A physicochemical investigation of ionic liquid mixtures† †Electronic supplementary information (ESI) available. See DOI: 10.1039/c4sc02931c Click here for additional data file.

A comprehensive study of ionic liquid mixtures reveals a remarkable adhesion to ideal mixing laws, with some consistent exceptions.


Introduction
Ionic liquids are, by denition, liquids composed exclusively of ions. Although this denition applies to all molten salts (e.g. molten NaCl at >801 C), the term is commonly used to refer to compounds that are liquid at much lower temperatures, with room temperature ionic liquids (RTILs) being of particular interest. 1 The broad range of possible cation and anion combinations has led to ionic liquids being labelled 'designer solvents', 2 and RTILs are nding increasing widespread application in synthetic chemistry, in engineering applications, 3,4 and in dissolution and modication of lignocellulosic biomass. 5 However, this synthetic exibility can render it difficult to choose the best ionic liquid for any given application. Further problems arise with the use of such a wide range of compounds outside of academic laboratories, whereby each distinct ionic liquid requires a full analysis under Registn, Evaluation, Authorisation & restriction of Chemicals, 'REACH' (or similar outside the European Union). 6 This is a lengthy and costly process.
One viable approach to circumvent these problems is the formulation of ionic liquid mixtures. [7][8][9][10] This offers a number of advantages: (i) the component ionic liquids have well-characterised properties; (ii) syntheses of the simple ionic liquids are well known, and the prepan of mixtures is trivial; (iii) only the pure components of mixtures currently require registn under REACH. 6 Mixing could potentially lead either to formulations that have properties outside the ranges dened by the pure components, or, if mixing is close to ideal, could allow precise ne-tuning of properties within the boundaries imposed by the simple ionic liquids. Either outcome would carry potential economic and scientic benets. In this paper we report the results of a study designed to determine which of these situations arises when common ionic liquids are mixed.
A constituent of a mixture refers to any chemical species present in the mixture; a component is a thermodynamically independent constituent. In an aqueous solution of sodium chloride, water, sodium and chloride are all constituents of the solution, but water and sodium chloride (because the concentn of the two ions is inseparable) are the components of the solution. An ion on its own cannot be a component.
In this contribution, we adopt a nomenclature for naming ionic liquid mixtures based upon the number of components in the product mixture. Hence, [ To understand the inuence of mixing on various physical and chemical parameters of ionic liquids, a series of binary and reciprocal binary ionic liquid mixtures were prepared and analysed. The incorporated cations and anions were selected in order to cover a wide range of commonly encountered species, including imidazolium, [C n C m im] + , pyrrolidinium, [C n C m pyrr] + , pyrazolium, [C n C m C p pz] + , and diazabicycloundeceniumderived, [R-DBU], ionic liquids. The investigated cations and anions are shown in Fig. 1. A mixture series is the set of ionic liquid mixtures created by altering the mole fraction, c, of the components. The mixture series investigated in this contribution are listed in Table 1.
Several recent publications have focused on attaining an understanding of the physical properties of ionic liquid mixtures. Foremost, the density and excess molar volume has been determined for mixtures of common ionic liquid cations and anions. Canongia Lopes et al. conducted an extensive early study into binary mixtures incorporating [C n C 1 im] + , [NTf 2 ] À , [PF 6 ] À and [BF 4 ] À ions. 11 The resultant mixtures were found to broadly obey the ideal mixing law; where exceptions arose, excess molar volumes were small and positive, indicating an absence of new strong interactions in the mixture. Indeed, such a trend is typically observed across the ionic liquid mixtures literature, [11][12][13][14][15] although specic examples of negative excess molar volumes (e.g. binary mixtures of [C 3 (C 1 ) 3 12,13 and of ordered nanostructures, 16 are known.

py][N(CN) 2 ][BF 4 ]),
Similarly, conductivity measurements exhibited either expected behaviour upon mixing, 17 or minor deviation above 14,18 or below 19,20 the anticipated values. Occasionally, mixtures were observed to deviate more substantially from the anticipated behaviour, e.g., the binary mixture series [C 2 C 1 im][N(CN) 2 ][BF 4 ]. 14 However, despite this deviation, conductivity values for the mixtures did fall within the boundaries dictated by the component ionic liquids.
Whilst studies of this type have yielded valuable data regarding the physical properties of ionic liquid mixtures, the investigations have generally focused on individual mixtures, or on a limited array of cations and anions, and each employing only a restricted group of techniques.
In this study, we thoroughly investigate a broad series of ionic liquid binary and reciprocal binary mixtures with respect to physical properties of density, viscosity, phase behaviour and conductivity. The incorporated cations and anions were selected in order to cover a wide range of commonly encountered species, varying in size, polarity and asymmetry. This has allowed us to provide key insights as to which properties of the ions control the extent of deviation from ideal mixing for ionic liquids for the rst time.

Experimental
Syntheses of the simple ionic liquids and the precise mole fractions, (c ¼ 0-1), of the mixtures are described in the ESI. † Prior to each measurement, all samples were dried under vacuum until a water content of <150 ppm (w/w) was established via Karl Fischer titn.
Density measurements were performed in an Anton Paar 'DMA38' vibrating tube density meter at 25 C. The error of the instrument given by the manufacturer was AE0.001 g cm À3 , although reproducibility was one order of magnitude better.
