Pressure-induced liquid-liquid transition in a family of ionic materials

Liquid−liquid transition (LLT) between two disordered phases of single-component material remains one of the most intriguing physical phenomena. Here, we report a first-order LLT in a series of ionic liquids containing trihexyl(tetradecyl)phosphonium cation [P666,14]+ and anions of different sizes and shapes, providing an insight into the structure-property relationships governing LLT. In addition to calorimetric proof of LLT, we report that ion dynamics exhibit anomalous behavior during the LLT, i.e., the conductivity relaxation times (τσ) are dramatically elongated, and their distribution becomes broader. This peculiar behavior is induced by isobaric cooling and isothermal compression, with the τσ(TLL,PLL) constant for a given system. The latter observation proves that LLT, in analogy to liquid-glass transition, has an isochronal character. Finally, the magnitude of discontinuity in a specific volume at LLT was estimated using the Clausius-Clapeyron equation.

W hen isotropic liquid is cooled below the melting point, it either solidifies into a crystal or enters into a metastable supercooled state, which then enters a nonequilibrium amorphous phase at the glass transition temperature T g 1 . The characteristic feature of the latter transformation is a continuous increase of density, accompanied by a slowing down of molecular dynamics and enormous elongation of structural relaxation times: from the time scale of picoseconds at T m up to hundreds of seconds in the vicinity of T g 2 . If cooled rapidly enough, nearly all materials can be transformed into an amorphous form. Thus, the glass-forming ability can be considered as a universal property of condensed matter.
Over the years, such a well-established physical picture of the liquid state has been upended by numerous examples of two distinct liquid phases in single-component materials. The firstorder liquid-liquid transition (LLT), separating fluids of different local structures, density, magnetic susceptibility and thermodynamic properties, has been reported for various systems, including atomic elements (sulfur, phosphorus 3 , silicon 4,5 , carbon 6 and strongly interacting liquids 7 , such as molten oxides 8,9 , e.g., Al 2 O 3 -Y 2 O 3 10 . Only four molecular liquids (water 11,12 , triphenyl phosphite (TPP) [13][14][15] , n-butanol 16 , and D-mannitol 17 have been found with compelling evidence for LLT. Nevertheless, the LLT in these systems remains controversial since it occurs in the supercooled state capable of cold crystallization 18 . The theoretical and experimental observations show that a first-order LLT can occur without a noticeable density change, making this phenomenon even more puzzling 19 . Furthermore, magnetic field can affect the local structure and lead to another liquid phase 20 . It was reported that an aligned liquid state of Co alloys can be transformed into another liquid phase under magnetic fields 21,22 . At the same time, except for a few cases 6,7,23,24 not much is known about the effect of molecular packing on LLT. Consequently, it has not been clarified how universal the LLT is and what is the critical factor inducing such a transition. Since it has been difficult to identify other examples of LLT in a systematic fashion, the experimental verification of these problems poses a great challenge.
Aprotic ionic liquids (AILs)-a class of glass-formers composed solely of ions 25 , give a unique opportunity to investigate the universality of LLT. The most interesting feature of AILs is that their structural and transport properties can be finely tuned within a wide range by the combination of different positively and negatively charged ions 26 . Thereby, a vast structural diversity of ionic species and various types of competing intermolecular interactions (van der Waals, H-bonding and Coulomb forces), make AILs excellent materials to probe the mechanism underpinning LLT. Furthermore, several previous studies show unique ordering behavior of ionic liquid, namely formation of nanoscale domains of polar and nonpolar groups [27][28][29] , that potentially can lead to LLT. However, over the years there was no proof of LLT in ILs capable for domains formation. The first report on LLT in ionic liquid has been provided very recently by Harris et al. for an AIL with a tetraalkylphosphopnium cation 30 . At a specific temperature, trihexyl(tetradecyl)phosphonium borohydride, noted as [P 666,14 ][BH 4 ], was found to undergo enhanced ordering of the alkyl chains in the nonpolar domains. Such a structural reorganization coincides well with the first-order thermodynamic transition, visible in calorimetric, XRD and IR spectroscopy data.
Motivated by this work, we embarked on a quest to identify not an isolated example but a systematically studied family of compounds that would exhibit LLTs, thereby gaining an insight into the structure-property relationships governing the LLT formation. Furthermore, by monitoring the relaxation dynamics of selected AILs under high-pressure conditions, we addressed the long-standing questions regarding the effect of compression on LLT and density fluctuations at T LL .
