Phase diagram of a solution undergoing inverse melting
aa r X i v : . [ c ond - m a t . s o f t ] F e b Phase diagram of a solution undergoing inverse melting
R. Angelini , G. Ruocco , , S. De Panfilis and F. Sette Research center SOFT INFM-CNR,Universit`a di Roma ”La Sapienza” I-00185, Roma, Italy. Dipartimento di Fisica,Universit`a di Roma ”La Sapienza” I-00185, Roma, Italy. European Synchrotron Radiation Facility B.P. 220 F-38043 Grenoble, Cedex France.
The phase diagram of α -cyclodextrin/water/4-methylpyridine solutions, a system undergoing in-verse melting, has been studied by differential scanning calorimetry, rheological methods, and X-raysdiffraction. Two different fluid phases separated by a solid region have been observed in the high α -cyclodextrin concentration range ( c ≥
150 mg/ml). Decreasing c , the temperature interval where thesolid phase exists decreases and eventually disappears, and a first order phase transition is observedbetween the two different fluid phases. PACS numbers: 61.10.Nz, 61.25.Em, 64.70.-p
Inverse melting indicates the counter-intuitive phe-nomenon of the solidification of a liquid upon heating.This phenomenon implies the existence of solids with en-tropy higher than their liquid counterparts, and this isrecently attracting the attention of both theoretical andexperimental works [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. A list ofmaterials showing inverse melting are reported in ref. [6].Theoretical studies, due to the difficulties of describ-ing real systems, developed different ad-hoc models. Allthese models allow for the competition between differentinterparticle multiple interactions, a feature which maylead to ”crystal” with an entropy content higher than thecorresponding ”liquid”. Examples are: i) a spin model forfragile glass-forming liquids [7]; ii) spin glasses [6, 8, 9];and iii) particles interacting with a specific model poten-tial [10]. These studies derive the temperature vs crystalfield phase diagrams, which turn out to be characterizedby: i) an inverse transition from a paramagnetic phase toa glass [7], or to a spin glass [6, 8, 9] phase for certain val-ues of the crystal field; ii) a reentrance in the transitionline [6, 7, 8, 9]; and iii) a first-order transition line be-tween two paramagnetic phases ending in a critical pointat high values of the crystal field [7].On the experimental side, real systems showing in-verse melting, also display complex and exotic phase di-agrams due to the variety of microscopic interactions.This, together with the extreme thermodynamic condi-tions often required, prevents comprehensive investiga-tions of the inverse melting phenomenon. With this re-spect, a particularly interesting system is the solutionscomposed of α -cyclodextrin ( α CD) (C H O ), waterand 4-methylpyridyne (4MP) (C H N). This system hasbeen recently discovered by Plazanet et al. [11] to un-dergo inverse melting at easily accessible thermodynamicconditions. These solutions, in fact, show a ”low tem-perature” liquid (LTL) phase which solidifies upon heat-ing [11, 12, 13] into a high temperature crystal phase(HTC). Therefore, they provide an ”ideal” situation tostudy experimentally the variety of phenomenologies re-cently predicted theoretically. In this work, using differential scanning calorime-try, rheological methods and X-rays diffraction, we fur-ther investigate the phase diagram of α -cyclodextrin( α CD) (C H O ), water and 4-methylpyridyne (4MP)(C H N) solutions, extending the concentration and tem-perature ranges with respect to previous studies. At α CDconcentrations c ≥
150 mg/ml we find that the ”high tem-perature” crystal (HTC), if further heated, melt into afluid phase, that we refer to as the ”high temperature”fluid (HTF). By decreasing the concentration, the tem-perature range of existence of the HTC decreases, andeventually disappears, and we observe a phase transitionbetween two fluid phases. Specifically, we found that:i) in the range of concentration c ≥
