Effect of Chemical Structure and Salt Concentration on the Crystallization and Ionic Conductivity of Aliphatic Polyethers

polymers

Article Effect of Chemical Structure and Salt Concentration on the Crystallization and Ionic Conductivity of Aliphatic Polyethers

Jorge L. Olmedo-Martínez 1, Leire Meabe 1, Andere Basterretxea 1, David Mecerreyes 1,2 and Alejandro J. Müller 1,2,*

1 POLYMAT and Polymer Science and Technology Department, Faculty of Chemistry, University of the Basque Country UPV/EHU, Paseo Manuel de Lardizabal 3, 20018 Donostia-San Sebastián, Spain; [email protected] (J.L.O.-M.); [email protected] (L.M.); [email protected] (A.B.); [email protected] (D.M.) 2 IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain * Correspondence: [email protected]; Tel.: +34-943018191

Received: 20 February 2019; Accepted: 6 March 2019; Published: 9 March 2019

Abstract: Poly(ethylene oxide) (PEO) is the most widely used polymer in the field of solid polymer electrolytes for batteries. It is well known that the crystallinity of polymer electrolytes strongly affects the ionic conductivity and its electrochemical performance. Nowadays, alternatives to PEO are actively researched in the battery community, showing higher ionic conductivity, electrochemical window, or working temperature range. In this work, we investigated polymer electrolytes based on aliphatic polyethers with a number of methylene units ranging from 2 to 12. Thus, the effect of the lithium bis(trifluoromethanesulfone) imide (LiTFSI) concentration on the crystallization behavior of the new aliphatic polyethers and their ionic conductivity was investigated. In all the cases, the degree of crystallinity and the overall crystallization rate of the polymers decreased drastically with 30 wt % LiTFSI addition. The salt acted as a low molecular diluent to the polyethers according to the expectation of the Flory–Huggins theory for polymer–diluent mixtures. By fitting our results to this theory, the value of the interaction energy density (B) between the polyether and the LiTFSI was calculated, and we show that the value of B must be small to obtain high ionic conductivity electrolytes.

Keywords: polyethers; crystallization; ionic conductivity; Flory–Huggins theory

1. Introduction Dry solid polymer electrolytes (SPEs) have attracted great attention as safe alternatives to liquid electrolytes in different energy storage technologies, such as lithium batteries for electric vehicles [1–3]. SPEs are formed by complexing an ionic salt within a polymer matrix. It is generally accepted that the ionic conductivity occurs in the amorphous part of the polymers, and the ion dynamics are governed by the segmental motion of the amorphous phases in polymers [4]. Several polymers and salts have been evaluated as SPEs, such as poly(ethylene oxide) (PEO), poly(vinyl alcohol) (PVA), poly(methyl methacrylate) (PMMA), poly(ε-caprolactone) (PCL), polycarbonates (PC), chitosan (CS), poly(vinylpyrrolidone) (PVP), poly(vinyl chloride) (PVC), poly(vinylidene ﬂuoride) (PVDF), and poly(ionic liquid)s [5,6], among other polymers. Different lithium salts have been employed, such as LiClO4, LiBF4, LiPF6, LiFSI [7], and lithium bis(triﬂuoromethanesulfone) imide (LiTFSI). In particular, LiTFSI has been widely employed as its low lattice energy favors salt dissolution and dissociation, leading to enhanced ionic conductivity [8].

Polymers 2019, 11, 452; doi:10.3390/polym11030452 www.mdpi.com/journal/polymers Polymers 2019, 11, 452 2 of 13

Among all the polymer matrices, PEO is the most studied polymer electrolyte in lithium batteries. Due to its polarity, lithium salts can be easily dissolved in PEO, a fact that promotes ion mobility [9–11]. The PEO/LiTFSI system has been widely studied because of the high dissociation and plasticizing abilities of LiTFSI that leads to better ionic conductivities, as compared to other salts. However, the low ionic conductivity obtained at low temperatures, the low lithium transference number, and the resulting high interfacial resistance are common problems for this electrolyte to be applied in lithium batteries. In these polymer electrolytes, the salt plays two roles; the introduction of ionic charge carriers and the suppression of crystallization of the PEO. Thus, Marzantowicz et al. studied the crystallization of PEO/LiTFSI by polarized optical microscopy and ionic conductivity simultaneously, and they found that the decrease of conductivity during crystallization is related to the reduction of amorphous conductivity pathways by growing spherulites [12]. An in-depth study of crystallization behavior of PEO helps in the understanding of the electrochemical properties of SPEs [13]. Generally, crystallization limits ionic conductivity. Consequently, different strategies have been developed to limit the crystallization of PEO and improve the ionic conductivity in SPEs. Some of the strategies employed in this direction are synthesizing block and random copolymers [14,15], cross-linked polymer electrolytes [16], or adding nano-particles [17]. Furthermore, the crystallization kinetics of polymer electrolytes has a direct effect on the structure and properties of the SPEs. Sim et al. studied the effect of molecular mass of PEO and LiClO4 content on the isothermal crystallization of PEO [18]. Their study reports a very large decrease in the isothermal crystallization rate with salt addition. In addition, they observed that the effect is more pronounced as the molecular weight of PEO increased. Additionally, Zhang et al. investigated the crystallization behavior of PCL/LiClO4, and the results indicated that Li salts affected the crystallization behavior of PCL without changing its crystalline structure [19]. Very recently, we have reported a new versatile synthetic pathway to a variety of aliphatic polyethers by organocatalyzed bulk self-condensation of aliphatic diols [20]. This prompted us to investigate the effect of the chemical structure of the aliphatic polyethers and the salt concentration in the crystallinity of the polymer electrolytes. In this work, we prepared solid polymer electrolytes (SPEs) composed of aliphatic polyethers, with different methylene numbers in their repeating units (between 2 and 12) and several LiTFSI concentrations (10, 30, 50, and 80 wt %). The objective was to study the effect of the chemical structure of the different polyethers and LiTFSI salt concentrations on the crystallization kinetics and ionic conductivity of polyethers/LiTFSI SPEs.

2. Materials and Methods

2.1. Materials

−1 Poly(ethylene oxide) (PEO) (MW 2000 g mol ) and polytetrahydrofuran P(THF) (Mw 2000 g mol−1) were purchased from Sigma Aldrich (Madrid, Spain). Chloroform (99%) was supplied by Scharlau (Barcelona, Spain) and acetone (99.5 %) by Acros Organics (Madrid, Spain). Finally, the lithium bis(triﬂuoromethane) sulfonimide (LiTFSI) (99.9%) salt was purchased from Solvionic (Toulouse, France).

