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Liu J, Zhao C, Lockerby DA, Sprittles JE. Thermal capillary waves on bounded nanoscale thin films. Phys Rev E 2023; 107:015105. [PMID: 36797965 DOI: 10.1103/physreve.107.015105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2022] [Accepted: 01/09/2023] [Indexed: 06/18/2023]
Abstract
The effect of confining walls on the fluctuation of a nanoscale thin film's free surface is studied using stochastic thin-film equations (STFEs). Two canonical boundary conditions are employed to reveal the influence of the confinement: (1) an imposed contact angle and (2) a pinned contact line. A linear stability analysis provides the wave eigenmodes, after which thermal-capillary-wave theory predicts the wave fluctuation amplitudes. Molecular dynamics (MD) simulations are performed to test the predictions, and a Langevin diffusion model is proposed to capture oscillations of the contact lines observed in MD simulations. Good agreement between the theoretical predictions and the MD simulation results is recovered, and it is discovered that confinement can influence the entire film. Notably, a constraint on the length scale of wave modes is found to affect fluctuation amplitudes from our theoretical model, especially for 3D films. This opens up challenges and future lines of inquiry.
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Affiliation(s)
- Jingbang Liu
- Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Chengxi Zhao
- Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
| | - Duncan A Lockerby
- School of Engineering, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - James E Sprittles
- Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
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2
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Clavaud C, Maza-Cuello M, Frétigny C, Talini L, Bickel T. Modification of the Fluctuation Dynamics of Ultrathin Wetting Films. PHYSICAL REVIEW LETTERS 2021; 126:228004. [PMID: 34152195 DOI: 10.1103/physrevlett.126.228004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/19/2021] [Accepted: 05/13/2021] [Indexed: 06/13/2023]
Abstract
We report on the effect of intermolecular forces on the fluctuations of supported liquid films. Using an optically induced thermal gradient, we form nanometer-thin films of wetting liquids on glass substrates, where van der Waals forces are balanced by thermocapillary forces. We show that the fluctuation dynamics of the film interface is strongly modified by intermolecular forces at lower frequencies. Data spanning three frequency decades are in excellent agreement with theoretical predictions accounting for van der Waals forces. Our results emphasize the relevance of intermolecular forces on thermal fluctuations when fluids are confined at the nanoscale.
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Affiliation(s)
- C Clavaud
- CNRS, Sciences et Ingénierie de la Matière Molle, ESPCI Paris, PSL Research University, Sorbonne Université, 75005 Paris, France
| | - M Maza-Cuello
- CNRS, Sciences et Ingénierie de la Matière Molle, ESPCI Paris, PSL Research University, Sorbonne Université, 75005 Paris, France
| | - C Frétigny
- CNRS, Sciences et Ingénierie de la Matière Molle, ESPCI Paris, PSL Research University, Sorbonne Université, 75005 Paris, France
| | - L Talini
- CNRS, Surface du Verre et Interfaces, Saint-Gobain, 93300 Aubervilliers, France
| | - T Bickel
- Univ. Bordeaux, CNRS, Laboratoire Ondes et Matière d'Aquitaine (UMR 5798), F-33400 Talence, France
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3
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Lal J, Lurio LB, Liang D, Narayanan S, Darling SB, Sutton M. Universal dynamics of coarsening during polymer-polymer thin-film spinodal dewetting kinetics. Phys Rev E 2020; 102:032802. [PMID: 33076025 DOI: 10.1103/physreve.102.032802] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2020] [Accepted: 08/23/2020] [Indexed: 06/11/2023]
Abstract
The dewetting dynamics of a supported bilayer polymer thin film on a solid substrate is investigated using grazing incidence x-ray photon correlation spectroscopy. We find that the top layer dewets via the spinodal mechanism. The kinetics of the dewetting is studied by monitoring the time evolution of the surface diffuse x-ray scattering intensity. We study the time evolution of fluctuations about the average surface structure by measuring the two-time x-ray intensity fluctuation correlation functions. Using these two-time correlation functions we quantify the crossover from early-time diffusive dynamics to hydrodynamics. The early diffusive regime satisfies dynamic universality. The two-time correlation functions also quantify the onset of hydrodynamic effects. The hydrodynamic regime is observed during the spinodal dewetting process as these interactions are not screened.
