Improved Route to Linear Triblock Copolymers by Coupling with Glycidyl Ether-Activated Poly(ethylene oxide) Chains

Poly(ethylene oxide) block copolymers (PEOz BCP) have been demonstrated to exhibit remarkably high lithium ion (Li+) conductivity for Li+ batteries applications. For linear poly(isoprene)-b-poly(styrene)-b-poly(ethylene oxide) triblock copolymers (PIxPSyPEOz), a pronounced maximum ion conductivity was reported for short PEOz molecular weights around 2 kg mol−1. To later enable a systematic exploration of the influence of the PIx and PSy block lengths and related morphologies on the ion conductivity, a synthetic method is needed where the short PEOz block length can be kept constant, while the PIx and PSy block lengths could be systematically and independently varied. Here, we introduce a glycidyl ether route that allows covalent attachment of pre-synthesized glycidyl-end functionalized PEOz chains to terminate PIxPSy BCPs. The attachment proceeds to full conversion in a simplified and reproducible one-pot polymerization such that PIxPSyPEOz with narrow chain length distribution and a fixed PEOz block length of z = 1.9 kg mol−1 and a Đ = 1.03 are obtained. The successful quantitative end group modification of the PEOz block was verified by nuclear magnetic resonance (NMR) spectroscopy, gel permeation chromatography (GPC) and differential scanning calorimetry (DSC). We demonstrate further that with a controlled casting process, ordered microphases with macroscopic long-range directional order can be fabricated, as demonstrated by small-angle X-ray scattering (SAXS), scanning electron microscopy (SEM) and transmission electron microscopy (TEM). It has already been shown in a patent, published by us, that BCPs from the synthesis method presented here exhibit comparable or even higher ionic conductivities than those previously published. Therefore, this PEOz BCP system is ideally suitable to relate BCP morphology, order and orientation to macroscopic Li+ conductivity in Li+ batteries.

This will be achieved by a new developed synthesis route, which ensures the use of consistent identical and very short as well as commercially available prefabricated PEOz chains for the attachment to BCPs.
Usually, such BCPs are prepared in a stepwise manner by synthesizing each polymer block sequentially [17][18][19]25]. Thus, each polymer block is formed from the respective monomers in a series of polymerization steps according to the principle of living sequential anionic polymerization (cf. Scheme 2I), as it offers the highest control over the polymerization process, hence the dispersity (Đ), and also proceeds without side reactions [5,[17][18][19][26][27][28][29]. However, due to the explosive and highly toxic properties of ethylene oxide (EO) gas, its use implies special safety requirements [30]. Therefore, the use of a short prefabricated PEOz block in our synthesis route leads to the fact that the handling of EO gas monomers during PIxPSyPEOz polymerization can be avoided. In this way, the necessary use of EO gas for the synthesis of PEOz chains can be carried out in a separate and upstream synthesis step.
Thus, in this study, an exact defined methoxy PEO (mPEOz) chain with a modified end group was chosen, enabling it accessible for direct and covalent attachment to the Scheme 1. Controlled compositional variations of the synthetized PI x PS y PEO z BCP by systematically and independently altering the PI x and PS y block lengths while keeping the PEO z block constant. (a) Changing the ratio of the M n of the PI x to the PS y block (M n,PI x /M n,PS y ) by keeping the total M n of the BCP (M n,total ) constant and therefore retaining identical PEO z block proportion. (b) Variation of the PEO z block proportion in the BCP by altering the M n,total and holding M n,PI x /M n,PS y = constant.
Thus, in this study, an exact defined methoxy PEO (mPEO z ) chain with a modified end group was chosen, enabling it accessible for direct and covalent attachment to the stable PI x PS y − carbanion of the living polymer chain. Considering the large variety of suitable end groups, tethering an epoxide end group to the mPEO z chain (EmPEO z ) enables a selective single one-step addition to the PI x PS y − anion by utilization of the strong Li-O interaction (cf. Scheme 2II) [5,17,[31][32][33][34]. This is similar to the general strategy of using epoxides as terminating agents as reported in literature [35][36][37][38][39][40][41]. The strong interaction between the hard oxygen anion and the hard Li + can be well explained based on the concept of "hard" and "soft" acids and bases (HSAB) [32,42]. In addition to the PEO z chain, at the junction point only an extra alcohol group is introduced in the polymer as (poly(isoprene)-b-poly(styrene)-b-alcohol methoxy poly(ethylene oxide) = PI x PS y AmPEO z ).
Our convergent synthetic method based on the modular principle aims to create ac cess to PIxPSyPEOz with constantlythe same very short and well-defined PEOz block, al lowing the PIx and PSy blocks to be varied systematically and independently. Moreover as this synthesis route only utilizes commercially available chemicals, it offers a high re producibility and up-scaling probability, making tailored and precisely defined PIxPSyAmPEOz BCPs accessible for large-scale production. We have already published prior patent application for this synthesis method [43].

End Group Modification (EmPEO 1.9 )
The complete end group modification reaction of mPEO 1.9 to EmPEO 1.9 was carried out at room temperature under argon atmosphere in a glovebox. NaO t Bu (1.5 equiv, 9.32 mmol, 0.896 g) was dissolved in THF (60 mL) and subsequently added to a solution of mPEO 1.9 (1.0 equiv, 6.29 mmol, 12.0 g) in THF (60 mL). After 72 h, epichlorohydrin (8.0 equiv, 50.3 mmol, 4.65 g, 3.94 mL) was added dropwise to the reaction within 15 min and stirred for six days. Subsequently, the volatile components were removed at 55 • C under vacuum and the solid residue was dissolved in THF. Undissolved components, mainly formed sodium chloride (NaCl), were removed by centrifugation (Sigma 3-18KS, Osterode am Harz, Germany, 10000 rpm for 10 min), followed by filtration with syringe filter (PTFE membrane, pore size = 0.2 µm, VWR) and drying at room temperature under vacuum. Afterwards, the product was dissolved in a little amount of toluene at 40 • C, precipitated into cold Et 2 O and collected by centrifugation as before. This process was repeated three times. The resulting EmPEO 1.9 was dried at 30 • C under vacuum < 1 × 10 −6 mbar (yield: 89-93%). The product was characterized by 1 H-nuclear magnetic resonance (NMR) spectroscopy, 13 C-NMR spectroscopy, gel permeation chromatography (GPC), differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA). The complete polymer synthesis reaction of PI x PS y AmPEO 1.9 was carried out at room temperature under argon atmosphere in a glovebox using a glass-coated magnetic stir bar for mixing. The PI x and PS y block was synthesized by living sequential anionic polymerization as reported in the literature (Scheme 2I) [17][18][19]. All PI x PS y AmPEO 1.9 materials were synthesized, as exemplarily described for the PI 14.6 PS 34.8 AmPEO 1.9 in the following, where only the sec-BuLi, monomers (isoprene and styrene) and EmPEO 1.9 amounts were adjusted according to the desired composition (cf. Table 1). The complete PI x PS y AmPEO 1.9 membrane casting process, for preparing the samples for the morphological characterization, was performed under argon atmosphere. In a glovebox, an 8 wt.% solution of the dried PI x PS y AmPEO 1.9 in THF was prepared and followed by transferring the mixture into a PTFE crucible. The filled PTFE crucible was placed in a Schlenk vessel and connected to the argon of a Schlenk line. A very low and constant argon flow over 6 days at room temperature in a THF-saturated atmosphere was used to allow a controlled evaporation to achieve distinct microphase separation.
Subsequently, for small-angle X-ray scattering (SAXS) measurement, the resulting membrane (cf. Figure S17) was carefully broken into smaller pieces in order to fit the sample into the glass capillary (borosilicate glass, outer diameter = 2.1 mm, wall thickness = 0.05 mm, Hilgenberg, Malsfeld, Germany). The filled glass capillary was sealed tightly.
For scanning electron microscopy (SEM) and transmission electron microscopy (TEM) investigations, a small piece of the resulting membrane (cf. Figure S17) was cut into ultrathin sections of about 50-100 nm using a cryo-ultramicrotome (cf. Scheme S2).

