Block copolymers for supercapacitors, dielectric capacitors and batteries

For block copolymers, the pore size is directly correlated to the domain size of the sacrificial blocks, which is correlated to the degree of polymerization (N), or the molecular weight. For example, polyacrylonitrile-block-poly(butyl acrylate) (PAN-b-PBA) is a typical precursor for mesoporous carbon powder [17], which contains a high carbon yield block of PAN and a sacrificial block of PBA (figure 2(a)). After pyrolysis, the pore sizes, either measured by Brunauer–Emmet–Teller (BET) or calculated from small angle x-ray scattering (SAXS), increased with the total degree of polymerization (DP^tot, figure 2(b)). The pore interconnectivity also increased as the pores broadened (figure 2(c)). Other reports on PAN-b-PMMA [18] and dopamine-doped PS-b-PEO [19] also validate that the degree of polymerization is an important parameter to tune the pore size of carbon films.

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The thermal and solvent annealing conditions control the pore size of mesoporous carbons during the self-assembly process of block copolymers. For instance, upon thermal or solvent annealing, the spin-casted PAN-b-PMMA thin films self-assembled into microphases with different PAN and PMMA domain sizes [20]. The subsequent pyrolysis decomposed PMMA to generate pores and carbonized PAN to form carbon matrices (figure 3(a)). The mesopore size of the resultant carbon thin films increased from ~40 to 48 nm as the annealing temperature was increased from 100 °C to 300 °C (figure 3(b), black curve). In general, the center-to-center spacing (L_o) of both the block copolymer domains (figure 3(b), blue curve) and carbon pores (figure 3(b), red curve) increased as the temperature was increased. The unique temperature-dependence of the pore size and domain spacing is attributed to the thermal expansion of PMMA and PAN, as well as the cyclization of PAN [21]. The thermal expansion coefficients of PAN and PMMA are ~1.4  ×  10⁻⁵ K⁻¹ [22] and ~7.0–9.3  ×  10⁻⁵ K⁻¹ [23], respectively. The higher thermal expansion coefficient of PMMA than that of PAN suggests that when increasing the thermal annealing temperature, PMMA expands faster than PAN and forms larger domains. Because PAN is crosslinked due to cyclization, the subsequent removal of PMMA results in larger pore sizes. Additionally, the degree of PAN cyclization increases with increasing temperature, which further reduces the free volume of PAN, shrinks the PAN domain size, and increases the pore size in the carbon after pyrolysis. The pore size tunability by thermal annealing temperature was corroborated by others [24, 25]. In addition, solvent annealing in various solvent vapors also produced carbon films with various pore sizes and center-to-center spacings (figure 3(c)). The controllability of solvent annealing is rooted in the different affinities of the solvent molecules to polymer blocks.

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The pore size can also be tuned by blending block copolymers of different degrees of polymerization, or mixing block copolymers with homopolymers. The pore size (D) of carbon films derived from a binary blend is proportional to the weight fractions of each component:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle D={{x}_{1}}{{D}_{1}}+{{x}_{2}}{{D}_{2}}={{x}_{1}}{{D}_{1}}+\left(1-{{x}_{1}} \right){{D}_{2}}\nonumber \end{align} \tag{ 4 }$$

where D_i and x_i are the pore size and the weight fraction of component i (i  =  1 and 2), respectively. For example, blending polystyrene-block-poly(4-vinylpyridine) (PS-b-P4VP) of different molecular weights can effectively tune the mesopore sizes of the resultant carbon films from ~20 to 50 nm (figure 4) [26]. In addition, because homopolymers selectively swell the corresponding block of the block copolymers [27, 28], the amount of homopolymers can tailor the pore size. A typical example is PS-b-P4VP containing 8, 16 and 31 wt.% of P4VP, which have average pore sizes of 22, 25 and 48 nm, respectively [29]. The tuning of pore sizes by polymer blends provides enormous simplicity and avoids arduous syntheses of block copolymers with various molecular weights.

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The ionic conductivities of block copolymer electrolytes strongly depend on their morphologies. Typically, the ionic conductivity ($\sigma$, in S m⁻¹) of a microphase-separated block copolymer can be derived from the effective medium theory [30]. In the simplest case, $\sigma$ increases linearly with the ionic conductivity (S m⁻¹) of the pure conducting phase at the same salt concentration (${{\sigma}_{{\rm c}}}$):

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \sigma =\frac{\alpha}{\tau}f{{\sigma}_{{\rm c}}}\nonumber \end{align} \tag{ 5 }$$

where the dimensionless $\alpha$, $\tau$, and $f$ are the morphology factor, tortuosity factor, and volume fraction of the conducting phase, respectively. $\alpha$ accounts for the morphological influence of the conducting phase on the ion mobility, and $\tau$ reflects the retardance to the ion diffusion caused by the tortuosity of the conducting phase. Table 1 summarizes the typical values of $\alpha$ and ${{\tau}^{-1}}$ for linear A–B di-block copolymers after self-assembly into thermodynamically stable microphases.

Table 1. Morphology and tortuosity factors of block copolymer electrolytes [31].

Morphology	Conducting phase	$\alpha$	τ−1
Sphere	Minority	0a	1
	Majority	1	2/(3  −  f )b
Cylinder	Minority	1/3	1
	Majority	1	1/(2  −  f )
Gyroid	Minority	1	½
	Majority	1	4/5
Lamella	N.A.	2/3	1

^aThe maximal and minimal values of both $\alpha$ and τ⁻¹ are 1 and 0, respectively. '1' represents zero impedance for ion diffusion. '0' means complete blockage for ion flow. ^bf  represents the volume fraction of the ion-conducting phase.

