Rheological scaling of ionic-liquid-based polyelectrolytes in ionic liquid solutions: the effect of the ion diameter of ionic liquids

Abstract

We investigate the effect of the ion diameter a of ionic liquids (ILs) on the shear viscosity of polymerized ionic liquids (PILs) in IL solutions. When both the PIL and IL contain large PFSI anions (a ≈ 0.57 nm), the specific viscosity η_sp first decreases with increasing IL concentration c_IL in the low c_IL regime, reaches a minimum and then increases with increasing c_IL in the high c_IL regime. By comparing the measured η_sp with the modified charge screening model proposed in our previous study [Matsumoto et al., Macromolecules, 2021, 54, 5648–5661], we attribute the observed non-monotonic trend of η_sp against c_IL to the charge underscreening phenomenon, i.e., an increase of the screening length at high c_IL leads to the upturn of η_sp. On the other hand, when the PIL and IL contain small BF₄ anions (a ≈ 0.34 nm), the η_sp decreases asymptotically with increasing c_IL, because the charge on the PIL chain is likely screened fully in the entire c_IL regime. Our results demonstrate that the ion diameter of ILs plays an important role in governing the charge screening mechanism of PILs in IL solutions, and thus influencing the viscoelastic properties of PIL solutions.

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1 Introduction

Polymerized ionic liquids (PILs) are a special type of polyelectrolytes with ionic liquid (IL) structures on their repeating units.¹ Since PILs combine unique features of ILs (e.g., CO₂ adsorption, high ionic conductivity, antimicrobial) with those of polymers (e.g., low glass transition temperatures, processability), they have attracted significant attention with applications in batteries,^2–4 molecular separations,^5,6 drug delivery,^7,8 lubrication,^9,10 and antimicrobial agents.^11–13 The performance of PIL-based materials can be further improved by adding solvents, e.g., ILs, as plasticizers.^14–20 Consequently, understanding the conformation and the polymer dynamics of PILs in IL solutions is of great importance because they are intimately related to the properties of PIL-based materials.

We recently investigated the viscoelastic properties of a PIL (PC₄-TFSI) in the mixture of non-ionic DMF and ILs (Bmim-TFSI) while varying IL concentrations from IL-free to IL ion saturated conditions at a fixed polymer concentration.^21,22 We reported that the specific viscosity η_sp = (η₀ − η_s)/η₀, where η₀ and η_s denote the zero shear viscosity of polymer solutions and the solvent viscosity respectively, initially decreased with increasing IL concentrations c_IL at low c_IL regime because IL ions acted as salt ions to screen the electrostatic force working between the PIL repeating units.^23,24 The observed behavior at low c_IL could be captured by Dobrynin's charge screening model for polyelectrolyte solutions,²⁵ based on the Debye–Hückel (DH) theory.²⁶ However, at high c_IL, we observed that the measured η_sp reached a minimum and then started to increase with increasing c_IL. A similar trend was observed in the longest relaxation time λ versus the IL concentration c_IL of the PIL solutions. These results suggested that extended PIL chains shrunk initially by the addition of ILs caused by the Debye screening, but reverted to an expanded conformation due to strong ionic correlations at high c_IL, i.e., the so-called charge underscreening.²⁷

In order to capture the observed non-monotonic dependence of η_sp and λ on the IL concentration c_IL, we proposed a modified charge screening model on the basis of Dobrynin's charge screening model for polyelectrolyte solutions at low IL concentrations.²⁵ In the Dobrynin model, the Debye screening effect is considered, and the specific viscosity η_sp,SU for semidilute unentangled (SU) solutions of polyelectrolytes in good solvents is given by