2.2. Synthesis of the Linear Polyethers The aliphatic polyethers were synthesized following the methodology described by Basterretxea et al. [20]. Direct polycondensation of diols containing 6, 8, 10, and 12 methylene units was performed in solvent free conditions. The reaction was catalyzed by protic ionic liquids previously prepared by mixing methanesulfonic acid (MSA) and 1,5,7-triazabicyclo[4.4.0]dec-5-ene (TBD) in a 3:1 molar ratio. The polymers were named using the following nomenclature: PEO = P1, Poly(THF) = P2, and the synthesized polymers with different numbers of methylene groups in their repeat units are poly(oxyhexamethylene) (P3) > poly(oxyoctomethylene) (P4) > poly(oxydecamethylene) (P5) > poly(oxydodecamethylene) (P6), as shown in Figure1. Polymers 2019, 11, 452 3 of 13 Polymers 2019, 11, x FOR PEER REVIEW 3 of 13

Figure 1. Chemical structure of the different polyethers employed in this work. Figure 1. Chemical structure of the different polyethers employed in this work. 2.3. Elaboration of SPE Solid Polymer Electrolytes 2.3. Elaboration of SPE Solid Polymer Electrolytes SPEs were prepared by the solvent casting method. Polyethers and lithium salt were dissolved in a chloroform/acetoneSPEs were prepared (90/10 by thev/ vsolvent%) mixture. casting The method. solutions Polyethers were directly and lithium casted ontosalt were a silicon dissolved mold. inFirst, a chloroform/acetone the membranes were (90/10 dried v/v at%) ambient mixture. conditions The solutions and, later,were thedirectly total evaporationcasted onto a of silicon the solvents mold. First,was completed the membranes applying were high dried vacuum at ambient at 90 conditions◦C during 24and, h. later, The SPEs the total were evaporation transferred intoof the a solvents nitrogen wasfilled completed glovebox toapplying assemble high the vacuum cell. In theat 90 first °C part,during SPEs 24 h. containing The SPEs 30were wt %transferred of LiTFSI into were a preparednitrogen filled(0.15 gglovebox of polymer to assemble and 0.064 the g of cell. salt In in the 3 mLfirst of part, chloroform). SPEs containing Later, polymers 30 wt % of P3 LiTFSI and P5 were were prepared selected (0.15to prepare g of polymer SPEs with and different 0.064 g of concentrations salt in 3 mL of of chloroform). LiTFSI: 10, 30, Later, 50, 80,polymers and 90 P3 wt and % LiTFSI. P5 were selected to prepare SPEs with different concentrations of LiTFSI: 10, 30, 50, 80, and 90 wt % LiTFSI. 3. Characterization Methods 3. Characterization Methods The electrolytes were characterized by differential scanning calorimetry (DSC). The experiments wereThe performed electrolytes in a were Perkin characterized Elmer 8500 by DSC different equippedial scanning with an calorimetry Intracooler (DSC). III and The calibrated experiments with wereindium performed and tin standards. in a Perkin For Elmer the non-isothermal 8500 DSC equippe scans,d thewith heating an Intracooler rate was III 20 and◦C min calibrated−1 in a rangewith indiumof −60 toand 150 tin◦C. standards. Samples betweenFor the non-isotherm 3 and 5 mg wereal scans, used. the Measurements heating rate werewas 20 performed °C min−1 byin a placing range ofthe −60 samples to 150 in°C. sealed Samples aluminum between pans. 3 and The 5 mg samples were used. were firstMeasurements heated with were a scan performed rate of 20 by◦C placing min−1, thefrom samples 25 to 150 in ◦sealedC and aluminum kept for 3 minpans. at The 150 samples◦C to erase were thermal first heated history, with then a scan cooling rate and of 20 subsequent °C min−1, fromheating 25 scansto 150were °C and recorded kept for at 3 20 min◦C at min 150−1 °C. to erase thermal history, then cooling and subsequent heatingIonic scans conductivities were recorded were at 20 measured °C min−1. by electrochemical impedance spectroscopy (EIS) in an AutolabIonic 302N conductivities potentiostat were galvanostat measured (Metrohm by electr AG,ochemical Herisau, impedance Switzerland) spectroscopy with the temperature(EIS) in an Autolabcontrolled 302N by a potentiostat Microcell HC galvanostat station. The (Metrohm SPE was sandwichedAG, Herisau, between Switzerland) two stainless with the steel temperature electrodes controlled(surface area by a = Microcell 0.5 cm2). HC The station. plots wereThe SPE obtained was sandwiched applying abetween 10 mV perturbationtwo stainless steel to open electrodes circuit (surfacepotential area in the = frequency0.5 cm2). The range plots of 100 were kHz obtained to 1 Hz. applying a 10 mV perturbation to open circuit potentialPrior in to the isothermal frequency crystallization range of 100 analysis,kHz to 1 theHz. isothermal Tc range employed for each electrolyte was determinedPrior to isothermal by the procedure crystallization recommended analysis, the by isothermal Lorenzo et T al.c range [21]. Thisemployed procedure for each was electrolyte employed wasin order determined to avoid by the the crystallizationprocedure recommended during the by cooling Lorenzo step. et al. Once [21]. theThis starting procedure minimum was employedTc was indetermined, order to avoid the samples the crystallization were subjected during to thethe followingcooling step. successive Once the stages: starting (i)heating minimum from Tc 25was to determined,100 ◦C at 20 ◦theC min samples−1; (ii) were isothermal subjected holding to the atfollowing 100 ◦C during successive 3 minutes; stages: (iii) (i) heating cooling from to the 25 selected to 100 ◦ −11 T°Cc atat 6020 °CC min ; ;(ii) (iv) isothermal isothermal holding holding at at100T c°Cuntil during the crystallization3 minutes; (iii) processcooling wasto the saturated, selected T and;c at −1 ◦ ◦ −1 60(v) °C heating min from; (iv) the isothermal selected Tholdingc to 100 atC T atc 20untilC the min crystallizationin order to register process the was melting saturated, behavior and; after (v) heatingthe isothermal from the measurement. selected Tc to 100 °C at 20 °C min−1 in order to register the melting behavior after the isothermal measurement. 4. Results and Discussion 4. Results and Discussion 4.1. Non-Isothermal Crystallization of Aliphatic Polyethers in the Presence of LiTFSI 4.1. Non-IsothermalAs mentioned Crystallization before, poly(ethylene of Aliphatic oxide) Polyethers (PEO) in isthe widely Presence explored of LiTFSI in the area of SPEs for lithiumAs batteriesmentioned [7 ].before, Adequate poly(ethylene coordination oxide) between (PEO) different is widely salts explored and PEO in has the been area investigatedof SPEs for lithium batteries [7]. Adequate coordination between different salts and PEO has been investigated for many years [22,23]. The crystallinity of PEO plays an important role, as it has been demonstrated

