Dynamic Crossover of Water Relaxation in Aqueous Mixtures: Effect of

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Dynamic Crossover of Water Relaxation in Aqueous Mixtures: Effect of Pressure K. Grzybowska,* M. Paluch, A. Grzybowski, and S. Pawlus Institute of Physics, University of Silesia, ul. Uniwersytecka 4, 40-007 Katowice, Poland

S. Ancherbak, D. Prevosto, and S. Capaccioli CNR-IPCF and Dipartimento di Fisica, Universit a di Pisa, Largo B. Pontecorvo 3, I-56127, Pisa, Italy

ABSTRACT In this Letter, we present results of dielectric measurements of water-propylene glycol oligomer mixtures at ambient and high pressure. The ν relaxation process that emerges with the addition of water exhibits unexpected behavior at elevated pressure. These features indicate local motions of water molecules as the origin of this relaxation process. In addition, we observe a pressure-induced change of the dynamics in the water-related relaxation; such a crossover occurs near the glass transition of the mixture and significantly differs from properties observed for confined water. SECTION Macromolecules, Soft Matter

(e.g., in molecular sieves) and the only relaxation observed in other water confinements (e.g., in clays).6 The relaxation of supercooled highly confined water exhibits an intriguing behavior with decreasing temperature, that is, a super-Arrhenius to Arrhenius transition also called a fragile-to-strong (FS) transition, which is observed usually at temperatures Tcross inside of the “no man's land” region and dependent on the geometry, size, and material of confinement.7-10 The origin of the water dynamic crossover in confined systems has different interpretations. (i) Swenson et al.10 claim that the FS transition is apparent. The crossover is due to merging of the primary and secondary relaxations at high temperatures and a confinement-induced collapse of the strongly cooperative primary R process near Tcross. Therefore, at T < Tcross, only the secondary process is effectively observed.11 Similar interpretation can be found in ref 12, where the dynamic crossover is ascribed to a finite size effect on water R relaxation in correspondence to the mixture vitrification. (ii) On the other hand, Liu et al.13 state that the transition from the Vogel-Fulcher-Tamman (VFT) to Arrhenius behavior concerns the structural relaxation of confined water, and it is a signature of FS dynamic transition predicted by Ito et al. and Sastry for bulk water.14,15 Moreover, they attribute the fragile behavior at high T to the high-density liquid (HDL) state where the locally tetrahedral H-bonded network is not fully formed, whereas the strong behavior at low T has been assigned to the low-density liquid (LDL), where this structure of the H-bonded network is fully developed. Studying the effect of pressure on the dynamic crossover (in the relatively narrow

T

he explanation of anomalous thermodynamic and dynamic properties of water is a particularly important assignment for researchers. The mysterious properties of water become more pronounced in the supercooled state,1,2 and they are frequently associated with the hypothesis of the existence of the phase equilibrium between lowand high-density liquids (LDL and HDL) as well as of a second low-temperature critical point C0 at about TC0 ≈ 220 K and PC0 ≈ 100 MPa. However, it is very difficult to prove experimentally the theoretically predicted liquid-liquid transition line and its end point C0 because they are expected to be placed in a so-called “no man's land” region where freezing makes experiments on supercooled bulk water almost impossible.3 In the inaccessible temperature range (150-235 K, P = 0.1 MPa), the properties of supercooled water can be studied only in severely confined systems (where the water clusters are smaller than a critical size of homogeneous crystallization4) or in the bulk state in aqueous mixtures of cryoprotectants (which prevent ice crystal formation by modifying the hydrogen bonding dynamics and structure of water). Results of ambient-pressure measurements on relaxation dynamics in supercooled aqueous solutions exhibit a slower (R) and a faster (ν) relaxation process.5 On the other hand, water in confined systems reveals one or two relaxations, depending on the confinement type. In water mixtures, the R relaxation reflects cooperative motions of water coupled together with solute molecules, and it is responsible for the glass transition of the solution, whereas in confined systems, the R process is due to water interaction with the inner surface of the pores. Various experimental data indicate that the ν relaxation in mixtures of high water content originates mainly from local motions of H2O molecules, and its relaxation times and activation energies are similar to those found for the faster process in some confined water systems

r 2010 American Chemical Society

Received Date: February 4, 2010 Accepted Date: March 12, 2010 Published on Web Date: March 22, 2010

