colloidal suspension, the system exhibits a dramatic increase in viscosity. Beyond a certain concn., the system is said to be a colloidal glass; structurally, the system resembles a liq., 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 mol. systems. The spatial and temporal scales involved allow these systems to be studied by a wide variety of exptl. techniques. The focus of this review is the current state of understanding of the colloidal glass transition, with an emphasis on exptl. observations. A brief introduction is given to important exptl. 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 mol. liqs. 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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- 4Debenedetti, P.; Stillinger, F. Supercooled liquids and the glass transition. Nature 2001, 410, 259– 267, DOI: 10.1038/350657044https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3MXitV2js7k%253D&md5=9dd5bb98eeb05ceead2fc6cdb00b18b9Supercooled liquids and the glass transitionDebenedetti, Pablo G.; Stillinger, Frank H.Nature (London, United Kingdom) (2001), 410 (6825), 259-267CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)Glasses are disordered materials that lack the periodicity of crystals but behave mech. like solids. The most common way of making a glass is by cooling a viscous liq. fast enough to avoid crystn. Although this route to the vitreous state - supercooling - has been known for millennia, the mol. processes by which liqs. acquire amorphous rigidity upon cooling are not fully understood. Here we discuss current theor. knowledge of the manner in which intermol. forces give rise to complex behavior in supercooled liqs. and glasses. An intriguing aspect of this behavior is the apparent connection between dynamics and thermodn. The multidimensional potential energy surface as a function of particle coordinates (the energy landscape) offers a convenient viewpoint for the anal. and interpretation of supercooling and glass-formation phenomena. That much of this anal. is at present largely qual. reflects the fact that precise computations of how viscous liqs. sample their landscape have become possible only recently. A review with 109 refs.
- 5Berthier, L.; Biroli, G. Theoretical perspective on the glass transition and amorphous materials. Rev. Mod. Phys. 2011, 83, 587– 645, DOI: 10.1103/RevModPhys.83.5875https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXos1eit74%253D&md5=4daac723fa8a9e435f3ed8a55e976e45Theoretical perspective on the glass transition and amorphous materialsBerthier, Ludovic; Biroli, GiulioReviews of Modern Physics (2011), 83 (2), 587-645CODEN: RMPHAT; ISSN:0034-6861. (American Physical Society)A review. A theor. perspective is provided on the glass transition in mol. liqs. at thermal equil., on the spatially heterogeneous and aging dynamics of disordered materials, and on the rheol. of soft glassy materials. We start with a broad introduction to the field and emphasize its connections with other subjects and its relevance. The important role played by computer simulations in studying and understanding the dynamics of systems close to the glass transition at the mol. level is given. The recent progress on the subject of the spatially heterogeneous dynamics that characterizes structural relaxation in materials with slow dynamics is reviewed. The main theor. approaches are presented describing the glass transition in supercooled liqs., focusing on theories that have a microscopic, statistical mechanics basis. We describe both successes and failures and critically assess the current status of each of these approaches. The physics of aging dynamics in disordered materials and the rheol. of soft glassy materials are then discussed, and recent theor. progress is described. For each section, an extensive overview is given of the most recent advances, but we also describe in some detail the important open problems that will occupy a central place in this field in the coming years.
- 6Berthier, L.; Biroli, G.; Bouchaud, J.-P.; Cipelletti, L.; van Saarloos, W. Dynamical heterogieneities in glasses, colloids and granular media; Oxford University Press Inc.: Oxford, U.K., 2011.There is no corresponding record for this reference.
- 7Malins, A.; Eggers, J.; Royall, C. P.; Williams, S. R.; Tanaka, H. Identification of long-lived clusters and their link to slow dynamics in a model glass former. J. Chem. Phys. 2013, 138, 12A535, DOI: 10.1063/1.4790515There is no corresponding record for this reference.
- 8Karmakar, S.; Dasgupta, C.; Sastry, S. Growing length and time scales in glass-forming liquids. Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 3675– 3679, DOI: 10.1073/pnas.08110821068https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXjt1Gksr0%253D&md5=c7e158219a7f9b3d93b888b9207f1a58Growing length and time scales in glass-forming liquidsKarmakar, Smarajit; Dasgupta, Chandan; Sastry, SrikanthProceedings of the National Academy of Sciences of the United States of America (2009), 106 (10), 3675-3679CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)The glass transition, whereby liqs. transform into amorphous solids at low temps., is a subject of intense research despite decades of investigation. Explaining the enormous increase in relaxation times of a liq. upon supercooling is essential for understanding the glass transition. Although many theories, such as the Adam-Gibbs theory, have sought to relate growing relaxation times to length scales assocd. with spatial correlations in liq. structure or motion of mols., the role of length scales in glassy dynamics is not well established. Recent studies of spatially correlated rearrangements of mols. leading to structural relaxation, termed "spatially heterogeneous dynamics," provide fresh impetus in this direction. A powerful approach to ext. length scales in crit. phenomena is finite-size scaling, wherein a system is studied for sizes traversing the length scales of interest. We perform finite-size scaling for a realistic glass-former, using computer simulations, to evaluate the length scale assocd. with spatially heterogeneous dynamics, which grows as temp. decreases. However, relaxation times that also grow with decreasing temp. do not exhibit std. finite-size scaling with this length. We show that relaxation times are instead detd., for all studied system sizes and temps., by configurational entropy, in accordance with the Adam-Gibbs relation, but in disagreement with theor. expectations based on spin-glass models that configurational entropy is not relevant at temps. substantially above the crit. temp. of mode-coupling theory. Our results provide new insights into the dynamics of glass-forming liqs. and pose serious challenges to existing theor. descriptions.
- 9Hocky, G. M.; Coslovich, D.; Ikeda, A.; Reichman, D. R. Correlation of local order with particle mobility in supercooled liquids is highly system dependent. Phys. Rev. Lett. 2014, 113, 157801, DOI: 10.1103/PhysRevLett.113.1578019https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhvFKqsL3O&md5=28129822a6f603392666f335bf54ad92Correlation of local order with particle mobility in supercooled liquids is highly system dependentHocky, Glen M.; Coslovich, Daniele; Ikeda, Atsushi; Reichman, David R.Physical Review Letters (2014), 113 (15), 157801/1-157801/5, 5 pp.CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)We investigate the connection between local structure and dynamical heterogeneity in supercooled liqs. Through the study of four different models, we show that the correlation between a particle's mobility and the degree of local order in nearby regions is highly system dependent. Our results suggest that the correlation between local structure and dynamics is weak or absent in systems that conform well to the mean-field picture of glassy dynamics and strong in those that deviate from this paradigm. Finally, we investigate the role of order-agnostic point-to-set correlations and reveal that they provide similar information content to local structure measures, at least in the system where local order is most pronounced.
- 10Royall, C. P.; Kob, W. Locally favoured structures and dynamic length scales in a simple glass-former. J. Stat. Mech. 2017, 2017, 024001, DOI: 10.1088/1742-5468/aa4e92There is no corresponding record for this reference.
- 11Leocmach, M.; Tanaka, H. Roles of icosahedral and crystal-like order in the hard spheres glass transition. Nat. Commun. 2012, 3, 974, DOI: 10.1038/ncomms197411https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BC38fislWhug%253D%253D&md5=b05d521149bae79f46af48074c5c024dRoles of icosahedral and crystal-like order in the hard spheres glass transitionLeocmach Mathieu; Tanaka HajimeNature communications (2012), 3 (), 974 ISSN:.A link between structural ordering and slow dynamics has recently attracted much attention from the context of the origin of glassy slow dynamics. Candidates for such structural order are icosahedral, exotic amorphous and crystal-like. Each type of order is linked to a different scenario of glass transition. Here we experimentally access local structural order in polydisperse hard spheres by particle-level confocal microscopy. We identify the key structures as icosahedral and FCC-like order, both statistically associated with slow particles. However, when approaching the glass transition, the icosahedral order does not grow in size, whereas crystal-like order grows. It is the latter that governs the dynamics and is linked to dynamic heterogeneity. This questions the direct role of the local icosahedral ordering in glassy slow dynamics and suggests that the growing length scale of structural order is essential for the slowing down of dynamics and the non-local cooperativity in particle motion.