Generally for a block copolymer electrolyte, the tortuosity of its conducting phase can be evaluated by the empirical Bruggeman equation (9) [32]:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \tau =\beta {{f}^{1-\gamma}}\nonumber \end{align} \tag{ 6 }$$

where $\beta$ and $\gamma$ are empirically determined parameters for each block copolymer electrolyte. Equation (6) is obtained under the assumption of $\alpha =1$.

The impact of morphology on the ionic conductivity is well demonstrated by a study on LiCF₃SO₃-doped PEO dendron electrolytes with two molecular weights (1-Li⁺: 4600 Da, 2-Li⁺: 7500 Da) [33]. As the temperature was increased, the morphology of 1-Li⁺ evolved from crystalline (k₁ and k₂), micellar (mc) to disordered (dis) mesophase. The ionic conductivity decreased sharply as the electrolyte changed from k₂ to mc, but did not change substantially during the mc-dis transition (figure 5(a)). 2-Li⁺ transited from crystalline (k₁ and k₂) to hexagonal columnar (hex), and to continuous cubic (cc) structure. Its ionic conductivity increased by nearly an order of magnitude at the hex-cc phase transition. In comparison with mc and dis whose conducting domains were discontinuous, the conducting domains in hex and cc were continuous and facilitated ion diffusion, as corroborated by others [34–36].

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A series of experiments have shown an inverse correlation between ionic conductivity and structural tortuosity. For example, the Li⁺ diffusion coefficient through a lamellar polystyrene-block-poly(ethylene oxide) (SEO) electrolyte decreased by ~80% after the adjacent poly(ethylene oxide) (PEO) lamellar domains became connected [39]. The interconnection of the conducting lamellar domains induced anisotropic ion flow, augmented structural tortuosity and hence reduced ion mobility. Based on random-walk molecular simulations [37], the ionic conductivity decreased with the tortuosity, as the conducting phase (red) changed from gyroid majority to lamellae, to gyroid minority, and to cylinders (figure 5(b)).

However, other experiments suggest that the ionic conductivity does not necessarily always increase inversely to the structure tortuosity. A number of reports have shown that the disordered phase with the highest tortuosity favored rapid ion diffusion [38, 40–42]. For example, when a lithium(trifluoromethylsulfonyl)imide (LiTFSI)-containing SEO electrolyte evolved from lamellar to disordered, its ionic conductivity abruptly increased nearly twice (figures 5(c) and (d)) [38]. In contrast, Wanakule et al concluded that neither order-to-order transitions (OOT) nor ODT significantly influenced the ionic conductivity of a LiTFSI-doped SEO electrolyte [43]. The exact causes of the discrepancies in the tortuosity effect are unclear but may be linked to various factors, such as the diverse natures of the different electrolytes, the presence of various structural defects, the non-uniform salt concentration within the conducting blocks, and the irregular ion partition between the conducting and insulating phases.

The ionic conductivity of a given microstructure generally increases as the temperature is increased. The ionic conductivity and temperature relationship can be described by the Vogel–Tammann–Fulcher (VTF) equation [41, 44],

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \sigma =A\exp \left[\frac{-{{E}_{{\rm a}}}}{R\left(T-{{T}_{0}} \right)} \right]\nonumber \end{align} \tag{ 7 }$$

where A is a pre-exponential factor that depends on ion concentration (S m⁻¹); T is the temperature (K); E_a is the effective ion-transport activation energy (J mol⁻¹); and T₀ is the reference temperature (K) that is typically set to the glass transition temperature (T_g) of the ion-conducting block. Equation (8) is specifically derived from equation (7) to evaluate the ionic conductivity of a block copolymer electrolyte with isotropic, well-connected and strongly confined conducting phases (i.e. the phases that contain ionic liquids): [45]

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \sigma ={{\sigma}_{\max}}{{\left({{\varphi}_{{\rm IL}}}-0.17 \right)}^{1.5}}\exp \left\{\frac{-B}{R\left[T-\left({{T}_{{\rm g}}}-50 \right) \right]} \right\}\nonumber \end{align} \tag{ 8 }$$

where ${{\varphi}_{{\rm IL}}}$ is the volume fraction of the added ionic liquid; B is a constant associated with the ion-transport activation energy (J mol⁻¹); and T_g depends on the composition and the concentration of the ionic liquid. Both T_g and B are characteristic for a given polymer/ionic liquid combination.

For a given microphase, the molecular weight changes the domain size of the conducting block and thus alters the ionic conductivity. For a lamellar SEO electrolyte with a molecular weight of over 10.4 kDa, its ionic conductivity increased as the molecular weight was increased [46], due to the increasing PEO domain size. At low molecular weights, the PS and PEO domains were weakly segregated and the diffusion of Li⁺ was hindered by the polymer chain entanglement. As the molecular weight was increased, so was the segregation strength, and therefore the PEO domains gradually broadened. Because the PEO chains in the central zone of the PEO domain were unrestrained, the mobility of Li⁺ was boosted. Based on the self-consistent field theory, the impedance to Li⁺ conduction near the PEO/PS interface stemmed from the edge stress that interfered Li⁺-PEO coordination [47].

By reducing the molecular weights, the conducting domains narrowed and facilitated ion diffusion. Compared to a conventional SEO electrolyte, S(EO)₃ with three shorter PEO arms showed an enhanced conductivity (figure 6(a)) [48]. SEM demonstrated that the S(EO)₃ self-assembled into PEO lamellar domains narrower than SEO (figures 6(b) and (c)). It was believed that the Li⁺ ions in the narrow channels tended to flow straightly through each PEO lamella due to the structure confinement, while those in the wide diffusion channels swayed around and resulted in slow movement across the electrolyte (figure 6(d)). Due to the structure confinement, the Li⁺ concentration in the narrow channels (1.92 mmol cm⁻³) was higher than that in the wide channels (1.57 mmol cm⁻³).

