Glass transition of ionic liquids under high pressure Mauro C. C. Ribeiro, Agílio A. H. Pádua, and Margarida F. Costa Gomes Citation: The Journal of Chemical Physics 140, 244514 (2014); doi: 10.1063/1.4885361 View online: http://dx.doi.org/10.1063/1.4885361 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/24?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Dielectric spectroscopy and ultrasonic study of propylene carbonate under ultra-high pressures J. Chem. Phys. 137, 084502 (2012); 10.1063/1.4746022 Glass Transitions and LowFrequency Dynamics of RoomTemperature Ionic Liquids AIP Conf. Proc. 832, 73 (2006); 10.1063/1.2204465 Equation of State for Liquid Nitromethane at High Pressures AIP Conf. Proc. 706, 149 (2004); 10.1063/1.1780205 Theoretical study of the molecular motion of liquid water under high pressure J. Chem. Phys. 119, 1021 (2003); 10.1063/1.1578624 Decoupling of the dc conductivity and (α-) structural relaxation time in a fragile glass-forming liquid under high pressure J. Chem. Phys. 116, 9882 (2002); 10.1063/1.1473819

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 131.230.42.7 On: Sat, 06 Dec 2014 01:56:03

THE JOURNAL OF CHEMICAL PHYSICS 140, 244514 (2014)

Glass transition of ionic liquids under high pressure Mauro C. C. Ribeiro,1 Agílio A. H. Pádua,2 and Margarida F. Costa Gomes2 1

Laboratório de Espectroscopia Molecular, Instituto de Química, Universidade de São Paulo, CP 26077, CEP 05513-970, SP, Brazil 2 Institut de Chimie de Clermont-Ferrand, UMR 6296, CNRS/Université Blaise Pascal, 63177 Aubière, France

(Received 17 April 2014; accepted 16 June 2014; published online 30 June 2014) The glass transition pressure at room temperature, pg , of six ionic liquids based on 1-alkyl-3methylimidazolium cations and the anions [BF4 ]− , [PF6 ]− , and bis(trifluromethanesulfonyl)imide, [NTf2 ]− , has been obtained from the pressure dependence of the bandwidth of the ruby fluorescence line in diamond anvil cells. Molar volume, Vm (pg ), has been estimated by a group contribution model (GCM) developed for the ionic liquids. A density scaling relation, TVγ , has been considered for the states Vm (pg , 295 K) and Vm (Tg , 0.1 MPa) using the simplifying condition that the viscosity at the glass transition is the same at pg at room temperature and at atmospheric pressure at Tg . Assuming a constant γ over this range of density, a reasonable agreement has been found for the γ determined herein and that of a previous density scaling analysis of ionic liquids viscosities under moderate conditions. Further support for the appropriateness of extrapolating the GCM equation of state to the GPa pressure range is provided by comparing the GCM and an equation of state previously derived in the power law density-scaling regime. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4885361] I. INTRODUCTION

A rich phenomenology of phase transitions has been found in ionic liquids at low temperature or high pressure as a given system might exhibit supercooling, pressurization beyond the freezing line, glass transition, crystallization, and polymorphism.1–4 Some ionic liquids are easily supercooled and hardly crystallize, whereas others are promptly crystallized as temperature decreases. The condition of the transition is dependent on the thermal history, in particular, the cooling rate. The effect of increasing pressure at room temperature in diamond anvil cells (DAC) has been investigated as the counterpart of temperature effect. For instance, in analogy with cold crystallization usually observed when supercooled ionic liquids are re-heated, Yoshimura et al.5, 6 showed that two different ionic liquids based on the [BF4 ]− anion can be pressurized above 5.0 GPa at room temperature, undergoing crystallization after releasing the pressure below ∼2.0 GPa. Ionic rearrangements related to phase transitions of ionic liquids have been unraveled by X-ray diffraction and vibrational spectroscopy, the latter being particularly suitable in showing the interplay between phase transitions and conformational changes from plots of vibrational frequencies and relative intensities as a function of pressure.7–11 Recently, Pison et al.12 calculated the vibrational frequency shift of the [PF6 ]− stretching normal mode in imidazolium ionic liquids which do not crystallize below ∼3.5 GPa. In this work, we address two issues related to the calculation performed in Ref. 12. We first determine whether some ionic liquids that do not crystallize undergo a glass transition after a few GPa of applied pressure. The second aim of this work is to provide experimental evidence that equations of state proposed for ionic liquids give reasonable estimate of molar volume into the GPa pressure range. In fact, theories relate shift 0021-9606/2014/140(24)/244514/6/$30.00

