Can the Transport Properties of Molten Salts and Ionic Liquids Be

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Can the Transport Properties of Molten Salts and Ionic Liquids be Used to Determine Ion Association Kenneth Robert Harris J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b08381 • Publication Date (Web): 31 Oct 2016 Downloaded from http://pubs.acs.org on November 1, 2016

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The Journal of Physical Chemistry

Can the Transport Properties of Molten Salts and Ionic Liquids be Used to Determine Ion Association?

Kenneth R. Harris,* School of Physical, Environmental and Mathematical Sciences, University College, University of New South Wales, PO Box 7916, Canberra BC, ACT 2610, Australia

AUTHOR INFORMATION Corresponding Author * E-mail: [email protected]; tel. +61 2 6268 8086

ACS Paragon Plus Environment

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ABSTRACT There have long been arguments supporting the concept of ion association in molten salts and ionic liquids, largely based on differences between the conductivity and that predicted from selfdiffusion coefficients by the Nernst-Einstein equation for non-interacting ions. It is known from molecular dynamics simulations that even simple models based on charged hard spheres show such a difference due to the correlation of ion motions. Formally this is expressed as a difference between the velocity cross-correlation coefficient of the oppositely charged ions and the mean of those for the two like-charged ions. This paper examines molten salt and ionic liquid transport property data, comparing simple and model associated salts (ZnCl2, PbCl2 and TlCl) including weakly dissociated molecular liquids (H2O, HCOOH, H2SO4). Analysis employing Laity resistance coefficients (rij) shows that the common ion-association rationalization is flawed, consistent with recent direct measurements of the degree of ionicity in ionic liquid chlorides and with theoretical studies. However, the protic ionic liquids [PyrOMe][BF4] and [DBUH][CH3SO3] have larger than usual NE deviation parameters (> 0.5), and large negative like-ion rii, analogous to those of ZnCl2. Structural, spectroscopic and theoretical studies are suggested to determine whether these are indeed genuine examples of association.


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Introduction The transport properties of ionic liquids are of prime importance in determining how such materials might be applied and much effort has been expended on computer simulation in attempts to understand these experimental properties in the absence of successful theoretical approaches. A simple empirical approach to their interpretation has been to postulate the formation of ion-pairs, a concept first employed by Walden for molten salts1,2,3 and re-introduced many times since for both molten salts and ionic liquids.4,5,6,7,8,9 This concept is commonly used to rationalize the differences observed between the experimentally measurable electrical conductivity (Λ) and that calculated from ion self-diffusion coefficients (DSi) for a salt formally dissociating as ν + A z+ + ν - B z-

Aν + Bν −

(1)

using the Nernst-Einstein (NE) relation, Λ=

(F

2

/ RT )(ν + z + 2 DS + + ν − z − 2 DS − ) (1 − ∆ ) = Λ NE (1 − ∆ )

(2)

and expressed through the deviation parameter, ∆. F and R are the Faraday and gas constants in this equation, T is the absolute temperature, νi are the stoichiometric numbers for the dissociated salt and zi are the ion charges, including the signs. Alternative forms employ the ionicity, 10,11 Y =

Λ/ΛNE < 1, or its inverse, the Haven ratio,12 HR =ΛNE/Λ > 1: thus, ∆ = 1−

RT Λ Λ 1 = 1− = 1− Y = 1− 2 F (ν + z+ DS+ + ν − z− DS− ) Λ NE HR 2

2


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The simple NE expression, i.e. with ∆ set equal to 0, can only apply to non-interacting ions, e.g. infinitely dilute electrolyte solutions, the case for which it was originally derived.13 Clearly the ions in molten salts and ionic liquids are in close contact and the liquid structure is ordered primarily by the Coulombic field: ∆ therefore contains information on the ion-ion interactions, but is a function of the three types present, cation-cation, anion-anion and cation-anion. Though there is some evidence from molecular dynamics simulations that the momentum and energy dissipation determining the transport properties of ionic melts are governed more by dispersion and repulsive forces rather than the Coulombic interaction,14,15 most authors16 favour the latter. Values for ∆ vary considerably for ionic liquids: e. g. 1-butyl-3-methylimidazolium tetrafluoroborate,

[BMIM][BF4]

(aprotic),

∆

=

0.41;17,

1-methyl-2-oxopyrrolidinium

tetrafluoroborate, [PyrOMe][BF4], (protic) ∆ = 0.79.18 The use of these quantitative parameters is an alternative (and sometimes a supplement) to the qualitative use19,20 of Walden plots of the conductivity versus viscosity relative to reference linesfor aqueous KCl solutions of various compositions21 introduced by Angell. These are almost universally interpreted in terms of ion association or aggregation, though Angell has pointed out that this is with the assumption that “inter-ionic friction” can be neglected.20 Similarly, in the literature it is often asserted that non-zero values of ∆ imply some sort of contact ion-pairing on a time scale comparable to that of NMR self-diffusion measurements (ms).6,9,22,23 Though H-bonding and other directional interactions can be inferred from spectroscopic measurements in many examples,24,25 no estimates of thermodynamic binding constants appear to have been made despite long precedent in electrolyte solution theory and this seems a serious weakness of the ion-pair rationalization approach for ionic liquids and molten salts.


