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Scientific Report 2007-2009
Condensed matter physics and biophysics
C10. Order in disorder: investigating fundamental mechanisms of
inverse transitions
Reversible Inverse Transitions (IT) are rare phenomena
recently observed in a widespread class of materials.
The hallmark is that what is usually considered
the “frozen” phase, that in standard systems appears as
the temperature is lowered and is stable down to zero
temperature, melt at low temperature. The typical case
is the transition occurring between a solid and a liquid
in the inverse order relation relatively to standard transitions.
The case of “ordering in disorder”, occurring
in a crystal solid that liquefies on cooling, is generally
termed inverse melting. If the solid is amorphous the IT
is termed inverse freezing (IF).
For the definition of IT we stick to the one hypothesized
by Tammann: a reversible transition in temperature
at fixed pressure - or generally speaking, at a
fixed parameter tuning the interaction strength externally,
such as concentration, chemical potential or magnetic
field - whose low temperature phase is an isotropic
fluid. Generalizing to non-equilibrium systems one can
address as IT also those cases in which the isotropic fluid
is blocked in a glassy state. This occurs, e.g., in the
poly(4-methylpentene-1) - P4MP1 as the temperature is
very low and pressure not too large and in molecular dynamics
simulations and mode-coupling computations of
attractive colloidal glasses.
With this definition IT is not an exact synonym of
reentrance. Indeed, though a reentrance in the transition
line is a common feature in IT’s, this is not always
present, as, e.g., in the case of α-cyclodextrine or methylcellulose
solutions for which no high temperature fluid
phase has been detected. Moreover, not all re-entrances
are signatures of an IT. In liquid crystals, ultra-thin films
and other materials phases with different kind of symmetry
can be found that are separated by reentrant isobaric
transition lines in temperature without any occurrence
of melting to a completely disordered isotropic phase.
Also re-entrances between dynamically arrested states,
aperiodic structures or amorphous solids of qualitatively
similar nature, like liquid-liquid pairs are not considered
as IT, since an a-priori order relationship between the
entropic content of the two phases is not established and
it cannot be claimed what is inverse and what is ”standard”.
For the same reasons also re-entrances between
equilibrium spin-glass and ferromagnetic phases do not
fall into the IT category.
IT’s are observed in different materials. The first
examples were the low temperature liquid and crystal
phases of helium isotopes He 3 and He 4 . A more recent
and complex material is methyl-cellulose solution in
water, undergoing a reversible inverse sol-gel transition.
Other examples are found in P4MP1 at high pressure,
in solutions of α-cyclodextrine and 4-methypyridine in
water, in ferromagnetic systems of gold nanoparticles
and for the magnetic flux lines in a high temperature
superconductor. A thourough explanation of the fundamental
mechanisms leading to the IT would require a
microscopic analysis of the single components behavior
and their mutual interactions as temperature changes
accross the critical point. Due to the complexity of
the structure of polymers and macromolecules acting
in such transformations a clear-cut picture of the state
of single components is seldom available. For the case
of methyl-cellulose, where methyl groups are distributed
randomly and heterogeneously along the polymer chain,
Haque and Morris proposed that chains exist in solution
as folded hydrophilic bundles in which hydrophobic
MGs are packed. As T is raised, bundles unfold, exposing
MGs to water molecules and causing a large increase
in volume and the formation of hydrophobic links eventually
leading to a gel condensation. The polymers in
the folded state are poorly interacting but also yield a
smaller entropic contribution than the unfolded ones.
To model the folded/unfolded conformation bosonic
spins can be used: s = 0 representing inactive state,
s ≠ 0 interacting ones. The randomness on the position
of the ”interaction carrying” elements is mimicked by
quenched disorder.
In the latter years we have focused the study on the
disordered spin models and the IF has been observed in
the spin-glass mean-field Blume-Emery-Griffiths-Capel
models with spin−1 variables. We have also considerd
the random Blume-Capel model, whose mean-field
solution predicts a phase diagram with both a spin
glass/paramagnetic second order and a first order phase
transition, i.e., displaying latent heat and phase coexistence.
This model is characterized by the phenomenon
of IT.
The connection of the mean-field solution with the
finite dimensional case in spin glass models is still an
open probles. This to go beyond the mean-field solution
recently we have studied [1] the three dimensional
version of the Blume-Capel model finding clear evidence
for inverse freezing. The next step, taht we are taking, is
studying a realistic computer model inspired to material
for which experimental evidence has been collected
in favour of an inverse transition, such as the poly(4-
methylpentene-1) polymer. This work is still in progress.
References
1. A. Crisanti, et al., Phys. Rev. B 76, 184417 (2007).
2. A. Crisanti, et al., Phys. Rev. B 75, 144301 (2007).
Authors
A. Crisanti, L. Leuzzi 2 , M. Paoluzi
Sapienza Università di Roma 63 Dipartimento di Fisica