Nuclear Magnetic Resonance (NMR) Spectroscopy
The NMR spectra of PI 14.6 PS 34.8 AmPEO 1.9 , PI 35.1 PS 14.8 AmPEO 1.9 and EmPEO 1.9 were recorded using an AVANCE NEO 500 MHz (Bruker, Billerica, MA, USA), that of mPEO 1.9 , PI 24.8 PS 25.0 AmPEO 1.9 and PI 26.1 PS 67.3 AmPEO 1.9 using an AVANCE NEO 400 MHz (Bruker) and for PI 6.8 PS 17.3 AmPEO 1.9 using an AVANCE III 400 MHz (Bruker). NMR measurements with number of scans = 64 were recorded, and the recycle delay D1 between transients was set to 30 s to ensure full relaxation to equilibrium magnetization and thus the acquisition of quantitative spectra, except for mPEO 1.9 . All NMR spectra were recorded at 300 K using CDCl 3 as deuterated solvent, where all signals were referenced to CDCl 3 (δ = 7.3 ppm for 1 H and δ = 77.2 ppm for 13 C relative to tetramethylsilane) [46]. The spectra were analyzed with the software MestReNova (version: 12.0.4-22023, Mestrelab Research, Santiago de Compostela, Spain).

Gel Permeation Chromatography (GPC)
GPC was carried out in THF using an HLC-8320GPC EcoSEC (Tosoh Bioscience, Griesheim, Germany) system equipped with three PSS SDV columns (100, 1000, 100,000 Å) (8 × 300 mm) of 5 µm, a UV and a differential refractive index (RI) detector. The operation temperature was set to 35 • C with a flow rate of 1 mL min −1 . Calibration of the system was carried out with poly(styrene) standards ranging from 800 to 2.2 × 10 6 g mol −1 . Typically, 50 µL of a 2.0 mg mL −1 sample solution was injected onto the columns.

Differential Scanning Calorimetry (DSC)
DSC was conducted using a heat flux calorimeter DSC-Q2000 (TA Instruments, New Castle, DE, USA) with LNCS (Liquid Nitrogen Cooling System) and the Tzero ® -technology for the precise recording of the baseline. Under argon atmosphere (inside glovebox),~10 mg of sample was enclosed in hermetically sealed Tzero ® aluminum pans. Two heating ramps in the temperature range from −140 • C to 190 • C with a heating rate of 10 K min −1 under helium as sample purge (25 mL min −1 ) were measured for all samples. The DSC signals were analyzed with the Universal Analysis 2000 software (version: 4.5A, Build 4.5.0.5, TA Instruments).

Thermogravimetric Analysis (TGA)
For TGA, an aluminum pan was filled with~10 mg of sample and hermitically sealed under argon atmosphere in a glovebox, subsequently loaded to the device without contact to ambient air and pierced in the furnace under helium atmosphere. The measurement was carried out on a TGA-5500 with IR furnace (TA Instruments) under helium flow (25 mL min −1 ) with a constant heating rate of 2 K min −1 from 30 • C to 600 • C. The TGA signals were analyzed with the TA Instruments TRIOS software (version: 5.1.1.46572, TA Instruments).

Small-Angle X-ray Scattering (SAXS)
The instruments "Ganesha-Air" from SAXSLAB/XENOCS (Grenoble, France) and Gallium Anode Low-Angle X-ray Instrument (GALAXI) were used. The X-ray source of the laboratory-based "Ganesha-Air" system is a D2-MetalJet (Excillum, Kista, Sweden) with a liquid metal anode operating at 70 kV and 3.57 mA with Ga-Kα radiation (wavelength λ = 0.134 nm). The beam is further focused with a focal length of 55 cm, using especially made X-ray optics (Xenocs) to provide a very narrow and intense beam at the sample position. Two pairs of scatterless slits are used to adjust the beam size depending on the detector distance. The data were acquired with a position-sensitive detector (PILATUS 300 K, Dectris, Baden-Daettwil, Switzerland). After calibration with silver behenate, the distance from the sample to the detector was set to 950 and 350 mm resulting in a Q-range 0.13-6.00 nm −1 . All samples were sealed in glass capillaries of 2 mm inner diameter. Data reduction and background subtraction were performed using the Python-based project Jscatter [47]. Fitting of radially averaged SAXS curves was done using Scatter [48].

Cryo-Ultramicrotomy
To prepare ultra-thin sections for electron microscopy, a Leica EM UC7 ultramicrotome (Wetzlar, Germany) equipped with an EM FC7 cryo-chamber was used. Temperature of sample, knives and chamber was set to −80 • C. The samples were trimmed with a diamond trimming knife from Diatome (trim 45, Nidau, Switzerland), and ultra-thin sections were made with a cryo-immuno diamond knife also from Diatome (cf. Scheme S2). Ultra-thin sections were collected dry on carbon-coated copper grids and section thickness was set to 50 nm.

Scanning Electron Microscope (SEM)
SEM measurements were performed using a Thermo-Fisher Volumescope (Waltham, MA, USA). Images were taken on unstained samples in high vacuum at an accelerating voltage of 30 kV and a working distance of 10 mm using an annular ring STEM detector in bright field mode at room temperature.

Transmission Electron Microscope (TEM)
For TEM measurements, a JEOL JEM-F200 (Freising, Germany) with field emission gun (FEG) operating at an accelerating voltage of 200 kV was used. Images were taken of the unstained sample with a STEM bright field detector at room temperature.