We designed six AILs based on the [P 666,14 ] + cation, combined with six different anions (chemical structures shown in Fig. 1). The [P 666,14 ][BH 4 ] was also examined as a reference. The commonly used phosphonium cation imparted the AILs a relatively high thermal and electrochemical stability, as well as decent ionic conductivity and apolar/polar solvation ability 31 . Anions have been selected to reflect differences in size, geometry, conformational flexibility and coordinating ability (i.e., Lewis basicity

Results and discussion
Calorimetric studies of phase transitions. To firmly establish the LLT scenario, it is desirable to show its reversibility without crystallization. For this purpose, we firstly analyzed the conventional differential scanning calorimetry (DSC) thermograms obtained on cooling and subsequent heating of tested materials (Fig. 2a) Table 1 The thermodynamic characterization of studied systems. anions appears at the same temperature for given IL (T ± 1 K), with the only difference in ΔH, i.e., the lower the ramp rate, the higher the ΔH value (see Table 1). However, even the highest obtained ΔH is still around five times lower than the enthalpy of melting process ΔH m obtained, e.g., for [P 666,14 ][BF 4 ]. Note that phase 2 observed below the endotherm is an optically transparent homogenous disordered phase, as confirmed by microscopic observations. These findings lead to conclusion that the  Fig. 2a and Supplementary Fig. 30). However, T g does not appear on thermogram of any other examined IL. Since an amorphous phase has a non-equilibrium nature, its thermodynamic and dynamic properties (e.g., the specific volume, enthalpy or relaxation dynamics) evolve over time 33 . This phenomenon, known as physical aging, is accompanied by an increase of heat capacity in the glass transition region (so-called overshoot peak) and therefore can be useful to reveal T g of [P 666,14 ] + -based ILs. Therefore, in the further step, aging experiments have been performed on all [P 666,14 ] + ILs, excluding that of [BF 4 ] − anion, to confirm that cooling transforms liquid 2 to the glassy state. The experimental protocol of aging involves: (i) decreasing temperature to 183 K (the T expected to fall below T g ), (ii) time-dependent isothermal step at this T, and (iii) subsequent heating. The thermograms corresponding to the final heating scans are compared with data obtained in standard DSC measurement in Fig. 2b [BOB]. The values of T g determined from the heating scan of aged glass with the rate of 10 K min −1 and the onset points of LLT are collected in Table 1.  To verify whether the LLT manifests itself in molecular dynamics behavior, the dielectric measurements over a wide frequency (10 −2 -10 7 Hz) and temperature range were performed. For ionic systems, the translational displacement of charge carriers (dc-conductivity) dominates the dielectric loss ε″(f) function, conventionally employed for data analysis 34 . Therefore, complex electric conductivity σ*(f) = ε 0 (Z*(f)C 0 ) −1 and complex electric modulus M*(f) = ε*(f) −1 , are usually adopted to express their dielectric properties 35 . The latter formalism allows for the determination of three relevant quantities describing the ion dynamics in AILs: dc-conductivity σ dc = 2πfε 0 (M″) −1 calculated from a low-frequency region of M″(f); conductivity relaxation times τ σ = (2πf max ) −1 determined directly form M″ maximum; and distribution of relaxation times reflected in the width of M″(f) peak. Therefore, this representation was selected to evaluate the data recorded in this work. [P 666,14 ][BF 4 ] has been excluded from these studies due to the high tendency to crystallization. Figure 3a shows the representative electric modulus spectra of [P 666,14 ] [TFSI] collected at 0.1 MPa and various temperatures. This graph shows that the M″(f) peak (denoted as σ-process or conductivity relaxation peak), describing the time scale of translational motions of ions, shifts to lower frequencies upon cooling. This gradual change is in keeping with cooling effects seen in other ionic systems and reflects ions' suppressed mobility 36 . However, starting from a certain temperature, coinciding well with the calorimetric LLT, the temperature sensitivity of the σ-process becomes markedly stronger while the M″ peak is broadening significantly. . For the latter ILs, the temperature decrease brings a usual slowing down of ion dynamics, i.e. the M″(f) peak is keeping the same shape over a broad T range (see Fig. 3b).
