Journal of Solution Chemistry, Vol. 28, No. 3, 1999

A New Relation Between the Maxima Conductivitiesof Nonaqueous Concentrated Electrolytes andChemical Hardness of Solvents and Salts

Guillaume Herlem,*,1,2 Bernard Fahys,2 Michel Herlem,1and Jean-Francois Penneau3

Received July 20, 1998

For nonaqueous electrolytes, using the HSAB principle, we tried to correlate theconductivity maxima KMAX, vs. only two intrinsic parameters: chemical hardnessn of the solvent and that of the salt. Thus, not only the nature of the solvent butalso that of the salt were taken into account. We were able to predict for a givensolvent the variation of KMAX as a function of the hardness of the salt and thatof the solvent: KMAX = K(1 - |An|/nSOLVENT) with |An| = |nSOLVENT - nSALT|and K a constant in S-cm-1 independent of the salt, but not of the solvent.

KEY WORDS: nonaqueous solvents; amides; acetonitrile; -y-butyrolactone; pro-pylene carbonate; conductivities; concentrated solutions; conductivity maxima;chemical hardness.

1. INTRODUCTION

The goal of this work was the study of concentrated nonaqueous electro-lytes for electrochemical devices, such as supercapacitors, based on saltsother than lithium and other solvents than "classical" PC-EC mixtures (whichwere the comparison standards), to obtain the highest possible conductivity.Consequently, it was also an attempt to predict the maximum conductivity

1 Institut Lavoisier, IREM-CNRS, Universite de Versailles St-Quentin, 45 Avenue des Etats-Unis, F 78000 Versailles.

2 LESM, Universite de Franche Comte,16 Route de Gray, La Bouloie, F 25030 Besancon Cedex.3DER-EDF, Les Renardieres, F 77250 Moret-sur-Loing.

2230095-9782/99/0300-0223$16.00/0 C 1999 Plenum Publishing Corporation

of concentrated electrolytes, KMAX, with good accuracy from the values foundin the literature in any solvent and with any salt.

We systematically measured the conductivity K vs. concentration C ofsalt solutions over the whole range of solubility for some solvents and somesalts at 20°C (see list below). We have been able to show that sodium salts,and even potassium salts, could give higher conductivities than lithium salts,showing that the goal was achievable.

For these very concentrated nonaqueous media, no simple "handy" rela-tions were established(1-4) between the conductivity, in particular KMAX, andthe concentration or others parameters. Salomon and Uchiyama(5) have shownthat the Fuoss-Hsia conductivity equation can be extended to fit the conduc-tivity K (vs. salt concentration) for low dielectric constant solvents, but itsutilization requires, for example, knowledge of KA (equilibrium constant forion pairing, and KT (equilibrium constant of bilateral triple-ion formation).Consequently, this last equation is difficult to use with new solvents and saltsto predict the maximum conductivity KMAX. The Casteel-Amis equation,(6)

although it is simpler, requires determination of four parameters and is noteasy to use for predicting KMAX in any solvent.

Different solvent parameters have been taken into account to determinethe role of the solvent of an electrolyte solution.(6) Curiously, no considerationhas been given to intrinsic properties of the salt itself, i.e., its chemicalhardness(7) n.

Although the ion aggregate formation was not taken into account throughion pairs, triple ions, quadruple ions,(4) etc., we have been able to find asimple relation between KMAX and two intrinsic parameters, the chemicalhardness n of the salt and that of the solvent, and, consequently, to predictKMAX for a given salt in any solvent through the knowledge of one KMAX ofthis salt in a given solvent. The chemical hardness n is a powerful and usefulconcept, for example, in chemical reactivity.(8)

The involvement of two contributions, electrostatic and charge-transfer,to acid-base interaction, as proposed by Pearson(9) (the "Hard-Soft Acid-Base principle" or HSAB principle), matches well the solvation interactionsbetween the salt (through its ions) and the solvent. Indeed, the solvation ofions by solvent molecules implies Lewis acid-base interactions, where bothelectrostatic (or ionic) and charge-transfer (or covalent) factors are involved.

