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Phase behavior of binary and ternary fluoropolymer (PVDF-HFP) solutions for single-ion conductors

A fluoropolymer poly(vinylidene fluoride-co-hexafluoropropylene) (PVDF-HFP) has a dielectric constant of ∼11, providing charge screening effects. Hence, this highly polar PVDF-HFP material has been employed as a matrix for solid polymer electrolytes (SPEs). In this study, the phase behavior of binary PVDF-HFP solutions was analyzed using the Flory–Huggins theory, in which ethylene carbonate, propylene carbonate, dimethyl carbonate, γ-butyrolactone, and acetone were employed as model solvents. In particular, for the binary PVDF-HFP/acetone system, the solid–liquid and liquid–liquid phase transitions were qualitatively described. Then, the phase diagram for ternary acetone/PVDF-HFP/polyphenolate systems was constructed, in which the binodal, spinodal, tie-line, and critical point were included. Finally, when a polyelectrolyte lithium polyphenolate was mixed with the PVDF-HFP matrix, it formed a single-ion conductor with a Li+ transference number of 0.8 at 23 °C. In the case of ionic conductivity, it was ∼10−5 S cm−1 in solid state and ∼10−4 S cm−1 in gel state, respectively.


Introduction
Poly(vinylidene uoride-co-hexauoropropylene) (PVDF-HFP) has been a benchmark matrix for solid-state polymer electrolytes due to its superior dielectric constant (3 r z 11), low glass transition temperature, high mechanical strength, and electrochemical stability. [1][2][3][4][5][6] Specically, the high 3 r affords a small binding energy with salt ions leading to an effective dissociation of charged particles, whereas the low T g allows the polymer segmental motion (to be active) in its amorphous regions. These characteristics provide a pathway for an enhanced ionic conductivity depending on both charge concentration and mobility. Basically, all the properties of the uoropolymer PVDF-HFP are largely governed by its chemical structure in the copolymer backbone. If the HFP content in the VDF/HFP units is less than 15-19 mol%, the copolymer is semicrystalline with thermoplastic properties, desirable for solid-state polymer electrolyte applications. [4][5][6][7] The polymer electrolytes are composed of a polymer matrix and salt (or ionic liquid or polyelectrolyte), in which both plasticizer and active/passive ller could be added for improving ionic conductivity and mechanical properties, respectively. [8][9][10][11] Furthermore, instead of a single polymer matrix, two different polymers can be mixed together to form a blend. For example, PVDF-HFP has been blended with other molecules such as poly(ethylene oxide) (PEO), poly(methyl methacrylate) (PMMA), poly(vinyl acetate) (PVAc), poly(vinyl chloride) (PVC), thermoplastic polyurethane (TPU), poly(methyl methacrylate-co-acrylonitrile-co-lithium methacrylate) (PMAML), poly(ionic liquid), polysiloxane, and carboxymethyl cellulose (CMC). 8,[12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] Here, it is notable that these polymer electrolytes have been developed for solid-state batteries (SSBs), which are one of the post-lithium-ion batteries (PLIBs) including sodium-ion batteries (SIBs), lithium-sulfur batteries (LSBs), and lithium-air batteries (LABs). [27][28][29][30][31][32] Specically, the peruoropolyether-based block copolymer electrolyte was designed for ultra-stable SIBs. 33 In addition, versatile new concepts such as exible cross-linked network electrolytes, metal-organic framework (MOF)-based electrolytes, porous organic cage ionic conductors, an aligned liquid crystalline polymer combined with ionic liquids and salt, polymer-in-salt electrolytes, and dual-/single-ion conductors have been introduced for the next-generation PLIB applications. [34][35][36][37][38] In this study, I investigated the single-ion conductor based on the polymer blend composed of PVDF-HFP and lithium polyphenolate (LPF), in which LPF is a polyelectrolyte providing Li + ions for the PVDF-HFP matrix. Through this work, I tried to improve the existing PEO/LPF-based single conductor 39 by replacing PEO with the high-performance PVDF-HFP matrix. This is because PEO has a low dielectric constant (3 r z 5) and too high crystallinity ($70-80%), leading to a relatively low ionic conductivity. [40][41][42] Hence, this work was focused on the analysis of PVDF-HFP solutions and then, the application of PVDF-HFP/ LPF blends to the solid polymer electrolytes (SPEs). Firstly, the phase behavior of binary and ternary PVDF-HFP solutions was investigated, for which the Flory-Huggins lattice theory was employed. [43][44][45][46][47][48] To date, most studies on the phase behavior of PVDF or PVDF-HFP solutions have been carried out through experiments. [49][50][51][52][53][54] An exception for this state is that Chen and his coworkers simply calculated the phase diagram of PVDF/ dimethylacetamide (DMAc)/H 2 O and described the PVDFmembrane formation via nonsolvent induced phase inversion. 