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The concept of long-lived ion-pairs seems to derive at least in part from the quasi-lattice model of activated jumps due to Bockris et al.,26 which is based on similar models applied to solid salts. While ion-pairing would clearly yield a non-zero NE deviation parameter, it is not true that this is the only possible cause as more subtle ion-ion interactions and correlations between ionic velocities contribute to ∆,27,28,29,30,31,32 as outlined below. It is of some relevance that in a subsequent paper, Bockris33 complains that his quasi-lattice model has been misunderstood by some authors. The model assumes both single and paired vacancies, the latter being necessary to achieve the fluidity required of a liquid. Hence ions can diffuse by moving into both single and paired vacancy sites, but the overall ionic mobility as determined by conductivity measurements is less than that estimated by the NE equation due to the simultaneous movement of neighbouring ions of opposite charge into paired vacancies. Bockris emphasised that in his model these pairs are not physically or chemically bound together on the time scale of the experiment, but this seems to have often been ignored subsequently due to the simplistic appeal of the concept of ion-pairing. As we have mentioned before,34,35 Berne and Rice36 have shown from statistical mechanical theory that the concept of pairing in ionic melts is generally unnecessary. In their words: “There is predicted to be a deviation from the Nernst-Einstein relation due to the distortion from spherical symmetry of the surroundings of a selected ion. Because of this distortion there is an internal electric field exerted on the selected ion which is opposed (antiparallel) to the external field. Since the net field exerted on an ion is less than the applied field, the diffusion mobility is expected to exceed the conductance mobility.”37,38 It should be noted that the recent molecular dynamics simulations by Zhang and Maginn39 do suggest a correlation between ionic liquid transport properties and ion-pair or ion-cage lifetimes. However these lifetimes are of the order


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of tens of ps to ns, (the definition is structural and not experimentally determinable), so are many orders of magnitude less than the times associated with transport property measurements, and should not be related to the ionicity rationalization. There are two approaches whereby the NE deviation parameter ∆ can be quantified in terms of ion-ion interactions. The first employs resistance coefficients derived from non-equilibrium thermodynamics, which are generalizations of the Einstein-Sutherland friction coefficient used for the tracer diffusion of a solute in a solution at infinite dilution.31,40 The second employs velocity correlation coefficients derived from statistical mechanical Green-Kubo theory, (VCC), introduced by McCall and Douglass41 for quantifying deviations from the Hartley-Crank equation relating the mutual and self-diffusion coefficients in non-electrolyte solutions. This use of VCC was subsequently expanded by Hertz42 and others to include the conductivity and transport numbers of electrolyte solutions43,44,45 and of molten salts.46 It has been directly linked to the phenomenological equations of non-equilibrium thermodynamics.45,46 The use of phenomenological coefficients such as VCC or resistance coefficients avoids the need for a particular model of ionic motion and the former can be as readily calculated by molecular dynamics29,32 as can self-diffusion coefficients, though this is not often done. Both methods distinguish and identify the separate cation-cation, anion-anion and cation-anion contributions to ∆, though in different ways. Here we apply both to examine transport property data for high-temperature molten salts from the literature and contrast and compare the observable trends with results obtained from our past work on ionic liquids. In doing so, the question of association in ionic liquids,6,9,19,20,39,47,48,49 both protic and aprotic, and its possible effects on the transport properties is examined.


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∆ for Molten Salts and Ionic Liquids Figures 1 and 2 show the temperature and pressure dependences of the NE deviation parameter, ∆, for a number of ionic liquids, determined in recent studies from this and our associated laboratories.17,30,31,50,51,52,53 These are, in the main, 1-alkyl-3-methylimidazolium salts, [RMIM]+, but also include N-butyl-N-methylpyrrolidinium, [Pyr14]+, and a number of substituted ammonium salts. The anions are tetrafluoroborate, [BF4]-, hexafluorophosphate, [PF6]-, and bis(trifluoromethanesulfonyl)amide,

[Tf2N]-,

tetracyanoborate,

[TCB]-,

methylsulfonate,

[CH3SO3]-, trifluoromethanesulfonate [CF3SO3]- and tris(perfluoroethyl)trifluorophosphate, [FAP]-. It can be seen that over the temperature and pressure ranges available ∆ is constant, or at most, increases slightly with increasing temperature. A constant value for ∆ is to be expected when slopes observed for Stokes-Einstein-Sutherland (SES) plots of self-diffusion coefficients against fluidity [eq (4)] equal those in the Walden plot of the molar conductivity against fluidity [eq (5)] (Table 1).17,30,34-35,50-53 ln( DSi / T ) = a + t D ln(1 / η )

(4)

ln( Λ ) = a ′ + t Λ ln(1 / η )

(5)

and

Where measured, high pressure isotherms have been found to overlie the atmospheric pressure isobar in such plots, so the self-diffusion coefficients and molar conductivity have a similar dependence on the viscosity, with tD ~ tΛ (Figure 3). Generally, for both ionic and molecular liquids, 0.85 < t < 1. 54 For high-temperature molten salts on the other hand, the data are more difficult to analyze. The experiments are difficult due to the temperatures involved and the number of systems where


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self-diffusion coefficients have been measured is limited. From experience with both ionic and molecular liquids, one can use two empirical consistency tests to examine the quality of experimental data. The first uses the ratio of the cation and anion self-diffusion coefficients. For ionic liquids, based on measurements from this laboratory, this has been found to be constant for a given salt, independent of both temperature and pressure.35,50-53 Table 2 lists values for a number of hightemperature molten salts from the sources given in Table S1 of the Supporting Information. 55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91

Constancy is only

found for KCl, KNO3, TlCl, PbCl2 and CdCl2. For ZnCl2, where ion association is known to occur, forming species such as [ZnCl4]2- bonded in a complex, labile network,92,93,94 a dependence on temperature is not unexpected, but that for the self-diffusion coefficients of LiCl, NaCl and CaCl2 casts some doubt on the data sets for these substances. The second employs the SES and Walden slopes, t, from eq (4) and (5). For ionic liquids, these are found to be equal within experimental error,34-35,50-53 with high-pressure isotherms overlapping the atmospheric pressure isobar, and for molecular liquids, they are equal for the self-diffusion of a solvent and for tracer-diffusion of solutes of similar shape in solutions in that solvent, again with coincidence of high-pressure isotherms and the atmospheric pressure isobar.54 For high-temperature molten salts on the other hand, Table 2 shows considerable variation. In part this is due to the short range of viscosities available for all the salts other than ZnCl2, generally less than 0.5 units on the ln scale (using Pa·s as the viscosity unit), whereas that for ionic liquids is typically 3 or 4 units. Consequently, a relatively small change in DS values can make a large difference in the calculated value of t, despite the use of smoothing functions to represent the experimental data. This can readily be seen using the entry for LiCl: the slope for


