Transport Properties of Short Alkyl Chain Length Dicationic Ionic

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Transport Properties of Short Alkyl Chain Length Dicationic Ionic Liquids – The Effects of Alkyl Chain Length and Temperature Majid Moosavi, Fatemeh Khashei, Ali Sharifi, and Mojtaba Mirzaei Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.6b02881 • Publication Date (Web): 31 Jul 2016 Downloaded from http://pubs.acs.org on August 1, 2016

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Industrial & Engineering Chemistry Research

Transport Properties of Short Alkyl Chain Length Dicationic Ionic Liquids – The Effects of Alkyl Chain Length and Temperature

Majid Moosavia,*, Fatemeh Khasheia, Ali Sharifib, Mojtaba Mirzaeib

a b

Dept. of Chemistry, University of Isfahan, Isfahan 81746-73441, Iran

Chemistry and Chemical Engineering Research Center of Iran, P.O. Box 14335-186, Tehran, Iran *

Corresponding author. E-mail: [email protected] Tel.: +98-313-7934942; Fax: +98-313-668-9732

1

ACS Paragon Plus Environment


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ABSTRACT In this work, some transport properties of imidazolium-based short alkyl chain length dicationic ionic liquids (DILs) ([Cn(mim)2][NTf2]2), including shear viscosity, diffusion coefficient and electrical conductivity, have been measured and analyzed as a function of temperature and alkyl chain length. Also, the dependence of viscosity on shear rate has been investigated. The small intercepts of plots of shear stress versus shear rate and also the small variations of the viscosity values with changing shear rate show that the studied DILs are moderately non-Newtonian fluids. Temperature dependence of the viscosity of these ILs shows non-Arrhenius behavior which can be fitted well using four well-known equations, namely, power law, Litovitz, Vogel– Fulcher–Tammann (VFT) and Ghatee et al. equations. The activation thermodynamic parameters of these DILs were calculated. The positive values of Gibbs free energy of activation show that the slip of two layers of the fluid is a non-spontaneous process. DOSY NMR spectroscopy was used to measure the diffusion coefficients of the ionic species in these DIL systems. Also, the other parameters such as hydrodynamic radii and transport numbers of anions and cations and dissociation and association degrees of IL molecules were calculated from the diffusion coefficient and viscosity data. We measured the electrical conductivity of these ILs at different temperatures. The ionicity of these DILs which was evaluated using the Walden plot diagnostic showed that these fluids are “subionic”. With the help of the m-fragility parameter, we measured the fragility of these fluids and indicated that these DILs are in the intermediate to fragile range. Also, we showed a correlation between the m-fragility and the ionicity of these ILs.

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1. INTRODUCTION Understanding of the unique physicochemical and transport properties of different classes of ionic liquids (ILs) as green solvents is an important area of ongoing investigations. The possibility of selection of different cations and anions in the structure of ILs allows for a large variety of tunable properties and applications. Dicationic ILs (DILs) with two charge centers are composed of two singly charged cations linked to each other by a spacer which is usually an alkyl chain. In their crystalline phase, a singly charged anion is associated with each charge center.1 DILs can be used as surfactants, solvents for high-temperature organic reactions2 and high-temperature lubricants3-6 because of their amphiphilicity, and their high thermal stability especially at high temperatures. They can be also used as stationary phase in gas chromatography columns,7-9 as electrolytes in secondary batteries,10 in electrospray ionization mass spectrometry, in gas-phase ion association for detection of small quantities of anions11 and in dye sensitized solar cells.12,13 Although, the more possibilities of combinations of cations and anions result in a broader variability of the properties in DILs with respect to the traditional mono cationic ones (MILs), the number of experimental and computational studies reported on DILs are very limited.4,14-19 Different kinds of DILs including imidazolium-, pyridinium- and ammonium-based ones with different spacers have been synthesized and characterized recently20-25 and have been used in chemical reactions.2,26,27 However, the most studies on the physicochemical properties of them have been restricted to their thermal properties and stabilities.18-20,28 Anderson et al.20 characterized some properties including thermal stability, shear viscosity (at 30 oC), surface tension and refractive index (at 23 oC) of 39 imidazolium and pyrrolidinium cation based DILs. Shirota et al.19 reported the data of liquid density, surface tension, shear viscosity and also thermal properties of imidazolium-based DILs with different anions at 297 K. It is interesting that the data reported by these two groups for the identical compounds is completely discrepant. The inconsistencies and discrepancies of the experimental studies on physicochemical and transport properties of this unusual class of ILs reveal that the more studies on DILs is indispensable to extend their data bank for both process and product design and development of new models. By changing an ionic species and leaving a counter ion unchanged, the properties of ILs can be systematically investigated. The present study looks into the effects of temperature and alkyl 3



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chain length on the transport properties of three imidazolium-based DILs with short alkyl chain length, (i.e. [Cn(mim)2][NTf2]2 with n=3,4,5), in which the cations are 1,3-bis(3methylimidazolium-1-yl)propane,

1,4-bis(3-methylimidazolium-1-yl)butane,

methylimidazolium-1-yl)pentane

([Cn(mim)2]2+),

respectively,

and

and the

1,5-bis(3anion

is

bis(trifluoromethylsulfonyl)imide ([NTf2]-). As the authors are aware, there is not any study on the transport properties of DILs at different temperatures in the literature. The studied transport properties are shear viscosity, diffusion coefficient and electrical conductivity. As well as the study of rheological behavior of these DILs, their activation thermodynamic parameters are calculated. The DOSY NMR spectroscopy is used to measure the diffusion coefficients of the ionic species in these DIL systems. Also, the other parameters such as hydrodynamic radii and transport numbers of anions and cations are calculated from the diffusion coefficients and viscosity data. With the help of electrical conductivity measuring, we try to investigate the ionicity and fragility characteristics of these systems and the existence of a relation between these parameters in the studied DILs.

2. EXPERIMENTAL SECTION 2.1. Spectral Information and Elemental Analysis. Chemical structures of the cation and anion for the DILs used in this work have been shown in Scheme 1. Abbreviations of the cation and anion have been also given in the scheme. The ILs were prepared according to the standard preparation procedures.20 The ILs were assigned by 1H NMR,

13

C NMR,

19

F NMR (using

BRUKER Ultra Shield 400 spectrometer) and elemental analysis (using a CHNS (Elementar, Vario EL III) elemental analyzer). No extra peak was found in the 1H NMR spectra. The obtained values for the elemental analysis were very close to the calculated values. 1H NMR spectra and all of the analysis data have been summarized in Supporting Information. Since the physical properties of ILs are sensitive to impurities and water content, the synthesized DILs were dried and degassed for 48h at T=333.15 K under vacuum in the presence of P2O5 as a very good water absorbent. The water content of the ILs was estimated by Karl Fischer titration to be less than 200 ppm. The water contents of the [C3(mim)2][NTf2]2, [C4(mim)2][NTf2]2, and [C5(mim)2][NTf2]2 were 184 ppm, 182 ppm, and 176 ppm, respectively. 2.2. Methods. The rheological properties of the samples were measured using a Brookfield Viscometer (DV-II+Pro) with a small sample adaptor. The adaptor consists of a cylindrical 4


