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