Differential Scanning Calorimetry (DSC) results were obtained using aluminium sample pans of diameter 7 mm. Between 7-9 mg of the ionic liquid was measured into the aluminium sample pan. A small incision was made in the tops of both the sample and reference pans. A drying procedure was then implemented: the sample pan was heated to 100 C for 20 minutes in the calorimeter, to remove water. The sample pan was then quickly re-weighed, in order to determine the dry weight of the ionic liquid. The sample was measured between À100 and +100 C, with a heating/cooling rate of 20 C min À1 .
Viscosity measurements were performed on a TA instruments 'AR2000ex' rheometer tted with a Peltier plate at 25 C, using a 40 mm, 2 steel cone. Measurements were performed at an angular velocity between 0.1 and 10 rad s À1 under a nitrogen atmosphere. An error of 5% was established from the manufacturer's information and measurements on standard liquids, although reproducibility was usually better.
Conductivity measurements were performed using a homebuilt conductivity probe with two platinum paddles of size approximately 5 mm Â 5 mm. The temperature was maintained at 25 C using a water bath in a jacketed beaker attached to a recirculator, and the samples were allowed to reach thermal equilibrium for 30 minutes. The measurements were performed under an inert argon atmosphere on a CH Instruments CHI760C apparatus in a frequency range from 1 Hz to 1 Â 10 5 Hz, and at an amplitude of 1 Â 10 À4 V. Prior to each set of measurements the probe was calibrated using three commercially available standards (HANNA instruments) with known conductivities of 84 mS cm À1 , 1413 mS cm À1 and 12 880 mS cm À1 . The average error was found to be 2%.  Temperature-ramped Thermogravimetric Analysis (TGA) experiments were performed on a PerkinElmer 'Pyris 1 TGA' thermogravimetric analyzer, and platinum sample pans of 6 mm diameter. Experiments were carried out in the range 120-600 C. Between 3 and 36 mg of the ionic liquid was measured into the platinum pan. A ramping rate of 10 C min À1 and a nitrogen ow of 20 ml min À1 were employed for all experiments.

Results and discussion
Mixing of the cations and anions in Fig. 1 yields, in the most part, binary and reciprocal binary ionic liquid mixtures that exhibit ideal or close to ideal behaviour with respect to the measured physical properties.
One notable exception is the binary mixture series [C 4  The thermal stability behaviour of the investigated ionic liquid mixtures could be best explained in terms of the stabilities of the component ionic liquids; Thermogravimetric Analysis (TGA) experiments of mixtures mostly exhibit two or more distinct thermal decomposition steps, corresponding to these component ionic liquids. Little or no cooperative behaviour could be observed from the temperature-ramped TGA experiments.
Results for separate physical and chemical properties (molar volumes, viscosity, conductivity, phase behaviour and thermal stability) are discussed individually below. Data for selected ionic liquid mixture series are shown in graphical form, chosen in order to represent at least one example of an ideal/linear mixture series and a non-ideal/non-linear mixture series in each circumstance. All other graphical data can be found in the ESI. †

Density/molar volume
Density measurements were carried out for all ionic liquid mixture series 1-11 (Table 1) Fig. 2. Graphs for the other investigated ionic liquid mixture series, and numerical data, can be found in the ESI (Fig. E2, Table E2 †).
Due to the temperature restrictions of the apparatus, it was not possible to obtain density data for mixtures or simple ionic liquids that were solid at room temperature. In these circumstances, the available data were extrapolated and the corresponding values are given in parenthesis in the ESI (Table E2 †).
The density results indicate that most of the investigated mixture series show clear linear behaviour within the precision of the instrument (AE0.001 g cm À3 ). The molar volume of a mixture is directly related to the chemical potentials of the components of the mixture and so shows linear dependence on the mole fractions of the pure components when ideal mixing occurs. Hence, these can be described as ideal mixtures.
Three mixture series do deviate systematically from linear behaviour, specically [C 4 4 ], a room-temperature solid, could not be measured directly, it was determined by linear extrapolation from the data of the mixtures of 5. The corresponding data should therefore be treated with caution.
To quantify the deviation from ideal behaviour for the abovementioned ionic liquid mixtures, the excess volume DV m was calculated: The corresponding data is shown for ionic liquid mixture series 7 and 10 below (Fig. 3), and for 5 in the ESI (Fig. E3 †).
For the mixture series 5, 7 and 10, the molar volume is larger than expected (excess molar volume) for ideal (linear) mixing. This suggests that there is more free space in these mixtures and the sum of favourable interactions is fewer than expected. These mixtures incorporate a highly-uorinated anion, [NTf 2 ] À , and another anion with no uorine atoms, [MeSO 4 ] À or [Me 2 PO 4 ] À . Hence, one possible explanation is that a loss of uorophilic interactions is occurring, causing a decrease in density. However, the similarity of these results to those of  ], all of which have only uorinated anions, suggest that this is unlikely to be the explanation for our results. 11 It has also previously been suggested that the size differences between ions, and thus packing effects, may be important. Navia 4 ], that differences in the amount of free space, driven by differences in the sizes of ions, in the pure components could lead to the negative DV m values that they observed. 12 Another possible explanation is that disruption of the cation-anion hydrogen bonding in these mixtures could lead to the observed deviation from ideal behaviour. Explanations for the small deviations from ideal behaviour of ionic liquid mixture series 5, 6, 7, 8 and 10 are discussed more fully below.