50 In contrast, Wang et al. compared in their experiments the phase behavior of two different uoropolymer-based ternary systems, i.e., PVDF/DMAc/H 2 O and poly(vinylidenediuorideco-chlorotriuoroethylene) (PVDF-CTFE)/DMAc/H 2 O. 52 Here, the former was more easily phase-separable than the latter. Then, Shi et al. studied the effect of additive (LiCl and glycerol) on the phase behavior of PVDF-HFP/n-methyl-2-pyrrolidone (NMP)/H 2 O and found that the additive may alter the morphology and structure of the resulting membrane through a facilitated phase separation. 53 Recently, Wei and his coworkers studied the effect of LiCl on phase behavior of the PVDF-CTFE/DMAc/H 2 O system and found that LiCl addition promoted both solid-liquid and liquid-liquid phase transitions, which is in line with Shi et al.'s results. 54 Therefore, considering the deciency of theoretical calculation for the PVDF-HFP solution thermodynamics, this work seems to bridge the gap in this eld by providing theoretical predictions about the phase behavior of PVDF-HFP solutions in terms of binodal, spinodal, tie line, and critical point. [43][44][45][46][47][48] For this purpose, the Flory-Huggins interaction parameter (c) was essential, which was calculated based on solubility parameter (d). 55,56 However, if d is unknown, it could be estimated through a group contribution method. 57 Finally, with the understanding of phase behavior of PVDF-HFP solutions, PVDF-HFP was blended with a polyelectrolyte lithium polyphenolate (LPF) in acetone for the SPE applications. The resulting SPE showed a Li + -transference number of $0.8 as a single-ion conductor minimizing a concentration gradient and cell polarization in rechargeable lithium batteries. 10,58,59 Materials and methods Materials PVDF-HFP (M n z 120.0 kg mol À1 , M w z 400.0 kg mol À1 , and polydispersity index (PDI) ¼ 3.3) was provided from Elf Atochem, which is composed of VDF : HFP with 88 : 12 by mole ratio (Kynar-FLEX® 2801). P-Toluenesulfonyl chloride, HEPES buffer solution, horseradish peroxidase II (HRP II), NaOH, MgSO 4 , SiO 2 , hydroquinone, and other solvents were purchased from Sigma-Aldrich and used as received.
Methods 1 H nuclear magnetic resonance (NMR) spectra were obtained using an NMR spectrometer (Bruker). Infrared (IR) absorption data were obtained from IR spectrometer (Bomem, MB 100-C15) at 4000-400 cm À1 . Here, the KBr disc method was used for sample preparation. Thermal analysis was carried out by differential scanning calorimetery (DSC) (DuPont model 910 thermal analyzer) at a scanning rate of 10 C min À1 under N 2 with a ow rate of 50 mL min À1 . Note that, in this study, the DSC data were reported based on the rst heating curve. Thermogravimetric analysis (TGA) was performed using a TA instruments over a temperature range of 25-700 C at a scanning rate of 10 C min À1 under N 2 with a ow rate of 50 mL min À1 . Impedance data were obtained for estimating both the ionic conductivity (s) and the transference number of Li + ions (t Li + ) by using a frequency response analyzer (FRA, Solartron SI 1260), for which a stainless steel (SUS) or Li symmetrical cell was used, respectively. Note that the performance of polymer electrolyte (e.g., the reproducibility of ionic conductivity data) was evaluated through the 1 st order linear tting as a function of composition, indicating that both y-intercept and slope have the standard errors of $10 À6 S cm À1 . Through this regression analysis, the data distribution could be estimated although there should be experimental uncertainties.
SPEs were prepared by dissolving LPF : PVDF-HFP (¼1 : 1 to 1 : 5 by wt ratio) in acetone and cast it in a Teon plate (see Scheme 1 for chemical structure of LPF). Then the cell with stainless steel (SUS)/SPE/SUS or Li/SPE/Li conguration was assembled and vacuum-sealed using a blue bag from Shield Pack, Inc. in a glove box under argon environment. Here, SUS/ SPE/SUS is for estimating the bulk resistance and ionic conductivity of SPE, whereas Li/SPE/Li is for measuring Li + ion's transference number (t Li +).

