Unusual Behavior of the Thermodynamic Response Functions of Ionic

Nov 16, 2009 - Telephone: +34-988387213. ... The whole experimental picture is coincident with that of a fluid characterized by a high degree of cohes...
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Unusual Behavior of the Thermodynamic Response Functions of Ionic Liquids ~ a, Paloma Navia, Yolanda A. Sanmamed, Jacobo Troncoso, Claudio A. Cerdeirin Diego Gonz alez-Salgado, and Luis Romaní* Departamento de Física Aplicada, Universidad de Vigo, As Lagoas s/n, Ourense 32004, Spain

ABSTRACT The behavior of the isobaric molar heat capacity Cp, the isobaric thermal expansivity Rp, and the isothermal compressibility κT of room-temperature ionic liquids (RTILs) is studied in detail. Accurate Cp(T,p), Rp(T,p), and κT(T,p) results for a number of RTILs, as obtained by using appropriate experimental techniques, are presented and discussed. It is observed that Rp decreases with T and that, consistently, Cp increases with p, thereby clarifying previous controversial results. The whole experimental picture is coincident with that of a fluid characterized by a high degree of cohesion. Such conclusion arises from the analysis of some loci of extrema of the above thermodynamic response functions as obtained from an equation of state based on thermodynamic perturbation theory. SECTION Statistical Mechanics, Thermodynamics, Medium Effects

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Here, by using accurate experimental techniques to obtain Rp(T,p) and Cp(T,p) for a number of RTILs, we show that (∂Rp/∂T)p < 0 and (∂Cp/∂p)T > 0. In addition, we provide information on the less but also interesting isothermal compressibility κT for these liquid salts. The results are analyzed and discussed within the framework of an EoS for the hard-core square-well fluid derived from thermodynamic perturbation theory. As will be seen, such an oversimplification yields significant insight into fundamental issues. Figure 1 shows Cp(T,p), Rp(T,p), and κT(T,p) for two of the studied RTILs, namely, [emim][BF4] and [omim][BF4]. As advanced, one observes that Rp decreases with T while Cp increases with p. In the light of the equation relating (∂Cp/∂p)T and (∂Rp/∂T)p alluded to above, such trends are mutually consistent. The remaining ones, namely, Cp and κT increasing with T and Rp and κT decreasing with p are of common occurrence in liquids. Furthermore, Figure 2 shows that the residual isobaric heat capacity Cp,res  Cp - Cp,id (where Cp,id denotes the ideal-gas heat capacity) decreases with T,7 which is one of the various Cp,res(T) behaviors reported in the literature.1 These features are representative of the behavior for all studied RTILs. To gain understanding as to why the behavior of RTILs departs from that of molecular liquids, one may first note that the strong and long-range nature of Coulombic interactions makes an RTIL to be (at the experimental working temperature) far below its critical temperature Tc.8 We are thus faced with a close-packed fluid in which, obviously, thermal fluctuations are small and cohesion predominates.

here are strong reasons for studying the behavior of thermodynamic response functions of fluids: on the one hand, some of them (especially, heat capacities) reflect salient features at a molecular level (see, e.g., ref 1); on the other, prediction of such properties as a function of temperature T and pressure p represents a stringent test for equations of state (EoS) as well as for atomistic force fields used in simulations. Analyses of response functions for (aprotic) room-temperature ionic liquids (RTILs) has revealed the following two facts: (i) the isobaric thermal expansivity Rp  -1/F (∂F/∂T)p and the isothermal compressibility κT  1 /F (∂F/∂F)T (where F stands for the density) are typically small and vary little with T and p (see, e.g., ref 2) and (ii) the isobaric (molar) heat capacity Cp  (∂H/∂T)p (where H stands for the enthalpy) increases with T and correlates with the molecular volume.3 There are, however, open questions that deserve further attention. Early reports on the thermodynamic properties of RTILs evidenced conflicting results regarding the temperature dependence of Rp.4 Subsequent experimental studies for a limited number of such liquids have shown that (∂Rp/∂T)p could be unexpectedly negative.5 Such conclusion must be taken with especial care since accurate determinations of Rp are difficult to obtain: this property is usually derived from F(T) data using procedures that can produce numerical artifacts;6 furthermore, when using vibrating-tube density meters to determine F, which is the most commonly used approach, the eventually large viscosity of RTILs induces errors that, if not properly corrected, lead to spurious effects in Rp(T) (see ref 5b). To overcome these shortcomings, alternative methods for determining Rp are called for. The problem can also be approached from Cp(p) measurements. Specifically, from the exact thermodynamic relation (∂Cp/∂p)T = -TV[Rp)2 þ (∂Rp/ ∂T)p] one infers that if (∂Cp/∂p)T g 0, then (∂Rp/∂T)p < 0.