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the anion can be made coincident with that for the cation merely by fixing the DS+/DS- ratio at a constant value, a change from 0.28 to 0.54. So interpretation of the values of t must be done with some caution. However it can be seen that a) the cation and anion SES slopes are approximately equal for the examples KCl, TlCl, KNO3, ZnCl2, PbCl2 and CdCl2; b) that those for the Bockris data sets for NaCl65 and CdCl270 are greater than unity and hence inconsistent with the StokesEinstein-Sutherland model where t ≤ 1,54,95 and c) that, with the exception of TlCl and ZnCl2, Clin LiCl, Cs+ in CsCl and Ca2+ in CaCl2, the Walden slope is less than the corresponding SES slopes. Therefore it seems prudent to eliminate the inconsistent data sets and to further consider only NaCl, using the Ejima self-diffusion results,66 KCl and KNO3 as models for hightemperature molten salts (noting that NaCl and KNO3 are standard reference materials in the field molten salt electrochemistry), and the special cases of TlCl, PbCl2 and ZnCl2. Notwithstanding these qualifications, ∆ appears to increase slightly with increasing temperature for KCl, NaCl and KNO3 (Figure 4), as noted by Ejima et al.66 for the chlorides and by Videa et al.96 more generally, though for KCl and KNO3 this increase is within the experimental standard uncertainty. If these salts are thought to be associated, then one would expect the opposite temperature dependence. That for TlCl is constant, but large, at 0.71. For PbCl2 and ZnCl2, ∆ is both close to unity and decreases with increasing temperature, markedly so for the latter. This decrease is consistent with the increasing dissociation of the complex anions with increasing temperature. In passing, it is noted that there are intermediate range salts with melting points above 100 oC for which Walden slopes can be determined.97,98 These behave like ionic liquids as can be seen in Figure 5. For example, the single system for which data are available at high pressure for both properties ([Bu4N][BBu4]98) has overlapping isotherms and those with a common cation also


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appear to overlie one another. Unfortunately there appear to be no self-diffusion data in the literature for any of these compounds.

Velocity Cross-Correlation Coefficients (VCC) We have shown elsewhere17,30-31 that the NE deviation parameter ∆ can be written in terms of differences between the unlike ion velocity correlation coefficient (f+-), which is proportional to the molar conductivity, and the mean of the two like-ion VCC (f++ and f--), which contain both conductivity and self-diffusion terms. ∆=−

c(2ν +ν − z+ z− f + − + ν +2 z+2 f + + + ν −2 z−2 f − − ) (ν + z+2 DS+ + ν − z−2 DS− )

c(2 f + − − f + + − f − − ) = ( DS+ / ν + + DS− / ν − )

(6)

using the electroneutrality condition ν+z+ = -ν-z-. The fij in these expressions were defined and expressed in terms of experimentally measurable quantities by Schönert46 as:

2 D N AV ∞ RT Λ  M −  f ++ ≡ v+α (0)v+ β (t ) dt = − S+   ∫ 3 0 c  z− FM  ν + c

(7)

2 D NAV ∞ RT Λ  M +  f −− ≡ v−α (0)v−β (t ) dt = − S− ,   ∫ c  z+ FM  ν −c 3 0

(8)

and

f +− ≡

N AV ∞ RT Λ M + M − v+α (0)v−β (t ) dt = , ∫ 3 0 c z z ( FM )2 + −

(9)

where NA is the Avogadro constant, V the volume of the ensemble, Λ is the molar conductivity, c the amount concentration (molarity) of salt, and M, M+, and M- are the molar masses of salt, cation, and anion, respectively. The VCCs are time (t) integrals of the ensemble average of the


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velocity correlation functions of different ions as indicated by the subscripts α and β. The VCC are all negative in a one-component molten salt, and represent anti-correlations of the velocities of the ions due to the principle of momentum conservation.29,32,42-43 As might be expected these anti-correlations are weakest for f+-. However it has been found that in [BF4]- and [PF6]- salts of 1-methyl-3-alkylimidazolium

salts,

and

for

[EMIM][CH3SO3],

[EMIM][TCB]

and

[EMIM][CF3SO3], the anti-correlations are larger for the cations (i.e. f++ < f--), but that this order is reversed for [Tf2N]- salts, for of a range of cations of different types. It is possible that these effects are related to ion size and liquid structure, but this is yet to be investigated theoretically. The magnitude of ∆ is proportional to the difference between f+- and the arithmetic mean of f++ and f-- (eq 6). Figure 6 illustrates this for the “poor” ionic liquid [PyrOMe][BF4]18 (∆ = 0.79) and the more typical [BMIM][BF4] (∆ = 0.41).17 ([EMIM][FAP] appears to be a special case53 with ∆ ~ 0 [Figure 1(c)], though this unexpected result requires confirmation.) Molecular dynamics simulations show that the VCC difference term in the numerator of the expression in eq. (6) is negative for simple model molten salts of varying degrees of sophistication27-29,32,99,100 and that there is no necessity to assume ion pairing in order to explain non-zero values of ∆. Angell et al.96 also made this point on the basis of the difference between diffusive and electrical mobilities when ions interact. It is of some interest that direct, experimental measurements of ionicity, that is the degree of ionization, of alkylimidazolium chlorides from measurements of

35

Cl-

quadrupolar coupling constants yields values between 97.8 and 99.6%,47 consistent with these simulation results. Similarly, in a recent review, and again based on molecular dynamics simulations, Kirchner et al.49 have concluded that “the life-times of ion-ion contacts and their joint motions are far too short to verify the existence of neutral units in these materials”. Very new work based on the measurement of anomalous Wein effects on the conductivity of several


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ionic liquids having mono- and di-valent cations is consistent with these results, though results for trihexyltetradecylphosphonium chloride are suggestive of association in this particular case.101 Figure 7 shows the analogue of an SES plot for the distinct diffusion coefficients17,35,50-53 (DDC) of NaCl, KCl, TlCl, KNO3, PbCl2.and ZnCl2. The distinct diffusion coefficients, defined by d

