Access to Thermodynamic and Viscoelastic Properties of Poly(ionic

Letter Cite This: ACS Macro Lett. 2019, 8, 996−1001

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Access to Thermodynamic and Viscoelastic Properties of Poly(ionic liquid)s Using High-Pressure Conductivity Measurements Shinian Cheng,† Zaneta Wojnarowska,*,† Małgorzata Musiał,† Dimitri Flachard,‡ Eric Drockenmuller,‡ and Marian Paluch† †

Institute of Physics, University of Silesia, SMCEBI, 75 Pulku Piechoty 1A, 41-500 Chorzow, Poland Univ Lyon, Université Lyon 1, CNRS, Ingénierie des Matériaux Polymères, UMR 5223, F-69003 Lyon, France

‡

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S Supporting Information *

ABSTRACT: In this paper, we examine the transport properties of a 1,2,3-triazoliumbased poly(ionic liquid) (PIL) at ambient and elevated pressure up to 475 MPa. We show that the isothermal and isobaric conductivity measurements analyzed in the 3D plane give a unique possibility to estimate the thermodynamic (isothermal compressibility and thermal expansion coefficient) properties for PILs having a charge transport fully controlled by viscosity. This result, providing a direct connection between thermodynamic and dynamic properties of PILs, is of significant importance for both material scientists and practical applications.

O

point of translational ionic motions at the liquid−glass transition temperature (Tg). This clearly indicates that ions are still moving when the segmental dynamics becomes frozen below Tg.11−15 The physical understanding of these observations has been recently provided by high-pressure dielectric measurements that reveal the frustration in chain packing (free volume) and fast proton hopping as main factors controlling the charge transport in PILs.7,16,17 It should be stressed that except a few examples used for recognizing the conductivity mechanism in polyelectrolytes the properties of PILs have not been investigated under highpressure conditions so far. However, such an experimental approach might be crucial to formulating a universal description of the transport properties for ionic conductors. This is because the isobaric change of temperature affects both the kinetic energy (thermal energy) and the packing density of ions, while isothermal compression influences only the interionic distances.18 According to the literature reports, the dynamic properties (structural relaxation times, σdc, etc.) measured under isothermal and isobaric conditions and analyzed together can provide much valuable information on the thermodynamic properties of glass-forming systems. As an example, the scaling exponent γ, that brings the T−P− relaxation data into a single curve when plotted as a function of TVγ, is directly related to the Gruneisen parameter (γG), which in turn provides a link to the heat capacity ratio and the thermal expansion coefficient.19−21 The connection between dynamic properties and thermodynamic quantities can also be

ne of the most commonly explored research directions of material science in the past decade is the design of thermally and mechanically stable conductive systems for diverse electrochemical applications.1−3 Polymerized ionic liquids or poly(ionic liquid)s (PILs) that merge the unique physical properties of ionic liquids (ILs) (e.g., low vapor pressure, nonflammability, thermal and chemical stability, and broad electrochemical window...) with those of polymer materials (e.g., viscoelasticity, processability, film-forming capacities and broad structural design...) are quite promising for this purpose. Due to the potential applications of PILs as solid electrolytes in batteries, fuel cells, or other electrochemical devices,4,5 the most desired feature of these media is their high ionic conductivity (σdc) that unfortunately drops down by about 2−3 decades compared to molecular ILs. Therefore, many recent efforts have been dedicated to understanding the conductivity mechanism in single-ionconducting PILs and consequently to predict the σdc behavior under various thermodynamic conditions.6−9 It is well-known that supercooling always results in a denser and more viscous material. In the case of PILs (or any other ionic systems), lowering temperature toward the glass transition region is also accompanied by a dramatic decrease of σdc. However, the investigations of the last five years have clearly shown that the σdc(T) of PILs strongly differs from the behavior of classical ionic conductors. Namely, regardless of the broad structural diversity of PILs, their temperature dependence of σdc reveals a well-defined kink from nonArrhenius-to-Arrhenius like behavior, being a manifestation of liquid−glass transition.10,11,13 Importantly, this characteristic inflection point occurs at σdc even many decades higher than 10−15 S cm−1, which is commonly identified as the freezing © XXXX American Chemical Society

Received: May 10, 2019 Accepted: July 12, 2019

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DOI: 10.1021/acsmacrolett.9b00355 ACS Macro Lett. 2019, 8, 996−1001