Strategy
In line with the introductory part, the main focus of this work is to develop a convergent synthesis route which enables the independent and systematic PI x and PS y block variation in BCPs with constantly the same PEO z block size, whereby the complete control over morphology and orientation of the BCP, especially of the very short PEO z block, should be obtained, as this is crucial for its possible application. For this purpose, PEO z blocks with an identical chain length were chosen and introduced into PI x PS y PEO z , in which the PI x and PS y blocks are synthesized by anionic polymerization of the monomers and therefore easily and precisely modified.
To do so, the commercially available and prefabricated mPEO z (M n = 1.9 kg mol −1 ) was activated for the attachment by functionalization with an epoxide end group (yielding EmPEO z ). In our synthesis route, the EmPEO z can be attached and thus covalently linked to the previously anionically synthesized PI x PS y − carbanion by a simple one-step addition (cf. Scheme 2). Herein, it is important that an appropriate end group is selected, because it will have a great influence on the properties of the whole PEO z block of the BCP, especially in our focus of very short PEO z chains [49]. Thus, the use of an epoxide as an end group ensures that the formed junction point in PI x PS y AmPEO z hardly differs from the PI x PS y PEO z obtained by using EO gas, i.e., only by an additional OH-group. This smallest possible difference enables the selective consideration solely of the variation of the two nonpolar blocks between the different synthesized PI x PS y AmPEO z . There are approaches that have been reported in literature thus far in which, for instance, benzophenone or diphenylethylene were attached to the PEO z chain as terminal groups [49]. However, regarding the reported end group modifications, multi-step synthesis has to be employed, making the overall synthesis of a PI x PS y PEO z more complex, and these groups are more chemically different compared to the ether and OH-group with unintended influence on the polarity [50]. Especially in the case of short PEO z chains, this could have a great impact on its domain structure formation.
Considering the end group modification shown in Scheme 3, the PEO z block was end-capped with an epoxide group in a simple literature-known and modified one-pot reaction [51,52]. In the first modification step, the terminal OH-group of mPEO z is selectively deprotonated by a strong base, i.e., NaO t Bu. Afterwards, the formed mPEO z alcoholate attacks the epoxide group of the added epichlorohydrin via a nucleophilic (S N 2) attack to form the desired product EmPEO z (Scheme 3). This method can also be extended for longer (M n = 6 kg mol −1 ) PEO z chains as reported by van Butsele et al. [52]. Here it should be mentioned, that the PEO z block has to be selectively functionalized at only one terminal OH-group. End-capping both terminal OH-groups would lead to the undesired formation of a symmetric five BCP (PI x PS y PEO z PS y PI x ). As mPEO z only possess one terminal OH-group allowing for a distinct functionalization, the linkage to the PI x PS y − anion happens in a selective manner, as indicated in (Scheme 3).
should be obtained, as this is crucial for its possible application. For this purpose, PEOz blocks with an identical chain length were chosen and introduced into PIxPSyPEOz, in which the PIx and PSy blocks are synthesized by anionic polymerization of the monomers and therefore easily and precisely modified.
To do so, the commercially available and prefabricated mPEOz (Mn = 1.9 kg mol −1 ) was activated for the attachment by functionalization with an epoxide end group (yielding EmPEOz). In our synthesis route, the EmPEOz can be attached and thus covalently linked to the previously anionically synthesized PIxPSycarbanion by a simple one-step addition (cf. Scheme 2). Herein, it is important that an appropriate end group is selected, because it will have a great influence on the properties of the whole PEOz block of the BCP, especially in our focus of very short PEOz chains [49]. Thus, the use of an epoxide as an end group ensures that the formed junction point in PIxPSyAmPEOz hardly differs from the PIxPSyPEOz obtained by using EO gas, i.e., only by an additional OH-group. This smallest possible difference enables the selective consideration solely of the variation of the two nonpolar blocks between the different synthesized PIxPSyAmPEOz. There are approaches that have been reported in literature thus far in which, for instance, benzophenone or diphenylethylene were attached to the PEOz chain as terminal groups [49]. However, regarding the reported end group modifications, multi-step synthesis has to be employed, making the overall synthesis of a PIxPSyPEOz more complex, and these groups are more chemically different compared to the ether and OH-group with unintended influence on the polarity [50]. Especially in the case of short PEOz chains, this could have a great impact on its domain structure formation.
Considering the end group modification shown in Scheme 3, the PEOz block was endcapped with an epoxide group in a simple literature-known and modified one-pot reaction [51,52]. In the first modification step, the terminal OH-group of mPEOz is selectively deprotonated by a strong base, i.e., NaO t Bu. Afterwards, the formed mPEOz alcoholate attacks the epoxide group of the added epichlorohydrin via a nucleophilic (SN2) attack to form the desired product EmPEOz (Scheme 3). This method can also be extended for longer (Mn = 6 kg mol −1 ) PEOz chains as reported by van Butsele et al. [52]. Here it should be mentioned, that the PEOz block has to be selectively functionalized at only one terminal OH-group. End-capping both terminal OH-groups would lead to the undesired formation of a symmetric five BCP (PIxPSyPEOzPSyPIx). As mPEOz only possess one terminal OHgroup allowing for a distinct functionalization, the linkage to the PIxPSy − anion happens in a selective manner, as indicated in (Scheme 3). Scheme 3. End group modification of mPEOz to selectively attach a terminal epoxide group to yield EmPEOz.
Another important aspect of the above-described usage of the prefabricated mPEOz block is the accurate characterization prior to its linkage, because a PEOz block that is already attached to the PIxPSy block is relatively small compared to the total BCP and therefore difficult to characterize and control accurately, especially in terms of its Đ.
The straightforward addition of EmPEOz to the reaction solution furthermore simplifies the polymerization by terminating the living PIxPSy − anion because it allows a onestep attachment in the presence of the Li + counterion in nonpolar solvent (Scheme 2II). After the addition of the EmPEOz to the reaction solution, the PIxPSy − anion attacks the Scheme 3. End group modification of mPEO z to selectively attach a terminal epoxide group to yield EmPEO z .
Another important aspect of the above-described usage of the prefabricated mPEO z block is the accurate characterization prior to its linkage, because a PEO z block that is already attached to the PI x PS y block is relatively small compared to the total BCP and therefore difficult to characterize and control accurately, especially in terms of its Ð.
The straightforward addition of EmPEO z to the reaction solution furthermore simplifies the polymerization by terminating the living PI x PS y − anion because it allows a one-step attachment in the presence of the Li + counterion in nonpolar solvent (Scheme 2II). After the addition of the EmPEO z to the reaction solution, the PI x PS y − anion attacks the epoxy group of the EmPEO z via a ring-opening reaction forming an alcoholate group and a covalent bond between the PI x PS y block and the AmPEO z . Hence, the charge of the carbanion is transferred to the O-atom of the alcoholate group. The negative charge on the O-atom of the alcoholate group is directly blocked by the Li + counterion, which strongly reduces the nucleophilicity. Therefore, a new ring-opening reaction with another epoxide group of a second EmPEO z molecule is inhibited due to the strong O-Li-ion pair (Scheme S1), thus blocking a further polymerization, or any other undesired crosslinking or side reaction Polymers 2023, 15, 2128 9 of 26 and highlighting the advantage of this one-pot synthesis route (Scheme 2) [17,31,[37][38][39][40]. Especially, a reaction of the living anions with O 2 is suppressed, so that immediately after the AmPEO z block attachment, the product is stable in air, providing an advantage in terms of reproducibility and up-scalability [53][54][55].
Moreover, the epoxide functionalization allows the EmPEO z to be added to the reaction solution in minimal excess (cf. Table 1), so that the PI x PS y − anions react stoichiometrically to form the PI x PS y AmPEO z and the excess and unbound EmPEO 1.9 is easily washed out after the polymerization reaction.

Synthesis
Triblock copolymers were synthesized in one-pot polymerization in three subsequential steps by living anionic polymerization. As indicated by Scheme 2Ia, the PI x block was prepared from isoprene monomers using sec-BuLi serving as initiator for formation of the living carbanion. Subsequently, the living PI x − anion was used for chain extension by addition of styrene (Scheme 2Ib). In the third step of this synthesis route, the PEO z block was covalently attached to the living PI x PS y − anion via a one-step reaction of the epoxide group-functionalized EmPEO z and thus terminated the polymerization to the BCP (Scheme 2II). The coupling of EmPEO z to a PI x PS y − anion enabled the selective and highly controllable preparation of PI x PS y AmPEO z in which the PEO 1.9 block features an identical chain length and a Ð very close one in all cases. The respective M n,PIx /M n,PSy and thus the M n,total of the BCP can be specifically tailored by systematically varying the used amount of initiator and the PI x and PS y monomers. However, as the living anionic polymerization is highly sensitive to impurities, because they directly lead to the termination of the corresponding living anion, special requirements for the synthesis conditions must always be ensured (cf. experimental section).
Here, it is worth noticing that the reaction of mPEO z to EmPEO z has to be quantitative, as no separation of both can be conducted due to the strong chemical similarity of mPEO z and EmPEO z . Even more, since acidic protons of residual mPEO z would protonate the PI x PS y − anions upon addition and therefore inhibit the reaction of EmPEO z and the PI x PS y − anions, the importance of a quantitative functionalization reaction is emphasized. In order to obtain a quantitative end group modification of mPEO z , the base used for deprotonation of the OH-group has to be a weak nucleophile, as otherwise it would compete with the formed mPEO z alcoholate regarding the S N 2 reaction with epichlorohydrin, thus minimizing the yield of the desired EmPEO z . Additionally, the following conditions have been optimized for the quantitative formation of EmPEO z : (1) The use of NaO t Bu and epichlorohydrin in excess (relative to the mPEO z ). (2) The reaction has to be carried out under argon atmosphere using anhydrous reactants to ensure that the precipitation of the formed NaCl in THF is quantitatively [56]. Furthermore, the absence of H 2 O prohibits the formation of nucleophilic OH − -ions, which would also compete with the formed mPEO z alcoholate regarding the reaction with epichlorohydrin.
By the use of EmPEO 1.9 , different BCPs with constant PEO 1.9 block size were synthesized, using this universally applicable and simplified synthesis method, by systematically varying the M n of their PI x and PS y blocks (cf. Scheme 1), namely PI 6 (cf. Scheme 4). While the M n,total of the BCP and thus the PEO 1,9 block fraction remained constant, the M n,PIx /M n,PSy was varied (cf. Scheme 1a). According to this, for PI 24.8 PS 25.0 AmPEO 1.9 the M n,PIx is equal to the M n,PSy , in the case of PI 35.1 PS 14.8 AmPEO 1.9 the M n,PIx is doubled compared to the M n,PSy , whereas for PI 14.6 PS 34.8 AmPEO 1.9 the M n,PSy is two times larger than the M n,PIx , which is exactly the opposite compared to PI 35.1 PS 14.8 AmPEO 1.9 .
In addition, by keeping a M n,PIx /M n,PSy constant, in which the M n,PSy is doubled compared to the M n,PIx , the PEO 1.9 block proportion was varied by changing the M n,total of the BCP (cf. Scheme 1b). Therefore, by halving the M n,total of PI 14.6 PS 34.8 AmPEO 1.9 , the PEO 1.9 block fraction was doubled in PI 6 Scheme 4. Comparison of the block weight ratio of the prepared PIxPSyAmPEO1.9, which are systematically and independently varied with constantly always the same PEO1.9 block size. The polymer chain length of each block is shown in relation to the theoretical Mn,calc. calculated from the ratio of the used masses of monomers to initiator (cf. Table 1).
In addition, by keeping a Mn,PI x /Mn,PS y constant, in which the Mn,PS y is doubled compared to the Mn,PI x , the PEO1.9 block proportion was varied by changing the Mn,total of the BCP (cf. Scheme 1b). Therefore, by halving the Mn,total of PI14.6PS34.8AmPEO1.9, the PEO1.9 block fraction was doubled in PI6.8PS17.3AmPEO1.9. In contrast, for PI26.1PS67.3AmPEO1.9 the Mn,total was varied exactly in the opposite way, i.e., the Mn,total of PI14.6PS34.8AmPEO1.9 was doubled, resulting in a reduced PEO1.9 block proportion.

