SUPPLEMENTARY INFORMATION

Transcription

1 Liquid liquid transition without macroscopic phase separation in a water glycerol mixture Ken-ichiro Murata and Hajime Tanaka Institute of Industrial Science, University of Tokyo, Komaba, Meguro-ku, Tokyo , Japan The relationship between liquid-liquid transition and cubic ice formation. Nanocrystal formation upon LLT is observed not only in a water-glycerol mixture but also in TPP [1, 2], n-butanol [3] and germanium [4]. In the case of a binary mixture (unlike the case of a single component liquid), however, there is a possibility that the transition we observe is not LLT, but merely phase separation induced by cubic ice formation (a crystallization-induced phase separation scenario). This possibility cannot simply be denied since the lines of the homogeneous nucleation temperature T H reported by Kanno [5] and MacKenzie [6] are located near the spinodal line of LLT, as shown in Fig. S1. In this scenario, spinodal-decomposition-like LLT is regarded to be a result of homogeneous nucleation of cubic ices. However, we note that nucleation of spherical droplets formed at T > T SD (see Fig. 1a), which consist of a newly emerged liquid phase and nm-sized cubic ices, is difficult to explain by this scenario. In this scenario, the glycerol-rich liquid phase after cubic ice formation looks as if it were liquid II even though there is no LLT and, thus, it should actually be liquid I. It is crucial to exclude this possibility for verifying that what we observe is truly LLT. Below we show a few pieces of experimental evidence excluding such a possibility and demonstrate that the transition we observed is genuine (isocompositional) LLT. Figure S2a and b show the annealing temperature T a dependence of the heat evolution during LLT and the enthalpy difference, H, between liquid I and II, respectively. The transformation kinetics slows down and H decreases with decreasing T a, which is consistent with the behaviour of LLT in TPP [2]. In particular, the decrease of H (Fig. S2b) indicates the decrease in the amount of the cubic ices formed during LLT with a decrease in T a. Around T L = K, the enthalpy change H almost reaches the value of the HDA/LDA transition in pure water [7]. Thus, we expect that pure liquid II without cubic ices is formed below T L, although the very slow kinetics prevents us from confirming this experimentally. NATURE MATERIALS 1

2 Liquid I (HDL-like) Homogeneous nucleation line (Stability limit of liquid I against crystallization) Liquid II (LDL-like) SD NG Stabiliy limit of liquid I against LLT T N [Kanno] T N [MacKenzie] Figure S1: Comparison between LLT spinodal T SD and homogeneous nucleation temperature T H in c T state diagram. T SD : LLT spinodal temperature (black filled circles); T H : homogeneous nucleation temperature (purple filled circles: the data of Kanno [5]; open circles: MacKenzie [6]); T m : the melting (liquidus) temperature (black filled squares: our data; open squares: the data of Lane [8]). a b T L Heat release from HDA/LDA transition Figure S2: Annealing temperature (T a ) dependence of heat release during LLT. a, The heat evolution H(t) estimated from DSC measurements for LLT observed at various T a for c = b, The enthalpy change H as a function of T a, indicating the suppression of cubic ice formation with decreasing T a. The red solid curve is a guide for the eye. Around T L = K, H almost reaches that of the HDA/LDA transition in pure water [7]. This conclusion is also directly confirmed by small (SAXS) and wide angle X-ray scattering (WAXS) measurements (see Fig. S3a and b). We found that both low q upturn of 2 NATURE MATERIALS