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DOI: 10.1021/jz100154u |J. Phys. Chem. Lett. 2010, 1, 1170–1175

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pressure range, up to 200 MPa), the authors relate the obtained dependence of Tcross(P) to the first-order liquidliquid transition line earlier predicted by MD simulations of water16 and speculate that the critical point C0 is located at elevated pressure, at which the cusplike FS transition is rounded off. Monte Carlo simulations17 and experimental results18,19 for water in 2D confinements indicate that the crossover relaxation time τcross is approximately independent of pressure, the Arrhenius activation energy Ea at T < Tcross slightly decreases with increasing P, and Tcross(P) decreases. In the case of high-water-content mixtures, ν relaxation times are very similar, irrespective to the other component, suggesting that the dynamics of water molecules is weakly affected by the presence of the solute; there, a dynamic crossover was also observed at ambient pressure.20,21 However, it is mostly described by a transition between two Arrhenius behaviors with different activation energies, probably due to the limited temperature range above Tcross available for the investigation. In this work, we present results of studies of water relaxation properties in aqueous mixtures under extremely high pressure and in a wide temperature range. For the rich-in-water mixture of propylene glycol oligomer, we check how pressure influences the crossover ν relaxation time, τνcross(P), the activation energy of the ν process, Ea(P), the isobaric fragility of the mixture, mP(P), as well as whether the dynamic crossover is related to the glass transition in various pressure conditions. As far as we know, this is the first study of relaxation dynamics of aqueous solutions close to the glass transition at high P. Polypropylene glycol of molecular weight Mw = 400 g/mol (PPG400) was mixed with water at several concentrations and investigated by broad-band dielectric spectroscopy at ambient pressure from room temperature down to 100 K. Moreover, spectra of the rich-in-water solution, PPG400 þ 26 wt % H2O (which corresponds to a mole fraction of water of xw = 0.89), were measured under high pressure (up to 1.8 GPa), at temperatures as low as 198.15 K. Systematic study of the influence of the gradual water adding to anhydrous PPG400 on dielectric spectra at ambient pressure provided us information about the origin of relaxation processes existing in the examined mixtures. Water significantly changes the relaxation dynamics of propylene glycol oligomer. Adding even a small amount of water to PPG400 causes the appearance of a new additional ν relaxation in the dielectric spectra (similarly as in the case of many other water mixtures). In our system, this process can be especially easily noticed in the glassy state of the mixture in the range of frequencies between the two resolved secondary relaxations β and γ PPG400 (see Figure 1). In the inset to Figure 1, one can observe a spectacular increase in the dielectric strength of the new process Δεν with increasing water content in the solution. This dramatic change in the dielectric spectra due to water addition is experimental evidence that the ν relaxation reflects mainly the water dynamics in the mixture. It is important to report that, in general, for aqueous mixtures, there is a threshold concentration (mole fraction of water 0.67, i.e., about 8 wt % H2O in our system) above which the dielectric strength of the ν process is rapidly increasing with water concentration and the relaxation times are not


Figure 1. Dielectric loss spectra of aqueous mixtures of PPG400 with various concentrations of water in the glassy state at T = 178 K and P = 0.1 MPa. The upper inset shows the dependence of the dielectric strength of the ν process on the mole fraction of water. The lower inset presents spectra of the water mixtures with the same R relaxation times in the liquid state.