- 12Coslovich, D. Locally preferred structures and many-body static correlations in viscous liquids. Phys. Rev. E 2011, 83, 051505, DOI: 10.1103/PhysRevE.83.05150512https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXotVeqsrY%253D&md5=25bda4dc24d9b116de384e796935596eLocally preferred structures and many-body static correlations in viscous liquidsCoslovich, DanielePhysical Review E: Statistical, Nonlinear, and Soft Matter Physics (2011), 83 (5-1), 051505/1-051505/8CODEN: PRESCM; ISSN:1539-3755. (American Physical Society)The influence of static correlations beyond the pair level on the dynamics of selected model glass formers is investigated. The pair structure, angular distribution functions, and statistics of Voronoi polyhedra of two well-known Lennard-Jones mixts. as well as of the corresponding Weeks-Chandler-Andersen variants, in which the attractive part of the potential is truncated, are compared. By means of the Voronoi construction, the at. arrangements corresponding to the locally preferred structures of the models are identified. It is found that the growth of domains formed by interconnected locally preferred structures signals the onset of the slow-dynamics regime and allows the rationalization of the different dynamic behaviors of the models. At low temp., the spatial extension of the structurally correlated domains, evaluated at fixed relaxation time, increases with the fragility of the models and is systematically reduced by truncating the attractions. In view of these results, proper inclusion of many-body static correlations in theories of the glass transition appears crucial for the description of the dynamics of fragile glass formers.
- 13Tanaka, H.; Tong, H.; Shi, R.; Russo, J. Revealing key structural features hidden in liquids and glasses. Nat. Rev. Phys. 2019, 1, 333– 348, DOI: 10.1038/s42254-019-0053-3There is no corresponding record for this reference.
- 14Hallett, J. E.; Turci, F.; Royall, C. P. The devil is in the details: pentagonal bipyramids and dynamic arrest. J. Stat. Mech. 2020, 2020, 014001, DOI: 10.1088/1742-5468/ab5369There is no corresponding record for this reference.
- 15Marín-Aguilar, S.; Wensink, H. H.; Foffi, G.; Smallenburg, F. Slowing down supercooled liquids by manipulating their local structure. Soft Matter 2019, 15, 9886– 9893, DOI: 10.1039/C9SM01746A15https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXit1GqtLnF&md5=3ceef17ba0abee61cf5af7bb3eed3115Slowing down supercooled liquids by manipulating their local structureMarin-Aguilar, Susana; Wensink, Henricus H.; Foffi, Giuseppe; Smallenburg, FrankSoft Matter (2019), 15 (48), 9886-9893CODEN: SMOABF; ISSN:1744-6848. (Royal Society of Chemistry)Glasses remain an elusive and poorly understood state of matter. It is not clear how we can control the macroscopic dynamics of glassy systems by tuning the properties of their microscopic building blocks. In this paper, we propose a simple directional colloidal model that reinforces the optimal icosahedral local structure of binary hard-sphere glasses. We show that this specific symmetry results in a dramatic slowing down of the dynamics. Our results open the door to controlling the dynamics of dense glassy systems by selectively promoting specific local structural environments.
- 16Boattini, E.; Marín-Aguilar, S.; Mitra, S.; Foffi, G.; Smallenburg, F.; Filion, L. Autonomously revealing hidden local structures in supercooled liquids. Nat. Commun. 2020, 11, 5479, DOI: 10.1038/s41467-020-19286-816https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXit1OjtLjJ&md5=31bbf257ad6f0d7690b126cdbfa072c0Autonomously revealing hidden local structures in supercooled liquidsBoattini, Emanuele; Marin-Aguilar, Susana; Mitra, Saheli; Foffi, Giuseppe; Smallenburg, Frank; Filion, LauraNature Communications (2020), 11 (1), 5479CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)Abstr.: Few questions in condensed matter science have proven as difficult to unravel as the interplay between structure and dynamics in supercooled liqs. To explore this link, much research has been devoted to pinpointing local structures and order parameters that correlate strongly with dynamics. Here we use an unsupervised machine learning algorithm to identify structural heterogeneities in three archetypical glass formers-without using any dynamical information. In each system, the unsupervised machine learning approach autonomously designs a purely structural order parameter within a single snapshot. Comparing the structural order parameter with the dynamics, we find strong correlations with the dynamical heterogeneities. Moreover, the structural characteristics linked to slow particles disappear further away from the glass transition. Our results demonstrate the power of machine learning techniques to detect structural patterns even in disordered systems, and provide a new way forward for unraveling the structural origins of the slow dynamics of glassy materials.
- 17Schoenholz, S. S.; Cubuk, E. D.; Kaxiras, E.; Liu, A. J. Relationship between local structure and relaxation in out-of-equilibrium glassy systems. Proc. Natl. Acad. Sci. U.S.A. 2017, 114, 263– 267, DOI: 10.1073/pnas.161020411417https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XitFGntr3M&md5=af4e898ff0b8a444ff33ec8e2e941444Relationship between local structure and relaxation in out-of-equilibrium glassy systemsSchoenholz, Samuel S.; Cubuk, Ekin D.; Kaxiras, Efthimios; Liu, Andrea J.Proceedings of the National Academy of Sciences of the United States of America (2017), 114 (2), 263-267CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)The dynamical glass transition is typically taken to be the temp. at which a glassy liq. is no longer able to equilibrate on exptl. timescales. Consequently, the phys. properties of these systems just above or below the dynamical glass transition, such as viscosity, can change by many orders of magnitude over long periods of time following external perturbation. During this progress toward equil., glassy systems exhibit a history dependence that has complicated their study. In previous work, we bridged the gap between structure and dynamics in glassy liqs. above their dynamical glass transition temps. by introducing a scalar field called "softness," a quantity obtained using machine-learning methods. Softness is designed to capture the hidden patterns in relative particle positions that correlate strongly with dynamical rearrangements of particle positions. Here we show that the out-of-equil. behavior of a model glass-forming system can be understood in terms of softness. To do this we first demonstrate that the evolution of behavior following a temp. quench is a primarily structural phenomenon: The structure changes considerably, but the relationship between structure and dynamics remains invariant. We then show that the relaxation time can be robustly computed from structure as quantified by softness, with the same relation holding both in equil. and as the system ages. Together, these results show that the history dependence of the relaxation time in glasses requires knowledge only of the softness in addn. to the usual state variables.
- 18Royall, C. P.; Williams, S. R. The role of local structure in dynamical arrest. Phys. Rep. 2015, 560, 1– 75, DOI: 10.1016/j.physrep.2014.11.00418https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXitV2mt73M&md5=ebae5a39f0ac2c20ef02169e9c7cc572The role of local structure in dynamical arrestRoyall, C. Patrick; Williams, Stephen R.Physics Reports (2015), 560 (), 1-75CODEN: PRPLCM; ISSN:0370-1573. (Elsevier B.V.)A review. Amorphous solids, or glasses, are distinguished from cryst. solids by their lack of long-range structural order. At the level of two-body structural correlations, glassformers show no qual. change upon vitrifying from a supercooled liq. Nonetheless the dynamical properties of a glass are so much slower that it appears to take on the properties of a solid. While many theories of the glass transition focus on dynamical quantities, a solid's resistance to flow is often viewed as a consequence of its structure. Here we address the viewpoint that this remains the case for a glass. Recent developments using higher-order measures show a clear emergence of structure upon dynamical arrest in a variety of glass formers and offer the tantalising hope of a structural mechanism for arrest. However a rigorous fundamental identification of such a causal link between structure and arrest remains elusive. We undertake a crit. survey of this work in expts., computer simulation and theory and discuss what might strengthen the link between structure and dynamical arrest. We move on to highlight the relationship between crystn. and glass-forming ability made possible by this deeper understanding of the structure of the liq. state, and emphasize the potential to design materials with optimal glassforming and crystn. ability, for applications such as phase-change memory. We then consider aspects of the phenomenol. of glassy systems where structural measures have yet to make a large impact, such as polyamorphism (the existence of multiple liq. states), ageing (the time-evolution of non-equil. materials below their glass transition) and the response of glassy materials to external fields such as shear.
- 19Gast, A. P.; Russel, W. B. Simple ordering in complex fluids. Phys. Today 1998, 51, 24– 30, DOI: 10.1063/1.88249519https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1MXhvF2qsw%253D%253D&md5=a1913b7f4fc955f651c02fe7257ece7aSimple ordering in complex fluids: colloidal particles suspended in solution provide intriguing models for studying phase transitionsGast, Alice P.; Russel, William B.Physics Today (1998), 51 (12), 24-30CODEN: PHTOAD; ISSN:0031-9228. (American Institute of Physics)A review with 17 refs. The topics include entropy and ordering of hard spheres, tunable repulsions of soft spheres, bcc→fcc transition, attraction and gas-liq. phase transition, and two-dimensional crystn.