Synthesis
Synthesis of (3). NaOH (11.4 g, 0.285 mol) was dissolved in 60 mL H 2 O to make 5 M NaOH. Tri(ethylene glycol) monomethyl ether (1) (32.84 g, 0.2 mol) was dissolved in 50 mL THF (Scheme 1). Subsequently, two solutions were mixed together in 1000 mL ask under less than 5 C. Then, p-toluenesulfonyl chloride (2) (36.2 g, 0.18 mol) in 50 mL of THF was dropwise added into the above solution and mixed. Aer about 2 hours, the solution's color was change into milky white, indicating the successful reaction. The solution was poured into 400 mL cold water. Using diethyl ether 50 mL, the synthesized chemical was extracted (Âthree times). It was washed several times and nally dried. The product was a transparent yellowish liquid.
Synthesis of PF. HRP II (24 mg) was dissolved in 55 mL HEPES buffer solution in 250 mL three-neck ask. Then (5) (8.83 g, 34.46 mmol) was dissolved in 25 mL 1,4-dioxane, and then this solution (5 in 1,4-dioxane) was added slowly into the above HRP-II/HEPES buffer solution. Then 30% H 2 O 2 solution (1 mL) was added into this buffer solution, which was repeated for 5 times per 10 min under below 5 C. Then solution's color was gradually changed to yellow. Then the reaction was allowed for additional $10-15 min under 23 C and stirred overnight, resulting in dark brown color.
Synthesis of LPF. PF (4 g, 15.7 mmol) was dissolved in 20 mL 1,4-dioxane. LiOH (38 mg, 15.7 mmol) was dissolved in 10 mL water. Then two solutions were mixed together, resulting in a black colored solution. Then 1,4-dioxane and water was removed from the product using a rotary evaporator. Then the product was stored in vacuum overnight.

Dielectric property of PVDF-HFP
The electric potential energy (U E ) between two charges (q 1 and q 2 ) in a dielectric is a function of the permittivity (3 ¼ 3 0 3 r ) of a material as well as charge-separation distance (r 12 ).
where 3 0 and 3 r are the vacuum permittivity and a relative permittivity (or dielectric constant), respectively. Fig. 1a shows the coulombic potential well describing the binding energy between cation and anion when the dielectric constant of polymer is 3 r z 11 for PVDF-HFP (its chemical structure in Fig. 1b) and 3 r z 5 for PEO, respectively. 6,39,60 According to eqn (1), when is high, the binding energy between cation and anion should be small because of the screening effect of a polarized medium on charges. Thus, PVDF-HFP displays a narrow coulombic potential well, whereas PEO exhibits a wide one. For example, when ion separation distance is 10Å, the binding energy is 0.29 eV in PEO, whereas 0.13 eV in PVDF-HFP. This characteristic implies that the charge concentration for ionic conductivity will be higher in PVDF-HFP than in PEO. Thus, for developing SPEs, it is reasonable to replace PEO with PVDF-HFP or other high dielectric uoropolymers, e.g., PVDF-CTFE (3 r z Fig. 1 (a) Binding energy as a function of ion separation distance. Here, a monovalent cation is assumed to be at the origin, whereas a monovalent anion at the indicated distance. Potential wells were calculated for PVDF-HFP with 3 r z 11 and PEO with 3 r z 5. (b) Chemical structure of PVDF-HFP copolymer.
13), and poly(vinylideneuoride-co-triuoroethylene) (PVDF-TrFE) (3 r z 18). [3][4][5][6] Phase behavior of binary PVDF-HFP solutions The Flory-Huggins theory can describe the phase behavior of polymer solutions, for which the two parameters such as interaction parameter (c) and the relative molar volume of a polymer (r 2 ) should be provided. In the case of solvent, r 1 ¼ 1.