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sample holder, a water jacket, and spindle. The viscometer drives the spindle immersed into the sample holder containing the test fluid sample. It measures viscosity by measuring the viscous drag of the fluid against the spindle when it rotates. The viscometer can provide a rotational speed that can be controlled to vary from 0.8 to 200 rpm yielding the shear rate from 0.22 to 56 s−1. The spindle type and speed combinations will produce satisfactory results when the applied torque is between 10% and 100%. The spindle SC4-34 was used in the measurements. The sample holder can hold a small sample volume of 9.7 mL and the temperature of the test sample was monitored by a temperature sensor embedded into the sample holder. The precision of measurements for viscosity, shear stress, and shear rate were lower than 1×10-2 mPa.s, 1×10-2 mPa and 1×10-3 s-1, respectively. Accurate temperature control is a fundamental requirement for the rheological measurements. In the current research, the water jacket was connected to a refrigerated/heating circulator (Julabo, F12-ED) to control the water temperature with a precision of ±0.1 K. The Anton Paar DMA-HPM densitometer was used for measuring the density with a precision of measurement of ±1×10-5 g.cm-3 and temperature was controlled using a circulating water bath (LAUDA ECO SILVER) with a precision of ±0.01 K. DOSY NMR spectra were recorded on a BRUKER Ultra Shield 400 spectrometer with a 4.258 × 103 (Hz/G) nuclear gyromagnetic ratio, 4.4 mm pulsed-field gradient probe, during a specified delay 79.9 ms, during which the diffusion coefficient measured (at different temperatures). The signals of H-C2 of imidazolium ring of [Cn(mim)2]2+ and

19

F in [NTf2]- were used to determine the diffusion

coefficients of cation and anion, respectively. Electrical conductivity of the studied DILs at different temperatures was measured using JENWAY4510 conductivity meter with a precision of measurement of ±0.01 mS.cm-1.

3. RESULTS AND DISCUSSION 3.1. Rheological Behavior of the Studied DILs ([Cn(mim)2][NTf2]2 (n=3,4,5)). Figure 1 shows the shear stress, τ, versus shear rate, γ0, for the studied DILs, [Cn(mim)2][NTf2]2 (with n=3,4,5), at different temperatures in the range of 298.15 to 363.15 K. The non-zero yintercepts of these DILs demonstrated in Table S1 show that the viscosity of these fluids depends upon shear rate and hence they have moderate non-Newtonian behavior. This moderate non-Newtonian behavior of these DILs appears to be similar to that of observed for traditional MILs in some previous works.29-33 The viscosities of the studied DILs as a function of shear 5



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rate at different temperatures were measured and illustrated in Figure 2. For better presentation of the shear-dependent of these DILs, the variation of the viscosity versus shear rate has been shown in the figures at 45oC. As these figures show that the variation of viscosity in the range of shear rate between 14 to 56.0 s−1 are 2.8, 2.5, and 1.5 mPa.s for [C3(mim)2][NTf2]2, [C4(mim)2][NTf2]2, and [C5(mim)2][NTf2]2, respectively. Thus, we can claim that these fluids show moderate non-Newtonian behavior. As these figures show, the dominant behavior of these DILs over the whole studied shear rate range is shear thinning which may be interpreted with the help of the orientation differences of the molecules in the fluids under the influence of stress.29 3.2. Temperature Dependence of the Viscosity of the Studied DILs. Most studies on the traditional MILs have shown that the Arrhenius equation,   0 exp( E R T ) , does not apply.34-36 To investigate the temperature dependence of studied DILs, ln η versus 1/T profiles at shear rate =14 s-1 for the studied DILs have been shown in Figure S1. According to this figure, the studied DILs show non-Arrhenius temperature dependence and thus the fluids may be considered as moderately fragile (non-Arrhenius) liquids. As the temperature of a fragile liquid decreases, its temperature dependence of viscosity smoothly crosses over to a strong (Arrhenius) liquid. The temperature in which this transition takes place is called fragile-to-strong, FS, or crossover temperature, Tx. The temperature dependencies of the experimental measured viscosity of the DILs at 5 oC intervals in temperature range of 25-90 oC have been illustrated in Figure 3 and Table S2. Accordingly, as expected, there is a monotonic decrease in the viscosity of all three studied fluids with increasing temperature. It must be mentioned that there is an unusual behavior in the phase behavior of [C4(mim)2][NTf2]2. While this DIL is solid till about 55 oC, it becomes liquid after this temperature. It is interesting that if we cool this liquid from higher to low temperatures, it will remain liquid at the temperatures as low as room temperatures for several hours. The values of reported viscosity, shear rate and shear stress for this IL in the range of 25-55 oC have been measured in this conditions. To our knowledge, there is a limited number of experimental viscosities of the studied DILs in the

literature.

Single

measurements

of

the

viscosities

of

[C3(mim)2][NTf2]2

and

[C5(mim)2][NTf2]2 have been reported so far. Shirota et al.19 reported the value of 738.9 cP for 6


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the viscosity of [C5(mim)2][NTf2]2 at 297 K which is in agreement with our measured value, 780.77 cP, at this temperature. Payagala et al.28 reported the values of 391.24 cP and 183.26 cP for [C5(mim)2][NTf2]2 at 30 oC and 50 oC, respectively. Our measured values at these temperatures are 519.6 cP and 171.9 cP, respectively, which are in relatively good agreement with Payagala et al. data. There is just one single measurement on the viscosity of [C3(mim)2][NTf2]2 at 30 oC by Anderson et al.20 Their reported value was 249 cP which is very lower than our measured value, 776.7 cP. It seems that their reported value is not reliable and this difference may be attributed to the difference in the methods of measurement and to the levels of water content in this work and their work. The temperature dependence of the viscosity of the ILs at T>Tx (where Tx is FS temperature) has been fitted using some well-known equations such as power law equation (based on the mode coupling theory),37, 38 Litovitz equation,39, 40 Vogel–Fulcher–Tammann (VFT) equation,4146

and recent proposed equation by Ghatee et al.40,

47

The power law equation, based on the

coupling theory has the following form:

 T  Tx    0    Tx 



(1)

where η0, Tx and γ are parameters that depend on the material. The VFT and Litovitz equations are given according to the eqs 2 and 3: B T /(T T )   A e  0 0 

  AeB/ RT

(2)

3

(3)

Both Litovitz and VFT equations are extensions of Arrhenius equation. Although the Litovitz fits viscosity values of some of the non-Arrhenius liquids with acceptable accuracy, it does not contain parameters adhere to some physical meaning. On the other hand, VFT can fit the viscosity of the ionic liquid, and its parameters are related to the dynamics of glass-forming processes. In VFT equation, at the temperature T0 (Vogel temperature), the viscosity becomes infinite and it could be related to Tg (T0 < Tg).47 However, Ueno et al.48 reported that this is often misleading if the range of viscosities being fitted is far above Tg, frequently yielding T0 values higher than Tg which is unphysical. In the VFT equation (eq 2) ɳ is the viscosity of the IL at a given temperature, T, and the fit parameters are the fragility ( B  ) which is related to the free activation energy of fluid, the Vogel 7



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temperature (T0 < Tg), and the limiting high temperature viscosity ( A ). T0 for ILs is usually between 100 and 200 K, A is between 0.1 and 1 mPa.s and B  is typically between 1 and 10.49-52 As it can be seen from Table 1, all of the values of

A , B  , and T0 of the VFT equation for the

studied DILs are within the mentioned ranges. Recently, based on the fluidity (i.e. 1/η) concept, which contrary to the viscosity is a smooth function of temperature, Ghatee et al.40, 47 showed that the viscosity of ILs can be described by the following simple linear equation: 

1     a  bT  

(4)

where a and b are constant characteristics of the fluid and  is a characteristic exponent (with