We used the chemical hardness of the salt to take into account the factthat the solubility depends on the nature of the anion as well as that of thecation. (In many cases, the driving force of the solubility of a salt in anonaqueous solvent is the intense solvation of the cation rather than that ofthe anion, e.g., the case of DMSO.)

We will see that when the chemical hardness of the salt and that of thesolvent are similar, the solubility of the salt can be important and, as well,

224 Herlem, Fahys, Herlem, and Penneau

the conductivity KMAX. A theorem can be derived that links KMAX to nsolvent

and nsalt.The chemical hardness n is deduced from the average energy gap(8,10)

of the molecule (salt or solvent):

Nonaqueous Concentrated Electrolytes 225

EHOMO and ELUMO are easily computed and easier to obtain than KMAX, whichrequires much more data to calculate with existing conductivity laws.(1,4)

2. EXPERIMENTAL

All the solvents and the salts [except lithium bis(trifluoromethanesul-fone)imide or LiTFSI, a gift of Electricite de France, EDF, France] wereobtained from Sigma-Aldrich (purest quality) and were used as received. Thesolutions were prepared in a globe box under a dehydrated and deoxygenatedargon stream.

The conductivities were measured through impedance data (Nyquistplots from a Solartron 1170 using electrochemical interface 1186) usingplatinized platinum electrodes XE150 from Radiometer Analytical.

The chemical hardness of every salt or solvent was computed by theab initio Hartree-Fock self-consistent field molecular orbital method. Calcu-lations were performed by using Gaussian 94W software.(11) The geometryof each salt was fully optimized using the STO 3-21+G* basis set,(12) which isknown to give a reliable description of molecular orbital long-range behavior.

In checking our computations against that of the chemical hardness ofLiTFSI by Sanchez et al.,(13) we found the same value.

3. RESULTS AND DISCUSSION

The following salts and solvents were used:

• LiBF4, LiPF6, LiTFSI, LiNO3, LiSO3CF3

• NaBF4, NaPF6,NaSO3CF3, NaClO4

• KBF4, KPF6, KClO4, KNO3

• NH4BF4, NEt4BF4

• W-methylformamide (NMF), N, W-dimethylformamide (DMF), N, N-dimethylacetamide (DMA), 1-methyl-2-pyrrolidinone (NMP), aceto-nitrile (ACN), -Y-butyrolactone (G-BL), propylene carbonate (PC).

The conductivity vs. concentration curves show a parabolic, or evengaussian-like shape, between 0.5 and <3M, as for other nonaqueous sol-

226 Herlem, Fahys, Herlem, and Penneau

vents(14) (see, for example, Figs. 1-6). The conductivity maxima KMAX at20°C are given Tables I and II.

3.1. Interpretation of Conductivity Data by HSAB Theory

Superposition of conductivity curves for all the salts of a same cationin a given solvent highlights an interesting relation: the KMAX values lie ona straight line. A dependence of KMAX vs. concentration corresponding to thismaximum for various salts in a solvent has already been found,(15) but notsuch a relationship.

It is necessary to search for an explanation of this behavior in thesolvation of salts and, consequently, in the acid-base reaction between thesalt and the solvent. The maximum of K = f(C) curves are on a straightline in the same range of concentration probably because the same kindof interactions and solvent-ions, rule the behavior of salts dissolved in agiven solvent.

From the point of view of the HSAB theory,(16) it is important to notethat all solvents are hard (see Table III, computed by ab initio calculationsfrom our data using the Gaussian 94W software) and that the salts, whichallow the highest conductivities, are also hard as well (see Table IV). Among

Fig. 1. Conductivity vs. Li salt concentration in NMF at 293K.