To quantify changes in the shape of conductivity relaxation peak across the LLT, the Kohlrausch function, ϕðtÞ ¼ exp½Àðt=τ α Þ β KWW 37 , has been used (exemplary fitting curves are presented in Fig. 3a, b). The β KWW parameters obtained from fitting of M″ peaks are plotted as a function of the frequency of M ″ peak maximum (f max ) in Fig. 3c. It is well-known that the broader and more asymmetric the peak is, the lower is the value of β KWW . As shown in Fig. 3c, for a given IL, the exponent characterizing the liquid 1 stays approximately constant and falls in the range 0.62 < β KWW < 0.67, which is in the middle of the range reported for various ionic glass-formers 38  Interestingly, this order corresponds well with the decrease of enthalpy accompanying LLT. The obtained results indicate that the distribution of the relaxation times becomes broader during the transformation from liquid 1 to liquid 2. In other words, in liquid 1 the species are more dynamically correlated (i.e., components relax with similar τ σ ), whereas in phase 2 there is higher heterogeneity (i.e., some components are more mobile and some are less mobile). This result is in agreement with dielectric data measured across LLT for TPP 39 .
At the same time, the LLT of [P 666,14 ][BOB] is not detectable on β KWW (f max ) graph mainly because the transition to liquid 2 overlaps with the liquid-glass transition, where the conductivity relaxation is too long to be directly measured (f max (T g ) = 1.6·10 −3 Hz) Consequently, the dielectric response of liquid 1 is recorded over the entire available frequency range, i.e., from 10 6 to 10 −2 Hz. In this context, it is not surprising that the shape of M″ (f) function collected for [P 666,14 ][BOB] is invariant, i.e., satisfy the time-temperature superposition (TTS) rule being a typical behavior of glass-forming systems in a supercooled state.
The temperature dependence of conductivity relaxation times τ σ (T −1 ), calculated directly from the modulus peak maxima, also exhibits a peculiar behavior near the calorimetric LLT (Fig. 3d). In particular, τ σ collected in liquid 1 reveals a typical non-Arrhenius behavior, and a substantial departure from the Vogel-Fulcher-Tammann (VFT) law occurs at the onset of phase transition; that is, an abrupt increase is observed in apparent activation energy. A closer inspection of Fig. 3d reveals that the values of τ σ (T LL ) are in the range 0.3-15 ms for most of the studied AILs that is far from the time scale commonly identified with the liquid-glass transition (τ σ = 100 s). The LLT is also clearly detectable when the Stickel operator, [dlogτ σ /d1000T −1 ] −0.5 , is applied; such procedure gives two linear regions that intersect at T LL (Supplementary Fig. 34). Notably, the sign of LLT is also detectable in dc-conductivity (σ dc ) behavior. As shown in Supplementary Fig. 35, further cooling of ILs below LLT brings a change of σ dc (T −1 ) from VFT to Arrhenius behavior observed at σ dc = 10 −14 S cm −1 , which is commonly accepted as the value characterizing T g . Note that T g values determined as a crossover point of σ dc (T −1 ) dependencies are in good agreement with calorimetric T g of aged glass (see Table 1).
As could be expected from raw dielectric spectra, the logτ σ (T −1 ) and σ dc (T −1 ) data obtained for [P 666,14 ][BOB] do not reveal any peculiar behavior. Namely, the experimental points follow a single VFT equation in almost the whole examined temperature range. The only deviation from VFT to Arrhenius dependence occurs at σ dc = 10 −14 S/cm and indicates the liquid-glass transition (see Fig. 3d and Supplementary Fig. 35).
The LLT under high-pressure conditions. Although rapid cooling is probably the most straightforward method for inducing a first-order phase transition, it is not the only route. The LLT of phosphorus 40 Fig. 4a (see Supplementary Note 2 for all collected high-pressure data). The observed pattern of behavior upon compression is analogous to the isobaric cooling experiment: despite maintaining the same pressure step, after reaching certain pressure the shifts in f max are markedly faster. Also, the shape of the M″(f) peak behaves similarly to the ambient pressure experiment-during the isothermal compression, past certain pressure, the peaks broaden significantly. A direct comparison of the spectra collected at given f max under various T-P conditions shows that the shape of the σ-relaxation is independent of thermodynamic variables if phase 1 is considered ( Fig. 4b and Supplementary Fig. 38). Such a phenomenon, called the temperature-pressure superposition principle, is a typical feature of glass-forming materials 42 . However, for superimposed spectra of liquid 2, the shape of M″(f) function at a given value of τ σ becomes narrower with increasing T and P. In other words, compression at higher temperatures reduces the distribution of relaxation times in phase 2, making it more homogenous in terms of molecular dynamics. The same pattern has been detected for [P 666,14 ][TFSI]; however, the dielectric spectra of [P 666,14 ][TAU] are getting slightly broader under pressure. In contrast, the σdispersion in [P 666,14 ][BOB] has been constant at any chosen τ σ (see Fig. 4c and Supplementary Fig. 38). Consequently, the changes of M″(f) peak with pressure cannot be treated as a feature unique to [P 666,14 ] + ILs, but rather as a unique characteristic of the liquid-liquid transformation. This peculiar behavior is, to some extent, similar to the effect of pressure on polymerization reactions when the material of a narrower distribution of molecular weight is obtained under higher pressure 43 .