3 SUPPLEMENTARY INFORMATION I(q) in SAXS and the sharp Bragg peak in WAXS, which are signals from nm-size cubic ices, monotonically decrease with decreasing T a : As shown in Fig. S3b, the volume fraction of cubic ices in the liquid II phase, φ c, and the scattering intensity at q =0.15nm 1, I(q =0.15nm 1 ), both decrease with decreasing T a and almost disappear around T L = 161 K, indicating that the amount of nm-size cubic ices in liquid II becomes zero around that temperature, which almost coincides with T L = K independently estimated from DSC measurements (see above). This should be regarded as a good coincidence on noting that the temperature of the DSC and X-ray scattering systems is calibrated independently. a b Ta=170 K Ta=166 K Ta=162 K Ta=170 K Ta=166 K Ta=162 K T L Figure S3: Annealing temperature (T a ) dependence of X-ray spectra of liquid II. a, The scattering function I(q) of liquid II formed at T a = 162, 166, and 170 K for c = Here we note that we vary only T a under the same composition (c =0.178), that is, the initial liquid I being annealed has the same composition. The inset shows those in a wide angle regime (linear plot). Red solid curves are the results of the fitting for the total signal by Eqs. (5). b, The volume fraction of cubic ices in the liquid II phase, φ c, (black filled circle, left axis) and the scattering intensity at q =0.15 nm 1, I(q =0.15 nm 1 ), (blue filled circle, right axis) as a function of T a. Here we choose the value of q =0.15 nm 1 rather arbitrarily. These results clearly indicate the decrease in the amount of cubic ices included in the liquid II phase with decreasing T a. The red solid curve is a guide for the eye. Both values approach zero towards T L = 161 K, suggesting the formation of pure liquid II without cubic ices below T L. NATURE MATERIALS 3

4 a b c TL H TgII TL T gii 174 K Genuine liquid II L TgII T gii Genuine liquid II 161 K Figure S4: Annealing temperature (T a ) dependence of calorimetric behaviour of liquid II around the glass transition temperature. a, Reversible heat flow of liquid II formed at various T a for c = b, TgII L (blue filled circle) and T gii H (black filled circle) as a function of T a, which are estimated from the results of a. The red and light blue solid curves are a guide for the eye. c, The temperature width of glass transition, T gii = TgII H T gii L, as a function of T a. The red and light blue solid curves are a guide for the eye. We also check the dynamical nature of liquid II by ac DSC measurements of the glass transition temperature and the glass transition width for samples prepared at various T a. Figure S4a shows the reversible heat flow of liquid II around its glass transition temperature. The average, period, and amplitude of the modulated heating rate were 1 K/min, 60 s, and 0.16 K, respectively. Figure S4b shows the T a dependence of the high and low edge temperatures of the glass transition of liquid II, TgII L and T gii H, whereas Fig. S4c shows the T a dependence of the temperature width of the glass transition of liquid II, T gii = TgII H T gii L. The glass transition temperature of liquid II, particularly, TgII L, decreases with decreasing T a, which is partly a result of the decrease in the glycerol concentration of the liquid component reflecting the decrease in the amount of cubic ices formed at lower T a. The glass transition temperatures of pure liquid II without cubic ices are estimated as TgII L (T L) =161 K and TgII H (T L) =174 K. Although the difference in Tg L between liquid I and liquid II becomes smaller with a decrease in T a (note that the glass transition temperatures of liquid I are TgI L =157 K and T gi H =163 K), T gii of liquid II largely increases with a decrease in T a and finally reaches 13 K (note that T gi = 6 K). This means that liquid II becomes stronger, i.e., less fragile, with decreasing T a. In other words, the difference in the fragility between liquid I and II is more pronounced for more pure liquid II containing less cubic ices. In the phase separation scenario, however, the system after transformation should approach 4 NATURE MATERIALS

5 SUPPLEMENTARY INFORMATION pure liquid I with decreasing T a as a consequence of less cubic ice formation, which should result in the increase in the fragility. Thus, the phase separation scenario cannot explain the stronger nature of more pure liquid II and we conclude that the transition we observe should be genuine LLT. We note that nanocrystal formation during LLT is widely observed in various systems such as TPP [1, 2], n-butanol [3], and germanium [4], which may be related to a lower liquid-crystal interface energy for liquid II than for liquid I. This problem needs further study. The difference between liquid-liquid transition and polyamorphic phase separation (phase separation induced by solvent LLT) We also discuss a possibility that the transition we observe is not LLT but polyamorphic phase separation. Here we address the case of water/licl solutions studied by Mishima as an example [9]. Mishima experimentally found that a polyamorphic transition (LLT) of water induced phase separation between LDA with little or no solute and HDA with more solute, which was theoretically supported by Chatterjee and Debenedetti [10]. Expanding this finding, crystallization to ice I c or I h at a higher temperature regime would be considered as a result of polyamorphic phase separation (strictly speaking, phase separation induced by solvent LLT) since, at the higher temperatures, separated LDL easily transforms to ice due to the structural similarity [11]. In other words, (hidden) phase separation induced by LLT can be the Ostwald stage prior to cubic ice crystallization. According to this scenario, cubic ice formation in our system may be regarded as a consequence of phase separation induced by LLT of the solvent (water). This scenario, however, can be excluded by the same consideration described in the previous section. If the transition we observe is phase separation induced by solvent LLT, the residual liquid component without ice I c should be HDL (liquid I), which is inconsistent with our experimental finding that the residual liquid component is actually LDL (liquid II) having composition identical to that of the parent liquid I (at least until cubic ice starts to form within it) but lower density. Thus, in addition to the discussion of the type of order parameter describing the transition, we may say that the transition we observed is not a polyamorphic phase separation but rather an isocompositional LLT. NATURE MATERIALS 5

