Hypersonic elastic excitations in soft mesoscopic structures [Elektronische Ressource] : a Brillouin light scattering study / vorgelegt von Wei Cheng

Chengwei

Sujets

• Physik

Informations

• Publié par: johannes_gutenberg-universitat_mainz
• Publié le: 01 janvier 2007
• Nombre de lectures: 15
• Langue: English
• Poids de l'ouvrage: 3 Mo

Extrait

Hypersonic Elastic Excitations in
Soft Mesoscopic Structures
—— A Brillouin light scattering study


DISSERTATION
zur Erlangung des Grades
"Doktor der Naturwissenschaften"

am Fachbereich Chemie, Pharmazie und Geowissenschaften
der Johannes Gutenberg-Universität Mainz


vorgelegt von
Master-Chem. Wei Cheng
geb.: 02.04.1979
aus Hunan/China


Mainz, 2007
rdTag der mündlichen prüfung: March 23 , 2007

Dekan: Prof. Dr. Peter Langguth
1. Berichterstatter: Prof. Dr. Hans-Jürgen Butt (MPIP)
2. rof. Dr. Manfred Schmidt (Uni-Mainz)
3. rof. Dr. Christos N. Likos (Uni-Düsseldorf)

























Die vorliegende Arbeit wurde im Zeitraum
von Juni 2004 bis Dezember 2006 am Max-

Planck-Institute für Polymerforschung in

Mainz unter der Anleitung von Herrn Prof.

Dr. H.-J. Butt und Herrn Prof. Dr. G. Fytas
angefertigt.











献给我最亲爱的父母…

(To my dearest parents...)Preface


This dissertation is devoted to the experimental exploration of the propagation of
elastic waves in soft mesoscopic structures with submicrometer dimensions. A strong
motivation of this work is the large technological relevance and the fundamental
importance of the subject. Elastic waves are accompanied by time-dependent
fluctuations of local stress and strain fields in the medium. As such, the propagation
phase velocities are intimately related to the elastic moduli. Knowledge of the elastic
wave propagation directly provides information about the mechanical properties of
the probed mesoscopic structures, which are not readily accessible experimentally.
On the other hand, elastic waves, when propagating in an inhomogeneous medium
with spatial inhomogeneities comparable to their wavelength, exhibit rather rich
behavior, including the appearance of novel physical phenomena, such as phononic
bandgap formation. So far, the experimental work has been restricted to macroscopic
structures, which limit wave propagation below the KHz range. It was anticipated
that an experimental approach capable of probing the interplay of the wave
propagation with the controlled mesoscopic structures would contribute to deeper
insights into the fundamental problem of elastic wave propagation in inhomogeneous
systems.
The mesoscopic nature of the structures to be studied precludes the use of
traditional methods, such as sound transmission, for the study of elastic wave
propagation. In this work, an optical method utilizing the inelastic scattering of
photons by GHz frequency thermally excited elastic waves, known as Brillouin light
scattering spectroscopy (BLS), was employed. Two important classes of soft
structures were investigated: thin films and colloidal crystals. For the former, the
main interest was the effect of the one-dimensional (1D) confinement on the wave
propagation due to the presence of the free-surface or interface of the layer and the
utilization of these waves to extract relevant material parameters. For the second
system, the primary interest was the interaction of the elastic wave and the strong
scattering medium with local resonance units in a three-dimensional (3D) periodic
arrangement.
I The dissertation is organized as follows. Chapter 1 serves as a general
introduction and the background of the present work. In Chapter 2 and Chapter 3, the
physical principles of elastic wave propagation and the BLS method necessary for
comprehending the results in later chapters are introduced. Chapter 4 is devoted to
the experimental technique encompassing the tandem Fabry-Perot interferometer and
the related scattering geometry. From Chapter 5 to Chapter 8, the BLS results for the
various mesoscopic structures are presented, including thin supported polymer films,
multilayer polymer films, dry colloidal crystals, and wet colloidal crystals. In
Chapter 9 a brief summary and perspectives are provided.



II Table of contents



Chapter 1
Introduction ............................................................................................................................ 1

Chapter 2
Elastic wave propagation in solids ........................................................................................ 6
2.1 Elasticity fundamentals ................................................................................................ 6
2.1.1 Stress and strain.................................................................................................... 6
2.1.2 Hook’s law............................................................................................................ 8
2.1.3 Elastic moduli of isotropic bodies ........................................................................ 9
2.2 Elastic waves in isotropic media ................................................................................ 11
2.2.1 Longitudinal and transverse waves .................................................................... 11
2.2.2 Spherical-wave solutions.................................................................................... 12
2.3 Elastic waves in supported thin layers 14
2.4 Vibrations of an elastic sphere ................................................................................... 21
2.4.1 Vibration eigenmodes......................................................................................... 21
2.4.2 Single sphere scattering...................................................................................... 23
2.5 Elastic waves in periodic elastic composites.............................................................. 26
2.5.1 General overview................................................................................................ 26
2.5.2 The plane-wave (PW) method............................................................................ 27
2.5.3 The multiple-scattering (MS) method ................................................................ 31

Chapter 3
Light scattering basics.......................................................................................................... 35
3.1 Fundamental light scattering theory ........................................................................... 35
3.2 Introduction to BLS.................................................................................................... 39
3.2.1 A simple approach to BLS ................................................................................. 40
3.2.2 A thermodynamic approach to BLS................................................................... 42
3.3 Some remarks ............................................................................................................. 47
3.4 Surface BLS................................................................................................................ 48

Chapter 4
Brillouin light scattering instrumentation.......................................................................... 50
4.1 Introduction to Fabry-Perot interferometer ................................................................ 50
4.1.1 Multiple beam interference 50
4.1.2 Standard Fabry-Perot interferometer.................................................................. 53
4.1.3 Tandem Fabry-Perot interferometer................................................................... 56
4.2 Experimental setup ..................................................................................................... 59
4.3 Scattering geometry.................................................................................................... 61

Chapter 5
Elastic excitations in supported thin polymer films .......................................................... 65
5.1 Introduction................................................................................................................ 65
5.2 Experimental 66
5.2.1 Sample preparation.............................................................................................66
III 5.2.2 Film characterization..........................................................................................67
5.3 Results and discussion................................................................................................69
5.3.1 Elastic constants.................................................................................................
5.3.2 Glass transition...................................................................................................76

Chapter 6
Elastic excitations in 1D polymeric photonic structures................................................... 83
6.1 Introduction................................................................................................................ 83
6.2 Film characterization..................................................................................................84
6.3 Results and discussion85
6.3.1 Dispersion relation for in-plane phonon propagation..................................