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Additionally, the molecular weights determine the crystallinity of the conducting block and therefore the ionic conductivity. A typical example is the poly[oligo(oxyethylene)methacrylate] with short PEO side chains that has lower crystallinity and thus higher ionic conductivity than SEO [49–52]. The underlying mechanism is that the polymer chain mobility increases as the crystallinity decreases, which helps with the ion conduction.

The ionic conductivities of block copolymer electrolytes depend on the salt incorporated in the conducting blocks, because the cation–anion interactions affect the ion mobility and therefore the ionic conductivity. Generally, conducting polymers with strong acid groups tend to be highly conductive [53, 54]. For example, the ionic conductivity of PEO-CF₃SO₃Li at 373 K was ~4  ×  10⁻⁴ S cm⁻¹, approximately one order of magnitude higher than that of PEO-CH₃COOLi at an identical lithium concentration [53]. Because CF₃SO₃H is more acidic than CH₃COOH, the interaction strength between ${\rm C}{{{\rm F}}_{{\rm 3}}}{\rm SO}_{3}^{-}/{\rm L}{{{\rm i}}^{+}}$ is much weaker than that of CH₃COO⁻/Li⁺, which leads to a higher Li⁺ conductivity. Recently, the addition of multiple salts [55] and the blending of salts with ionic liquids [56] were proven to be effective in improving the ionic conductivities of SEO. The improved ionic conductivity was correlated to multiple factors including decreased crystallinity, reduced T_g of PEO, improved PEO chain flexibility, and enhanced solubility of the lithium salt.

The Li⁺ concentration strongly influences the ionic conductivities of SEO electrolytes. The ionic conductivity of a SEO electrolyte displayed three local maxima at r  =  ~0.14, ~0.28 and ~0.34 (r represents the concentration ratio of Li⁺ to the EO unit) [57]. In contrast, the ionic conductivity of a PEO electrolyte only peaked at r ~ 0.06 (figure 7(a)). These characteristics do not follow the effective medium theory (equation (5)), which states that the number of the ionic conductivity maxima and their r values of a block copolymer electrolyte should be the same as those of the corresponding homopolymer electrolyte. Alternatively, the anomalous behavior of the ionic conductivity of SEO was correlated to the different morphologies and the deviation in the T_g from the PEO electrolyte (figure 7(b)).

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In addition, the partition and distribution of the ions in the conducting domains of single-ion electrolytes (electrolytes that conduct only cations or anions, section 3.3.3) can profoundly modify their ionic conductivities. The incorporation of free counterions in the conducting domains reduced the overall conductivity of single-ion electrolyte poly(lauryl methacrylate)-block-poly(lithium methacrylate)-block-poly[(oxyethylene)₉ methacrylate] (PLMA-b-PLiMA-b-POEM) by more than ten times [58]. Conversely, the incorporation of mobile ions in the conducting domains of single-ion electrolyte poly(ethylene oxide)-block-polystyrenesulfonyllithium(trifluoromethylsulfonyl)imide (PEO-b-PSLiTFSI) enhanced the ionic conductivity by over three orders of magnitude [59].

Block copolymers are widely used as soft-templates in conjunction with carbon precursors to prepare mesoporous carbon electrodes. Particularly, the mesoporous carbons derived from block copolymer templates possess high surface areas and ordered mesopores. Pluronic^® F127, a.k.a. P-123 or Poloxamer 407 (PEO-b-PPO-b-PEO), is a commonly used block copolymer template [65–87]. Other block copolymers with strong segregation strengths are also potent templates, such as poly(ethylene glycol)-block-poly(4-vinylpyridine) (PEG-b-P4VP) [88], PS-b-P4VP [89], PS-b-PEO (SEO) [80, 90–92], and PS-b-poly(2-vinylpyridine)-b-PEO [93]. Since these block copolymer templates are thermally instable and have low char yields, they are infiltrated with carbon precursors to generate mesoporous carbons. Typical carbon precursors are resorcinol-formaldehyde (RF) resin [74, 81, 83, 87, 89, 94], phenolic resin (PF) [68, 72, 73, 76, 78, 82, 84, 85, 90, 93], amino acid [69], graphene oxide [70], polybenzoxazine [71], polyaniline [91], melamine [75], fructose [88], chitosan [77], furfuryl alcohol [86], and dopamine [19, 92]. High temperature treatment produces replicas of mesoporous carbon by carbonizing the infiltrated carbon precursors and removing the block copolymer templates.

Block copolymers are also prominent precursors of mesoporous carbons that can be directly used as supercapacitor electrodes. A thermal liable sacrificial polymer block creates mesopores upon thermal decomposition or sublimation, while a high-char-yield polymer block is used as the carbon precursor. Example sacrificial polymers include poly(butyl acrylate) (PBA) [95, 96], polystyrene (PS) [19, 25, 97–99], poly(ethylene oxide) [19, 97, 100], poly[2-(methacryloyloxy)ethyl]trimethylammonium chloride (PDMC) [101], poly(acrylic acid) (PAA) [102], poly(propylene oxide) (PPO) [94] and poly(methyl methacrylate) (PMMA) [18, 103–105]. Typical high char yield polymers include polyacryonitrile (PAN) [18, 25, 96, 103–106] and poly(vinylidene chloride) (PVDC) [99]. Particularly, carbons derived from N-rich polymers such as PAN are inherently doped with pseudocapacitive nitrogen, which increases the capacitances of the carbon electrodes.

PAN-b-PMMA-derived porous carbon fibers (PCFs) are excellent electrode materials. In our recent work [107], PAN-b-PMMA was first synthesized by RAFT polymerization and then electrospun into fiber mats. The subsequent thermal treatments removed PMMA and carbonized PAN into PCFs (PAN-b-PMMA-CFs) with uniform mesopores of ~10 nm (figures 9(a)–(c)). The high surface area (>500 m² g⁻¹), interconnected meso-micro-pores, and small electrical resistance (6.83  ±  0.27 Ω cm) provided PAN-b-PMMA-CFs with an ultra-high gravimetric capacitance of 334  ±  17 F g⁻¹ at a current density of 1 A g⁻¹. This value is significantly higher than those of the carbon fibers produced from the PAN/PMMA blend (PAN/PMMA-CFs) and the PAN homopolymer (PAN-CFs) (figure 9(d)). In addition, PAN-b-PMMA-CFs achieved a record high surface area-normalized capacitance of 66 µF cm⁻² among all the state-of-the-art PCFs.