- 20Marín-Aguilar, S.; Wensink, H. H.; Foffi, G.; Smallenburg, F. Tetrahedrality dictates dynamics in hard sphere mixtures. Phys. Rev. Lett. 2020, 124, 208005, DOI: 10.1103/PhysRevLett.124.20800520https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhsFCntrnJ&md5=e339ead5a2ca0330742cdb2bea2af487Tetrahedrality Dictates Dynamics in Hard Sphere MixturesMarin-Aguilar, Susana; Wensink, Henricus H.; Foffi, Giuseppe; Smallenburg, FrankPhysical Review Letters (2020), 124 (20), 208005CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)The link between local structure and dynamical slowdown in glassy fluids has been the focus of intense debate for the better part of a century. Nonetheless, a simple method to predict the dynamical behavior of a fluid purely from its local structural features is still missing. Here, we demonstrate that the diffusivity of perhaps the most fundamental family of glass formers-hard sphere mixts.-can be accurately predicted based on just the packing fraction and a simple order parameter measuring the tetrahedrality of the local structure. Essentially, we show that the no. of tetrahedral clusters in a hard sphere mixt. is directly linked to its global diffusivity. Moreover, the same order parameter is capable of locally pinpointing particles in the system with high and low mobility. We attribute the power of the local tetrahedrality for predicting local and global dynamics to the high stability of tetrahedral clusters, the most fundamental building and densest-packing building blocks for a disordered fluid.
- 21Zhang, Z.; Kob, W. Revealing the three-dimensional structure of liquids using four-point correlation functions. Proc. Natl. Acad. Sci. U.S.A. 2020, 117, 14032– 14037, DOI: 10.1073/pnas.200563811721https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhsVCgsrfN&md5=cab7fc04743baeebe2728231e466c6e1Revealing the three-dimensional structure of liquids using four-point correlation functionsZhang, Zhen; Kob, WalterProceedings of the National Academy of Sciences of the United States of America (2020), 117 (25), 14032-14037CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)Disordered systems like liqs., gels, glasses, or granular materials are not only ubiquitous in daily life and in industrial applications, but they are also crucial for the mech. stability of cells or the transport of chem. and biol. agents in living organisms. Despite the importance of these systems, their microscopic structure is understood only on a rudimentary level, thus in Stark contrast to the case of gases and crystals. Since scattering expts. and anal. calcns. usually give only structural information that is spherically averaged, the three-dimensional (3D) structure of disordered systems is basically unknown. Here, we introduce a simple method that allows probing of the 3D structure of such systems. Using computer simulations, we find that hard sphere-like liqs. have on intermediate and large scales a simple structural order given by alternating layers with icosahedral and dodecahedral symmetries, while open network liqs. like silica have a structural order with tetrahedral symmetry. These results show that liqs. have a highly nontrivial 3D structure and that this structural information is encoded in nonstandard correlation functions.
- 22Schöpe, H. J.; Bryant, G.; van Megen, W. Two-step crystallization kinetics in colloidal hard-sphere systems. Phys. Rev. Lett. 2006, 96, 175701, DOI: 10.1103/PhysRevLett.96.17570122https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28Xkt12hsbY%253D&md5=c7475daf2ec0ea490e1372e6647a895bTwo-Step Crystallization Kinetics in Colloidal Hard-Sphere SystemsSchope, Hans Joachim; Bryant, Gary; van Megen, WilliamPhysical Review Letters (2006), 96 (17), 175701/1-175701/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)The crystn. kinetics of colloidal hard spheres was studied using a special Bragg spectrometer with high sensitivity. In contrast with the classical scenario we observe a two-step nucleation process: the no. of crystallites increases slowly at early times, followed by a dramatic redn. at intermediate times, prior to undergoing a rapid increase at late times. We explain these results in terms of a polydispersity limited growth of crystallites, where the crystn. at early times is governed by local fractionation processes, leading to a long delay prior to final crystn.
- 23Tan, P.; Xu, N.; Xu, L. Visualizing kinetic pathways of homogeneous nucleation in colloidal crystallization. Nat. Phys. 2014, 10, 73– 79, DOI: 10.1038/nphys281723https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXhvFent7%252FP&md5=4411f12feb2f56fa1dfeeed0eca118efVisualizing kinetic pathways of homogeneous nucleation in colloidal crystallizationTan, Peng; Xu, Ning; Xu, LeiNature Physics (2014), 10 (1), 73-79CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)When a system undergoes a transition from a liq. to a solid phase, it passes through multiple intermediate structures before reaching the final state. However, our knowledge on the exact pathways of this process is limited, mainly owing to the difficulty of realizing direct observations. Here, we exptl. study the evolution of symmetry and d. for various colloidal systems during liq.-to-solid phase transitions, and visualize kinetic pathways with single-particle resoln. We observe the formation of relatively ordered precursor structures with different symmetries, which then convert into metastable solids. During this conversion, two major cross-symmetry pathways always occur, regardless of the final state and the interaction potential. In addn., we find a broad decoupling of d. variation and symmetry development, and discover that nucleation rarely starts from the densest regions. These findings hold for all of our samples, suggesting the possibility of finding a unified picture for the complex crystn. kinetics in colloidal systems.
- 24Russo, J.; Tanaka, H. Crystal nucleation as the ordering of multiple order parameters. J. Chem. Phys. 2016, 145, 211801, DOI: 10.1063/1.496216624https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhsFWnurfI&md5=49091a43a50415d8fa29531a5831bf57Crystal nucleation as the ordering of multiple order parametersRusso, John; Tanaka, HajimeJournal of Chemical Physics (2016), 145 (21), 211801/1-211801/17CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Nucleation is an activated process in which the system has to overcome a free energy barrier in order for a first-order phase transition between the metastable and the stable phases to take place. In the liq.-to-solid transition, the process occurs between phases of different symmetry, and it is thus inherently a multi-dimensional process, in which all symmetries are broken at the transition. In this Focus Article, we consider some recent studies which highlight the multi-dimensional nature of the nucleation process. Even for a single-component system, the formation of solid crystals from the metastable melt involves fluctuations of two (or more) order parameters, often assocd. with the decoupling of positional and orientational symmetry breaking. The authors needed at least two order parameters to describe the free-energy of a system including its liq. and cryst. states. This decoupling occurs naturally for asym. particles or directional interactions, focusing here on the case of water, but we will show that it also affects spherically sym. interacting particles, such as the hard-sphere system. They will show how the treatment of nucleation as a multi-dimensional process has shed new light on the process of polymorph selection, on the effect of external fields on the nucleation process and on glass-forming ability. (c) 2016 American Institute of Physics.
- 25Lehmkühler, F.; Roseker, W.; Grübel, G. From femtoseconds to hours─measuring dynamics over 18 orders of magnitude with coherent X-rays. Appl. Sci. 2021, 11, 6179, DOI: 10.3390/app1113617925https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXit1Gqsb%252FO&md5=ea1f8411e8cec370531ef0c27c5b4531From Femtoseconds to Hours-Measuring Dynamics over 18 Orders of Magnitude with Coherent X-raysLehmkuehler, Felix; Roseker, Wojciech; Gruebel, GerhardApplied Sciences (2021), 11 (13), 6179CODEN: ASPCC7; ISSN:2076-3417. (MDPI AG)X-ray photon correlation spectroscopy (XPCS) enables the study of sample dynamics between micrometer and at. length scales. As a coherent scattering technique, it benefits from the increased brilliance of the next-generation synchrotron radiation and Free-Electron Laser (FEL) sources. In this article, we will introduce the XPCS concepts and review the latest developments of XPCS with special attention on the extension of accessible time scales to sub-μs and the application of XPCS at FELs. Furthermore, we will discuss future opportunities of XPCS and the related technique X-ray speckle visibility spectroscopy (XSVS) at new X-ray sources. Due to its particular signal-to-noise ratio, the time scales accessible by XPCS scale with the square of the coherent flux, allowing to dramatically extend its applications. This will soon enable studies over more than 18 orders of magnitude in time by XPCS and XSVS.
- 26Grübel, G.; Madsen, A.; Robert, A. Soft matter characterization; Springer Netherlands: Dordrecht, The Netherlands, 2008; pp 953– 995.There is no corresponding record for this reference.
- 27Sandy, A. R.; Zhang, Q.; Lurio, L. B. Hard X-ray photon correlation spectroscopy methods for materials studies. Annu. Rev. Mater. Res. 2018, 48, 167– 190, DOI: 10.1146/annurev-matsci-070317-12433427https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXmsVensro%253D&md5=cb131e737010cd09e572d44ace789f94Hard X-Ray Photon Correlation Spectroscopy Methods for Materials StudiesSandy, Alec R.; Zhang, Qingteng; Lurio, Laurence B.Annual Review of Materials Research (2018), 48 (), 167-190CODEN: ARMRCU; ISSN:1531-7331. (Annual Reviews)Understanding and designing sophisticated new materials require measurements of not only their av. structural properties but also their dynamic behavior. X-ray photon correlation spectroscopy (XPCS) provides this information by characterizing fluctuations in condensed matter across a broad range of length scales and timescales. Over the past two decades, XPCS has provided a wide variety of results in the study of materials properties. In this review, we provide an overview of coherence, photon correlation spectroscopy, and the dynamic structure factor as well as information on the mechanics of XPCS expts. We highlight the impact that this infrastructure has had on materials research and the bright future that is forthcoming with the anticipated upgrade of many third-generation synchrotron sources to fourth-generation multibend achromat sources.