of vibrational frequency to density,13, 14 i.e., the calculation demands knowledge of density as a function of pressure. Pison et al.12 used the equation of state of a group contribution model (GCM) previously proposed by Jacquemin et al.15 on the basis of volumetric data within the MPa pressure range, extending it to pressures of GPa, a common range in vibrational spectroscopy of liquids using DACs. Piermarini et al.16, 17 showed 40 years ago that the method of shift of the ruby R1 fluorescence line, commonly used for pressure calibration in DAC, can be used to estimate the glass transition pressure, pg . The signature of pg is the increase of bandwidth of the ruby emission line because of local non-hydrostatic stresses as the sample undergoes the glass transition. This method has been used by Yoshimura et al.5, 6 to estimate pg in an ammonium and an imidazolium ionic liquid, both with the [BF4 ]− anion. In this work, we used this method to obtain pg at room temperature for six different ionic liquids whose glass transition temperatures at atmospheric pressure, Tg , are well known from the literature.18 Then, the GCM equation of state15 is used to estimate molar volumes of the two states V ( pg , 295 K) and V (Tg , 0.1 MPa). The volume and temperature dependences of transport coefficients of liquids follow a master curve when scaled in terms of ρ γ /T, where ρ is the density and γ is an empirical parameter.19–24 Density scaling of transport coefficients of liquids has been intensively investigated in the last years as the scaling parameter γ can be related to thermodynamic properties and to the intermolecular potential function. In this work, the two states V ( pg , 295 K) and V (Tg , 0.1 MPa) with the same viscosity at the glass transition, η ∼ 1012 Pa.s, have been related by ρ γ /T. The γ parameters we obtained are consistent with the density scaling analysis performed by López et al.25 for several ionic liquids. It was found, however, that the function f(ρ γ /T)

140, 244514-1

© 2014 AIP Publishing LLC

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 131.230.42.7 On: Sat, 06 Dec 2014 01:56:03

244514-2

Ribeiro, Pádua, and Gomes

used in density scaling of ionic liquids25 does not lead to the expected high value of the viscosity at Tg or pg . Further support for the analysis performed here is provided by the agreement between the GCM and the equation of state proposed by Grzybowski et al.23, 24 on the basis of a power law regime for the density scaling of transport coefficients.

II. EXPERIMENTAL

The ionic liquids investigated in this work contained the cations 1-butyl-3-methylimidazolium, [C4 C1 im]+ , 1-hexyl-3-methylimidazolium, [C6 C1 im]+ , and 1-octyl-3methylimidazolium, [C8 C1 im]+ , and the anions tetrafluoroborate, [BF4 ]− , hexafluorophosphate, [PF6 ]− , and bis(trifluromethanesulfonyl)imide, [NTf2 ]− . The ionic liquids actually investigated were: [C4 C1 im][BF4 ], [C8 C1 im][BF4 ], [C6 C1 im][PF6 ], [C8 C1 im][PF6 ], [C4 C1 im[NTf2 ], and [C6 C1 im[NTf2 ]. The ionic liquids purchased from Iolitec were used without further purification, but they were dried under high vacuum (below 10−8 bar) for at least 48 h before measurements. Raman spectra as a function of pressure at room temperature were recorded in a Renishaw Raman imaging microscope (inVia) with a Leica microscope and CCD detector. The laser line at 632.8 nm of a He-Ne laser was focused into the sample by a 20× Leica objective. High-pressure measurements were performed with a diamond anvil cell from EasyLab Technologies Ltd., model Diacell LeverDAC Maxi, having a diamond culet size of 500 μm. The Boehler microDriller (EasyLab) was used to drill a 250 μm hole in a stainless steel gasket (5 mm diameter, 250 μm thick) preindented to ∼150 μm. Pressure calibration was done by the usual method of mea-

J. Chem. Phys. 140, 244514 (2014)

suring the shift of the fluorescence line of ruby spheres added to the sample chamber.16, 17, 26 The bandwidth of the emission spectrum of ruby was obtained from fit of Lorentzian functions to the band shape. III. RESULTS AND DISCUSSION

