1 Ionic Conductivity, Diffusion Coefficients and Degree of Dissociation

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Ionic Conductivity, Diffusion Coefficients and Degree of Dissociation in Lithium Electrolytes, Ionic Liquids and Hydrogel Polyelectrolytes Leoncio Garrido, Inmaculada Aranaz, Alberto Gallardo, Carolina García, Nuria García, Esperanza Benito, and Julio Guzman J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b06424 • Publication Date (Web): 09 Aug 2018 Downloaded from http://pubs.acs.org on August 12, 2018

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The Journal of Physical Chemistry

Ionic Conductivity, Diffusion Coefficients and Degree of Dissociation in Lithium Electrolytes, Ionic Liquids and Hydrogel Polyelectrolytes

Leoncio Garrido*, Inmaculada Aranaz,† Alberto Gallardo, Carolina García, Nuria García, Esperanza Benito, Julio Guzmán*

Instituto de Ciencia y Tecnología de Polímeros, Consejo Superior de Investigaciones Científicas (ICTP-CSIC), Juan de la Cierva 3, 28006 Madrid, Spain.

*

Corresponding authors: Leoncio Garrido and Julio Guzmán Departamento de Química-Física Instituto de Ciencia y Tecnología de Polímeros, CSIC Juan de la Cierva 3 E-28006 Madrid, Spain E-mail: [email protected]; [email protected]

†

Current address: Departamento de Química en Ciencias Farmacéuticas Instituto de Estudios Biofuncionales Facultad de Farmacia Universidad Complutense de Madrid Plaza de Ramón y Cajal s/n E-28040 Madrid, Spain

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Abstract The conductive and diffusional behavior of electrolytes in media with different dielectric and viscoelastic properties is investigated. A revised model to separate the contribution of dissociated and non-dissociated species to the diffusion coefficients determined with NMR is proposed. Impedance spectroscopy is used to measure the ionic conductivity of lithium salts in aqueous medium, ionic liquids in aprotic solvents and hydrogel polyelectrolytes. The diffusion coefficients of the species of interest in those systems are determined with multinuclear pulsed-gradient spin-echo (PGSE) NMR. The results are analyzed using the revised model. It is shown that the degree of ionization could be determined directly from measurements of ionic conductivity and diffusion coefficients in very different types of electrolytes and in a wide range of concentrations. Furthermore, these findings support the original Arrhenius’ hypothesis about electrolytes and show that the assumption of a complete dissociation is not required to describe their conductive behavior. The reduced conductivity observed in hydrogels, at or near swelling equilibrium, compared to that in solutions could be attributed mainly to the hindered ionic mobility caused by the network structure.


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INTRODUCTION The ionic conductivity of electrolytes is a topic of broad research interest in physical chemistry, driven partly by the need to advance the understanding of essential processes taking place in diverse fields, such as those of material and life sciences. Moreover, the outcome of this effort would most likely facilitate the improvement of current developments of new applications involving electrochemistry, including the design and synthesis of electrolytes/polyelectrolytes for energy production and storage, biomedical devices, drug delivery, etc. In this context, it is worthwhile highlighting that, despite the century that has elapsed since Arrhenius’ hypothesis about electrolytes was first proposed,1 the electric behaviour of electrolytes continues to be subject of active discussion. Initially, electrolytes were considered to be molecules partially dissociated in ions with positive and negative charges. However, the observed deviations from theoretical predictions led to the proposal of a new theory to describe the properties of electrolyte solutions assuming that, in strong electrolytes, all molecules are completely dissociated, even at high concentrations. Nevertheless, this theory is valid only at the limit of infinite dilution.2 Subsequent modifications that introduced activity coefficients3 and empirical models4-6 broadened the applicability of the theory to explain experimental observations of electrolytes effects on solutions, i.e., electrical conductivity and colligative properties. More recently, the formation of ion-pairing has been considered to explain some spectroscopic observations and justify the non-ideal behavior of electrolyte solutions at moderate concentrations.7 Despite these efforts, a unified theory on the behaviour of electrolytes in solution is still lacking. Meanwhile, other research groups8-10 have proposed a return to the original idea of partial dissociation of electrolytes showing that, if a correct account of the electrolyte-solvent