Overall, the most striking feature of the mixture series studied here, and others that have been reported in the literature 21 is that, with respect to molar volume, their mixing is remarkably close to ideal. Even for the greatest deviations found, the maximum value of DV m was <0.5% (relative to the expected molar volume) for the reciprocal binary mixture series 10, and were smaller still (<0.35%) for the two binary mixture series 5 and 7.
It is, perhaps, unsurprising that binary mixture series 5 and 7 exhibit notably smaller percentage deviations than the reciprocal binary mixtures of 10. For the binary mixtures incorporating, for example, a common cation, chemically distinct anions are likely to be surrounded by a solvation sphere of the common cation as they are in the simple ionic liquids, and therefore the major changes occur in their second solvation sphere where anion-anion interactions will be both long range and weak. These relatively small structural changes would also lead to the corresponding entropy of mixing, DS mix to be small. In the case of reciprocal binary mixtures, the rst solvation spheres of all of the constituent ions liquid are disrupted in comparison to the simple ionic liquids by the introduction of new cations and anions. As well as giving rise to the possibility of larger values of DH mix , DS mix will also be more substantial. The other reciprocal binary mixture series investigated in this study, 11, involves the pairing of far more chemically similar ions than 10, which will partially offset this effect. Precise properties of the ions that inuence non-ideality are examined more thoroughly below.

Phase behaviour
It is well established that many ionic liquids are glass-transforming materials, 22 and therefore do not exhibit a clear freezing point. Introducing additional ionic liquid species generates a further likelihood that no crystalline phase will be observed. 23 For this reason, full phase diagrams are sometimes difficult to obtain. Inorganic salt mixtures oen exhibit eutectic behaviour. 24,25 A recent example of a binary ionic liquid mixture series in the literature, 4 ], demonstrated that the glass transition temperature (T g ) of the mixture may behave as a weighted average of the simple ionic liquid components. 26  ] that the value of T g was a weighted average of the two simple ionic liquids, although T g values for the simple ionic liquids were only 5 C apart. 18 We employed Differential Scanning Calorimetry (DSC) to elucidate the phase behaviour of ionic liquid mixture series, 1-11. A value of T g was measured for each ionic liquid mixture. The DSC conditions are described fully in the experimental section and in the ESI. † Graphs demonstrating the change in T g with changing mole fraction, c, for selected ionic liquid binary and reciprocal binary mixture series are displayed in Fig. 4. Graphs for the other mixture series, tables of numerical data, and one example of a DSC trace are shown in the ESI (Fig. E4, Table E4 †).
For the majority of ionic liquid mixture series in this study, DSC data reveals that the change in T g with changing mole fraction is close to linear. This is most apparent for those mixture series where the T g values of the simple ionic liquids are far apart, for example mixtures of [C 4 Several of the simple ionic liquids, and the majority of the ionic liquid mixtures in this investigation, did not exhibit a clear melting point in the accessible temperature range (À100 to +100 C) of the DSC apparatus. Therefore, the DSC experiments were unable to determine whether the melting points (T m ) for the ionic liquid mixtures behave in an ideal or non-ideal manner. Nevertheless, the DSC experiments demonstrate the linear or close to linear relationship between T g and c for the majority of the investigated ionic liquid mixture series, 1-11. The greatest deviation from linear behaviour was for the two binary ionic liquid mixture series that contain both the [NTf 2 ] À and [Me 2 PO 4 ] À anions, 6 and 7. Series 7 also showed substantial deviation from ideal mixing in the molar volume data.

Viscosity
Graphs of the viscosity data for selected ionic liquid binary mixture series are presented in Fig. 5. Graphs for the other mixture series are shown in the ESI (Fig. E5 †). The corresponding numerical data, including non-ideality parameters 'f', is listed in the ESI (Table E5 †).
Unlike densities, viscosities do not necessarily vary linearly with the mole fraction of the components of a mixture, even when ideal mixing is occurring. Instead, two plausible correlation functions are shown below. The rst is the ideal Katti and Chaudhri mixing law under the assumption of perfectly linear mixing with c (shown as a dashed line in Fig. 5 and E5 †): The viscosity data shows good agreement with the Katti and Chaudhri law 27 for certain mixture series; 11. These represent mixtures where overall changes in viscosity are small, thus errors in viscosity measurements are comparatively high, giving the impression of close adherence to ideal mixing law. For all other mixtures, some deviation towards either higher or lower viscosities was observed.
To quantify the non-ideality of the mixture series, a variation of the Grunberg and Nissan mixing law was employed, 28 which includes an additional parameter, f, to account for nonideality:   (2)), continuous lines include the additional 'f' non-ideality parameter of Grunberg and Nissan (eqn (3)).
Eqn (3) was optimised for all mixture series, and is shown as a continuous line in the corresponding graphs ( Fig. 5 and E5 †).