The analysis of isothermal τ σ -P dependences determined for the studied ILs reveals another intriguing feature of the LLT. As illustrated in Fig. 5a, isothermal compression has fundamentally 3.6 4.   [TFSI] markedly rise in slope at certain P bringing an almost four-fold increase in apparent activation volume V # = 2.303RT(dlogτ σ / dP) T . (Fig. 5b). However, what is interesting, the kink of the τ σ -P curve, being a manifestation of LLT, is independent of T-P conditions and appears at constant conductivity relaxation times for a given system; specifically, at τ σ of milliseconds. This result shows that in analogy to liquid-glass transition, the L-L transformation is isochronal in nature. Nevertheless, the time scale of ion dynamics at LLT, τ σ (T LL ,P LL ) is not universal but depends on intermolecular interactions.
Defining P LL as the pressure at which the activation volume starts to increase, we obtain the pressure dependence of T LL plotted in Fig. 5c. As presented, T LL increases with pressure in a linear fashion, with the slope equal to 81 K GPa . It means that the pressure in the order of 1.2 GPa is required to observe the LLT at room temperature conditions. Interestingly, when the isothermal τ σ (P) data are extrapolated to τ σ = 100 s (that is a standard definition of T g , i.e. T g = T(τ σ = 100 s) or σ dc = 10 −14 S cm −1 , non-linear T g (P) dependences with the dT g /dP coefficient of 125 ± 5 K GPa − [TAU] was slightly lower (106 K GPa −1 ), but still much higher than dT LL /dP.
The [TAU] respectively. To put these numbers into perspective, we measured the density of these ILs as a function of temperature and extrapolated the obtained dependence to T LLT (see Supplementary Fig. 39). Such procedure gives V LLT = 0.8759 cm 3  , indicating that changes of around 0.5% occur at LLT, that is within the error in dilatometric measurements. These small variations in the specific volume can be easily overlooked in direct V(T,P) measurements and reveal that density is not the dominant order parameter governing the LLT in ILs. This is in agreement with the experimental data recorded for sodium acetate trihydrate (CH 3 COONa·3H 2 O) where a first-order LLT without density discontinuity was identified 19 . Moreover, LLTs without density change were suggested to take place in several metallic glass-formers 44 .
In summary, our findings provide experimental support for the hypothesis that the LLT occurs in ion-containing systems. [BOB], the LLT overlaps with the liquid-glass transition. Interestingly, T g is approximately the same for all studied AILs, while T LL is decreasing with an increase of anion van der Waals volume. This demonstrates that ILs can be fine-tuned to display T LL , which is dependent on several parameters, such as anion size, geometry, conformational flexibility, Lewis basicity and the strength of interionic interactions. In this context, the question about the differences between liquid structures formed by [P 666,14 ] + -based AILs appears and should be addressed in the future e.g. by using SAXS or neutron scattering.
Our study also provides an important approach to the LLTcorrelated properties. We found that the parameters characterizing the ion dynamics (τ σ , σ dc ) and distribution of relaxation times (β KWW ) monitored on isobaric cooling and isothermal compression reveal peculiar behavior at the LLT. Furthermore, independently of T-P conditions, the sign of LLT is observed at τ σ = const. within a given system, i.e., it occurs at a certain time scale of ionic motions dependent on interionic interactions. Further studies of this issue e.g. by using dynamic light scattering (DLS) under high pressure conditions are desired. Upon transition liquid 1→liquid 2 (induced by cooling or highpressure), the AILs become more heterogeneous in terms of ion recorded at various T-P conditions however at the same τ σ superimposed to each other in liquid 1 and liquid 2, respectively. Note that time temperature pressure superposition (TTPS) rule is valid. c The β KWW exponent is plotted as a function of the frequency of modulus peak maximum at various thermodynamic conditions. IBA denotes 0.  30-80°C), and the crude product was dissolced in dry acetonitrile and stored in the fridge (5°C, 12 h) until the excess taurine crystallised and was filtered off. Acetonitrile was removed via rotary evaporation (30 min, 60°C) and the ionic liquid was dried under high vacuum (overnight, 70°C, 10 -2 mbar). The product was analysed 1H, 13C and 31P NMR spectroscopy (d6-DMSO) and by XRF for chloride content. [Cl] (0.10 mol eq.) and Na[BH 4 ] (0.13 mol eq.) were separately dissolved in deionised water, combined in a round-bottomed flask, and left to react (48 h, RT, 600 rpm). Chloroform was added to dissolve the ionic liquid layer, and the aqueous layer was separated. The organic layer was washed ten times with Na[BH 4 ] solution, then chloroform was removed via rotary evaporation (30 min, 35°C) and the solution was dried overnight under high vacuum (12 h, 70°C, 10 −2 mbar). Chloride removal was carried out in three subsequent polishing steps (multiple sodium borohydride washes) until chloride content was below 2000 ppm by XRF analysis.