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interactions is taken, the Arrhenius’ theory adequately describes their behavior across a wide range of concentrations, from very low to highly concentrated solutions. If partial dissociation of electrolytes is considered at any concentration, the relationship between molar electrical conductivity (Λ) of electrolytes and ionic diffusion coefficients is given by the Nernst-Einstein equation

Λ=

= + 1

where α is the degree of dissociation, σ is the conductivity of the electrolyte, and c is the molar concentration of the electrolyte. D+ and D‒ represent the diffusion coefficients of the ions in the electrolyte solution, F is the Faraday number, R is the gas constant, and T is the absolute temperature. The product α c would represent the true concentration of the charge carriers. Also, eq 1 could be expressed in another form using the ionic mobilities of the cation and anion, µ+ and µ-, respectively. In the case of monovalent electrolytes, this would lead to

Λ = μ + μ 2 From either eq 1 or 2, the values of α could be determined, but the experimental determination of two magnitudes, molar conductivity and ion diffusion coefficients or ionic mobility coefficients, is required. The experimental charge mobility measured with electrophoretic NMR (eNMR)11 is exclusively due to the ionic movement and, therefore, it would be possible to obtain accurate values of the transport number. However, the methodology for experimental determination of the ionic mobility by eNMR is not straightforward and presents some limitations due to, among other factors, sample heating and electroosmosis.12 Recent developments in the methodology have contributed to improve the accuracy of the eNMR measurements in dilute (10 mM) electrolyte solutions.13


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Concerning the diffusion coefficients, it is known that, in principle; the diffusion coefficients determined by pulsed gradient spin echo (PGSE) NMR, DNMR, do not correspond to the values of D+ and D- in eq 1 because, in addition to the free ions, the non-dissociated species also contribute to the measured values of the diffusion coefficients14,15 and, consequently, the value of α cannot be obtained directly from the experimental Λ and DNMR. However, in this work we will show that the values of the diffusion coefficients determined by NMR are practically equivalent to the corresponding D+ and D- coefficients, and independent of the degree of dissociation. In previous work,16 a simple model was proposed to separate the contribution of dissociated and non-dissociated species to the diffusion coefficients of lithium and fluorine determined by NMR for different solutions of lithium triflate in aprotic solvents, such as ethylene and propylene carbonate. Analysis of the experimental results suggested that the model, with certain reasonable assumptions, allows the determination of the degree of dissociation, and of all the diffusion coefficients that intervene in the transport of charge. In this report, a revised model is proposed and its applicability to describe the conductive behavior of several types of electrolytes is shown. Thus, the conductivity and the diffusion coefficients in dilute and concentrated solutions of monovalent Li ionic salts in water are described. Measurements of electrical conductivities using impedance spectroscopy, as well as diffusion measurements by PGSE NMR, are performed and the analysis of the data enables the determination of the degrees of dissociation, the diffusion coefficients of the ions and, consequently, the ionic mobility. Also, the model is applied to the characterization of conductivity of ionic liquids in bulk and in solution with different solvents. In addition, the conductivity in a specific medium of interest, a hydrogel



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polyelectrolyte, is investigated in order to compare the mobility of ions in solution and in hindered media. In particular, we studied polyelectrolytes prepared by copolymerization of vinylpyrrolidone, V, and sulfopropylmethacrylate (potassium salt), Ms. These two monomers, with very high differential reactivity in radical copolymerization, lead to a bicomponent network with a structure tending to an interpenetrated network (IPN) in the presence of a mixture of homologous crosslinkers MM and VV, as previously described.17,18 If [MM]>>[VV] (being [MM] and [VV] the concentration of each compound), the structure tends to a specific type of IPN with crosslinking gradient named double network (DN), which have exhibited an excellent performance as substrates for cell manipulation.19 True DNs have been reported to show astonishing mechanical properties in despite of their high hydration.20 In this work, the conductivity of prepared robust, flexible and superabsorbent pseudo-DN hydrogels are evaluated. The polyelectrolyte networks initially in the form of potassium salt are transformed into the corresponding lithium salt in order to study the diffusion of lithium by 7Li PGSE NMR. The effects of charge load and water content on the conductivity and ion mobility of these hydrogels are investigated in order to compare their electrical and ionic transport properties with those corresponding to simple inorganic lithium salts in water.