The molar Gibbs energy of mixing (DG mix ) for a binary polymer solution is expressed as follows, 45,61 where R, T, and f i are the gas constant, temperature (K), and the volume fraction of component i (¼1 for solvent and 2 for polymer). Here, c ij could be estimated from the solubility parameter information as follows, whereV 1 and d i are a molar volume of solvent and a solubility parameter of component i. Here, the c parameter is inversely proportional to temperature. Then, the equilibrium condition of chemical potentials, Dm i (¼ vDG mix /vn i ), is expressed as follows, where a and b indicate two different phases at equilibrium. Using eqn (4), the upper critical solution temperature (UCST) phase behavior could be predicted. Furthermore, the melting point of a binary polymer solution could be described as follows, where T m and T 0 m are the temperatures of a binary solution and a pure polymer, respectively. DH u is the enthalpy of polymer's structural unit (when crystallinity is 100%), and V u is the volume of polymer's structural unit. In general, the chain length of polymer is much larger than that of solvent (i.e., r 2 [ r 1 ¼ 1). Thus, the eqn (5) could be reduced as follows, Specically, propylene carbonate (PC), ethylene carbonate (EC), dimethyl carbonate (DMC), and g-butyrolactone (GBL) have been used as solvent (or plasticizer) for polymer electrolytes. [62][63][64] Thus, using these solvents, the UCST phase behavior of PVDF-HFP solutions was calculated. As a rst step, the model polymer (PVDF-HFP) was assumed to have a moderate molecular weight M n ¼ 40.0 kg mol À1 with d 2 ¼ 11.3 (cal cm À3 ) 1/2 . 63 Then, the properties of solvents were summarized in Table 1. 64 According to the Flory-Huggins model, the PVDF-HFP solutions exhibited a better miscibility with the sequence of GBL > DMC > EC > PC, which was largely governed by c 12 parameters ( Table  1). Note that smaller c 12 , more miscible each other. In Fig. 2 For the binary PVDF-HFP/acetone (Ace) system, not only liquid-liquid phase equilibria (LLE), but also solid-liquid phase Table 1 Solubility parameter (d 1 ), molecular weight (MW), density (d), molar volume (V 1 ), relative molar volume (r 2 ), and interaction parameter (c 12 ) for PVDF-HFP/solvent systems. Here, PVDF-HFP as a model system has d 2 ¼ 11.3 (cal cm À3 ) 1/2 , d ¼ 1.77 g cm À3 , M n ¼ 40.0 kg mol À1 , and molar volume ¼ 22 600 cm 3  equilibria (SLE) were calculated because the acetone was used as a processing solvent for fabricating a SPE in this study. Note that both Ace and DME have the same d 1 ¼ 9.9 (cal cm À3 ) 1/2 , but they have different molecular weights and densities, distinguishing the phase behavior. Hence, the LLE curve for PVDF-HFP/Ace was slightly different from that of PVDF-HFP/DMC. Furthermore, using eqn (6), i.e., Nish-Wang model, the SLE curve was calculated as shown in Fig. 3a. Here, the parameters used are DH u ¼ 104.7 J g À1 Â 202 g mol À1 ¼ 21 148.4 J mol À1 , V u ¼ 114 cm 3 mol À1 ,V 1 ¼ 74.03 cm 3 mol À1 , T 0 m ¼ 143 + 273 ¼ 416 K, and R ¼ 8.314 J mol À1 K À1 . Note that PVDF-HFP copolymer has the unit molecular weight of 202 g mol À1 and an enthalpy of fusion, ca. 104.7 J g À1 . 65,66 The phase behavior in Fig. 3a suggests that PVDF-HFP may be crystallized out before liquid-liquid (L-L) phase separation if kinetics is sufficiently slow. Furthermore, the critical points (f c 2 ,T c ) were calculated for various molecular weights (or chain lengths) of PVDF-HFP (Fig. 3b)

Phase behavior of ternary PVDF-HFP solutions
The Flory-Huggins model (eqn (2)) could be extended for describing the phase behavior of ternary polymer solutions with components, i ¼ 1, 2, 3. 43,47   where c ij ¼V 1 /RT(d i À d j ) 2 with i or j ¼ 1, 2, 3 from eqn (2). In this work, the components, 1, 2, and 3 correspond to acetone, PVDF-HFP, and PF, respectively. Importantly, DG mix in the eqn (7) is expressed 'per lattice site'. 61 However, if one converts DG mix into DG sys mix ¼ DG mix /(n 1 r 1 + n 2 r 2 + n 2 r 2 ) 'per the system' by multiplying (n 1 r 1 + n 2 r 2 + n 2 r 2 ) in both right-and le-hand sides, the Flory-Huggins model could be expressed as follows, 47,61 DG sys mix RT ¼ DG mix RTðn 1 r 1 þ n 2 r 2 þ n 2 r 2 Þ ¼ n 1 ln f 1 þ n 2 ln f 2 þ n 3 ln f 3 þ c 12 n 1 f 2 þ c 13 n 1 f 3 þ c 23 n 2 f 3 (8) where n i is the number of moles of component i. Now for calculating the phase boundary for ternary systems, the chemical potential (Dm i ) of component i should be expressed by differentiating the free energy of mixing in eqn (8) per the system. 46,48 Here, v i is molar volume of component i. The binodal curve could be estimated for ternary systems by extending eqn (2) as below.