  0.3 for ILs).40 Ghatee et al.47 illustrated the physical significance of the parameters of the linear eq 4 and derived this equation from the power law equation (eq 1) resulted from mode coupling theory based on sharply varying viscosity. Accordingly, the temperature dependent fluidity with characteristic exponent is indeed the same as the temperature dependent viscosity based on the power law in the context of the mode coupling theory.47 Ghatee et al.47 also calculated the relation between the parameters of power law equation (eq 1), i.e. η0 and Tx, and the parameters of eq 4, i.e. a and b, as T x   (a b ) and 0  (a) . The calculated values for the studied DILs have been listed in Table 2. It can be seen that there is a strong agreement in the values of η0 and Tx, which obtained using two different methods, i.e. by fitting of eq 1 and using parameters of eq 4. Also, the values of Tx obtained from the power law equation for [C3(mim)2][NTf2]2 and [C5(mim)2][NTf2]2 are 256.95 K and 242.31 K, respectively, while the values of Tg for these DILs are 219 K53 and 209.9 K19, respectively. It can be seen that, similar to the traditional MILs,47 for the studied DILs, Tg < Tx. The experimental data of the studied DILs, [Cn(mim)2][NTf2]2 (with n=3,4,5) were fitted well by these four equations. The results of fitting have been demonstrated in Figure 3 and the fitted parameters and the coefficients of determination (R2) for the power law, Litovitz, VFT and Ghatee et al. equations for [C3(mim)2][NTf2]2, [C4(mim)2][NTf2]2, [C5(mim)2][NTf2]2 DILs have been given in Table 1. Accordingly, all of these four equations can describe the temperaturedependent viscosity of these DILs quite accurately. It is interesting that the two-parameter

8


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equations, i.e. Ghatee et al. and Litovitz equations, fit the data as good as three-parameter equations, i.e. power law and VFT equations. The viscosities of the DILs ([Cn(mim)2][NTf2]2 (n=3,4,5)) have been compared with those of some short alkyl chain length MILs (i.e. [Cnmim][NTf2] (n=1,2,3,4,5)) at different temperatures in Figure 4. Filled symbols indicate DILs and open symbols indicate MILs. The data for MILs have been taken from Refs.54,55. As this figure show, the viscosity of DILs decreases with increasing alkyl chain length from C3 to C5 at each temperature. This is in agreement with the results obtained by Tokuda et al.54 for MILs with shorter alkyl chain. As one can see from Figure 4, while viscosity increases from C3 to C5 in a series of [Cnmim][NTf2], it decreases from C1 to C2. Also, the results of Shirota et al.19 show that the viscosity of the DILs decreases from C5 (738.9 cP) to C6 (649.5 cP) and then increases for C8, C9, C10 and C12 (662.9, 678.8, 720.6, and 842.4 cP , respectively) in a series of [Cn(mim)2][NTf2]2 which is in agreement with our results. All these observations show that the trend of variation of viscosity in shorter alkyl chain length ILs is greatly in contrast with that of for longer alkyl chain length ILs. It seems that a balance between two opposite factors determines the properties of ILs. Tokuda et al.54 showed that the addition of a –CH2– unit to the cation of an IL causes a decrease in the molar concentration, which decreases the electrostatic attraction between the cation and anion. On the other hand, the increase in the –CH2– units enhances the van der Waals interactions by means of the alkyl chainion inductive forces and the hydrocarbon-hydrocarbon interactions. With increasing the number of carbon atoms in the alkyl chain, the van der Waals (inductive) forces play more important role and causes the enhancement of the viscosity owing to the frictional forces among ions, aggregates, and clusters. Angell et al.56 also showed that the cumulative effects of the ions and the molecular characters of the ILs along with the Tg and fragility (which will be discussed in the next section) are important in determining the viscosity of electrolyte salts including ILs. The viscosity behavior of the DILs shows the law of corresponding states in the forms of two universal viscosity behaviors as illustrated in Figure 5. In Figure 5 (a), based on the power law equation, plotting (η/η0)-1/γ against (T/Tx) (where Tx is FS temperature) has been led in a single master curve. Also, there is a universal trend in the fluidity of these DILs. As Figure 5 (b) shows, by plotting (η-Φ/-a) versus (T/(-a/b)) in the context of eq 4, it can be seen that a single curve with a strong correlation exists. Therefore, both eqs 1 and 4 demonstrate the law of corresponding

9



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states for the viscosity behavior of the studied DILs using the predicted crossover temperature (FS temperature) as the scaling temperature. 3.3. The Association Activation Parameters for the Studied DILs. The association activation parameters, namely, ΔH* (enthalpy of activation), ΔG* (free energy of activation), ΔS* (entropy of activation), and ΔCp* (change in heat capacity of activation) for their viscous flow were evaluated based on the viscosity results of the studied DILs under the influence of temperature and shear rate. Mukherjee et al.29 showed that the activation parameters of a fluid can be obtained via the following relations. The details of the derivation of these equations have been given in our previous works.31-33 Since, ln η versus T for the studied DILs can be fitted well by a quadratic function (see Figure S1 (b) in supporting information), we have ln   a  b T  c T

(5)

2

where a, b, and c are coefficients of the polynomial. Therefore, the above mentioned association activation parameters can be obtained from the following equations: 

H RT

* 2



d ln  dT

 b  2cT

(6)

* * d H C P   2RT b  3cT  dT

(7)

  V * G  RT ln    hN

(8)

  

* * * H  G S  T

(9)

where, h, N, and V in eq 8 are the Planck's constant, Avogadro's number, and the molar volume of the IL, respectively. The profiles of the evaluated activation parameters versus T for the viscous flow of the studied DILs have been shown in Figures S2-S4 at different temperatures and shear rates. The values of ΔH*, ΔS* and ΔG* for these DILs are positive whereas ΔCp* values are negative. These values reflect the states of internal conditions of the systems. The variations in the activation parameters were guided by their stress-induced conditions. The positive values of ΔG* show that the viscous flow is faced the activation barrier making the process nonspontaneous as is expected. The results show that the magnitude of the activation barrier for each DIL is in the same order of magnitude of its viscosity values. The process was associated with 10


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absorption of heat resulting in positive ΔH*, which expectedly declined with increasing temperature. It can be observed that the ΔCp* values are all negative and they decrease with increasing temperature. Since ΔH* decline with temperature, the ΔCp* values are all negative and also declining for the studied DILs. The diminishing curves of ΔCp* versus temperature are almost linear with almost comparable slopes at a fixed shear rate. Figure 6 shows the compensation plots between ΔH* and ΔS* at different shear rates for the studied DILs. The compensation temperature, Tcomp, at which the activation parameters ΔH* and ΔS* compensate each other, for [C3(mim)2][NTf2]2, [C4(mim)2][NTf2]2, [C5(mim)2][NTf2]2 DILs are 337, 334 and 337 K, respectively. This isokinetic effect is often found in dynamics of chemical processes.57-60 Compensations for the studied DILs at all shear rates supported comparable physicochemical processes operative in these fluids. 3.4. Electrical Conductivity, Ionicity, and Fragility. The electrical conductivity as a function of temperature has been illustrated in Figure 7 and Table S3 for the [C3(mim)2][NTf2]2 and [C5(mim)2][NTf2]2 DILs and the profiles fitted to the VFT equation have been represented by solid lines in Figure 7. Fitted parameters, the coefficients of determination, R2, and the statistical parameters of the VFT equation for the electrical conductivity of the studied DILs have been given in Table S4. The results show that the electrical conductivity greatly contrasts with the viscosity of the samples. This is in agreement with this fact that the liquids with high conductivities are also those with high fluidities (where fluidity is the inverse of viscosity (η-1)). While the viscosity decreases drastically with increasing the temperature for each DIL, the electrical conductivity behaves inversely. Also, while the viscosity of DILs decreases from C3 to C5 with the extension of the alkyl chain length of the cation, the electrical conductivity values of these ILs are almost identical at low temperatures, but these values increase from C3 to C5 at high temperatures. Ionicity is related to the freedom of ions to carry their charge in response to the electrical field, i.e., to the degree of ionic dissociation.48 The ionicity which may be assessed by a Walden plot, is an indicator of how ideally ionic an IL is. The plot of logΛ versus logφ (where φ is fluidity) can be used to classify ILs into ideal, subionic and superionic fluids.49 Walden rule connects the charge mobility of a fluid to its frictional resistance. Usually, there is a direct relation between the conductivity and fluidity of a fluid. Figure 8 shows the Walden plot for the 11