Experimental Materials All

reactants

and

solvents

are

commercially

available.

1-Ethyl-3-

methylimidazolium bis(trifluorosulfonyl)imide (EMITF) (Solvionic, 99.5%), lithium acetate

and

lithium

trifluoromethanesulfonate

(LiTf),

potassium

sulfopropyl

methacrylate (Ms), vinylpyrrolidone (V), ethylene glycol dimethacrylate (MM) and 1-


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hydroxyl cyclohexyl phenyl ketone (HCPK) were purchased from Sigma-Aldrich. V was distilled prior to used and stored at 4 ºC. The divinyl compound VV shown in Figure 1, which is a V derivative, was synthesized in our laboratory according to a route previously described.21 The water used was milli-Q from a water purification facility (Millipore Milli-U10).

Polyelectrolytes Hydrogel networks were prepared by conventional radical polymerization photoinitiated by UV light. Monomers V and Ms, and crosslinker MM were mixed in the proper amounts as shown in Table 1. Crosslinker VV was added at 0.1 mol% with respect to V. Water was used as solvent (concentration of V of 6 mol L-1), and HCPK as photoinitiator (0.5 wt % with respect to the total weight of monomers). Nitrogen was fluxed during 20 minutes to replace the oxygen of the solution. The solutions were poured with a syringe in polypropylene molds with a silicone spacer to attain samples of 0.5 mm. The polymerization was carried out for 40 minutes under UV radiation λ = 365 nm in a UVP ultraviolet crosslinker lamp (model CL-1000L, 230V). The samples were allowed to swell in water and washed to remove any residual monomers and sol fraction. The samples were produced and washed with deoxygenated water prepared by boiling milli-Q water. Two representative samples with different Ms content (samples 1 and 4) were selected to determine the conversion and sol content by gravimetric analysis. Fresh samples were weighted, extracted with deuterated CDCl3, vacuum dried at 60 ºC until constant weight and weighted. Measurements were carried out in duplicate. For all the samples, the 1H-NMR analysis of the soluble fraction showed that the extraction media was composed only by V monomer and polyV sol. This could be expected since Ms is



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much more reactive than V and all the methacrylic functionalities are incorporated to the network. The average gel fraction determined by gravimetry was found to be 90 and 91%. According to these results, a gel fraction of 90 % was estimated for all the samples and the remaining 10% was attributed to V and V-based residues.

Figure 1. Chemical structures of the monomers and crosslinkers used in this work.

In order to substitute K+ ions for H+ ions, swollen networks were equilibrated in H2SO4/H2O 80:20 overnight and were extensively washed until neutral pH was reached. In order to substitute H+ ions for Li+ ions, swollen membranes were immersed in a saturated solution of Li2CO3 for 24 hours. The treatment was repeated twice. After that, the residual Li+ was removed washing extensively the membranes with water.

Swelling at equilibrium The swelling at equilibrium was determined gravimetrically in triplicate, at room temperature. Dry samples were allowed to swell until equilibrium was reached and the weight of the swell and the dry sample were measured. The swelling was calculated as weight percentage according to this equation


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=

− 3

where Wh is the weight of the hydrated sample and Wd is the weight of the dry sample.

Table 1. Composition and characteristics of networks with K+ ions.a Sample

FMs

fMs

FMMMs

FMM

S

ref.

CK+, (dry

CK+, (wet

network)

network)

+

mol K m

mol K+ m-3

1-K+

0.20

0.22

0.08

1.6

0.86

1984

221

+

0.20

0.22

0.16

3.2

0.76

1920

375

+

0.17

0.19

0.08

1.3

0.87

1769

182

+

0.17

0.19

0.16

2.7

0.79

1711

290

+

5-K

0.14

0.16

0.08

1.2

0.74

1539

327

6-K+

0.10

0.11

0.08

0.8

0.79

1121

190

+

0.10

0.11

0.16

1.6

0.74

1106

235

2-K

3-K 4-K

7-K

a

-3

FMs: Ms molar fraction in feed; fMs: Ms molar fraction in the network after extraction of

soluble fraction; FMMMs: MM feed molar ratio with respect to Ms; FMM: global feed MM molar ratio; S: swelling ratio at equilibrium (water weight fraction in network); CK+: K+ concentration in the hydrogel (mol K+ m-3) considering a dry network density of 1,240 Kg m-3.

