The phenomenon of inverse melting happens when a liquid heated at constant pressure undergoes a reversible liquid-to-crystal transition [1,2]. Such a transition of endothermic nature implies the passage from a low-temperature liquid (LTL) to a high-temperature crystal (HTC) with absorption of heat. This behaviour, which is the opposite to what is expected for common liquids, indicates the presence of a crystal with entropy higher than its liquid counterpart. On further heating, the HTC may eventually melt into a high temperature liquid (HTL).

Using differential scanning calorimetry (DSC) and X-ray diffraction methods we have investigated the phase diagram of a system belonging to this class of materials, a solution of -cyclodextrin (CD) (C36H60O30), water and 4-methylpyridine (4MP) (C6H7N) [3]. DSC measurements were performed to determine and characterise the inverse phase transitions from an energetic point of view. The measurements of heat absorption as a function of the temperature show peaks of endothermic nature. In Figure 59 the temperature of the peak (Tpeak) and of the onset (Tonset) are reported as full circles and squares respectively.

Fig. 59: Phase diagram of CD-water-4MP solutions. The transition temperatures obtained with the DSC measurements at a heating rate r = 10 K/min are reported as a function of the concentration. The full squares and the full circles represent the onset and the peak transition temperature respectively. The open circles are obtained from neutron scattering measurements of ref. [3] performed at a heating rate r = 6 K/hour. The stars and triangles represent the transition temperatures obtained by the X-ray static structure factors of Figure 60. They are associated to the jump of the Q position of the first maximum and first minimum respectively of the integrated scattered intensity I(Q) of Figure 60.

In the concentration region 150-350 mg/ml of CD-in 4MP three endothermic transitions are observed on increasing the temperature: the first corresponds to the LTL-HTC, the second has been associated to a solid-solid transition, the third corresponds to the HTC-HTL transition. At decreasing CD concentration, in the region 50-150 mg/ml, the solid region becomes thinner until it disappears and single endothermic transition peak is observed. This experimental observation is compatible with a direct LTL-HTL transition.

In order to give a microscopic interpretation of the behaviour of the liquid and to investigate its local structure in the low concentration region, an X-ray diffraction experiment was performed as a function of the temperature along the LTL-HTL transition on the beamline BM29. Three different concentrations of CD in 4MP have been investigated. An example of the integrated scattered intensity I(Q) at the concentration 108 mg/ml and in the temperature range 295 to 413K is reported in Figure 60. It confirms the existence of a disordered structure both below and above the transition temperature detected by DSC. The temperature evolution of the structure of the liquid has been followed looking at the Q position of the first maximum (around Q = 13 nm-1) and minimum (around Q = 4 nm-1) of the I(Q) respectively identified as positions QA and QB. The Q values of these two points reported as a function of temperature in the insets of Figure 60 show a jump at the temperatures corresponding to the LTL-HTL transition, as derived by the DSC measurements. The three transition temperatures for the maxima (full triangle) and the minima (full stars) of I(Q) reported on the phase diagram of Figure 59 show a good agreement.

Fig. 60: Integrated scattered intensity from a solution of CD-water-4MP at the concentration 108 mg/ml of CD-in 4MP in the temperature range 295K-413K The insets show the Q position of the maxima QA (top panel) and the minima QB (bottom panel) of the integrated scattered intensity reported as a function of the temperature at the indicated concentration.

The combination of DSC and X-ray diffraction allowed us to draw the phase diagram of a solution undergoing inverse melting and to characterise the microscopic local different structure of the two disordered liquid phases, the LTL and the HTL, observed in the low concentration region.



[1] A. Lindsay Greer, Nature 404, 134 (2000).
[2] A. Crisanti and L. Leuzzi, Phys. Rev. Lett. 95, 087201 (2005) and references within.
[3] M. Plazanet , C. Floare, M.R. Johnson, R. Schweins, and H.P. Trommsdroff, J. Chem. Phys. 121, 5031 (2004).

Principal Publication and Authors

R. Angelini (a), G. Ruocco (a,b), S. De Panfilis (c), F. Sette (c), submitted.
(a) CRS SOFT- INFM-CNR, Università “La Sapienza”, Roma (Italy)
(b) Dipartimento di Fisica, Università “La Sapienza”, Roma (Italy)
(c) ESRF