Figure 2. Comparison of dielectric spectra with the same R relaxation times obtained at different P and T for a water mixture of PPG400 and anhydrous PPG400. Solid lines denote fits of entire spectra as a superposition of the two HN functions (dotted lines).

very dependent on the concentration.20,22 In this concentration regime, the ν process is believed to reflect the true dynamics of water molecules surrounded by other water molecules. Dielectric measurements of a rich-in-water mixture of PPG400 performed under high pressure provided us new information about relaxation processes of the solution and especially about the dynamics of water. Similarly as it was observed at P = 0.1 MPa, the spectra of the mixture PPG400 þ 26% H2O obtained at elevated pressures of 360 and 500 MPa exhibit two well-resolved relaxation peaks, the slower (R process) and faster (ν process) (see Figure 2), whereas in

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Figure 3. Temperature dependences of the R (closed symbols) and ν (open symbols) relaxation times at various pressures for PPG400 þ 26% H2O. Solid lines indicate VFT fits to the R relaxation time. Dashed lines are Arrhenius fits to the ν relaxation times. The green thick straight line is the extrapolation of the Arrhenius behavior from the glassy state toward higher temperatures for τν at 0.1 MPa. Stars are the predicted values for the “effective” τν that would be obtained by adopting the Williams ansatz procedure. The inset shows the spectrum at 219 K and 0.1 MPa, identified as the merging temperature.

Figure 4. (a) Pressure dependence of the glass transition temperatures Tg obtained from isobaric (O) and isothermal (g) data for PPG400 þ 26% H2O. The solid line indicates a fit to the Avramov model. (b) Crossover relaxation times τνcross(Tcross) decrease exponentially with increasing P. (c) Pressure dependences of the ν process activation energies Ea for the mixture PPG400 þ 26% H2O. The energies at T < Tg are evaluated from Arrhenius law (b), whereas in the liquid state, they are from Arrhenius (for P = 0.1 MPa and 1.8 GPa) and VFT (for P = 360 and 500 MPa) equations at Tg (red O). (d) Pressure dependences of the isobaric fragility mP determined at τR = 10 s for DPG, TPG, and a mixture of PPG400 þ 26% H2O. Lines are guides for the eyes. Three values of mP for DPG and TPG at intermediate P are taken from ref 43.

the case of spectra measured at the highest pressure of 1.8 GPa, the R relaxation peak is hidden by the large contribution of dc conductivity to dielectric loss. Nevertheless, some information about the R relaxation was obtained from the real part of permittivity. From inspection of the spectra, we found that the ν process originating from motions of water molecules has the same features (its sensitivity to pressure and temperature) as secondary relaxation in many glassforming liquids. For isobaric and isothermal data, we observe that both relaxations, R and ν, slow down with decreasing T and increasing P, but the R relaxation time has a much stronger dependence. Moreover, the ν relaxation is much less sensitive to changes of pressure than temperature. Consequently, one can induce a greater separation between R and ν processes during isobaric experiments carried out at elevated pressure (see Figure 2) or by isothermal scans under pressure. It was experimentally recognized that such properties are typical for a local secondary process.23,24 In this respect, the ν relaxation can be considered as a secondary relaxation reflecting some local dynamics of the water component in the aqueous mixtures. It is consistent with the discussion recently carried out by Capaccioli et al.6 for many water systems at ambient pressure. From dielectric spectra, we found the relaxation maps for an aqueous mixture of PPG400 with 26% content of water obtained under isobaric (P = 0.1, 360, 500, 1800 MPa) and isothermal (T = 213, 233.8 K) conditions (see Figure 3 where only isobars are shown). The temperature and pressure dependences of R relaxation times, τR, are well-described by using the temperature and pressure VFT equations,25-29 respectively. Similarly to other glass formers, the glass transition temperature Tg of the considered mixture (determined for τR = 100s) increases with increasing pressure