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The mesopores brought by block copolymers allows fast ion diffusion and enable excellent rate capability of supercapacitors [108, 109]. The ion diffusion is sluggish in micropores (pore width  <  2 nm), which is the culprit of low capacitance retention at high charging/discharging rates. Macropores (pore width  >  50 nm) enhance electrolyte infiltration and ion diffusion, but reduce the electrode packing density and consequently the volumetric capacitance. Being larger than micropores but smaller than macropores, mesopores not only serve as ion diffusion 'highways' but also permit high packing densities and high volumetric capacitances.

Accompanied with other porogens (materials for pore generation), block copolymers can create hierarchical porous structures with multiscale pore sizes. For example, coupled with physical hard templates [86] or chemical etching methods (e.g. KOH [25, 82] or HNO₃ etching [105]), block copolymers can provide nanostructures with pore sizes spanning from sub-nanometers to hundreds of micrometers. The multiple length scales improve the capacitance and accelerate the ion diffusion of supercapacitors.

Besides pure carbons, block copolymers can also be applied to create composite electrodes composed of mesoporous carbon scaffolds and pseudocapacitive materials such as iron oxide [95], niobium pentoxide [97], ruthenium dioxide [100], tungsten oxide [110], manganese dioxide [111], molybdenum trioxide [112], hematite [113], polypyrrole [114] and vanadium nitride [77, 101, 102, 106]. Pseudocapacitive precursors are introduced to the thermal liable blocks via hydrogen bonding or electrostatic interactions. Upon removing the thermal labile blocks at elevated temperatures, the non-volatile precursors are converted to pseudocapacitive materials in the carbon scaffold. Since the pseudocapacitive materials intrinsically have high capacitances, these composite electrodes usually exhibit higher capacitances than the bare porous carbons. Compared to other composite pseudocapacitive electrodes with non-porous substrates such as stainless steel plates [115], the mesoporosity of block copolymer-derived substrates imparts low ion diffusion resistance and mitigates the slow reaction kinetics of pseudocapacitive materials. For example, vanadium nitride (VN) embedded porous carbons were synthesized from ammonium metavanadate (NH₄VO₃) impregnated in PAN-b-PDMC-b-PAN (figure 10(a)) [101]. PAN-b-PDMC-b-PAN was dissolved in dimethyl sulfoxide (DMSO) and then added to a binary mixture of DMSO and water to form a hydrophilic PDMC core/hydrophobic PAN shell structure. After adding NH₄VO₃, ${\rm VO}_{3}^{-}$ anions were electrostatically attracted to the positively charged tertiary nitrogen in PDMC. Upon thermal annealing at 500 °C in NH₃, the ${\rm VO}_{3}^{-}$-adsorbed polymer colloids were converted to carbon scaffolds uniformly embedded with VN nanoparticles (5–10 nm in diameter, figure 10(b)). With an optimal VN to C mass ratio of 1:6, the VN/C nanocomposite achieved high gravimetric capacitances of 195.7 F g⁻¹ (based on the total masses of VN and C) and 782.8 F g⁻¹ (based on the mass of VN only) at 1 A g⁻¹ as a supercapacitor electrode. At a high current density of 16 A g⁻¹, the VN/C nanocomposite electrodes preserved ~40% of its highest capacitance (figure 10(c)).

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Depositing functional materials on block copolymer-derived porous carbons represents an effective route toward composite electrodes. Recently, MnO₂ was deposited on PAN-b-PMMA PCFs, and the resulting composite (PCF@MnO₂) showed the highest gravimetric capacitance of 1148 F g⁻¹ of MnO₂, ~84% of the theoretical limit of MnO₂. Pseudocapacitive MnO₂ nanosheets were deposited in the mesopores of the PCFs via a solution-based redox reaction (figure 11(a)). After 2 h of deposition, MnO₂ nanosheets were uniformly coated on the fiber surfaces (figure 11(b)), and the thickness of the MnO₂ layer was ~2 nm. The thin MnO₂ layer partially filled the mesopores as evidenced from the shift of the mesopore size from 11.7 nm to 9.3 nm (figure 11(c)). The partially filled and interconnected mesopores of PCF@MnO₂ provided ultra-small ion diffusion resistivities, which were significantly smaller than the MnO₂ electrodes prepared by other means (figure 11(d)). The overall gravimetric and areal capacitances of PCF@MnO₂ outperformed the conventional MnO₂-based composite electrodes at comparably high mass loadings (figure 11(e)). The PCFs derived from block copolymers highlight the advantages of enhancing the capacitances and reducing the ion diffusion resistance in composite electrodes, especially at high mass loadings of functional materials.

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Due to the electrically insulating nature, most block copolymers cannot be directly used as supercapacitor electrodes. Instead, they are useful electrode modification agents. For example, poly(acrylic acid)-block-poly(acrylonitrile)-block-poly(acrylic acid) (PAA-b-PAN-b-PAA) improves the hydrophilicity of activated carbon electrodes [126]. In PAA-b-PAN-b-PAA, PAN was incorporated into the activated carbon and PAA dangled on the carbon surface (figure 12(a)). After incorporating PAA-b-PAN-b-PAA, the activated carbon film became highly flexible (figure 12(b)). SEM showed that the surface layer (~30 µm in thickness) was more porous than the underlying layer (figure 12(c)). The surface layer was composed of activated carbon particles entangled with PAA-b-PAN-b-PAA, which helped the electrolyte completely wet the activated carbon. The hydrophilic PAA attracted cations and facilitated the formation of EDL on the electrode surface. The electrode displayed near-ideal capacitive behavior as evidenced by its quasi-rectangular cyclic voltammograms (CVs) at scan rates from 5 to 50 mV s⁻¹ (figure 12(d)). The strategy of modifying electrode surfaces with block copolymers to improve the capacitance was later extended to other block copolymers including F127, PDMC-b-PAN-b-PDMC and PVP-b-PAN-b-PVP [127].