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Affiliation(s)
- J Lal
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
- Intense Pulsed Neutron Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
- Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA
| | - L B Lurio
- Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA
| | - D Liang
- Intense Pulsed Neutron Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - S Narayanan
- X-ray Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - S B Darling
- Chemical Sciences and Engineering, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - M Sutton
- Physics Department, McGill University, Montréal, H3A 2T8, Canada
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4
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Hill J, Campbell S, Carini G, Chen-Wiegart YCK, Chu Y, Fluerasu A, Fukuto M, Idir M, Jakoncic J, Jarrige I, Siddons P, Tanabe T, Yager KG. Future trends in synchrotron science at NSLS-II. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:374008. [PMID: 32568740 DOI: 10.1088/1361-648x/ab7b19] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2020] [Accepted: 02/28/2020] [Indexed: 06/11/2023]
Abstract
In this paper, we summarize briefly some of the future trends in synchrotron science as seen at the National Synchrotron Light Source II, a new, low emittance source recently commissioned at Brookhaven National Laboratory. We touch upon imaging techniques, the study of dynamics, the increasing use of multimodal approaches, the vital importance of data science, and other enabling technologies. Each are presently undergoing a time of rapid change, driving the field of synchrotron science forward at an ever increasing pace. It is truly an exciting time and one in which Roger Cowley, to whom this journal issue is dedicated, would surely be both invigorated by, and at the heart of.
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Affiliation(s)
- John Hill
- National Synchrotron Light Source II (NSLS-II), Brookhaven National Laboratory, Upton, NY, United States of America
| | - Stuart Campbell
- National Synchrotron Light Source II (NSLS-II), Brookhaven National Laboratory, Upton, NY, United States of America
| | - Gabriella Carini
- Instrumentation Division (IO), Brookhaven National Laboratory, Upton, NY, United States of America
| | - Yu-Chen Karen Chen-Wiegart
- National Synchrotron Light Source II (NSLS-II), Brookhaven National Laboratory, Upton, NY, United States of America
- Materials Science & Chemical Engineering, Stony Brook University, Stony Brook, NY, United States of America
| | - Yong Chu
- National Synchrotron Light Source II (NSLS-II), Brookhaven National Laboratory, Upton, NY, United States of America
| | - Andrei Fluerasu
- National Synchrotron Light Source II (NSLS-II), Brookhaven National Laboratory, Upton, NY, United States of America
| | - Masafumi Fukuto
- National Synchrotron Light Source II (NSLS-II), Brookhaven National Laboratory, Upton, NY, United States of America
| | - Mourad Idir
- National Synchrotron Light Source II (NSLS-II), Brookhaven National Laboratory, Upton, NY, United States of America
| | - Jean Jakoncic
- National Synchrotron Light Source II (NSLS-II), Brookhaven National Laboratory, Upton, NY, United States of America
| | - Ignace Jarrige
- National Synchrotron Light Source II (NSLS-II), Brookhaven National Laboratory, Upton, NY, United States of America
| | - Peter Siddons
- National Synchrotron Light Source II (NSLS-II), Brookhaven National Laboratory, Upton, NY, United States of America
| | - Toshi Tanabe
- National Synchrotron Light Source II (NSLS-II), Brookhaven National Laboratory, Upton, NY, United States of America
| | - Kevin G Yager
- Center for Functional Nanomaterials (CFN), Brookhaven National Laboratory, Upton, NY, United States of America
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Das A N, Begam N, Chandran S, Swain A, Sprung M, Basu JK. Thermal stability and dynamics of soft nanoparticle membranes: role of entropy, enthalpy and membrane compressibility. SOFT MATTER 2020; 16:1117-1124. [PMID: 31894229 DOI: 10.1039/c9sm01946d] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Nanoparticle based ultra-thin membranes have been shown to have remarkable mechanical properties while also possessing novel electrical, optical or magnetic properties, which could be controlled by tailoring properties at the level of individual nanoparticles. Since in most cases the ultra-thin membranes are coupled to some substrates, the role of membrane-substrate interactions, apart from nanoparticle-nanoparticle interactions become very crucial in understanding their mechanical and thermal stability, as well as their plethora of applications. However, systematic studies in this direction have been conspicuously absent. Here we report thermal stability and the corresponding microscopic dynamics of polymer supported ultra-thin membranes comprising of self-assembled, ordered grains of polymer grafted nanoparticles having tunable mechanical properties. The initially ordered membranes show distinct pathways for temperature induced disordering depending on membrane flexibility as well as on interfacial entropic and enthalpic interactions with the underlying polymer thin film. We also observe contrasting temperature dependence of microscopic dynamics of these membranes depending on whether the graft polymer-substrate polymer interactions are predominantly entropic or enthalpic in nature. Our results suggest that apart from their varied applications, the soft nanoparticle-polymer hybrid membranes are a playground for rich physics involving subtle entropic and enthalpic effects along with the nanoparticles softness, which eventually determine their thermo-mechanical stability.