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[C3(mim)2][NTf2]2 and [C5(mim)2][NTf2]2 DILs. As this figure shows, for all cases, the conductivities are below the ideal line and thus, the “subionic” conductivity is illustrated. The position of ideal line was established using 0.01 M aqueous KCl solution. The results show that the studied DILs behave as if there is only a small population of ions and therefore they are subionic. Just for comparison, Figure 8 shows also the Walden plot for some MILs, namely [C2mim][NTf2] and [C4mim][NTf2]. In Figure 8, the curves can be approximated by straight lines for both MILs and studied DILs. Also, according to this figure, although both MILs and DILs are subionic, the ionicity of the studied DILs is more than that of the MILs. This can be attributed to the more number of ions in the DILs compared to the MILs. The fragility of a liquid is referred to the temperature-dependent dynamics of supercooled liquids near the glass transition.61 To quantify fragility, it is usual to use the m-fragility parameter. This parameter quantifies the deviation from Arrhenius law in the logη versus (Tg/T) plot and is defined as m=dlogη/d(Tg/T) at Tg where Tg is the glass transition temperature. Strong liquids that show almost Arrhenius behavior have small m values, while the fragile liquids, which show significant deviations from Arrhenius equation, have larger m values. Wang et al.62,

63

showed that a limiting value of m=170, because the glass transition at that limit would resemble a second order thermodynamic transition. While the strong liquids such as SiO2 and GeO2 obey the conventional Arrhenius kinetics and are of little interest, the fragile liquids are full of novelty due to their unusual relaxation behavior.48 Figure 9 shows the fragility plot for [C3(mim)2][NTf2]2 and [C5(mim)2][NTf2]2 DILs and also [C2mim][NTf2] and [C4mim][NTf2] MILs. The values of Tg used in this plot for [C3(mim)2][NTf2]2 and [C5(mim)2][NTf2]2 have been considered as 219 K53 and 209.9 K19, respectively. Also, the values of Tg for [C2mim][NTf2] and [C4mim][NTf2] are 181.15 K55 and 184.51 K55, respectively. As this figure shows, both studied DILs and also MILs are fragile liquids and the alkyl chain length has a little effect in each case which is in agreement with the results obtained by Leys and co-workers.64 To quantify the fragility-ionicity relationship, the measured m-fragilities of both studied DILs and also MILs (for comparison) have been plotted as a function of departure from ideal Walden line, ΔW, in Figure 10 according to the method which proposed by Ueno et al.48 As this figure shows, these ILs may be classified as “poor” ILs. The values of m-fragility for [C3(mim)2][NTf2]2 and [C5(mim)2][NTf2]2 DILs are 99.7 and 76.2, respectively.

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3.5. Diffusion Coefficients, Hydrodynamic Radii, Dissociation and Association Degrees, and Transport Numbers. Since the diffusion coefficient depends on the nature of fluid and intermolecular interactions, it can give good information about the events occurred in the fluid. The 1H and

19

F DOSY-NMR techniques were used to measure the diffusion coefficients of

cation and anion of the DIL molecules. Table 3 shows the values of the total diffusion coefficients (D) and also the diffusion coefficients of cation (D+) and anion (D-) of the studied DILs at 60 oC. This is noticeable that the temperature, molecular aggregation and viscosity are important parameters which can effect on the molecular diffusion. Among these quantities, viscosity has special importance. According to the Table 3, the behavior of diffusion coefficients of cation (D+) and anion (D-) of DILs are similar to that of the total diffusion coefficient of DIL molecules. In each case, the diffusion coefficients increase from [C3(mim)2][NTf2]2 to [C5(mim)2][NTf2]2. This can be attributed to the decreasing of viscosity in the [Cn(mim)2][NTf2]2 DILs from n=3 to n=5. Lower viscosity in [C5(mim)2][NTf2]2 results in the higher rates of ions in the solution and so the larger diffusion coefficient. Since the anions are smaller than the cations in the studied DILs, it is expected that they have more diffusion coefficients. The Hydrodynamic radius can refer to the Stokes-Einstein radius of a solute which is defined as the radius of a hard sphere that diffuses at the same rate as that solute.65 Hydrodynamic radii of the cation and anion in the studied DILs can be calculated using the Stokes-Einstein relation as follow: D 

kT

(10)

c  rh

where D is the self-diffusion coefficient, rh is the hydrodynamic radius, η is the viscosity, k is the Boltzmann constant, T is the absolute temperature and c is a constant. The value of c is different depends on the viscosity of fluid. For large molecular size solutes in small molecular size solvent environments, c can be as high as 6. As the solute and solvent become more similar in size, especially in higher viscous liquids such as ILs, the value of c is reduced to about 4.66 We used the value of c=4 in all calculations. According to eq 10, the hydrodynamic radius is an inverse function of the viscosity and diffusion coefficient: rh 

1 D

(11)

13



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Thus, the hydrodynamic radii of the cation and anion depend on the competition between these two factors, i.e. the viscosity and diffusion of ILs. As mentioned, the trends of variation of diffusion coefficient and viscosity are opposite in these DILs. Hydrodynamic radii of the cation and anion of the studied DILs were calculated using the diffusion and viscosity data and illustrated in Table 3. This table shows that the hydrodynamic radii of the cation and anion increase with increasing the length of alkyl chain in these DILs. As expected, the values of the hydrodynamic radius of cation is greater than that of the anion in these DILs. According to this table, the radius of the imidazolium-based cations increase with increasing the alkyl chain length (i.e. adding -CH2- unites), equal to 0.174 nm and 0.184 nm, for C3 to C4 and C4 to C5 in [Cn(mim)2][NTf2]2 DILs, respectively, which are in an relatively good agreement with the approximated value of 0.16 nm proposed by Tokuda et al. for a series of imidazolium-based MILs.54 Ion transport number or transference number is the fraction of the total current carried in an electrolyte by a given ion. Differences in transport numbers arise from differences in electrical mobility. The tendency of IL molecules to form the associated conformations will effect on the transport numbers of anion and cation. The transport numbers of cations and anions of the studied DILs were evaluated using their diffusion coefficients as D  D  D  and D  D  D  , respectively. Table 3 shows the transport numbers of cations and anions in each of the studied DILs. As this table shows, the anion transport number is larger than the cation which is expected according to the trends of diffusion coefficients in these DILs. It is interesting that the variation in the chain length of cation has no a significant effect on the transport numbers. The ionic association behavior appears to be a common feature of ILs. It is important to have an insight in the physicochemical processes in the ILs based on ionic association.54 The molar conductivity ratio, imp NMR , which is the ratio of molar conductivity obtained from the impedance measurements ( imp ) to the molar conductivity calculated from the ionic diffusivity ( NMR ), may be defined as “dissociation degree” or ionicity for an IL. In fact, the dissociation degree can be used as a parameter which shows the percentage of ions contributing to the ionic conduction within the diffusing component. 1-( imp NMR ) is also defined as association degree.67

