The Glass Transition: Relaxation Dynamics in Liquids and Disordered Materials

432 Pages·2001·12.077 MB·English

by  Prof. Ernst-Joachim Donth (auth.)

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E. Donth
The Glass Transition
Relaxation Dynamics
in Liquids and Disordered Materials
With56Figures and11Tables
, Springer
Prof. Ernst-IoachimDonth
UniversityofHalle
DepartmentofPhysics
06099Halle (Saale)
Germany
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NREL UniversityofVirginia
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Theglasstransition:relaxationdynamicsinliquids anddisorderedmaterials1Ernst-]oachimDonth.
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Preface
The glass transition is well known to glass makers or from the common ex
perience of drying a used chewing gum. A liquid melt or a rubber becomes a
solid glass when its temperature is lowered or a solvent is extracted without
crystallization. There are also dynamic effects. The viscosity of a liquid is
small at high temperatures but increases dramatically as cooling proceeds
down to the glass temperature Tg• The increase is continuous and amounts
to about fifteen orders of magnitude! The technical importance of the glass
transition cannot be overestimated. A few examples will be presented in the
Introduction. Most practical knowledge of the glass transition needed for
glass or plastic technologies and applications is now readily available.
Where then isthe problem? Inthe last fewyears, glass transition research
has enormously intensified. We now have several hundred papers a year in
expensive, top scientific journals. In a 1995 Science magazine ranking, the
glass transition belongs to the six major physical quests, along with broken
charges, physical input for low-dimensional geometry, measurement philoso
phy in quantum mechanics, coherent X-ray radiation for materials research,
and applications of superconductivity. On the other hand, interested people
outsidetheglass transitioncommunityhave difficulty seeing exactlywhat the
glass transition problems are. Inaddition, even insiders split into groupsover
which questioncould be themostimportantforslowdynamicsin cold liquids.
There is much misunderstanding and sometimes intolerance,even within the
glass transition community itself. Some theorists think it may be impossible
to invent a general theory of liquid dynamics because liquid structures are
too varied - compare a metallic glass with a polymer such as polyvinylac
etate - and because no small parameter for a Taylor series expansion could
be detected. In spite of the multifarious structural peculiarities in liquids
and disordered materials, we do observe a general relaxation dynamics, i.e.,
a general scenario for the glass transition.
I would not expect anybody to find one single decisive experiment or idea
that could solve the problem. A good counterexample from 20th century
physics, in which this is not the case, is superconductivity. There were two
basic experiments: that of Kamerlingh and annes which found zero conduc
tivity in 1904, and that of Meissner and Ochsenfeld which found zero induc
tion in 1933;and there was one decisive idea,the Cooper pairs ofthe elegant
VI Preface
BCS theory 1956. Research has never ceased since that time, of course, but
the basic problem was solved.
The history of the glass transition is quite different. In 1970 everything
seemedclear.Viscosityincreaseswith theshortageoffreevolume, and molec
ular cooperativity must help to save fluidity at lowtemperatures.The essen
tial problems evolved later because it was not only details that were left to
be solved, but an unexpected and previously hidden complexity.
(i) There is a mysterious crossover region of dynamic glass transition at
medium viscosity.
(ii) The two processes separated there are distinct and independent: a non
trivial high-temperature process above and a cooperative process below
the crossover. The molecular dynamics differs in warm and cold liquids.
(iii) Two fast picosecond processes were discovered in the angstrom and ten
angstrom scales, together with an ultraslow megasecond process in the
thousand angstrom scale. These may be connected with the dynamic
glass transition.
(iv) Despite much progress over the last decade, long-running issues have
survived from glass and polymer physics that may depend on essentials
of the glass transition:tunneling systems at temperatures near 1 kelvin,
the mixed alkali effect in silicate glasses, the flowtransition of polymers,
and others.
The glass transition problem acquires a 'biological' level of complexity,
wherebywecombine poorly understood elementsinto a better understanding
ofa less wellunderstood whole.Will this perhaps be a feature of21st century
physics, without elegant breakthroughs?
The central question was mentioned above: How can we get a general
liquid dynamics, with a clear architecture in the Arrhenius diagram, from
the multifarious liquid structures of the different substance classes? Is there
any common medium, such as the spatia-temporal pattern of some dynamic
heterogeneity? The central concept used in this book is a dynamic approach
to molecular cooperativity for the cold liquid. The field used to combine
unknowns is the Arrhenius diagram with traces for the different processes
and with one central point, the crossover region.