(see Figure 4a). The experimental dependence of Tg on P, obtained from both isobaric and isothermal measurements, was well-fitted with the Avramov model30 function. The lowpressure derivative of the glass transition temperature, dTg/dP, is 86 K/GPa, a value typical of H-bonded systems and much lower than that of pure polypropylene glycol (nearly 200 K/GPa). We observed that the relaxation time of water dynamics in mixtures considerably increases upon increasing pressure, at odds with what is observed and predicted for bulk water.31 Unusual and very surprising results were obtained for isobaric temperature dependences of ν relaxation times τν. We observed that the relaxation dynamics of water reflected in the ν process is sensitive to the glass transition of the mixture, which is manifested by a change in the character of the dependence log[τν(T)] just at Tcross ≈ Tg and Pcross ≈ Pg for isobaric and isothermal measurements, respectively (see Figure 3). It is worth noting that the correspondence of the measured Tcross with Tg is valid for the whole pressure range (from 0.1 MPa up to 1.8 GPa). Such a change at Tg in the temperature dependence of the ν process from the glassy state is very similar to that reported recently for secondary relaxation in different glass formers both at ambient32 and high pressure.24 It is remarkable that this crossover is not due to the influence of the merging with R relaxation, as it was argued in some studies.33,34 In fact, we also tried to apply the Williams ansatz procedure, as suggested in those studies; we extrapolated τν from the Arrhenius glassy behavior to higher temperatures, convoluting it with the R process. The predicted “effective” ν relaxation time, so obtained, resulted in being much longer than that experimentally observed (see Figure 3). That proves that the change in the temperature behavior of the ν relaxation that we found upon crossing Tg is a real phenomenon.


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mixture PPG400 þ 26% H2O, followed by a smaller value reported at 1.8 GPa. It indicates that, similarly to the case of pure PG oligomers, the dynamics of H bonds considerably influence also the R relaxation of the water mixture. In summary, we found that pressure considerably affects the relaxation dynamics of water in an aqueous mixture of PPG400. We observed the dynamic crossover in the waterrelated ν relaxation near the glass transition of the mixture in the whole pressure range (0.1 MPa-1.8 GPa). At medium pressures, it is characterized by the VFT-to-Arrhenius transition of τν(T) similarly to that established for water in confined systems. Other pressure-dependent properties of the crossover of water relaxation in the aqueous mixture are significantly different from properties observed for confined water. (i) Contrary to what occurs for aqueous systems of confined geometry,13,17-19 the dependence Tcross(P) for our water mixture has an increasing character, and therefore, we cannot relate it to the liquid-liquid phase transition line in a T-P plane. (ii) The crossover relaxation time τνcross decreases exponentially with increasing P for the mixture PPG400 þ 26% H2O, whereas τcross(P) ≈ const for confined water. These two findings can indicate that the ν process is not the structural relaxation of water, but it reflects more local dynamics of H2O molecules. (iii) Moreover, the pressure dependence of the Arrhenius activation energy Ea for the ν relaxation is nonmonotonic and reveals a maximum at about 1 GPa, while the Arrhenius activation energy for the confined water process decreases with increasing P at T < Tcross. The dependences Ea(P) for the ν process and the isobaric fragility mP for the aqueous mixture correspond well with each other. It is shown that the compression effect on hydrogen bonding in water mixtures is strongly dependent on the pressure value; increasing pressure reinforces the structuring of a H-bonded network until a certain pressure value after which the degree of H bonds decreases due to the increase of temperature following Tg(P). Thus, the values of Ea for the ν process and mP for the aqueous mixture depend on the dynamics of H bonds, whereas the crossover relaxation time τνcross depends on the system density, which manifests the well-known “elbow shape” temperature dependence with a change of slope at Tg as a consequence of the structural arrest.