- 28Madsen, A.; Fluerasu, A.; Ruta, B. In Synchrotron light sources and free-electron lasers: accelerator physics, instrumentation and science applications; Jaeschke, E. J., Khan, S., Schneider, J. R., Hastings, J. B., Eds.; Springer International Publishing: Cham, Switzerland, 2016; pp 1617– 1641.There is no corresponding record for this reference.
- 29Kurta, R. P.; Altarelli, M.; Vartanyants, I. A. Advances in Chemical Physics; John Wiley and Sons, Ltd.: Hoboken, NJ, 2016; pp 1– 39.There is no corresponding record for this reference.
- 30Wochner, P.; Gutt, C.; Autenrieth, T.; Demmer, T.; Bugaev, V.; Ortiz, A. D.; Duri, A.; Zontone, F.; Grübel, G.; Dosch, H. X-ray cross correlation analysis uncovers hidden local symmetries in disordered matter. Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 11511– 11514, DOI: 10.1073/pnas.090533710630https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXptVKjsLg%253D&md5=5bb7ee07cdc5a5505ac0d1c3669680a1X-ray cross correlation analysis uncovers hidden local symmetries in disordered matterWochner, Peter; Gutt, Christian; Autenrieth, Tina; Demmer, Thomas; Bugaev, Volodymyr; Ortiz, Alejandro Diaz; Duri, Agnes; Zontone, Federico; Gruebel, Gerhard; Dosch, HelmutProceedings of the National Academy of Sciences of the United States of America (2009), 106 (28), 11511-11514, S11511/1-S11511/5CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)The authors explore the different local symmetries in colloidal glasses beyond the std. pair correlation anal. Using the newly developed x-ray cross correlation anal. (XCCA) concept together with brilliant coherent X-ray sources, the authors were able to access and classify the otherwise hidden local order within disorder. The emerging local symmetries are coupled to distinct momentum transfer (Q) values, which do not coincide with the maxima of the amorphous structure factor. Four-, 6-, 10- and, most prevalently, 5-fold symmetries are obsd. The observation of dynamical evolution of these symmetries forms a connection to dynamical heterogeneities in glasses, which is far beyond conventional diffraction anal. The XCCA concept opens up a fascinating view into the world of disorder and will definitely allow, with the advent of free electron x-ray lasers, an accurate and systematic exptl. characterization of the structure of the liq. and glass states.
- 31Zaluzhnyy, I. A.; Kurta, R. P.; Scheele, M.; Schreiber, F.; Ostrovskii, B. I.; Vartanyants, I. A. Angular X-ray cross-correlation analysis (AXCCA): basic concepts and recent applications to soft Matter and nanomaterials. Materials 2019, 12, 3464, DOI: 10.3390/ma1221346431https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXotFGksLY%253D&md5=7802ba1bbbef7307ccf5c43878c52a73Angular X-ray cross-correlation analysis (AXCCA): basic concepts and recent applications to soft matter and nanomaterialsZaluzhnyy, Ivan A.; Kurta, Ruslan P.; Scheele, Marcus; Schreiber, Frank; Ostrovskii, Boris I.; Vartanyants, Ivan A.Materials (2019), 12 (21), 3464CODEN: MATEG9; ISSN:1996-1944. (MDPI AG)Angular X-ray cross-correlation anal. (AXCCA) is a technique which allows quant. measurement of the angular anisotropy of X-ray diffraction patterns and provides insights into the orientational order in the system under investigation. This method is based on the evaluation of the angular cross-correlation function of the scattered intensity distribution on a two-dimensional (2D) detector and further averaging over many diffraction patterns for enhancement of the anisotropic signal. Over the last decade, AXCCA was successfully used to study the anisotropy in various soft matter systems, such as solns. of anisotropic particles, liq. crystals, colloidal crystals, superlattices composed by nanoparticles, etc. This review provides an introduction to the technique and gives a survey of the recent exptl. work in which AXCCA in combination with micro- or nanofocused X-ray microscopy was used to study the orientational order in various soft matter systems.
- 32Lehmkühler, F.; Hankiewicz, B.; Schroer, M. A.; Müller, L.; Ruta, B.; Sheyfer, D.; Sprung, M.; Tono, K.; Katayama, T.; Yabashi, M. Slowing down of dynamics and orientational order preceding crystallization in hard-sphere systems. Sci. Adv. 2020, 6, eabc5916 DOI: 10.1126/sciadv.abc5916There is no corresponding record for this reference.
- 33Hu, Z.; Donatelli, J. J.; Sethian, J. A. Cross-correlation analysis of X-ray photon correlation spectroscopy to extract rotational diffusion coefficients. Proc. Natl. Acad. Sci. U. S. A. 2021, 118, e2105826118 DOI: 10.1073/pnas.210582611833https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhvVOqu73F&md5=1e42858badc92c4e7a62d926ea8332fbCross-correlation analysis of X-ray photon correlation spectroscopy to extract rotational diffusion coefficientsHu, Zixi; Donatelli, Jeffrey J.; Sethian, James A.Proceedings of the National Academy of Sciences of the United States of America (2021), 118 (34), e2105826118CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)Coeffs. for translational and rotational diffusion characterize the Brownian motion of particles. Emerging X-ray photon correlation spectroscopy (XPCS) expts. probe a broad range of length scales and time scales and are well-suited for investigation of Brownian motion. While methods for estg. the translational diffusion coeffs. from XPCS are well-developed, there are no algorithms for measuring the rotational diffusion coeffs. based on XPCS, even though the required raw data are accessible from such expts. In this paper, we propose angular-temporal cross-correlation anal. of XPCS data and show that this information can be used to design a numerical algorithm (Multi-Tiered Estn. for Correlation Spectroscopy [MTECS]) for predicting the rotational diffusion coeff. utilizing the cross-correlation: This approach is applicable to other wavelengths beyond this regime. We verify the accuracy of this algorithmic approach across a range of simulated data.
- 34Hallett, J. E.; Turci, F.; Royall, C. P. Local structure in deeply supercooled liquids exhibits growing lengthscales and dynamical correlations. Nat. Commun. 2018, 9, 3272, DOI: 10.1038/s41467-018-05371-634https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BB3c7ovFWluw%253D%253D&md5=1ed02edf2d5394e0ddc48342179d7517Local structure in deeply supercooled liquids exhibits growing lengthscales and dynamical correlationsHallett James E; Turci Francesco; Royall C Patrick; Hallett James E; Turci Francesco; Royall C Patrick; Royall C PatrickNature communications (2018), 9 (1), 3272 ISSN:.Glasses are among the most widely used of everyday materials, yet the process by which a liquid's viscosity increases by 14 decades to become a glass remains unclear, as often contradictory theories provide equally good descriptions of the available data. Knowledge of emergent lengthscales and higher-order structure could help resolve this, but this requires time-resolved measurements of dense particle coordinates-previously only obtained over a limited time interval. Here we present an experimental study of a model colloidal system over a dynamic window significantly larger than previous measurements, revealing structural ordering more strongly linked to dynamics than previously found. Furthermore we find that immobile regions and domains of local structure grow concurrently with density, and that these regions have low configurational entropy. We thus show that local structure plays an important role at deep supercooling, consistent with a thermodynamic interpretation of the glass transition rather than a principally dynamic description.
- 35Di Cola, E.; Moussaïd, A.; Sztucki, M.; Narayanan, T.; Zaccarelli, E. Correlation between structure and rheology of a model colloidal glass. J. Chem. Phys. 2009, 131, 144903, DOI: 10.1063/1.324034535https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXht1yjsrrK&md5=7e3b57394d8cbca38e2d707ad1c4d3f6Correlation between structure and rheology of a model colloidal glassDi Cola, E.; Moussaid, A.; Sztucki, M.; Narayanan, T.; Zaccarelli, E.Journal of Chemical Physics (2009), 131 (14), 144903/1-144903/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)The microstructure and rheol. properties of a model colloidal system was probed in the vicinity of the glass transition by small-angle and ultra small-angle x-ray scattering, dynamic light scattering (DLS) and bulk rheol. The vol. fraction of the particles was deduced by modeling the structure factor and the abs. scattered intensity in a self-consistent way. The glass transition (φG) was identified from the frequency dependence of the shear moduli in the linear regime. The exptl. obsd. behavior was then compared with the viscoelastic properties derived from mode-coupling theory (MCT) using the exptl. structure factor as input to the theory. The ensemble-averaged intermediate scattering functions from DLS measurements were also compared with those calcd. from the MCT and reasonable agreement was obtained. (c) 2009 American Institute of Physics.