1

H, 7Li and 19F PGSE NMR measurements The 1H, 7Li and 19F PGSE NMR measurements of electrolyte aqueous solutions

of LiTf and lithium acetate and of the ionic liquid were performed using aliquots in 5 mm o.d. NMR tubes. In the case of networks, gel strips were placed also in a 5 mm o.d. NMR tube and mixed with water at the desired swelling degree. In all cases, the maximum height or length of samples in tubes was ≤ 14 mm. These measurements were performed in a Bruker Avance 400 spectrometer equipped with an 89 mm wide bore 9 ACS Paragon Plus Environment


superconductive magnet operating at 9.4 T (Larmor frequencies of 1H,

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19

F and 7Li at

400.14, 376.51 and 155.51 MHz, respectively). All data were acquired at 25 ± 0.1 °C with a Bruker diffusion probe head, Diff60, using a pulsed gradient stimulated spin echo pulse sequence.22 The time between the first two 90° rf pulses (the echo time), τ1, was 3.2 ms and the diffusion coefficients were measured varying the amplitude of the gradient pulse between 5 and 500 G cm–1. The diffusion time, ∆, and length of the gradient pulses, δ, were 50-80 and 2 ms, respectively. The repetition rate was always five times the spin–lattice relaxation time, T1, of the nuclei being observed. The total acquisition time for these experiments varied from 10 min to 20 h. The decay of the echo amplitude was monitored typically to at least 50% of its initial value, and the apparent diffusion coefficient was calculated by fitting a mono-exponential function to the decay curve. Previously, the magnetic field gradient and temperature were calibrated as described elsewhere.23

Impedance spectroscopy. The liquid electrolytes were placed in Novocontrol sample cell BDS 1307 for accurate measurements of the dielectric properties of liquids. The hydrated networks were sandwiched between two Au blocking electrodes in a closed dispositive to avoid water evaporation during the assays. The complex impedance measurements were carried out isothermally by means of a Novocontrol GmbH Concept 40 broadband dielectric spectrometer in the frequency range between 10-1 and 107 Hz, at 25 °C and voltage amplitude of 20 mV. The temperature was controlled to ± 0.1 °C with a nitrogen jet during the sweep in frequency. An electrolyte is a simple electrochemical system that can be considered equivalent to an electrical circuit constituted by a resistor and a capacitor connected in


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parallel. In this ideal case the real and imaginary parts of the impedance, Z´ and Z´´ are given by =

4 1 +

=

5 1 +

and

where C is the capacitance and ω = 2π f is the angular frequency, with f the frequency in Hz. A graphical representation in the complex plane of ‒Z´´ vs Z´ (Nyquist diagram) must give a semicircle of diameter R and center (R/2.0), enabling the determination of the direct current conductivity σDC =

1 ! 6 "

where l and A are the thickness and area of the measurement cell, respectively. However, frequently the Nyquist diagram is not well defined and it is better to use another method to determine σDC. The dielectric permittivity is a complex magnitude whose real (ε´) and imaginary part (ε´´) are related to the impedance through the equations $´ =

´´ ! 7 $& "

$´´ =

´ ! 8 $& "

and

At the same time, the real and imaginary parts of the complex conductivity are related to the permittivity by ´ = $& $´´ 9 and



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´´ = $& $´ 10 The value of σ´ increases with frequency until a plateau is attained where practically no variation of σ´ is observed. This almost constant value can be considered as equivalent to the value of σDC, though is better to extract the value of σ´ at the frequency of the maximum in dielectric loss tangent (tan φ = ε´´/ε´) that must correspond with the minimum value of Z´´ in the Nyquist diagram. All the experimental values of σDC of this work have been determined by using this criterion.

Results and Discussion The experimental results and their corresponding discussion are structured in three parts according to the type of electrolyte to facilitate their description. Thus, we start this section with the account on aqueous solutions of lithium salts; follow by that on ionic liquid solutions and lastly the hydrogel polyelectrolyte.