Dij = cfij (ν + + ν − ) = ν cfij

(10)

are convenient for the inter-comparison of VCC. Like the VCC, the DDC are necessarily negative quantities so ln(-Ddij/T) is plotted. For ionic liquids, the analogue-SES slopes are usually similar to those obtained directly from SES and Walden plots, but show regularities depending on the nature of the anion. Similar regularities appear here: thus the order for the nitrate is similar to that for [Tf2N]- containing ionic liquids50-52 (both anions have extensive charge delocalization) and for the chlorides, including ZnCl2, it is similar to that for [BF4]- and [PF6]- containing ionic liquids,17,30 and for [EMIM][CH3SO3], [EMIM][CF3SO3] and [EMIM][TCB].53 The cation-cation and anion-anion DDC SES plots show some curvature for ZnCl2 as it approaches the melting point, perhaps due to the glassy nature of this melt. The larger values of ∆ for TlCl, PbCl2. and ZnCl2 are reflected in the large separations of the like-ion lines (Dd++ and Dd--) and those for the unlike ions (Dd+-).

Resistance Coefficients For molten salts, the Laity form of the resistance coefficients,102,103 (which differ from those of Klemm,4) are employed. These are defined by


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N

X i ≡ −(grad µi )T = ∑ rik xk (vi − vk )

(11)

k =1

where Xi is the thermodynamic or generalised frictional force on ion species i in an electrochemical potential gradient, xk is the mole fraction, (vi - vk) is the velocity of species i relative to that of species k, and the rik are the resistance coefficients. The Onsager reciprocity relation, rik = rki holds. For a one component system with two ionic species,102 r+ − = z +ν + ( z + + z − ) F 2 / Λ

(12)

and rii =

 1  ( z+ + z− ) RT − zi r+−  , i = +,-; j ≠ i  DSi zj  

(13)

r+- is necessarily positive, but the two rii may be positive or negative. If r+−2 = r++ r−−

(14)

that is, the cation-anion resistance coefficient is the geometric mean of the cation and anion resistance coefficients, then ∆ is zero.104 (Compare eq 6 for VCC). For a single component salt, the rij are independent of the frame of reference used for ion fluxes, as are the self-diffusion coefficients and molar conductivities from which they derive. (Note that Laity used the obsolete equivalent conductivity, Λequiv = Λ/(ν+z+) in his papers.) Eq (15) to (17) link the VCC and resistance coefficients: f +− = −

f ++ =

ν RT M + M − cr+−

M2

2 ν RT  M −   ν − 

 1 −      c  M   r+−  (ν + r++ +ν − r+− ) 

(15)

(16)

and


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f −− =

2 ν RT  M +   ν + 

 1     − c  M   r+−  (ν − r−− +ν + r+− ) 

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(17)

The inverse relations are for the like-ion resistance coefficients are

ν RT ν +c

  M M 1  ν −  + −  −  f + ν − f (M − / M + )   f  M2   +− ++ +− 

(18)

ν RT = ν −c

ν M M   1  +  + − −  f + ν + f (M + / M − )   f  M2   +− −− +− 

(19)

r++ =

and

r−−

Figure 8 shows resistance coefficients, again as linear analogue SES plots of ln(rij) against ln(φ), for NaCl, KCl and KNO3, for which the geometric ratio r+-/√(r++r--) is of the order 1.6 – 2.5, 1.8 - 2.2 and 3.4 – 4.1, increasing with increasing temperature. All are positive, with r+- > r-> r++. The figure establishes a pattern for un-associated molten salts and corresponds to that found for ionic liquids, illustrated in Figure 9. (Interestingly, r+- > r-- > r++ for both [BMIM][PF6] and [BMIM][Tf2N] whereas the order for the VCC of these two ionic liquids differ as mentioned above.) TlCl, PbCl2 and ZnCl2, on the other hand, have negative values for both r++ and r--, though those for TlCl are very much smaller than those of ZnCl2, consistent with the large difference between the viscosities (Figure 10). ∆ decreases with increasing temperature for both ZnCl2 and PbCl2 (Figure 4). For ZnCl2 these negative values may be taken as what is to be expected when ion association occurs in a melt. Laity103 conjectured this on the basis of the limited database available to him in 1960 and on arguments based on the behaviour of very weakly dissociating molecular liquids


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such as water, discussed in the following section. Association in this melt is well established on the basis of numerous structural studies.92-94 For PbCl2, the structural evidence for association is less certain,105 with X-ray and neutron scattering reports106,107,108 yielding different Pb-Cl coordination numbers. The resistance coefficients, however, show the same behaviour as ZnCl2, suggesting ion association does take place in the melt, though the rij are smaller in size and the viscosity is less. For TlCl, one can surmise that negative like-ion resistance coefficients may be due to the influence of covalent bonding between the co-ions, leading to very weak association. This type of bonding has been suggested on the basis of analyses of Tl NMR chemical shifts109 (but also questioned75) and of molar volumes.110

Weakly Dissociating Molecular Liquids as Associated Ionic Liquids Laity suggested the extreme example of water as an almost fully associated ionic liquid and calculated resistance coefficients using an estimate of the self-diffusion coefficient of water for the self-diffusion coefficients of the oxonium ion, H3O+, and the hydroxide ion, OH-, obtaining extremely large and negative values for both r++ and r--.103 However it seems more logical to use self-diffusion coefficients calculated from the well-determined limiting ionic conductivities using the standard Nernst relation. This is consistent with estimates of Ds(H3O+) at infinite dilution that can be made from the tracer diffusion measurements of Woolf111 for H3O+ in dilute aqueous salt solutions. Table 3 lists VCCs and resistance coefficients for water, formic and sulfuric acids. The conductivity of pure water is difficult to determine by direct experiment and was calculated from the limiting molar conductivity, Λ∞(H3O+, OH-),112 and the ionization constant, Kw,113 using the relation114,115


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(

)

κ = Λ ∞ H3O + , OH - pK w

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(20)