- 36Frenzel, L.; Dartsch, M.; Balaguer, G. M.; Westermeier, F.; Grübel, G.; Lehmkühler, F. Glass-liquid and glass-gel transitions of soft-shell particles. Phys. Rev. E 2021, 104, L012602, DOI: 10.1103/PhysRevE.104.L01260236https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhvValt7bK&md5=c88dee4a530c6d691bf64d6712db86d7Glass-liquid and glass-gel transitions of soft-shell particlesFrenzel, Lara; Dartsch, Michael; Balaguer, Gerard Marti; Westermeier, Fabian; Gruebel, Gerhard; Lehmkuehler, FelixPhysical Review E (2021), 104 (1), L012602CODEN: PREHBM; ISSN:2470-0053. (American Physical Society)We study the structure and dynamics of colloidal particles with a spherical hard core and a thermo-responsive soft shell over the whole phase diagram by means of small-angle x-ray scattering and x-ray photon correlation spectroscopy. By changing the effective vol. fraction by temp. and particle concn., liq., repulsive glass. and attractive gel phases are obsd. The dynamics slow down with increasing vol. fraction in the liq. phase and reflect a Vogel-Fulcher-Tamann behavior known for fragile glass formers. We find a liq.-glass transition above 50 vol.% that is independent of the particles' concn. and temp. In an overpacked state at effective vol. fractions above 1, the dispersion does not show a liq. phase but undergoes a gel-glass transition at an effective vol. fraction of 34 vol.%. At the same concn., extrema of subdiffusive dynamics are found in the liq. phase at lower wt. fractions. We interpret this as dynamic precursors of the glass-gel transition.
- 37Philippe, A.-M.; Truzzolillo, D.; Galvan-Myoshi, J.; Dieudonné-George, P.; Trappe, V.; Berthier, L.; Cipelletti, L. Glass transition of soft colloids. Phys. Rev. E 2018, 97, 040601, DOI: 10.1103/PhysRevE.97.04060137https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXkvFOkt7s%253D&md5=fa9c59371bf5e847f1ee2e22acb65e55Glass transition of soft colloidsPhilippe, Adrian-Marie; Truzzolillo, Domenico; Galvan-Myoshi, Julian; Dieudonne-George, Philippe; Trappe, Veronique; Berthier, Ludovic; Cipelletti, LucaPhysical Review E (2018), 97 (4), 040601CODEN: PREHBM; ISSN:2470-0053. (American Physical Society)We explore the glassy dynamics of soft colloids using microgels and charged particles interacting by steric and screened Coulomb interactions, resp. In the supercooled regime, the structural relaxation time ταof both systems grows steeply with vol. fraction, reminiscent of the behavior of colloidal hard spheres. Computer simulations confirm that the growth of τα on approaching the glass transition is independent of particle softness. By contrast, softness becomes relevant at very large packing fractions when the system falls out of equil. In this nonequil. regime, τα depends surprisingly weakly on packing fraction, and time correlation functions exhibit a compressed exponential decay consistent with stress-driven relaxation. The transition to this novel regime coincides with the onset of an anomalous decrease in local order with increasing d. typical of ultrasoft systems. We propose that these peculiar dynamics results from the combination of the nonequil. aging dynamics expected in the glassy state and the tendency of colloids interacting through soft potentials to refluidize at high packing fractions.
- 38Tong, H.; Tanaka, H. Structural order as a genuine control parameter of dynamics in simple glass formers. Nat. Commun. 2019, 10, 5596, DOI: 10.1038/s41467-019-13606-338https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXitlyntrbE&md5=81bc411fbedc82d670dae09c32a9e4ccStructural order as a genuine control parameter of dynamics in simple glass formersTong, Hua; Tanaka, HajimeNature Communications (2019), 10 (1), 5596CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)Glass transition is characterised by drastic dynamical slowing down upon cooling, accompanied by growing spatial heterogeneity. Its rationalisation by subtle changes in the liq. structure has been long debated but remains elusive, due to intrinsic difficulty in detecting the underlying complex structural ordering. Here we report that structural order parameter characterizing local packing capability can well describe the glassy dynamics not only macroscopically but also microscopically, no matter whether it is driven by temp. or d. A Vogel-Fulcher-Tammann (VFT)-like relation is universally identified between the structural relaxation time and the order parameter for supercooled liqs. with isotropic interactions. More importantly, we find such an intriguing VFT-like relation to be statistically valid even at a particle level, between spatially coarse-grained structural order and microscopic particle-level dynamics. Such a unified description of glassy dynamics based solely on structural order is expected to contribute to the ultimate understanding of the long-standing glass-transition problem.
- 39Laurati, M.; Maßhoff, P.; Mutch, K. J.; Egelhaaf, S. U.; Zaccone, A. Long-lived neighbors determine the rheological response of glasses. Phys. Rev. Lett. 2017, 118, 018002, DOI: 10.1103/PhysRevLett.118.01800239https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXpt1Gntb4%253D&md5=bc9ba6c5497a3088a9bcb5fee2cff24bLong-lived neighbors determine the rheological response of glassesLaurati, M.; Masshoff, P.; Mutch, K. J.; Egelhaaf, S. U.; Zaccone, A.Physical Review Letters (2017), 118 (1), 018002/1-018002/6CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)Glasses exhibit a liquidlike structure but a solidlike rheol. response with plastic deformations only occurring beyond yielding. Thus, predicting the rheol. behavior from the microscopic structure is difficult, but important for materials science. Here, we consider colloidal suspensions and propose to supplement the static structural information with the local dynamics, namely, the rearrangement and breaking of the cage of neighbors. This is quantified by the mean squared nonaffine displacement and the no. of particles that remain nearest neighbors for a long time, i.e., long-lived neighbors, resp. Both quantities are followed under shear using confocal microscopy and are the basis to calc. the affine and nonaffine contributions to the elastic stress, which is complemented by the viscoelastic stress to give the total stress. During start-up of shear, the model predicts three transient regimes that result from the interplay of affine, nonaffine, and viscoelastic contributions. Our prediction quant. agrees with rheol. data and their dependencies on vol. fraction and shear rate.
- 40Higler, R.; Krausser, J.; van der Gucht, J.; Zaccone, A.; Sprakel, J. Linking slow dynamics and microscopic connectivity in dense suspensions of charged colloids. Soft Matter 2018, 14, 780– 788, DOI: 10.1039/C7SM01781B40https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXitVWnsbvN&md5=7c7a325f307f81abe8f827925b674d69Linking slow dynamics and microscopic connectivity in dense suspensions of charged colloidsHigler, Ruben; Krausser, Johannes; van der Gucht, Jasper; Zaccone, Alessio; Sprakel, JorisSoft Matter (2018), 14 (5), 780-788CODEN: SMOABF; ISSN:1744-6848. (Royal Society of Chemistry)The quest to unravel the nature of the glass transition, where the viscosity of a liq. increases by many orders of magnitude, while its static structure remains largely unaffected, remains unresolved. While various structural and dynamical precursors to vitrification have been identified, a predictive and quant. description of how subtle changes at the microscopic scale give rise to the steep growth in macroscopic viscosity is missing. It was recently proposed that the presence of long-lived bonded structures within the liq. may provide the long-sought connection between local structure and global dynamics. Here we directly observe and quantify the connectivity dynamics in liqs. of charged colloids en route to vitrification using three-dimensional confocal microscopy. We det. the dynamic structure from the real-space van Hove correlation function and from the particle trajectories, providing upper and lower bounds on connectivity dynamics. Based on these data, we extend Dyre's model for the glass transition to account for particle-level structural dynamics; this results in a microscopic expression for the slowing down of relaxations in the liq. that is in quant. agreement with our expts. These results indicate how vitrification may be understood as a dynamical connectivity transition with features that are strongly reminiscent of rigidity percolation scenarios.
- 41Schaertl, W.; Sillescu, H. Brownian dynamics of polydisperse colloidal hard spheres: Equilibrium structures and random close packings. J. Stat. Phys. 1994, 77, 1007– 1025, DOI: 10.1007/BF02183148There is no corresponding record for this reference.
- 42Kwaśniewski, P.; Fluerasu, A.; Madsen, A. Anomalous dynamics at the hard-sphere glass transition. Soft Matter 2014, 10, 8698– 8704, DOI: 10.1039/C4SM01671H42https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhsVGjtL3P&md5=22f50226221cfb94a29ce20ec4649157Anomalous dynamics at the hard-sphere glass transitionKwasniewski, Pawel; Fluerasu, Andrei; Madsen, AndersSoft Matter (2014), 10 (43), 8698-8704CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)We use X-ray photon correlation spectroscopy to study the dynamics of hard sphere suspensions and report the emergence of ergodicity restoring anomalous intermittent relaxation modes in the highest concn. suspension that is estd. to be above the glass transition concn. We assoc. these phenomena with non-thermal stress induced relaxations and support our interpretation by a direct comparison of the results with predictions of the mode coupling theory.