Additionally, we found that pressure considerably influences the nature of the ν process dynamic crossover. At 0.1 MPa, the temperature dependence of τν obeys the Arrhenius law both in the glassy and liquid states. On the other hand, for the medium values of pressure (360 and 500 MPa) the dependence log[τν(T)] can be described by using the VFT equation above Tg and the Arrhenius equation below Tg. Finally, at the highest pressure (1.8 GPa), again, the Arrhenius law can be used both in the glassy and liquid states, having a different activation energy than that in the ambient-pressure case. It is worth pointing out that the temperature interval of the investigation above Tg at 1.8 GPa is small because of the experimental limit, and this can make the identification of the VFT difficult. The value of the ν relaxation time, τνcross, at the dynamic crossover is also pressure-dependent, that is, it decreases exponentially with compression, approaching τνcross(Pf¥) = 3 μs (see Figure 4b). The time scale of τνcross is similar to that found by dielectric spectroscopy in other aqueous mixtures6,20,22 and also for water confined or present in hydration shells of proteins.10 Only in some neutron scattering studies was a much shorter crossover time scale found (tens of ps).13,19 Moreover, it is remarkable that the crossover temperature is, at ambient pressure, much lower than the critical temperature (225 K) usually characterizing some anomalous behavior of the dynamics, viscosity, and transport coefficients of water confined in different environments with different effective dimensions and even in water-rich aqueous mixtures.35 We also found unusual pressure dependences of activation energies Ea for the ν relaxation, which exhibit maxima over pressure variation for both the liquid and glassy state behaviors. As can be seen in Figure 4c, initially, Ea increases but eventually decreases with pressure in the GPa range. It may indicate that, initially, the increase in pressure can facilitate the hydrogen bonds forming, whereas the reversal of the direction of change in Ea during compression may be due to significant reduction of hydrogen bonds in the PPG400 þ 26% H2O mixture when P > 1 GPa. It is noteworthy that at that high pressure, measurements have been done in the temperature range of 270-300 K, where hydrogen bonds are known to be weakened.36 Actually, both types of Ea in Figure 4c have been determined in the vicinity of Tg, and even the number of H bonds frozen in the glass (affecting Ea below Tg) should be related to the temperature of glass formation. In the literature, an increase of the strength of the H bond with increasing P was usually found,37-39 although a negligible effect or even a decrease was sometimes reported.40,41 It is intriguing that a similar effect of pressure on the activation energy due to H bonds was observed for the pure samples (i.e., without water) of small oligomers of propylene glycol (DPG42 and TPG), reflecting the nonmonotonic pressure dependence of isobaric fragility mp = [d log τR/ d(Tg/T)]T=Tg (see Figure 4d). Values of mP for these materials was reported to increase up to nearly 1 GPa and then to decrease. It is contrary to what occurs usually for nonassociated liquids, which reveal a quite different variation of the function mp(P), monotonically slightly decreasing with increasing pressure. In analogy to DPG and TPG, also here (see Figure 4d), we found an initially increasing character of the dependence of mp(P) for the R relaxation times of the


EXPERIMENTAL SECTION To study the dynamics of supercooled water, we performed broad-band dielectric spectroscopy (Novocontrol Alpha Impedance Analyzer, 10-2-107 Hz) measurements of aqueous mixtures of polypropylene glycol of molecular weight Mw = 400 g/mol (PPG400) with water at several concentrations (Cw=2, 4, 8, 12, 16, 18, 20, 26, and 36%) at ambient pressure from room temperature down to 100 K. Moreover, spectra of the rich-in-water solution, PPG400 þ 26 wt % H2O, were measured under high pressure (up to 1.8 GPa), at temperatures as low as 198.15 K.

AUTHOR INFORMATION Corresponding Author: *To whom correspondence should be addressed. E-mail: kgrzybow@ us.edu.pl.

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ACKNOWLEDGMENT This research was financially supported

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within the framework of the executive program of scientific and technological cooperation between the Republic of Poland and the Italian Republic (2007-2009). M.P. acknowledges the support of the Polish Ministry of Sciences and Information Technology, Grant No. N202 14732/4240. S.P. acknowledges financial support from the Foundation for Polish Science in HOMING Program (supported by EEA Financial Mechanism).

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