The method proposed by Piermarini et al.16, 17 for measuring pg from the pressure dependence of the bandwidth, ( p), of the R1 fluorescence line of ruby has been applied for several glass-formers and more recently for two ionic liquids.5, 6 In a study of glycerol-water mixtures, Klotz et al.27 proposed an alternative method based on changes in the standard deviation of the pressure given by different ruby spheres placed in the DAC:   n 1  (pi − p)2 , (1) σ = n i=1 where pi is the pressure of each of the n ruby spheres and p is the average value of pressure. In this work, we measured pg of ionic liquids by using both of these methods, ( p) and σ ( p), typically with five ruby spheres in the DAC for measuring σ ( p). Figure 1 illustrates the method of ( p) for ionic liquids based on [BF4 ]− and [NTf2 ]− anions, and Fig. 2 illustrates the method of σ ( p) for ionic liquids based on [PF6 ]− . In these figures, the pressure of the sharp increment of ( p) or σ ( p) indicates the glass transition pg . Table I shows the experimental pg for the ionic liquids investigated in this work. The pg of [C2 C1 im][BF4 ] obtained by Yoshimura et al.6 is also given in Table I. We have considered a similar ionic liquid, [C2 C1 im][NTf2 ], but it will be not used in this work because it crystallizes at p ∼ 1.0 GPa. The

FIG. 1. The pressure dependence of the bandwidth of the R1 fluorescence line of ruby for different ionic liquids (black circles). The red lines are linear fits to low and high pressure regimes.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 131.230.42.7 On: Sat, 06 Dec 2014 01:56:03

244514-3

Ribeiro, Pádua, and Gomes

J. Chem. Phys. 140, 244514 (2014)

The GCM equation of state proposed by Jacquemin et al.15 allows the calculation of an effective molar volume from the molecular structure of a cation or an anion, V m,ion (T,p), with the molar volume of the ionic liquid given by V m = V cation + V anion . This modified Tait equation has been parameterized from a large database of volumetric properties: Vm,ion (T , p) =

Vm,ion (T , pref ) ,  (δT )+p 1 − G ln HH(δT )+pref

(2)

where V m,ion (T,pref ) is calculated at the reference pressure pref = 0.1 MPa as Vm,ion (T ) =

2 

Di δT i

(3)

i=0

FIG. 2. The pressure dependence of standard deviation of the pressure of ruby spheres in the diamond anvil cell (black circles). The red lines are linear fits to low and high pressure regimes.

ionic liquid [C4 C1 im][PF6 ] has been also left out of this work because it promptly crystallizes at p ∼ 0.5 GPa.8–10, 12 Concerning the Raman spectroscopy study of [C6 C1 im][PF6 ] and [C8 C1 im][PF6 ] up to p ∼ 3.5 GPa,12 Fig. 2 shows that they undergo glass transition in this pressure range.12 This finding is in line with the slow modulation regime of vibrational frequency fluctuation suggested by a Raman band shape analysis of the totally symmetric stretching mode ν s (PF6 ).12 The glass transition temperature at atmospheric pressure, Tg , given in Table I is the average value for each ionic liquid given in the Zhang et al.18 review of physical properties of ionic liquids. Inspection of Table I does not indicate any clear trend in pg and Tg . The relationship between them will appear from the calculation of the corresponding molar volumes and the concept of density scaling of viscosity.

with δT = T − 298.15 K. The parameters G, Di , and the function H(δT), which is a second order polynomial of temperature, have been optimized for several cations and anions.15 The ( p, V , T) database used by Jacquemin et al.15 to parameterize the GCM included volumetric data within the typical range 273 < T/K < 423 and pressures up to 65 MPa, and only for few systems, for instance, [C8 C1 im][BF4 ] and [C8 C1 im][PF6 ], up to ∼200 MPa. The GCM was used by Pison et al.12 to calculate molar volumes in a Raman spectroscopy investigation of ionic liquids under GPa pressure range. In order to check whether the GCM is valid at such high pressures, we first extrapolated the equation of state to calculate Vm at pg and at room temperature, Vm ( pg , 295 K), and Vm at Tg and at atmospheric pressure, Vm (Tg , 0.1 MPa). Figure 3 illustrates the isotherm and the isobar of [C4 C1 im][NTf2 ] calculated by the GCM. Table I shows Vm ( pg , 295 K) and Vm (Tg , 0.1 MPa) calculated for all ionic liquids. In the following, we will relate Vm ( pg , 295 K) and Vm (Tg , 0.1 MPa) with the concept of density scaling of transport coefficients as these thermodynamic states are of equal viscosities, η ∼ 1012 Pa.s. Density scaling of dynamical properties is based on the idea that the relaxation time or transport coefficients of a given system overlap, in a wide range of thermodynamic conditions, on a master curve if data are plotted as a function of (V γ T )−1 or ρ γ /T, where ρ is the density and γ is a system dependent parameter.20–25 In the case of a model system with intermolecular potential u(r) ∝ (1/r)n , where r is the