where N, b, c_p, and K₁ are the degree of polymerization, the monomer size, the molar concentration of monomers, and the scaling prefactor, respectively. B = (bA²/l_B)^2/7 is the dimensionless contour length parameter, where A and l_B = e²/4πε₀ε_rk_BT are the number of monomers between uncondensed charges and the Bjerrum length, respectively. Here e, ε₀, ε_r, k_B, and T are the elementary charge, the vacuum permittivity, the relative dielectric constant of solvents, the Boltzmann constant, and the absolute temperature, respectively. The screening length r_B of polyelectrolyte solutions is proposed as²⁵Here, N_A and c_IL is the Avogadro constant and the molar concentration of ILs, respectively. Eqn (2) predicts that the screening length decreases monotonically with increasing c_IL, similar to the model prediction by the DH theory. Thus, the specific viscosity, given by eqn (1), predicts a monotonic decrease with the increasing c_IL, suggesting a reduction in the chain size of polyelectrolytes with increasing c_IL. However, eqn (1) may not be applicable at high c_IL because, in reality, polyelectrolyte chains shrink and eventually reach the initial polyelectrolyte chain size at high c_IL when the charge is completely screened.^28–30 Dobrynin and co-workers^31,32 have recently reported that the finite chain dimension of polyelectrolytes in the absence of electrostatics depends on chains persistent length and the second virial coefficient. Assuming the second virial coefficient for PC₄-TFSI monomers in the mixture of DMF and Bmim-TFSI is independent of c_IL in the high c_IL regime, as observed by Dobrynin et al., we can adjust the Dobrynin model of eqn (1) by adding parameter η^int_sp, a constant denoting the intrinsic specific viscosity:The specific viscosity, given by eqn (3), decreases asymptotically with increasing c_IL due to the complete charge screening based on the Debye screening, shown as the red dashed curve in Fig. 1. Since η^int_sp is related to the size of polyelectrolyte chains in the absence of electrostatic forces, the value of η^int_sp should follow the scaling of η_sp for electrically neutral polymers, e.g., η^int_sp ∝ c_p^1.3 for neutral polymers in good solvents.³³ However, the model prediction by eqn (3) does not capture the non-monotonic dependence of η_sp on c_IL, observed for PIL solutions. To account for the charge underscreening,²⁷ we replaced the screening length r_B in eqn (3) with the modified screening length r_B^mod, proposed by Lee et al. as³⁴Here, a is the ion diameter of ILs. The specific viscosity η_sp,SU can be rewritten as²²In eqn (4), the modified screening length r^mod_B is initially equal to the screening length r_B at low c_IL, given by eqn (2), but starts to increase with increasing c_IL when a > r_B at high c_IL. As a result, the specific viscosity, given by eqn (5), is predicted to exhibit a non-monotonic trend against c_IL due to the charge underscreening following the Debye screening effects, illustrated as black solid curve in Fig. 1.

Fig. 1 The dependence of the specific viscosity η_sp,SU on c_IL for semidilute unentangled (SU) solutions of polyelectrolytes in IL solutions, predicted by eqn (5). The black solid curve represents the trend of η_sp,SU against c_IL when the charge underscreening is dominant, i.e., the ion diameter of ILs is large. On the other hand, the red dashed curve represents the trend of η_sp,SU against c_IL when the complete charge screening is dominant, i.e., the ion diameter of ILs is small.

Subsequently, we validated eqn (5) by measuring η_sp for a polymerized ionic liquid, poly(1-butyl-3-vinylimidazolium bis(trifluoromethanesulfonyl)imide) (PC₄-TFSI), in the mixture of DMF and an IL, 1-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide (Bmim-TFSI), while varying c_IL at a fixed c_p. Both the charge underscreening and complete charge screening were observed in the trend of η_spversus c_IL for the PC₄-TFSI in the mixture of DMF and Bmim-TFSI.²²

Motivated by our prior results involving PC₄-TFSI in the mixture of DMF and Bmim-TFSI (ion diameter a = 0.49 nm) supported by the modified charge screening model described above, in this study, we focus on the effect of the ion diameter of ILs on the shear viscosity of PILs in IL solutions. According to eqn (4), the ion diameter of ILs is related to the charge underscreening behavior, i.e., the larger the ion diameter of ILs, the smaller the molar concentration of ions where the charge underscreening is observed since for a fixed molar concentration (i.e., at the fixed number of ions per unit volume), the distance of larger ions is shorter than those of smaller ions. We vary the ion diameter a of ILs by changing the anion structure of PILs and ILs while keeping their cation structure the same as that of PC₄-TFSI and Bmim-TFSI. We show a clear upturn of η_sp when choosing larger sized bis(pentafluoroethanesulfonyl)imide (PFSI) anions with an estimated ion diameter a = 0.57 nm, indicating a significant charge underscreening effect on the viscoelastic response of PC₄–PFSI solutions. On the other hand, when using tetrafluoroborate (BF₄) anions with smaller anion size of a = 0.34 nm, the η_sp decreases asymptotically with increasing c_IL, indicating that only charge screening is at play. The model predictions of eqn (5) (η_sp on c_IL) are able to capture very distinct behavior for both PFSI and BF₄ systems. Our results also demonstrate that the ion diameter of ILs does influence the viscoelastic properties of PILs in IL solutions, as predicted by the modified charge screening model.