6 Evidence for the decrease in tetrahedral order of water with an increase in the glycerol concentration from Raman spectroscopy measurements. Here we show a strong indication for the decrease in tetrahedral order with an increase in the glycerol concentration c, which was provided by Raman spectroscopy measurements in a heavy water/glycerol mixture [12]. Walrafen [13] reported that the T -dependence of the OH stretching Raman spectrum provides information key to the two-state model of water. The low-frequency shoulder of the OH stretching Raman spectrum has been used as a probe of in-phase collective motions specific to tetrahedrally coordinated water structures. Recent numerical simulations supported this view by comparing the distribution of the tetrahedral order parameter q of a model water (SPC/E) with the shape of Raman spectra [14]. a Pure D2O b c=0.02 c c=0.12 d c=0.32 Figure S5: c-dependence of the polarized Raman spectra of a mixture of glycerol and D 2 O. The Raman spectra were taken from Ref. [12]. D 2 O was used to separate O-D stretching modes of water from O-H stretching modes of glycerol. Red curves are results of the fitting for the total signal by Eq. (1). Blue curves are attributed to the OD stretching mode in ice-like tetrahedral ordering whereas green curves are attributed to those in disordered configurations. Note that the peak around 2780 cm 1 is from glycerol and not from D 2 O. The area fraction of the Raman modes associated with tetrahedral order was estimated as 0.31 for pure water, 0.25 for c =0.02, 0.19 for c =0.12, and 0.16 for c =0.32. The results clearly indicate the decrease of tetrahedral order with an increase in c. 6 6 NATURE MATERIALS

7 SUPPLEMENTARY INFORMATION We reanalysed the Raman spectra measured by Mudalige and Pemberton [12] by fitting the following function (so called pseudo-voigt function) to the spectra: I(ν) = 3or4 i=1 [ A i µ 2 γ i + (1 µ) π 4(ν ν i )+γi 2 4 ln 2 πγi ( exp 4 ln 2 γi 2 (ν ν i ) 2 ) ], (1) where I(ν) is the Raman spectrum, ν the Raman frequency, ν i the peak position of peak i, A i the integral amplitude, γ i the peak width, and µ the mixing ratio between Gaussian (µ = 0) and Lorentzian (µ = 1). We set µ =0.5, following [12]. The results are shown in Fig. S5. We note that our fitting results are almost identical to those by Mudalige and Pemberton [12]. The decrease of the lowest frequency Raman mode (blue curve) with an increase in c suggests that the addition of glycerol indeed decreases tetrahedral structural order in water: Addition of glycerol to water plays the similar role as applying pressure to it, although the former has local effects and the latter has global effects. Protocol for dielectric measurements of liquid I. In the temperature range shown in Fig. 2a, liquid I is metastable or unstable against liquid II. Thus it is necessary to measure the dielectric spectra of liquid I before the transformation starts to proceed. It takes 5 min to obtain the dielectric spectra covering the frequency range from 10 mhz to 1 MHz. This duration of 5 min is short enough to avoid effects of liquidliquid transformation (e.g., it takes 220 min for the completion of the transformation at 167 K (see Fig. 3b). Thus, we quenched a system to a given temperature and right after the quench we performed a dielectric measurement. Once the transformation was initiated, we heated up the sample above the melting temperature at which liquid I is stable. Then we repeated this procedure to obtain the spectra shown in Fig. 2a. We confirmed whether the transformation starts or not, by checking both dielectric spectra and patterns observed with phase-contrast microscopy. Analysis of dielectric spectra of liquid I and II. We analysed the temperature dependences of dielectric spectra of liquid I and II by fitting the following function to the data: ɛ (ω) =ɛ + ɛ α 1+(iωτ α ) + ɛ β βcc 1+(iωτ slowβ ) i σ dc βcc ɛ 0 ω, (2) where ɛ is the relaxation strength, τ is the relaxation time, β cc is the shape parameter NATURE MATERIALS 7