TABLE I. Glass transition pressure, pg , and temperature, Tg , corresponding molar volume estimated by the GCM equation of state, Eq. (2), Vm (pg ) and Vm (Tg ), and resulting thermodynamic scaling parameter, γ .

[C2 C1 im][BF4 ] [C4 C1 im][BF4 ] [C8 C1 im][BF4 ] [C6 C1 im][PF6 ] [C8 C1 im][PF6 ] [C4 C1 im][NTf2 ] [C6 C1 im][NTf2 ]

pg (295 K) (GPa)

Tg (0.1 MPa) a (K)

Vm (pg ) (cm3 mol−1 )

Vm (Tg ) (cm3 mol−1 )

2.8 c 1.9 2.1 1.6 1.6 1.6 1.7

182 189 194 194 197 186 189

128 154 198 199 223 238 260

154 185 247 232 264 280 311

γ

b

2.6 2.4 (2.83) 1.9 (2.18) 2.7 (2.54) 2.4 (2.28) 2.8 (2.89) 2.5 (2.36)

a

Reference 18. Values in parenthesis from Ref. 25. c Reference 6. b

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 131.230.42.7 On: Sat, 06 Dec 2014 01:56:03

244514-4

Ribeiro, Pádua, and Gomes

200

250

J. Chem. Phys. 140, 244514 (2014)

T/K 300

350

400

320

3

Vm / cm .mol

-1

300

Vm(T, 0.1 MPa) 280 260

Vm(295 K, p)

240 0.0

0.5

1.0

1.5

p / GPa FIG. 3. Molar volume of [C4 C1 im][NTf2 ] as a function of pressure, Vm (295 K, p) (black line, bottom scale), and temperature, Vm (T, 0.1 MPa) (red line, top scale), calculated by the GCM equation of state, Eq. (2). The fit of Vm (295 K, p) by the equation of state derived by Grzybowski et al.,23 Eq. (6), with γ EOS = 8.39 and BT ( po ) = 2.81 GPa, is shown by the circles.

interparticle distance, the relationship n = 3γ is valid. The scaling parameter γ is obtained from the collapse of experimental data, e.g., η(ρ, T), independently of the actual function f(ρ γ /T). A thermodynamic interpretation of γ was given by Casalini et al.,21 who used the entropy model of Avramov to derive the function  γ ϕ  γ ρ ρ = C.exp A , (4) f T T where A, φ, and C are fitted parameters. Equation (4) has been used to fit relaxation time, viscosity, conductivity, etc. as a function of density and temperature for several molecular, polymeric, and ionic liquids.21, 25 Another relationship between intermolecular potential, thermodynamics, and dynamics was given by Grzybowski et al.,23, 24 who derived an equation of state (see Eq. (6)) for systems with inverse power law intermolecular potential. Recently, Grzybowski et al.28 discussed the application of their equation of state beyond the power law density scaling regime for liquids under GPa of applied pressure. López et al.25 showed that the density scaling approach is valid for viscosity of ionic liquids. Therefore, if the extrapolation of GCM to Vm ( pg , 295 K) and Vm (Tg , 0.1 MPa) is correct, these two states are related by V1 γ T1 = V2 γ T2 , and the γ parameter should agree with the previous density scaling study.25 The last column of Table I shows the resulting γ parameter. Keeping in mind that López et al.25 obtained γ from a large database of η(ρ, T) for ionic liquids above room temperature and at tens of MPa of applied pressure, the agreement is satisfactory as in this work we consider only two glassy states. It is worth noting that the parameter γ obtained here decreases as the length of the alkyl chain of the [Cn C1 im]+ cation increases while keeping the same anion. This finding holds for the [BF4 ]− based ionic liquids including one system whose pg was measured independently by Yoshimura et al.,6 namely, [C2 C1 im][BF4 ], which was not considered in the density scaling study of López et al.25 The fact that γ decreases with increasing length of the alkyl chain of [Cn C1 im]+ has been assigned to a similar effect seen in linear alkanes, as a