Polymers 2019, 11, 452 4 of 13 Polymers 2019, 11, x FOR PEER REVIEW 4 of 13 forthat many it can years hinder [22, 23the]. ionic The crystallinity conductivity. of Neverthele PEO playsss, an there important are no role, reports as it hason the been ionic demonstrated conductivity thatand it the can effect hinder of the crystallinity ionic conductivity. on other aliphatic Nevertheless, polyethers there arewith no higher reports amounts on the ionicof methylene conductivity units. andFor the this effect reason, of crystallinity we first examined on other the aliphatic thermal polyethersproperties withof pure higher polyethers amounts and of their methylene mixtures units. with For30 thiswt % reason, LiTFSI we by ﬁrstDSC. examined In total, six the different thermal po propertieslyethers have of pure been polyethers compared: and commercially their mixtures available with 30PEO wt % (P1)LiTFSI with by two DSC. methylene In total, sixunits, different poly(tetrahydr polyethersofurane) have been PTHF compared: (P2) with commercially four methylene available units, PEOand (P1) the withsynthesized two methylene aliphatic units, polyethers poly(tetrahydrofurane) with 6, 8, 10, and PTHF 12 methylene (P2) with fourunits, methylene respectively units, (labeled and theP3, synthesized P4, P5, P6). aliphatic All the studied polyethers polymers with 6, have 8, 10, a and similar 12 methylene number average units, respectively molar mass (labeled of around P3, 2,000 P4, P5,g P6).mol-1 All. the studied polymers have a similar number average molar mass of around 2000 g mol−1. AsAs a a reference,reference, FigureFigure2 a2a showsshows thethe coolingcooling scans for for the the neat neat aliphatic aliphatic polyethers. polyethers. The Thecrystallization crystallization temperature temperature generally generally increases increases betw betweeneen 10 10 and 65 ◦°CC asas thethe number number of of methylene methylene groupsgroups in in the the polyethers polyethers repeating repeating units units increases. increases. The The only only exception exception being being the P1 the (PEO) P1 (PEO) sample; sample; this samplethis sample also shows also ashows bimodal a bimodal distribution distribution of crystallization of crystallization temperatures temperatures whose origin whose is unknown origin is asunknown it would meritas it would further merit studies further outside studies the scopeoutside of the presentscope of work. the present As the work. number As ofthe methylene number of unitsmethylene increases, units the increases, polyethers the start polyethers to behave start in ato similar behave way in a tosimilar polyethylene way to polyethylene showing a higher showingTm, a ashigher the effect Tm, ofas thethe polareffect oxygenof the polar atom oxygen is progressively atom is progressively diluted by the diluted aliphatic by chain.the aliphatic chain.

a) b) P6 P6 30wt% LiTFSI P5 P5 30wt% LiTFSI

P4 P4 30wt% LiTFSI

P3 P3 30wt% LiTFSI

Heat flow Endo Up flow Endo Heat P2

Heat flow Endo Up Endo flow Heat P2 30wt% LiTFSI -1

-1 P1 30wt% LiTFSI P1 5 g W 5 W g W 5 0 20406080100 0 20406080100 Temperature (ºC) Temperature (ºC)

c) 90

Polyethers, T 60 m Temperature (ºC) Temperature Polyethers + 30 wt% LiTFSI, Tm 0 Polyethers, Tm 50 0 Polyethers + 30 wt% LiTFSI, Tm

6789101112 Number of methylene units

Figure 2. (a) Differential scanning calorimetry (DSC) cooling scans of neat aliphatic polyethers, (b) DSC coolingFigure scans 2. (a) ofDifferential polymer electrolytes scanning calorimetry composed (DSC) of aliphatic cooling polyethers scans of neat including aliphatic 30 wtpolyethers, % LiTFSI, (b) (c)DSC experimental cooling scans melting of polymer peak valueselectrolytes (Tm) composed (determined of aliphatic during the polyethers second DSCincluding heating 30 wt runs) % LiTFSI, and 0 equilibrium(c) experimental melting melting point values peak values (Tm ) determined (Tm) (determined by the Hoffman–Weeksduring the second extrapolation DSC heating procedure runs) and

(seeequilibrium Supplementary melting Information) point values after (Tm isothermal0) determined crystallization. by the Hoffman–Weeks extrapolation procedure (see Supplementary Information) after isothermal crystallization. Additionally, Figure2b shows the crystallization temperature of the polyether SPEs with 30 wt % LiTFSI.Additionally, In all cases, homogenous Figure 2b shows SPEs werethe crystallizatio obtained, exceptn temperature for the SPE of based the polyether on P6, as LiTFSI SPEs with has poor 30 wt solubility% LiTFSI. in P6.In all Figure cases,2b homogenous shows that P1 SPEs and P2were with obtained, 30% LiTFSI except are for completely the SPE amorphousbased on P6, materials. as LiTFSI has poor solubility in P6. Figure 2b shows that P1 and P2 with 30% LiTFSI are completely amorphous materials. However, in the case of P3, P4, P5, and P6, the crystallization temperature decreases as

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Polymers 2019, 11, x FOR PEER REVIEW 5 of 13 However, in the case of P3, P4, P5, and P6, the crystallization temperature decreases as compared with thecompared neat polyethers, with the indicating neat polyethers, that LiTFSI slowsindicating down thethat non-isothermal LiTFSI slows crystallization down the non-isothermal kinetics from −1 thecrystallization melt at 20 ◦C kinetics min−1. from the melt at 20 °C min . FigureFigure2c 2c represents represents the the change change in in the the melting melting temperature temperature of of the the neat neat polyethers polyethers and and the the polyetherspolyethers with with 30 30 wt wt % % of of LiTFSI. LiTFSI. As As expected, expected, the the melting melting temperature temperature increases increases with with the the number number ofof methylene methylene units units and and for for anyany givengiven polyether,polyether, it de decreasescreases with with salt salt addition addition.. The The depression depression ofof the themelting melting temperature temperature with with the the addition addition of LiTFSI of LiTFSI could could be bedue due to a to di alution dilution effect effect of the of thesalt. salt. This Thispossibility possibility is examined is examined in indetail detail below below by by varyin varyingg the the salt concentrationconcentration inin selectedselected samples samples and and applyingapplying the the Flory–Huggins Flory–Huggins theory. theory. Figure Figure2c 2c also also shows shows how how the the values values of of the the equilibrium equilibrium melting melting pointpoint change change as as a functiona function of of the the number number of of methylene methylene groups groups in in the the repeating repeating units units for for synthesized synthesized polyethers.polyethers. These These values values were were obtained obtained using using the the Hoffman–Weeks Hoffman–Weeks extrapolation extrapolation for for isothermally isothermally crystallized samples, as shown in the Supplementary Information. The T0m0 values also follow the crystallized samples, as shown in the Supplementary Information. The Tm values also follow the samesame trend trend with with the the number number of methylene of methylene units, units, as the apparentas the apparent or experimentally or experimentally determined determined melting points,melting as points, expected. as expected. In Figure 2Inc, Figure the data 2c, for the P1 data and for P2 P1 are and not P2 reported, are not reported, as the Hoffman–Weeks as the Hoffman– extrapolationWeeks extrapolation yielded unsatisfactory yielded unsatisfactory data, a fact data, that a mayfact that be due may to be the due lower to the molecular lower molecular weight values weight forvalues these for samples. these samples. GivenGiven the the results results obtained obtained above, above, samplessamples P3 and P5 were were chosen chosen in in order order to to study study in in detail detail the effect of salt concentration on ionic conductivity and crystallization. P3 has the lowest Tm and Tc the effect of salt concentration on ionic conductivity and crystallization. P3 has the lowest Tm and values while P5 has one of the highest Tm and Tc values, from the series of long chain polyethers Tc values while P5 has one of the highest Tm and Tc values, from the series of long chain polyethers synthesized in this work. We need to remark that the mixture of P6 and LiTFSI was not homogeneous, synthesized in this work. We need to remark that the mixture of P6 and LiTFSI was not homogeneous, thus P6 was not chosen for further analysis. thus P6 was not chosen for further analysis. P3 and P5 were evaluated with different salt concentrations: 10, 30, 50, and 80 wt % LiTFSI. The P3 and P5 were evaluated with different salt concentrations: 10, 30, 50, and 80 wt % LiTFSI. general trends of crystallization temperature of either polyether were to decrease gradually with the The general trends of crystallization temperature of either polyether were to decrease gradually with addition of salt, as shown in Figure 3. This trend can be attributed to a dilution effect of the salt. In the addition of salt, as shown in Figure3. This trend can be attributed to a dilution effect of the salt. other words, the salt acts as a solvent that depresses both the crystallization and melting temperature In other words, the salt acts as a solvent that depresses both the crystallization and melting temperature of the polyether. In addition, P3 was completely amorphous with 50 wt % or more LiTFSI, whereas of the polyether. In addition, P3 was completely amorphous with 50 wt % or more LiTFSI, whereas in in the case of P5, the SPE-P% was rendered amorphous only when 80 wt % LiTFSI was added. the case of P5, the SPE-P% was rendered amorphous only when 80 wt % LiTFSI was added.

