Solid-state polymer electrolytes have become increasingly attractive for lithium-based battery applications as they exhibit low volatility, provide sufficient mechanical strength, and increase the thermal and electrochemical stability of batteries in comparison to conventional liquid electrolytes that use flammable organic solvents.^[Reference Young, Kuan and Epps^1, Reference Hallinan and Balsara^2] Among the various macromolecular architectures of polymer electrolytes, block polymers (BPs) are of particular interest due to their ability to self-assemble into ordered nanostructures such as lamellae (LAM), hexagonally packed cylinders (HEX), body-centered cubic spheres (BCC), and double-gyroid (DG) networks.^[Reference Matsen^3–Reference Widin, Schmitt, Schmitt, Im and Mahanthappa^5] A number of studies have shown that BP nanostructures, which are governed by the segregation strength (χN, χ: Flory–Huggins interaction parameter and N: degree of polymerization) and volume fraction (f) of the block, can form well-defined conducting pathways, which leads to enhanced ionic conductivities in comparison to corresponding random copolymers.^[Reference Ye, Sharick, Davis, Winey and Elabd^6, Reference Soo, Huang, Jang, Chiang, Sadoway and Mayes^7] Of the more common BP nanostructures, the DG network phase is one of the most appealing due to its three-dimensional (3D) domain connectivity.^[Reference Meuler, Hillmyer and Bates^8] A 3D continuous morphology allows each domain to contribute directly to the modulus of the material, which leads to improvements in toughness, stress at break, and high-temperature creep resistance;^[Reference Dair, Honeker, Alward, Avgeropoulos, Hadjichristidis, Fetters, Capel and Thomas^9, Reference Pernot, Baumert, Court and Leibler^10] thus, a network morphology is desirable from a mechanical property perspective. Additionally, network morphologies can form 3D conducting pathways, which enhances ion transport in battery electrolyte membranes without costly and time-consuming alignment procedures that may be necessary for 1D and 2D nanostructures.^[Reference Young and Epps^11–Reference Weber, Ye, Schmitt, Banik, Elabd and Mahanthappa^15] These advantages make BP networks promising candidates for potential conducting applications.

However, the design of network-forming polymer electrolytes is complicated by the relatively narrow network composition windows in the BP phase diagram, especially at high effective segregation strengths (χ _effN).^[Reference Matsen^3] As one avenue to overcome this limitation, recent efforts on tapered block polymers (TBPs) are noteworthy.^[Reference Kuan, Roy, Rong, Hsiao and Epps^16, Reference Roy, Park, Young, Mastroianni, Tureau and Epps^17] TBPs are a class of BPs with well-defined and synthetically controlled interfacial regions that taper from one polymer block to another. A common example used in this work is shown in Fig. 1(a). Previous studies have reported that incorporating a tapered region between pure blocks in a copolymer can decrease the effective segregation strength by reducing χ _eff;^[Reference Pakula and Matyjaszewski^18, Reference Hodrokoukes, Floudas, Pispas and Hadjichristidis^19] in other words, BP thermal morphology transitions may be tuned independent of the chemical constituents and molecular mass using tapered interfaces. Moreover, theoretical work by Hall and co-workers demonstrated that the normal-tapered interface in BPs can relieve some of the packing frustration inherent in the DG morphology, thus widening the network phase window and increasing the propensity to generate network structures.^[Reference Brown, Sides and Hall^20] Therefore, TBPs offer exciting potential for creating novel polymer electrolytes with complex co-continuous nanostructures.

Figure 1.

(a) Illustration of non-tapered, normal-tapered, and inverse-tapered BPs. (b) Phase behavior of non-tapered P(S-OEM), normal-tapered P(S-SOEM-OEM), and inverse-tapered P(S-OEMS-OEM) BPs as a function of the ion-doping ratio. LAM, lamellae; HEX, hexagonally packed cylinders; DIS, disordered phase; DG, double gyroid.