2 Experimental section

2.1 Materials

1-Vinylimidazole and lithium bis(pentafluoroethanesulfonyl) imide (Li-PFSI) were purchased from Tokyo Chemical Industry, Japan. Sodium tetrafluoroborate (Na–BF₄), 1-bromobutane, 2.2′-azobis(isobutyronitrile) (AIBN), super dehydrated dimethylformamide (DMF), methanol, and silver nitrate (AgNO₃) at 0.1 M in an aqueous solution were purchased from Wako Pure Chemicals, Japan. 1-Butyl-3-methylimidazolium bis(pentafluoroethanesulfonyl)imide (Bmim-PFSI; Purity >99%) and 1-butyl-3-methylimidazolium tetrafluoroborate (Bmim–BF₄; Purity >99%) were purchased from Ionic Liquid Technologies, Germany. 1-Vinylimidazole was used after distillation at 85 °C under vacuum, while the other chemicals were used as received. After passing through a Q-POD Element unit (Merck Millipore, Japan), Milli-Q water with a resistivity higher than 18.2 MΩ was obtained and used as solvents for the PIL synthesis.

2.2 Synthesis of PC₄–BF₄ and PC₄–PFSI

Two vinylimidazolium-based PILs, PC₄–BF₄ and PC₄–PFSI, were prepared through three synthetic steps illustrated in Fig. 2. Since we obtained PC₄–BF₄ and PC₄–PFSI from the same precursor polymer (i.e., PC₄-Br with bromide anions) used for PC₄-TFSI in our previous study,²² it is reasonable to assume that the degree of polymerization of PC₄–BF₄ and PC₄–PFSI is the same as that of the PC₄-TFSI. As described in Section S1 of the ESI,† we measured the weight-averaged molecular weight M_w of the PC₄-TFSI based on static light scattering measurements, and estimated the degree of polymerization N = 2944 for PC₄–BF₄ and PC₄–PFSI. We note that the estimated M_w of the PC₄-TFSI may have an uncertainty in magnitude because we omitted a dialysis process to determine an accurate refractive index increment.³⁶ Moreover, we assumed the form factor P(θ) = 1 to estimate M_w based on the Debye plot obtained from our static light scattering measurements.³³ More detailed reasons are provided in Section S1 of the ESI.† The details for each step are explained below.

Fig. 2 Three-step synthesis is conducted to prepare two PILs with different counter-anions, i.e., PC₄–BF₄ and PC₄–PFSI. Step I: the quaternization of 1-vinylimidazole with 1-bromobutane to obtain the PIL monomer of C₄–Br. Step II: free radical polymerization of C₄–Br to prepare the precursor polymer of PC₄–Br. Step III: counter-anion exchange of PC₄–Br from Br to BF₄ and PFSI anions via the counter-anion conversion method by Marcilla et al.³⁵

2.2.1 Step I: synthesis of C₄-Br monomers. The monomer of 1-butyl-3-vinylimidazolium bromide (C₄-Br) was synthesized by refluxing 1-vinylimidazole (157.2 g, 1.67 mol) with excess 1-bromobutane (256.0 g, 1.87 mol) in methanol (150 mL) at 60 °C for 3 days. The molar ratio of the 1-vinylimidazole and the 1-bromobutane was set at 1.2. The quaternization of 1-vinylimidazole with 1-bromobutane proceeded with the change in solution color from colorless to yellowish. After removing the unreacted 1-vinylimidazole and 1-bromobutane at 50 °C under vacuum, a viscous yellowish solution of C₄-Br was obtained. The purity of C₄-Br was confirmed by ¹H-NMR in deuterated water.²²

2.2.2 Step II: free radical polymerization of C₄–Br. The precursor polymer PC₄-Br was prepared via free radical polymerization of C₄–Br (356.5 g, 1.54 mol) in Milli-Q water (200 mL) with an initiator of AIBN (7.662 g, 0.0467 mol) at 60 °C for 16 h. The molar ratio of the monomer to the initiator was set at 100. After polymerization, the obtained solution was dialyzed against Milli-Q water for 3 days using a dialysis tube (Fisher Scientific Japan, Ltd), with a nominal molecular cut-off of 6000–8000. The Milli-Q solvent was replaced with a fresh one 2 times per day. The resultant solution was dried using a freeze-drying method, and PC₄-Br was obtained in powder form.