Lithium triflate and lithium acetate aqueous solutions The conductivities and diffusion coefficients of the aqueous solutions of lithium triflate and lithium acetate were determined according to the procedures described earlier and the results are summarized in Tables S1 and S2 (Supporting Information). The diffusion coefficients determined by PGSE NMR include the contribution of dissociated and non-dissociated species, the latter not contributing to the conductivity. Thus, the experimental NMR diffusion coefficients DLi and DA, where the sub-index A indicates the triflate or acetate group, would be described by eqs 11 and 12 +, = + 1 − ± 11

. = + 1 − ± 12


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being ± the diffusion coefficient corresponding to non-dissociated species, i.e. such as ionic pairs or higher aggregates, not contributing to σ. These equations are analogous to those indicated by several authors for the mutual diffusion coefficient in the case of electrolytes exhibiting association.24-27 In the model proposed in previous work,16 we assumed that the ratio between the diffusion coefficients of ions contributing to the conductivity is constant, γ = D- /D+, independently of the concentration and equal to the ratio between the molar conductivities of ions at infinite dilution. A more detailed analysis of the equations derived in that work shows that is not required to assume that γ is constant because, using eqs 11 and 12, it is straightforward to arrive to the following expressions

/ − 01 = 2 − 1 13

+ =

/ − 01 2 + 1 14 2−1

2 + 1

Λ= + = − 01 15 2 − 1 /

Using eq 15 and the values of the diffusion coefficients measured with NMR, and those of Λ obtained from impedance spectroscopy measurements, the values of γ at each concentration could be directly determined. A look over the results shown in tables S1 and S2 clearly shows that the values of γ for solutions of lithium triflate and lithium acetate are in good agreement with the corresponding value of γ at infinite dilution, and only at very concentrated solutions of lithium triflate differences are observed. Also, the calculation of the values of γ using the experimental results indicated in ref. 16 for electrolytes based in lithium triflate in aprotic solvents, showed a fair agreement, with similar γ values for the concentrations 13 ACS Paragon Plus Environment


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studied, supporting the hypothesis previously formulated. Once the values of γ are determined, the transport number of the Li+ (β) is directly obtained from β = 1/(γ+1). Thus, the only remaining parameter to be assessed is the degree of dissociation α, which is not possible to determine with only the magnitudes known until now. In this regard, the values of D+ and D- should be used and not those of D+α, D-α, and D±(1-α), already known. Several decades ago, Nielsen et al.28 and Guggenhein29 showed that the experimental mean diffusion coefficient for the salt (D± in our case) of sodium chloride solutions is given by

± =

2 16

+

This is correct at infinite dilution, but in Nielsen’s work this equation is applied at different concentrations, finding a good agreement between calculated and measured D± diffusion coefficients at low concentrations and significant discrepancies at high concentrations. However, these were adequately solved when the solvent effect on the measurements of D± was taken into consideration. It should be noted that, in eq 16, the value of D± is the harmonic mean of the ionic diffusion coefficients D+ and D-, something that generally applies in rate processes, such as diffusion. Then, considering that D± is given by eq 16, the values of the degree of dissociation α for all the electrolyte solutions could be estimated using the following equation

+ 1 + 2 = 17 1 − ± 22 1 −


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Figure 2 illustrates the values of α obtained from the relationship between the experimental molar conductivities, plotted versus αNMR obtained from the NernstEinstein equation using the NMR diffusion coefficients DLi and DA. It is shown that α and αNMR are practically equivalent, as it could be expected since the harmonic mean is practically equal to the arithmetic mean when γ ≅ 1 and, consequently, DLi and DA are equivalent to D+ and D-, respectively. Similar results are obtained if the geometric mean is used.

1.0 0.9 0.8 0.7 0.6

α

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


0.5 0.4 0.3 0.2 0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

αNMR

Figure 2. Plot of α resulting from the relationship between the experimental molar conductivities versus αNMR obtained from the Nernst-Einstein equation using the NMR diffusion coefficients DLi and DA in aqueous solutions of LiTf (red circles) and LiAc (black squares).