Furthermore, the spinodal curve and the critical point could be calculated according to my previous work. 67 For constructing the phase diagram of ternary Ace/PVDF-HFP/PF system, the eqn (12) was employed, enabling the calculation of the phase boundaries. Here, it is noteworthy that the Flory-Huggins theory can consider only van-der-Waals forces in terms of the c interaction parameter. Thus, it was assumed that PF is a non-ionizable molecule as a model molecule. However, the density and solubility parameter for PF are unknown. Hence, they were estimated through the group contribution method as summarized in Tables 2 and 3. 57 Accordingly, the density of PF is 1.74 g cm À3 (¼ P M i / P V wi ¼ 257.92/148.35), where M i (g mol À1 ) and V wi (cm 3 mol À1 ) are the mass and van der Waals volume of structural group i, respectively. The molar volume is 987 cm 3 mol À1 , which was estimated from the relation of M n /d ¼ 1717/1.74. The unit-molar volume (V u ) is 193 cm 3 mol À1 from unit molecular weight divided by density like MW u /d ¼ 336/1.74. Lastly, the solubility parameter of PF was estimated to be 16.6 (cal cm À3 ) 1/2 ¼ 34.1 MPa 1/2 by using the Hoyzer-Van Krevelen method as below. where F di and F pi are force contributed from dispersion and polar components, respectively. E hi is an energy contributed from hydrogen bonding component. Then, the solubility parameter was nally calculated from the relation, q ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 20:3 2 þ 4:9 2 þ 26:9 2 p ¼ 34.1 MPa 1/2 was converted to 16.6 (cal cm À3 ) 1/2 for estimating the c interaction parameter. Fig. 4 shows the phase diagrams for a ternary Ace/PVDF-HFP/ PF system, in which the components 1, 2, and 3 correspond to acetone, PVDF-HFP, and PF, respectively. Here, the physical parameters are c 12 ¼ 0.25,c 13 Table 4). Resultantly, the phase diagram exhibited the critical point at (f c 1 , f c 2 , f c 3 ) ¼ (0.83152, 0.01541, 0.15308), indicating that the phase-separation regions are very large. Specically, when f 1 z 0, the metastable region is from f 3 z 0.01223 to 0.14265, whereas the unstable region is from f 3 z 0.14265 to 1. Here, it is noteworthy that the nucleation-growth is undergone in a metastable region, whereas the spinodal decomposition proceeds in an unstable region. Hence, the dominant phaseseparation process is through the spinodal decomposition in most compositions. Furthermore, two polymers are usually immiscible because of no entropic gain, i.e., DG mix ¼ DH mix À TDS mix z DH mix $ 0. In particular, for the PVDF-HFP/PF blend, ffiffiffiffiffiffiffiffi 916 p þ 1= ffiffiffiffiffi 13 p Þ 2 z 0:05. 62 Note that if onlyc 23 < c c 23 , two polymers are miscible. However, currently, c 23 ¼ 3.51 > c c 23 ¼ 0.05, indicating PVDF-HFP and PF are immiscible.