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ACS Macro Letters delivered by analysis of T−P experimental points in terms of entropic models. The Avramov entropic model originally introduced to describe the viscosity of supercooled liquids in T−P thermodynamic space22 affords the determination of the thermal expansion coefficient αP = V−1(∂V∂T)P in the limit of ambient pressure without carrying out the additional measurements. Another advantage is the possibility to get insight into the “modulus of elasticity” M for PILs that in turn is related to the bulk modulus B = 1/κT and shear modulus G, describing the resistance to compression and response to shear, i.e., viscoelastic properties of PILs. In this paper, we explore the transport properties of a 1,2,3triazolium-based PIL (TPIL) that contains cations in the main chain and free bis(trifluoromethylsulfonyl)imide (TFSI) counteranions (Scheme 1).23,24 This single-ion conductor

In both these cases, the experimental data were collected during the heating. Visual inspection of dc-conductivity spectra (Figure 1a) reveals three characteristic features: (i) the plateau region where ionic conductivity becomes independent of frequency, i.e., σdc; (ii) the rise of the dc-conductivity value with increasing temperature; and (iii) the drop of σ at low frequencies due to the electrode polarization. From the frequency dependencies of ionic conductivity and viscosity, the plateau values were plotted against reciprocal temperature in Figure 2. As can be easily seen, the

Scheme 1. Chemical Structure of Studied TPIL

Figure 2. Temperature dependence of σdc (open squares), viscosity (closed circles), and segmental relaxation times τs (stars). Solid lines denote VFT fits of experimental data with the following parameters: BDS log σ0 = −0.38, D = −4.05, T0 = 213.30 K; RH: log η0 = 2.82, D = −5.01, T0 = 207.93 K; RH segmental dynamics: −log τ0 = 11.82, D = −3.73, T0 = 217.6 K. The inset panel presents the ratio of conductivity and segmental relaxation as well as conductivity and viscosity as a function of temperature. The upper inset presents the results of TMDSC measurements.

exhibits rather high ionic conductivity (i.e., σdc = 1.6 × 10−5 S cm−1 at 30 °C and under anhydrous conditions) and can be synthesized in high scale (see the experimental procedure in the SI).25,26 Dielectric measurements were performed over wide temperature and pressure ranges and were combined with rheological and calorimetric data to investigate the charge transport mechanism in the examined TPIL. This analysis revealed a strong coupling between the viscosity, segmental dynamics, and σdc that stays unchanged at high-pressure conditions which to the best of our knowledge has never been observed earlier for PILs. Additionally, we show that isothermal and isobaric conductivity data plotted in the 3D plane can be very well described by means of the Avramov entropic model, with the fitting parameters directly related to the thermodynamic quantities. In order to investigate the behavior of ionic conductivity and viscoelastic properties of TPIL at ambient pressure conditions, we performed both dielectric and rheological measurements over a wide temperature range from 223 to 373 K and from 253 to 393 K, respectively. Results from these studies are presented in Figure 1a and 1b.

experimental data follow a super-Arrhenius behavior and can be reproduced well by means of the Vogel−Fulcher− Tammann (VFT)27−29 equation log10σdc(or η) = log10σ0(or η0) +

log10e· DT0 T − T0

(1)

where log10σ0 (or log10η0) is a pre-exponential factor; D is a material constant; and T0 is known as the “ideal” glass temperature. The obtained fitting parameters are reported in the figure caption. However, at a certain temperature, the log10σdc(T−1) dependence reveals a well-defined crossover from VFT-like to Arrhenius behavior. Such a phenomenon is typical for polymerized ionic liquids,30,31 and it is identified with the liquid−glass transition. The value of Tgcross for TPIL is equal to 241.2 K, and it is consistent with the calorimetric Tg (TgDSC = 245 K at a heating rate 0.5 K min−1; see the inset to Figure 2). Moreover, the value of σdc(Tgcross) is equal to 10−14 S cm−1 that is typical for coupled ionic conductors, i.e., materials characterized by charge transport governed by structural/segmental dynamics. To verify whether or not these two parameters are indeed coupled in TPIL, we have performed additional mechanical measurements and determined the segmental relaxation times τs over a broad temperature range. In the vicinity of liquid−glass transition, τs were determined directly from the crossover of loss G″(ω) and storage G′(ω) modulus (see panel A of Figure S1). On the other hand, to estimate τs above 254 K, we have used the time−temperature superposition (TTS) rule and constructed the master curve (see panel B of Figure S1). Since TTS is

Figure 1. (a) Ambient pressure conductivity spectra measured above Tg of TPIL in the 10−1−107 Hz frequency range. (b) Viscosity as a function of frequency measured in the 253−393 K temperature range. 997