2.2.3 Step III: counter-anion conversion of PC₄-Br from Br to BF₄ or PFSI anions. PC₄–BF₄ and PC₄–PFSI were prepared by applying the counterion conversion method proposed by Marcilla et al.³⁵ Specifically, PC₄–BF₄ was synthesized by slowly titrating an aqueous solution containing excess amount of Na–BF₄ (10.67 g, 0.50 mol L⁻¹) into an aqueous solution of PC₄-Br (12.08 g, 0.12 mol L⁻¹), followed by the stirring of the mixture for 3 days at room temperature (∼25 °C). The molar ratio of the Na–BF₄ to the repeating unit of PC₄-Br was set at 1.9. The counterion conversion was proceeded soon after titrating the solution of Na–BF₄, resulting in the precipitation of PC₄–BF₄. The precipitate was washed with Milli-Q water until the filtrate remained transparent when adding an aqueous solution containing 0.1 M of Ag–NO₃. Finally, a yellowish chunk of PC₄–BF₄ was obtained after drying the precipitate at T_g + 10 K under vacuum. The same procedure was applied to obtain PC₄–PFSI while setting the molar ratio of alkali salts to the repeating unit at 1.3, i.e., Li-PFSI: 20.25 g, 0.54 mol L⁻¹; PC₄-Br: 9.56 g, 0.12 mol L⁻¹. The final product of the PC₄–PFSI was in powder form. The prepared PILs were then stored in a desiccator before use. The glass transition temperatures of PC₄–BF₄ (T_g = 141 °C) and PC₄–PFSI (T_g = 51 °C) were reported from literature.^37,38

2.3 Preparation of the test mixture

Our test mixtures consist of the PIL and solvent mixture of an IL and a non-ionic DMF. We selected the appropriate IL with its ionic structures similar to those of the PIL, i.e., Bmim–BF₄ for PC₄–BF₄ and Bmim-PFSI for PC₄–PFSI since prior literature^39–41 reported the change in the viscosity of ILs by the dissolution of ions consisting of different chemical structures. The test mixture was prepared using two different methods, depending on the concentration of the PIL and the IL. At high concentrations (both c_p and c_IL ≥ 0.01 M), test mixtures were prepared by directly adding the components into a glass vial. The PIL was dissolved quickly and homogeneous solutions were obtained by shaking the vial gently at room temperature. The concentration of ILs, c_IL, in the high concentration regime, was calculated as where m_IL, d_mix, M₀, and m_mix are the mass of ILs, the density of the solvent mixture, the molar mass of ILs, and the mass of the solvent mixture, respectively. The density of the solvent mixture d_mix was measured using a density meter (DMA 35 Basic, Anton Paar) at room temperature (∼25 °C), and the plot of d_mixversus c_IL is provided in Fig. S3 of the ESI.† The monomer concentration of PILs, c_p, was calculated as the ratio of the number of moles of the repeating unit to the volume of the solvent mixture added to the polymer sample: where m_p and M_r are the mass of PILs and the molar mass of the repeating unit of PILs associated with the counter-anion, respectively. At low concentrations of c_p and c_IL, the test mixtures were prepared by diluting more concentrated solutions. The value of c_IL varied in the range of 0 M ≤ c_IL ≤ 5.26 M for the mixture of Bmim–BF₄ and DMF and 0 M ≤ c_IL ≤ 2.91 M for the mixture of Bmim-PFSI and DMF, with 1.77 × 10⁻⁴ M ≤ c_p ≤ 3.16 × 10⁻¹ M. The obtained solutions were hermetically sealed, and then stored in a desiccator while maintaining humidity lower than 30% until use.