150 mg/ml of α CDin 4MP, two fluid phases exist in two different tempera-ture ranges, separated by a temperature interval wherethe material is in a crystalline phase, ii) at concentrationsmaller than 150 mg/ml, the crystal phase is no longerobservable and the two fluids are contiguous in the phasediagram, and iii) the phase transition between the twofluids is of first order nature.Differential scanning calorimetric (DSC) measure-ments, using a Diamond Perkin-Elmer calorimeter, havebeen used to locate the different phase transitions, andto measure the latent heat of transformation. Sealedstandard aluminium sample pans with a volume of 10and 50 µ l have been used as cells and references. Sam-ples have been prepared using alpha-cyclodextrin hydrate(Aldrich), water and 4MP (Aldrich) at different concen-trations with molar ratios respectively of 1:6:x, and xvarying between 30-200. The powder was dispersed in4MP and water and then stirred for almost 4 hours untilthe suspensions were cleared. The thermograms shown inFig 1, i.e. the heat flows ( dH/dt ) as a function of temper-ature, have been obtained at a heating rate r =10 K/min.The measurements were repeated at least five times foreach concentration, and all transitions have been foundto be reproducible and reversible.In the concentration region 170-340 mg/ml of α CD in4MP, as shown in Fig. 1, three endothermic peaks are de-
310 320 330 340 350 360 370 380
258 mg/ml
T (K)
204 mg/ml
147 mg/ml172 mg/ml h ea t f l o w ( a r b . un it s ) E ndo up
338 mg/ml
FIG. 1: DSC thermograms of solutions of α CD-water-4MP atthe indicated concentrations of α CD in 4MP and at a heatingrate r = 10 K/min. The transition peaks are indicated by thearrows. tected on increasing temperature: the first one, signatureof inverse melting, corresponds to the LTL-HTC transi-tion [11], the intermediate one has been associated to asolid-solid transition between two of the five crystallinephases detected by X-rays on similar samples [14]. Thethird one corresponds to the melting of HTC into theHTF phase.The solid and liquid nature of the HTC, LTL and HTFphases have been assessed by visual inspection. Thetransition temperatures, as determined from the ther-mograms, are shown as a function of the concentrationin Fig. 2. The temperatures of the peak (T peak ) and ofthe onset (T onset ) are shown as full circles and squaresrespectively, and provide a range for the absolute valueof the transition temperatures. In the high concentrationrange, the phase diagram in Fig. 2, beside reproducingthe known inverse melting LTL-HTC transition, also re-ports the melting of the crystal in the high temperaturefluid, HTF. At lower concentrations, below and close to c =150 mg/ml, not only the intermediate solid-solid tran-sition is no longer visible, but the whole solid phase disap-pears and the LTL-HTC and HTC-HTF transition linesmerge into each other. Most importantly, as shown inFig. 3, for concentration c ≤
130 mg/ml, the thermogramsshow only one well defined peak.
Liquid(LTL) Fluid(HTF) Solid 2
Solid 1(HTC) T ( K ) concentration (mg/ml) Diffraction r = 6 k/h DSC onset r = 10 k/min DSC peak r = 10 k/min
FIG. 2: Phase diagram of α CD-water-4MP solutions. Thetransition temperatures obtained with DSC measurements ata heating rate r = 10 K/min are plotted as a function of theconcentration of α CD in 4MP. The full squares and the fullcircles represent the onset and the peak transition tempera-tures respectively. The error bars are calculated through thestandard deviation on five measurements at the same concen-tration. The transition temperatures as obtained by X raydiffraction measurements are also shown: the full trianglesand the empty stars represent respectively the temperaturesof the jump in the Q position of the first maximum and firstminimum of the scattered intensity shown in Fig. 4. OurDSC and X ray data are also compared with previous neu-tron scattering measurements on similar samples [11] (opencircles), performed at a heating rate r = 6 K/h.