a) b) P3 80wt% LiTFSI P5 80wt% LiTFSI

P3 50wt% LiTFSI P5 50wt% LiTFSI P3 30wt% LiTFSI P5 30wt% LiTFSI

P3 10wt% LiTFSI P5 10wt% LiTFSI

P3 P5 Heat flow Endo Up Heating flow Endo Up -1 -1 2 W g W 2 2 W g 0 20406080100 0 20406080100 Temperature (ºC) Temperature (ºC)

Figure 3. DSC cooling scans of neat P3 and P5 polyethers and their mixtures with different LiTFSI salt concentrationsFigure 3. DSC (solid cooling polymer scans of electrolytes: neat P3 and SPEs): P5 polyethers (a) P3, (b and) P5. their mixtures with different LiTFSI salt concentrations (solid polymer electrolytes: SPEs): (a) P3, (b) P5. 4.2. Ionic Conductivity of Aliphatic Polyethers in the Presence of LiTFSI 4.2.The Ionic ionic Conductivity conductivity of Aliphatic of these Polyethers solid polymer in the Presence electrolytes of LiTFSI (SPEs) was studied by impedance spectroscopy.The ionic The conductivity ionic conductivity of these of polymersolid polymer electrolytes electrolytes with different (SPEs) saltwas contents studied was by evaluated.impedance First,spectroscopy. the ionic conductivityThe ionic conductivity of all polyethers of polymer with 30% electrolytes LiTFSI was with analyzed different and salt the contents results arewas presentedevaluated. in First, Figure the4. ionic conductivity of all polyethers with 30% LiTFSI was analyzed and the results areFigure presented4a shows in Figurea decrease 4. in ionic conductivity with the increase of the number of methylene groupsFigure along 4a the shows repeating a decrease units ofin theionic polyethers conductivity employed. with the P1increase and P2 of provide the number the highest of methylene ionic mobilitygroups asalong they the were repeating amorphous. units Theof the amorphous polyethers nature employed. of these P1 materialsand P2 provide can be the deduced highest from ionic mobility as they were amorphous. The amorphous nature of these materials can be deduced from

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Polymers 2019, 11, x FOR PEER REVIEW 6 of 13 their monotonic behavior in the Arrhenius representation plotted in Figure4, and corroborated by DSCtheir analysis,monotonic as behavior shown in in Figure the Arrhenius2b. representation plotted in Figure 4, and corroborated by DSC analysis, as shown in Figure 2b. Temperature (ºC) 100 80 60 40 20 a) 10-3 10-3 b) 2 )

) 10 ) -1 -1 -1 10-4 S cm ( 10-4 10-5

10-6

-5 -7 10 10 P1 30% LiTFSI P2 30% LiTFSI -8 P3 30% LiTFSI 10 P4 30% LiTFSI Ionic conductivity (S cm (S conductivity Ionic Ionic Conductivity Activation Energy (E ) P5 30% LiTFSI a Activation energy (KJ mol P6 30% LiTFSI Ionic conductivity at 90 ºC 10-9 10-6 101 2.6 2.8 3.0 3.2 3.4 246810 1000/T (K-1) Number of methylene units