- 43Zaccone, A. Explicit analytical solution for random close packing in d = 2 and d = 3. Phys. Rev. Lett. 2022, 128, 028002, DOI: 10.1103/PhysRevLett.128.02800243https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XitFCktr0%253D&md5=f5a3016d8ebf479a10309b1714c320a3Explicit Analytical Solution for Random Close Packing in d=2 and d=3Zaccone, AlessioPhysical Review Letters (2022), 128 (2), 028002CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)We present an anal. derivation of the vol. fractions for random close packing (RCP) in both d=3 and d=2, based on the same methodol. Using suitably modified nearest neighbor statistics for hard spheres, we obtain .vphi.RCP=0.658 96 in d=3 and .vphi.RCP=0.886 48 in d=2. These values are well within the interval of values reported in the literature using different methods (expts. and numerical simulations) and protocols. This statistical derivation suggests some considerations related to the nature of RCP: (i) RCP corresponds to the onset of mech. rigidity where the finite shear modulus emerges, (ii) the onset of mech. rigidity marks the maximally random jammed state and dictates .vphi.RCP via the coordination no. z, (iii) disordered packings with .vphi.>.vphi.RCP are possible at the expense of creating some order, and z=12 at the fcc limit acts as a boundary condition.
- 44Anzivino, C.; Casiulis, M.; Zhang, T.; Moussa, A. S.; Martiniani, S.; Zaccone, A. Estimating random close packing in polydisperse and bidisperse hard spheres via an equilibrium model of crowding. J. Chem. Phys. 2023, 158, 044901, DOI: 10.1063/5.013711144https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3sXhs1Orsro%253D&md5=73328a3deddb83a0cb6ea47bc88830b6Estimating random close packing in polydisperse and bidisperse hard spheres via an equilibrium model of crowdingAnzivino, Carmine; Casiulis, Mathias; Zhang, Tom; Moussa, Amgad Salah; Martiniani, Stefano; Zaccone, AlessioJournal of Chemical Physics (2023), 158 (4), 044901CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)It is shown that an analogy between crowding in fluid and jammed phases of hard spheres captures the d. dependence of the kissing no. for a family of numerically generated jammed states. This analogy is extended to jams of mixts. of hard spheres in d = 3 dimensions and, thus, obtain an est. of the random close packing vol. fraction, ΦRCP, as a function of size polydispersity. First mixts. of particle sizes with discrete distributions are considered. For binary systems, agreement between the predictions and simulations is shown using both our own results and results reported in previous studies, as well as agreement with recent expts. from the literature. The approach is applied to systems with continuous polydispersity using three different particle size distributions, namely, the log-normal, Gamma, and truncated power-law distributions. In all cases, the agreement is obsd. between the theor. findings and numerical results up to rather large polydispersities for all particle size distributions when using as ref. the simulations and results from the literature. In particular, it was found that ΦRCP to increase monotonically with the relative std. deviation, sσ, of the distribution and to sat. at a value that always remains < 1. A perturbative expansion yields a closed-form expression for ΦRCP that quant. captures a distribution-independent regime for sσ < 0.5. Beyond that regime, it is shown that the gradual loss in agreement is tied to the growth of the skewness of size distributions. (c) 2023 American Institute of Physics.
- 45Dallari, F.; Martinelli, A.; Caporaletti, F.; Sprung, M.; Grübel, G.; Monaco, G. Microscopic pathways for stress relaxation in repulsive colloidal glasses. Sci. Adv. 2020, 6, eaaz2982 DOI: 10.1126/sciadv.aaz2982There is no corresponding record for this reference.
- 46Jain, A.; Schulz, F.; Dallari, F.; Markmann, V.; Westermeier, F.; Zhang, Y.; Grübel, G.; Lehmkühler, F. Three-step colloidal gelation revealed by time-resolved x-ray photon correlation spectroscopy. J. Chem. Phys. 2022, 157, 184901, DOI: 10.1063/5.012311846https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XivVKntL3J&md5=1c560b81febbabad9dacfff0fb3d840fThree-step colloidal gelation revealed by time-resolved x-ray photon correlation spectroscopyJain, Avni; Schulz, Florian; Dallari, Francesco; Markmann, Verena; Westermeier, Fabian; Zhang, Yugang; Gruebel, Gerhard; Lehmkuehler, FelixJournal of Chemical Physics (2022), 157 (18), 184901CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)The gelation of PEGylated gold nanoparticles dispersed in a glycerol-water mixt. is probed in situ by x-ray photon correlation spectroscopy. Following the evolution of structure and dynamics over 104 s, a three-step gelation process is found. First, a simultaneous increase of the Ornstein-Zernike length ξ and slowdown of dynamics is characterized by an anomalous q-dependence of the relaxation times of τ ∞ q-6 and strongly stretched intermediate scattering functions. After the structure of the gel network has been established, evidenced by a const. ξ, the dynamics show aging during the second gelation step accompanied by a change toward ballistic dynamics with τ ∞ q-1 and compressed correlation functions. In the third step, aging continues after the arrest of particle motion. Our observations further suggest that gelation is characterized by stress release as evidenced by anisotropic dynamics once gelation sets in. (c) 2022 American Institute of Physics.
- 47Ruta, B.; Chushkin, Y.; Monaco, G.; Cipelletti, L.; Pineda, E.; Bruna, P.; Giordano, V. M.; Gonzalez-Silveira, M. Atomic-scale relaxation dynamics and aging in a metallic glass probed by X-ray photon correlation spectroscopy. Phys. Rev. Lett. 2012, 109, 165701, DOI: 10.1103/PhysRevLett.109.16570147https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38Xhs1CisLnN&md5=e46954e866df320b2c1443d50d09b074Atomic-scale relaxation dynamics and aging in a metallic glass probed by X-ray photon correlation spectroscopyRuta, B.; Chushkin, Y.; Monaco, G.; Cipelletti, L.; Pineda, E.; Bruna, P.; Giordano, V. M.; Gonzalez-Silveira, M.Physical Review Letters (2012), 109 (16), 165701/1-165701/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)We use x-ray photon correlation spectroscopy to investigate the structural relaxation process in a metallic glass on the at. length scale. We report evidence for a dynamical crossover between the supercooled liq. phase and the metastable glassy state, suggesting different origins of the relaxation process across the transition. Furthermore, using different cooling rates, we observe a complex hierarchy of dynamic processes characterized by distinct aging regimes. Strong analogies with the aging dynamics of soft glassy materials, such as gels and concd. colloidal suspensions, point at stress relaxation as a universal mechanism driving the relaxation dynamics of out-of-equil. systems.
- 48Wu, Z.; Kob, W.; Wang, W.; Xu, L. Stretched and compressed exponentials in the relaxation dynamics of a metallic glass-forming melt. Nat. Commun. 2018, 9, 5334, DOI: 10.1038/s41467-018-07759-w48https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXisFersLrE&md5=ed4faf497b081c816507000bd7c63a88Stretched and compressed exponentials in the relaxation dynamics of a metallic glass-forming meltWu, Zhen Wei; Kob, Walter; Wang, Wei-Hua; Xu, LimeiNature Communications (2018), 9 (1), 5334CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)The dynamics of glass-forming systems shows a multitude of features that are absent in normal liqs., such as non-exponential relaxation and a strong temp.-dependence of the relaxation time. Connecting these dynamic properties to the microscopic structure of the system is challenging because of the presence of the structural disorder. Here we use computer simulations of a metallic glass-former to establish such a connection. By probing the temp. and wave-vector dependence of the intermediate scattering function we find that the relaxation dynamics of the glassy melt is directly related to the local arrangement of icosahedral structures: Isolated icosahedra give rise to a liq.-like stretched exponential relaxation whereas clusters of icosahedra lead to a compressed exponential relaxation that is reminiscent to the one found in a solid. Our results show that in metallic glass-formers these two types of relaxation processes can coexist and give rise to a dynamics that is surprisingly complex.