DOI: 10.1021/acsmacrolett.9b00355 ACS Macro Lett. 2019, 8, 996−1001

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ACS Macro Letters

fit of the experimental data recorded at P < Pg was achieved by employing the pressure counterpart of temperature in the VFT equation:

satisfied in studied TPIL, the τs(T) dependence was determined from the shift factor of G″(ω) and G′(ω) curves. As can be clearly seen in Figure 2, log τs(T−1) dependence fully follows the log η(T−1) behavior identified with the chain dynamics. This behavior, remarkable for polymers, can be explained by relatively low polymerization degree of studied TPIL (DPn = 36, see SI). Additionally, in contrast to PILs investigated recently7 at the crossover temperature (Tgcross), the segmental relaxation time τs of TPIL is equal to 103 s, which is usually identified with the freezing point of global dynamics at Tg. These results clearly indicate that the mobility of ions mimics both viscosity and segmental relaxation behavior in studied TPIL. To recognize to what extent these parameters are coupled we have calculated the

log10 σdc −log10 τs

and

log10 σdc −log10 η

log10 σdc = log10 σ0 +

log10 e·CP P0 − P

(2)

Similar to the temperature VFT law, the above equation also has three fitting parameters: σ0, C, and P0. However, the parameter σ0 can be experimentally determined because its value is equal to dc conductivity at ambient pressure. Thus, the number of fitting parameters in eq 2 can be reduced from three to two. Applying the strategy from the previous section, we calculated the glass transition pressure, Pg, for each isotherm. Again we benefited from the crossover phenomenon assuming that Pg = P for which log σdc(P) changes the behavior from the VFT to Arrhenius type. Note that σdc(Pg) = σdc(Tg) = 10−14 S cm−1. Since the universal feature of crossover is its isochronal character in T−P thermodynamic space, i.e., τs(Tg, Pg) = 103 s,32 one can assume that the charge transport stays coupled to segmental dynamics in TPIL also under high-pressure conditions. In this way, it was possible to determine the effect of pressure on Tg for TPIL. A useful quantity which can be used to characterize pressure sensitivity of Tg in the limit of ambient pressure is the dTg/dP|p=0.1 MPa coefficient. Its value can be calculated from the fitting parameters of the Anderson− Anderson equation (eq 3)33 which was applied for the description of the Tg(Pg) curve displayed in the inset to Figure 3.

ratios

(see the inset in Figure 2). As can be clearly seen, the ratio of conductivity to segmental dynamics (as well as conductivity to viscosity) is practically constant over a wide temperature range. Thus, at T > Tg the charge transport in TPIL is practically fully controlled by segmental dynamics, or alternatively, in the polymer matrix there is no extra free volume allowing fast motions of anions. Herein, it should be noted that the examined TPIL is the first example of fully coupled PIL. The most probable reason for such behavior lies in the very flexible and charged polymer chain combined with short methyl side groups. Molecular packing is a key factor for understanding charge transport properties. The average interionic distances can be varied in a controlled way by applying hydrostatic pressure. To investigate the effect of molecular packing on the ionic transport in TPIL, we carried out high-pressure dielectric measurements. The representative frequency-dependent conductivity spectra collected in the pressure range from 0.1 to 480 MPa at isothermal conditions (T = 283 K) are shown in Figure 3.

ij k yz Tg = k1jjj1 + 2 P zzz j k 3 z{ k

1/ k 2

; dTg /dP| p = 0.1MPa = k1/k 3

(3)

The value of dTg/dP|p=0.1 MPa determined in this way is equal to 110 K GPa−1 and lies pretty close to the dTg/dP|p=0.1 MPa value experimentally found for PILs with the flexible PDMS polymer chain (125 K GPa−1).17 Recently, a new approach was developed based on the phenomenological observation made for several polymer electrolytes that there is a linear relationship between the apparent activation energy and activation volume. Both these quantities can be easily determined by taking the derivatives of isobaric and isothermal dependences of σdc, respectively: i ∂log σdc yz zz ΔE = 2.303R jjjj z k ∂(1/T ) {

(4)

i ∂log σdc yz zzz ΔV = 2.303RT jjjj k ∂P {

(5) −1

Here, R is a gas constant with a value of 8.314 J mol K−1. The results of such analysis for TPIL are separately given in Figure 4a and 4b. Both quantities ΔE and ΔV are temperature and pressure dependent. The increase of apparent activation energy during the isobaric cooling process reflects the growth of energy barriers for segmental rearrangement which might come from an increase of molecular packing caused by the rise of density. In other words, it is expected that intermolecular energy barriers are density dependent. If so, the activation volume should also increase with compression. Such behavior is indeed observed (see Figure 4b). Interestingly, activation volume and apparent activation energy have the same trend with respect to temperature. In fact, there is a linear dependence between