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Received Date: September 26, 2009 Accepted Date: October 28, 2009 Published on Web Date: November 16, 2009

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Figure 2. Residual isobaric heat capacities Cp,res as a function of temperature T (at p = 0.1 MPa) for two RTILs. Points are experimental data, while solid lines are smoothed curves.

Figure 3. Loci of isobaric extrema of the isobaric thermal expansivity Rp for the hard-core square-well fluid in the (dimensionless) pressure-temperature (p*-T*) plane. Hypothetically, 1 and 2 correspond to a molecular liquid and an RTIL, respectively, with γ values (γ1=1.5 < γ2=1.8) making the difference between both. The þ symbol indicates that (∂Rp/∂T)p is positive inside the loops, while it is negative outside them. Red and blue lines represent maxima and minima, respectively. The black lines are the binodals ending at the critical point, where loci originate. The arrow serves to locate RTILs at typical experimental ranges.

constant and the number density. In this scheme, cohesion is simply characterized by sufficiently high values of ε and γ. By applying standard procedures, Cp,res, Rp, and κT were calculated. To study the predictions as a function of T and p, we draw loci of extrema in the p-T plane. Such loci are interesting by themselves and will prove especially useful for our purposes, for they delimitate regions of positive and negative signs of the slopes of Cp,res, Rp, and κT with respect to T and p. For the sake of clarity, we only show in Figure 3 loci of isobaric extrema for Rp. The relevant feature is that (∂Rp/∂T)p is negative far below Tc. Accordingly, (∂Cp/∂p)T is positive at sufficiently low temperatures. Nothing especial is, however, encountered for the remaining derivatives: (∂Rp/∂p)T, (∂κT/∂p)T, and (∂Cp,res/∂T)p are negative, while (∂κT/∂T)p takes on positive values. On the basis that the data of Figures 1 and 2 exhibit exactly this pattern of behavior, we conclude that the experimental picture for RTILs may be a natural consequence of their high degree of cohesion within the working ranges.

Figure 1. Isobaric heat capacities Cp, isobaric thermal expansivities Rp, and isothermal compressibilities κT for two RTILs as a function of temperature T and pressure p. For Cp and κT, symbols mean (O) T = 283.15 K, ()) T = 303.15 K, (4) T = 323.15 K. For Rp, symbols mean: (O) p = 10 MPa, ()) p = 30 MPa, (4) p = 50 MPa. Solid lines are smoothed curves.

This should be qualitatively described by an EoS with working ability at sufficiently low temperatures and/or high densities. It is at this point where thermodynamic perturbation theory enters play. In our opinion, overlooking the microscopic complexity of RTILs (e.g., they are known to be microheterogenous media composed of polar and nonpolar domains of nanoscopic size9) may not constitute a problem in the actual context. With the above provisos, we consider the perturbation expansion, up to first order, for a hard-core square-well fluid10 of depth ε and range γd (where d is the hard-sphere diameter). Relevant parameters are the packing fraction y  πFd3/6 and the dimensionless temperature T*  kBT/ε and pressure p* = p/(6ε/πd3), where kB and F  N/V denote the Boltzmann