2.4 Shear viscosity measurements

The shear viscosity η of the test mixture at 25 °C was measured using a strain-controlled rheometer ARES-G2 (TA Instruments) by varying shear rates [small gamma, Greek, dot above] from 0.1 s⁻¹ to 1000 s⁻¹. A stainless steel cone and plate geometry with 50 mm in diameter and 1° in cone angle was used as an upper geometry, while a stainless steel flat plate with 60 mm in diameter was attached into an advanced Peltier system (TA Instruments) as a lower geometry to regulate temperature with temperature accuracy of ±0.1 °C. The sample solution loaded between the top and bottom geometry was covered with a solvent trap to prevent both moisture absorption from the ambient environment and the sample evaporation. The obtained shear viscosity curve was then used to estimate the zero-shear viscosity of both solvent and polymer solutions.

3 Results and discussion

3.1 Salt-free solutions in DMF

Fig. 3(a) shows the dependence of the measured shear viscosity η at 25 °C on the shear rate [small gamma, Greek, dot above], i.e., the so-called shear viscosity curve, for PC₄–BF₄ solutions in non-ionic DMF at representative monomer concentrations. The value of η increased monotonically with increasing c_p. For a given c_p, e.g., at c_p = 3.16 × 10⁻³ M (red open square in Fig. 3(a)), the shear viscosity remained a constant at low [small gamma, Greek, dot above] and then decreased with increasing [small gamma, Greek, dot above], showing a typical shear thinning behavior observed for polymer solutions. A similar trend of η with respect to the increasing [small gamma, Greek, dot above] and c_p was observed for PC₄–PFSI solutions, as shown in Fig. 3(b).

Fig. 3 Shear viscosity curves of (a) PC₄–BF₄ and (b) PC₄–PFSI in non-ionic DMF at various representative monomer concentrations c_p. The value of the shear viscosity η at 25 °C is plotted as a function of the shear rate [small gamma, Greek, dot above].

The observed increase of the solution shear viscosity with the increasing PILs concentration c_p can be further analyzed by estimating the specific viscosity η_sp, defined as³³

where η₀ and η_s are the zero-shear viscosity of the polymer solution and the solvent, respectively. Fig. 4 shows the dependence of η_sp on c_p for PC₄–BF₄ and PC₄–PFSI solutions in DMF. The plot also includes the η_sp data for PC₄-TFSI solutions in DMF (red symbols) reported in our previous study.²² Here, the values of η₀ and η_s, used to calculate η_sp by eqn (6), were estimated by averaging the shear viscosity data in Fig. 3 at shear rates where η was independent of [small gamma, Greek, dot above] at low [small gamma, Greek, dot above]. In Fig. 4, the values of η_sp are very similar among the three PILs in DMF over the entire c_p range investigated. Since the specific viscosity is related to the chain size in a given solvent,³³ our results indicate that three different PIL chains in our studies are expanded equally due to the electrostatic interaction. As a result, the charge fraction, characterized by A in eqn (2), for PC₄–BF₄ and PC₄–PFSI in DMF was found to be A = 2, the same value determined for PC₄-TFSI in DMF in our previous study.²¹

Fig. 4 The dependence of the specific viscosity η_sp at 25 °C on the monomer concentration c_p for PC₄–BF₄ (black circles), PC₄-TFSI (red squares), and PC₄–PFSI (blue triangles) solutions in DMF. The green line represents the predicted slope of η_sp against c_p for dilute (DL) polymer solutions, i.e., η_sp,DL ∝ c_p^1.0, while the cyan dashed line represents the predicted slope of η_sp against c_p for salt-free semidilute unentangled (SU) solutions at c_IL = 0 M, i.e., η_sp,SU ∝ c_p^0.5, given by eqn (1).²⁵ The η_sp data for PC₄-TFSI were copied from ref. 22.