These results show that the degree of ionization of the studied salts in water, up to concentrations of 5 M, could be determined directly from the electrical measurements of the ionic conductivity and those of the diffusion coefficients corresponding to the 15 ACS Paragon Plus Environment


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species involved with multinuclear PGSE NMR. The values of α varied from 0.87 to 0.47 in the concentration range between 0.01 and 5 M. These results suggest that the assumption of a complete dissociation of ionic salts, considered as strong electrolytes in solvents of high dielectric permittivity, is not required to adequately describe their behavior, as Arrhenius originally proposed.1

Ionic Liquids The case of ionic liquids as electrolytes is of special interest due to their high ionic conductivity and excellent physico-chemical stability. Initially, we analyze the behavior of two ionic liquids whose electrical properties, diffusion coefficients and ionic mobility, in bulk, have been determined. Thus, the diffusion coefficients and the separated

ionic

([C2mim][BF4])

mobilities and

of

1-ethyl-3-methyl

1-ethyl-3-methyl

imidazolium

imidazolium

tetrafluoroborate

trifluoromethanesulfonate

([C2mim][TfO]) measured with PGSE NMR and eNMR,30 respectively, are shown in Table 2. Taking into account only the values of the diffusion coefficients and assuming that the diffusion of the ionic pair represents the harmonic mean of the diffusion coefficients of the anion and cation, the values of γ and α obtained with our model are 0.676 and 0.577 for the ionic liquid [C2mim][BF4], and 0.456 and 0.558 for [C2mim][TfO], respectively. Using these values, the calculated diffusion coefficients of the free ions D+ and D-, are shown in Table 2, column 3. After calculating the diffusion coefficients, the ionic mobility (µ+ and µ-) of the ions could be estimated with the following expression μ, =

, 3 = + 45 − 18


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and the values obtained are listed in Table 2, column 5. The calculated values of ionic mobilities for the ionic liquid [C2mim][BF4] are higher than the eNMR values reported in refs. 30 and 31, but notably smaller than those in ref. 32. In the case of [C2mim][TfO], the values obtained with the model are also higher than those published.30 In this work, Zhang and Madsen used the values of µ+ and µ- to determine the molar conductivities, Λ, with eq 2, but considering α = 1. Thus, the calculated values of Λ are practically equal to the experimental ones. However, this might not be appropriate since the concentration of charge carriers in bulk would be, most likely, lower than the nominal concentration and only at infinite dilution it may be correct.

Table 2. Diffusion coefficients and ionic mobilities of [C2mim][BF4] and [C2mim][TfO], in bulk, at 25 ºC determined from PGSE NMR and eNMR measurements (lit.) and calculated (this work).

a

a

DNMR x10-11

Dcal x10-11

m2s-1 [C2mim]+

a

µNMR x10-10

µcal x10-10

m2s-1

m2s-1V-1

m2s-1V-1

5.45

5.93

8.90

23.09

[BF4]-

4.34

4.01

11.7

15.63

[C2mim]+

4.40

5.27

6.58

20.54

[TfO]-

2.80

2.41

7.78

16.78

reference 30

Also, ionic mobilities allow the estimation of the transport numbers β for the cation of [C2mim][BF4] and [C2mim][TfO] equal to 0.596 and 0.687, respectively, which are higher than those derived from the electrophoretic mobilities: 0.432 and 0.458. Moreover, it should be taken into consideration that, according with eq 18, 17 ACS Paragon Plus Environment


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higher diffusion coefficients must correspond with higher ionic mobilities, which it does not seem to be the case with the experimental results reported.30 The proposed model could be used to analyze many other results available on diffusion coefficients of ionic liquids,33 but we believe this would not provide any additional insight to what has already been shown. Therefore, we continue exploring the electric and transport properties of ionic liquids in different solvents. Keeping this in mind, we choose an ionic liquid electrolyte 1-ethyl-3-methyl imidazolium bis(trifluoromethanesulfonylimide) (EMITF) having very low glass transition temperature (Tg = −87 ºC) and also low melting temperature (Tm = −18)33 whose electrical and transport properties will be studied in bulk and solution in solvents of high and low dielectric permittivity34 shown in Table S3 (Supporting Information). The results of the conductivity and diffusion coefficient measurements are shown in Tables S4 and S5 (Supporting Information). In Figure 3, the molar conductivities (Λ) as a function of the squared root molarity for all solvents are illustrated. It could be seen that in the solvents of high dielectric permittivity, such as ethylene carbonate and propylene carbonate, Λ, follows the usual trend observed in conventional electrolytes with higher values of Λ at low concentrations. Meanwhile, in the solvents of low polarity, a maximum is observed at concentrations of about 1 M, as a consequence of ionic association. Similar results were observed in other pair solutions such as lithium triflate or tetrabutylammonium triflate in diglyme.15 The electric conductivities and diffusion coefficients were analyzed according to the procedures described earlier for aqueous solutions of lithium triflate and lithium acetate and the experimental results are shown in Tables S4 and S5. The calculated values of γ and α and αNMR, at concentrations between 0.01M and the corresponding to the bulk ionic liquid, are shown in columns 8, 9 and 10 of those tables. 18 ACS Paragon Plus Environment