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Specific electrical conductivity ( NMR ) can be evaluated from the Nernst-Einstein equation using the diffusion coefficients of cation and anion of IL as follow: NMR 

N A e 2  Z 2 D   Z 2 D  

(12)

kT

where NMR is the specific electrical conductivity (S.cm-1), NA is the Avogadro’s number, e is electron charge (1.602  10-19 coulombs), Z+ and Z- are the charge of ions, D+ and D- are diffusion coefficients of cation and anion (cm2.s-1), respectively, k is Boltzmann constant and T is the absolute temperature. Dissociation and association degrees of the studied DIL molecules have been given in Table 3. Similar to all of the MILs, DILs give the dissociation degrees less than unity, which indicates that only a part of the diffusive species contributes to the ionic conduction due to the presence of ionic associations which generate nonconductive species in the system. 3.6. Some Regularities Observed in the DILs. ILs obey some relatively simple regularities and useful relations between their thermophysical and transport properties. These relations can be also used as predictive models. Some relations between density, viscosity and electrical conductivity of the studied DILs have been illustrated in Figures 11 and 12. Doolittle equation68 which was proposed originally for the polymeric solutions can be used to correlate the viscosity and density data of these DILs (the experimental data of density of the studied DILs in g.cm-3 have been given in Table S5). The solid curves in Figure 11a show this correlation. Doolittle equation is as follow:

  a exp  b 1  c   

(13)

where a, b, and c are constants. As well as the Doolittle equation, Gardas and Coutinho69 used an Orrick-Erbar-type equation70 to show another relation between density, viscosity and molecular weight of ILs:

ln

  MW

 A

B T

(14)

where A and B are constants, η is the viscosity in cP, ρ is the density in g.cm-3, MW is the molecular weight and T is the absolute temperature. Figure 11b shows these relation for the

15



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studied DILs. As Figures 11a and 11b show, the DILs obey both Doolittle and Orrick-Erbar equations well. There is also a correlation between electrical conductivity and molar volume of ILs. This relation which was proposed by Krossing and co-workers71 is as follow:

  ce dV (15) where  is the electrical conductivity, Vm is the molar volume, and c and d are constants. Figure 12 shows this relation between  and Vm of [C3(mim)2][NTf2]2 and [C5(mim)2][NTf2]2 DILs. As m

this figure shows, the DILs obey this relation with good accuracy. Fitted parameters, the coefficient of determination, R2, and the statistical parameters of fitting for each of eqs 13 to 15 have been given in Table S6. The statistical values show that the studied DILs obey these regularities well.

4. CONCLUSIONS The transport properties of some imidazolium-based short alkyl chain length DILs (i.e. [Cn(mim)2][NTf2]2 [n=3,4,5]),

including shear viscosity, diffusion coefficient and electrical

conductivity were measured and analyzed at different temperatures and compared with some MILs. The results show that the studied DILs are moderately non-Newtonian fluids. The activation thermodynamic parameters of these ILs were also evaluated. The positive values of Gibbs free energy of activation show that the slip of two layers of the fluid is a non-spontaneous process. The ionic diffusion coefficients of these fluids obtained from PGSE-NMR method greatly contrast with the viscosities which indicates the relation between microscopic ion dynamics and macroscopic physical properties. The hydrodynamic radii and transport numbers of anions and cations and dissociation and association degrees of IL molecules were calculated from the diffusion coefficients and the viscosity data. The variation of the alkyl chain length of cation of the studied DILs causes change in the interactive forces. The competition between cumulative effect of the electrostatic interaction between ionic species and the van der Waals (inductive) interactions between ions, aggregates and clusters can effect on the properties of these DILs. The values of electrical conductivities as well as diffusion coefficient and viscosity data were used to investigate the ionicity and fragility characteristics of these DILs. The results indicate that these fluids are “subionic” and relatively “superfragile” fluids. The values of m-

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fragility for [C3(mim)2][NTf2]2 and [C5(mim)2][NTf2]2 DILs are 99.7 and 76.2, respectively. Also, we show a correlation between the m-fragility and the ionicity of these ILs.

Supporting Information The contents of Supporting Information file is as follow: 1

H NMR spectra, all of the analysis data including elemental analysis and also water contents of

the studied DILs have been summarized in Supporting Information as well as some figures and tables. Figure Captions: Figure S1. (a) ln η versus 1/T profiles and (b) ln η versus T profiles at shear rate =14 s-1 for the studied DILs. Figure S2. Activation parameters at different temperatures and shear rates for [C3(mim)2][NTf2]2, (a) ΔG* profiles (b) ΔH* profiles, (c) ΔS* profiles, and (d) ΔCp* profiles. Figure S3. The same as Fig. S2 for [C4(mim)2][NTf2]2. Figure S4. The same as Fig. S2 for [C5(mim)2][NTf2]2. Table Captions: Table S1. Y-Intercept and Slope Values of Regression Lines Drawn through Plots of Shear Stress against Shear Rate for [C3(mim)2][NTf2]2, [C4(mim)2][NTf2]2, [C5(mim)2][NTf2]2 DILs. Table S2. Experimental Data of Viscosity (mPa.s) of the Studied DILs. Table S3. Experimental Data of Electrical Conductivity (mS.cm-1) of the Studied DILs. Table S4. Fitted Parameters, Coefficient of Determination, R2, and the Statistical Parameters of the VFT Equation for the Electrical Conductivity of the Studied DILs Table S5. Experimental Data of Density (g.cm-3) of the Studied DILs Table S6. Fitted Parameters, Coefficients of Determination, R2, and the Statistical Parameters of Fitting for the Doolittle Equation (eq 13), Orrik-Erbar Equation (eq 14), and Krossing et al. Equation (eq 15) for the Studied DILs This information is available free of charge via the Internet at http://pubs.acs.org.

Acknowledgement

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This research was supported by the Research Council of University of Isfahan. The national elite foundation of Iran is also kindly acknowledged to provide Dr. Ashtiyani research grant to support this project.