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Affiliation(s)
- Nimmi Das A
- Department of Physics, Indian Institute of Science, Bangalore, 560012, India.
| | - Nafisa Begam
- Institute of Applied Physics, University of Tuebingen, 72076 Tuebingen, Germany
| | | | - Aparna Swain
- Department of Physics, Indian Institute of Science, Bangalore, 560012, India.
| | - Michael Sprung
- Deutsches Elektronen Synchrotron DESY, Notkestresse 85, 22607 Hamburg, Germany
| | - J K Basu
- Department of Physics, Indian Institute of Science, Bangalore, 560012, India.
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Majewski PW, Yager KG. Rapid ordering of block copolymer thin films. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:403002. [PMID: 27537062 DOI: 10.1088/0953-8984/28/40/403002] [Citation(s) in RCA: 58] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
Block-copolymers self-assemble into diverse morphologies, where nanoscale order can be finely tuned via block architecture and processing conditions. However, the ultimate usage of these materials in real-world applications may be hampered by the extremely long thermal annealing times-hours or days-required to achieve good order. Here, we provide an overview of the fundamentals of block-copolymer self-assembly kinetics, and review the techniques that have been demonstrated to influence, and enhance, these ordering kinetics. We discuss the inherent tradeoffs between oven annealing, solvent annealing, microwave annealing, zone annealing, and other directed self-assembly methods; including an assessment of spatial and temporal characteristics. We also review both real-space and reciprocal-space analysis techniques for quantifying order in these systems.
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Affiliation(s)
- Pawel W Majewski
- Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, NY, USA. Department of Chemistry, University of Warsaw, Warsaw, Poland
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Sinha SK, Jiang Z, Lurio LB. X-ray photon correlation spectroscopy studies of surfaces and thin films. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2014; 26:7764-7785. [PMID: 25236339 DOI: 10.1002/adma.201401094] [Citation(s) in RCA: 57] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2014] [Revised: 06/24/2014] [Indexed: 06/03/2023]
Abstract
The technique of X-ray Photon Correlation Spectroscopy (XPCS) is reviewed as a method for studying the relatively slow dynamics of materials on time scales ranging from microseconds to thousands of seconds and length scales ranging from microns down to nanometers. We focus on the application of this technique to study dynamical fluctuations of surfaces, interfaces and thin films. We first discuss instrumental issues such as the effects of partial coherence (or alternatively finite instrumental resolution) and optimization of signal-to-noise ratios in the experiments. We then review what has been learned from recent XPCS studies of capillary wave fluctuations on liquid surfaces and polymer films, of nanoparticles used as probes to study the interior dynamics of polymer films, of liquid crystals and multilamellar surfactant films, and of metal surfaces, and magnetic domain wall fluctuations in antiferromagnets. We then discuss studies of non-equilibrium dynamics described by 2-time correlation functions. Finally, we briefly speculate on possible future XPCS experiments at new synchrotron sources currently under development including studies of dynamics on time scales down to femtoseconds.