The additional 'f' parameter (ESI Table E5 †) allows near quantitative tting for seven of the eight mixture series that were not well described by the Katti  Therefore, 10 of the 11 studied mixture series can be described by either Katti and Chaudhri or Grunberg and Nissan mixing laws. Those only described by Grunberg and Nissan mixing law cannot be regarded as adhering to ideality, because of the inclusion of the f parameter.
[  PO 4 ] are disrupted upon the inclusion of ions from the other component. However, similarly to the density and glass transition temperature experiments, the absolute deviations from ideal viscosity are very small. Thus, within a very reasonable error, it remains possible to predict and obtain the desired property (within the boundaries set by the simple ionic liquids).

Conductivity
The conductivity, measured by impedance spectroscopy, is referred to as L m,Imp . The conductivity was also calculated from the self-diffusion constants using the Nernst-Einstein equation, and is presented as L m,NMR . The 'Haven ', R H , is dened as the between the measured conductivity (L m,Imp ) and the conductivity calculated from diffusion coefficients (L m,NMR ), and should be equal to one in a system of fully dissociated and independent ions (eqn (4)).
The conductivity is not directly related to Raoult's law, and therefore does not necessarily scale linearly with the mole fraction, c. Instead, a logarithmic relationship between the conductivity and c has previously been identied as a likely outcome for ionic liquids. 18 Therefore, each of the two conductivity curves (L m,Imp and L m,NMR ) were tted by a logarithmic eqn (5):  Fig. 6. Graphs for other studied mixture series and the corresponding numerical data, including the non-ideality parameter 'f', is shown in the ESI (Fig. E6, Table E5 †).
With the inclusion of the f parameter, the conductivity data can be well tted for the majority of ionic liquid mixture series investigated; all values fall within or close to within the error. The reciprocal binary mixture [C 4 11, exhibits the worst t for the conductivity measured from diffusion coefficients, L m,Imp (Fig. E6b †). However, the differences in measured conductivities of the two simple ionic liquids, [C 4 C 1 im][OTf] and [C 4 C 1 pyrr][NTf 2 ], are relatively small (DL m,Imp ¼ 2.0 Â 10 À5 S m 2 mol À1 , DL m,NMR ¼ 1.0 Â 10 À5 S m 2 mol À1 ). Therefore, even proportionally large deviations from a logarithmic curve amount to very small deviations from the expected conductivity for any ionic liquid mixture.
In contrast to the molar volume, glass transition temperature and viscosity studies, the two binary mixture series incorporating both the [NTf 2 ] À and [Me 2 PO 4 ] À anions, 6 and 7, demonstrate a reasonable logarithmic correlation between the conductivity and mole fraction.
A Walden plot representing the relationship between the log of viscosity and log of conductivity for [C 4 C 1 im][NTf 2 ][Me 2 PO 4 ], 7, is shown in Fig. 7 and in the ESI for all other mixture series (Fig. E7 †). 29 Considering the Stokes-Einstein and Nernst-Einstein equations, one would expect that a lower viscosity causes a higher conductivity, and vice versa. Therefore the non-ideality parameters, 'f', for the two conductivities are expected to always be of opposite sign relative to the corresponding calculated viscosity parameter. However as demonstrated by the tabulated f values in the ESI (Table E5 †), this is not the case. There appears to be a general tendency for the bulk conductivities from impedance spectroscopy, L m,Imp , to be higher than ideal, while those calculated from self-diffusion constants, L m,NMR , tend to be lower. However, no linear or other correlation between f visc and f Imp or f NMR is apparent. It must, therefore, remain unclear whether a relationship exists.
The overall deviations from ideal behaviour for both viscosity and conductivity are relatively small and the anticipated linear relationship between log L m and log h À1 holds well, with the exception of the more strongly deviating mixture series, most notably [C 4 C 1 im][NTf 2 ][Me 2 PO 4 ], 7 (Fig. 7).
Overall, the majority of mixture series investigated, 1-11, exhibit either ideal or close to ideal conductivity with respect to both the measured and the calculated values (L m,Imp and L m,NMR , respectively). Moreover, a linear or fairly close to linear relationship between log L m and log h À1 is established for all the investigated ionic liquid mixture series. Even for the mixture series that exhibited the largest deviation from expected behaviour, notably 11, absolute differences in L m,Imp and L m,NMR are minor. Therefore, ionic liquid mixtures can be expected to behave systematically with respect to conductivity; data points are tted well by a logarithmic curve.

Thermal stability
Thermogravimetric Analysis (TGA) has frequently been used to investigate the thermal stability of simple ionic liquids. [30][31][32][33][34][35][36] The T onset parameter, acquired by employing a step-tangent method, is oen used to quantify thermal stabilities of ionic liquid compounds. [36][37][38] This method suffers from an overestimation of long-term thermal stabilities, 36,39,40 however, the T onset parameter is benecial when comparing thermal stabilities of like compounds. This assumes that care is taken to keep experimental conditions uniform. 41 However, the thermal decomposition behaviour of ionic liquid mixtures has only been partially studied. 42 Thermal decomposition is a chemical property and not a physical property. Thermal stability experiments can demonstrate whether individual components in a mixture decompose separately, with similar T onset values to those of the neat ionic liquids. Alternatively, cooperative thermal decomposition behaviour may occur.