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(47) Ghatee, M. H.; Zare, M. Power-Law Behavior in the Viscosity of Ionic Liquids: Existing a Similarity in the Power Law and a New Proposed Viscosity Equation. Fluid Phase Equilib. 2011, 311, 76. (48) Ueno, K.; Zhao, Z.; Watanabe, M.; Angell, C. A. Protic Ionic Liquids Based on Decahydroisoquinoline: Lost Superfragility and Ionicity-Fragility Correlation. J. Phys. Chem. B 2011, 116, 63-70. (49) Belieres, J.-P.; Angell, C. A. Protic Ionic Liquids: Preparation, Characterization, and Proton Free Energy Level Representation. J. Phys. Chem. B 2007, 111, 4926-4937. (50) Yoshizawa, M.; Xu, W.; Angell, C. A. Ionic Liquids by Proton Transfer: Vapor Pressure, Conductivity, and the Relevance of Δp K a from Aqueous Solutions. J. Am. Chem. Soc. 2003, 125, 15411-15419. (51) Capelo, S. B.; Méndez-Morales, T.; Carrete, J.; López Lago, E.; Vila, J.; Cabeza, O.; Rodriguez, J.; Turmine, M.; Varela, L. Effect of Temperature and Cationic Chain Length on the Physical Properties of Ammonium Nitrate-Based Protic Ionic Liquids. J. Phys. Chem. B 2012, 116, 11302-11312. (52) Smith, J.; Webber, G. B.; Warr, G. G.; Atkin, R. Rheology of Protic Ionic Liquids and Their Mixtures. J. Phys. Chem. B 2013, 117, 13930-13935. (53) Bodo, E.; Chiricotto, M.; Caminiti, R. Structure of Geminal Imidazolium Bis (Trifluoromethylsulfonyl) Imide Dicationic Ionic Liquids: A Theoretical Study of the Liquid Phase. J. Phys. Chem. B 2011, 115, 14341. (54) Tokuda, H.; Hayamizu, K.; Ishii, K.; Susan, M. A. B. H.; Watanabe, M. Physicochemical Properties and Structures of Room Temperature Ionic Liquids. 2. Variation of Alkyl Chain Length in Imidazolium Cation. J. Phys. Chem. B 2005, 109, 6103. (55) Tariq, M.; Carvalho, P. J.; Coutinho, J. A.; Marrucho, I. M.; Lopes, J. N. C.; Rebelo, L. P. Viscosity of (C2–C14) 1-Alkyl-3-Methylimidazolium Bis (Trifluoromethylsulfonyl) Amide Ionic Liquids in an Extended Temperature Range. Fluid Phase Equilib. 2011, 301, 22. (56) Xu, W.; Wang, L.-M.; Nieman, R. A.; Angell, C. A. Ionic Liquids of Chelated Orthoborates as Model Ionic Glassformers. J. Phys. Chem. B 2003, 107, 11749. (57) Tsunashima, K.; Kawabata, A.; Matsumiya, M.; Kodama, S.; Enomoto, R.; Sugiya, M.; Kunugi, Y. Low Viscous and Highly Conductive Phosphonium Ionic Liquids Based on Bis (Fluorosulfonyl) Amide Anion as Potential Electrolytes. Electrochem. Commun. 2011, 13, 178. 23



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(58) Acharya, A.; Sanyal, S.; Moulik, S. Physicochemical Investigations on Microemulsification of Eucalyptol and Water in Presence of Polyoxyethylene (4) Lauryl Ether (Brij-30) and Ethanol. Int. J. Pharm. 2001, 229, 213. (59) Acharya, A.; Sanyal, S.; Moulik, S. Formation and Characterization of a Pharmaceutically Useful Microemulsion Derived from Isopropylmyristate, Polyoxyethylene (4) Lauryl Ether (Brij 30), Isopropyl Alcohol and Water. Cur. Sci. Banglore 2001, 81, 362. (60) Acharya, A.; Moulik, S.; Sanyal, S.; Mishra, B.; Puri, P. Physicochemical Investigations of Microemulsification of Coconut Oil and Water Using Polyoxyethylene 2-Cetyl Ether (Brij 52) and Isopropanol or Ethanol. J. Colloid Interface Sci. 2002, 245, 163-170. (61) Angell, C. A. Spectroscopy Simulation and Scattering, and the Medium Range Order Problem in Glass. J. Non-Cryst. Solids 1985, 73, 1. (62) Wang, L.-M. Enthalpy Relaxation Upon Glass Transition and Kinetic Fragility of Molecular Liquids. J. Phys. Chem. B 2009, 113, 5168. (63) Wang, L.-M.; Mauro, J. C. An Upper Limit to Kinetic Fragility in Glass-Forming Liquids. J. Chem. Phys. 2011, 134, 044522. (64) Leys, J.; Wübbenhorst, M.; Menon, C. P.; Rajesh, R.; Thoen, J.; Glorieux, C.; Nockemann, P.; Thijs, B.; Binnemans, K.; Longuemart, S. Temperature Dependence of the Electrical Conductivity of Imidazolium Ionic Liquids. J. Chem. Phys. 2008, 128, 064509. (65) Atkins, P.W.; Julio De, P., Physical Chemistry. 9th ed.; Oxford University Press: 2010. (66) Kowsari, M.; Alavi, S.; Ashrafizaadeh, M.; Najafi, B. Molecular Dynamics Simulation of Imidazolium-Based Ionic Liquids. I. Dynamics and Diffusion Coefficient. J. Chem. Phys. 2008, 129, 224508. (67) Wu, T.-Y.; Sun, I.-W.; Gung, S.-T.; Lin, M.-W.; Chen, B.-K.; Wang, H. P.; Su, S.-G. Effects of Cations and Anions on Transport Properties in Tetrafluoroborate-Based Ionic Liquids. J. Taiwan Inst. Chem. Eng. 2011, 42, 513. (68) Doolittle, A. K. The Dependence of the Viscosity of Liquids on Free‐Space. J. Appl. Phys. 1951, 22, 1471. (69) Gardas, R. L.; Coutinho, J. A. A Group Contribution Method for Viscosity Estimation of Ionic Liquids. Fluid Phase Equilib. 2008, 266, 195. (70) Reid, R.C.; Prausnitz, J.M.; Poling, B. E. The properties of gases and liquids. 4th ed.; McGraw-Hill, New York: 1987. 24


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(71) Slattery, J. M.; Daguenet, C.; Dyson, P. J.; Schubert, T. J.; Krossing, I. How to Predict the Physical Properties of Ionic Liquids: A Volume‐Based Approach. Angew. Chem. 2007, 119, 5480.

25



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure Captions Figure 1. Shear stress, τ, versus shear rate, γ0, for (a) [C3(mim)2][NTf2]2, (b) [C4(mim)2][NTf2]2, and (c) [C5(mim)2][NTf2]2 DILs at different temperatures. The non-zero y-intercepts show that these DILs have moderate non-Newtonian behavior. Figure 2. Viscosity versus shear rate for (a) [C3(mim)2][NTf2]2, (b) [C4(mim)2][NTf2]2, and (c) [C5(mim)2][NTf2]2 DILs at different temperatures. For better presentation, the variation of the viscosity versus shear rate has been shown at 45 oC in each case which shows the non-Newtonian behavior of these DILs. Figure 3. The temperature dependence of the viscosity for the studied DILs, [Cn(mim)2][NTf2]2 (n=3,4,5). Plots of (a) η versus T fitted with eq 1 (power law equation), (b) η versus T fitted with eq 2 (VFT equation), (c) ln η versus T -3 fitted with eq 3 (Litovitz equation) and (d) η -0.3 versus T fitted with eq 4 (Ghatee et al. equation) for the studied DILs. The symbols are experimental results and solid lines are due to fittings. Figure 4. Comparison between the viscosities (η) of the studied DILs with those of corresponding monoatomic ILs (MILs) ([Cnmim][NTf2] (n=1,2,3,4,5)) at different temperatures. Filled symbols indicate DILs and open symbols indicate MILs. The data for MILs have been taken from Refs.54 and 55. Figure 5. Two universal viscosity behaviors. (a) Scaling of viscosity data (η/η0)-1/γ as a function of scaled temperature (T/Tx) (based on power law equation), and (b) Scaled viscosity data (η-Φ/-a) as a function of scaled temperature (T/(-a/b)) (based on Ghatee et al. equation) for the studied DILs. Figure 6. Compensation plots between ΔH*and ΔS* at different shear rates for (a) [C3(mim)2][NTf2]2, (b) [C4(mim)2][NTf2]2, and (c) [C5(mim)2][NTf2]2 DILs at different shear rates. Figure 7. Electrical conductivity versus temperature for the [C3(mim)2][NTf2]2 and [C5(mim)2][NTf2]2 DILs. Figure 8. The Walden plot for the [C3(mim)2][NTf2]2 and [C5(mim)2][NTf2]2 DILs. The solid straight line is the ideal line for 0.01 M aqueous KCl solution. The Walden plot for some MILs, namely [C2mim][NTf2] and [C4mim][NTf2] has been also illustrated for comparison. The data for MILs have been taken from Ref. 55. Figure 9. Fragility plot for [C3(mim)2][NTf2]2 and [C5(mim)2][NTf2]2 DILs and also [C2mim][NTf2] and [C4mim][NTf2] MILs which have been illustrated just for comparison. The data for MILs have been taken from Refs. 54 and 55. Figure 10. The ionicity/m-fragility plot of the studied DILs. The plot also includes MILs for comparison.