[P 666,14 ][BOB]. Was synthesized in a two-step synthesis. Firstly, oxalic acid (0.03 mol eq.) and boric acid (0.01 mol eq.) were separately dissolved in water and then combined under vigorous stirring. Na 2 CO 3 (0.5 mol eq.) was slowly added and the turbid solution was heated in an oil bath at 120°C. Water was distilled off until a dry white powder was obtained, which then was dispersed in hot acetonitrile (60°C, 1 h), filtered, washed with cold ethanol and finally dried overnight under high vacuum (12 h, 60°C, 10 −2 mbar). Subsequently, [P 666,14 ][Cl] (0.01 mol eq.) and Na[BOB] (0.01 mol eq.) were stirred in dichloromethane (overnight, RT, 600 rpm) and then water was added, inducing phase separation. The organic layer was separated and washed with solution of Na[BOB] in deionized water, then with deionised water, until no chloride could be detected with silver nitrate solution. Subsequently, DCM was removed via rotary evaporation (30 min, 35°C) and the ionic liquid was dried overnight under high vacuum (12 h, 60°C, 10 −2 mbar). For more details see Supplementary Information file.
Differential scanning calorimetry (DSC). Calorimetric experiments of studied ILs were performed by means of a Mettler Toledo DSC1STAR System equipped with a liquid nitrogen cooling accessory and an HSS8 ceramic sensor (a heat flux sensor with 120 thermocouples). Each sample with a mass of around 10-20 mg was measured in aluminum crucibles with a 40 μL volume. During the experiments, the flow of nitrogen was kept at 60 mL min -1 . Enthalpy and temperature calibrations were performed using indium and zinc standards. Low-temperature verification was made using CCl 4 and n-heptane (182.15 K, 140.5 J g −1 ) at different scanning rates (0.7, 1, 5, and 10 K min −1 ). The baseline was constructed as a straight line from the onset to the endpoint. A dedicated software Mettler Toledo DSC1STAR allows various calculations (onset, heat, peak temperature, etc.) from the original  (from left to right respectively). a Presents the pressure dependence of conductivity relaxation time measured at various T. Solid lines denote the pVFT fit τ σ ¼ τ 0 expð BP P 0 ÀP Þ to experimental data. Dashed lines indicate liquid-liquid transition pressure (P LL ) and τ σ at LLT. P g denotes liquid-glass transition pressure. b Presents pressure dependence of apparent activation volume, V # . The four-time increase in V # at LLT indicates a formation of nonpolar domains of large scale in liquid 2. c T LL and T g as a function of P is presented. The color area on a and c denotes the liquid 1 phase (gray) and glass region (blue). L1 denotes liquid 1 while L2 liquid 2. Source data are provided as a Source Data file.
recorded DSC curves. Prior to the measurement, the samples were annealed 30 min at 373 K. Temperature ramps involved cooling to 143 K and then heating to 373 K with a rate of 10 K per min. Samples were cycled at least 3 times to ensure reproducibility and high accuracy. The 6-h aging experiment was performed at 183 K after cooling with the rate of 10 K min −1 .
Dielectric measurements. The dielectric measurements at ambient pressure for studied ILs were carried out over a frequency range from 10 −1 Hz to 10 7 Hz by means of Novo-Control GMBH Alpha dielectric spectrometer. The Novocool system controlled the temperature with an accuracy of 0.1 K. During this measurement the sample was placed between two stainless steel electrodes (diameter = 15 mm). The distance of 0.08 mm was provided by the quartz ring. For the pressure-dependent dielectric measurements, we used the capacitor filled with the studied sample, which was next placed in the high-pressure chamber and compressed using silicone oil. Note that during the measurement, the sample was only in contact with stainless steel. The pressure was measured by the Unipress setup with a resolution of 1 MPa. The temperature was controlled within 0.1 K by means of a Weiss fridge.

Data availability
All data generated or analyzed during this study are included in this published article (and its Supplementary information files). Source data are provided with this paper.