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exact thermodynamic relation (∂V/∂T)p = -(∂S/∂p)T,19 the difficulties exposed in the introduction being avoided as a result. Densities were also used to derive κT(T,p) (see, e.g., ref 20). Experimental uncertainty is (0.005 mK-1 for Rp, (0.2% for Cp, and it ranges from 0.5% at intermediate p to 1.5% at low p for κT. Data have been obtained for temperatures close to room temperature and at pressures up to 50 MPa. Measurements have been performed for [bmim][BF4], [hmim][BF4], [emim][NTf2], [bmim][NTf2], [hmim][NTf2], [bpyr][BF4], [opyr][BF4], [emim][EtSO4], [bmim][MeSO4], [bmim][CF3SO3], [hmim][CF3SO3], [bmim][SbF6], and [hmim][Br]. All these data as well as more detailed information on experiments can be found elsewhere.21

Loci for “low” and “high” γ in Figure 3 can be thought of to represent the behavior of a molecular liquid and an RTIL, respectively. Thus, for the same temperature and pressure ranges (∂Rp/∂T)p and (∂Cp/∂p)T change sign in going from molecular liquids to RTILs (this is restricted to moderate pressures), the signs of all other “third-order” derivatives remaining invariant. Figure 3 also dictates that one may recover RTIL-like behavior for molecular liquids at sufficiently high pressures: early results11 indicated that (∂Rp/∂T)p < 0 at high pressures, while more recent experimental data for hexane confirmed that (∂Rp/∂T)p < 0 but also that (∂Cp/∂p)T > 0.12 Therefore, RTILs are especial in that (∂Rp/∂T)p < 0 and (∂Cp/∂p)T > 0 at atmospheric pressure. The behavior of loci of extrema when ε is varied (at constant γ) is embodied in the definitions of p* and T* (see above). Thus, for the same values of p and T, p* and T* decrease as ε is increased (i.e., in going from a molecular liquid to an RTIL). In summary, it is fair to assert that the enhanced strength and range of Coulombic interactions are the fundamental reason for the behavior of RTILs (at the actual temperature and pressure ranges) to correspond to that of a fluid in the low-temperature region of the p-T plane. Although some reported tools for the prediction and/or correlation of the thermodynamic properties of RTILs are successful,9,13 they lack the consistency of a molecular-based EoS. The EoS used here provides valuable information on qualitative grounds; however, it is desirable to have a more detailed, more realistic one. Such a goal could be achieved in the framework of the statistical associating fluid theory (SAFT); in fact, there is work along this direction, but focused on PVT behavior.14 Certainly, carefully assessing the ability of SAFT-like EoS for simultaneously describing vapor pressures, densities, and response functions of RTILs would be of high interest. A further prediction from Figure 3 is that (∂Rp/∂T)p and (∂Cp/∂p)T should change sign at sufficiently high temperatures, where a rich variety of behaviors is likely to be found as long as fluid structure is being destroyed. With the recent discovery that many RTILs are vaporizable without decomposing,15 experiments at such high temperatures appear to be feasible. An alternative route is provided by molecular simulation, which has been proven to be a powerful tool for studying thermodynamic and transport properties of RTILs.16 Likewise, it seems interesting to compare the behavior of aprotic RTILs against that of protic RTILs and molten electrolytes. Elucidating all these issues is an unexplored task; it is, however, a worthwhile and important one from the standpoint of fundamental knowledge. Both Cp(T,p) and Rp(T,p) were determined by Calvet-type microcalorimetry assisted by a precise temperature and pressure control.17 The measuring principle is summarized as follows: the heat fluxes associated with (isobaric) temperature and (isothermal) pressure scans are converted, after proper calibration, to CpV-1 and Rp, respectively. (Implicit in this statement is that the detection zone of the calorimeter is of constant volume.) Accordingly, density data, as obtained using vibrating-tube densitometry,18 yielded Cp(T,p). On the other hand, Rp was directly determined by exploiting the

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AUTHOR INFORMATION Corresponding Author: *To whom correspondence should be addressed. E-mail: romani@ uvigo.es. Telephone: þ34-988387213. Fax: þ34-988387227.

ACKNOWLEDGMENT Comments on the manuscript from LPN Rebelo and JAP Coutinho are greatly appreciated. We are grateful to “Xunta de Galicia” and “Universidad de Vigo” for financial support under Grants No. PGIDIT-06PXIB3832828PR and 08 VI-A12.

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