The values for formic (as HCOOH2+, HCOO-)116,117 and sulfuric (as H3SO4+, HSO4-)118,119acids are from direct determinations with limiting ionic molar conductivities being determined with the aid of transport number measurements.117,120 [Other possibilities for H2SO4, e.g. (H3O+, HS2O7),120 are not considered here.] Table 3 also includes self-diffusion coefficients of molecular water,121,122 formic123,124 and sulfuric125,126 acids for comparison with the corresponding ionic values. For water and formic acids which have very low dissociation constants and conductivities, the diffusion term dominates the like-ion VCC and Ddii equals -DSi. For the same reasons, as Laity noted, the like-ion resistance coefficients rii equal – r+-, the unlike ion resistance coefficient. Though the dissociation constant for formic acid is approximately seven orders of magnitude higher and its conductivity one thousand times higher than that of water, these values are low enough that it still behaves similarly to water. Consequently the ionicity Y is extremely small (Table 3), the NE deviation factor is effectively unity and r+- is the geometric mean of the likeion resistance coefficients. The important point is that the like-ion resistance coefficients are negative, as is the case for ZnCl2. Sulfuric acid has still larger dissociation constant and conductivity values (pK = 3.54 and κ = 1.04 S/m)118 and this is sufficient to introduce differences between the resistance coefficients such that NE deviation factor deviates slightly from unity and r+- is greater than √ (r++r--). Again the like-ion resistance coefficients are negative and taking all

these results into account, Laity’s conjecture that this can be used as a diagnostic for ion association in a molten salt or ionic liquid is confirmed.


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Ionic Liquids Resistance coefficients have been calculated by Harris and Kanakubo from experimental transport property data for a number of salts of 1-alkyl-3-methylimidazolium ions,52,53 including [BMIM][Tf2N] and [BMIM][PF6] which have been studied under high pressure. Other examples deriving from previous studies17,50-53 are given in the Supporting Information (those for the 1alkyl-3-methylimidazolium tetrafluoroborates and hexafluorophosphates include new data to extend the temperature range to 90 oC, new results for [HMIM][BF4] along the coexistence line, and corrections to the previously published data for both ions for [HMIM][PF6] and the anion for [OMIM][BF4],127) (Figures S1 to S5). Generally, the like-ion resistance coefficients are both positive, though some take quite small values such as r++ for [OMIM][Tf2N] and [HMIM][PF6]. The r— for [OMIM][BF4] are negative, but small, of similar magnitude to r++. Analysis of the results of the Brennecke group for a number of aprotic [EMIM]+ salts,128,and phosphonium salts129

shows

negative

for

r++

1-ethyl-3-methylimidazolium

3-methyl-5-

trifluoromethylpyrozalide ([EMIM][3CH35CF3pyra]) and negative r-- for the 3-trifluoromethyl and 3-methyl-5-trifluorotrifluoromethylpyrozalide salts of the triethylbutylphosphonium and the triethyloctylphosphonium ions (Figures S6 and S7), though again the uncertainties are large.130 In all cases for the salts of 1-alkyl-3-methylimidazolium ions, r+- >> r++, |r--|, corresponding to |f+-| r-- (that is, less negative) for [PyrOMe][BF4], whereas the order for ZnCl2 is reversed. The pattern is quite different from those of the other protic tetrafluoroborates studied by this group (Figure S9): though some have negative r—, the uncertainties in these cases are of like magnitude to the r—themselves. The observation of moderately large negative rii, for both ions [PyrOMe][BF4], analogous to those found for ZnCl2, suggests that there may possibly be some form of ion-association in this case. It is likely that the cation has a large quadrupole moment due to the proximity of the electron-withdrawing keto group next to the charged quaternary nitrogen in the pyrrolidinium ring,131 giving the likelihood of a tautomeric structure with a hydrogen midway between the carbonyl oxygen and the ring nitrogen that could form a hydrogen bond with a fluorine atom on


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the anion.132 At present the liquid structure is yet to be determined. It should be noted that 1methyl-2-oxopyrrolidine is a very weak base (estimated pKa ~ - 0.41133), so that proton transfer to form the salt may not be complete.134 A

second,

similar

example

is

that

of

1,8-diazabicyclo-[5,4,0]-udec-7-eneium

methanesulfonate, [DBUH][CH3SO3].135,136 Here there is more variation in (DS+/DS-), (1.0 ± 0.1) and in the SES and Walden slopes, t, (DS+: 0.69, DS-: 0.73, Λ: 1.04; Dd++: 0.67, Dd--: 0.66, Dd+-: 1.04), and those for the self-diffusion and like-ion distinct diffusion coefficients are unusually low. However the like-ion resistance coefficients are both large and negative, again suggestive of ion association or a labile H-bonded network. The two rii are equal, within experimental error, at the same viscosity. [Figure 10(c)] No such behavior is seen for the other [DBUH]+ salts for which data is available,135,136 (Figure S9) nor for protic trifluoromethanesulfonates137 (Figure S10). Protic ionic liquids differ from aprotic ones in that they result from equilibrium between an acid, a base and the ions resulting from proton transfer between the two. They are thus formally three component systems and their treatment as single component systems, as above, is an approximation that assumes full proton transfer. This is to be expected when the difference in pKa values is sufficiently large,21 as is believed to be the case for [DBUH][CH3SO3], (∆pKa 15.4),135,138 but may not be so for [PyrOMe][BF4] (∆pKa ~ 0). Figure 11 shows the NE deviation factor, ∆, as a function of temperature for both liquids: the curve for [DBUH][CH3SO3] is much more like that of ZnCl2 (Figure 4), consistent with increasing dissociation with increasing temperature. A full phenomenological treatment, for a three component system, would require nine VCC or resistance coefficients, deriving from nine transport properties, (four self-diffusion coefficients