- 49Trachenko, K.; Zaccone, A. Slow stretched-exponential and fast compressed-exponential relaxation from local event dynamics. J.Phys. Condens. 2021, 33, 315101, DOI: 10.1088/1361-648X/ac04cd49https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhvF2gsrbO&md5=4fd231901e9fe00e2aabfe920c29faf8Slow stretched-exponential and fast compressed-exponential relaxation from local event dynamicsTrachenko, K.; Zaccone, A.Journal of Physics: Condensed Matter (2021), 33 (31), 315101CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)We propose an atomistic model for correlated particle dynamics in liqs. and glasses predicting both slow stretched-exponential relaxation (SER) and fast compressed-exponential relaxation (CER). The model is based on the key concept of elastically interacting local relaxation events. SER is related to slowing down of dynamics of local relaxation events as a result of this interaction, whereas CER is related to the avalanche-like dynamics in the low-temp. glass state. The model predicts temp. dependence of SER and CER seen exptl. and recovers the simple, Debye, exponential decay at high temp. Finally, we reproduce SER to CER crossover across the glass transition recently obsd. in metallic glasses.
- 50Liu, A. C. Y.; Tabor, R. F.; de Jonge, M. D.; Mudie, S. T.; Petersen, T. C. Favored local structures in amorphous colloidal packings measured by microbeam X-ray diffraction. Proc. Natl. Acad. Sci. U.S.A. 2017, 114, 10344– 10349, DOI: 10.1073/pnas.170719811450https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXhsV2jtLrE&md5=cece575aee26b10d41b4ea05b6cc51d6Favored local structures in amorphous colloidal packings measured by microbeam X-ray diffractionLiu, Amelia C. Y.; Tabor, Rico F.; de Jonge, Martin D.; Mudie, Stephen T.; Petersen, Timothy C.Proceedings of the National Academy of Sciences of the United States of America (2017), 114 (39), 10344-10349CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)Local structure and symmetry are keys to understanding how a material is formed and the properties it subsequently exhibits. This applies to both crystals and amorphous and glassy materials. In the case of amorphous materials, strong links between processing and history, structure and properties have yet to be made because measuring amorphous structure remains a significant challenge. The authors demonstrate a method to quantify proportions of the bond-orientational order of nearest neighbor clusters [Steinhardt, et al. (1983) Phys Rev B 28:784-805] in colloidal packings by statistically analyzing the angular correlations in an ensemble of scanning transmission microbeam small-angle X-ray scattering (μSAXS) patterns. Local order can be modulated by tuning the potential between monodisperse, spherical colloidal silica particles using salt and surfactant additives and that more pronounced order is obtained by centrifugation than sedimentation. The order in the centrifuged glasses reflects the ground state order in the dispersion at lower packing fractions. This diffraction-based method can be applied to amorphous systems across decades in length scale to connect structure to behavior in disordered systems with a range of particle interactions.
- 51Ackerson, B. J.; Taylor, T. W.; Clark, N. A. Characterization of the local structure of fluids by apertured cross-correlation functions. Phys. Rev. A 1985, 31, 3183– 3193, DOI: 10.1103/PhysRevA.31.318351https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaL2MXktFWlsr8%253D&md5=f719da6ee0e5c992706f6f14958358f1Characterization of the local structure of fluids by apertured cross-correlation functionsAckerson, Bruce J.; Taylor, Thomas W.; Clark, Noel A.Physical Review A: Atomic, Molecular, and Optical Physics (1985), 31 (5), 3183-93CODEN: PLRAAN; ISSN:0556-2791.The described apertured cross-correlation functions (ACCF's) can be used to study local structure in disordered systems. A formal expression for the apertured intensity cross-correlation function was obtained in terms of multiparticle ACCF's. This expression is related to a variety of correlation functions, which can be studied via scattered-light-intensity cross-correlation expts. (C., et al., 1983). ACCF's were obtained for a two-dimensional hard-disk system by computer simulation. Three- and four-body correlations must, in general, be included to give accurate representation of the apertured intensity cross-correlation function.
- 52Lehmkühler, F.; Fischer, B.; Müller, L.; Ruta, B.; Grübel, G. Structure beyond pair correlations: X-ray cross-correlation from colloidal crystals. J. Appl. Crystallogr. 2016, 49, 2046– 2052, DOI: 10.1107/S160057671601731352https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XitVSqsr3L&md5=766d7f3a4c97abf0ce29a168073540e2Structure beyond pair correlations: X-ray cross-correlation from colloidal crystalsLehmkuehler, Felix; Fischer, Birgit; Mueller, Leonard; Ruta, Beatrice; Gruebel, GerhardJournal of Applied Crystallography (2016), 49 (6), 2046-2052CODEN: JACGAR; ISSN:1600-5767. (International Union of Crystallography)The results of an X-ray cross-correlation anal. (XCCA) study on hard-sphere colloidal crystals and glasses are presented. The article shows that cross-correlation functions can be used to ext. structural information beyond the static structure factor in such systems. In particular, the powder av. can be overcome by accessing the crystals' unit-cell structure. In this case, the results suggest that the crystal is of face-centered cubic type. It is demonstrated that XCCA is a valuable tool for X-ray crystallog., in particular for studies on colloidal systems. These are typically characterized by a rather poor cryst. quality due to size polydispersity and limitations in exptl. resoln. because of the small q values probed. Furthermore, nontrivial correlations are obsd. that allow a more detailed insight into crystal structures beyond conventional crystallog., esp. to extend knowledge in structure formation processes and phase transitions.
- 53Lokteva, I.; Koof, M.; Walther, M.; Grübel, G.; Lehmkühler, F. Monitoring nanocrystal self-assembly in real time using in situ small-angle X-ray scattering. Small 2019, 15, 1900438, DOI: 10.1002/smll.201900438There is no corresponding record for this reference.
- 54Lokteva, I.; Dartsch, M.; Dallari, F.; Westermeier, F.; Walther, M.; Grübel, G.; Lehmkühler, F. Real-time X-ray scattering discovers rich phase behavior in PbS nanocrystal superlattices during in situ assembly. Chem. Mater. 2021, 33, 6553– 6563, DOI: 10.1021/acs.chemmater.1c0215954https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhs12ms7rI&md5=70c1c51463bb68b7af73b6214890cabaReal-Time X-ray Scattering Discovers Rich Phase Behavior in PbS Nanocrystal Superlattices during In Situ AssemblyLokteva, Irina; Dartsch, Michael; Dallari, Francesco; Westermeier, Fabian; Walther, Michael; Gruebel, Gerhard; Lehmkuehler, FelixChemistry of Materials (2021), 33 (16), 6553-6563CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)During the self-organization of colloidal semiconductor nanoparticles by solvent evapn., nanoparticle interactions are substantially detd. by the org. ligands covering the inorg. core. However, the influence of the ligand grafting d. on the assembly pathway is often not considered in expts. Here, we carry out an in situ synchrotron small-angle X-ray scattering and X-ray cross-correlation anal. study of the real-time assembly of oleic acid-capped PbS nanocrystals at a low ligand coverage of 2.7 mols./nm2. With high temporal and spatial resoln., we monitor the transitions from the colloidal suspension through the solvated superlattice states into the final dried superstructure. In a single in situ expt., we observe a two-dimensional hexagonal, hcp., body-centered cubic, body-centered tetragonal (with different degrees of tetragonal distortion), and face-centered cubic superlattice phases. Our results are compared to the self-organization of PbS nanocrystals with a higher ligand coverage up to 4.5 mols./nm2, revealing different assembly pathways. This highlights the importance of detg. the ligand coverage in assembly expts. to approach a complete understanding of the assembly mechanism as well as to be able to predict and produce the targeted superstructures.
- 55Schulz, F.; Lokteva, I.; Parak, W. J.; Lehmkühler, F. Recent notable approaches to study self-assembly of nanoparticles with X-Ray scattering and electron microscopy. Part. Part. Sys. Charact. 2021, 38, 2100087, DOI: 10.1002/ppsc.202100087There is no corresponding record for this reference.
- 56Duri, A.; Bissig, H.; Trappe, V.; Cipelletti, L. Time-resolved-correlation measurements of temporally heterogeneous dynamics. Phys. Rev. E 2005, 72, 051401, DOI: 10.1103/PhysRevE.72.05140156https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXhtlSgtbzJ&md5=b82962c69b4dbbaa456b59579ade1df7Time-resolved-correlation measurements of temporally heterogeneous dynamicsDuri, Agnes; Bissig, Hugo; Trappe, Veronique; Cipelletti, LucaPhysical Review E: Statistical, Nonlinear, and Soft Matter Physics (2005), 72 (5-1), 051401/1-051401/17CODEN: PRESCM; ISSN:1539-3755. (American Physical Society)Time resolved correlation (TRC) is a recently introduced light scattering technique that allows one to detect and quantify dynamic heterogeneities. The technique is based on the anal. of the temporal evolution of the speckle pattern generated by the light scattered by a sample, which is quantified by cI(t,τ), the degree of correlation between speckle images recorded at time t and t+τ. Heterogeneous dynamics results in significant fluctuations of cI(t,τ) with time t. We describe how to optimize TRC measurements and how to detect and avoid possible artifacts. The statistical properties of the fluctuations of cI are analyzed by studying their variance, probability distribution function, and time autocorrelation function. We show that these quantities are affected by a noise contribution due to the finite no. N of detected speckles. We propose and demonstrate a method to correct for the noise contribution, based on a N→∞ extrapolation scheme. Examples from both homogeneous and heterogeneous dynamics are provided. Connections with recent numerical and anal. works on heterogeneous glassy dynamics are briefly discussed.