Figure 4. (a) Ionic conductivity of the polyethers with 30 wt % LiTFSI. (b) Ionic conductivity of the Figure 4. (a) Ionic conductivity of the◦ polyethers with 30 wt % LiTFSI. (b) Ionic conductivity of the polyethers with 30 wt % LiTFSI at 90 C and activation energy (Ea) calculated in the molten state for polyethers with 30 wt % LiTFSI at 90 °C and activation energy (Ea) calculated in the molten state for the SPEs. the SPEs. Figure4a also shows how the ionic conductivity of P3, P4, P5, and P6 dramatically decreases as Figure 4a also shows how the ionic conductivity of P3, P4, P5, and P6 dramatically decreases as soon as these polyethers crystallize below 70 ◦C, as also shown in Figure2b [ 24]. These data, where soon as these polyethers crystallize below 70 °C, as also shown in Figure 2b [24]. These data, where SPE-P1 provides the highest ionic conductivity, reveal that PEO is the best candidate, from the series SPE-P1 provides the highest ionic conductivity, reveal that PEO is the best candidate, from the series of polyethers examined here, for hosting LiTFSI (ionic conductivity of 5·× 10−4 S cm−1 at 70 ◦C of polyethers examined here, for hosting LiTFSI (ionic conductivity of 5·× 10−4 S cm−1 at 70 °C and 4.8 and 4.8 × 10−5 S cm−1 at room temperature). This high ionic conductivity can be explained by the × 10−5 S cm−1 at room temperature). This high ionic conductivity can be explained by the favorable favorable helical wrapping of Li ions on the polyether chain, when the ether oxygens are separated by helical wrapping of Li ions on the polyether chain, when the ether oxygens are separated by exactly exactly two carbon atoms [6]. This favorable coordination shows the highest ionic conductivity of the two carbon atoms [6]. This favorable coordination shows the highest ionic conductivity of the entire entire polyether family. polyether family. It should be noted that the behavior of SPE-P6 in Figure4a was out of the general trend (i.e., It should be noted that the behavior of SPE-P6 in Figure 4a was out of the general trend (i.e., the the trend of decreasing conductivity as the number of methylene groups in the polyether repeating trend of decreasing conductivity as the number of methylene groups in the polyether repeating unit unit increases), due to its compromised solubility in the mixture of solvents and LiTFSI. Such poor increases), due to its compromised solubility in the mixture of solvents and LiTFSI. Such poor solubility affects the homogeneity of the resulting SPE-P6. solubility affects the homogeneity of the resulting SPE-P6. Figure4b reports the ionic conductivity and the activation energies ( Ea) of the polyethers (except Figure 4b reports the ionic conductivity and the activation energies (Ea) of the polyethers (except P6) at 90 ◦C (a temperature at which all samples are in the melt) in the linear region (only molten state P6) at 90 °C (a temperature at which all samples are in the melt) in the linear region (only molten state data were employed); these values were calculated using the Arrhenius Equation [25]: data were employed); these values were calculated using the Arrhenius Equation [25]: −Ea σ = σ exp( −𝐸) (1) 𝜎=𝜎0 exp(RT ) (1) 𝑅𝑇 where σ is the ionic conductivity, σ0 is the pre- exponential factor, Ea is the activation energy, R the where σ is the ionic conductivity, σ0 is the pre- exponential factor, Ea is the activation energy, R the universal gas constant, and T the absolute temperature. universal gas constant, and T the absolute temperature. For P1, P2, and P3, the activation energies obtained (Ea) were of the same order of magnitude, but For P1, P2, and P3, the activation energies obtained (Ea) were of the same order of magnitude, for P4 and P6 the activation energy signiﬁcantly increased. In addition, a large decrease in conductivity but for P4 and P6 the activation energy significantly increased. In addition, a large decrease in with respect to the number of methylene groups in the repeating units of the polyethers was observed conductivity with respect to the number of methylene groups in the repeating units of the polyethers as expected. As a result, the ionic conductivity decreases with increasing Ea. The activation energy was observed as expected. As a result, the ionic conductivity decreases with increasing Ea. The values found in this work are similar to those reported in the literature [5]. activation energy values found in this work are similar to those reported in the literature [5]. Among all SPEs, SPE-P3 and SPE-P5 were selected to study the effect of salt concentration (10, Among all SPEs, SPE-P3 and SPE-P5 were selected to study the effect of salt concentration (10, 30, 50, 80 wt % of LiTFSI) on the ionic conductivity, and the results are shown in Figure5. The ionic 30, 50, 80 wt % of LiTFSI) on the ionic conductivity, and the results are shown in Figure 5. The ionic conductivity of SPE-P3 increased with the increase of salt concentration from 10 to 50 wt %, whereas conductivity of SPE-P3 increased with the increase of salt concentration from 10 to 50 wt %, whereas the crystallinity decreased, as shown in Figure3a. The optimum ionic conductivity value at room the crystallinity decreased, as shown in Figure 3a. The optimum ionic conductivity value at room temperature was 2.05·10−5 S cm−1, with 50 wt % LiTFSI. At higher salt concentrations the ionic temperature was 2.05·10−5 S cm−1, with 50 wt % LiTFSI. At higher salt concentrations the ionic conductivity of SPE-P3 decreased. In P5, the increase of ionic conductivity with the amount of salt is more evident; this value increased from 1.61·10−9 S cm−1 with 10 wt % LiTFSI to 8.8·10−6 S cm−1 with more evident; this value increased from 1.61·10−9 S cm−1 with 10 wt % LiTFSI to 8.8·10−6 S cm−1 with 80 wt % LiTFSI (at room temperature), and then with 90 wt % the conductivity dropped two orders of magnitude. In both cases, the conductivity was lower than with PEO with 30 wt % LiTFSI.

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80 wt % LiTFSI (at room temperature), and then with 90 wt % the conductivity dropped two orders of magnitude.Polymers 2019 In, 11 both, x FOR cases, PEER the REVIEW conductivity was lower than with PEO with 30 wt % LiTFSI. 7 of 13

a) Temperature (ºC) Temperature (ºC) 100 80 60 40 20 b) 100 80 60 40 20 10-3 10-3 P3 10wt% LiTFSI P5 10wt% LiTFSI P5 30wt% LiTFSI ) -4 P3 30wt% LiTFSI ) -4 -1 10 -1 10 P5 50wt% LiTFSI P3 50wt% LiTFSI P5 80wt% LiTFSI P3 80wt% LiTFSI P5 90wt% LiTFSI

S cm -5 -5 ( 10 10

10-6 10-6

10-7 10-7

10-8 10-8 Ionic ConductivitycmIonic (S Ionic Conductivity 10-9 10-9 2.6 2.8 3.0 3.2 3.4 2.6 2.8 3.0 3.2 3.4 1000/T (K-1) 1000/T (K-1)

Figure 5. Ionic conductivity of SPE-P3 (a) and SPE-P5 (b) with different amounts of LiTFSI. Figure 5. Ionic conductivity of SPE-P3 (a) and SPE-P5 (b) with different amounts of LiTFSI. The degree of crystallinity (XC) of the polyether components was calculated for the two families of SPEs,The using degree the following of crystallinity Equation: (XC) of the polyether components was calculated for the two families of SPEs, using the following Equation: ∆H X = m ∗ C ∆𝐻0 100 (2) f ∆Hm 𝑋 = ∗ 100 (2) 𝑓 ∆𝐻 0 where ∆Hm is the equilibrium melting enthalpy for the 100% crystalline polyether, ∆Hm is the where ΔHm0 is the equilibrium melting enthalpy for the 100% crystalline polyether, ΔHm is the experimental melting enthalpy of the sample, and f is the weight fraction of the polymer in the sample. experimental melting0 enthalpy of− 1the sample, and 0f is the weight−1 fraction of the polymer in the The values of ∆Hm = 244.7 J g for P3 and ∆Hm = 258.3 J g for P5 were employed. These sample. 0 values were obtained by the Flory–Huggins theory, where ∆Hm is denoted as ∆Hu (as explained The values of ΔHm0 = 244.7 J g−1 for P3 and ΔHm0 = 258.3 J g−1 for P5 were employed. These values below, in Section 4.4). Table1 reports the crystallinity values obtained, and it was observed that the were obtained by the Flory–Huggins theory, where ΔHm0 is denoted as ΔHu (as explained below, in degree of crystallinity decreased as LiTFSI content increased, as was expected if the salt is considered a Section 4.4). Table 1 reports the crystallinity values obtained, and it was observed that the degree of diluent for the polyethers. This crystallinity reduction is one of the reasons why SPEs exhibit a larger crystallinity decreased as LiTFSI content increased, as was expected if the salt is considered a diluent ionic conductivity as the content of LiTFSI increases. for the polyethers. This crystallinity reduction is one of the reasons why SPEs exhibit a larger ionic conductivity as the content of LiTFSI increases. Table 1. ∆Hm and degree of crystallinity of SPE-P3 and SPE-P5 with different amounts of LiTFSI.