Interestingly, the phase behavior of the Ace/PVDF-HFP/PF system in Fig. 4 is very similar to that of the solvent/polymer/ nonsolvent system (e.g., NMP/PVDF-HFP/H 2 O). 53,54 Hence, just like nonsolvent induced phase separation (NIPS), it is expected that PF-induced phase separation takes place in the Ace/PVDF-HFP/PF system because PVDF-HFP and PF are immiscible. Importantly, according to Shi et al., the addition of salts (e.g., LiCl) into this solvent/polymer/nonsolvent system induced the binodal to shi further towards the polymer-solvent axis (i.e., an enlarged phase-separation probability). 53 At this moment, it is important to remind that the Flory-Huggins theory cannot deal with coulombic interactions. However, if the ternary Ace/ PVDF-HFP/LPF system (here, LPF is ionizable) is considered, the two phenomena are basically expected. One is that the ionization of LPF may increase the entropy of electrolyte system, and the other is that Li + ions may have a coordination bonding (a weak transient crosslinking) with Lewis base (Florine) in PVDF-HFP, indicating the modied intra-/inter-molecular interactions (i.e., enthalpy) among component molecules. Hence, based on the two thermodynamic (entropic and Fig. 5 (a) 1 H NMR spectra and chemical structure of PF. (b) GPC data for PF: M n ¼ 1.7 kg mol À1 , M w ¼ 3.2 kg mol À1 , and PDI z 1.9. enthalpic) effects, the phase-separation boundaries should be shied for adjusting a new equilibrium point. 53,54 Single Li-ion conducting solid polymer electrolyte: synthesis, properties and performance In the backdrop of aforementioned PVDF-HFP thermodynamics, LPF was synthesized and blended with PVDF-HFP using acetone (recall Scheme 1). Fig. 5a shows 1 H NMR spectra for PF, i.e., a precursor for LPF, in which '-H from benzene, -OH, -CH 2 -, and -CH 3 ' were observed at $7 ppm, $5.5 ppm, $4-3.5 ppm, and $3.7 ppm, respectively. The molecular weights of PF are about M n z 1.7 kg mol À1 (equivalent to $7 structural units) and M w z 3.2 kg mol À1 , indicating that PDI z 1.9. Here, it is noticeable that the spatial size of PF is close to oligomer, suggesting a partial increase of (f 3 /r 3 ) ln f 3 in eqn (8) by reducing the relative molar volume (r 3 ) of PF. In addition, Fig. 6 shows the TGA data for the synthesized PF, displaying the major thermal decomposition at $300-400 C.
As a next step, I examined the infrared (IR) spectra for PF and LPF, respectively. As shown in Fig. 7a, -O-H stretching at 3438 cm À1 , -C-H stretching at 2881 cm À1 , -C]C stretching at 1610 cm À1 and 1500 cm À1 , -C-O (phenol) stretching at 1192 cm À1 , -C-O-C (ethylene oxide) stretching at 1106 cm À1 , and (Bz)-C-O-C stretching at 1004 cm À1 were observed. Interestingly, based on the IR spectra, LPF and PF show a partial difference in the relative intensity (not position) of peaks. Notably, the -O-H stretching was observed at 3438 cm À1 for a hygroscopic LPF sample also, suggesting the H 2 O absorption during FT-IR measurement in air. However, it is notable that in the case of electrical measurement, the device was fabricated in a glove box under argon environment, not in air. Fig. 7b shows the DSC thermogram for LPF, PVDF-HFP, and the polymer blend LPF : PVDF-HFP ¼ 1 : 1.7, which was recorded during the rst heating scans at 10 C min À1 . The melting points (T m ) of the pure components (LPF and PVDF-HFP) were observed at 87 C and 142 C, respectively. In the case of LPF : PVDF-HFP ¼ 1 : 1.7, the blend exhibited T m at the same temperature of each components, indicating that PVDF-HFP and LPF are basically immiscible as expected from most two polymers. As shown in Fig. 7b, when blended, the enthalpy was reduced from 57.01 J g À1 to 1.26 J g À1 for LPF, whereas from 38.08 J g À1 to 22.78 J g À1 for PVDF-HFP, indicating the diminished crystallinity (98% reduction for LPF and 38% for PVDF-HFP). Here, if one compares PVDF-HFP and LPF, the crystalline region of PVDF-HFP could survive more than that of LPF when blended each other. Finally, in the case of PVDF-HFP, its ideal enthalpy of melting is 104 J g À1 . 68 Hence, the crystallinity of pure PVDF-HFP is ca.    