FIG. 4. Isobaric curve of viscosity, η(T, 0.1 MPa), of [C4 C1 im][NTf2 ] calculated by Eq. (4), black line, and Eq. (5), red line, as a function of ρ γ /T, γ = 2.89, extrapolated to Tg = 186 K. The dashed line is Eq. (4) with the same scaling parameter γ , but with modified parameters (C = 2.8 mPa.s, A = 139 K.g−γ .cm3γ , φ = 4.0) in order to constraint the viscosity at Tg . The arrow at ρ γ /T ∼ 0.011 K−1 gγ cm−3γ indicates the room temperature, which is the lowest temperature of experimental η(T, 0.1 MPa) data available for [C4 C1 im][NTf2 ]. The inset shows the database of density at atmospheric pressure and different temperatures (circles),15 and isobaric curves ρ(T, 0.1 MPa) predicted by the GCM (black line) and the quadratic fit of Ref. 29 (red line). The arrow at ρ ∼ 1.59 g.cm−3 is the density of crystalline [C4 C1 im][NTf2 ].31

more flexible molecular structure softens the effective intermolecular potential leading to smaller scaling parameter.25 The empirical scaling parameter γ does not depend on the actual function f(ρ γ /T). On the other hand, if Eq. (4) is valid for temperatures down to Tg , or pressures up to pg , the viscosity predicted in these limits should be η ∼ 1015 mPa.s. However, this limiting value of viscosity at glass transition is not satisfied if density in Eq. (4) is calculated by the GCM, Eq. (2), and the best fit parameters A, φ, and C are used.25 For instance, in the case of [C4 C1 im][NTf2 ], if Vm (295 K, pg ) or Vm (Tg , 0.1 MPa) given in Table I is inserted in Eq. (4) with the parameters of this system (C = 1.37 mPa.s, A = 184 K.g−γ .cm3γ , φ = 2.28, and γ = 2.89),25 the resulting viscosity at Tg or pg is η ∼ 106 mPa.s. This is illustrated in Fig. 4 for the isobar (0.1 MPa) of the [C4 C1 im][NTf2 ] viscosity calculated by Eq. (4). For comparison purpose, the red line in Fig. 4 is the fit performed by Harris et al.29 of the VogelFulcher-Tammann (VFT) equation for [C4 C1 im][NTf2 ] at 0.1 MPa:  B (5) η (T ) = C.exp (T − To ) with C = 0.163 mPa.s, B = 766.28 K, and To = 164.739 K. It is worth stressing that Eq. (4) provides an excellent fit of η(ρ,T) under moderate pressure and temperature conditions, but it does not take into account the constraint of very high viscosity at the glass transition. Figure 4 shows that both Eqs. (4) and (5) give the same high temperature dependence for the [C4 C1 im][NTf2 ] viscosity at atmospheric pressure. In fact, Lopez et al.25 pointed out that the fit by Eq. (4) is poorer as density increases or temperature decreases. On the other

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 131.230.42.7 On: Sat, 06 Dec 2014 01:56:03