Nonaqueous Concentrated Electrolytes 227

Fig. 2. Conductivity vs. K salt concentration in NMF at 293K.

the values reported in Table IV we have chosen those that are on a straightline for KMAX vs. EHOMO curve. Such a curve is given Fig. 7 in the case ofDMSO. The same curves are observed for other solvents. Thus, the consideredvalues for chemical hardness are given in the Table V.

Triflate salts and LiTFSI are known for their high chemical stability(17)

and are used as references for comparison with other salts.A first remark can be formulated if the solvation reaction is considered

an acid-base reaction, i.e., an electronic transfer between species. It seemsinteresting to compare absolute chemical hardness n of alkaline salts withmaximal conductivities, as was done between EHOMO of the salt and the valueof the oxidation limit of the electrolyte.(18) Second, it is possible to choosebetween several hardness values for a given salt.(13,19,20) Indeed, for salt-ionpairs, the coordination of the cation by the anion can be monodentate, biden-tate, or tridentate; the magnitude of their electrical interactions differsaccording to their geometry. A good correlation between the conductivitymaxima and the EHOMO of salts for monodentate, bidentate, or tridentatecations allows the determination of the cation coordination in vacuum. If thishypothesis is confirmed, it will allow a better understanding of the solvationof ions in solutions.

with An = |nSOLVENT - nSALT|.ATI is the absolute value of the chemical hardness difference between

the solvent and the salt and K1 (in mS-cm-1) is a constant that depends onlyon the temperature and on the solvent.

3.2. Verification of Equation (1)

Equation (1) is for a given solvent; K1 must be computed for one solventand must have the same value whatever the salt. The computed values of

Fig. 3. Conductivity vs. Li salt concentration in DMF at 293K.

As stated earlier, it is remarkable to note that solvents and salts thathave very conductive electrolytes have the same hardness: solutions areespecially conductive when hardness of salt and hardness of solvent are closeto each other. This suggests that the larger the conductivity, the smallerdifference of hardness between the constituents of the electrolytes. We havetried to formalize this observation by proposing a relationship between themaximum conductivity, KMAX, and the hardness of the salt nSALT and hardnessof the solvent nSOLVENT.

We propose the relationship:

228 Herlem, Fahys, Herlem, and Penneau

Fig. 4. Conductivity vs. Na salt concentration in DMF at 293K.

nSOLVENT and nSALT are given in Tables III-V; Table VI gives the computedvalues of K1.

n could be chosen in two basis sets, STO 3-21G and STO 3-21+G*.The best basis should be the second, but the first is interesting, because itgives values of dipole moments close to experimental ones and has beenused for the computations.

One can see that, for a given solvent, K1 is almost constant except fora few salts.

Although the accuracy may seem poor, it must be recalled that there isa large scatter of literature data, even for "classical" salts in usual solvents,e.g., LiClO4. The conductivity of 1M solutions of this salt in propylenecarbonate, at 25°C, range from 3.9 to 5.6X 10-3 S-cm-1,(21) which is a variationof 40% of the low value.

Since n values play important roles (as a difference in the numeratorand as denominator), any value error yields large variations of K1. The choiceof the basis set is crucial.

The so-called "universal solubility equation"(22) was proposed 10 yearsago. Although successful, it requires determination of 17 parameters. By

Nonaqueous Concentrated Electrolytes 229

Fig. 6. Conductivity vs. Na salt concentration in NMP at 293K.

Fig. 5. Conductivity vs. Li salt concentration in NMP at 293K.

230 Herlem, Fahys, Herlem, and Penneau

using Eq. (1), we have fairly good accuracy with only two chemical hardnessesto compute and one KMAX to determine or to obtain from the literature.