NMR Characterization
First, the EmPEO1.9 obtained from the functionalization reaction of mPEO1.9 (Scheme 3) was analyzed for its quality via 1 H-and 13 C-NMR to verify that the end group modification was quantitative as required. The 1 H-NMR spectrum of EmPEO1.9 (Figure 1) shows the proton and satellite peaks (highlighted by the grey box) from the polyether chain in the chemical shift region of δ = 3.4-3.7 ppm (c in orange circle) [51,52]. The sharp singlet at δ = 3.3 ppm (d in grey circle) can be assigned to the three protons of the terminal methoxy group [51,52]. The three protons of the epoxide group attached by functionalization reaction split into three characteristic signals located at δ = 2.5 ppm (a in blue circle), δ = 2.7 ppm (a' in blue circle) and δ = 3.1 ppm (b in yellow circle) [51,52]. The integrals of these three signals are equal and have a value of one with respect to the three protons of the terminal methoxy group, indicating that the attachment of the epoxide group took place quantitatively. Scheme 4. Comparison of the block weight ratio of the prepared PI x PS y AmPEO 1.9 , which are systematically and independently varied with constantly always the same PEO 1.9 block size. The polymer chain length of each block is shown in relation to the theoretical M n,calc. calculated from the ratio of the used masses of monomers to initiator (cf. Table 1).

NMR Characterization
3.3.1. EmPEO 1.9 First, the EmPEO 1.9 obtained from the functionalization reaction of mPEO 1.9 (Scheme 3) was analyzed for its quality via 1 H-and 13 C-NMR to verify that the end group modification was quantitative as required. The 1 H-NMR spectrum of EmPEO 1.9 (Figure 1) shows the proton and satellite peaks (highlighted by the grey box) from the polyether chain in the chemical shift region of δ = 3.4-3.7 ppm (c in orange circle) [51,52]. The sharp singlet at δ = 3.3 ppm (d in grey circle) can be assigned to the three protons of the terminal methoxy group [51,52]. The three protons of the epoxide group attached by functionalization reaction split into three characteristic signals located at δ = 2.5 ppm (a in blue circle), δ = 2.7 ppm (a' in blue circle) and δ = 3.1 ppm (b in yellow circle) [51,52]. The integrals of these three signals are equal and have a value of one with respect to the three protons of the terminal methoxy group, indicating that the attachment of the epoxide group took place quantitatively.
The comparison of the 13 C-NMR spectra of mPEO 1.9 and EmPEO 1.9 ( Figure 2) highlights the characteristic carbon signal changes due to the modification reaction (cf. for entire spectrum of mPEO 1.9 Figure S4 and EmPEO 1.9 Figure S2). For mPEO 1.9 (Figure 2a), the carbon atom signal at δ = 61.7 ppm (a in dark blue circle) corresponds to the carbon atom directly linked to the OH-group and the signal at δ = 72.5 ppm to its directly adjacent carbon atom (b in yellow circle). Both carbon atom signals are not detected in the 13 C-NMR spectrum of the EmPEO 1.9 (Figure 2b), confirming that the functionalization of all OH-groups with epoxide groups to form EmPEO 1.9 is quantitatively [51]. The carbon atoms of the polyether chain at δ = 70.5 ppm (c in orange circle) and the terminal methoxy group at δ = 59.0 ppm (e in light green circle) are not affected during the modification reaction, thus the respective signals can be found in both 13 C-NMR spectra [51]. In contrast to the 13 C-NMR spectrum of mPEO 1.9 (Figure 2a), two carbon atom signals appear at δ = 44.1 ppm (f in light blue circle) and δ = 50.7 ppm (g in brown circle) in 13 C-NMR spectrum of EmPEO 1.9 (Figure 2b) which are characteristic for the attached epoxide group [51]. The comparison of the 13 C-NMR spectra of mPEO1.9 and EmPEO1.9 ( Figure 2) high lights the characteristic carbon signal changes due to the modification reaction (cf. for en tire spectrum of mPEO1.9 Figure S4 and EmPEO1.9 Figure S2). For mPEO1.9 (Figure 2a), the carbon atom signal at δ = 61.7 ppm (a in dark blue circle) corresponds to the carbon atom directly linked to the OH-group and the signal at δ = 72.5 ppm to its directly adjacen carbon atom (b in yellow circle). Both carbon atom signals are not detected in the 13 C-NMR spectrum of the EmPEO1.9 (Figure 2b), confirming that the functionalization of all OH groups with epoxide groups to form EmPEO1.9 is quantitatively [51]. The carbon atoms o the polyether chain at δ = 70.5 ppm (c in orange circle) and the terminal methoxy group a δ = 59.0 ppm (e in light green circle) are not affected during the modification reaction, thu the respective signals can be found in both 13 C-NMR spectra [51]. In contrast to the 13 C-NMR spectrum of mPEO1.9 (Figure 2a), two carbon atom signals appear at δ = 44.1 ppm (f in light blue circle) and δ = 50.7 ppm (g in brown circle) in 13 C-NMR spectrum of Em PEO1.9 (Figure 2b) which are characteristic for the attached epoxide group [51].  The comparison of the 13 C-NMR spectra of mPEO1.9 and EmPEO1.9 ( Figure 2) high lights the characteristic carbon signal changes due to the modification reaction (cf. for en tire spectrum of mPEO1.9 Figure S4 and EmPEO1.9 Figure S2). For mPEO1.9 (Figure 2a), th carbon atom signal at δ = 61.7 ppm (a in dark blue circle) corresponds to the carbon atom directly linked to the OH-group and the signal at δ = 72.5 ppm to its directly adjacen carbon atom (b in yellow circle). Both carbon atom signals are not detected in the 13 C-NMR spectrum of the EmPEO1.9 (Figure 2b), confirming that the functionalization of all OH groups with epoxide groups to form EmPEO1.9 is quantitatively [51]. The carbon atoms o the polyether chain at δ = 70.5 ppm (c in orange circle) and the terminal methoxy group a δ = 59.0 ppm (e in light green circle) are not affected during the modification reaction, thu the respective signals can be found in both 13 C-NMR spectra [51]. In contrast to th 13 C-NMR spectrum of mPEO1.9 (Figure 2a), two carbon atom signals appear at δ = 44.1 ppm (f in light blue circle) and δ = 50.7 ppm (g in brown circle) in 13 C-NMR spectrum of Em PEO1.9 (Figure 2b) which are characteristic for the attached epoxide group [51].  The successful and quantitative attachment of the epoxide group to the mPEO 1.9 molecule was verified by the integrals in 1 H-NMR as well as the altered signals in 13 C-NMR. Furthermore, the absence of additional signals in the 1 H-and 13 C-NMR spectra of EmPEO 1.9 (Figures 1 and 2b) indicated that during the modification reaction, no side reaction occurred, and no impurities were introduced (cf. Figures S1 and S2 for entire spectrum).