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Affiliation(s)
- Sunil K Sinha
- Dept. of Physics, University of California San Diego, 9500 Gilman Drive, La Jolla, CA, 92093-0319, USA
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Wang SF, Yang S, Lee J, Akgun B, Wu DT, Foster MD. Anomalous surface relaxations of branched-polymer melts. PHYSICAL REVIEW LETTERS 2013; 111:068303. [PMID: 23971618 DOI: 10.1103/physrevlett.111.068303] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2012] [Indexed: 06/02/2023]
Abstract
The dynamics of thermally stimulated surface fluctuations of 100 nm thick films of long-branched polymers are measured for the first time. In contrast to comparable films of linear or cyclic chains that show no change in viscosity upon confinement, films of 6-pom, 6-star, and 6-end end-branched stars show viscosities, inferred from x-ray photon correlation spectroscopy, as much as 100 times higher than in the bulk. This difference varies in magnitude with chain architecture. Branching has a profound effect on confinement, even for these unentangled chains.
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Affiliation(s)
- Shih-fan Wang
- Department of Polymer Science, The University of Akron, Akron, Ohio 44325-3909, USA
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Evans CM, Narayanan S, Jiang Z, Torkelson JM. Modulus, confinement, and temperature effects on surface capillary wave dynamics in bilayer polymer films near the glass transition. PHYSICAL REVIEW LETTERS 2012; 109:038302. [PMID: 22861904 DOI: 10.1103/physrevlett.109.038302] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2012] [Revised: 05/08/2012] [Indexed: 06/01/2023]
Abstract
We report relaxation times (τ) for surface capillary waves on 27-127 nm polystyrene (PS) top layers in bilayer films using x-ray photon correlation spectroscopy. At ∼10 °C above the PS glass transition temperature (T(g)), τ tracks with underlayer modulus, being significantly smaller on softer substrates at low in-plane scattering wave vector. Relative to capillary wave theory, we also report stiffening behavior upon nanoconfinement of the PS layers. At PS T(g)+40 °C, both effects become negligible. We demonstrate how neighboring polymer domains impact dynamics over substantial length scales.
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Affiliation(s)
- Christopher M Evans
- Department of Chemical and Biological Engineering, Northwestern University, Evanston, Illinois 60208, USA
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12
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Jiang Z, Li X, Strzalka J, Sprung M, Sun T, Sandy AR, Narayanan S, Lee DR, Wang J. The dedicated high-resolution grazing-incidence X-ray scattering beamline 8-ID-E at the Advanced Photon Source. JOURNAL OF SYNCHROTRON RADIATION 2012; 19:627-636. [PMID: 22713900 DOI: 10.1107/s0909049512022017] [Citation(s) in RCA: 75] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2012] [Accepted: 05/15/2012] [Indexed: 06/01/2023]
Abstract
As an increasingly important structural-characterization technique, grazing-incidence X-ray scattering (GIXS) has found wide applications for in situ and real-time studies of nanostructures and nanocomposites at surfaces and interfaces. A dedicated beamline has been designed, constructed and optimized at beamline 8-ID-E at the Advanced Photon Source for high-resolution and coherent GIXS experiments. The effectiveness and applicability of the beamline and the scattering techniques have been demonstrated by a host of experiments including reflectivity, grazing-incidence static and kinetic scattering, and coherent surface X-ray photon correlation spectroscopy. The applicable systems that can be studied at 8-ID-E include liquid surfaces and nanostructured thin films.
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Affiliation(s)
- Zhang Jiang
- X-ray Science Division, Argonne National Laboratory, Argonne, IL 60439, USA
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14
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Daillant J. Recent developments and applications of grazing incidence scattering. Curr Opin Colloid Interface Sci 2009. [DOI: 10.1016/j.cocis.2009.04.003] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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15
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Yang J, Zhao J, Han CC. Lateral Mobility of Single Chains at a Liquid Polymer Interface. Macromolecules 2008. [DOI: 10.1021/ma8015135] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jingfa Yang
- Beijing Laboratory of Molecular Sciences, Joint Laboratory of Polymer Sciences and Materials, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
| | - Jiang Zhao
- Beijing Laboratory of Molecular Sciences, Joint Laboratory of Polymer Sciences and Materials, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
| | - Charles C. Han
- Beijing Laboratory of Molecular Sciences, Joint Laboratory of Polymer Sciences and Materials, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
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Béziel W, Fragneto G, Cousin F, Sferrazza M. Neutron reflectivity study of the kinetics of polymer-polymer interface formation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:022801. [PMID: 18850877 DOI: 10.1103/physreve.78.022801] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2008] [Indexed: 05/26/2023]
Abstract
We have investigated how the interface width between two thin polymer films approaches its equilibrium state. Neutron reflection for different polyolefin bilayers of various degrees of incompatibility as a function of the annealing time was measured. By tuning the interaction parameter, we have probed both an immiscible polymer couple and systems approaching criticality where the interface is wider. Since polymer chains have slow dynamics, we have observed the slow broadening of the interface connected to the growth at long times of the wavelength capillary-wave modes, which involve large-scale hydrodynamic flows.