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0.005

-1

0.004

0.003

2

Λ, S m 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


0.002

0.001

0.000 0

1 1/2

c , mol

2 1/2

L

-1/2

Figure 3. Variation of the molar conductivity with the concentration for solutions of EMITF in different solvents (ethylene carbonate, black squares; propylene carbonate, green diamonds; methylene chloride, red circles; and tetrachloroethane, blue triangles).

The results show that the pure ionic liquid is partly dissociated, supporting our previous statement. In addition, it is observed that in the solvent with higher dielectric constant (ethylene carbonate), the degree of dissociation increases with dilution reaching almost complete dissociation. It should be noted that the anomalous result obtained in ethylene carbonate at the lowest concentration, 0.01 M, (see Table S4, last raw; Supporting Information) it is most likely caused by partial crystallization of the solvent taking place during the measurement.

Polyelectrolytes In energy production and storage applications, solid electrolytes are desirable to facilitate the fabrication of safer devices. However, this type of electrolytes shows a 19 ACS Paragon Plus Environment


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major reduction in the mobility of charge species. Thus, the understanding of ion mobility in polymer based electrolytes to improve conduction efficiency is of great interest. In this context, we studied the influence of structural parameters, such as the ionic load, the counterion, degree of crosslinking and swelling, on the ionic conductivity and diffusion coefficients of the species of interest. Taking this into consideration, the hydrogels listed on Table 1 were prepared and studied (0.10 < FMs < 0.20; MM degree of cross-linking of 8 or 16% molar with respect to Ms). Attempts to produce samples with higher FMs were unsuccessful due to poor mechanical properties shown. FMs = 0.1 was chosen as lower limit of ionic loading. To keep the tendency to the DN structure and the crosslinking asymmetry, which we believe is the responsible of the robustness,18 VV was kept very low (0.1 mol% respect to V) and the two MM degrees of crosslinking mentioned before were tested. This series was labeled as K+ because the free cation is the original K+ present in the commercial monomer Ms. The conductivity of the hydrated K+ networks was studied in the temperature range between 5 and 80 ºC. As shown in Figure 4, the conductivity values were in the range of 10-2 to 10-1 S m-1 at room temperature increasing up to 1 S m-1 at 80 ºC. The conductivity depends on both K+ load (in terms of FMs) and the degree of crosslinking (which modulates the swelling); the higher FMs and the lower the crosslinking degree, respectively, the higher the conductivity would be. Hydrogel 1-K+, with the highest FMs, exhibited the highest values of conductivity at swelling equilibrium and was chosen to investigate the influence of water content on conductivity. The Table S6 (Supporting Information) shows the degrees of swelling, S, studied and the corresponding conductivities are illustrated in Figure 5. An abrupt drop in conductivity is observed at the lowest degree of swelling studied, most likely due to a significant reduction of macromolecular and ionic mobilities.


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Figure 4. Variation of conductivity of the K+ hydrogel series with temperature.

Figure 5. Conductivity of the 1-K+ hydrogel with decreasing water content.

In order to expand the possible applicability of these pseudo-DNs, K+ was exchange with H+ in samples 1-K+, 6-K+ and 7-K+, being the new networks labeled as 1-H+, 6-H+ and 7-H+, respectively. The protonic membranes prepared were tested at 25 21 ACS Paragon Plus Environment


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ºC. As shown in Table S7 (Supporting Information), the new networks showed a similar water content that their parental samples and, therefore, the ion concentration was in a similar range. In Figure 6, the conductivity of the H+ networks in comparison with their parental samples is shown. As expected, once K+ is exchanged with H+ an increase of the conductivity was observed in all cases. Furthermore, the observed effect was directly correlated with higher values of FMs and lower degrees of crosslinking or, in other words, with incresed concentration of ionic charge and higher degree of ion mobility. Sample 1-H+ showed a conductivity value in the range of 1 S m-1 at room temperature.