PI x PS y AmPEO 1.9
The quantitatively epoxy-functionalized EmPEO 1.9 was used for the synthesis of different PI x PS y AmPEO 1.9 , which were subsequently characterized by 1 H-NMR measurements. In the following, PI 14.6 PS 34.8 AmPEO 1.9 is discussed exemplarily based on its 1 H-NMR result, whereas in Figure S10 and Table S1, the results of all synthesized PI x PS y AmPEO 1.9 are summarized, while the individual spectra are depicted in Figures S5-S9.
The 1 H-NMR spectrum of PI 14.6 PS 34.8 AmPEO 1.9 is displayed in Figure 3. The signals in the range of δ = 7.4-6.2 ppm can be assigned to the five aromatic protons of the phenyl group of PS 34.8 block (red circles). The signal of the olefinic proton from the 1,4-PI 14.6 block (blue circle) is located at δ = 5.2 ppm and the two terminal protons of the 3,4-PI 14.6 block (blue circle) are located at δ = 4.8 and 4.7 ppm, respectively [57]. The integral ratio of the 1,4-PI 14.6 block to the 3,4-PI 14.6 block is 1.00: 0.15, being the same for all prepared PI x PS y AmPEO 1.9 [57]. The protons of the polyether chain of the AmPEO 1.9 (dark green circle) are localized at δ = 3.7 ppm. The signal at δ = 3.4 ppm can be attributed to the terminal methoxy group of AmPEO 1.9 (light green circle), and the alkyl backbone protons of the entire PI 14.6 PS 34.8 AmPEO 1.9 (light grey circles) are located in the range of δ = 2.3-1.3 ppm. The fact that the proton signals from AmPEO 1.9 are still present after the purification procedure of PI 14.6 PS 34.8 AmPEO 1.9 indicates that AmPEO 1.9 was covalently linked to the PI 14.6 PS 34.8 − anion by a nucleophilic attack on the epoxide group of EmPEO 1.9 , as described previously (cf. Scheme 2II). The nonbonded EmPEO 1.9 was removed during the purification procedure because it dissolves in MeOH, which is used in the purification process [58].
The 1 H-NMR spectrum of PI14.6PS34.8AmPEO1.9 is displayed in Figure 3. The si the range of δ = 7.4-6.2 ppm can be assigned to the five aromatic protons of the group of PS34.8 block (red circles). The signal of the olefinic proton from the 1,4-PI1 (blue circle) is located at δ = 5.2 ppm and the two terminal protons of the 3,4-PI1 (blue circle) are located at δ = 4.8 and 4.7 ppm, respectively [57]. The integral rat 1,4-PI14.6 block to the 3,4-PI14.6 block is 1.00: 0.15, being the same for all p PIxPSyAmPEO1.9 [57]. The protons of the polyether chain of the AmPEO1.9 (dark g cle) are localized at δ = 3.7 ppm. The signal at δ = 3.4 ppm can be attributed to the t methoxy group of AmPEO1.9 (light green circle), and the alkyl backbone proton entire PI14.6PS34.8AmPEO1.9 (light grey circles) are located in the range of δ = 2.3-1 The fact that the proton signals from AmPEO1.9 are still present after the purificat cedure of PI14.6PS34.8AmPEO1.9 indicates that AmPEO1.9 was covalently linked PI14.6PS34.8anion by a nucleophilic attack on the epoxide group of EmPEO1.9, as de previously (cf. Scheme 2II). The nonbonded EmPEO1.9 was removed during the p tion procedure because it dissolves in MeOH, which is used in the purification [58]. The theoretical molar mass (Mn,calc.) of the individual blocks shown in Table 2 was calculated from the ratio of the used masses of monomers (isoprene and sty sec-BuLi (initiator) (cf. Table 1), fit to the respective 1 H-NMR integrals of the chara protons from the PIx, PSy and AmPEO1.9 blocks for all synthesized PIxPSyAmPE ble 3, Figure S10, Table S1). The theoretical molar mass (M n,calc. ) of the individual blocks shown in Table 2, which was calculated from the ratio of the used masses of monomers (isoprene and styrene) to sec-BuLi (initiator) (cf. Table 1), fit to the respective 1 H-NMR integrals of the characteristic protons from the PI x , PS y and AmPEO 1.9 blocks for all synthesized PI x PS y AmPEO 1.9 (Table 3, Figure S10, Table S1).   Table 3 determined from the respective proton number of 1 H-NMR integrals (cf . Table S1) agree with the corresponding M n,calc. indicates a nearly stoichiometric conversion of the utilized masses listed in Table 1 to the desired PI x PS y AmPEO 1.9 without any side reactions. This close to quantitative polymerization process is due to the high reaction control by living anionic polymerization, the controlled synthesis conditions and the use of a slight excess of the EmPEO 1.9 during the polymer synthesis. The slight excess (10%) of EmPEO 1.9 ensures that all PI x PS y − anions are stoichiometrically saturated with the corresponding AmPEO 1.9 blocks, whereby the chosen epoxide end group modification ensures that not more than one EmPEO 1.9 molecule can be covalently attached per PI x PS y − anion (cf. Scheme 2 and Scheme S1). Therefore, the excess of unattached EmPEO 1.9 was removed during the purification process. In addition, the strong O-Li-ion pair acts as a kind of protecting group, avoiding unwanted crosslinking, side and termination reactions.

GPC Measurements
The GPC measurements were conducted to determine the molar mass (M n,GPC ), to confirm the M n,NMR results, the efficiency of the polymer synthesis and to determine the Ð of the EmPEO 1.9 as well as the synthesized PI x PS y AmPEO 1.9 . The corresponding GPC traces are shown in Figure 4, and Table 4 lists the results (cf. Figures S11-S15 for the complete traces). From the GPC traces, it can be seen that all synthesized PI x PS y AmPEO 1.9 polymers and EmPEO 1.9 have a narrow, unimodal shape and as a result, a Ð smaller than 1.  Figure 4, Table 4). The deviation towards higher molar mass in the M n,GPC compared to the M n,NMR values is attributed to the fact that the GPCs used polystyrene calibration standards. Furthermore, the GPC trace of EmPEO 1.9 with M n,GPC = 2.8 kg mol −1 shows a very narrow chain length distribution of Ð = 1.03. Thus, it was successfully characterized prior to linkage, showing a major advantage over the short PEO z block control. corresponds to their respective Mn,calc. and Mn,NMR (cf. Figure 4, Table 4). The deviation to wards higher molar mass in the Mn,GPC compared to the Mn,NMR values is attributed to th fact that the GPCs used polystyrene calibration standards. Furthermore, the GPC trace o EmPEO1.9 with Mn,GPC = 2.8 kg mol −1 shows a very narrow chain length distribution o Đ = 1.03. Thus, it was successfully characterized prior to linkage, showing a major ad vantage over the short PEOz block control. By linking the PEOz block via EmPEOz, it prevents unwanted chain termination caused by the introduction of impurities, which has a considerable influence on Đ.
The result that the Đ values are close to one (Đ ≤ 1.08) indicates that the synthesized PIxPSyAmPEOz polymer chains have nearly the same length, which means that there ar almost no chain terminations during the polymerization process. This is consistent with the 1 H-NMR results that the polymerization process is nearly quantitative and thu Mn,calc. = Mn,NMR. Therefore, this simplified polymerization procedure allows a fast and ef ficient polymer synthesis of tailored PIxPSyAmPEOz BCPs in a controlled and reproducibl way.    Figure S10, Table S1). 3 Determined by GPC measurement in THF using polystyrene standards (cf. Figure 4).
By linking the PEO z block via EmPEO z , it prevents unwanted chain termination caused by the introduction of impurities, which has a considerable influence on Ð.
The result that the Ð values are close to one (Ð ≤ 1.08) indicates that the synthesized PI x PS y AmPEO z polymer chains have nearly the same length, which means that there are almost no chain terminations during the polymerization process. This is consistent with the 1 H-NMR results that the polymerization process is nearly quantitative and thus M n,calc. = M n,NMR . Therefore, this simplified polymerization procedure allows a fast and efficient polymer synthesis of tailored PI x PS y AmPEO z BCPs in a controlled and reproducible way.

Thermal Analysis
The synthesized PI x PS y AmPEO 1.9 polymers were analyzed by DSC (cf. Figure 5a). Besides the thermal induced phase transitions, these measurements were carried out in order to obtain relevant information regarding the microphase separation.
block is amorphous. Moreover, the two ϑg and the ϑmp,PEO1.9 are equal to those of the pure polymer blocks, and the absence of additional ϑg and ϑmp suggests the exclusion of any mixing of the individual blocks even at the phase boundaries. In consequence of the high tendency of phase separation (affected by the nearly monodisperse polymer chain lengths (Đ ≤ 1.08)), a correlation between the chain length of the individual polymer blocks and the respective ϑg is observed. An increase of the block length, which corresponds to a higher Mn of the corresponding polymer block, leads to a shift of the ϑg to higher temperature; for instance, an increase in Mn,PSy by ~10 kg mol −1 leads to a ϑg,PSy temperature increase of ~5 °C (cf. Table 5). Furthermore, the fact that there is no mixing between different polymer blocks indicates that a linear dependence of change of heat capacity ∆Cp with the weight fraction of the respective polymer block at ϑg is detected. For example, an increase in Mn,PIx of ~20 wt.% leads to a rise in the ∆Cp,PIx by ~0.12 J (g K) −1 for the ϑg,PIx (Table 5).