8 which represents the distribution of the relaxation time, ɛ is the high frequency limit of dielectric constant, σ dc is the dc conductivity, and ω =2πf is the angular frequency (f: the frequency). τ α and τ slowβ denote the α and Johari-Goldstein (JG) (or slow β) process, respectively. Here note that, for liquid II (see in Fig. 2c), the two relaxation processes merge around 190 K. The dielectric spectrum above this merging temperature becomes an asymmetric single peak, and thus we employed the following single Havriliak-Negami function instead of Eq. (2) above K: ɛ (ω) =ɛ + ɛ (1+(iωτ) β ) δ i σ dc ɛ 0 ω, (3) where β is the broadness parameter and δ the asymmetry parameter. For liquid I, its relaxation processes can always be fitted by Eq. (2) in the measured temperature range. The examples of the fittings for the dielectric loss spectra of for liquid I and II are shown in Fig. S6. a Liquid I K (c=0.178) b Liquid II 182 K (c=0.178) I JG I II JG II dc I dc II ( /Hz) ( /Hz) Figure S6: Examples of the functional fittings for the dielectric loss spectra of liquid I and II. a, Dielectric loss spectrum of liquid I at K (c =0.178). b, Dielectric loss spectrum of liquid II at 182 K (c =0.178). Red curves are fits to the data by Eq. (2) and green curves represent the contributions from the α process, the Johari-Goldstein (or slow β) process, and the dc conductivity, respectively (see Eq. (2)). Analysis of the wide angle X-ray scattering spectra, I(q), of liquid I and II. We analysed the wide angle X-ray scattering spectra, I(q) (5 nm 1 <q<27 nm 1 ), of 8 NATURE MATERIALS

9 SUPPLEMENTARY INFORMATION liquid I and II by fitting the following functions to the spectra: I I (q) = I II (q) = 2 i=1 3 i=1 2B i π 2B i π γ i, (4) 4(q q i )+γi 2 γ i ( 2 (q q 4) 2 ), (5) 4(q q i )+γ 2 i + B 4 γ 4 π/2 exp γ 2 4 where I I (q) and I II (q) are the scattering functions of liquid I and II, respectively. Here q i, B i, and γ i are the position, the amplitude, and the width of peak i, respectively. The results for liquid I and II are shown in Fig. S7. a b Liquid I Liquid II Figure S7: Examples of the decomposition of the wide-angle X-ray scattering spectra I(q) of liquid I and II. a, I(q) of liquid I at 167 K (c =0.178). Red curve is the result of the fitting for the total signal by Eq. (4). Green curves show the Lorentzian peaks obtained by decomposing the total signal into the individual peaks. b, I(q) of liquid IIat167K(c =0.178). Red curve is the result of the fitting for the total signal by Eq. (5). The dark blue curves represent the Gaussian and Lorentzian peaks from ice I c (the Bragg peaks at 16.1 and 16.9 nm 1, respectively), whereas the light blue curves represent those from liquid II. The behaviour of the Johari-Goldstein (slow β) relaxation. As observed in other supercooled liquids, the slow β process blow T g almost obey the Arrhenius law: τ slowβ = τ β 0 exp( E a /RT ), where E a is the activation energy for the relaxation process and R the gas constant. The slow β processes of both liquids share the NATURE MATERIALS 9