We also found that the dependence of η_sp on c_p was independent of three different counter-anions used in our studies, see Fig. 4. The value of η_sp increased linearly with increasing c_p for c_p < 3 × 10⁻³ M, beyond which the increase of η_sp with c_p became more gradual at higher c_p. In particular, the power-law exponent changed from η_sp ∝ c_p^1.0 to η_sp ∝ c_p^0.5 at η_sp ∼ 1, corresponding to the transition from dilute (DL) to semidilute unentangled (SU) polymer concentration regimes for salt-free solutions of polyelectrolytes in good solvents.²⁵ Consequently, the overlap monomer concentration could be determined as . Thus, our result in the SU regime indicates that DMF, used as a non-ionic solvent, acts as a good solvent for PC₄–BF₄ and PC₄–PFSI. As the c_p was further increased, the chain overlap usually grows and the motion of a polyelectrolyte chain starts to be constrained topologically by other chains. Such polymer concentration regime is called as the semidilute entangled (SE) regime, and the specific viscosity in the SE regime is predicted to be scaled as η_sp,SE ∝ c_p^1.5 for salt-free solutions.²⁵ However, the measured η_sp for exhibited a c_p – dependence weaker than the model predicted of η_sp,SE ∝ c_p^1.5, indicating that our tested PIL solutions (3.0 × 10⁻² M < c_p < 3.16 × 10⁻¹ M) still lie in the SU regime.

3.2 Salt-rich solutions in the mixture of DMF and ILs

We now investigate the effect of the ion diameter of ILs on the charge screening behavior for PIL solutions in the SU regime. In doing so, we measured η_sp of PC₄–BF₄ and PC₄–PFSI solutions at a fixed c_p in the semidilute unentangled polymer concentration regime while varying c_IL.

3.2.1 Charge screening behavior with small BF₄ anions. Fig. 5 shows shear viscosity curves for PC₄–BF₄ in the mixture of DMF and Bmim–BF₄ obtained at a fixed c_p = 0.25 M while varying c_IL. When adding Bmim–BF₄ to the solvent mixture, the value of η decreased with increasing c_IL for c_IL ≤ 0.222 M, showing a typical Debye screening behavior for polyelectrolyte solutions.^42–45 On the other hand, for c_IL > 0.222 M, the η increased monotonically with increasing c_IL until c_IL reached its saturation concentration for the mixture of DMF and Bmim–BF₄, i.e., c_IL = 5.26 M for pure Bmim–BF₄. The observed increase in η is mainly caused by an increase in the solvent viscosity with respect to the increasing c_IL. Fig. 6 shows the dependence of the zero-shear solvent viscosity η_s at 25 °C on c_IL for the solvent mixture of Bmim–BF₄ and DMF: the value of η_s started to increase rapidly with increasing c_IL at c_IL ∼ 0.2 M.

Fig. 5 Shear viscosity curves of the PC₄–BF₄ in the mixture of DMF and Bmim–BF₄ at c_p = 0.25 M. The values of the shear viscosity η at various representative Bmim–BF₄ concentrations are plotted as a function of the shear rate [small gamma, Greek, dot above].

Fig. 6 The dependence of the zero-shear viscosity η_s at 25 °C on the IL concentration c_IL for the solvent mixture of Bmim–BF₄ and DMF.

Next, we estimated the specific viscosity η_sp using eqn (6), and the obtained values of η_sp were plotted as a function of c_IL in Fig. 7. The η_sp remained a constant for c_IL < 2 × 10⁻³ M, and then decreased with increasing c_IL at higher c_IL until c_IL reached its saturation value, i.e., c_IL = 5.26 M for pure Bmim–BF₄. We also observed a similar trend of η_sp against c_IL for a PC₄–BF₄ solution at a smaller c_p = 0.05 M, shown as red circles in Fig. 7. The absence of a clear upturn of the measured η_sp suggests that the charge screening is completed before the charge underscreening takes effect on η_sp. To examine this hypothesis, we compared the measured η_sp at c_p = 0.25 M with the model prediction of η_sp,SU, given by eqn (5), while assuming η^int_sp = 0, i.e., neglecting the complete charge screening effect on η_sp. The dashed curve in Fig. 7 represents the fitted curve of η_sp,SU, obtained using eqn (5) at η^int_sp = 0. In the curve fitting, the value of ε_r was obtained from independent measurements of ε_r, as shown in Fig. S4 of the ESI.† The diameter of Bmim–BF₄ ions was estimated as a = 0.34 nm, in good agreement with the value predicted by Lee et al.³⁴ by using a = c_IL^−1/3/2. Moreover, since the chemical structure of the repeating unit of PC₄–BF₄ is similar to that of Bmim–BF₄, the monomer size b should be similar to the ion diameter (b = a). As a result, there was only one adjustable parameter in the curve fitting, that is, the scaling prefactor K₁ determining the vertical position of the fitted curve. From the comparison shown in Fig. 7, we found that the measured η_sp agreed well with the predicted η_sp,SU (at η^int_sp = 0) only for c_IL < 3 × 10⁻² M. However, a significant discrepancy between the predicted curve of η_sp,SU and the measured η_sp was observed for c_IL > 3 × 10⁻² M. In particular, although the modified charge screening model, given by eqn (5), predicts the upturn of η_sp to occur at η_sp ∼ 3 and c_IL ∼ 3 M, the measured η_sp was significantly larger in magnitude and exhibited an asymptotic decrease of η_sp around c_IL = 3 M. A similar result was obtained for the comparison between the measured η_sp and the model prediction of η_sp,SU at c_p = 0.05 M.