TGA experiments were performed for all ionic liquid mixtures in this investigation. TGA thermographs for ionic liquid mixture series 1, 7 and 10 are displayed below in Fig. 8. TGA thermographs for the other investigated mixture series are shown in the ESI (Fig. E8 †). T onset decomposition temperatures for investigated ionic liquids and mixtures are listed in the ESI (Table E6 †).
For the binary ionic liquid mixture series in this study the temperature-ramped TGA experiments reveal that no signicant stabilizing or de-stabilizing effect is conferred on the constituent ions by the incorpon of additional constituents into a mixture. Instead, TGA thermographs for the mixtures display two distinct steps. This phenomenon is particularly pronounced for the mixtures where the T onset temperatures of the component ionic liquids are substantially different, for example in the case of [C 4 C 1 im]Cl[OTf], 1 (DT onset ¼ 155 C), shown in Fig. 8a.
It has been noted that for ionic liquids incorporating the [NTf 2 ] À anion, vaporisation of the intact ionic liquid is likely to make a signicant contribution to mass loss. [43][44][45][46][47][48][49][50] Only two reciprocal binary ionic liquid mixture series were studied, Therefore in summary, the temperature-ramped TGA experiments demonstrate that, in the majority of cases, the thermal stability of ionic liquid mixtures can be understood in terms of separate decomposition of the individual constituent ions. This, in agreement with previous literature, manifests as multiple weight loss steps. 42 There were no observed examples where the thermal stability of a mixture was substantially lower (>30 C) than that of the less stable component ionic liquid. This is likely to prove benecial when selecting ionic liquids for high-temperature applications.

nalisation of ionic liquid mixing behaviour
For each of the physical and chemical parameters investigated, the majority of the studied ionic liquid mixture series behaved in an ideal manner. Upon changing c of the component ionic liquids, the molar volume, V m , glass transition temperature, T g , viscosity, h, and conductivity, L m,Imp and L m,NMR , each exhibited the expected linear or logarithmic pattern, for the overwhelming majority of mixture series. Deviations from ideality are typically very small. This is in accord with the available literature. [11][12][13][14][15][17][18][19][20] Ideality arises when DH mix is equal to zero and mixing is entirely entropy driven. Navia 12 This does not mean that all interactions in the mixture are the same as the interactions in the pure components, but rather that the sum of the interactions in the mixture are the same as the sum of the interactions in the pure components. We have previously shown on the basis of uv-vis spectroscopy of 1-ethyl-4-(methoxycarbonyl)pyridinium iodide in a variety of ionic liquids that this can be the case. 10 This is, at least partly, due to the high degree of charge screening that is found in ionic liquids. [51][52][53][54] In addition to this, we should recognise that the choice to study the mixing of room temperature ionic liquids has an important effect. Many room temperature ionic liquids have much in common, e.g., containing ions having similar size, charge delocalisation and asymmetry. Hence, we have selected systems in which it is relatively likely that the condition, that the sum of the interactions in the pure components is close to the sum of the interactions in the mixtures, is met, although the strengths of individual interactions are likely to differ. Hence, the close to ideal mixing that has been observed for many ionic liquid mixtures is partly an expression of the similarities of many of the ions commonly used in ionic liquids.
Nevertheless, perfect ideality is rare and while similar in many ways, different ionic liquid ions are not identical. In our examples, the greatest behavioural range of adherence to ideal mixing occurred when mixtures containing different anions, rather than different cations, were formulated. Two binary ionic liquid mixture series with the [NTf 2 ] À and the [Me 2 PO 4 ] À anions (6 and 7) repeatedly demonstrated small, but systematic, deviations from the anticipated ideal behaviour. Ionic liquid mixture series with the [NTf 2 ] À and the [MeSO 4 ] À anions (5 and 10) showed somewhat lesser deviations, while the ionic liquid mixture series with [OTf] À and Cl À (1), [OTf] À and [NTf 2 ] À (3 and 11) or [Me 2 PO 4 ] À and [MeSO 4 ] À anions (2) exhibited almost no deviation from ideal behaviour. Similar results have also been observed by others. 20 In the following section we attempt to determine which properties are most signicant in leading to non-ideal behaviour. Selected experimental and computational physical parameters, relating either to the component ionic liquids or the constituent cations and anions, have been tabulated (Tables 2-5, below). Data was acquired from the ionic liquid literature, or measured where required. All computational calculations were performed using DFT at the B3LYP/6-311+G(d,p) level of theory. Complete procedures are described in the ESI. † One possible explanation for the deviations from ideal behaviour is that they are due to differences in the sizes of ions. Navia 4 ], that differences in the sizes of the ions of the component ionic liquids could lead to differences in the availability of free space, which in turn could lead to the negative DV m values upon mixing. 12 To explore this possibility, the differences in the molar volumes, DV m , of the constituent cations and anions were obtained from DFT volume calculations for all the mixture series 1-11 (Table 2). Where multiple stable conformations of an ion occur, V m for the different conformations were found to be similar (AE2 cm 3 mol À1 ), and the lowest in energy or demonstrably most prevailing conformer (see later discussion of [NTf 2 ] À ) was used to construct the data in Table 2. Single ion V m are reported in the ESI (Table E7 †).