Figure 5.
(a) DSC measurements of the synthesized PIxPSyAmPEO1.9 polymers, which show that they are microphase-separated as proven by the distinct ϑg (glass transition temperature) of the PIx and PSy phase as well as the ϑmp (melting point) of the PEO1.9 phase. An exception is PI26.1PS67.3Am-PEO1.9, where the ϑmp,PEO1.9 is not detected. (b) TGA curves of the EmPEO1.9 and the synthesized PIxPSyAmPEO1.9 BCPs and their respective decomposition temperature at 5% weight loss (ϑd5).
In Figure 5b, the decomposition temperature at a weight loss of 5% (ϑd5) of EmPEO1.9 and the synthesized PIxPSyAmPEO1.9 polymers as determined by TGA measurements are shown. The ϑd5 values are similar and independent of the polymer composition, with a slight trend of decreasing ϑd5 with higher PIx content and range from 322 to 334 °C. Figure 5. (a) DSC measurements of the synthesized PI x PS y AmPEO 1.9 polymers, which show that they are microphase-separated as proven by the distinct ϑ g (glass transition temperature) of the PI x and PS y phase as well as the ϑ mp (melting point) of the PEO 1.9 phase. An exception is PI 26.1 PS 67.3 AmPEO 1.9 , where the ϑ mp,PEO 1.9 is not detected. (b) TGA curves of the EmPEO 1.9 and the synthesized PI x PS y AmPEO 1.9 BCPs and their respective decomposition temperature at 5% weight loss (ϑ d5 ).
The occurrence of the three characteristic thermal phase transitions, i.e., the glass transition temperature (ϑ g ) for the PI x phase ϑ g,PIx in the range of −68 to −60 • C, the ϑ g,PSy for the PS y phase in the range of 75 to 96 • C, as well as the melting point ϑ mp,PEO1.9 of the PEO 1.9 (from AmPEO 1.9 ) at~50 • C (cf. Figure S16 for DSC measurement of pure EmPEO 1.9 ), evidence a microphase separation of the synthesized PI x PS y AmPEO 1.9 BCPs (Table 5) [59]. The existence of ϑ mp,PEO1.9 indicates the phase separation of the PEO 1.9 block from both nonpolar blocks. An exception is PI 26.1 PS 67.3 AmPEO 1.9 , where the ϑ mp,PEO1.9 is not detected. The reason for the absence of the ordered crystalline structure of the PEO 1.9 chains in PI 26.1 PS 67.3 AmPEO 1.9 can be attributed either to their low content of 1.7 wt.% or to the minimal contamination, which was detected in GPC measurement, so that the entire PEO 1.9 block is amorphous. Moreover, the two ϑ g and the ϑ mp,PEO1.9 are equal to those of the pure polymer blocks, and the absence of additional ϑ g and ϑ mp suggests the exclusion of any mixing of the individual blocks even at the phase boundaries. In consequence of the high tendency of phase separation (affected by the nearly monodisperse polymer chain lengths (Ð ≤ 1.08)), a correlation between the chain length of the individual polymer blocks and the respective ϑ g is observed. An increase of the block length, which corresponds to a higher M n of the corresponding polymer block, leads to a shift of the ϑ g to higher temperature; for instance, an increase in M n,PSy by~10 kg mol −1 leads to a ϑ g,PSy temperature increase of~5 • C (cf. Table 5). Furthermore, the fact that there is no mixing between different polymer blocks indicates that a linear dependence of change of heat capacity ∆C p with the weight fraction of the respective polymer block at ϑ g is detected. For example, an increase in M n,PIx of~20 wt.% leads to a rise in the ∆C p,PIx by~0.12 J (g K) −1 for the ϑ g,PIx (Table 5). In Figure 5b, the decomposition temperature at a weight loss of 5% (ϑ d5 ) of EmPEO 1.9 and the synthesized PI x PS y AmPEO 1.9 polymers as determined by TGA measurements are shown. The ϑ d5 values are similar and independent of the polymer composition, with a slight trend of decreasing ϑ d5 with higher PI x content and range from 322 to 334 • C. Therefore, they have a high thermal stability for the application as polymer electrolyte templates.