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Block copolymers containing electrically conductive and redox active blocks (e.g. polyaniline) can be directly used as supercapacitor electrodes. A tri-block copolymer hydrogel composed of a central PEO block and two polyaniline-capped poly(acrylamide) terminal blocks stored a large amount of charge (919 F g⁻¹ at 0.5 A g⁻¹) with good stability (90% capacitance retention after 1000 cycles) [128].

Flexible, stretchable and wearable supercapacitors prefer solid or quasi-solid-state gel electrolytes. Compared to liquid-state electrolytes, the self-standing solid-state polymer electrolytes minimize the possibility of electrolyte leaking and simplify device fabrication. The ionic conductivity of polymer electrolytes originates from their ion solvation. PEO-containing block copolymers are the most used ion-conducting polymer electrolytes [129–131], because PEO is hydrophilic and it conducts ions. To maintain self-standing films, PEO is often copolymerized with mechanically robust polymers such as PPO [130], PMMA [132], PS [129, 132], and poly(styrene-co-divinylbenzene) [P(S-co-DVB)] [131]. The affinity of the polymer electrolytes to electrodes can be tuned by the chemistries and molecular weights of the conducting and non-conducting blocks [130].

Minimizing the contact resistances between polymer electrolytes and electrodes is a key to improve the electrochemical performance of supercapacitors with solid-state electrolytes. The contact resistance is associated with the difficulty in completely infiltrating the solid or highly viscous gel electrolytes into the porous electrodes. High contact resistance reduces the capacitances, rate capabilities and power densities of supercapacitors. A series of poloxamers (PEO-b-PPO-b-PEO) end capped with triethoxysilane groups significantly improved the infiltration of electrolytes in supercapacitors and minimized the contact resistances [130]. The triethoxysilane groups reduced the viscosity and allowed the electrolytes to easily permeate into the pores of the activated carbon/graphene electrodes (figure 13(a)). The subsequent solvent evaporation attached the chain ends of the block copolymers to the electrodes. The advantages of the block copolymer electrolytes are their ultrahigh ionic liquid uptake and more than one order of magnitude higher ionic conductivity than the conventional PEO electrolyte (figure 13(b)). A symmetric supercapacitor with the most ionically conductive PEO-b-PPO-b-PEO electrolyte exhibited the highest capacitance, as evidenced by the largest area enclosed by its CV curve (figure 13(c)). The device was also highly flexible and retained  >93% of the capacitance after 5000 bending cycles (figure 13(d)).

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The direct use of block copolymers as dielectrics has gained increasing interests due to its simplicity. However, most polymers cannot be readily polarized by an electric field, and hence they exhibit dielectric constants incomparable to ceramics. To enhance the dielectric constants of polymers, there are three main strategies:

• (1)  
  Reinforce dipole polarity (electrical polarization) by introducing electron-rich groups or electron conjugated structures. Polar groups such as –F [133, 134], –CN [135], and sulfone [136, 137] substantially boost the degree of polarization, especially when the groups are aligned in the direction of the applied electric field. In addition, polymers with conjugated structures such as polythiophene [138], poly(isobutylene) [136], and poly(arylene ether ketone) [135] are also potent to improve the dielectric constant.
• (2)  
  Improve the polarizability (ionic polarization) by introducing ionic clusters. The charged polymer units and the counterions form permanent dipoles that can be readily polarized by an electric field. These charged units increase the dielectric constant in a similar fashion to electrical polarization, except the polarization is induced by ion pairs rather than delocalized electrons.
• (3)  
  Enhance the breakdown voltage (interfacial polarization) by creating conductive/insulating interfaces. Near the conductive/insulating interfaces, the space charge layers provide an electric-field shielding effect and prevent the growth of 'electric trees'. Lamellar block copolymers are ideal to construct the conductive/insulating layered structures.

Practically, the three strategies are often executed together to maximize the performance of dielectric capacitors. An example is two-stranded and ladder-shaped N-3,5-bis(trifluoromethyl)biphenyl-norbornene pyrrolidine (TNP)-based block copolymers (figure 15(a)) [139–141]. Three characteristics of this type of block copolymers are beneficial for dielectric capacitors. First, the C–F bonds and conjugated strand linkers impart electrical dipolar polarization. Second, the charged quaternary N and the surrounding counter ions provides ionic polarization. Third, the alternating conductive and insulating blocks induce interfacial polarization. Figure 15(b) presents a synthesis protocol for a TNP-based block copolymer dielectric. The TNP-based block copolymer displayed a high relative permittivity of 33 and an energy density of 9.95 J cm⁻³ at an electric field strength of 370 MV cm⁻¹ [140]. In comparison, dielectric capacitors based on commercial biaxially oriented polypropylene (BOPP) dielectrics only stored 1.6 J cm⁻³ at 400 MV cm⁻¹.

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A lamellar PS-b-PMMA dielectric is an excellent example highlighting the advantage of insulating/conducting alternating structure [142]. PS with a dielectric constant of 2.6 served as the conducting phase, and PMMA with a dielectric constant of 3.2 was the insulating phase. An annealing technique termed cold zone annealing-soft shearing (CZA-SS) induced the self-assembly into lamellae parallel to the substrate (figures 16(a) and (b)). If treated with conventional oven-heating, the same block copolymer only evolved into randomly oriented lamellae. The CZA-SS annealed block copolymer dielectric achieved the highest energy density of 4.6 J cm⁻³ among all the tested polymers, which was ~2.25 and ~3.5 times higher than those of the as-cast and oven-heated films, respectively (figure 16(c)).