- 57Dallari, F.; Martinelli, A.; Caporaletti, F.; Sprung, M.; Baldi, G.; Monaco, G. Stochastic atomic acceleration during the X-ray-induced fluidization of a silica glass. Proc. Natl. Acad. Sci. U. S. A. 2023, 120, e2213182120 DOI: 10.1073/pnas.2213182120There is no corresponding record for this reference.
- 58Schroer, C. G.; Agapov, I.; Brefeld, W.; Brinkmann, R.; Chae, Y.-C.; Chao, H.-C.; Eriksson, M.; Keil, J.; Nuel Gavaldà, X.; Röhlsberger, R. PETRA IV: the ultralow-emittance source project at DESY. J. Synchrotron Rad. 2018, 25, 1277– 1290, DOI: 10.1107/S160057751800885858https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhs1GktbzE&md5=f00f665ddd2c274f03839d9043d5de0cPETRA IV: the ultralow-emittance source project at DESYSchroer, Christian G.; Agapov, Ilya; Brefeld, Werner; Brinkmann, Reinhard; Chae, Yong-Chul; Chao, Hung-Chun; Eriksson, Mikael; Keil, Joachim; Nuel Gavalda, Xavier; Roehlsberger, Ralf; Seeck, Oliver H.; Sprung, Michael; Tischer, Markus; Wanzenberg, Rainer; Weckert, EdgarJournal of Synchrotron Radiation (2018), 25 (5), 1277-1290CODEN: JSYRES; ISSN:1600-5775. (International Union of Crystallography)The PETRA IV project aims at upgrading the present synchrotron radiation source PETRA III at DESY into an ultralow-emittance source. Being diffraction limited up to X-rays of about 10 keV, PETRA IV will be ideal for three-dimensional X-ray microscopy of biol., chem. and phys. processes under realistic conditions at length scales from at. dimensions to millimetres and time scales down to the sub-nanosecond regime. In this way, it will enable groundbreaking studies in many fields of science and industry, such as health, energy, earth and environment, mobility and information technol. The science case is reviewed and the current state of the conceptual design is summarized, discussing a ref. lattice, a hybrid multi-bend achromat with an interleaved sextupole configuration based on the ESRF-EBS design, in more detail as well as alternative lattice concepts.
- 59Revol, J.-L. ESRF-EBS: implementation, performance and restart of user operation. Proc. IPAC’21 2021, 3929– 3932, DOI: 10.18429/JACoW-IPAC2021-THPAB074There is no corresponding record for this reference.
- 60White, S. Commissioning and restart of ESRF-EBS. Proc. IPAC’21 2021, 1– 6, DOI: 10.18429/JACoW-IPAC2021-MOXA01There is no corresponding record for this reference.
- 61Borland, M.; The upgrade of the advanced photon source. Proceedings of the 9th International Particle Accelerator Conference (IPAC’18), Vancouver, BC, Canada, April 29 to May 4, 2018; Geneva, 2018; pp 2872– 2877.There is no corresponding record for this reference.
- 62Royall, C. P.; Poon, W. C. K.; Weeks, E. R. In search of colloidal hard spheres. Soft Matter 2013, 9, 17– 27, DOI: 10.1039/C2SM26245B62https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhslKktb7K&md5=33717dd66c6a8a156ca1ae20d2af549fIn search of colloidal hard spheresRoyall, C. Patrick; Poon, Wilson C. K.; Weeks, Eric R.Soft Matter (2013), 9 (1), 17-27CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)A review. We recently reviewed the exptl. detn. of the vol. fraction, [phis], of hard-sphere colloids, and concluded that the abs. value of [phis] was unlikely to be known to better than ±3-6%. Here, in a second part to that review, we survey effects due to softness in the interparticle potential, which necessitates the use of an effective vol. fraction. We review current exptl. systems, and conclude that the one that most closely approximates hard spheres remains polymethylmethacrylate spheres sterically stabilized by polyhydroxystearic acid hairs'. For these particles their effective hard sphere diam. is around 1-10% larger than the core diam., depending on the particle size. We argue that for larger colloids suitable for confocal microscopy, the effect of electrostatic charge cannot be neglected, so that mapping to hard spheres must be treated with caution.
- 63Wertheim, M. S. Exact solution of the Percus-Yevick integral equation for hard spheres. Phys. Rev. Lett. 1963, 10, 321– 323, DOI: 10.1103/PhysRevLett.10.321There is no corresponding record for this reference.
- 64Westermeier, F.; Fischer, B.; Roseker, W.; Grübel, G.; Nägele, G.; Heinen, M. Structure and short-time dynamics in concentrated suspensions of charged colloids. J. Chem. Phys. 2012, 137, 114504, DOI: 10.1063/1.475154464https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhtlKisrbJ&md5=c06e02b6c3618f63d80d120f4389be65Structure and short-time dynamics in concentrated suspensions of charged colloidsWestermeier, Fabian; Fischer, Birgit; Roseker, Wojciech; Gruebel, Gerhard; Naegele, Gerhard; Heinen, MarcoJournal of Chemical Physics (2012), 137 (11), 114504/1-114504/17CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)The authors report a comprehensive joint exptl.-theor. study of the equil. pair-structure and short-time diffusion in aq. suspensions of highly charged poly-acrylate (PA) spheres in the colloidal fluid phase. Low-polydispersity PA sphere systems with 2 different hard-core radii, R0 = 542 and 1117 Å, are explored over a wide range of concns. and salinities using static and dynamic light scattering (DLS), small angle x-ray scattering, and x-ray photon correlation spectroscopy (XPCS). The measured static and dynamic scattering functions are analyzed using state-of-the-art theor. methods. For all samples, the measured static structure factor, S(Q), is in good agreement with results by an anal. integral equation method for particles interacting by a repulsive screened Coulomb plus hard-core pair potential. In DLS and XPCS measurements, the authors detd. the short-time diffusion function D(Q) = D0 H(Q)/S(Q), comprising the free diffusion coeff. D0 and the hydrodynamic function H(Q). The latter is calcd. anal. using a self-part cor. version of the δγ-scheme by Beenakker and Mazur which accounts approx. for many-body hydrodynamic interactions (HIs). Except for low-salinity systems at the highest studied vol. fraction φ ≈ 0.32, the theor. predictions for H(Q) are in excellent agreement with the exptl. data. In particular, the increase in the collective diffusion coeff. Dc = D(Q → 0), and the decrease of the self-diffusion coeff., Ds = D(Q → ∞), with increasing φ is well described. In accord with the theor. prediction, the peak value, H(Qm), of H(Q) relates to the nearest neighbor cage size ∼2π/Qm, for which concn. scaling relations are discussed. The peak values H(Qm) are globally bound from below by the corresponding neutral hard-spheres peak values, and from above by the limiting peak values for low-salinity charge-stabilized systems. HIs usually slow short-time diffusion on colloidal length scales, except for the cage diffusion coeff., Dcge = D(Qm), in dil. low-salinity systems where a speed up of the system dynamics and corresponding peak values of H(Qm) > 1 are obsd. exptl. and theor. (c) 2012 American Institute of Physics.
- 65Poon, W. C. K.; Weeks, E. R.; Royall, C. P. On measuring colloidal volume fractions. Soft Matter 2012, 8, 21– 30, DOI: 10.1039/C1SM06083J65https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXhsFCmsLvL&md5=89ca418624e7a0f32b9e9c98f44a0467On measuring colloidal volume fractionsPoon, Wilson C. K.; Weeks, Eric R.; Royall, C. PatrickSoft Matter (2012), 8 (1), 21-30CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)Hard-sphere colloids are popular as models for testing fundamental theories in condensed matter and statistical physics, from crystal nucleation to the glass transition. A single parameter, the vol. fraction ([phis]), characterizes an ideal, monodisperse hard-sphere suspension. In comparing expts. with theories and simulation, researchers to date have paid little attention to likely uncertainties in exptl.-quoted [phis] values. We critically review the exptl. measurement of [phis] in hard-sphere colloids, and show that while statistical uncertainties in comparing relative values of [phis] can be as low as 10-4, systematic errors of ⪆3% are probably unavoidable. The consequences of this are illustrated by way of a case study comparing literature data sets on hard-sphere viscosity and diffusion.
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2D simulations for particles undergoing free diffusion and additional analysis of particle dynamics (PDF)
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