Morphological Characterization
Based on the previous results, it is evident that this polymerization route provides precise control over the chain length distribution respectively structure on a molecular level. In the following, it is investigated how this in combination with the controlled solvent casting process affects the morphology of the membrane. In particular, the self-assembly induced highly ordered microphase separation, which was already observed from DSC measurement, is crucial for the properties of the PI x PS y AmPEO 1.9 polymers and therefore plays a key role in their application. The morphology of all synthesized PI x PS y AmPEO 1.9 is determined using SAXS, SEM and TEM measurements. The results of above-mentioned morphological characterizations performed on the PI x PS y AmPEO 1.9 membranes are shown in Figures 6-9 and Table 6, which were controlled-cast from THF without annealing them later.
SAXS measurements were performed at room temperature on the as-cast membranes for all synthesized PI x PS y AmPEO 1.9 . Figure 6 and Table 6 show the results. All of the synthesized PI x PS y AmPEO 1.9 specimens exhibited strong scattering, as seen in the 2D SAXS patterns in Figure 7, Figure 8 and Figure S18, and a clear first scattering peak (q*), which was marked by a yellow filled circle in the SAXS curves in Figure 6, confirming the microphase separation [60,61].
In the SAXS curve of PI 6.8 PS 17.3 AmPEO 1.9 , in addition to the q* = 0.32 nm −1 , additional peaks were measured at a relative peak position at q/q* of √ 1 , √ 3 , √ 4 and √ 7 , indicating a HEX structure (cf. Figure 6) [18]. The same characteristic scattering peaks of a microphase-separated HEX morphology are detected for the membranes consisting of PI 14.6 PS 34.8 AmPEO 1.9 , PI 35.1 PS 14.8 AmPEO 1.9 and PI 26.1 PS 67.3 AmPEO 1.9 , as shown in Figure 6 [18]. However, all q values of these polymers are shifted in comparison to PI 6.8 PS 17.3 AmPEO 1.9 to lower q values, whereby PI 26.1 PS 67.3 AmPEO 1.9 has the lowest q* value with 0.11 nm -1 . In the case of PI 24.8 PS 25.0 AmPEO 1.9 , the q* value = 0.20 nm −1 is the same as for PI 14.6 PS 34.8 AmPEO 1.9 (0.20 nm −1 ) and PI 35.1 PS 14.8 AmPEO 1.9 (0.19 nm −1 ). In addition to the q* peak, further peaks at a relative position of q/q* 2 and 3 are clearly observed for PI 24.8 PS 25.0 AmPEO 1.9 , indicating a LAM morphology (cf. Figure 6) [18,60].  Figure 6. SAXS curves measured at room temperature of as-cast membranes from the synthesized PIxPSyAmPEO1.9, by plotting the scattering intensity as a function of the magnitude of the scattering vector (q). The first reflection peak (q*) determined from SAXS measurement is marked by a yellow filled circle. Black squares with the values below indicate the calculated relative peak positions at q/q* due to hexagonally close-packed cylindrical structure and black stars indicate the respective peaks due to the lamellar structure. The theoretical fit for the morphology (black lines) and the curve obtained from SAXS measurement, as well as the calculated peak positions, match almost perfectly. On the right side are 3D drawings of the corresponding structure, therein blue represents PIx, red PSy and green PEO1.9 volume fraction and the size ratios of the drawing are equal to the average domain spacing (d) obtained from SAXS measurement. Figure 6. SAXS curves measured at room temperature of as-cast membranes from the synthesized PI x PS y AmPEO 1.9 , by plotting the scattering intensity as a function of the magnitude of the scattering vector (q). The first reflection peak (q*) determined from SAXS measurement is marked by a yellow filled circle. Black squares with the values below indicate the calculated relative peak positions at q/q* due to hexagonally close-packed cylindrical structure and black stars indicate the respective peaks due to the lamellar structure. The theoretical fit for the morphology (black lines) and the curve obtained from SAXS measurement, as well as the calculated peak positions, match almost perfectly. On the right side are 3D drawings of the corresponding structure, therein blue represents PI x , red PS y and green PEO 1.9 volume fraction and the size ratios of the drawing are equal to the average domain spacing (d) obtained from SAXS measurement.
cylinder pattern of the HEX structure is clearly visible and almost identical in the FFT spectrum in (c) as well as in the SAXS pattern in (d). This means that the cylinders have the same arrangement and distance to each other in the macroscopic sample volume (2 mm sample diameter in the SAXS capillaries) and in the microscopic sample area in the SEM image and are aligned straight through the entire volume. Furthermore, from the SEM image, it is evident that for the cast film HEX structure, the cylinder axes are located in plane. For better visibility, the hexagonal cylinder pattern of the HEX structure is marked in black as an example. (c) Two-dimensional FFT spectrum of inset area. (d) Two-dimensional SAXS pattern obtained at room temperature from the membrane in as-cast condition with a sample diameter of 2 mm.
In case of PI24.8PS25.0AmPEO1.9 in the large overview image in Figure 8a, respectively, in the inset in b), a long-range and highly ordered LAM structure is clearly evident, which is also consistent with the SAXS result and corroborated by the 2D FFT result. The obtained 2D FFT spectrum reveals two "beam-like shapes" according to the LAM structure The q* values were used to calculate the respective average domain spacing (d) for all PI x PS y AmPEO 1.9 ; this means for a HEX structure, the distance is from cylinder to adjacent cylinder, and for a LAM structure, from center to the next center, which is listed in Table 6. In addition, from SAXS measurement of PI 24.8 PS 25.0 AmPEO 1.9 the layer thickness (t) and for samples with the HEX morphology, the cylinder radius (r cylinder ) were determined and summarized in Table 6. Details concerning the fits to the radially averaged SAXS data in Figure 6 and the values in Table 6 are given in the supporting information.
The extra hump in the SAXS curve from PI 6.8 PS 17.3 AmPEO 1.9 at low q value = 0.16 nm −1 , which therefore precedes the q* value = 0.32 nm −1 and was not fitted, comes most probably from heterogeneities in the structure on length scales larger than the unit cell. The reason that only the one peak is seen and the others are suppressed lies in the ratio of r cylinder and d because in this combination, the peaks fall on the minima and are suppressed.
For all investigated polymers, the PEO 1.9 block is with a volume fraction (ϕ) of 2-6% too small to be detected by SAXS measurements. Thus, it was not necessary to include the PEO 1.9 block in the fit, as from DSC measurements it is known to be phase-separated from the nonpolar blocks, so a simplified diblock model was used.
going vertical through the sample (cf. Figure 8c). Also, the SAXS pattern in Figure 8d shows the two "beam-like shapes" which differ from those in the FFT nearly only by the fact that they are slightly tilted. Most likely this is due to the placement of the sample into the SAXS capillary. Considering that the FFT spectrum and the SAXS pattern look almost the same, the lamellae are microscopically as well as macroscopically equally oriented and have the same distance to each other. Moreover, a TEM image of PI24.8PS25.0AmPEO1.9 of the unstained membrane was obtained in STEM mode. Usually, stained samples are measured [18,24,63,64]. The TEM result shown in Figure 9 displays the same LAM structure as already seen in SEM. For all samples, the fit used to determine the morphology matches very well to the measured SAXS curve shapes (cf. plotted black line in the SAXS curves in Figure 6). Therefore, the calculated relative peak positions at q/q* (cf. black squares for HEX and black stars for LAM structure in Figure 6) fit almost perfectly to the maxima and minima in the respective obtained SAXS curves. The model used for the fitting is either using homogenous cylinder form factor for the HEX or platelets form factor for the LAM phases. Even with this rather simple model, a precise fit of the radially averaged scattering data was achieved. The ϕ for different blocks were calculated from the ratio of r cylinder or t to the fitted d and are listed in Table 6.
The d values calculated from measured q* correlate with the total M n,NMR of the PI x PS y AmPEO 1.9 . This means that PI 6 AmPEO 1.9 about two times larger. Therefore, the structure size ratios of the different PI x PS y AmPEO 1.9 to each other are in accurate accordance with their respective M n,NMR (cf. Scheme 4, Table 4). Also, the measured r cylinder have the same relationship to each other as the previously described d (cf. Table 6). As a result, PI14.6PS34.8AmPEO1.9 and PI24.8PS25.0AmPEO1.9 possess a nearly perfectly ordered HEX respectively LAM structure, at least over the total SEM and TEM measurement µm size area as well as the 2 mm thick sample volume for the SAXS measurement. Therefore, they show an extraordinary long-range orientation. The strongly distinct microphase separation, most likely caused by the very narrow polymer chain length distribution, in combination with the controlled solution casting process ensuring enough time for self-assembly, leads to these exceptional morphological properties. These properties are crucial for an excellent polymer electrolyte matrix, because the conductive pathways and finally the Li + transport should be aligned almost optimally to each other over an extremely long range inside the BCP membrane.
Furthermore, particularly in case of PI24.8PS25.0AmPEO1.9, horizontal cutting artifacts can be recognized in the sample overview image as brighter and darker waves. This is a common cutting artifact of cryo-ultramicrotomy, which results from compression of the section during sectioning and extends perpendicular to the cutting direction [65]. As the cutting direction was perpendicular to the membrane and a ribbon of sections could be imaged on the grid by SEM, it is possible to determine the orientation of the lamellae within the membrane over a larger sample surface area and at several sample positions (cf. Scheme S2). The lamellae are arranged from top to bottom, i.e., vertically across the sample. Compression artefacts are perpendicular to the lamellae, indicating that the cutting direction across the membrane is the same as the orientation of the lamellae in the BCP. In other words, the lamellae are continuous aligned orthogonally to the polymer surface and therefore also at the potential use in electrolytes as a structure-giving BCP matrix to the electrode interface, i.e., connecting both electrodes to each other. It has already been shown in our patent that these BCPs can be used as a structure-giving BCP matrix in electrolytes to obtain very high ionic conductivities [43]. Such electrolytes provide comparable, and in some cases even better, ionic conductivities than those reported   Table 3). Note that these densities were determined for 140 • C, which may cause deviations. 2 q* is the position of the first scattering peak, determined by SAXS. 3 HEX = hexagonally close-packed cylindrical and LAM = lamella structure, determined by SAXS measurement. 4 d = average domain spacing. 5 r cylinder = radius of cylinder determined by SAXS. 6 ϕ cylinder = volume fraction of cylinder based on ratio of r cylinder to d. 7 t = layer thickness determined by SAXS. 8 Volume fraction of lamella based on ratio of t to d. 9 Domain size = determined by SAXS.
Using the M n,NMR of the individual polymer blocks (cf. Table 3) and on basis of published homopolymer densities (ρ PIx = 0.830, ρ PSy = 0.969, ρ PEOz = 1.064 in g cm −3 , note that these densities were determined for 140 • C, which may cause slight deviations) [61], the monomer volume fractions (f i ) of the PI x block (f PIx ), the PS y block (f PSy ) and the PEO 1.9 block (f PEO1.9 ) were calculated and listed in Table 6. For PI 6.8 PS 17.3 AmPEO 1.9 , PI 14.6 PS 34.8 AmPEO 1.9 and PI 26.1 PS 67.3 AmPEO 1.9 , the volume ratio of the PI x block to the PS y AmPEO 1.9 block always remains the same and was in the range of~29-33% for f PIx and~68-71% for f PSyAmPEO1. 9 . The volume fraction of the cylinder (ϕ cylinder ) was equal for all with~28-34%, which matches very well with the f PIx . Accordingly, it was obvious that they have the same HEX structure. Consequently, the cylinder from the HEX structure corresponds to the PI x block, because the r cylinder ratio of the different polymers, i.e., PI 6.8 PS 17.3 AmPEO 1.9 , PI 14.6 PS 34.8 AmPEO 1.9 and PI 26.1 PS 67.3 AmPEO 1.9 , agrees exactly with the respective M n,NMR,PIx ratio. As a result, the HEX structures differ from each other only in terms of size.
The volume ratio for PI 35.1 PS 14.8 AmPEO 1.9 with f PI35.1 = 71% and f PS14.8AmPEO1.9 = 29% is exactly the opposite compared to the previously discussed PI x PS y AmPEO 1.9 . The determined ϕ cylinder with 31% matches quite closely with the f PS14.8AmPEO1.9 . Consequently, the detected HEX structure fits accurately; however, due to the inverted volume fractions, a reverse phase with PS 14.8 AmPEO 1.9 cylinders exists. Hence, r cylinder with a value of 10.9 nm corresponds to the M n,NMR of PS 14.8 and AmPEO 1.9 block and is the same size as r cylinder of PI 14 Indeed, as expected from the PI x PS y phase diagram, the nearly symmetric PI 24.8 PS 25.0 AmPEO 1.9 forms a LAM, while all other, more asymmetric PI x PS y AmPEO 1.9 show a HEX morphology [18,24].
In order to visualize the previously described structures more clearly, corresponding 3D drawings were plotted based on the parameters obtained from the SAXS measurements with the assumption that the PEO 1.9 block is fully phase-separated (cf. 3D drawings on the right site in Figure 6).
The obtained SAXS results match almost perfectly for all PI x PS y AmPEO 1.9 with their respective polymer composition determined from NMR, thermal analysis and GPC measurements, and in particular, when they are compared with each other.
For all PI x PS y AmPEO 1.9 , the SAXS measurement results indicate a high degree of long-range order in the structure due to the strong scattering in the respective 2D SAXS pattern, but also due to the fact that the curve shape shows a number of clear peaks that agree very well with the fit as well as with the calculated peak positions. For instance, in PI 24.8 PS 25.0 AmPEO 1.9 the presence of 2q* and 3q* suggests that the LAM morphology is present with a highly long-range arrangement [60,62].
In order to determine a more detailed, local long-range order as well as the orientation of the structure, SEM measurements were carried out. In particular, these two structural parameters of the membrane are crucial for the application of BCP as a structure-giving polymer matrix in electrolyte. In addition, the structure determined from the SAXS results is also checked. For this purpose, exemplary SEM measurements were performed on unstained ultra-thin sections of about 50 to 100 nm thickness from PI 14.6 PS 34.8 AmPEO 1.9 for the HEX structure and from PI 24.8 PS 25.0 AmPEO 1.9 for the LAM structure. In Scheme S2, the procedure of sample preparation by cryo-ultramicrotomy as well as sample placement onto the grid is schematically shown.
Results of PI 14.6 PS 34.8 AmPEO 1.9 are shown in Figure 7; the ones for PI 24.8 PS 25.0 AmPEO 1.9 are displayed in Figure 8. In (a), an overview image of several µm 2 in size is shown. The marked area in a) was enlarged as inset in b) to make the structure visible in more detail (i.e., periodic lamellae or hexagonal cylinder arrangement). In (c), the fast Fourier transformation (FFT) of the area in (a) in case of the LAM and of the inlet (b) in case of the HEX structure is added to indicate the average orientation of the structure. The good contrast of the sample is achieved through the relatively low accelerating voltage of 30 kV used for STEM-imaging in the SEM. Hence, samples can be measured without staining. Additionally, in both figures under (d), the corresponding SAXS pattern is shown to compare it with the FFT spectrum.
For PI 14.6 PS 34.8 AmPEO 1.9 , a long-range and highly ordered HEX structure of cylinders is clearly visible in the overview image of Figure 7a, respectively, in the enlarged inset in (b) and corresponds with the SAXS result. In particular, it is remarkable that the hexagonal cylinder pattern of the HEX structure is clearly visible and almost identical in the FFT spectrum in (c) as well as in the SAXS pattern in (d). This means that the cylinders have the same arrangement and distance to each other in the macroscopic sample volume (2 mm sample diameter in the SAXS capillaries) and in the microscopic sample area in the SEM image and are aligned straight through the entire volume. Furthermore, from the SEM image, it is evident that for the cast film HEX structure, the cylinder axes are located in plane.
In case of PI 24.8 PS 25.0 AmPEO 1.9 in the large overview image in Figure 8a, respectively, in the inset in b), a long-range and highly ordered LAM structure is clearly evident, which is also consistent with the SAXS result and corroborated by the 2D FFT result. The obtained 2D FFT spectrum reveals two "beam-like shapes" according to the LAM structure going vertical through the sample (cf. Figure 8c). Also, the SAXS pattern in Figure 8d shows the two "beam-like shapes" which differ from those in the FFT nearly only by the fact that they are slightly tilted. Most likely this is due to the placement of the sample into the SAXS capillary. Considering that the FFT spectrum and the SAXS pattern look almost the same, the lamellae are microscopically as well as macroscopically equally oriented and have the same distance to each other.
Moreover, a TEM image of PI 24.8 PS 25.0 AmPEO 1.9 of the unstained membrane was obtained in STEM mode. Usually, stained samples are measured [18,24,63,64]. The TEM result shown in Figure 9 displays the same LAM structure as already seen in SEM.
As a result, PI 14.6 PS 34.8 AmPEO 1.9 and PI 24.8 PS 25.0 AmPEO 1.9 possess a nearly perfectly ordered HEX respectively LAM structure, at least over the total SEM and TEM measurement µm size area as well as the 2 mm thick sample volume for the SAXS measurement. Therefore, they show an extraordinary long-range orientation. The strongly distinct microphase separation, most likely caused by the very narrow polymer chain length distribution, in combination with the controlled solution casting process ensuring enough time for selfassembly, leads to these exceptional morphological properties. These properties are crucial for an excellent polymer electrolyte matrix, because the conductive pathways and finally the Li + transport should be aligned almost optimally to each other over an extremely long range inside the BCP membrane.
Furthermore, particularly in case of PI 24.8 PS 25.0 AmPEO 1.9 , horizontal cutting artifacts can be recognized in the sample overview image as brighter and darker waves. This is a common cutting artifact of cryo-ultramicrotomy, which results from compression of the section during sectioning and extends perpendicular to the cutting direction [65]. As the cutting direction was perpendicular to the membrane and a ribbon of sections could be imaged on the grid by SEM, it is possible to determine the orientation of the lamellae within the membrane over a larger sample surface area and at several sample positions (cf. Scheme S2). The lamellae are arranged from top to bottom, i.e., vertically across the sample. Compression artefacts are perpendicular to the lamellae, indicating that the cutting direction across the membrane is the same as the orientation of the lamellae in the BCP. In other words, the lamellae are continuous aligned orthogonally to the polymer surface and therefore also at the potential use in electrolytes as a structure-giving BCP matrix to the electrode interface, i.e., connecting both electrodes to each other. It has already been shown in our patent that these BCPs can be used as a structure-giving BCP matrix in electrolytes to obtain very high ionic conductivities [43]. Such electrolytes provide comparable, and in some cases even better, ionic conductivities than those reported by Dörr and Pelz et al. [10,11,37].