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and the conductivity, which do not depend on the measurement frame of reference, and a twoby-two inter-diffusion coefficient matrix, of which three elements are independent due to the Onsager reciprocal relations, and a transport number, that do require specification of the frame of reference), together with density, viscosity and activity coefficient measurements, a daunting task. In addition the necessary equations have yet to be derived (they do exist in part for twocomponent salt mixtures with a common ion (rij139,140) and ternary electrolyte solutions (VCC141) of two salts). Furthermore, the measurement of the inter-diffusion coefficients and transport numbers would likely require new techniques for such systems. Distinguishing between the selfdiffusion coefficients of an ion and its corresponding neutral species is extremely difficult by spin-echo NMR, the usual technique employed. All in all, treating protic ionic liquids as single component liquids is very much simpler, provided that the results are interpreted with the approximation in mind. There are also further experimental constraints in that the property measurements of protic ionic liquids are even more susceptible to the effects of trace amounts of water than aprotics and both samples and apparatus need be scrupulously dried. In addition the effects of nonstoichiometric amounts of acid or base must be guarded against where vacuum evaporation is used in their preparation and one component is more volatile than the other.142 Despite these qualifications, it is interesting that these two different ionic liquids show such similar resistance coefficient behavior seemingly characteristic of ion association. Consequently it would be of some interest to see whether ion association could be established by spectroscopic or liquid structural studies or tested by theoretical calculations. These would then the first truly known cases of ion association in an ionic liquid determined from transport property measurements.


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Conclusions There have long been arguments supporting the concept of ion association in molten salts and ionic liquids. These are largely based on differences between the molar conductivity and that predicted from self-diffusion coefficients by the Nernst-Einstein equation for non-interacting ions. It is known from early molecular dynamics simulations that even simple models based on charged hard spheres show such a difference due to the correlation of ion motions, for both likecharged and oppositely charged ions. Formally this can be expressed as a difference between the the velocity cross-correlation coefficient of the oppositely charged ions and the mean of those for the two like-charged ions. There is no necessity to assume ion pairing in order to explain nonzero values of ∆, the Nernst-Einstein deviation parameter.

This article has examined molten salt transport property data, selected the more reliable and compared Laity resistance coefficients and velocity cross-correlation coefficients for simple salts such as KCl, NaCl and KNO3 with molten ZnCl2 where ion-association is known to exist, PbCl2 where the evidence from structural studies is inconclusive, but the friction coefficient results suggest association, and TlCl where covalent bonding may also produce weak ion association. The resistance coefficient analysis is shown to be the more fruitful in that the conjecture of Laity that association leads to negative like-ion resistance coefficients is confirmed. This result is reinforced by the examination of highly associated pseudo-salts such as water, formic and sulfuric acids, which also have negative like-ion resistance coefficients.

These arguments show that the ion-pairing or “ionicity” model6,9,18,20 is flawed in its simplistic application to ionic liquids and most inorganic salts. This result is consistent with recent direct measurements of the degree of ionicity in ionic liquid chlorides47 and theoretical


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studies48-49 which suggest that ion-pairing is unlikely in normal ionic liquids. However, two examples have been found of protic ionic liquids with a larger than usual NE deviation parameters and large, negative like-ion resistance coefficients, analogous to those found for ZnCl2. One, [PyrOMe][BF4] may be an example of incomplete transfer and thus be a threecomponent system, a mixture of the salt and the unionized acid and base from which it derives; the other, [DBUH][CH3SO3], which has a large value for ∆pKa, is like ZnCl2 in that the NernstEinstein ∆ decreases with increasing temperature. Structural, spectroscopic and perhaps computational studies are required to determine whether this is a genuine example of association in an apparently otherwise normal room temperature ionic liquid or whether there is an alternative explanation.

ASSOCIATED CONTENT Supporting Information. Reference table for the transport properties of molten salts; tables of resistance coefficients for ionic liquids. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author *Email: [email protected]

Notes The author declares there are no competing financial interests.


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ACKNOWLEDGMENTS The author is grateful to Dr Mitsuhiro Kanakubo (AIST-Tohoku, Sendai, Japan) for helpful discussions and his collaboration on ionic liquids over many years. Some parts of this work were presented at the 33rd International Conference on Solution Chemistry, Kyoto, Japan, in July 2013, and the post-symposium meeting, "Ionic Liquids from Science to Green Chemical Applications", at the AIST-Tokyo-Waterfront, Tokyo, Japan, on 13 July 2013. Dr Thomas Rüther (CSIRO Energy, Clayton, Victoria, Australia) also kindly commented on a draft of the manuscript and suggested the tautomeric structure for the [PyrOMe]+ ion. Professor Masuyoshi Watanabe (Yokohama University) and Dr M. S. Marin (University of Dhaka) kindly provided self-diffusion data for DBU-based ionic liquids. The author particularly acknowledges one of the reviewers for helpful and constructive comment.


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(126) It is interesting that the very high viscosity of sulfuric acid relative to water and formic acids (24.5, 0.89 and 1.51 mPa·s respectively at 25 oC, has considerable effect on the molecular self-diffusion coefficient, but none on the ion self-diffusion coefficients, presumably due to the dominance of proton exchange by the Grotthuss mechanism over Brownian mobility. (127) Harris, K. R.; Kanakubo, M. J. Phys. Chem. B., jp-2016-10341d, submitted 12 Oct 2016. (128) Sun, L.; Morales-Collazo, O.; Xia, H.; Brennecke, J. F. Effect of Structure on Transport Properties (Viscosity, Ionic Conductivity, and Self-Diffusion Coefficient) of Aprotic Heterocyclic Anion (AHA) Room-Temperature Ionic Liquids. 1. Variation of Anionic Species. J. Phys. Chem. B 2015, 119, 15030-15039. DOI: 10.1021/acs.jpcb.5b09175


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(129) Sun, L.; Morales-Collazo, O.; Xia, H.; Brennecke, J. F. Effect of Structure on Transport Properties (Viscosity, Ionic Conductivity, and Self-Diffusion Coefficient) of Aprotic Heterocyclic Anion (AHA) Room Temperature Ionic Liquids. 2. Variation of Alkyl Chain Length in the Phosphonium Cation. J. Phys. Chem. B 2016, 120, 5767-5776. DOI: 10.1021/acs.jpcb.6b03934 (130) Based on a comparison of the slopes of Walden and Stokes-Einstein-Sutherland plots against the viscosity and of the Nernst-Einstein deviation parameter against temperature the selfdiffusion coefficients reported in both papers seem too high at 70 oC. This shows in Fig. 9 of both papers. This effect is probably due to convection, as noted by the authors of these works. Examination of the VCC suggests the lower temperature conductivities of the phosphonium salts may also be too high, consistent again with Fig. 9 of ref. 129. (131) Wu, T.-Y.; Su, S.-G.; Gung, S.-T.; Lin, M.-W.; Lin, Y. C.; Ou-Yang, W. C.; Sun, I.-W.; Lai, C. A. Synthesis and Characterization of Protic Ionic Liquids Containing Cyclic Amine Cations