10 common nature of the Johari-Goldstein β process of water [15], which originates from noncooperative, local orientational motion of single water molecules. The activation energy E a are estimated as 20.9 and 15.5 kj/mol for liquid I and II, respectively. We note that these values are comparable to that obtained from a nanoconfined water ( 20.1 kj/mol) [16] at lower temperatures. It should be noted that for liquid II, τ slowβ has a non-monotonic T -dependence. The origin of this behaviour is not clear at this moment, but the similar behaviour was also observed in other molecular liquids [17, 18]. This issue may be related to the way of the fitting analysis of dielectric spectra. In the region where we see the peculiar behaviour, the two spectra, the structural relaxation (α) mode and the Johari-Goldstein (or, slow β) mode, are largely overlapped. The decomposition of these spectra is thus a bit tricky, which is a common problem in many dielectric spectroscopy studies in literature. Thus, the results might depend upon the choice of the functional forms of spectra and parameters (including the way of constraints on them) (see, e.g., Refs. [19, 20]). However, we have confirmed that the results of the structural relaxation time are very robust, not dependent on the ways of analysis. We reanalyze the data carefully by using a few different fitting methods and confirmed that the non-monotonic behaviour is also not due to an artefact and is rather robust. Polarized Raman spectrum of liquid II without the contribution of nanocrystalline ice I c. According to the results in Fig. 3c and d, the Raman spectra shown in Fig. 3a should also be composed of the contributions from liquid II and nanocrystallites. Thus we decompose the spectra of liquid II into these two contributions by using the molar fraction of ice I c included in liquid II, φ m. From the wide-angle X-ray scattering measurements, we obtain the volume fraction of ice I c, φ Ic = A Ic /A tot = 0.17, in liquid II (see Fig. S3b). Then the molar fraction of nanocrystallites, φ m, can be estimated from the relation φ m =(ρ c M/ρII M w )φ Ic, where ρ Ic and ρ II are the density of cubic ice (we used ρ Ic =0.95 g/cm 3 ) and liquid II, respectively, and M and M w are the averaged molecular weight of the solution and water (ice), respectively. We used M = 31.2 and M w = The value of ρ II is unknown, but we may assume ρ Ic <ρ II <ρ I, from the fact that tetrahedral ordering more develops in liquid II than in 10 NATURE MATERIALS

11 SUPPLEMENTARY INFORMATION liquid I. We also confirmed ρ II <ρ I by visual observation of volume expansion during the transformation from liquid I to II. In the above, ρ I was estimated by a linear extrapolation of high temperature data as ρ I =1.2 g/cm 3. Using these bounding values for ρ II, we obtain the fraction of water molecules in I c as % and hereafter we take the middle value φ m = 32 %. In Fig. S8, we show the Raman spectrum of liquid II including ice I c, that of pure liquid II extracted by the spectrum decomposition, and that of LDA of pure water. We can see that the spectrum of the pure liquid II is almost identical with that of LDA of pure water, considering the additional contribution from the OH-stretching modes of glycerol molecules in the frequency range from 3200 cm 1 to 3600 cm 1. This further supports a link between LLT in a water/glycerol mixture and the transition between HDL and LDL of pure water. Figure S8: Raman spectra of liquid II. Pure liquid II (red line), liquid II containing cubic ice I c (blue line), and LDA of pure water (black line) [21]. Glycerol concentration vs temperature (c T ) state diagram of light water/glycerol and heavy water/glycerol mixtures. Here we show the c-t state diagrams of light water/glycerol and heavy water/glycerol mixtures. All the characteristic temperatures for the heavy water system shift towards higher temperatures than those for light water, due to the stronger hydrogen bonding ability of the former. The significant shift of T SD by deuteration clearly indicates that LLT is primarily induced by the local structural ordering of water molecules rather than glycerol molecules. NATURE MATERIALS 11

12 The trend is consistent with the difference in the P -T phase diagram between light and heavy water [22]. Relying on the similarity between our state diagram and the P -T phase diagram of pure water, we locate an LLT critical point on the extrapolated spinodal line at the same temperature as that for pure water estimated by Mishima [23] (P 0.05 GPa and T 223 K for light water; P 0.05 GPa and T 230 K for heavy water). Although there is no firm basis for this, the critical molar fraction c c estimated in this way (c c =0.032 for a light water/glycerol mixture; c c =0.051 for a heavy water/glycerol mixture) are not so unrealistic, on noting that the melting point at c c, T m (c c ) = 270 K, agrees well with that at critical pressure T m (P c ) = 269 K (for heavy water, T m (c c ) = 270 K, T m (P c ) = 273 K). Figure S9: c T state diagram of light water/glycerol (black symbols) and heavy water/glycerol mixtures (blue symbols). T SD : LLT spinodal temperature; T gi : the glass transition temperature of liquid I (For pure water (c = 0), we use the widely accepted value of T gi, 136 K [22]), T gii : the glass transition temperature of liquid II; T X : the transition temperature from ice I c to I h, which was determined from microscopy observation; T m : the melting (liquidus) temperature (full and open squares are for our data and the data of Lane [8], respectively). We make a linear extrapolation of T SD to locate the position of the hypothetical critical point (CP), which is shown by open circle. 12 NATURE MATERIALS