3.3. Correlation KMAX/HOMO of the Salt

A remarkable correlation is obtained between EHOMO of the salts andKMAX for NMF, DMF, DMA, and NMP. (See, for example, the case of DMF

Nonaqueous Concentrated Electrolytes 231

Table I. Conductivity Maxima KMAX for Salts in Amides at 20°Ca

LiPF6

NaPF6

KPF6

tBuNPF6

LiBF4

NaBF4

KBF4

NH4BF4

NEt4BF4

LiSO3CF3

LiTFSI

HCONH2

FA

13.54 [1.88M]12.71 [1.76M]10.39 [0.88M]

—17.36 [2.42M]14.28 [1.78M]3 [1.3M]

33.4 [4M]17.61 [1.54M]10.44 [1.6M]8.3 [1.46M]

HCONHCH3

NMF

15.36[1.34M]16.10[1.3M]15.35 [1.6M]7.18 [0.56M]

17.47 [ 1 . 4 M ]17.0[1.42M]3.62 [1.27M]

—6.6 [2M]

12.16 [1.19M]10.78 [1.13M]

HCON(CH3)2

DMF

19.35 [1.11M]22.43 [1.16M]25.2b[1.22M]12.56 [0.75M]20.61 [1.09M]21.81 [1.28M]

6.71 [1.91M]

—24.63 [1.07M]15 [0.9M]14.3 [1.2M]

C3H6CONCH3

NMP

7.27 [0.90M]8.51 [0.92M]7.81 [0.83M]5.54 [0.68M]8.30 [0.89M]8.07 [1M]1.4 [0.8M]11.07[1.3M]8 [0.6 1M]6.38 [0.79M]6.21 [0.79M]

CH3CON(CH3)2

DMA

12.27 [0.91M]13.9 [1.10M]11.86[0.80M]9.38 [0.68M]

13.5 [0.9M]13.25 [0.98M]4 [1.8M]

—Sat'd soln. [0.1M]10.57 [0.79M]10.76 [0.85M]

aEntries give KMAX in mS-cm-1 followed by salt molarity in brackets.b25°C.

Table II. Conductivity Maxima for Salts in -y-Butyrolactone, Acetonitrile, and PropyleneCarbonate at 20°Ca

LiBF4

NaBF4

KBF4

NH4BF4

NEt4BF4

LiPF6

NaPF6

KPF6

UNO3

KNO3

NaSO3CF3

NaClO4

KClO4

G-Butyrolactone

6.55 [0.94M]K < 2 [solubility < 0.5M]K < 1 [solubility < 0.4M]—18* [ 1 M ]9.3 [ 1 M ]9.8 [1.2M]11 [1.45M]2.1 [1.68M]K < 0.3 [solubility < 0.4M]6 [ 1 M ]10.2 [1.33M]2.3 [0.18M]

Acetonitrile

14.8 [1.3M]——

—47.2 [1.67M]41.5 [1.5M]35.3 [ 1 M ]26 [1M]K <0.5 [solubility < 0.1 M]K < 10 [solubility < 0.2M)13 [0.55M]31.1 [0.55M]~1.5 [0.3M]

Propylenecarbonate

4.0 [1M]1.51 [1.5M]<0.10[1.5M]—15.2[1.17M]5.4 [0.857M]6.15 [0.97M]6.4 [1.06M]—————

aUnits, mS-cm-1 followed by salt molarity or solubility in brackets.b25°C.

232 Herlem, Fahys, Herlem, and Penneau

Table III. Chemical Hardness of the Solvents Used in this Study Calculated in STO3-21 +G* Basis Set

Solvent

FormamideN-MethylformamideN,N-DimethylformamideN-MethylacetamideN,N-Dimethylacetamide1 -Methyl-2-pyrrolidinoneAcetonitriley-ButyrolactonePropylene carbonate

EHOMO (eV)

-11.579-10.854-10.269- 10.632-10.128-10.132- 12.969- 12.035-12.919

ELUMO (eV)

+ 1.810+ 1.910+ 1.888+ 1.906+ 1.940+2.010+ 1.690+ 1.828+ 1.620

n (eV)

6.696.386.086.276.036.077.336.937.27

in Fig. 7.) The straight line is obtained only for one configuration of thecation: monodentate, bidentate, or tridentate. This configuration is taken intoaccount when choosing the best chemical hardness of the salt in Eq. (1).This means that the calculated structure of the solvated salt will have thisconfiguration, i.e., for high concentrations (ion pairing), at maximumconductivity.