In this work, we systematically investigated the phase behavior of lithium ion-doped tapered and non-tapered BPs based on poly(styrene-b-oligo-oxyethylene methacrylate) [P(S-OEM)] over a range of ion-doping ratios. The polymers were synthesized via atom transfer radical polymerization and doped with lithium trifluoromethanesulfonate (lithium triflate, LiCF₃SO₃) as described elsewhere.^[Reference Kuan, Remy, Mackay and Epps^21] The normal-tapered and inverse-tapered interfaces between blocks were generated through a semi-batch feed approach using programmable syringe pumps. All polymers had consistent number-average molar masses (M _n ≈ 33 kg/mol) and overall polymer compositions (f _POEM ≈ 0.52); see Table S1 in Supplementary Material. Both the normal-tapered and inverse-tapered BPs had a taper volume fraction of ≈ 0.6. The associated phase behavior is illustrated in Fig. 1(b). Over the experimental range of salt-doping levels, the non-tapered samples exhibited a transition from LAM to HEX, while the inverse-tapered BPs showed a transition from a disordered morphology (DIS) to HEX. Interestingly, the normal-tapered materials demonstrate an increase in the richness of phase behavior, sampling several morphologies including the desirable DG network. Thus, it is evident that the tapered interfaces significantly influence the phase behavior of ion-doped BPs.

The morphologies of all polymers were identified via small-angle X-ray scattering (SAXS) performed on the DND-CAT 5-ID-D beamline at the Advanced Photon Source (APS, Argonne National Laboratory). SAXS traces of non-tapered, normal-tapered, and inverse-tapered BPs as a function of ion-doping ratio ([EO]:[Li]) are shown in Fig. 2. In all cases, as the lithium ion concentration increases, the primary scattering peak location (q*) shifts to smaller q values, indicating larger domain spacings (d = 2π/q*). This shift is expected as ion-doping previously has been shown to induce polymer chain stretching.^[Reference Young and Epps^22] Additionally, primary diffraction peaks of the ion-doped polymers appear to broaden at the higher ion concentrations ([EO]:[Li] = 8:1 and 6:1). This broadening may be attributed to a combination of higher segregation strength and the transient crosslinking between lithium ions and unpaired electrons on the oxygen atoms in POEM block.^[Reference Epps, Bailey, Pham and Bates^23] These two factors may reduce polymer chain mobility or ordering kinetics. In Fig. 2(a), the non-tapered P(S-OEM) samples with neat (non-doped), 48:1, and 24:1 ion-doping ratios exhibit a LAM morphology with observed SAXS reflections at q/q* = 1, 2, and 3, whereas the samples with ion-doping ratios from 18:1 to 6:1 display HEX structures with observed SAXS reflections at q/q* = 1, √3, 2, √7, and 3.^[Reference Young and Epps^22] Three additional ion-doped P(S-OEM) samples ([EO]:[Li] = 22:1, 20:1, and 19:1) were prepared to examine the BP morphologies between 24:1 and 18:1 ion-doping ratios. The corresponding SAXS patterns (see Fig. S1 in Supplementary Material) indicate that the LAM-to-HEX phase transition occurs between 20:1 and 19:1 ion-doping levels in the non-tapered BP.

Figure 2.

SAXS profiles for (a) P(S-OEM), (b) P(S-SOEM-OEM), and (c) P(S-OEMS-OEM) with various ion-doping ratios at 120 °C. The relative peak ratios (q/q*) are indicated by arrows, and the phase assignment is color-coded: red, LAM; green, HEX; gray, DIS; purple, DG. All SAXS samples were pre-annealed at 120 °C for 2 h, heated to 150 °C for 2 h, and then cooled to 30 °C, all under dynamic vacuum. Data are shifted vertically for clarity.

In Fig. 2(b), the SAXS patterns for normal-tapered P(S-SOEM-OEM) demonstrate a disordered morphology at neat and 48:1 ion-doping ratios, whereas the non-tapered P(S-OEM) exhibits a lamellar morphology at the same ion-doping ratios. As both samples have a similar molecular mass and overall composition, this difference in morphology likely is a result of the reduction in χ _eff for the TBPs. Upon the addition of lithium salt to a doping ratio of 24:1, the primary peak narrows noticeably [Fig. 2(b)], suggesting a transition to an ordered nanostructure occurs between [EO]:[Li] = 48:1 and 24:1. The ordered phase in the 24:1 ion-doped P(S-SOEM-OEM) sample, as indicated by the SAXS peaks at q/q* = 1 and 2, likely is LAM. More significantly, P(S-SOEM-OEM) with an 18:1 ion-doping ratio exhibits diffraction peaks at q/q* = √6, √8, √14, and √22. With the primary peak corresponding to q*√6 (q* = q ₁₁₂), the relative peak ratios suggest a DG network morphology.^[Reference Jo, Ahn and Park^13, Reference Tureau and Epps^24] This nanostructure was stable during thermal annealing from 30 to 150 °C. To probe the breadth of the DG phase region, two additional ion-doped normal-tapered samples, [EO]:[Li] = 20:1 and 16:1, were prepared. Although the P(S-SOEM-OEM) sample at a 20:1 ion-doping ratio exhibits a LAM morphology, the 16:1 sample retains the DG network phase (see Fig. S2 in Supplementary Material). This finding indicates that a DG network phase window was generated in the ion-doped TBP system even though no DG morphology was detected in the non-tapered P(S-OEM) BPs at a similar composition over the experimental range of doping ratios. At higher ion concentrations (from [EO]:[Li] = 15:1 to 6:1), P(S-SOEM-OEM) samples show SAXS reflections at q/q* = 1, √3, 2, and √7, which are consistent with HEX structures and similar to the nanostructures at higher ion concentrations in the ion-doped P(S-OEM) system.