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Affiliation(s)
- W Béziel
- Département de Physique, Faculté des Sciences, Université Libre de Bruxelles, Boulevard du Triomphe, CP223, 1040 Bruxelles, Belgique
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Jiang Z, Kim H, Jiao X, Lee H, Lee YJ, Byun Y, Song S, Eom D, Li C, Rafailovich MH, Lurio LB, Sinha SK. Evidence for viscoelastic effects in surface capillary waves of molten polymer films. PHYSICAL REVIEW LETTERS 2007; 98:227801. [PMID: 17677879 DOI: 10.1103/physrevlett.98.227801] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2007] [Indexed: 05/16/2023]
Abstract
The surface dynamics of supported ultrathin polystyrene films with thickness comparable to the radius of gyration were investigated by surface sensitive x-ray photon correlation spectroscopy. We show for the first time that the conventional model of capillary waves on a viscous liquid has to be modified to include the effects of a shear modulus in order to explain both static and dynamic scattering data from ultrathin molten polymer films.
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Affiliation(s)
- Zhang Jiang
- Department of Physics, University of California at San Diego, La Jolla, California 92093, USA
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Narayanan S, Lee DR, Hagman A, Li X, Wang J. Particle dynamics in polymer-metal nanocomposite thin films on nanometer-length scales. PHYSICAL REVIEW LETTERS 2007; 98:185506. [PMID: 17501587 DOI: 10.1103/physrevlett.98.185506] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/05/2007] [Indexed: 05/15/2023]
Abstract
X-ray photon correlation spectroscopy was used in conjunction with resonance-enhanced grazing-incidence small-angle x-ray scattering to probe slow particle dynamics and kinetics in gold/polystyrene nanocomposite thin films. Such enhanced coherent scattering enables, for the first time, measurement of the particle dynamics at wave vectors up to approximately 1 nm(-1) (or a few nanometers spatially) in a disordered system, well in the regime where entanglement, confinement, and particle interaction dominate the dynamics and kinetics. Measurements of the intermediate structure factor f(q,t) indicate that the particle dynamics differ from Stokes-Einstein Brownian motion and are explained in terms of viscoelastic effects and interparticle interactions.
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Affiliation(s)
- Suresh Narayanan
- Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA.
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Roth CB, McNerny KL, Jager WF, Torkelson JM. Eliminating the Enhanced Mobility at the Free Surface of Polystyrene: Fluorescence Studies of the Glass Transition Temperature in Thin Bilayer Films of Immiscible Polymers. Macromolecules 2007. [DOI: 10.1021/ma062864w] [Citation(s) in RCA: 189] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Henle ML, Levine AJ. Capillary wave dynamics on supported viscoelastic films: single and double layers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:021604. [PMID: 17358350 DOI: 10.1103/physreve.75.021604] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2006] [Indexed: 05/14/2023]
Abstract
We study the capillary wave dynamics of a single viscoelastic supported film and of a double layer of immiscible viscoelastic supported films. Using both simple scaling arguments and a continuum hydrodynamic theory, we investigate the effects of viscoelasticity and interfacial slip on the relaxation dynamics of these capillary waves. Our results account for the recent observation of a wavelength-independent decay rate for capillary waves in a supported polystyrene/brominated polystyrene double layer [X. Hu, Phys. Rev. E 74, 010602(R) (2006)].
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Affiliation(s)
- Mark L Henle
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, USA
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