The DV m values indicate no clear correlation between the size difference of the ions and the extent of deviation from expected behaviour. Typically, the size differences between the anions were of greater magnitude than size differences between the investigated cations. The largest molar volume differences were encountered for mixtures of [NTf 2 ] À with either [OTf] À or [MeSO 4 ] À ; mixture series 3, 5, 10 and 11 (DV anion m ¼ 59-61 cm 3 mol À1 ). Mixtures of 5 and 10 exhibited positive deviation with respect to molar volume (Fig 3b and E3 †), yet in contrast series 3 and 11 displayed almost perfect linear behaviour. Furthermore, the two mixture series that exhibited consistent deviation from the anticipated behaviour, 6 and 7, incorporating the [NTf 2 ] À and [Me 2 PO 4 ] À anions, have comparatively small values of DV anion m , 41 AE 8 cm 3 mol À1 . This value for 6 and 7 was similar to that of mixtures of [C 4 C 1 im]Cl[OTf], 1, a mixture series which gave close to ideal behaviour across the spectrum of investigated physical properties. Therefore, explanation for nonideality on the basis of size differences between the ions seems implausible.
An alternative explanation may lie in the difference in polarity or hydrogen bond character of the ionic liquid ions that are incorporated into the mixture.
The multi-parameter Kamlet-Ta empirical polarity scale has been employed extensively for the characterization of ionic liquids. 55 Of particular interest to the ionic liquid mixtures discussed in this investigation are 'hydrogen bond acidity', a, 56 dictated largely by the cation, and the 'hydrogen bond basicity', b, 57 which depends heavily on the nature of the anion.
Previously, we have demonstrated that the values of a and b can be predicted effectively by using a variety of computational descriptors. 58 Table 3.
Strikingly However, these values are comparable to other mixture series which did exhibit ideal mixing behavior, e.g., 1 and 2.  Thus, it appears that substantial differences in hydrogen bonding behaviours might contribute to the observed deviations from ideality for the investigated ionic liquid mixtures. For example, incorporating the poor hydrogen bond acceptor [NTf 2 ] À (b ave ¼ 0.25) anion into a [Me 2 PO 4 ] À (b ave ¼ 1.01) containing liquid would place the [NTf 2 ] À anion into a cavity formerly occupied by a [Me 2 PO 4 ] À anion. The inability of the [NTf 2 ] À anion to maintain the network of hydrogen bonds could lead to a change in the structure and ordering of the liquid in which there is a net reduction in favourable interactions and an increase in molar volume. However, this could not be the only explanation and other factors do appear to be critical as well.
The anisotropy of ionic liquid ions and the directional nature of bonding interactions contribute to the structural and dynamic properties of the bulk liquid. 59,60 The dipole moment, p, of a chemical species is a measure of its polarity and anisotropy, given as the magnitude of two equal, but opposite, charges multiplied by the distance between these (in units of debye, D).
Strictly, the term 'dipole moment' can refer only to species with no overall charge; ions therefore cannot have a dipole moment, instead possessing a monopole moment. 64 However, a value of 'dipole moment' evolves from DFT calculations. This value is the distance between the centre of mass of the ion and its centre of charge.
Kobrak and co-workers developed the concept of the 'charge arm', as a description of the anisotropy of ionic liquid ions, and related these values to the viscosity of ionic liquids. 65,66 The charge arm, R ca , is dened as the distance between the center of mass and the center of charge (Fig. 9), using the 'Natural Bond Orbital' (NBO) model. 67 The charge arm is able to describe multipoles in ions (with overall charge), unlike the true dipole moment, p, which describes neutral species. For simplicity, and to differentiate from the 'charge arm' parameter which is also a measure of distance between the centres of charge and mass of the ions, we will refer to DFT-calculated p values as the 'dipole moment'. In practice, our calculated 'dipole moments' differ from the 'charge arm' because of the model by which atomic charges are calculated; the DFT 'dipole moments' are determined using the CHelpG model, 68 our 'charge arm' calculations employ the NBO model, 67,69 a method acknowledged for being relatively insensitive to the basis set. 70 Hence, performing 'charge arm' calculations with the ChelpG model instead of the NBO model reproduces values in close agreement with the DFT 'dipole moment' values.
Differences in the dipole moment for the cations and anions (Dp cation and Dp anion , respectively) were calculated for all ionic liquid mixture series, 1-11 (Table 4). The principle values of Dp are listed rst, followed by values in parentheses referring to when an ion conformer of higher energy or demonstrably less prevalent in solution is employed. Particular ions, notably [Me 2 PO 4 ] À , [NTf 2 ] À and [(HOC 2 ) 3 C 1 N] + , show a signicant dipole moment dependence on ion conformation.
The most signicant Dp values correspond to series 1 and 4; in these instances, large differences in the cation dipole moment, Dp cation , provides the explanation (although comprehensive conformational analysis of the alkyl chain-containing [C 4 C 1 im] + cation would be necessary, to fully conrm this). These mixture series adhere closely to ideal law, with little deviation. Thus, differences in ion dipole moments do not appear to provide a convincing nale for deviation from ideality when it does occur.