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FIGURES

0.6 (a) 0.4

0.2

0.0 (b)

∆

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


0.4

0.2

0.0 (c)

0.5

0.3

0.1

-0.1

0

20

40

60

80

100

θ/ C o

Figure 1. NE deviation parameter ∆ as a function of temperature at 0.1 MPa. Data from ref. 17, 30, 34, 50-53. (a) Circles, [Tf2N]- salts52; red, [EMIM]+; black, [BMIM]+; blue, [HMIM]+; green, [OMIM]+; squares, [PF6]- salts17,30; triangles, [BF4]- salts17; open diamonds, [Pyr14][Tf2N].34


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(b) Open symbols: diamonds, [Pyr14][Tf2N]34; circles, 1-ethyl-1,4-dimethyl piperazinium ([C2dmppz]+) [Tf2N];50 squares, 1-(2-dimethylaminoethyl)dimethyl-ethylammonium ([C2TMEDA]+) [Tf2N];50 closed circles, ammonium [Tf2N]- salts:51 red, N-acetoxyethyl-N,Ndimethyl-N-ethylammonium ([N112,2OCO1]+) and its non-functionalised analogue, N,N-dimethylN-ethyl-N-pentylammonium ([N1125]+), and N,N-dimethyl-N-ethyl-N-

methoxyethoxyethylammonium ([N112,2O2O1]+), and its analogue, N,N-dimethyl-N-ethyl-Nheptylammonium ([N1127]+); black, [BMIM]+; blue, [HMIM]+; green, [OMIM]+. c) [EMIM]+ salts:53 blue squares, tetracyanoborate, [TCB]-; black circles, methylsulfonate, [CH3SO3]-; green triangles, trifluoromethanesulfonate, [CF3SO3]-; red circles, [Tf2N]-; black inverted triangles, tris(perfluoroethyl)trifluorophosphate, [FAP]-.

Figure 2. NE deviation parameter ∆ as a function of pressure for [BMIM][Tf2N]. Symbols: circles, 25 oC; squares, 50 oC; triangles, 75 oC. Reproduced from ref. [52] (Fig. 15) with permission from the Royal Society of Chemistry.


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0

7

-1

6

-2

5

-3

4

Λ -4

ln(Λ /µ µ S⋅⋅m2⋅ mol-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


ln[(1012D/T)/m2⋅ s-1⋅ K-1]

Page 45 of 56

-6

D+

-5

D-

-4 ln(mPa⋅⋅s/η)

-3

-2

3

Figure 3. Stokes-Einstein-Sutherland plots for the self-diffusion coefficients of [BMIM][Tf2N] together with the corresponding Walden plot for the molar conductivity. tΛ = 0.931; tD(cation) = 0.927; tD(anion) = 0.956.52 Triangles, molar conductivity, Λ; circles cation DS+; squares, anion DS-; green symbols, atmospheric p isobaric points; red, 25 oC isotherm; blue, 50 oC isotherm; black, 75 oC isotherm. Reproduced from ref. [35] (Fig. 1) with permission from the Royal Society of Chemistry.


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Figure 4. NE deviation parameters ∆ for high temperature molten salts calculated from literature conductivity and self-diffusion data (Table 2). Symbols: unassociated salts - squares, NaCl, diffusion data of Ejima et al.;66 diamonds, KCl; triangles, KNO3; associated salts - inverted triangles, TlCl; open squares, PbCl2, circles, ZnCl2.

Figure 5. Walden plots for intermediate-temperature molten salts. Symbols: blue, tetrapropylammonium salts; black, tetrabutylammonium salts; red, tetrahexylammonium salts; circles, tetrafluoroborates; squares, hexafluorophosphate; triangles, tetrabutylborate; diamonds, tetraphenylborate. Slopes, tΛ: [Pr4N][BF4], 0.83; [Bu4N][BF4], 0.90; [Hex4N][BF4], 0.92; [Bu4N][BBu4], 0.77; [Bu4N][BPh4], 0.83; [Pr4N][PF6], 0.94.


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Figure 6. SES analogue plot of the distinct diffusion coefficients (DDC) (in the form ln(-Ddij/T) as a function of the fluidity φ (=1/η) for [PyrOMe][BF4] and [BMIM][BF4] showing how the NE deviation parameter is related to the difference between the mean for the cation-cation DDC (or VCC, see eq 6), given by the dashed lines, and that for the cation-anion DDC. Symbols: squares, [PyrOMe][BF4]; circles, [BMIM][BF4]; blue, Dd++; red, Dd--; black, Dd+-.


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Figure 7. Analogue SES plots of distinct diffusion coefficients (Ddij) for high-temperature molten salts. (a) NaCl, KCl, TlCl and KNO3, (b) PbCl2 and ZnCl2. Symbols as in Figure 4; blue cation-cation, red - anion-anion, black – cation-anion. As f+- is always smaller in magnitude (less negative) than the like-ion VCC, the Dd+- plots lie lowest for each substance. Note that the order for the nitrate is similar to that for [Tf2N]- containing ionic liquids34,50--52 and for the chlorides it is similar to that for [BF4]- and [PF6]- containing ionic liquids,17,30,35 and for the [EMIM]+ salts of the [CH3SO3]-, [CF3SO3]- and [TCB]- anions.53


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Figure 8. Analogue SES plot of Laity resistance coefficients rij for NaCl (circles), KCl (squares) and KNO3 as a function of fluidity, φ, (reciprocal viscosity). Symbols: black, r+-; blue, r++; red, r-.


