Glasses are used as versatile materials in numerous applications of daily life, and their manufacturing techniques reach back millennia [1]. However, the rst used glasses were not made by man but were found in nature. In meteoric impacts or volcanic eruptions the extreme heating and subsequent rapid cooling forms natural glasses from molten stone. In lava ows of volcanic regions Obsidian is found, a shiny black glassy stone, used for the rst sharp blades and arrowheads by chipping o pieces.
Even nowadays, broken glass belongs to the sharpest available materials.
The tailoring of desired material properties of manmade glasses has been highly developed, and nowadays the use of glasses ranges from simple mass products like bottles, light bulbs, or window glass to sophisticated 'high-tech' applications. A well known example for such a 'high-tech' glass with specially designed properties is CERAN°R glass1 used for hot plates: it practically does not expand upon heating and therefore does not break even when quenched with cold water from tempera-tures as high as 700◦C. At the same time, CERAN°R glass does not shield heat, a necessary property for a hot plate. Examples that exploit the adjustability of the optical properties of glasses are eyeglasses, laser optics, or imaging objectives. These completely dierent applications show how widely the glass properties can be adjusted by combining dierent substances and applying dierent manufacturing techniques.
Although the methods to control the material properties are highly developed, the basic mechanisms of glassy solidication are not suciently understood so far.
In fact, the terminus 'glass' describes a more general class of materials. The most general denition is as follows (from C. A. Angell [2]): 'A glass is a condensed state of matter which has become non-ergodic by virtue of the continuous slow-down of one or more of its degrees of freedom'. This denition includes spin glasses, orientational glasses, and vortex glasses, as well as the 'classical' glasses that are characterized by
1Schott AG, http://www.schott.com/german/ (December 9, 2008).
5
0 1
Figure 1.1: Left: Viscosity η of dierent glass formers as a function of the normalized inverse temperature. The glass temperature TG is dened as the temperature where the viscosity exceeds a value of η = 1013P oise. Dierent glass formers are classied as 'strong' or 'fragile' according to their approach of the arrest. Right: The temperature dependence of the volume v or the enthalpy h is sketched for decreasing temperatures.
TM is the melting temperature. Curve a) results from a slower cooling rate than curve b) leading to a lower glass transition temperature. The derivatives of the curves (the ther-mal expansion coecientαp = (∂lnv∂T )p and the isobaric heat capacitycp = (∂T∂h)p) change abruptly but continuously at the glass transition (graphs from P. Debenedetti [3]).
their static amorphous structure [2]. In this work the terminus 'glass' will be always used to describe the latter, the so-called structural glasses.
Such glasses can be based on silicates, polymers, metals, and also on colloidal particles. Although these systems are totally dierent on the scale of their con-stituents, they all have common features that characterize them as a glass: 'Glasses are disordered materials that lack the periodicity of crystals but behave mechanically like solids' (P. G. Debenedetti [3]). When lowering the temperature of a uid, glass formers dynamically arrest into a non-equilibrium state while the uid structure does not change signicantly. No long-range order can be established by crystallization.
This continuous phenomenon is called the glass transition and characteristically the viscosity of the system is increased by many orders of magnitude [2, 3, 4, 5]. For several glass formers this is demonstrated in Figure 1.1, where the viscosityη is shown versus the normalized inverse temperature TG/T (with glass transition temperature TG).
A drastic continuous increase of up to 15 orders of magnitude is found in these examples. Although the curves do not follow a universal behavior in this normalized graph, they can be compared and labeled by two groups of glass formers: fragile and
strong systems2. The fragile systems approach the dynamic arrest more abruptly with a steeper η-curve than the strong glass formers. Here, the organic molecules form fragile glass formers, whereas the inorganic systems as silicon dioxide (SiO2) form strong glasses. The origin of the dierence is suspected in the individual chemical near order, but a satisfying description of the curves over the whole temperature range is still missing.
Unlike a phase transition, the glass transition does not occur at a well dened temper-ature [3]. One denition of the glass transition tempertemper-ature, as used in the examples of the left graph of Figure 1.1, is the temperature where the viscosityη exceeds a value of ηG = 1013P oise, and the system can be considered solid-like. However, this value is chosen arbitrarily. Another denition of the glass transition temperature TG is given by characteristic changes of the thermodynamic quantities volume and enthalpy as illustrated in the right graph of Figure 1.1. Dilatometric measurements show that the expansion coecient α is lowered at the glass transition upon cooling. Calorimetric measurements show a characteristic step in enthalpy because degrees of freedom contributing to the heat capacity are 'frozen'. This eect is stronger in fragile than in strong glass formers. The temperature TG, where both changes happen, is dependent on the rate of cooling. The lower the cooling rate, the lower is the measured glass transition temperature TG. This is important as it emphasizes the nature of the glass transition in comparison to a phase transition: the glass transition occurs, when the system is not able to follow into the equilibrium state on the timescale of the externally applied temperature change. The relaxation timescales of the system are too slow. Thus, the glass transition is not just a property of the system but is also related to the external timescale of the temperature treatment. Therefore, information of the thermal history may be 'memorized' in a glassy system.
This phenomenon of kinetic vitrication may take place even when a phase transition into a long-range ordered state is possible and eventually may occur under appropriate conditions3; examples are one-component hard spheres [6], semicrystalline stacks of lamellar crystals in polymers [7], or binary mixtures in metal alloys [8]. They all do crystallize if the system temperature is lowered suciently slowly.
It appears obvious that disordered structure and dynamics are related. One example for a close formal connection between structure and dynamics of a glass forming system is provided by Mode Coupling Theory (MCT), a theory describing the dy-namical glass transition. There, the only input into the MCT equations is the static structure factor [9, 10]. Nevertheless, the microscopic connection between structure and dynamics is still under strong debate [11, 12, 13, 14], especially the question
2Here, systems are chosen that seem to collapse on two distinct curves, two extreme cases for strong and fragile systems. However, there are many glass formers that form curves in between.
3In fact, the example of CERAN°R glass mentioned above, earns the 'zero-expansion' property from its partially crystalline structure, a combination of micro-crystallites embedded in an amorphous glassy matrix. The expansion coecient of the crystalline regions is negative, i.e. those parts shrink upon heating. However, the glassy regions have a positive expansion coecient and therefore conventionally expand upon heating. By adjusting the volume ratio of both parts an expansion coecient of α≈0 can be reached over a suciently large temperature range.
how crystallization is connected to vitrication and dynamical heterogeneity [15, 16].
Simulations suggest that crystallization plays a key role for the glass transition [16].
H. Tanaka et al. propose that 'liquids tend to order into the equilibrium crystal, but frustration eects of locally favored short-range ordering on long-range crystalline ordering prevent crystallization and help vitrication'.