The method in the first half of this book is a verbal description of the
phenomena, reflecting history to a certain extent. When we have the choice,
thermodynamic or phenomenological arguments will be preferred. Most ex
perimental methods for glass transition research (e.g., linear response and
dynamic scattering) consist in detecting and evaluating subsystem fluctua
tions. To be precise, we start with a definite model: the Glarum-Levy de
fect diffusion model. Although we do not have unequivocal evidence for this
model, we use it as a vehicle for expressing ideas and speculation.
The presentation is inductive, i.e., generalizing from examples. In the
present state of such a complex subject as the glass transition, the truth of
Preface VII
elements increases not only through decisive experiments (these are scarce),
theory, and computer simulation, but also through their ability to fit into
a consistent scenario. Put simply, I describe the tested pictures. For clarity,
repetitions are not always avoided. I describe many aspects of few facts,
ratherthantheopposite,and Iwillconcentrateupongeneral features ofglass
formers with moderate complexity. The particularities of certain substances,
especially exceptional glass formers such as amorphous water, Si02, BeF2,
and proteins, will not be considered, apart from a few examples. This book
therefore differs from a review. The culmination of the descriptive part is a
preliminaryphysical picture ofthe main transition.A deductive scheme for a
possible explanation ofthe cooperative process in the cold liquid is indicated
in Appendix B.
The second half of this book is a compilation of theoretical concepts
adapted to the glass transition (Chap. 3) and an attempt to present a
theoretical explanation for the slowing down of each of the following pro
cesses: the high-temperature process, Johari-Goldstein process, cooperative
process,Fischermodes, and structuralrelaxation belowtheglass temperature
(Chap. 4).
The explanation of the cooperative process and Fischer modes contains
elements of nonconventional thermodynamics. I believe it is legitimate to
raise the question of nonconventional aspects after such an intensive period
of research since 1970. The risk in using such features is that they may pro
vide merely ad hoc explanations which, in the end, only explain the partic
ular phenomenon in question. Chapter 3 makes a careful analysis of what
should be explained before conventional statistical mechanics can be applied.
I consider representative thermodynamic subsystems with temperature fluc
tuations, here discussed within the framework of the von Laue approach
to thermodynamics, and the fluctuation-dissipation theorem, here discussed
from the standpoint of the quantum mechanical measuring process. I think
that the dynamic glass transition, especially near the crossover, is sensitive
to such nonconventional features. This differs from the example provided by
superconductivity, where a conventional explanation has been successful.
According to the French mathematician and philosopher Poincare, a lim
ited number ofexperimental facts can be explained by an unlimited number
of theoretical models. But the idea is not to wait until an unlimited number
of experimental facts has been collected before seeking the true explanation
through one theoretical model.
I would like to thank the Deutsche Forschungsgemeinschaft DFG and the
Fonds Chemische Industrie FCI for financial support.
I had useful and mostly controversial discussions with the following
colleagues: H. Rotger (1975), S. Kastner (1977), W. Holzmiiller (1978),
D.R. Uhlmann (1982, 1990), C.T. Moynihan (1982, 1997), W. Vogel (Jena)
(1983), G.M. Barteniev (1985),O.V.Mazurin (1985),E.W. Fischer (1985ff.),
H. Sillescu (1986 ff.), G.H. Michler (1986 ff.), V.P. Privalko (1988, 1998 ff.),
VIII Preface
J. Kriiger (1988, 1999), J. Jackle (1990, 1997), D. Richter (1990 £1'.),
U.Buchenau (1990£1'.),K Binder (1990£1'.), J.M.O'Reilly(1990), LM.Hodge
(1990, 1996), C.A. Angell (1990, 1999), H.W. Spiess (1990 £1'.), F. Kremer
(1990 £1'.), M. Schulz (1992 £1'.), M.D. Ediger (1994 £1'.), S.R. Nagel (1994),
W. Pechhold (1995), G. Heinrich (1995£1'.), G.B. McKenna(1996£1'.),E.A.Di
Marzio (1996), D.J. Plazek (1996 £1'.), KL. Ngai (1996), W. Gotze (1996 £1'.),
M. Fuchs (1996 £1'.), R. Richert (1996 £1'.), J.M. Hutchinson (1997 £1'.),
Y.H. Jeong (1997£1'.), E.Rossler (1997£1'.), SHunklinger (1997£1'.), W. Petry
(1998), J. Wuttke (1998), P. Maass (1998), G.P. Johari (1998), R. Bohmer
(1999), B. Roling (1999), B.Wunderlich (2000), K Funke (2000), D. Fioretto
(2000), N.O. Birge (2000), and A. Heuer (2000). I also thank colleagues
from our former group in Merseburg, mainly C. Schick (now in Rostock),
A. Schonhals (now in Berlin), and K Schneider (now in Dresden), and from
our group in Halle, mainly K Schroter, M. Beiner, F. Garwe, S. Kahle, and
Elke Hempel for many discussions that have gone to form the picture pre
sented in the book, and K Schroter, M. Beiner, H. Huth, and Elke Hempel
for their help with literature, files, and tables.