For the inverse-tapered P(S-OEMS-OEM), the LiCF₃SO₃-doped polymers retain a disordered morphology from neat (no-salt) to 18:1, and the polymers form a HEX morphology at higher ion concentrations [Fig. 2(c) and Fig. S3]. The expanded disordered phase window (from neat to 18:1 instead of from neat to 48:1 in the normal-tapered material) is expected as the inverse-tapered interfaces are suspected to have a greater ability to increase block compatibility (i.e. lowering of order–disorder transition temperatures) relative to their normal-tapered analogs.^[Reference Roy, Park, Young, Mastroianni, Tureau and Epps^17, Reference Brown, Sides and Hall^20, Reference Singh, Tureau and Epps^25]

Transmission electron microscopy (TEM, JEM-3010) and dynamic mechanical analysis (DMA, ARES-G2 rheometer, TA Instruments) also were used to characterize the self-assembly of ion-doped tapered and non-tapered BPs. The experiments were performed on samples with ion-doping ratios of 18:1, in which the three polymers exhibited different morphologies according to the SAXS data. One can see in the TEM micrograph of LiCF₃SO₃-doped P(S-OEM) [Fig. 3(a)] that there are parallel stripes and hexagonally packed dots, supporting a HEX assignment. The TEM micrograph for LiCF₃SO₃-doped P(S-SOEM-OEM) in Fig. 3(b) displays the “wagon-wheel” [111] projection, which is characteristic of DG network structures.^[Reference Meuler, Hillmyer and Bates^8, Reference Roy, Park, Young, Mastroianni, Tureau and Epps^17, Reference Tureau and Epps^24] The TEM micrograph given in Fig. 3(c) lacks obvious ordering, suggesting a disordered morphology for the inverse-tapered P(S-OEMS-OEM).

Figure 3.

TEM images for LiCF₃SO₃-doped polymers at [EO]:[Li] = 18:1: (a) P(S-OEM); (b) P(S-SOEM-OEM); (c) P(S-OEMS-OEM). TEM specimens were cut into ≈70 nm slices from the thermally annealed SAXS samples at −120 °C on a cryo-microtome. The POEM domains were stained preferentially with RuO₄ vapor to enhance domain contrast prior to imaging. (d) Isothermal frequency sweeps for 18:1 LiCF₃SO₃-doped P(S-OEM) at 110 °C and 18:1 LiCF₃SO₃-doped TBPs. DMA results for both TBPs were shifted according to time-temperature superposition using a reference temperature of 70 °C. 8 mm diameter parallel plates were utilized for the DMA experiments. Data were collected at a strain of 3%. Dash lines are included for visual clarity of the terminal responses. The number in the legend represents the [EO]:[Li] ion-doping ratio for the sample. The brightness in (c) was enhanced for visual clarity.

The isothermal frequency sweep analysis for all three ion-doped polymers at [EO]:[Li] = 18:1 is shown in Fig. 3(d). Linear dynamic shear moduli of BP melts strongly are influenced by the morphology in the terminal response regime (low-frequency region), in which the storage modulus follows a power-law relationship to frequency (G′ ∝ ω^a; G′ is the storage modulus, and ω is the frequency).^[Reference Kossuth, Morse and Bates^26] The power-law exponent, a, ranges from 0 for an elastic solid to 2 for a disordered melt.^[Reference Kossuth, Morse and Bates^26] The DMA data for LiCF₃SO₃-doped P(S-OEM) presents a terminal response with G′ ∝ ω ^1/3, in which the exponent of 1/3 is indicative of a HEX morphology.^[Reference Kossuth, Morse and Bates^26] For LiCF₃SO₃-doped P(S-SOEM-OEM), G′ approaches a plateau as the frequency is decreased. This nearly frequency-independent behavior is a solid-like response that suggests triply periodic structures,^[Reference Kossuth, Morse and Bates^26, Reference Tureau and Epps^27] further supporting a DG phase assignment. For LiCF₃SO₃-doped P(S-OEMS-OEM), the modulus obeys a power law of G′ ∝ ω ² in the low-frequency region. This scaling behavior suggests a disordered phase for P(S-OEMS-OEM) at [EO]:[Li] = 18:1. Both TEM and DMA results are consistent with the morphological characterization data from SAXS. The combination of SAXS, TEM, and DMA strongly indicates that the tapered interfaces present an efficient method for manipulating the morphologies of ion-doped BPs at constant molecular mass and chemical composition.