Fig. 7 The dependence of the specific viscosity η_sp at 25 °C on the Bmim–BF₄ concentration for PC₄–BF₄ in the mixture of Bmim–BF₄ and DMF at two monomer concentrations c_p = 0.25 M (black squares) and c_p = 0.05 M (red circles). The dashed curve represents the curve fit of η_sp,SU to the measured η_sp at η^int_sp = 0, while the solid curve represents the predicted curve of η_sp,SU to the measured η_sp, obtained with η^int_sp = 11.2 at c_p = 0.25 M and η^int_sp = 1.1 at c_p = 0.05 M.

The observed discrepancy between the model prediction and the experimental result can be explained by considering the complete charge screening effect on η_sp. The best curve fit of η_sp,SU, obtained using eqn (5) with varying η^int_sp, was shown as the solid curve in Fig. 7. The predicted curve of η_sp,SU captured the measured η_sp over the entire c_IL range, regardless of different values of c_p. Moreover, as shown in Fig. 8, the estimated values of η^int_sp, i.e., η^int_sp = 11.2 at c_p = 0.25 M and η^int_sp = 1.1 at c_p = 0.05 M, satisfied the required scaling law of η^int_sp ∝ c_p^1.3 for neutral polymer solutions in good solvents. A good agreement between the model prediction and the experimental results confirms our hypothesis that the charge on the PC₄–BF₄ chain is fully screened in the mixture of Bmim–BF₄ and DMF. Our results demonstrate that the charge underscreening can be suppressed when choosing IL ions sufficiently small (i.e., when a ≤ 0.34 nm).

Fig. 8 The dependence of the intrinsic specific viscosity η^int_sp on the monomer concentration c_p for PC₄–BF₄ in the mixture of Bmim–BF₄ and DMF (black squares) and PC₄–PFSI in the mixture of Bmim-PFSI and DMF (blue triangles). The value of η^int_sp is obtained from the curve fitting to the measured η_sp with the model prediction of η_sp,SU, given by eqn (5). The plot includes the data for PC₄-TFSI in the mixture of Bmim-TFSI and DMF, copied from our previous study in ref. 22. The dashed line represents the scaling relation of η^int_sp ∝ c_p^1.3 predicted for neutral polymers in good solvents.

3.2.2 Charge screening behavior with large PFSI anions. If the dominant charge screening process for PIL solutions depends on the diameter of IL ions, we anticipate that the viscoelastic response of PC₄–PFSI solutions will be affected by the charge underscreening since PFSI anions are larger in diameter than TFSI anions. Fig. 9 shows the dependence of η_sp on c_IL for PC₄–PFSI in the mixture of Bmim-PFSI and DMF at a fixed c_p = 0.20 M. The value of η_sp remained a constant at low c_IL, and then decreased with increasing c_IL until c_IL ∼ 1 M. However, the η_sp increased with increasing c_IL for c_IL > 1 M, showing an upturn of the measured η_sp. A similar upturn of η_sp was observed at c_IL ∼ 1 M for PC₄–PFSI solutions at a smaller c_p = 0.05 M, shown as red circles in Fig. 9.