−1 Table 1. ΔHm and degreeSample of crystallinity of∆H SPE-P3m (J g and) SPE-P5Crystallinity with different (%) amounts of LiTFSI. P1 149 69 Sample ΔHm (J g−1) Crystallinity (%) P2 85 36 P3 P1 127149 5169 P3 10 wt % LiTFSIP2 9985 4536 P3 30 wt % LiTFSIP3 49127 2951 P3 50P3 wt 10 % wt LiTFSI % LiTFSI 099 45 0 P4 145 56 P3 30P5 wt % LiTFSI 13549 5229 P5 10P3 wt 50 % wt LiTFSI % LiTFSI 1190 510 P5 30 wt % LiTFSIP4 80145 4456 P5 50 wt % LiTFSIP5 47135 3652 P5 80 wt % LiTFSI 0 0 P5 10 wt % LiTFSI 119 51 P6 142 53 P5 30 wt % LiTFSI 80 44 P5 50 wt % LiTFSI 47 36 P5 80 wt % LiTFSI 0 0 P6 142 53

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4.3. Isothermal Crystallization of Aliphatic Polyethers in the Presence of LiTFSI Isothermal crystallization experiments performed by DSC were useful to determine the overall crystallizationPolymers 2019, 11 kinetics, x FOR PEER of the REVIEW polymeric samples employed here. These experiments were performed8 of 13 to study how the lithium salt concentration affects the overall crystallization kinetics of the τ differentFigure polyethers. 6a shows plots of the inverse of the half-crystallization time (1/ 50%) as a function of the crystallizationFigure6a shows temperature plots of the(Tc) inverse of the neat of the polyethers. half-crystallization The invers timee of (1/the τhalf-crystallization50%) as a function oftime τ the(1/ crystallization50%) is an experimentally temperature (T cdetermined) of the neat value polyethers. that is The directly inverse proportional of the half-crystallization to the overall timecrystallization (1/τ50%) is anrate experimentally [21,26]. The crystallization determined temp valueerature that isvalues directly where proportional the kinetics to were the overallable to be crystallizationmeasured decreased rate [21,26 as]. the The number crystallization of methylene temperature units decreased values where in the thepolyether kinetics repeating were able unit. to If bethe measured supercooling decreased is calculated as the number as ΔT=T ofm methylene0-Tm, employing units decreasedthe equilibrium in the melting polyether temperature repeating unit.values 0 If thedetermined supercooling by isthe calculated Hoffman–Weeks as ∆T = T mextrapolatio− Tm, employingn, the theresults equilibrium of which melting are temperatureshown in the valuesSupplementary determined Information by the Hoffman–Weeks and in Figure 2, extrapolation, the overall crystallization the results of kinetics which can are be shown represented in the as Supplementarya function of Informationsupercooling. and Figure in Figure 6b shows2, the overallhow the crystallization overall crystallization kinetics can kinetics be represented plots for the as adifferent function polyethers of supercooling. are now Figure much6 closerb shows together how the (using overall the same crystallization relative temperature kinetics plots range), for the since differentthe supercooling polyethers arenormalizes now much the closer plottogether with resp (usingect to the thermodynamic same relative temperature effects. The range), supercooling since therequired supercooling for crystallization normalizes the decreases plot with as respect the number to thermodynamic of methylene effects. units in The the supercooling polyether increases, required as forshown crystallization in Figure decreases 6b. This asresult the numberis consistent of methylene with the non-isothermal units in the polyether crystallization increases, data as shown reported in in FigureFigure6b. 3. This result is consistent with the non-isothermal crystallization data reported in Figure3.

0.9 2.5 P3 b) P3 a) 0.8 P4 P4 P5 P5 0.7 2.0 P6 P6 0.6 L-H fit L-H fit 1.5 0.5 (1/min) (1/min) 0.4 50% 50% 1.0 τ τ 1/ 1/ 0.3

0.2 0.5 0.1

0.0 0.0 40 50 60 70 80 90 -10 0 10 20 30 40 Temperature (ºC) ΔT (ºC)

Figure 6. (a) Overall crystallization rate (expressed as the inverse of the half-crystallization time) versus Figure 6. (a) Overall crystallization rate (expressed as the inverse of the half-crystallization time) isothermal crystallization temperature. (b) Overall crystallization rate (expressed as the inverse of the versus isothermal crystallization temperature. (b0) Overall crystallization rate (expressed as the half-crystallization time) versus supercooling (∆T = Tm − Tc). Symbols: experimental data. Solid lines inverse of the half-crystallization time) versus supercooling (ΔT = Tm0-Tc). Symbols: experimental data. show ﬁts to the Lauritzen and Hoffman theory. Solid lines show fits to the Lauritzen and Hoffman theory. The overall crystallization rate of P3 and P5 with different amounts of LiTFSI (5–30 wt %) was studiedThe and overall the results crystallization are presented rate in of Figure P3 and7. In P5 the wi caseth different of the SPE-P3 amounts samples, of LiTFSI the crystallization (5–30 wt %) was ratestudied decreased and the with results salt content, are presented a result in thatFigure is 7. explained In the case by of the the dilution SPE-P3 samples, effect caused the crystallization by LiTFSI. Similarrate decreased results were with obtained salt content, for SPE-P5 a result samples, that is except explained for the by sample the dilution with 10 effect wt % caused LiTFSI, by which LiTFSI. exhibitedSimilar aresults larger were value obtained than expected. for SPE-P5 Apart samples, from except this particular for the sample sample, with all the10 wt rest % behavedLiTFSI, which as expectedexhibited and a thelarger results value indicate than expected. that the Apart overall from crystallization this particular kinetics sample, of these all the polyethers rest behaved was as substantiallyexpected and depressed the results by theindicate incorporation that the overall of LiTFSI. crystallization The best way kinetics to visualize of these this polyethers change inwas crystallizationsubstantially rate depressed is to plot by the the overall incorporation crystallization of LiTFSI. rate atThe a constantbest way temperature to visualize (45 this◦C change in the in casecrystallization of P3 and 71 ◦rateC for is P5)to plot as a the function overall of LiTFSIcrystalli content,zation rate as shown at a constant in Figure temperature7c. The results (45 clearly°C in the showcase that of P3 the and overall 71 °C crystallization for P5) as a function rate of polyethersof LiTFSI content, P3 and as P5 shown generally in Figure decrease 7c. withThe results increasing clearly LiTFSIshow content. that the overall crystallization rate of polyethers P3 and P5 generally decrease with increasing LiTFSI content.