26


Page 26 of 44

Page 27 of 44

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 11. (a) Variation of η versus  for the DILs, [Cn(mim)2][NTf2]2 (n=3,4,5). Solid curves are the correlations based on the Doolittle equation (eq 13). (b) Plot of ln   M W  versus 1 T for the studied DILs. The solid lines are fitted lines according to the Orrick-Erbar-type equation. Figure 12. The plot of electrical conductivity versus molar volume for [C3(mim)2][NTf2]2 and [C5(mim)2][NTf2]2 DILs. The solid lines are fitted lines based on eq 15.

27



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

N

N

Page 28 of 44

O

(CH2)n N

O N

N

S

S

F3C

n=3,4,5

CF3 O

[Cn(mim)2]2+

O

[NTf2]-

Scheme 1. Structures of the cation and anion for the DILs studied in this work.

28


Page 29 of 44

Figure 1. 180

(a) 160

-2

Shear stress (N.m )

140 120

T= 30°C 35°C 40°C 45°C 50°C 55°C 60°C 65°C 70°C 75°C 80°C 85°C 90°C

100 80 60 40 20 0 0

10

20

30

-1

Shear rate (s )

40

50

60

40

50

60

40

50

60

180

(b) 160 T= 25°C 30°C 35°C 40°C 45°C 50°C 55°C 60°C 65°C 70°C 75°C 80°C 85°C 90°C

-2

Shear stress (N.m )

140 120 100 80 60 40 20 0 0

10

20

30 -1

Shear rate (s )

180

(c) 160 T= 25°C 30°C 35°C 40°C 45°C 50°C 55°C 60°C 65°C 70°C 75°C 80°C 85°C 90°C

140 -2

Shear stress (N.m )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


120 100 80 60 40 20 0 0

10

20

30 -1

Shear rate (s )

29



Figure 2. T= 30°C 35°C 40°C 45°C 50°C 55°C 60°C 65°C 70°C 75°C 80°C 85°C 90°C

(a)

Viscosity (Pa.s)

0.8

0.6

0.3045

T= 45°C 0.3040

0.3035

Viscosity (Pa.s)

1.0

0.4

0.3030

0.3025

0.3020

0.2

0.3015 0.0 0

10

20

30

40

50

0

60

10

T= 25°C 30°C 35°C 40°C 45°C 50°C 55°C 60°C 65°C 70°C 75°C 80°C 85°C 90°C

(b)

30

40 -1

50

60

0.8

0.6

0.2570

T= 45°C 0.2565

Viscosity (Pa.s)

1.0

Viscosity (Pa.s)

20

Shear rate (s )

-1

Shear rate (s )

0.4

0.2560

0.2555

0.2550 0.2

0.2545 0.0 0

10

20

30

40

50

0

60

10

20

30

40

50

60

-1

Shear rate (s )

-1

Shear rate (s )

T= 25°C 30°C 35°C 40°C 45°C 50°C 55°C 60°C 65°C 70°C 75°C 80°C 85°C 90°C

(c) 0.6

0.4

0.2190

T= 45°C

0.2188 0.2186

Viscosity (Pa.s)

0.8

Viscosity (Pa.s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 44

0.2

0.2184 0.2182 0.2180 0.2178 0.2176 0.2174

0.0 0

10

20

30

40

50

60

0

10

20

30

40 -1

Shear rate (s )

-1

Shear rate (s )

30


50

60

Page 31 of 44

Figure 3. 1.2

(a)

Symbols: Experimental data Lines: Fitting to power law. Eq. (1)

1.0

[C3(mim)2][NTf2]2

(b)

Symbols: Experimental data Lines: Fitting to VFT Eq. (2)

1.4

[C3(mim)2][NTf2]2

1.2

[C4(mim)2][NTf2]2

[C4(mim)2][NTf2]2 1.0

[C5(mim)2][NTf2]2

(Pa.s)

 (Pa.s)

0.8

0.6

0.4

[C5(mim)2][NTf2]2

0.8 0.6 0.4

0.2 0.2

0.0

0.0

290

300

310

320

330

340

350

360

280

370

290

300

310

320

0.5 0.0

330

340

350

360

370

380

T(K)

T(K) 2.8

(c)

Symbols: Experimental data Lines: Fitting to Litovitz Eq. (3)

2.6

Symbols: Experimental data Lines: Fitting to Ghatee et al. Eq. (4)

(d)

2.4

-0.5

2.2 -1.0

( /Pa.s)-0.3

ln ( /Pa.s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-1.5 -2.0

1.8 1.6 1.4

-2.5

[C3(mim)2][NTf2]2 [C5(mim)2][NTf2]2 2.0e-8

2.5e-8

3.0e-8

3.5e-8

4.0e-8

[C3(mim)2][NTf2]2

1.2

[C4(mim)2][NTf2]2

-3.0 -3.5 1.5e-8

2.0

[C4(mim)2][NTf2]2

1.0

4.5e-8

0.8 280

T-3(K-3)

[C5(mim)2][NTf2]2 290

300

310

320

330

T(K)

31


340

350

360

370

380


Figure 4. 1.4

[C1mim][NTf2]

1.2

[C2mim][NTf2] [C3mim][NTf2]

1.0

[C4mim][NTf2]

0.08

[C 1mim][NTf2]

0.06

[C 3mim][NTf2]

[C5mim][NTf2]

0.8

  (P a .s)

0.07

[C 2mim][NTf2] [C 4mim][NTf2] [C 5mim][NTf2]

0.05

 (P a .s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 44

[C3(mim)2][NTf2]2 [C4(mim)2][NTf2]2

0.6

[C5(mim)2][NTf2]2 0.4

0.04 0.03

0.2

0.02

0.0 0.01 0.00 280

290

300

310

320

330

340

350

360

370

380

280

290

300

310

320

T (K)

32


330

T (K)

340

350

360

370

380

Page 33 of 44

Figure 5. 1.5

(a)

-1/

1.4

0

(  )

1.3

1.2 [C3 (mim)2 ][NTf2 ]2

1.1

[C4 (mim)2 ][NTf2 ]2 [C5 (mim)2 ][NTf2 ]2

1.0 2.0

2.1

2.2

2.3

2.4

2.5

2.6

T/Tx

1.50 1.45

(b)

[C3 (mim)2 ][NTf2 ]2 [C4 (mim)2 ][NTf2 ]2

1.40

[C5 (mim)2 ][NTf2 ]2

1.35 -

 /-a

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.30 1.25 1.20 1.15 1.10 0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

T/(-a/b)