Conclusions
Herein, we introduced a convergent synthesis method based on the modular principle, which ensures the access to well-defined PI x PS y PEO z linear triblock copolymers with consistently the same very short and precise PEO z block. For this purpose, a prefabricated and commercially available mPEO z block is used, which is selectively functionalized with an epoxy end group to EmPEO z . The EmPEO z block is covalently attached to the PI x PS y − anion synthesized by living anionic polymerization and thus terminated to the corresponding BCP. Thereby, by utilizing the O-Li ion pair formation between the epoxide group of the EmPEO z and the living anion, it is ensured that only a single ring-opening reaction occurs. Therefore, the handling of EO gas monomers during the BCP polymerization can be avoided.
The systematic variation of the block length reveals two major and independent influences of the polymer structure. By varying the M n,PIx /M n,PSy at a constant M n,total , the morphology could be precisely controlled. Alternatively, by changing the M n,total at the same M n,PIx /M n,PSy , only the PEO z block fraction could be altered and adjusted, while keeping the morphology constant.
This simplified and reproducible one-pot polymerization, with 100% reaction efficiency, obtains highly ordered PI x PS y AmPEO z BCPs whose morphology can be largely controlled within the polymer membrane on microscopic and macroscopic levels. Largely controlled means at the microscopic or molecular level that the polymer chain lengths can be precisely selected, are nearly monodisperse and the respective BCP possesses a very high degree of phase separation. Moreover, the highly uniform polymer blocks combined with the controlled solution casting process lead to PI x PS y AmPEO z membranes with a very high and exceptionally long-range ordered structure up to the mm scale.
Overall, due to the always constant PEO z block size, the high control over the order and orientation of the morphology as well as the PEO z block fraction, these BCPs are suitable for subsequent targeted investigation of their influence as a structure-giving matrix in corresponding solid polymer electrolytes with respect to Li + transport up to the macroscale level.
Supplementary Materials: The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/polym15092128/s1, Scheme S1: Illustration of the utilization of the blocking effect for single EmPEO z chain attachment to the PI x PS y − anion with Li + as counterion due to the strong O-Li affinity. Figure S1: 1 H-NMR spectrum of EmPEO 1.9 . Figure S2: 13 C-NMR spectrum of EmPEO 1.9 . Figure S3: 1 H-NMR spectrum of mPEO 1.9 . Figure S4: 13 C-NMR spectrum of mPEO 1.9 . Figure S5: 1 H-NMR spectrum of PI 6.8 PS 17.3 AmPEO 1.9 . Figure S6: 1 H-NMR spectrum of PI 14.6 PS 34.8 AmPEO 1.9 . Figure S7: 1 H-NMR spectrum of PI 24.8 PS 25.0 AmPEO 1.9 . Figure S8: 1 H-NMR spectrum of PI 35.1 PS 14.8 AmPEO 1.9 . Figure S9: 1 H-NMR spectrum of PI 26.1 PS 67.3 AmPEO 1.9 . Figure S10: Comparison of the characteristic signals in the 1 H-NMR spectra of the synthesized PI x PS y AmPEO 1.9 . Table S1: Comparison of the number of protons determined from 1 H-NMR integrals of the individual polymer blocks of the synthesized PI x PS y AmPEO 1.9 . Figure S11: Full GPC trace of PI 6.8 PS 17.3 AmPEO 1.9 . Figure S12: Full GPC trace of PI 14.6 PS 34.8 AmPEO 1.9 . Figure S13: Full GPC trace of PI 24.8 PS 25.0 AmPEO 1.9 . Figure S14: Full GPC trace of PI 35.1 PS 14.8 AmPEO 1.9 . Figure S15: Full GPC trace of PI 26.1 PS 67.3 AmPEO 1.9 . Figure S16: DSC measurement of EmPEO 1.9 . Figure S17: Exemplary photo of a colorless and transparent PI x PS y AmPEO 1.9 membrane cast from THF. Figure S18: Two-dimensional SAXS patterns obtained at room temperature from the membrane in as-cast condition with a sample diameter of 2 mm of the synthesized PI 6