244514-5

Ribeiro, Pádua, and Gomes

hand, the best fit parameters of Eq. (5) obtained by Harris et al.29 implied the Tg /To ratio is in agreement with the empirical relation proposed by Angell.30 The low viscosity predicted by Eq. (4) at Tg should not be assigned to a failure of the GCM, Eq. (2), resulting in a low value of density when extrapolated to Tg . For instance, in order to attain η ∼ 1012 Pa.s for [C4 C1 im][NTf2 ] at Tg , the density of the glass in Eq. (4) should be ρ ∼ 1.7 g.cm−3 . The inset of Fig. 4 shows the ρ(T, 0.1 MPa) database used in the parameterization of the GCM equation of state.15 Those data include the Harris et al.29 results of ρ(T, 0.1 MPa) for [C4 C1 im][NTf2 ], and the inset of Fig. 4 also shows the reported quadratic fit.29 Both the extrapolations of ρ(T, 0.1 MPa) to Tg shown in the inset of Fig. 4 give density below the value reported by Paulechka et al.31 in a structural investigation of crystalline phases of ionic liquids based on the [NTf2 ]− anion. Thus, the value ρ ∼ 1.7 g.cm−3 , which is needed for Eq. (4) to extrapolate the typical viscosity at Tg , corresponds to a physically unrealistic situation of the supercooled liquid [C4 C1 im][NTf2 ] with density higher than ρ ∼ 1.59 g.cm−3 of the corresponding crystal. There are no experimental η(ρ,T) data to suggest a better form of f(ρ γ /T) for [C4 C1 im][NTf2 ] in the deeply supercooled liquid regime. Nevertheless, if one maintains Eq. (4) using as constraints of the fit the limiting values of viscosity at high and low temperatures (dashed line in Fig. 4), the parameters should be modified to C = 2.8 mPa.s, A = 139 K.g−γ .cm3γ , φ = 4.0. The parameter γ = 2.89 is not modified because it is obtained independently of the actual form of the function f(ρ γ /T). The most important modification is the higher value of φ needed for Eq. (4) to predict high viscosity at Tg . In the original fit of Eq. (4) for different molecular, polymeric, and ionic liquids, López et al.25 drew attention to the fact that the product φ.γ is lower when Eq. (4) is used for viscosity, φ.γ ∼ 6, than if the equation is used for relaxation times, φ.γ ∼ 18. In the case of [C4 C1 im][NTf2 ] illustrated in Fig. 4, this product increases to φ.γ ∼ 11.5 if the high viscosity at Tg is considered as a constraint to Eq. (4). In this work we assumed constant γ within the range of densities given by Vm ( pg , 295 K) and Vm (Tg , 0.1 MPa). Molecular dynamics simulations showed that γ might depend on density, γ (ρ), for dynamical properties in wide density range.28, 32 A more general form of density scaling is f [h(ρ)/T], the commonly used function h = ρ γ being a particular form of h(ρ) valid for intermolecular potentials with a single inverse power law term. Grzybowski et al.23, 24, 28 suggested an equation of state derived in the power law densityscaling regime:

 γEOS ρ BT (po ) p = po + −1 , (6) γEOS ρo where BT (ρ) = ρ(∂p/∂ρ)T is the isothermal bulk modulus, and po and ρ o are pressure and density of reference. Recently, Grzybowski et al.28 extended this equation for non-constant γ at high pressures after replacing (ρ/ρ o )γ EOS in Eq. (6) by a more general term [h(ρ)/h(ρ o )]γ EOS . It is worth stressing that γ EOS obtained by the fit of Eq. (6) to volumetric data is usually larger than γ obtained from density scaling of dynamical properties. Moreover, Grzybowski et al.24 showed that

J. Chem. Phys. 140, 244514 (2014)

γ EOS and γ are different from the thermodynamic interpretation proposed by Casalini et al.,21 who assigned γ to the Grüneisen constant γG = V αp CV −1 /κT , where α p is the isobaric volume expansivity, CV is the isochoric heat capacity, and κ T is the isothermal compressibility. If dynamical properties are scaled according to the model of Eq. (4), the relationship between these parameters is24 γEOS = φ.(γ − γG ).

(7)

The above equation provides an explanation for the experimental findings γ EOS  γ and γ G  γ . We consider again the ionic liquid [C4 C1 im][NTf2 ] in order to compare Eqs. (2) and (6). The isothermal Vm ( p, 295 K) calculated by the GCM for [C4 C1 im][NTf2 ] (black line in Fig. 3) was fit by the Grzybowski et al.23 equation of state, Eq. (6). We estimate γ EOS by Eq. (7), considering the scaling parameter γ obtained by López et al.25 for [C4 C1 im][NTf2 ], γ = 2.89. We used φ = 4.0 as suggested by the dashed line in Fig. 4 according to the above discussion, rather than the original parameter φ = 2.28.25 The Grüneisen constant γ G is estimated at 298.15 K and 0.1 MPa from experimental data for [C4 C1 im][NTf2 ]: Vm = 291,98 cm3 mol−1 , α p = 0.660×10−3 K−1 , κ T = 0.498 GPa−1 .33 The experimental value Cp = 565.05 JK−1 mol−1 ,34 was used to calculate CV = 488.91 JK−1 mol−1 , from CV – Cp = α p 2 TV/κ T . The resulting γ G = 0.79 implies γ EOS = 8.39 according to Eq. (7). Figure 3 shows good agreement between Eqs. (6) and (2). This finding gives further support for the calculation of molar volume from the GCM equation of state of ionic liquids in the GPa pressure range, and the assumption of constant γ in density scaling the viscosities at Vm ( pg , 295 K) and Vm (Tg , 0.1 MPa). IV. CONCLUSIONS