33


0.50


Figure 6. s

-1

50.4 s

-1

44.8 s

-1

42.0 s

-1

39.2 s

-1

37.8 s

-1

33.6 s

-1

29.4 s

-1

28.0 s

-1

25.2 s

-1

22.4 s

-1

21.0 s

-1

19.6 s

-1

16.8 s

-1

14.0 s

-1

SR=56.0 50

(a) H*=33.2581+336.904 S* R2 =0.9993

-1

 H*(KJ.mol )

45

40

35

30

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

0.06

 S*(KJ.mol-1 )

(b) H*=33.1074+334.128 S* R2 =0.9996

-1

 H*(KJ.mol )

45

40

35

30

-0.01

0.00

0.01

0.02

0.03

0.04

SR= 56.0 s

-1

50.4 s

-1

44.8 s

-1

42.0 s

-1

39.2 s

-1

37.8 s

-1

33.6 s

-1

29.4 s

-1

28.0 s

-1

25.2 s

-1

22.4 s

-1

21.0 s

-1

0.05

 S*(KJ.mol-1 )

50

(c) -1

SR= 56.0 s -1 50.4 s -1 44.8 s -1 42.0 s -1 39.2 s -1 37.8 s -1 33.6 s -1 29.4 s -1 28.0 s -1 25.2 s -1 22.4 s -1 21.0 s -1 19.6 s -1 16.8 s -1 14.0 s

H*=32.6837+336.986S* 45 R2 =0.9990 -1

 H*(KJ.mol )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 44

40

35

30

25 -0.02

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

 S*(KJ.mol-1 )

34


0.06

Page 35 of 44

Figure 7. 7

[C 3(mim)2][NTf2]2

6

[C 5(mim)2][NTf2]2

5

(mS.cm-1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


4

3

2

1

0 295

300

305

310

315

320

325

330

335

340

345

T (K)

35


350

355

360


Figure 8.

3

[C3 (mim)2 ][NTf2 ]2

superionic

[C5 (mim)2 ][NTf2 ]2 [C2 mim][NTf2 ] [C4 mim][NTf2 ]

2

-1

log  (S.cm .mol )

subionic

2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1

0

-1 -1

0

1

2

log  (10 .Pa.s) -1

-1

-1

36


3

Page 36 of 44

Page 37 of 44

Figure 9. 10 [C3 (mim)2 ][NTf2 ]2 [C5 (mim)2 ][NTf2 ]2

8

Strong

[C2 mim][NTf2 ]

log ( /poise)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


[C4 mim][NTf2 ]

6

Fragile

4 2 0 -2 0.2

0.3

0.4

0.5

0.6

Tg /T

37


0.7

0.8


Figure 10. fragile

140

120

nonionic liquid

Fragility m

100

80

"poor" IL 60

[C3 (mim)2 ][NTf2 ]2

"good" IL strong

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 44

[C5 (mim)2 ][NTf2 ]2

40

[C2 mim][NTf2 ]

superionic liquid

[C4 mim][NTf2 ]

20 -1

0

1

2

W

3

38


4

5

Page 39 of 44

Figure 11. 1.2

(a)

[C 3(mim)2 ][NTf2]2 [C 4(mim)2 ][NTf2]2

1.0

[C 5(mim)2 ][NTf2]2

(Pa.s)

0.8

0.6

0.4

0.2

0.0 1.50

1.52

1.54

1.56

1.58

1.60

1.62

1.64

 (g.cm-3)

0.0

(b)

[C3 (mim)2 ][NTf2 ]2 R2 =0.9974 [C4 (mim)2 ][NTf2 ]2 R2 =0.9980

-0.5

ln( / .Mw)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


[C5 (mim)2 ][NTf2 ]2 R2 =0.9978

-1.0

-1.5

-2.0

-2.5

-3.0 0.0030

0.0031

0.0032 -1

0.0033

-1

T (K )

39


0.0034


Figure 12. 3.5

[C3(mim)2][NTf2]2 3.0

[C5(mim)2][NTf2]2

2.5 -1

 (mS.cm )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 40 of 44

2.0

1.5

1.0

0.5

0.0 470

480

490

500

3

510

-1

Vm (cm .mol )

40


520

530

Page 41 of 44

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Table 1. Fitted Parameters and the Coefficients of Determination (R2) for the Power Law, Litovitz, VFT and Ghatee et al. Equations for [C3(mim)2][NTf2]2, [C4(mim)2][NTf2]2, [C5(mim)2][NTf2]2 ILs [C3(mim)2][NTf2]2

[C4(mim)2][NTf2]2

Power law Equation:   0

[C5(mim)2][NTf2]2

 

T Tx  Tx

0 /Pa s

0.0025

0.0029

0.0026

Tx/K

256.95 3.3473 0.9993 0.0026 0.0124

246.83 3.6191 0.9999

242.31 3.8332 0.9999 0.0007 0.0104



R2 bias AAD

-0.0027 0.0064 B T0 /(T T0 )

VFT Equation:   A  e

A   10 3 Pa s B K

T0/K R2 bias AAD

0. 2597 4.80 189.561 1.0000 0.0007 0.0028

0. 11702 6.85 168.315 1.0000 0.0040 0.0077

0. 14681 6.03 174.429 1.0000 0.0046 0.0083

Litovitz Equation:   A exp( B / RT 3 ) ln(A/Pa s) (B/R).10-8/K3 R2 bias AAD

-6.9085 1.8497 0.9995 0.0278 0.0404

-6.7876 1.7530 0.9998 0.0129 0.0214

-6.8615 1.7280 0.9997 0.0718 0.0824

Ghatee et al. Equation: 0.3  a  bT a/(Pa s)-0.3 b/(Pa s)-0.3K-1 R2 bias AAD

-5.98048 0.023291 0.9999 0.0000 0.0017

-5.81564 0.023019 0.9999 0.0001 0.0019

41


-5.95368 0.023671 0.9999 0.0000 0.0018


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Table 2. The parameters of power law equation for the studied

DILs. The values of 0 and T x have been obtained using two different methods, i.e., by fitting of eq 1 and using parameters of eq 4 Power law Equation:   0

[C3(mim)2][NTf2]2

0 0.0025

[C4(mim)2][NTf2]2 [C5(mim)2][NTf2]2

  T Tx Tx

Ghatee et al. Equation



 0.3  a  bT

Tx   ( a / b )

256.95

 0  (a ) 0.0025

0.0029

246.83

0.0015

252.64

0.0026

242.31

0.0011

251.52

Tx

42


256.77

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Table 3. The Diffusion Coefficients, Hydrodynamic Radii, and Transport Numbers of Cation and Anion of the Studied DILs and also their Dissociation and Association Degrees at T=60 oC [C3(mim)2][NTf2]2

[C4(mim)2][NTf2]2

[C5(mim)2][NTf2]2

Diffusion coefficient of cation (1011 m2.s-1)

1.098

1.114

1.170

Diffusion coefficient of anion (1011 m2.s-1)

1.806

1.810

1.999

Diffusion coefficient of molecule (1011 m2.s-1)

2.904

2.924

3.169

rH (cation) (1010 m)

2.287

2.547

2.823

rH (anion) (1010 m)

1.391

1.568

1.652

Percent of transport number of cation

37.82

38.10

36.92

Percent of transport number of anion

62.18

61.90

63.08

Dissociation degree

0.7081

-----

0.7318

Association degree

0.2919

-----

0.2682

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Transport Properties of Short Alkyl Chain Length Dicationic Ionic

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