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Embedding ceramic particles in polymer matrices is an effective method for achieving high-energy-density dielectrics. The composite dielectrics combine the inherently high dielectric constants of ceramics and the excellent breakdown tolerance of polymers. However, because of the weak interactions between polymer matrices and ceramic particles, the embedded ceramic particles tend to aggregate. The particle aggregation increases the likelihood of forming continuous particle-polymer interfaces that become electron conduction pathways and substantially reduce the overall breakdown strength [143].

Surface modification of the particles with block copolymers is effective in addressing the challenge of filler dispersion, which is a common problem of polymer composites. For example, a grafted layer of PS-b-poly(styrene-co-vinylbenzylchloride) (PS-b-PSVBC) helped the uniform distribution of ceramic barium titanate (BaTiO₃) nanoparticles, whose relative permittivity is ~7000 [143]. To graft PS-b-PSVBC onto BaTiO₃, the nanoparticles were treated with ultraviolet-ozone radiation to generate negative charges on the surface. The chloromethyl groups of PSVBC reacted with BaTiO₃ and the polymer chains were covalently attached to the particles. The chloromethyl groups were then converted to polar ammonium groups using triethylamine, and the block copolymer chains collapsed and formed a dense layer on the BaTiO₃ particles (figure 17(a)). SEM showed a uniform polymer shell with a thickness of ~3 nm (figure 17(b)). The nonpolar PS chains improved the compatibility of block copolymer-coated BaTiO₃ nanoparticles with the PS matrix, which assisted the uniform distribution of BaTiO₃ in the composites. The BaTiO₃/PS-b-PSVBC composites with 25 wt% BaTiO₃ exhibited the smallest leaking current density of 0.38 nA cm⁻² at an ultrahigh electric field of 0.2 MV cm⁻¹ (figure 17(c)). The composites with 75 wt% BaTiO₃ achieved the highest energy density of 9.7 J cm⁻³.

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The selection of Li-ion battery electrode materials is determined by the charge-storage mechanism. Electrode materials that store charges via ion intercalation-deintercalation must possess ion-diffusion channels such as layered/tunneled structures (figure 18). Materials that form alloys or undergo conversion reactions with Li⁺ must maintain their structural integrity during the repeated charge–discharge cycles. Block copolymers have found uses in both types of electrodes.

Electrically conductive and redox active block copolymers can directly serve as battery electrodes. For example, 2,2,6,6-tetramethylpiperidinyl-N-oxyl (TEMPO) is redox active and can store charges via radical formation. Poly(TEMPO methacrylate)-block-polystyrene micelles with poly(TEMPO methacrylate) corona are potent cathode materials for flow batteries [149]. However, the direct use of block copolymers as battery electrodes remains in its infancy because most block copolymers are electrical insulating and inert to electron/ion storage.

Block copolymers are used as structure-directing agents or soft templates to create mesoporous battery electrodes with improved cycling stability. Peng et al recently synthesized two-dimensional zinc ferrite (ZnFe₂O₄) mesoporous sheets using F127 [150]. Electrochemical cycling stability test revealed that the cycling stability of the mesoporous sheets was much better than the nonporous ones. Operando TEM characterizations revealed that the improved stability was associated with the mesopores which effectively reduced the destruction imposed by the volume expansion upon lithiation. In addition to ZnFe₂O₄, F127 has also templated the synthesis of mesoporous Ni_xCo_3−xO₄ [151], silica [152], TiNb₂O₇ [153] and bronze-phase TiO₂ [154] cathodes.

Besides electrodes and templates, block copolymers also function as additives in battery electrodes. For example, vanadium pentoxide (V₂O₅) is a high-capacity cathode material with an energy density of 294 mAh g⁻¹, but it has a low electrical conductivity and limited structural robustness. Combining V₂O₅ with block copolymer poly(3-hexylthiophene)-block-poly(ethylene oxide) (P3HT-b-PEO) mitigated the drawbacks of V₂O₅ [155]. P3HT was electrically conductive and thus alleviated the limited electrical conductivity of V₂O₅, while PEO prevented V₂O₅ nanosheets from severe re-stacking during the synthesis process. After the dispersion of P3HT-b-PEO micelles in water, a suspension of V₂O₅ nanosheets was added and the mixture was vacuum filtrated into V₂O₅/P3HT-b-PEO hybrid films (figure 19(a)). Electron microscopy showed that the block copolymer micelles were sandwiched between the V₂O₅ nanosheets. Thanks to the block copolymer, the stretchability of the electrodes drastically improved, as shown by the tensile profiles (figure 19(b)). In addition, the block copolymer enhanced the cycling stability. The neat V₂O₅ electrode without P3HT-b-PEO suffered from constant capacity degradation, while the hybrid electrodes with 5 wt% and 10 wt% of P3HT-b-PEO exhibited no appreciable capacity loss (figure 19(c)), due to the minimization of V₂O₅ pulverization during charging and discharging by the soft P3HT-b-PEO buffer fillers.

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Similar to supercapacitor electrodes, block copolymers are pyrolyzed into nanostructured carbons and used as battery electrodes. An excellent example is oxygen-anchored carbon nanosheets converted from F127 mixed with sodium chloride (figure 20(a)) [156]. These carbon sheets (figure 20(b)) with graphitized regions (figure 20(c)) allowed for rapid Li-ion intercalation. The capacity reached ~600 mAh g⁻¹ at 1 A g⁻¹ and only experienced marginal loss, as the current density was increased from 1 to 20 A g⁻¹ (figure 20(d)). The outstanding rate capability was ascribed to the interlayer oxygen atoms that widened the interlayer gap and reduced the steric hindrance for Li⁺ intercalation and de-intercalation.