Polymers 2019, 11, x FOR PEER REVIEW 9 of 13

Polymers 2019, 11, 452 9 of 13

1.0

1.0 b) P5 a) P5 5 wt% LiTFSI P3 0.8 P5 10 wt% LiTFSI P3 5 wt% LiTFSI P5 20 wt% LiTFSI 0.8 P3 10 wt% LiTFSI P5 30 wt% LiTFSI P3 20 wt% LiTFSI 0.6 L-H fit P3 30 wt% LiTFSI L-H fit 0.6 (1/min)

50% 0.4 τ (1/min) 0.4 1/ 50% τ 0.2 1/ 0.2 0.0

0.0 62 64 66 68 70 72 74 76 30 35 40 45 50 55 60 Temperature (ºC) Temperature (ºC)

c) 1.2 P3, T = 45 ºC 1.0 c

P5, Tc = 71 ºC 0.8

0.6 (1/min) 50%

τ 0.4 1/

0.2

0.0

0 5 10 15 20 25 30 Content of LiTFSI (wt%)

Figure 7. (a) Overall crystallization rate (expressed as the inverse of the half-crystallization time) versus Figure 7. (a) Overall crystallization rate (expressed as the inverse of the half-crystallization time) isothermal crystallization temperature for P3 and SPEs-P3. (b) Overall crystallization rate (expressed versus isothermal crystallization temperature for P3 and SPEs-P3. (b) Overall crystallization rate as the inverse of the half-crystallization time) versus isothermal crystallization temperature for P5 and (expressed as the inverse of the half-crystallization time) versus isothermal crystallization SPEs-P5. Symbols: experimental data. Solid lines show ﬁttings to the Lauritzen and Hoffman theory. temperature for P5 and SPEs-P5. Symbols: experimental data. Solid lines show fittings to the (c) Overall crystallization rate (expressed as the inverse of the half-crystallization time) versus the Lauritzen and Hoffman theory. (c) Overall crystallization rate (expressed as the inverse of the half- content of LiTFSI at constant crystallization temperatures (notice that Tc values are different for each crystallization time) versus the content of LiTFSI at constant crystallization temperatures (notice that series), whose values are indicated in the legend. Tc values are different for each series), whose values are indicated in the legend. 4.4. Diluent Effect of LiTFSI 4.4. Diluent Effect of LiTFSI LiTFSI may act as a solvent that depresses the melting temperature of polyethers [27]. In order to demonstrateLiTFSI may if LiTFSI act as behavesa solvent likethat adepresses low molecular the melting weight temperature diluent, we of polyethers have employed [27]. In the order Flory–Hugginsto demonstrate theory if LiTFSI for polymer–diluent behaves like a low mixtures molecular [28 weight,29]. The diluent, fundamental we have employed Equation canthe Flory– be writtenHuggins as: theory for polymer–diluent mixtures [28,29]. The fundamental Equation can be written as: 1 1 T − 0 m 1 Tm 1 R Vu BV1 υ1 − = 1 − (3) υ ∆Hu V R Tm 𝑇1 𝑇 𝑅1 V BV υ (3) = 1− where ∆Hu is the melting enthalpy perυ mole of∆𝐻 repeating V unit,𝑅 Vu𝑇and V1 are the molar volumes of the polymer repeating unit and the diluent, respectively, υ1 is the volume fraction of the where ΔHu is the melting enthalpy per mole of repeating unit, Vu and V1 are the molar volumes of the diluent, B is the interaction energy density character of the polymer-diluent pair, Tm is the polymer repeating unit and the diluent, respectively, υ1 is the volume fraction0 of the diluent, B is the apparent melting temperature (taken from the DSC second heating run), and Tm is the equilibrium interaction energy density character of the polymer-diluent pair, Tm is the apparent melting melting temperature (determined by the Hoffman–Weeks extrapolation method), as shown in the temperature (taken from the DSC second heating run), and Tm0 is the equilibrium melting Supplementary Information and Figure2. All temperatures are expressed in Kelvin degrees and R is temperature (determined by the Hoffman–Weeks extrapolation method), as shown in the the gas constant. Supplementary Information and Figure 2. All temp0eratures are3 expressed in Kelvin degrees and3 R is Figure8 shows that the plot of [(1/ Tm − 1/Tm )/υ1] × 10 as a function of (υ1/Tm) × 10 the gas constant. is a straight line. This linear relationship indicates that the Flory–Huggins theory was obeyed

Polymers 2019, 11, x FOR PEER REVIEW 10 of 13

Polymers 2019, 11, x FOR PEER REVIEW 10 of 13 Polymers 2019Figure, 11, 4528 shows that the plot of [(1/Tm – 1/Tm0)/υ1] x 103 as a function of (υ1/Tm) x 103 is a10 straight of 13

line.Figure This linear8 shows relationship that the plot in dicatesof [(1/T thatm – 1/ theTm 0)/Flory–Hugginsυ1] x 103 as a function theory wasof (υ 1obeyed/Tm) x 10 for3 is LiTFSI a straight and polyether (P3-P5) mixtures, or in other words, that LiTFSI acts as diluent for the employed polyethers. forline. LiTFSI This and linear polyether relationship (P3-P5) indicates mixtures, that or the in Flory–Huggins other words, that theory LiTFSI was acts obeyed as diluent for LiTFSI for the and employedpolyether polyethers. (P3-P5) mixtures, or in other words, that LiTFSI acts as diluent for the employed polyethers. 0.15 P3 0.15 P5 3 P3 Linear fit P5 3 x 10

] Linear fit 1

ν 0.10 / ) x 10 0 m ] 1 T

ν 0.10 / ) 0 m - 1/ T m T 1/ - 1/ [( m

T 0.05 1/ [( 0.05 0.0 0.2 0.4 0.6 0.8 (ν /T ) x 103 0.0 0.2 0.41 m 0.6 0.8 ν 3 ( 1/Tm) x 10 Figure 8. Graph of [(1/Tm – 1/Tm0)/υ1] × 103 as a function of (υ1/Tm ) × 103. 0 3 3 Figure 8. Graph of [(1/Tm − 1/Tm )/υ1] × 10 as a function of (υ1/Tm) × 10 . Figure 8. Graph of [(1/Tm – 1/Tm0)/υ1] × 103 as a function of (υ1/Tm) × 103. From the intercept of the straight line it is possible to obtain the value of ΔHu, whereas from the

