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M. Svrˇ cek
properties such as volume, energy (latent heat), and viscosity. This is a transition
between states of thermodynamic equilibrium at a single, well-defined temperature
and is time reversible. In the second case there is no first-order phase transition, no
latent heat and no well-defined temperature: the slower the cooling, the lower the
transition temperature. This is a non-equilibrium and irreversible process forming a
quenched disorder state, kinetically locked. Its entropy, density and structure depend
on the thermal history. By extrapolating the heat capacity of the supercooled liquid
below its glass transition temperature, it is possible to calculate the Kauzmann temperature [149] at which the difference in entropy between the liquid and solid phase
becomes zero. Cooling below this temperature leads to the Kauzmann paradox: A
supercooled liquid displays a lower entropy than the crystal phase. This paradox
was not resolved till now, although there are several proposals how to deal with it.
Kauzmann himself postulated that all supercooled liquids must crystallize before
the Kauzmann temperature is reached. But the scientific community has no unique
opinion.
The most striking enigma of the liquid–glass transition is this: If we use classical physics for its calculation, i.e. classical thermodynamics and thermodynamics of
irreversible processes, we end up with the Kauzmann paradox and the negative residual entropy at absolute zero. But on the other hand if we perform the computation of
energy landscapes based on the concept of broken ergodicity in the configurational
phase space with an entropy loss, a glass does not appear to have any residual entropy
at absolute zero. Anderson was inspired by this controversy so utterly that he wrote
[150]: “The deepest and most interesting unsolved problem in solid state theory is
probably the theory of the nature of glass and the glass transition.”
Different results from macroscopic and microscopic calculations imply that the
physical microscopic description in this case does not reveal all facts about the
macroscopic world. Simply the macroscopic and microscopic entropies are not the
same. The irreversible and the non-equilibrium processes behind the glass transition
are chemical reactions, giving rise to the creation of anisotropic covalent bonds in
polymorphic forms of glass. Analogous to the case of Pauling’s ice, we need here a
separation of the physical microscopic entropy from the megascopic chemical one,
in order not to violate the third law of thermodynamics.
Another paradox arises from the query: do chemical reactions exist on the macroscopic level? A nice example of the type C → A + B is brittle fracture. Unlike
ductile fracture this effect has no microscopic quantum explanation and is described
phenomenologically only by classical physics. Once a crack starts to propagate in
a brittle solid its velocity may quickly reach unbelievable several thousands of m/s
[151], whereas in ductile fracture there is only a slow propagation of the crack. Further differences are [152]: Ductile material fractures after plastic deformation and
its surface obtained at the fracture is dull or fibrous in appearance. A ductile crack
will usually not propagate unless an increased stress is applied and generally cease
propagating when loading is removed. On the other hand, brittle fractures are characterised as having little or no plastic deformation prior to failure and the fracture
surface of a brittle failure is usually reasonably smooth. The cracks that propagate
in a brittle material will continue to grow once initiated. Although brittle fracture
M. Svrˇ cek
properties such as volume, energy (latent heat), and viscosity. This is a transition
between states of thermodynamic equilibrium at a single, well-defined temperature
and is time reversible. In the second case there is no first-order phase transition, no
latent heat and no well-defined temperature: the slower the cooling, the lower the
transition temperature. This is a non-equilibrium and irreversible process forming a
quenched disorder state, kinetically locked. Its entropy, density and structure depend
on the thermal history. By extrapolating the heat capacity of the supercooled liquid
below its glass transition temperature, it is possible to calculate the Kauzmann temperature [149] at which the difference in entropy between the liquid and solid phase
becomes zero. Cooling below this temperature leads to the Kauzmann paradox: A
supercooled liquid displays a lower entropy than the crystal phase. This paradox
was not resolved till now, although there are several proposals how to deal with it.
Kauzmann himself postulated that all supercooled liquids must crystallize before
the Kauzmann temperature is reached. But the scientific community has no unique
opinion.
The most striking enigma of the liquid–glass transition is this: If we use classical physics for its calculation, i.e. classical thermodynamics and thermodynamics of
irreversible processes, we end up with the Kauzmann paradox and the negative residual entropy at absolute zero. But on the other hand if we perform the computation of
energy landscapes based on the concept of broken ergodicity in the configurational
phase space with an entropy loss, a glass does not appear to have any residual entropy
at absolute zero. Anderson was inspired by this controversy so utterly that he wrote
[150]: “The deepest and most interesting unsolved problem in solid state theory is
probably the theory of the nature of glass and the glass transition.”
Different results from macroscopic and microscopic calculations imply that the
physical microscopic description in this case does not reveal all facts about the
macroscopic world. Simply the macroscopic and microscopic entropies are not the
same. The irreversible and the non-equilibrium processes behind the glass transition
are chemical reactions, giving rise to the creation of anisotropic covalent bonds in
polymorphic forms of glass. Analogous to the case of Pauling’s ice, we need here a
separation of the physical microscopic entropy from the megascopic chemical one,
in order not to violate the third law of thermodynamics.
Another paradox arises from the query: do chemical reactions exist on the macroscopic level? A nice example of the type C → A + B is brittle fracture. Unlike
ductile fracture this effect has no microscopic quantum explanation and is described
phenomenologically only by classical physics. Once a crack starts to propagate in
a brittle solid its velocity may quickly reach unbelievable several thousands of m/s
[151], whereas in ductile fracture there is only a slow propagation of the crack. Further differences are [152]: Ductile material fractures after plastic deformation and
its surface obtained at the fracture is dull or fibrous in appearance. A ductile crack
will usually not propagate unless an increased stress is applied and generally cease
propagating when loading is removed. On the other hand, brittle fractures are characterised as having little or no plastic deformation prior to failure and the fracture
surface of a brittle failure is usually reasonably smooth. The cracks that propagate
in a brittle material will continue to grow once initiated. Although brittle fracture