To further explore the influence of tapered interfaces on BP phase behavior, χ _eff values between pure blocks in non-tapered, normal-tapered, and inverse-tapered BP systems were estimated using random phase approximation (RPA) theory (see Supplementary Material for details).^[Reference Naidu, Ahn, Gong, Kim and Ryu^28–Reference Teran and Balsara^30] The temperature dependence of χ _eff for the neat and LiCF₃SO₃-doped polymers is summarized in Fig. 4. It is important to note that, because the RPA approach for calculating χ _eff requires disordered samples, the window over which χ _eff can be evaluated narrows rapidly with increasing ion concentration. Additionally, as neat P(S-SOEM-OEM) and P(S-OEMS-OEM) samples exhibit nearly featureless SAXS patterns [Figs. 2(b) and 2(c)], the fitting of χ _eff for neat TBPs is not appropriate. The increase of ion concentration in TBPs as shown in Fig. 4, from [EO]:[Li] = 48:1 to 24:1, leads to the increase in χ _eff between two block components. Also, the normal-tapered materials, in both 48:1 and 24:1 ion-doping ratios, exhibit higher χ _eff values in comparison to inverse-tapered analogs, again suggesting the enhanced block compatibility of inverse-taper relative to the normal-taper. Most importantly, the neat P(S-OEM) sample displays the largest χ _eff among all polymers in Fig. 4, demonstrating that tapered interfaces significantly reduced polymer–polymer interactions between blocks, especially for the inverse-tapered materials. This reduction in χ _eff can lead to lower order–disorder transition temperatures, improving materials processability by decreasing processing temperatures and potential solvent usage.

Figure 4.

Temperature dependence of χ _eff for disordered P(S-OEM), P(S-SOEM-OEM), and P(S-OEMS-OEM). The number in the legend represents the [EO]:[Li] ion-doping ratio for the sample.

The normalized domain spacing data (d/d ₄₈, in which d ₄₈ is the domain spacing of the corresponding polymer at an ion-doping ratio of 48:1) for polymers at various ion-doping ratios is given in Fig. 5. (The domain spacing of each sample can be found in Table S2.) The domain spacing of the BPs was calculated using the primary peak location from the SAXS patterns in Fig. 2. In all cases, the normalized domain spacing increases as the ion concentration increases. For the majority of the ion-doping ratios, the normalized domain spacings of LiCF₃SO₃-doped P(S-OEM) materials are larger than those of LiCF₃SO₃-doped TBPs, especially in comparison to the inverse-tapered P(S-OEMS-OEM) system. As all three samples are of comparable molecular mass and composition, the smaller domain spacing changes in TBPs most likely are caused by the presence of the tapered interfaces. Similar domain spacing behavior was suggested by Hall and co-workers using self-consistent field theory calculation.^[Reference Brown, Sides and Hall^20] The Hall work on TBP domain spacings demonstrated that different chain conformations at the block interface could impact the polymer chain stretching at increasing χN, which is consistent with the findings herein.

Figure 5.

Normalized domain spacings as a function of ion-doping ratio for P(S-OEM), P(S-SOEM-OEM), and P(S-OEMS-OEM). d ₄₈ represents the domain spacing of each polymer at [EO]:[Li] = 48:1. Error bars are standard deviations from the SAXS data. For comparison purposes, the normalized domain spacing of the DG-forming P(S-SOEM-OEM), [EO]:[Li] = 18:1, was using d = 2π/(q*√6).

In summary, the self-assembly of lithium ion-doped P(S-OEM) BPs and TBPs exhibits a strong dependence on the presence of tapered interfaces, the profile of the tapers (normal or inverse), and the concentration of lithium ions. Of particular importance is the experimental discovery of a DG network phase window in the ion-doped, normal-tapered system despite the fact that no network morphologies were detected in the non-tapered and inverse-tapered materials. Moreover, this work shows that tapered interfaces present a promising strategy for reducing the polymer–polymer interactions and polymer chain stretching upon lithium ion addition. The results highlighted herein suggest an advanced design pathway for the next generation of nanostructured and highly processable materials in transport applications.