13 SUPPLEMENTARY INFORMATION [1] Tanaka, H., Kurita, R. & Mataki, H. Liquid-liquid transition in the molecular liquid triphenyl phosphite. Phys. Rev. Lett. 92, (2004). [2] Kurita, R. & Tanaka, H. Kinetics of the liquid-liquid transition of triphenyl phosphite. Phys. Rev. B 73, (2006). [3] Kurita, R. & Tanaka, H. On the abundance and general nature of the liquid-liquid phase transition in molecular systems. J. Phys.: Condens. Matter. 17, L293 L302 (2005). [4] Bhat, M. H. et al. Vitrification of a monatomic metallic liquid. Nature 448, (2007). [5] Miyata, K. & Kanno, H. Supercooling behavior of aqueous solutions of alcohols and saccharides. J. Mol. Liq. 119, (2005). [6] Rasmussen, D. H. & MacKenzie, A. P. Water Structure at the Water-Polymer Interface (Plenum Press, 1972). [7] Loerting, T., Kohl, I., Schustereder, W., Winkel, K. & Mayer, E. High density amorphous ice from cubic ice. ChemPhysChem 7, (2006). [8] Lane, L. B. Freezing points of glycerol and its aqueous solutions. Ind. Eng. Chem. 17, 924 (1925). [9] Mishima, O. Phase separation in dilute LiCl-H 2 O solution related to the polyamorphism of liquid water. J. Chem. Phys. 126, (2007). [10] Chatterjee, S. & Debenedetti, P. G. Fluid-phase behavior of binary mixtures in which one component can have two critical point. J. Chem. Phys. 124, (2006). [11] Mishima, O. Application of polyamorphism in water to spontaneous crystallization of emulsified LiCl-H 2 O solution. J. Chem. Phys. 123, (2005). [12] Mudalige, A. & Pemberton, J. E. Raman spectroscopy of glycerol/d 2 O solutions. Vib. Spectrosc. 45, (2007). [13] Walrafen, G. E. Raman spectral studies of the effects of temperature on water structure. J. Chem. Phys. 47, (1967). [14] Paolantoni, M., Lago, N. F., Albertí, M. & Laganà, A. Tetrahedral ordering in water: Raman profiles and their temperature dependence. J. Phys. Chem. A 113, (2009). [15] Capaccioli, S., Ngai, K. L. & Shinyashiki, N. The johari-goldstein β relaxation of water. J. Phys. Chem. B 111, (2007). NATURE MATERIALS 13

14 [16] Liu, L., Chen, S. H., Faraone, A., Yen, C. W. & Mou, C. Y. Pressure dependence of fragileto-strong transition and a possible second critical point in supercooled confined water. Phys. Rev. Lett. 95, (2005). [17] Olsen, N. B. Scaling of β-relaxation in the equilibrium liquid state of sorbitol. J. Non-Cryst. Solids , (1998). [18] Dyre, J. C. & Olsen, N. B. Minimal model for beta relaxation in viscous liquids. Phys. Rev. Lett. 91, (2003). [19] Tanaka, H. Origin of the excess wing and slow β relaxation of glass formers: A unified picture of local orientational fluctuations. Phys. Rev. E 69, (2004). [20] Tanaka, H. Reply to gcomment on eorigin of the excess wing and slow β relaxation of glass formers: A unified picture of local orientational fluctuationsfh. Phys. Rev. E 70, (2004). [21] Suzuki, Y. & Tominaga, Y. Polarized raman spectroscopic study of relaxed high density amorphous ices under pressure. J. Chem. Phys. 133, (2010). [22] Debenedetti, P. G. Supercooled and glassy water. J. Phys.: Condens. Matter 15, R1669 R1726 (2003). [23] Mishima, O. Volume of supercooled water under pressure and liquid-liquid critical point. J. Chem. Phys. 133, (2010). 14 NATURE MATERIALS