Fig. 9 The dependence of the specific viscosity η_sp at 25 °C on the Bmim-PFSI concentration for PC₄–PFSI in the mixture of Bmim-PFSI and DMF at two monomer concentrations c_p = 0.20 M (black squares) and c_p = 0.05 M (red circles). The solid curve represents the curve fit of η_sp,SU to the measured η_sp at η^int_sp = 0, while the dashed curve represents the predicted curve of η_sp,SU to the measured η_sp, obtained with η^int_sp = 2.0 at c_p = 0.20 M and η^int_sp = 0.40 at c_p = 0.05 M.

We compared the dependence of the measured η_sp on c_IL with the model prediction of η_sp,SU, given by eqn (5). The best fit curve was obtained with a = 0.57 nm and η^int_sp = 2.0 for PC₄–PFSI solutions at c_p = 0.20 M, shown as the solid curve in Fig. 9. Note that the ion diameter estimated from our curve fit based on eqn (5) is about 1.4 times larger than the value (a = 0.42 nm) predicted by using c_IL^−1/3/2 based on Lee et al.³⁴ This discrepancy is likely due to different screening process in our experimental systems. Lee et al.³⁴ confined ILs between smooth plates and used surface force apparatus to estimate the screening length from the measured separation force-distance profiles. In our system, a three dimensional charge screening process on charged polymer molecules with strong steric constraints for large PFSI anions may increase a effectively, resulting in a reduction of c_IL where the charge underscreening is observed (see eqn (4)). We also performed curve fitting to the measured η_sp for PC₄–PFSI solutions at c_p = 0.05 M by using eqn (5) with η^int_sp = 0.4 while keeping the ion diameter fixed as a = 0.57 nm. As shown in Fig. 8, we obtained the scaling of η^int_sp ∝ c_p^1.3 using η^int_sp values from the curve fitting, further validating the fitting procedure shown in Fig. 9. The predicted solid curve of η_sp,SU is able to capture the measured η_sp over the entire c_IL range, regardless of c_p. These results indicate that the charge underscreening is dominant for the dependence of η_sp on c_IL for PC₄–PFSI in the mixture of Bmim-PFSI and DMF.

4 Conclusions

The electrostatic interaction plays an important role in determining the viscoelastic properties of PIL solutions. Therefore, it is important to understand how IL ions screen the charge on PIL chains and affect the viscoelastic properties of PILs in IL solutions. In this study, we evaluated the dependence of the specific viscosity η_sp in the semidilute unentangled (SU) regime on the IL concentration c_IL for two PIL solutions possessing anions with different ion diameters: PC₄–BF₄ in the mixture of Bmim–BF₄ and DMF and PC₄–PFSI in the mixture of Bmim-PFSI and DMF. We showed that the η_sp for PC₄–BF₄ solutions with small anions exhibited an asymptotic decrease with the increasing c_IL, while the value of η_sp for PC₄–PFSI solutions with large anions decreased initially at low c_IL but increased at high c_IL as c_IL was increased. By comparing the measured η_sp with the model prediction of η_sp,SU by eqn (5), the observed asymptotic decrease of η_sp for PC₄–BF₄ solutions was attributed to the full screening of charges on the PC₄–BF₄ chain. On the other hand, the upturn of η_sp observed for PC₄–PFSI solutions was caused by the charge underscreening associated with the increase in the screening length at high c_IL. Our results demonstrate that the ion diameter of IL ions is a key parameter determining the charge screening mechanism and thus the viscoelastic properties of PILs in IL solutions.

Author contributions

Conceptualization, A. M. and A. Q. S.; data collection, A. M.; data analysis, A. M.; funding acquisition, A. M. and A. Q. S.; writing-original draft, A. M.; writing-review & editing, A. M. and A. Q. S. Both A. M. and A. Q. S. have read and agreed to the published version of the manuscript.

Conflicts of interest

The authors declare no conflict of interest.

Acknowledgements

A. M and A. Q. S acknowledge the support of the Okinawa Institute of Science and Technology Graduate University with subsidy funding from the Cabinet Office, Government of Japan. A. M. acknowledges funding from the Japanese Society for the Promotion of Science (Grants-in-Aid for Early-Career Scientists, Grant No. 21K14686). Both authors acknowledge the funding from the Joint Research Projects (JRPs) supported by JSPS. A. M. also gratefully acknowledges the financial support of University of Fukui to complete and publish this work.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d2sm00484d

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