Fig. 8a shows a typical Nyquist plot of the impedance data for the PVDF-HFP/LPF system at 23 C, displaying a bulk resistance (R b ), for which the symmetric cell with a SUS/SPE/SSU structure was fabricated. Here, the ionic conductivity (s) could be estimated from the relation of l/(R b A), where l and A are thickness and area of a lm, respectively. For example, when R b ¼ 514.25 U, l ¼ 172 mm, and A ¼ 4 cm 2 , s would be 8.4 Â 10 À6 S cm À1 . In the same way, the resulting ionic conductivity as a function of composition is displayed in Fig. 8b. In this range of 1 # wt PVDF-HFP /wt LPF # 5, the average ionic conductivity is s ¼ 1.4 Â 10 À5 S cm À1 with the maximum s ¼ 3.4 Â 10 À5 S cm À1 at wt PVDF-HFP /wt LPF ¼ 2 and the minimum s ¼ 6.5 Â 10 À6 S cm À1 at wt PVDF-HFP /wt LPF ¼ 5. Although there were partial uctuations in data, the overall trend indicated that the ionic conductivity was enhanced with increasing the LPF amounts in the SPEs. Furthermore, when the experimental data were tted linearly, the result was y ¼ (2.45 Â 10 À5 ) + (À3.56 Â 10 À6 )x with the standard errors (y-intercept: 8.97 Â 10 À6 S cm À1 and slope: 2.83 Â 10 À6 S cm À1 ), in which y and x denote ionic conductivity and weight fraction (wt PVDF-HFP /wt LPF ), respectively. On the other hand, it is notable that the ionic conductivity for PEO/LPF was reported to be $10 6 S cm À1 at 23 C and $10 5 S cm À1 at 100 C, 39 indicating that PVDF-HFP/LPF is superior to PEO/LPF as a polymer electrolyte system. Furthermore, the Li + ion's transference number (t Li +) for the PVDF-HFP/LPF system was estimated based on the below relation, 10,69 where I 0 and I S are the initial and steady-state currents under the DC polarization voltage (DV ¼ 10 mV), R 0 and R S are the initial and steady-state interfacial resistance by the AC impedance method before and aer DC polarization. For the PVDF-HFP/LPF system, the AC impedance spectra for the cell were measured before and aer DC polarization as shown in Fig. 7c. Here, during the DC polarization under a constant potential of 10 mV, the current response was measured for the Li/SPE/Li cell as a function of time as shown in Fig. 7d. Resultantly, t Li + z 0.8 was estimated using eqn (16) with the values of which is a promising result as a single-ion conducting SPE. However, it is notable that t Li + is only 0.8 below the ideal $1.0, indicating that 20% of electricity was transferred through anions. Hence, although minus charges were embedded in the oligomeric polyphenolate with PDI $ 1.9, some anions (relatively smaller molecules among polydisperse LPFs) may migrate under the electric eld. This phenomenon suggests that for increasing t Li + , the minus charges should be well xed on the macromolecular polyelectrolyte. More importantly, although many research groups have reported t Li + at high temperature (e.g., $60-90 C), [70][71][72][73][74] here I reported t Li + at 23 C. This observation suggests that the polar polymer PVDF-HFP is an effective matrix for ionic conductor applications. Finally, although the research theme of mine was in the development of solid-state polymer electrolyte, I carried out the preliminary study about the ller and plasticizer effect on the ionic conductivity. Resultantly, when the inorganic ller SiO 2 was added $25 wt% of LPF, the ionic conductivity (LPF : PVDF-HFP : SiO 2 ¼ 1 : 1.7 : 0.25) was improved up to $1.03 Â 10 À4 S cm À1 (compared to average 1.4 Â 10 À5 S cm À1 without ller). Furthermore, when a plasticizer (EC : PC ¼ 1 : 1) was added into the above system like LPF : PVDF-HFP : SiO 2 :EC : PC ¼ 1 : 1.7 : 0.25 : 0.5 : 0.5, the ionic conductivity was similarly $1.0-1.1 Â 10 À4 S cm À1 (see Table 5). This indicates that there is a trade-off relationship between the exibility (increase of chain motion) and dilution (decrease of carrier concentrations per volume) of electrolyte system. Hence, the ionic conductivity was $10 À4 S cm À1 in the case of the aforementioned gel polymer electrolyte (GPE).

Conclusion
When the highly polar PVDF-HFP uoropolymer was blended with a polyelectrolyte lithium polyphenolate (LPF) for single-ion conductor applications, the ionic conductivity was $10 À5 S cm À1 in solid state and $10 À4 S cm À1 in gel state. More importantly, this LPF/PVDF-HFP single-ion conductor displayed a lithium transference number of ca. 0.8 at 23 C, indicating that 20% of charges were transported through the anions xed in the oligomeric polydisperse polyphenolate. Finally, considering the limited thermodynamic studies on the phase behavior of PVDF-HFP solutions and blends, I believe this work should be a signicant progress, providing the insight for the phase behavior of PVDF-HFP solutions and blends based on the classical Flory-Huggins lattice theory.

Conflicts of interest
The authors declare no competing nancial interest.