From the intercept of the straight line it is possible to obtain the value of ∆Hu, whereasu from the slope,From the thevalue intercept of B is determined.of the straight It linehas beenit is possible demonstrated to obtain that the the value value of of Δ HΔHu, whereaswas a property from the of slope, the value of B is determined. It has been demonstrated that the value of ∆Hu was a property of slope,the crystallizing the value of chain B is determined. repeating unit It has and been did demonstratednot depend on that the thenature value of ofthe Δ diluent.Hu was a It property is therefore of the crystallizing chain repeating unit and did not depend on the nature of the diluent. It is therefore thea fundamental crystallizing thermodynamicchain repeating unitproperty and did of thenot polyethedepend onr crystal the nature that isof directly the diluent. related It is to therefore its chain a fundamental thermodynamic property of the polyether crystal that is directly related to its chain astructure. fundamental ΔH uthermodynamic is therefore the propertyenthalpy ofof themelting polyethe of ar 100%crystal crystalline that is directly material related expressed to its chainas the structure.heat of ∆fusionHu is per therefore repeating the enthalpyunit [29]. of The melting values of obtained a 100% crystalline from Figure material 8 for P3 expressed are ΔHu = as 24,741 the heat J mol- structure. ΔHu is therefore the enthalpy of melting of a 100% crystalline material expressed as− the1 of fusion1 per repeating-3 unit [29]. The values obtained−1 from Figure8 for−3 P3 are H = 24,741 J mol and B = 3.7 J cm , and for P5, ΔHu = 40,300 J mol and B = 48 J cm . The value∆ ofu ΔHu for P3 is similar- heat of fusion per−3 repeating unit [29]. The values obtained−1 from Figure−3 8 for P3 are ΔHu = 24,741 J mol and B = 3.7 J cm , and for P5, ∆Hu = 40,300 J mol and−1 B = 48 J cm . The value of ∆Hu for P3 is 1 toand that B = reported 3.7 J cm-3 in, and the forliterature P5, ΔH [29],u = 40,300 i.e., 23,640 J mol− 1J and mol B .= 48 J cm−3. The value of ΔHu for P3 is similar similar to that reported in the literature [29], i.e., 23,640 J mol−1. to thatIn reported the case in of the P5, literature the value [29], of i.e.,the 23,640equilibrium J mol− 1melting. temperature and equilibrium melting In the case of P5, the value of the equilibrium melting temperature and equilibrium melting enthalpyIn the were case reportedof P5, the in valuethis work of the for equilibrium the first time, melting as far as temperature the authors andare aware.equilibrium Figure melting 9 shows enthalpy were reported in this work for the ﬁrst time, as far as the authors are aware. Figure9 shows enthalpythe data wereof some reported polyethers in this reported work for in the the first literat time,ure as [29] far and as the the authors experimental are aware. values Figure obtained 9 shows here the data of some polyethers reported in the literature [29] and the experimental values obtained here by theby datathe applicationof some polyethers of the Flory–Huggins reported in the theoryliterature to our[29] data.and the It canexperimental be seen that values the obtainedvalues of here ΔH u the application of the Flory–Huggins theory2 to our data. It can be seen that the values of ∆Hu increased byincreased the application with the of number the Flory–Huggins of –CH – and theory in the caseto our of data.P3 (six It methylenecan be seen units), that theour valuesvalue was of Δ veryHu withsimilar the number to that of reported –CH2– andin the in theliterature, case of P3as (sixalready methylene mentioned. units), In our addition, value was the very value similar for P5 to (10 increased with the number of –CH2– and in the case of P3 (six methylene units), our value was very that reported in the literature, as already mentioned. In addition, the value for P5 (10 methylene units) similarmethylene to that units) reported followed in the expectedliterature, trend. as already mentioned. In addition, the value for P5 (10 followed the expected trend. methylene units) followed the expected trend.

5x104

4 5x10 Reported in ref. 30 4x104 Obtained in this work Reported in ref. 30 4x104 Obtained in this work ) -1 3x104 ) -1 3x104 (J mol

u 2x104 H

(J mol Δ

u 2x104 H Δ 1x104

1x104 0 0246810 0 0246810Number of methylene units Number of methylene units Figure 9. ∆Hu values of polyethers as a function of the number of methylene units in the repeating unit. The black points are values reported in the literature [29] and the red points are the values obtained in this work.

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The value of B is related to the polymer–diluent interaction and therefore it depends on the chemical structure of the diluent component. The different slopes that are observed in Figure8 reﬂect differences in the Flory–Huggins interaction parameters for the mixtures. The Flory–Huggins polymer–diluent interaction parameter (χ1) can be expressed as [28]:

χ1 = κ1 − ψ1 + 1/2 (4) where κ1 and ψ1 are enthalpic and entropic parameters related to the partial molar enthalpy ∆H1 = RT 2 2 κ1υ2 and the partial molar entropy ∆S1 = RT ψ1 υ2 . The enthalpic term can also be represented as:

κ1 = BV1/RT. (5)

As can be seen from the above equations, B is directly proportional to the enthalpic contribution (κ1) to the Flory–Huggins parameter χ1. The lower the value of χ1, the higher the thermodynamic interaction between the polymer and the diluent. The B values obtained from Figure8 are B = 3.7 J cm−3 for P3, and B = 48 J cm−3 for P5. Therefore, LiTFSI was a better solvent for P3 than for P5, an expected result based on the chemical structure of P3 and P5, as the polarity degree within the polyether molecules decreased as the number of methylene units increased along the repeating unit. From the application of the Flory–Huggins theory, we can extrapolate the results to conclude that small values of B are necessary to increase the ionic conductivity.

5. Conclusions In this paper the impact of the chemical structure of aliphatic polyethers and salt concentration on crystallization rate, crystallization temperature, and ionic conductivity has been investigated. As a general observation, the LiTFSI salt acts as a diluent for all the aliphatic polyethers, reducing the crystallization rate and crystallization temperature. The ionic conductivities of the SPEs were obtained in the order of 10−8–10−4 S cm−1 at 70 ◦C. A higher number of methylene units in the polyether repeating unit caused a decrease in the ionic conductivity of the SPEs in the following order PEO (P1) > P(THF) (P2) > poly(oxyhexamethylene) (P3) > poly(oxyoctomethylene) (P4) > poly(oxydecamethylene) (P5) > poly(oxydodecamethylene) (P6) with 30 wt % of LiTFSI. The reason for this behavior is probably due to the decreasing solvation of lithium atoms in the same order. Additionally, as salt concentration increased, both crystallization temperature and melting enthalpies of the SPE-P3 and SPE-P5 were found to decrease. By applying the Flory–Huggins theory, we demonstrated that LiTFSI acts as a thermodynamic diluent for the polyethers examined. The interaction energy parameter (B) was calculated for SPEs prepared with P3 and P5. We showed that the value of B must be small to obtain high ionic conductivity electrolytes. In the case of the poly(oxydecamethylene), the value of the equilibrium melting temperature and equilibrium melting enthalpy were reported in this work for the ﬁrst time, as far as the authors are aware.

Supplementary Materials: The following are available online at http://www.mdpi.com/2073-4360/11/3/452/ s1. Author Contributions: J.L.O.-M. performed most of the experimental work and data analysis, he also wrote the first draft of the manuscript. L.M. and A.B. synthesized the polyethers used in this work. D.M. designed and supervised the experiments regarding polymer synthesis and conductivity. He also corrected the final draft of the manuscript. A.J.M. supervised the experimental work dealing with crystallization, crystallization kinetics and analysis of crystallization data. He also interpreted the melting data in terms of the Flory-Huggins theory and worked on corrections and additions to the manuscript and prepared the final version. Acknowledgments: We wish to thank the National Council of Science and Technology (CONACYT), Mexico for the grant awarded to Jorge L. Olmedo Martínez (471837). We are grateful to the financial support of the European Commission through the project SUSPOL-EJD 642671 and European Research Council by Starting Grant Innovative Polymers for Energy Storage (iPes) 306250. Alejandro J. Müller acknowledges the support of MINECO through grant MAT2017-83014-C2-1-P. Leire Meabe thanks Spanish Ministry of Education, Culture and Sport for the predoctoral FPU. Polymers 2019, 11, 452 12 of 13

Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

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