Previously, we evaluated charge arm lengths, R ca , for the [C 4 C 1 im] + cation, and a novel siloxane-incorporating imidazolium cation, [(SiOSi)C 1 C 1 im] + . 71 Using the same methodology, the charge arm lengths were calculated for all cations and anions in this study, using the 'Natural Bond Orbital' (NBO) charge model, and are tabulated in the ESI (Table E7 †). Subsequently, charge arm differences (DR cation ca and DR anion ca ) were determined for all mixture series 1-11, and are listed in Table 5. Given the high degree of exibility and large number of conformations possible for several of the ions, the principle DR ca values in Table 5 were determined using the lowest energy (most prevalent) conformer of each ion, as for the Dp values above ( Table 4). The DR ca values in parentheses refer to calculations based on a less prevalent or higher energy conformer for one or several ions.
The results indicate a possible relationship between the magnitude of DR ca values and the extent of deviation from ideality for ionic liquid mixture series ( Table 5). Mixtures of 6 and 7, which consistently deviated from ideal mixing law, exhibited the largest primary DR anion ca value for mixtures containing different anions (0.61Å), caused by the long charge arm of low-energy [Me 2 PO 4 ] À (1.42Å) and the comparatively short charge arm of cis [NTf 2 ] À (0.81Å). Larger values of DR ca were exhibited by mixture series 4, 8, 9 and 10, which contain different cations series. However, the mixture series 5 and 10, which gave the highest excess molar volumes, exhibited low primary DR anion ca values of 0.23Å. Therefore, on initial inspection, the charge arm differences, DR ca , do not account well for the deviations from ideal behaviour.
However, R ca values vary dramatically upon changing the ion conformation. This is in contrast to calculated molar volumes, V m , which were almost identical for differing conformations of the same ion. One individual conformer of [(HOC 2 ) 3 C 1 N] + exhibited a very high R ca value of 1.56Å, in contrast to another conformer with a charge arm length of just 0.50Å. The impact of the ion geometry on the charge arm, R ca , is highlighted in Fig. 9, with reference to the 1-decyl-3-methylimidazolium cation, [C 10 C 1 im] + .
The disparity in R ca between different conformers was exemplied by [NTf 2 ] À ; the cis conformer (C1 symmetry) has a charge arm of 0.81Å, whereas the trans conformer (C2 symmetry) has a charge arm length of just 0.03Å suggesting that the centers of mass and of charge almost coincide. Critically, the uncorrected energy difference between these two conformers (<3.5 kJ mol À1 ) is smaller than the error in the calculation, consistent with previous investigations. 72 76 our DFT-calculated wavenumbers were scaled by a factor of 1.047, based on the disparity between the intense peak at $736 cm À1 in the experimental spectra and the calculated value, 702.9 cm À1 , for the same peak. Full experimental and computational procedures are detailed in the ESI. † Furthermore, experimental and calculated Raman spectra are displayed in the ESI (Fig. E10 †).
The experimental Raman spectra, for each of the four abovedescribed liquids, exhibited fairly broad peaks that were nontrivial to assign. To differentiate between the predominant trans or cis geometries of the [NTf 2 ] À anion, specic regions of the Raman spectra were focused upon.
The Raman spectra from 595-675 cm À1 were also examined ( Fig. E10c-f †). With reference to mixtures of salt Li[NTf 2 ] with diglyme, it has been demonstrated that peaks in this lowintensity region may be used in order to distinguish between trans (629 cm À1 ) and cis (653 cm À1 ) ion conformers. 77,78 Each of the Raman spectra in this investigation exhibited both of these two peaks indicating some appreciable contribution from each of the trans and cis ion conformers of [NTf 2 ] À . Therefore, the obtained Raman spectra, and previous investigations, highlight a contribution from both the cis and trans geometries of [NTf 2 ] À . However, on the basis of the abovedescribed experiments, it is sensible to obtain primary DR ca and Dp values for mixture series 3 and 11 using the calculated R ca and Dp values of trans [NTf 2 ] À , instead using cis [NTf 2 ] À for series 5, 6, 7 and 10 (Tables 4 and 5). Nevertheless, we acknowledge that these values represent only a rudimentary approximation.
We further considered the potential inuence of ion geometry on the charge arm. R ca , and the SCF energy, DE (kJ mol À1 ), with detailed investigation into the [NTf 2 ] À , [Me 2 PO 4 ] À and [MeSO 4 ] À anions; conformational analysis was performed about an S-N-S-CF 3 , O-P-O-CH 3 or O-S-O-CH 3 dihedral angle, respectively (shown in graphical form in Fig. E11 †). These anions were selected because their mixtures gave the most signicant (but still small) deviations from ideal behaviour in the measured physical properties. The other two anions in this investigation, Cl À and [OTf] À , have little or no conformational exibility, and therefore the charge arm value is relatively xed (or zero for chloride, by denition).
The results reveal signicant differences between the charge arm 'exibility' of the anions. The charge arm of [NTf 2 ] À changes substantially with the ion conformation, with an R ca range of >1.1Å and the energy barrier for rotation is fairly low (<25 kJ mol À1 ). Therefore, [NTf 2 ] À may be regarded as a relatively exible ion, able to adapt its charge arm length with ease. Similarly, the [Me 2 PO 4 ] À anion has a difference of $1Å between its largest and smallest charge arm values (although the dihedral scan of one methoxy group, with free rotation of the other, does not reveal all the stable ion geometries). By contrast, the R ca range of [MeSO 4 ] À is smaller (<0.1Å); therefore, this ion may be considered inexible.