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Figure 9. Analogue SES plot of Laity resistance coefficients rij for [BMIM][Tf2N] and [BMIM][PF6]as a function of fluidity, φ, (reciprocal viscosity). Symbols: black, r+-; blue, r++; red, r--; open circles, 0.1 MPa; filled symbols, high pressure isotherms. Modified from ref. [52] (Fig. 18) with permission from the Royal Society of Chemistry.


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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 ACS Paragon Plus Environment

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Figure 10. Plots of Laity resistance coefficients rij for (a) ZnCl2 (b) [PyrOMe][BF4], (c) [DBUH][CH3SO3] and (d) TlCl as a function of viscosity, η. Note the differences in the axes scales due to the very different viscosities.

Figure 11. NE deviation parameters ∆ for protic ionic liquids calculated from literature conductivity

and

self-diffusion

data.

Symbols:

circles,

[PyrOMe][BF4];18

squares,

[DBUH][CH3SO3].135,136 Compare ZnCl2, Figure 4.


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TABLES.

Table 1. Exponents (t) for Stokes-Einstein-Sutherland and Walden fits of the Self-diffusion coefficients, DSi, Molar Conductivity Λ and Distinct Diffusion Coefficients, Ddij, and the consistency test plot of ln(ΛT) against ln (DS+ + DS-) Substance

t(DS+)

t(DS-)

t(Λ)

[BMIM][BF4]

0.852

0.898

0.878

ln(ΛT) vs ln(DS++DS-) 1.001

[OMIM][BF4]

0.888

0.888

0.936

1. 019

[BMIM][PF6]

0.883

0.920

0.913

0.986

[HMIM][PF6]

0.845

0.868

0.912

1.009

[OMIM][PF6]

0.860

0.948

0.962

0.986

[EMIM][Tf2N]

0.923

0.971

0.899

0.954

[BMIM][Tf2N]

0.927

0.956

0.931

0.977

[Pyr14][Tf2N]

0.937

0.933

0.925

0.992


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.

Table 2. SES and Walden Plot Slopes for Molten Salts. salt DS+/DStD tD Dd+Dd++ tΛ LiF

(cation)

(anion)

Dd--

-

0.565

-

-

0.578

-

-

NaF (Grjotheim DS+)

-

0.806

0.992

-

0.806

1.064

-

KF (Grjotheim60DS+)

-

0.621

0.891

-

0.621

0.938

-

LiCl

1.82 -

0.439

0.539

0.284

0.439

1.00

0.274

1.05

1.15

1.65

1.44

0.756

0.912

1.02

1.09

60

2.02 NaCl (Bockris65 DSi)

1.37 1.42

NaCl (Ejima66 DSi)

1.38 -

0.468

0.468

1.47 KCl

1.12

0.570

0.772

0.817

0.569

0.866

1.015

CsCl

-

0.893

0.512

-

0.893

0.492

-

TlCl

0.94

1.05

0.880

0.886

1.05

0.878

0.767

KNO3

1.12

0.825

0.982

1.025

0.825

1.18

1.08

CaCl2

0.59 -

0.664

0.543

0.932

0.664

0.408

1.01

0.881

0.623

0.662

0.881

0.608

0.645

0.72 ZnCl2

0.75 0.91

CdCl2

0.99

0.748

1.51

1.50

0.748

1.59

2.17

PbCl2

0.54

1.86

0.904

0.902

1.86

0.896

0.815

[H3O][OH]

1.4-1.9

2.34

0.569

0.745

2.34

0.568

0.745


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Table 3. Transport Property and Derived VCC and Resistance Coefficients Data for Weakly Dissociating Molecular Liquids. T

pKw, pKd a

Ds+

/oC

Ds-

Ds

/10-9·m2·s-1

κ /µS·m-1

f++

f--

106f+-

Dd++

/10-15·m5·mol-1·s-1

Dd --

106 Dd +-

/10-9·m2·s-1

r+-

r++

r--

/104·J·s·m-2·mol-1

109Y b (Y=1-∆)

water 0

14.95

5.52 2.90

1.118

1.11

-199 -104 -0.0873 -5.52 -2.90

-2.42

4.67

-4.67

-4.67

1.21

5

14.73

6.22 3.31

1.313

1.65

-224 -119

-0.113

-6.22 -3.31

-3.68

3.13

-3.13

-3.13

1.55

18

14.24

8.16 4.52

1.916

3.70

-294 -163

-0.313

-8.16 -4.52

-8.66

1.39

-1.39

-1.39

2.75

25

13.99

9.26 5.26

2.298

5.54

-335 -190

-0.448

-9.26 -5.26

-13.3

0.929 -0.929 -0.929

3.66

50

13.26

13.4 8.27

3.983

1.76

-488 -302

-1.68

-13.4 -8.27

-46.2

0.290 -0.290 -0.290

8.55

75

12.75

17.5 11.9

6.112

3.97

-647 -435

-4.20

-17.5 -11.9

-114

0.127 -0.127 -0.127

15.6

100

12.25

21.3 15.5

8.579

8.10

-800 -584

-9.51

-21.3 -15.5

-253

0.061 -0.061 -0.061

28.2

-2.12 -1.33

-30680

0.202 -0.202 -0.202

35.6

Dd++

103Dd +-

HCOOH 25

6.66

2.12 1.33

T

pKd

Ds+

/oC

Ds-

1.04

6080

Ds98,99

κ

/10-9·m2·s-1

/S·m-1

-161 -101 f++

f--

-2300 f+-

/10-15·m5·mol-1·s-1

Dd --

/10-9·m2·s-1

r+-

r++

r--

∆

/1012·J·s·m-2·mol-1

H2SO4 25

3.54

6.44 4.55 0.0657

1.044

-579 -409

-0.561

-6.44 -4.55

-6.24

99.3

-98.5

-98.2

0.998

a

pKd is the analogue of pKw for HCOOH and H2SO4

b

It is more convenient to use Y when ∆ ~ 1. Note that it increases with increasing temperature, that is, d∆/dT is negative, as is found for ZnCl2.


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TOC GRAPHIC


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Can the Transport Properties of Molten Salts and Ionic Liquids Be

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