Figure 3. (a) Frequency dependence of conductivity measured at 283 K and pressure ranging from 0.1 to 480 MPa. (b) Pressure dependence of σdc at five different temperatures. Solid lines denote the fits of experimental data with the VFT equation. Inset panel presents the pressure dependence of Tg for TPIL parametrized by means of the Anderson−Anderson equation (eq 3) with the following fitting parameters: k1 = 238.84 K, k2 = 3.29, k3 = 2180 MPa.

It can be noted that the value of σdc drops with increasing pressure. Thus, elevating pressure has basically the same effect on σdc as isobaric cooling. Four additional isothermal measurements were carried out at temperatures of 293, 273, 263, and 253 K. All these spectra were analyzed to determine the pressure dependence of σdc (see Figure 3). A very accurate 998

DOI: 10.1021/acsmacrolett.9b00355 ACS Macro Lett. 2019, 8, 996−1001

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ACS Macro Letters α=

2Cp

β=

2αpVm

Π (8) ZR ZR where Z is the degeneracy of the system, that is, the number of escape channels available for a moving ion; Vm is the molar volume; and αp is the volume expansion coefficient. Very recently the model has also been modified to better describe the pressure dependence of the isobaric fragility parameter of van der Waals glasses and polymer melts. As pointed out in ref 39, it requires taking into account the pressure dependence of the isobaric heat capacity. In this general case the parameter α is no more constant but changing with pressure: É ÅÄÅ P yÑÑÑ i Å α(P) = α0ÅÅÅ1 − k lnjjj1 + zzzÑÑÑ ÅÅÇ Π {ÑÑÖ (9) k ,

where α0 = 2C p /ZR and k = C /C p . 0 0 As displayed in Figure 5, the generalized Avramov model is capable of reproducing all the experimental points. The wired

Figure 4. Apparent activation energy (a) and activation volume (b) calculated for isobaric and isothermal conductivity data, respectively. The activation energy determined as presented in the inset to panel (a) plotted as a function of activation volume for TPIL is depicted in panel (c). Panel (d) presents the activation volume calculated in the limit of ambient pressure plotted as a function of temperature.

these two quantities (see Figure 4c) which can be written as follows:

ΔE = Mσ ΔV

(6) 34,35

According to Ingram et al., the slope of this line defines a new quantity, Mσ, called modulus for ionic conductivity (or “modulus of elasticity”). From a simple linear regression, we found that its value is equal to 2.04 ± 0.09 GPa. Interestingly, it has been recently demonstrated that in the normal liquid state of a given system Mσ is equal to bulk moduli (B).36 This gives us a possibility to determine the isothermal compressibility of studied TPIL. Using a simple relation B (= Mσ) = 1/ κT, we determined κT for TPIL as 0.49 GPa−1 that corresponds well to the values of isothermal compressibility of ILs at hightemperature conditions.37,38 This comparative analysis suggests that Mσ can be treated as a measure of the elastic forces operating within the polymer matrix that controls the ionic charge transport. In the previous two sections, we have analyzed isothermal and isobaric dependences of ionic conductivity separately in terms of temperature and pressure VFT equations, respectively. However, a more comprehensive approach requires the application of a new model capable to provide a description of the combined effects of T and P. This can be achieved by using the entropic model developed by Avramov to predict the effects of T and P on the viscosity of glass-forming liquids. Naturally, it can be also adapted for a description of ionic charge transport in both ILs and PILs. The main equation of the model is ÅÄÅ ÑÉ ÅÅ ij Tr yzα ij P yz β ÑÑÑÑ Å j z σdc = σdc∞ expÅÅ30j z jj1 + zz ÑÑ ÅÅ k T { k Π { ÑÑÑÖ (7) ÅÇ

Figure 5. σdc as a function of temperature and pressure. The blue surface is the fit of Avramov model to the experimental data.

surface in Figure 5 was plotted based on the following fitting parameters: log σdc∞ = −2.50 ± 0.08 S cm−1, α0 = 7.30 ± 0.18, β = 3.11 ± 0.53, k = −0.21 ± 0.04, Π = 842 ± 159 MPa, and Tr = 241.2 K. Having the analytical model for the description of temperature−pressure dependence of σdc, one can easily derive the expression for the dynamic modulus: Mσ = Π

α0 β

P = 0.1 MPa

(10)