The endothermic peak of Fig. 3 is observable down to c =50 mg/ml of α CD in 4MP, and below this concentra-tion it falls below the sensitivity of the present experi-ment. The peak area is reported in the inset of Fig. 3as a function of the α CD/4MP mass ratio. These dataindicate the decrease of the heat necessary to the systemto complete the LTL-HTF transition.A different rheological behavior between the LTL andHTF is also observed in the shear dependent viscositymeasurements reported in Fig. 4. In Fig. 4A, as an ex-ample, we report shear viscosity measurements as a func-tion of shear rate at c=125 mg/ml in the HTF (circles)and LTL (squares) phases, which show an opposite be-havior: shear thinning for the HTF and shear thickeningfor the LTL. In Fig. 4B we report shear viscosity mea-surements at almost the same temperatures of Fig. 4A fora much lower concentration sample, c=50 mg/ml, in theLTL phase, the behavior is again shear thickening-like.In conclusion, the HTF is structurally different from theLTL.The phenomenology described so far provides only a
340 360 38002040
50 mg/ml86 mg/ml103 mg/ml108 mg/ml129 mg/ml
T(K) N o r m a li ze d h ea t f l o w ( K ) E ndo up r = 10K/min Concentration (mg/ml) N o r m a li ze d a r ea ( K ) FIG. 3: Normalized DSC thermograms of α CD-water-4MPsolutions. The measurements have been performed at theindicated concentrations of α CD in 4MP and at a heating rater = 10 K/min. A peak of endothermic nature is observed, andis associated to a phase transition between the LTL and HTFdisordered fluid phases. In the inset, the normalized area ofthe peaks is shown as a function of concentration togetherwith a guideline to the eyes. The error bars represent thestandard deviation on five measurements performed at thesame concentration. macroscopic description of the two liquid phases, with-out suggestion on how they differ from each other atthe microscopic level. In order to investigate this point,the HTF and LTL phases have been studied by X-raydiffraction. The experiment has been performed on thebeamline BM29 at the European Synchrotron RadiationFacility, using 15 keV ( λ = 0.86 ˚ A ) incident photons.The samples were contained in a 2 mm diameter boro-silicate capillary. The scattered intensity was collectedusing a MAR345 image plate detector, and the geomet-rical parameters were calibrated via Ag standard. Thedata analysis was performed using the FIT2D softwarepackage [15]. We investigated three α CD-water-4MPsolutions with c =50, 86 and 108 mg/ml. As an exam-ple, data at c =108 mg/ml and in the temperature range295 ÷
413 K are shown in Fig. 5 after empty cell subtrac-tion. The diffraction data, I(Q), reproduce the typicalshape of the static structure factor of a liquid, both be-low and above the LTL-HTF transition. More important,the temperature dependence of I(Q) shows changes in the Q -region of the first minimum and first maximum.In order to qualitatively represent the temperaturechanges of the structural features we arbitrarily selectedtwo representative Q points. Namely, we chose the Q positions of the first maximum (around Q = 13 nm − ) -4 -3 -2 -1
125 mg/ml
50 mg/ml h ( P a s ) g (s -1 ) (B) -3 -2 -1
293 K373 K293 K
371 K(A)