Common ionic liquids based on 1-alkyl-3methylimidazolium cations which do not crystallize under high pressure undergo glass transition within the 1.5–3.0 GPa range at room temperature. In other words, typical glass transition temperature of ionic liquids is Tg ∼ 190 K at atmospheric pressure, and Tg increases to room temperature at GPa of applied pressure. This work suggests measuring the full Tg ( p) curve with temperature controlled diamond anvil cells for testing the Prigogine-Defay ratio of ionic liquids.22, 35, 36 The calculation of Vm ( pg ,295 K) and Vm (Tg ,0.1 MPa) by the GCM equation of state,15 and the density scaling relationship between them, V1 γ T1 = V2 γ T2 , is an experimental indication that the GCM can be extrapolated to much higher pressures than the MPa range considered in its parameterization. Recently, we provided additional evidence of the appropriateness of the GCM in the GPa pressure range by molecular dynamics simulations of the ionic liquid 1-butyl-3-methylimidazolium trifluoromethanesulfonate (or triflate), [C4 C1 im][TfO].37 In this work, we related the two states Vm ( pg ,295 K) and Vm (Tg ,0.1 MPa) under the assumption of constant scaling parameter γ . Inspection of Table I already suggests that this assumption is reasonable because of relatively small variation of molar volume, ∼20%, between

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 131.230.42.7 On: Sat, 06 Dec 2014 01:56:03

244514-6

Ribeiro, Pádua, and Gomes

these two states. The assumption of a density independent γ was corroborated by the good agreement between isotherms calculated by the GCM and the equation of state derived by Grzybowski et al.23, 24 under the power law regime of density scaling. ACKNOWLEDGMENTS

M.C.C.R. acknowledges FAPESP and CNPq for financial support. 1 A.-V.

Mudring, Aust. J. Chem. 63, 544 (2010).

2 P. M. Dean, J. M. Pringle, and D. R. MacFarlane, Phys. Chem. Chem. Phys.

12, 9144 (2010). Saouane, S. E. Norman, C. Hardacre, and F. P. A. Fabbiani, Chem. Sci. 4, 1270 (2013). 4 M. Imanari, K. Fujii, T. Endo, H. Seki, K.-i. Tozaki, and K. Nishikawa, J. Phys. Chem. B 116, 3991 (2012). 5 Y. Yoshimura, H. Abe, Y. Imai, T. Takekiyo, and N. Hamaya, J. Phys. Chem. B 117, 3264 (2013). 6 Y. Yoshimura, H. Abe, T. Takekiyo, M. Shigemi, N. Hamaya, R. Wada, and M. Kato, J. Phys. Chem. B 117, 12296 (2013). 7 R. W. Berg, Monats. Chem. 138, 1045 (2007). 8 L. Su, M. Li, X. Zhu, Z. Wang, Z. Chen, F. Li, Q. Zhou, and S. Hong, J. Phys. Chem. B 114, 5061 (2010). 9 O. Russina, B. Fazio, C. Schmidt, and A. Triolo, Phys. Chem. Chem. Phys. 13, 12067 (2011). 10 T. Endo, T. Kato, K.-I. Tozaki, and K. Nishikawa, J. Phys. Chem. B 114, 407 (2010). 11 L. Su, X. Zhu, Z. Wang, X. Cheng, Y. Wang, C. Yuan, Z. Chen, C. Ma, F. Li, Q. Zhou, and Q. Cui, J. Phys. Chem. B 116, 2216 (2012). 12 L. Pison, M. F. C. Gomes, A. A. H. Padua, D. Andrault, S. Norman, C. Hardacre, and M. C. C. Ribeiro, J. Chem. Phys. 139, 054510 (2013). 13 K. S. Schweizer and D. Chandler, J. Chem. Phys. 76, 2296 (1982). 14 D. Benamotz and D. R. Herschbach, J. Phys. Chem. 97, 2295 (1993). 15 J. Jacquemin, P. Nancarrow, D. W. Rooney, M. F. C. Gomes, P. Husson, V. Majer, A. A. H. Padua, and C. Hardacre, J. Chem. Eng. Data 53, 2133 (2008). 3 S.