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The block copolymer-derived carbon nanostructures are versatile substrates for a wide range of functional materials in composite electrodes. High-capacity functional materials usually suffer from high electrical resistance and poor cycling stability, and thus they are integrated with conductive carbons to address their shortcomings. For example, sulfur [157–160], NiO [161], and Nb₂O₅ [162] are representative functional materials coupled with block copolymer-derived carbons. The incorporation of the functional materials is achieved by either conversion of preloaded precursors or direct post-infiltration into mesoporous carbons.

C/S hybrid electrodes for Li-S batteries are examples of the block copolymer-based composite battery electrodes. Li-S batteries are promising rechargeable batteries with a high specific energy density of ~500 Wh kg⁻¹, in comparison to Li-ion batteries with energy densities of 150–250 Wh kg⁻¹. However, the development of Li-S batteries is greatly hindered by the drawbacks of sulfur: the electrically insulating nature, the charge/discharge-induced structural instability, and the polysulfide shuttling effect [163]. All these drawbacks significantly shorten the lifespan of Li-S batteries. In 2009, Nazar and coworkers reported for the first time that ordered mesoporous carbon CMK-3 was a suitable scaffold for S to relieve these problems [163]. Thereafter, a number of C/S composite electrodes with superior performances originated from block copolymers have been demonstrated [157, 159, 164]. One notable example is a 3D Li-S nano-battery assembled from a gyroid carbon matrix [157]. The gyroid carbon matrix was obtained by the pyrolysis of poly(isoprene)-block-poly(styrene)-block-poly(ethylene oxide) (PIO-b-PS-b-PEO) infiltrated with phenol-formaldehyde (PF) resol. The as-formed gyroid carbon matrix was sequentially coated with PPO electrolyte and poly-(3,4-ethylenedioxythiophene)-blended S cathode. A 3D nano-battery was assembled by connecting the carbon matrix with a piece of Li metal and submerging in a Li⁺-containing organic electrolyte (figure 21(a)). SEM confirmed the uniformly filled PPO and S in the cavities of the gyroid carbon network (figures 21(b) and (c)). The 3D nano-battery exhibited a wide voltage plateau at 1.4 V versus Li⁺/Li and an areal capacity of ~7.5 mAh cm⁻² (figure 21(d)). The most important merit of the nano-battery is the nanoscale gaps between the cathode and the anode, which decreased the Li⁺ diffusion distance and augmented the charge-storage capacity at high rates.

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In the last decade, we have witnessed steady improvements in energy density and output voltage of batteries, thanks to the development of new electrodes and diverse batteries (e.g. Li-S [146], Li-air [145], Na-ion batteries [148]). However, safety becomes an increasingly concern as the energy density continues to increase. In case of overcharging or poor thermal management, the highly flammable liquid electrolytes could ignite and cause battery combustion and even explosion. Chemically stable, non-flammable and solid-state electrolytes are highly desirable to improve the safety and minimize electrolyte leaking.

The mutual exclusiveness of high ionic conductivity and structural robustness is a long-lasting challenge for conventional PEO-based solid-state electrolytes. The ion transport in PEO relies on the chain flexibility in the amorphous regions [165–167]. The crystalline regions, however, have a melting point (T_m) of ~65 °C which greatly reduces the room-temperature ion conductivity to the magnitude of ~10⁻⁵ S cm⁻¹ (see table 1 of [165]). The conductivity increases at temperatures above T_m but at the cost of reduced structural integrity. Additionally, because salts elevate the glass transition temperature (T_g) of PEO, the ionic conductivity of PEO at room temperature decreases appreciably as the salt concentration increases [31].

PEO-containing block copolymers circumvent the drawbacks of pure PEO by decoupling ionic conductivity and mechanical strength. The PEO block solvates with lithium salts, such as lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) and lithium triflate (LiSO₃CF₃), and are responsible for ion conduction. The rest blocks provide structural robustness [168–183]. The structure-supporting blocks are typically made of Jeffamine (a comb polymer containing polyether chains) [184], poly[2-(2-(2-methoxyethoxy)ethoxy)ethyl glycidyl ether] [185], and poly(1-((2-acryloyloxy)ethyl)-3-butylimidazolium bis(trifluoromethanesulfonyl)imide) [186].

In addition to the copolymerization with mechanically strong blocks, the use of guest particles is another strategy to reinforce the structure integrity of electrolytes. In addition, the guest particles hinder the crystallization of PEO and improve its ionic conductivity. Example particles include titanium dioxide (TiO₂) [187] and poly(styrene trifluoromethanesulphonylimide of lithium)-grafted polyhedral oligomeric silsesquioxane (POSS) [188].

Block copolymers can also function as a group of unique solid-state electrolytes termed 'single-ion electrolytes'. In single-ion electrolytes, either cations or anions are mobile, while both cations and anions are movable in dual-ion electrolytes. For example, in PEO-based dual-ion electrolytes, metal cations (e.g. Li⁺) coordinate strongly with the EO units but anions only interact weakly with them [189]. The different interaction strengths result in an impeded Li⁺ conduction but a dominating anion conduction, that is, ~80% of the total charges are carried by the anions under an external bias [190]. In dual-ion PEO-based electrolytes, the different ion flow rates induce an anion concentration gradient in the electrolytes, lower the battery capacity, and cause the formation of Li dendrites. In contrast, in Li⁺-conducting single-ion electrolytes, anions are covalently tethered to the polymer chains, and thus their long-range motion is prohibited. The immobilized anions diminish the concentration polarization and improve the battery performance [191].