FIG. 4: (Colors online) Viscosity as a function of the shearrate at the two indicated concentrations. The samples at c=50mg/ml (T=293K, T=373K) and c=125 mg/ml (T=293K) inthe LTL phase show shear thickening while the sample c=125mg/ml T=371K in the HTF phase shows shear thinning. Asshown in panel (A) the viscosity profile is perfectly reversibleand it can be obtained by increasing (full symbols) or bydecreasing (open symbols) the applied shear rate.. and minimum (around Q = 4 nm − ), identified as Q A and Q B . The Q values of these two points are reportedin the insets of Fig. 5 as a function of temperature forthe three investigated concentrations. Each curve showsa jump at the temperatures which are reported (stars) inthe phase diagram of Fig. 2. They, within the error bars,are in agreement with the DSC measurements. We alsonote that the amplitude of the jumps in Fig. 5 are morepronounced at the higher concentration, suggesting, sim-ilarly to the inset of Fig. 3, that the phase transitionline between the LTL and HTF tends to disappear onlowering c . The present diffraction data do not allow todetermine the structure of the LTL and HTF phases atthe molecular level, although they clearly underline thepresence of a marked structural difference. These resultstherefore stimulate further experimental and theoreticalinvestigations. In particular a point which needs to beassessed and which cannot be completely excluded on thebasis of the present measurements, is the presence of aphase separation in the HTF.In conclusion, combined DSC, shear viscosity and Xray diffraction studies on a molecular solution undergo-ing inverse melting, allowed us to observe the existenceof two fluid phases in two different temperature ranges
10 20 30 Q B ( n m - ) Q A ( n m - )
50 mg/ml86 mg/ml108 mg/ml86 mg/ml
50 mg/ml
108 mg/ml
300 350 40012.513.013.5
T (K)300 350 400 345 B T = 295 K T = 313 K T = 343 K T = 358 K T = 363 K T = 368 K T = 373 K T = 393 K T = 413 K
108 mg/ml I( Q ) ( a r b . un it s ) Q(nm -1 ) A FIG. 5: (Colors online) Scattered intensity from a solutionof α CD, water and 4MP. The measurement has been done atthe concentration 108 mg/ml of α CD in 4MP as a functionof temperature in the range 295 ÷
413 K. In the inset theQ-position of the maxima Q A (left panels) and the minimaQ B (right panels) of the scattered intensity are plotted as afunction of temperature for the three indicated concentrationsof α CD in 4MP. The arrows indicates the LTL-HTF transitiontemperature as derived by DSC. separated by a temperature interval where the materialis in a crystalline phase. Most importantly, by chang-ing the α CD concentration control parameter, we iden-tify the existence of a region in the phase diagram wheretwo contiguous fluid phases are separated by a first orderphase transition line. These experimental results can beframed within the recent theoretical prediction of inversemelting in a spin model for fragile glasses [7]. They alsocall for further experimental and simulation works aim-ing to understand the interacting mechanism leading tosuch phenomenology.R.A. thanks L. Leuzzi for discussions. [1] S. Rastogi, M. Newman, and A. Keller, Nature , 55(1991).[2] S. Rastogi, G. W. H. H¨ohne, and A. Keller, Macro-molecules , 8897 (1999).[3] A. L. Greer, Nature , 134 (2000).[4] O. Portmann, A. Vaterlaus, and D. Pescia, Nature ,701 (2003).[5] F. H. Stillinger and P. G. Debenedetti, Biophys. Chem. , 211 (2003).[6] N. Schupper and N. M. Shnerb, Phys. Rev. E , 046107(2005).[7] M. Sellitto, PRB , 180202(R) (2006).[8] N. Schupper and N. M. Shnerb, Phys. Rev. Lett. ,037202 (2004).[9] A. Crisanti and L. Leuzzi, Phys. Rev. Lett. , 087201 (2005).[10] M. R. Feeney, P. G. Debenedetti, and F. H. Stillinger, J.Chem. Phys. , 4582 (2003).[11] M. Plazanet, C. Floare, M. R. Johnson, R. Schweins, andH. Trommsdroff, J. Chem. Phys. , 5031 (2004).[12] R.Angelini and G.Ruocco, Phil. Mag. , 553 (2007).[13] E. Tombari, C. Ferrari, G. Salvietti, and G. P. Johari, J.Chem. Phys. , 051104 (2005).[14] M. Plazanet, M. Dean, M. Merlini, H. Huller,H. Hemerich, C. Meneghini, M. Johnson, andH. Trommsdroff, J. Chem. Phys. , 154504 (2006).[15] A. P. Hammersley, S. O. Svensson, M. Hanfland, A. N.Fitch, and D. Husermann., High Pres. Res.14