In a previous paper,(23) we have studied the solvation numbers of LiNO3,LiTFSI, and LiSO3CF3 in n-butylamine. We obtained the following resultsby changing the anion and the salt concentration: (1) LiNO3 was the moresolvated salt and (2) LiSO3CF3 was the less solvated salt. A priori, there didnot seem to be an obvious relation between conductivity and the solvationnumber. It was surprising that the triflate anion was less solvated than theTFSI anion, which is larger.

If the HSAB approach is used, it seems possible to explain these results.Contrary to all expectations, TFSI anion is larger than the triflate anion, but

Table IV. Chemical Hardness of the Salts Used in this Study Computed in STO 3-21 +G*Basis Set

Salt

LiBF4

NaBF4

LiPF6

NaPF6

LiSO3CF3

NaSO3CF3

LiTFSILiNO3

NaNO3

nmonodentate

_6.967.467.295.855.61—

5.405.15

nbidentate

7.94

7.668.167.926.546.266.516.305.96

ntridentate

8.25

8.068.398.18—

6.166.62—

5.96

Nonaqueous Concentrated Electrolytes 233

Fig. 7. Correlation KMAX/HOMO of some salts in DMF. The correlation coefficient of thestraight line "KMAX vs. HOMO" is equal to 0.998 only for one configuration of the salt:monodentate, bidentate, or tridentate.

is less hard. The increase in solvation number of salts seems to followthe reverse order of chemical hardness: the harder the salts, the less theyare solvated.

4. CONCLUSION

Through the concept of absolute hardness n of a species, introduced byParr and Pearson and defined as

Table V. Chemical Hardness of Some Salts

Salt

LiBF4

LiPF6

LiNO3

LiTFSI

Chemical hardness (n) in eV

8.257.455.406.50

Herlem, Fahys, Herlem, and Penneau

Table VI. Computation of K1 from the Eq. (1) and the KMAX Given in Tables I and II

LiBF4

NaBF4

LiPF6

NaPF6

LiTFSILiSO3CF3

NaSO3CF3

DMF

21.522213017——

NMF

17.517.716171113—

y-BL

7

—9.5

10——8

ACN

17

—4742

——19

PC

4.6—67.1———

deduced from the HSAB principle, that ties KMAX to the chemical hardnessof the salt and that of the solvent, giving the variation of the conductivitymaximum of any salt in a given solvent, leads to coherent results for thecomputation of the constant K1. From knowledge of the KMAX for one saltin a solvent, one can estimate the maximum conductivity of any other saltin this solvent through the computation of two chemical hardness values.Although the dependence of the chemical hardness on the chosen basis sethas a repercussion on K1, the accuracy of the predicted values is good enoughsince conductivities can vary from one salt to another by more than a factorof 10.

This simple relation is of interest since knowledge of KMAX values isuseful for producing supercapacitors (the resistance of electrolyte should beas low as possible). Furthermore, it gives the upper limit of conductivity and,consequently, the available range of concentration for battery electrolytes.

ACKNOWLEDGMENTS

The present work was supported financially by EDF. One of the authors(G. Herlem) wishes to thank ADEME for a grant.

234

we can account not only for the nature of the solvent but also for the saltand predict the conductivity maxima of any salt in a given solvent. Accountingfor the nature of the salt through its chemical hardness is original because inother empirical equations only parameters without physical meaning are fitted.

The relation,

Nonaqueous Concentrated Electrolytes

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