One might expect that ions with exible charge arms would reorient themselves to minimize the difference in charge arm of the ions in the mixture. To an extent, this appears to be the case, based upon the Raman spectra for [C 4 PO 4 ] À or simply [C 4 C 1 im] + ), it adopts a predominant cis (high R ca ) geometry. By contrast, the incorpon of low charge arm [OTf] À seems to change the prevailing composition of [NTf 2 ] À towards low charge arm trans geometry. However, when the highly 'exible' [NTf 2 ] À anion is paired with the fairly exible [Me 2 PO 4 ] À anion, the deviation from ideal mixing law is similar, or greater, than when incorporated with the highly inexible [MeSO 4 ] À anion, depending on the investigated physical property. Therefore, it is apparent that ion exibility does not play a substantial role in minimising deviation from ideal mixing.
We did not measure ionic liquid mixtures containing cations of different alkyl chain lengths via experimental methods. However, we can apply the charge arm analysis to a series of [C n C 1 im] + (n ¼ 1-10) cations, previously investigated by Canongia Lopes et al., 11 and furthermore for cation series [C n (C 1 ) 3 N] + (n ¼ 1-14), and the anion series [C n CO 2 ] À and [C n SO 4 ] À (n ¼ 1-14). For simplicity, all cations and anions were optimised in the 'all trans/anti' conformation, with maximal extension of the alkyl chain. R ca values for the cations are tabulated and shown in graphical form in the ESI (Table E8 and Fig. E12 †).
Unsurprisingly, the results demonstrate a sequential increase in R ca as the alkyl chain 'n' is extended from one carbon (R ca ¼ 0.16Å for [C 1 C 1 im] + ) to 10 (R ca ¼ 4.49Å for [C 10 C 1 im] + ). For the example of dialkylimidazolium cations, additional CH 2 units in the homologous series shi the centre of mass away from the imidazolium ring, whilst the positive charge remains primarily on the ring.
Applying these charge arm calculations retroactively to these prior results, they are consistent with the observation that [C 2 C 1 im] 0.5 [C 10 C 1 im] 0.5 [NTf 2 ] exhibits a greater excess molar volume than ionic liquid mixture [C 4 C 1 im] 0.47 [C 8 C 1 im] 0.53 -[NTf 2 ]. 11 Therefore, large values of DR ca for [C n C 1 im] + ions may be a contributing factor to deviation from ideality in this circumstance, although conformation of the ions is an important considen.
The substitution of long alkyl chains onto the cations and anions introduces a further complication, namely, the potential for the formation of hydrophobic/hydrophilic regions. The presence of such ordered 'domains' is likely to represent an additional source of non-ideality for ionic liquid mixtures. Although we have herein chosen to omit ions with large aliphatic groups, a study into amphiphilic ions is nevertheless worthy of further study and is an area of our ongoing research.
Of the investigated experimental and computational parameters, it is clear that no single property is able to account for, or predict, the extent of deviation from ideality for ionic liquid mixtures on its own. Our results indicate that differences in hydrogen-bond acidity/basicity of ions, and/or in the length and exibility of the charge arm (or dipole moment) each contribute partially to the mixing behaviours of the ionic liquids studied. It is simple to imagine that inserting, for example, an anion of high charge arm into a site in the structure of an ionic liquid composed of anions of low charge arm will be more disrupting to that structure than replacing the low charge arm ion with another of similarly low charge arm. Equally, mixing a low hydrogen-bond basicity ion into the cavity formerly occupied by a high basicity ion may result in the net number of favourable interactions being diminished.
In all the discussion of the factors contributing to nonideality, it must be recognised and remembered that the absolute deviations are extremely small. Practically, then, stoichiometric mixing of well-dened simple ionic liquids provides mixtures with predictable properties. Therefore, the fact that deviation is very minimal, and also that the number and variety of contributing factors to non-ideality is large, contributes to the difficulty in their elucidation.

Conclusions
For each physical property investigated, both here and in other literature, [11][12][13][14][15][17][18][19][20] the majority of ionic liquid mixture series were found to behave in a close-to-ideal manner, arising via a combination of the ionic liquid ions being similar in many respects and the high degree of charge screening found in ionic liquids. [51][52][53][54] Deviations from ideal mixing behaviors are small (values for the studied mixtures were always conned within the boundaries dened by the pure ionic liquids), and arise from differences between the constituent ions, but are not driven by one individual controlling property. It is clear that what little deviation is seen is related to both the differences in short-range interactions, e.g. hydrogen bonding, and steric factors, particularly differences in the asymmetry of ions. In our continuing studies, we will be seeking to further elucidate these factors.
Considering the whole body of information available on ionic liquid mixtures, it is striking to what extent the effects of mixing can be correlated with ideal mixing laws, in the absence of chemical reactions leading to new constituent ions. [79][80][81][82] For the academic or industrial chemist, understanding that formulations of ionic liquids consistently adhere closely to ideal mixing laws allows for a desired physical property to be obtained by careful stoichiometric mixing of two or more well-dened simple ionic liquids. Substantial economic and scien-tic benets are implied by these physical insights, and this additional handle for ne-tuning of ionic liquids further strengthens their reputation as 'designer solvents'.