Figure 6. Comparison of the conducting properties with the temperature, at swelling equilibrium, of K+ networks and H+ networks. In a second stage, aiming to produce Li+ membrane for lithium batteries, the cation in 1-H+ networks was exchanged with Li+. In Figure 7, the conductivity at swelling equilibrium of the three networks (1-K+, 1-H+ and 1-Li+) is shown. 1-Li+


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network exhibited lower conductity that the 1-K+ network with conductivity values in the range of 0.1 to 0.7 S m-1.

Figure 7. Comparison of the conducting properties with the temperature of different ionic networks at swelling equilibrium in water and with FMs = 0.2.

Measurements of conductivity and diffusion coefficients in the Li+ networks were performed at different degrees of swelling in water, in order to obtain the degrees of dissociation of these polyelectrolytes and compare with behaviour of the lithium salts in aqueous solutions described earlier. The results are summarized in Table S8 (Supporting Information). In this case, the measured Li diffusion coefficients correspond in effect to the Li+. The non-dissociated Li present in the network, would exhibit negligible diffusion. Therefore, the degrees of dissociation α can be calculated directly from the results of conductivity and diffusion coefficients measurements according to eq 1 and they are shown in column 9 of Table S8.



On the other hand, Figure 8 illustrates the variation of the molar conductivity of lithium with the concentration of various electrolytes in water, specifically lithium acetate, lithium triflate and lithium chloride (data from ref. 35), and the corresponding values found in the lithium hydrogel networks. It is observed a great reduction of the molar conductivity of lithium in the networks compared to that in solution. This could be attributed to the decrease of the Li+ diffusion coefficients in the hydrogels caused by a reduction of network chain mobility with the decrease of water content.

0.008

-1

0.006

0.004

2

Λ, S m 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

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0.002

0.000

0

2000

4000 c, mol m

6000

-3

Figure 8. Variation of the molar conductivity of lithium with concentration of various electrolytes in water, specifically lithium acetate (black squares), lithium triflate (green triangles) and lithium chloride35 (red circles), and the corresponding values found in the lithium hydrogel networks (blue triangles).

CONCLUSIONS The conductivity and diffusivity of different kinds of electrolytes have been investigated to assess the validity of a proposed model that separates the contribution of


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dissociated and non-dissociated species to the diffusion coefficients determined with NMR. The conductivity of aqueous solutions of several lithium salts, solutions in aprotic solvents of the ionic liquid EMITF, and polyelectrolyte hydrogels were measured with impedance spectroscopy. In addition, the diffusion coefficients of the species of interest in those samples were measured with multinuclear PGSE NMR. The analysis of the experimental results using the model shows that the degree of ionization could be determined directly from measurements of ionic conductivity and diffusion coefficients of the species involved, in a wide range of concentrations. Moreover, the model could be applied to analyze data corresponding to very different types of electrolytes. The assumption of a complete dissociation of the electrolytes, regardless of their weak or strong character, is not required to describe their conductive behavior, in agreement with Arrhenius’ theory. The model only assumes that the diffusion coefficient of non-dissociated species is given by the harmonic mean of those of the individual ions, to fully characterize the conductive behavior of electrolytes. The reduced conductivity observed in polyelectrolytes, at or near swelling equilibrium, compared to that in solutions could be attributed mainly to the hindered ionic mobility caused by the network structure.

ACKNOWLEDGEMENTS Financial support provided by the Ministerios de Ciencia e Innovación (MICINN) and de Economía y Competitividad (MINECO) of Spain through projects MAT-2010-20001 and MAT2013-42957-R, respectively, and CSIC is acknowledged.



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SUPPORTING INFORMATION Tables of results summaries

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35. Garrido, L.; Pozuelo, J.; López-González, M.; Yan, G.; Fang, J.; Riande, E. Influence of the water content on the diffusion coefficients of Li+ and water across naphthalenic based copolyimide cation-exchange membranes. J. Phys. Chem. B 2012, 116, 11754-11766.


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Table of Contents Graphic


1 Ionic Conductivity, Diffusion Coefficients and Degree of Dissociation

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