Taking into account the values of fitting parameters of α0, β, and Π, this expression returns to 1.97 GPa which is very close to the value obtained from the analysis of the data in Figure 4c. Interestingly, eq 10 can be further transformed by using α0 and β from eq 9 to the following form:

where σdc∞ represents the conductivity at high temperatures; Tr is a reference temperature (e.g., Tg); and Π is a constant with the dimension of pressure. The parameters, α and β, can be expressed as

M= 999

Cp αpVm

(11) DOI: 10.1021/acsmacrolett.9b00355 ACS Macro Lett. 2019, 8, 996−1001

Letter

ACS Macro Letters Consequently, it affords a new important relationship between dynamic modulus and two fundamental thermodynamic quantities: isobaric heat capacity and thermal expansion coefficient. The value of Cp was determined directly from the temperature-modulated DSC (TMDSC) data (Cpliq = 1.569 J g−1 K−1) at 303 K. On the other hand, Vm at 303 K was taken as 0.717 cm3 g−1 that corresponds to the density 1.395 g cm−3. The value of αp should be equal to 12 × 10−4 K−1 to satisfy eq 11. However, the thermal expansion coefficient determined directly from ρ(T) dependence of TPIL is equal to 5.608 × 10−4 K−1 at 303 K (see SI for measurement details) and falls in the range reported for most polymers and ILs (5.5−6.5 × 10−4 K−1).40,41 Thus, the αp calculated from eq 11 is around two times higher than the experimental value. Interestingly, when both Cpliq and αp are replaced by ΔCp = Cpliq − Cpglass = 0.513 J g−1 K−1 and Δαp = αpliq − αpglass = 3.6 × 10−4 K−1, respectively, then eq 11 is satisfied. Further, it can be noted that the modulus M is related to pressure coefficient of the glass transition temperature by M =

Tg dTg / dP

■

dP

=

*E-mail: [email protected]. ORCID

Zaneta Wojnarowska: 0000-0002-7790-2999 Małgorzata Musiał: 0000-0002-1624-6617 Eric Drockenmuller: 0000-0003-0575-279X Author Contributions

The manuscript was written through the contributions of all authors. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors are deeply grateful for the financial support by the National Science Centre within the framework of the Opus15 project (grant no. DEC-2018/29/B/ST3/00889). D.F. gratefully acknowledges the financial support from the Région Rhône-Alpes Auvergne.

. Finally, we arrive at a

Tg ΔαpVm ΔCp

■

(12)

Thus, it is straightforward to conclude that the Ehrenfest equation is satisfied in the case of studied herein TPIL. This is in agreement with the data available for different glass formers that indicate the validity of the second Ehrenfest equation. Nevertheless, this is the first time when eq 12 has been verified for ionic systems. This result stimulates further investigations of ILs and their macromolecular analogues in terms of Avramov entropic model and Ehrenfest equation as well. Herein, we studied the ion transport in a special type of PIL containing main-chain 1,2,3-triazolium cations, methyl side groups, and free TFSI counteranions. A direct comparison of ion-conducting and viscoelastic properties of TPIL has clearly shown that charge transport is mainly controlled by the segmental dynamics over a broad temperature range. Additionally, these two quantities stay coupled under high-pressure conditions. This result together with quite low Tg (241.2 K) and relatively high-pressure sensitivity of ion dynamics (reflected by dTg/dP = 110 K GPa−1 coefficient) suggest strong flexibility of the 1,2,3-triazolium-based polymer backbone and limited free volume created in the polymer matrix. The direct analysis of isothermal and isobaric dc-conductivity data in terms of apparent activation energy ΔE and activation volume ΔV has shown that the ratio ΔE/ΔV, called “modulus of elasticity” (or dynamic modulus) Mσ, is directly related to the bulk modulus B, thereby providing valuable insight into mechanical properties of studied TPIL. On the other hand, the confirmed validity of the second Ehrenfest equation provides a possibility to estimate the thermal expansion coefficient from T−P conductivity behavior supported by heat capacity data and density measurements at a given temperature.

■

AUTHOR INFORMATION

Corresponding Author

well-known second Ehrenfest equation: dTg

Dielectric, rheology, and DSC experimental details together with the procedure employed for the synthesis of TPIL (PDF)

REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsmacrolett.9b00355. 1000

DOI: 10.1021/acsmacrolett.9b00355 ACS Macro Lett. 2019, 8, 996−1001

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ACS Macro Letters

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DOI: 10.1021/acsmacrolett.9b00355 ACS Macro Lett. 2019, 8, 996−1001