J. Chem. Phys. 140, 244514 (2014) 16 G. J. Piermarini, S. Block and J. D. Barnett, J. Appl. Phys. 44, 5377 (1973). 17 R. G. Munro, S. Block, and G. J. Piermarini, J. App. Phys. 50, 6779 (1979). 18 S.

Zhang, N. Sun, X. He, X. Lu, and X. Zhang, J. Phys. Chem. Ref. Data 35, 1475 (2006). 19 C. M. Roland, S. Hensel-Bielowka, M. Paluch, and R. Casalini, Rep. Prog. Phys. 68, 1405 (2005). 20 C. Alba-Simionesco and G. Tarjus, J. Non-Cryst. Solids 352, 4888 (2006). 21 R. Casalini, U. Mohanty, and C. M. Roland, J. Chem. Phys. 125, 014505 (2006). 22 D. Gundermann, U. R. Pedersen, T. Hecksher, N. P. Bailey, B. Jakobsen, T. Christensen, N. B. Olsen, T. B. Schroder, D. Fragiadakis, R. Casalini, C. M. Roland, J. C. Dyre, and K. Niss, Nat. Phys. 7, 816 (2011). 23 A. Grzybowski, M. Paluch, and K. Grzybowska, J. Phys. Chem. B 113, 7419 (2009). 24 A. Grzybowski, M. Paluch, K. Grzybowska, and S. Haracz, J. Chem. Phys. 133, 161101 (2010). 25 E. R. Lopez, A. S. Pensado, M. J. P. Comunas, A. A. H. Padua, J. Fernandez, and K. R. Harris, J. Chem. Phys. 134, 144507 (2011). 26 W. A. Bassett, High Press. Res. 29, 163 (2009). 27 S. Klotz, K. Takemura, T. Straessle, and T. Hansen, J. Phys. Condens. Matter 24, 325103 (2012). 28 K. K. A. Grzybowski, K. Koperwas, and M. Paluch, J. Chem. Phys. 140, 044502 (2014). 29 K. R. Harris, M. Kanakubo, and L. A. Woolf, J. Chem. Eng. Data 52, 1080 (2007). 30 C. A. Angell, Science 267, 1924 (1995). 31 Y. U. Paulechka, G. J. Kabo, A. V. Blokhin, A. S. Shaplov, E. I. Lozinskaya, D. G. Golovanov, K. A. Lyssenko, A. A. Korlyukov, and Y. S. Vygodskii, J. Phys. Chem. B 113, 9538 (2009). 32 T. S. Ingebrigtsen, L. Bohling, T. B. Schroder, and J. C. Dyre, J. Chem. Phys. 136, 061102 (2012). 33 J. Jacquemin, P. Husson, V. Mayer, and I. Cibulka, J. Chem. Eng. Data 52, 2204 (2007). 34 A. V. Blokhin, Y. U. Paulechka, A. A. Strechan, and G. J. Kabo, J. Phys. Chem. B 112, 4357 (2008). 35 M. C. C. Ribeiro, T. Scopigno, and G. Ruocco, J. Phys. Chem. B 113, 3099 (2009). 36 R. Casalini, R. F. Gamache, and C. M. Roland, J. Chem. Phys. 135, 224501 (2011). 37 M. C. C. Ribeiro, A. A. H. Pádua, and M. F. C. Gomes, J. Chem. Thermodyn. 74, 39 (2014).

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 131.230.42.7 On: Sat, 06 Dec 2014 01:56:03

Glass transition of ionic liquids under high pressure.

The glass transition pressure at room temperature, pg, of six ionic liquids based on 1-alkyl-3-methylimidazolium cations and the anions [BF4](-), [PF6...
640KB Sizes 2 Downloads 3 Views