Single-ion block copolymer electrolytes typically contain blocks with negatively charged functional groups, which are linked with structure-reinforcing blocks [192, 193]. These negatively charged polymer blocks are often based on imide [42, 59, 190, 194, 195], carboxylate [58, 172, 173, 196], borate [192, 193], and sulfonate [181, 194, 197].

For example, in a linear P(STFSILi)-b-PEO-b-P(STFSILi) tri-block copolymer, where P(STFSILi) is poly(styrene trifluoromethanesulphonylimide of lithium [190], the central PEO block served as the Li⁺ conduction channel, and the peripheral P(STFSILi) blocks contained the immobile anions of negatively charged sulphonylimide groups (figure 22(a)). Regardless of the weight percentages of STFSILi, the ionic conductivities of the electrolytes increased from 45 °C to 90 °C (figure 22(b)). The electrolyte that contained 20 wt% P(STFSILi), corresponding to an EO/Li⁺ molar ratio of ~30, achieved the highest ionic conductivity of 1.3  ×  10⁻⁵ S cm⁻¹ at 60 °C (figure 22(b) inset). This conductivity was about an order of magnitude higher than that of the pure PEO electrolyte with similar EO/Li⁺ ratios. The tensile strength of the P(STFSILi)-b-PEO-b-P(STFSILi) single-ion electrolyte was substantially higher than that of PS-b-PEO-b-PS (SEO) dual-ion electrolytes (figure 22(c)). The improved mechanical strength was ascribed to the ionic coupling between the negatively charged P(STFSILi) blocks and the Li⁺-impregnated PEO central block. Electrochemically, the single-ion electrolyte exhibited a stable potential window of 5 V (figure 22(d)), which was much larger than the nominal ~4 V window of most Li-ion batteries. The electrolyte also showed better rate capability at 80 °C than a previously reported ZrO₂-PEO composite electrolyte [198] (figure 22(e)).

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In batteries, binders bundle powder and particulate electrode materials and firmly fix them onto current collectors. The binders are also crucial for stabilizing the electrode materials that undergo large volumetric changes (e.g. Si, Sn, and S). Conventional polyvinylidene fluoride (PVdF) binder has the shortcomings of inelasticity and gradual volume swell in organic electrolytes, which shorten battery lifetime. In addition, PVdF is prone to self-aggregation that induces a substantial interfacial resistance.

The drawbacks of PVDF have stimulated the design and synthesis of block copolymer-based alternatives. Most block copolymer binders have a common ionically conductive PEO block impregnated with salts [199–202]. The other block(s) can be diverse. Mechanically strong polyimide [202–204], polydopamine [200], polybutylene [205], and PS [206] provide binders with ultrahigh strength and excellent flexibility, which are required to maintain battery durability. Electrically conductive poly(3-hexylthiophene) (P3HT) offers electrical conductivity and eliminates the need for conductive carbon black to serve as conductive additives. For example, P3HT-b-PEO could disperse much more uniformly in V₂O₅ nanosheets than a P3HT/PEO polymer blend [199]. Because PEO adhered more strongly to V₂O₅ than P3HT, PEO was well mixed with V₂O₅ but P3HT aggregated locally if the two polymers were simply blended together. The aggregated P3HT could not efficiently transport electrons and hence severely limited the performance. On the contrary, the use of P3HT-b-PEO binder mitigated the aggregation problem of P3HT, because the covalent link between P3HT and PEO forced the uniform dispersion of P3HT along with PEO. As a result, the block copolymer bound V₂O₅ electrode showed a much higher capacity than that of the polymer blend bound V₂O₅ or the neat V₂O₅ nanosheets without any binders (figure 23).

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Separators are important to prevent electric short circuits between the cathode and anode, especially in contemporary miniaturized batteries whose electrodes are extremely close to each other. To allow for fast ion diffusion, the separators must have low ionic resistances. Most separators contain a large number of macropores and mesopores that facilitate ion conduction, except for Li-air batteries, whose separators must be void-free to prevent air permeation [207]).

With the capability of self-assembling into porous structures, block copolymers are attractive materials for battery separators. An excellent example is a hierarchical porous Li-ion battery separator derived from PS-b-P4VP [208]. This separator was prepared by grafting 3-glycidoxypropyl-trimethylsilane (GPTMS) groups onto P4VP to increase the segregation strength between PS and P4VP (figure 24(a)). The GPTMS modified PS-b-P4VP was solution-cast into thin films and submerged in ethanol. The poor solubility of the block copolymer in ethanol resulted in non-solvent-induced phase separation which produced macropores. Meanwhile, the microphase separation of the two blocks created mesopores (figure 24(b)), leading to a hierarchical porous structure with P4VP on the surface (figure 24(c)). The hierarchical porous structure was beneficial for fast ion conduction, which reduced the battery internal resistance and minimized the separator-induced concentration polarization between the electrodes. The discharge capacity of a battery equipped with the PS-b-P4VP based separator outperformed that of a similar battery with a conventional polyolefin-based separator (figure 24(d)). The non-solvent-induced phase separation was also useful for the synthesis of porous poly(styrene-b-butadiene-b-styrene) membranes. The membranes were highly stretchable (~270% strain) and functioned as separators in flexible Li-ion batteries [209].

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Block copolymers are also used as ion exchange membranes in flow batteries. Flow batteries are a family of rechargeable batteries whose two electrodes are liquid ionized reactants [210]. The power output of a flow battery depends on the reactant concentration difference in the anode and cathode chambers. Any cross-mixing of the reactants is detrimental and must be strictly prohibited. Therefore, ion-exchange separators must physically segregate the ionized reactants but allow inert ions (e.g. protons) to flow through. So far, the preparation of block copolymer-based ion-exchange separators is similar to that of conventional porous membranes, except that it involves an additional step of anchoring functional groups onto the pore inner walls to impart ion-exchange capability. Example functional groups are sulfone [211, 212] for cation exchange and quaternary nitrogen [213, 214] for anion exchange.