I also thank Springer-Verlag in Heidelberg, especially Angela M. Lahee
for her pleasant collaboration, and Stephen Lyle for improving the English.
Katrin Herfurt typeset the manuscript, produced thefigures with uncom
mon skill, and never complained about my endless additions and revisions.
I thank her. My wife, Jutta Donth, provided the love, support, and under
standing without which this book would not have been completed.
E. Donth Halle (Saale), April 2001
IX
Symbols and Names for Traces in Arrhenius Diagrams
14 ...A.
b
.... ---=--=-======-=--=
c
~
C
-2
"
warm liTe cold liT
A Molecular transient
Al a:precursor, Andrade process for shear, Nagel wing for
dielectrics (f)
a High-temperature process, Williams-Cotze process (a:or a:(3 not
used)
b Boson peak
c Cage rattling «(3fast not used)
C Crossover region
D Diffusion modes
G Thermal glass transition, freezing-in
T Crossover temperature
c
T >T; Warm liquid
T <T; Cold liquid
<p Ultraslow modes (usm), Fischer modes
a: Cooperative process
{a,a:} Dynamic glass transition, main transition
(3 Local mode, Johari-Goldstein process «(3s1ow not used)
Gmy shading represents the glass state and white the liquid state.
x
Quotations from the Classical Age
of Glass Transition Research
Der isothermeUbergangin einen Ordnungszustand,der dem innerenthermi
schen Gleichgewichteiner anderenTemperaturentspricht und dahervom Zu
stand kleinster freier Energie nicht durch eine Potentialschwelle getrennt ist,
sondern mit ihm durch eine kontinuierliche Folge von stabileren Zustanden
zusammenhangt, ist aber offenbar prinzipiell unmoglich. [It is obvious that
the isothermal transition into an ordered state, corresponding to an internal
thermal equilibrium at another temperature and not, therefore, separated
by a potential barrier from the state of minimal free energy, but rather con
nected withit via a continuoussuccession ofmore stablestates, isin principle
impossible.]
F. Simon, 1930
Das Kriterium fur die thermodynamischeUnbestimmtheit einer Phaseist die
Feststellung, daf es prinzipiell unrnoglich ist, reversibel in sie iiberzugehen.
- Es lage zunachst nahe, als direkteres experimentelles Kriterium die Tat
sache der Zeitabhangigkeit des Zustandes der thermodynamisch unbestimm
ten Gebilde einzufiihren. Solange man aber nicht zwischen dem Unendlich
werden von Zeiten in verschiedenen Grofenordnungen unterscheidet, kann
dieses Kriterium leicht mifiverstandlich werden. [The criterion for the ther
modynamic uncertainty of a phase is the statement that it is in principle
impossible to enter it in a reversible manner. For the moment we could in
troduce a more direct experimental criterion, such as the time dependence
of the state for the thermodynamically uncertain outcome. Ifone does not
discriminate between the way times tend to infinity by different orders of
magnitude, this criterion may easily become misleading.]
F. Simon, 1930
In einem Transformationsintervall zwischen dem fliissigen und dem Glaszu
stande muf also die Molekularrotation auftreten, und dieses Intervall ist aller
Wahrscheinlichkeit nach das Erweichungsintervall, in dem etwas Besonderes
vor sich geht, was allen Glasern eigentiimlich ist. [Molecular rotation must
occur in a transformation interval between the liquid and the glass state, and
this interval is probably the softening interval where something particular
happens that is characteristic of all glasses.]
G. Tammann, 1933
Daher ist es wahrscheinlich, daf bei hinreichender Abkiihlungsgeschwindig
keit alle oder doch die meisten Stoffe,wenn auch nur in geringen Mengen,in
den Glaszustand iibergefiihrt werden konnen. [Itis therefore probable that,